Ancient and Modern Engineering and the Isthmian Canal

PART I. ANCIENT CIVIL-ENGINEERING WORKS. — CHAPTER I.

1. Introductory.—It is a common impression even among civil engineers that their profession is of modern origin, and it is frequently called the youngest of the professions. That impression is erroneous from every point of view. Many engineering works of magnitude and of great importance to the people whom they served were executed in the very dawn of history, and they have been followed by many other works of at least equal magnitude and under circumstances scarcely less noteworthy, of which we have either remains or records. During the lapse of the arts and of almost every process of civilization throughout the darkness of the Middle Ages there was little if any progress made in the art of the engineer, and what little was done was executed almost entirely under the name of architecture. With the revival of intellectual activity and with the development of science the value of its practical application to the growing nations of the civilized world caused the modern profession of civil-engineering to take definite shape and to be known by the name which it now carries, but which was not known to ancient peoples. Unfortunately the beginnings of engineering cannot be traced; there is no historical record running back far enough to render account of the earliest engineering works whose ruins remain as enduring evidence of what was then accomplished.

It is probably correct to state that the material progress of any people has always been concurrent with the development of the art of civil-engineering, and, hence, that the practice of civil engineering began among the people who made the earliest progress in civilization, to whom “the art of directing the Great Sources of Power in Nature for the use and convenience of man” became an early and imperative necessity. Indeed that conclusion is confirmed by the most ancient ruins of what may be termed public works that archæological investigations have revealed to us, among which are those to be found in the Chaldean region, in India, and in Egypt. Obviously, anything like a detailed account of the structural and other works of such ancient character must be lacking, as some of them were built before even the beginnings of history. Our only data, therefore, are the remains of such works, and unfortunately they have too frequently been subject to the destructive operations of both man and nature.

2. Hydraulic Works of Chaldea and Egypt.—It is absolutely certain that the populous centres of prehistoric times could not have existed nor have been served with those means of communication imperatively necessary to their welfare without the practice of the art of engineering, under whatever name they may have applied to it. It is known beyond any doubt that the anciently populous and prosperous country at the head of the Persian Gulf and watered by the Euphrates and the Tigris was irrigated and served by a most complete system of canals, and the same observation can be made in reference to the valley of the Nile. It is not possible at this period of that country’s history to determine to what extent irrigation was practised or how extensively the former country was served by water transportation conducted along artificial channels; but hydraulic works, including dams and sluices with other regulating appliances designed to bring waters from the rivers on to the land, were certainly among the earliest executed for the benefit of the communities inhabiting those regions. The remains of those works, spread over a large territory in the vicinity of ancient Babylon, Nippur, and other centres of population, show beyond the slightest doubt that there existed a network of water communication throughout what was in those days a country rich in agricultural products and which supported the operations of a most prosperous commerce. These canals were of ample dimensions to float boats of no mean size, although much smaller than those occupied in our larger systems of canal transportation. They were many miles in length, frequently interlacing among themselves and intersecting both the Tigris and the Euphrates. The remains of these canals, some of them still containing water, show that they must originally have been filled to depths varying from five or six to fifteen or twenty feet, and that their widths may have been twenty-five or thirty feet or more. Another curious feature is their occasional arrangement in twos and threes alongside of each other with embankments only between. The entire Euphrates-Tigris valley from the head of the Persian Gulf at least to modern Baghdad (i.e., Babylonia) and possibly to ancient Nineveh was served by these artificial waterways. Later, when Alexander the Great made one of his victorious expeditions through the Assyrian country, he found in the Tigris obstructions to the passage of his ships down-stream in the shape of masonry dams. This was between 356 and 322 B.C. These substantial dams were built across the river for the purpose of intakes to irrigating-canals for the benefit of the adjacent country. These canals, like those of Egypt, were fitted with all the necessary regulating-devices of sluices or gates, both of a crude character, but evidently sufficiently effective for their purpose.

It is known that there were in those early days interchanges of large amounts and varieties of commodities, and it is almost if not quite certain that the countries tributary to the Persian Gulf not only produced sufficient grain for their own needs, but also carried on considerable commerce with the Asiatic coast. We have no means of ascertaining either the volume or the precise character of the traffic, but there is little or no doubt of its existence. It is established also that the waters of the Red Sea and the Nile were connected by a canal about 1450 B.C. Recent investigations about Nippur and other sites of ancient cities in that region confirm other indications that the practice of some branches of hydraulic engineering had received material development from possibly two to four thousand years before the Christian era.

3. Structural Works in Chaldea and Egypt.—The ruins of ancient buildings which have been unearthed by excavations in the same vicinity show with the same degree of certainty that the art of constructing buildings of considerable dimensions had also made material progress at the same time, and in many cases must have involved engineering considerations of a decided character both as to structural materials and to foundations. Bricks were manufactured and used. Stones were quarried and dressed for building purposes and applied so as to produce structural results of considerable excellence. Even the arch was probably used to some extent in that locality in those early days, but stone and timber beams were constantly employed. In the prehistoric masonry constructions of both the Egyptians and Chaldeans and probably other prehistoric peoples, lime or cement mortar was not employed, but came into use at a subsequent period when the properties of lime and cement as cementing materials began to be recognized. The first cementing material probably used in Egypt was a sticky clay, or possibly a calcareous clay or earth. The same material was also used in the valley of the Euphrates, but in the latter country there are springs of bitumen, where that material exudes from the earth in large quantities. The use of this asphaltic cement at times possibly involved that of sand or gravel in some of the early constructions. Later, lime mortar and possibly a weak hydraulic cement came to be employed, although there is little if any evidence of the latter material.

Iron was manufactured and used at least in small quantities, and for some structural purposes, even though in a crude manner. Bituminous or other asphaltic material was found as a natural product at various points, and its value for certain structural purposes was well known; it was used both for waterproofing and for cement. It is practically certain that the construction of engineering works whose interesting ruins still remain involved a considerable number of affiliated engineering operations of which no evidence has yet been found, and of the employment of tools and appliances of which we have no record. So far as these works were of a public character they were constructed by the aid of a very different labor system from that now existing. The kings or ruling potentates of those early times were clothed with the most arbitrary authority, sometimes exercised wisely in the best interests of their people, but at other times the ruling motive was selfishness actuated by the most intense egotism and brutal tyranny. Hence all public works were executed practically as royal enterprises and chiefly by forced labor, perhaps generally without compensation except mere sustenance. Under such conditions it was possible to construct works on a scale out of all proportion to national usefulness and without structural economy. When it is remembered that these conditions existed without even the shadow of engineering science, it is obvious that structural economy or the adaptation of well-considered means to an end will not be found to characterize engineering operations of prehistoric times. Nevertheless there are evidences of good judgment and reasonable engineering design found in connection with some of these works, particularly with those of an hydraulic character. Water was lifted or pumped by spiral or screw machines and by water-wheels, and it is not improbable that other appliances of power served the purposes of many industrial and crude manufacturing operations which it is now impossible for us to determine.

Fig. 1.—Home Built on Piles in the Land of Punt.

It is an interesting fact that while many ancient works were exceedingly massive, like the pyramids, the largest of those of which the ruins have been preserved seldom seem to show little or any evidence of serious settlement. Whether the ancients had unusually sound ideas as to the design of foundation works, or whether those only have come down to us that were founded directly upon rock, we have scarcely any means of deciding. Nor can we determine at this time what special recourses were available for foundation work on soft ground. Probably one of the earliest recognized instances, if not the earliest, of the building of structures on piles is that given by Sir George Rawlinson, when he states that a fleet of merchant vessels sent down the northeast African coast by the Egyptian queen Hatasu, probably 1700 B.C. or 1600 B.C., found a people whose huts were supported on piles in order to raise them above the marshy ground and possibly for additional safety. A representation (Fig. 1) of one of these native homes on piles is found among Egyptian hieroglyphics of the period of Queen Hatasu.

4. Ancient Maritime Commerce.—It is well known that both the Chaldean region and the Nile valley and delta, at least from Ethiopia to the Mediterranean Sea, were densely populated during the period of two to four or five thousand years before the Christian era. By means of the irrigation works to which reference has already been made both lands became highly productive, and it is also well known that those peoples carried on a considerable commerce with other countries, as did the Phœnicians also, at least between the innumerable wars which seemed to be the main business of states in those days. These commercial operations required not only the construction of fleets of what seem to us small vessels for such purposes, but also harbor-works at least suitable to the vessels then in use. The marine activity of the Phœnicians is undoubted, and there is strong reason to believe that there was also similar activity between Babylonian ports and those east of them along the shores of the Indian Ocean, perhaps even as far as ancient Cathay, and possibly also to the eastern coast of Africa.

Investigations in the early history of Egypt have shown that a Phœnician fleet, constructed at some Egyptian port on the Red Sea, undoubtedly made the complete circuit of Africa and returned to Egypt through the Mediterranean Sea the third year after setting out, over 2100 years (about 600 B.C.) before the historic fleet of the Portuguese explorer Vasco da Gama sailed the same circuit in the opposite direction. It is therefore probable, in view of these facts, that at least simple harbor-works of sufficient efficiency for those early days found place in the public works of the ancient kingdoms bordering upon the Mediterranean and Red seas and the Persian Gulf.

5. The Change of the Nile Channel at Memphis.—Although such obscure accounts as can be gathered in connection with the founding of the city of Memphis are so shadowy as to be largely legendary, it has been established beyond much if any doubt that prior to its building the reigning Egyptian monarch determined to change the course of the Nile so as to make it flow on the easterly side of the valley instead of the westerly. This was for the purpose of securing ample space for his city on the west of the river, and, also, that the latter might furnish a defence towards the east, from which direction invading enemies usually approached. He accordingly formed an immense dam or dike across the Nile as it then existed, and compelled it to change its course near the foot of the Libyan Hills on the west and seek a new channel nearer the easterly side of the valley. This must have been an engineering work of almost appalling magnitude in those early times, yet even with the crude means and limited resources of that early period, possibly, if not probably, at least 5000 B.C., the work was successfully accomplished.

6. The Pyramids.—Among the most prominent ancient structural works are the pyramids of Egypt, those royal tombs of which so much has been written. These are found chiefly in the immediate vicinity of Memphis on the Nile. There are sixty or seventy of them in all, the first of which was built by the Egyptian king Khufu and is known as the “Great Pyramid” or the “First Pyramid of Ghizeh.” They have been called “the most prodigious of all human constructions.” Their ages are uncertain, but they probably date from about 4000 B.C. to about 2500 B.C. These are antedated, however, by two Egyptian pyramidal constructions of still more ancient character whose ages cannot be determined, one at Meydoum and the other at Saccarah.

A Corner of the Great Pyramid.

(Copyright by S. S. McClure Co., 1902.
Courtesy of McClure’s Magazine.)

Fig. 2.—Section of the Great Pyramid.

Fig. 3.

The pyramids at Memphis are constructed of limestone and granite, the latter being the prominent material and used entirely for certain portions of the pyramids where the stone would be subjected to severe duty. The great mass of most of the pyramids consists of roughly hewn or squared blocks with little of any material properly considered mortar. The interior portions, especially of the later pyramids, were sometimes partially composed of chips, rough stones, mud bricks, or even mud, cellular retaining-walls being used in the latter cases for the main structural features. In all pyramids, however, the outer or exposed surfaces and the walls and roofs of all interior chambers were finished with finely jointed large stones, perhaps usually polished. The Great Pyramid has a square base, which was originally 764 feet on a side, with a height of apex above the surface of the ground of over 480 feet. This great mass of masonry contains about 3,500,000 cubic yards and weighs nearly 7,000,000 tons. The area of its base is 13.4 acres. The Greek historian Herodotus states that its construction required the labor of 100,000 men for twenty years. An enormous quantity of granite was required to be transported about 500 miles down the Nile from the quarries at Syene. Some of the blocks at the base are 30 feet long with a cross-section of 5 feet by 4 or 5 feet. The bulk of the entire mass is of comparatively small stones, although so squared and dressed as to fit closely together. Familiar descriptions of this work have told us that the small passages leading from the exterior to the sepulchral chambers are placed nearly in a vertical plane through the apex. The highest or king’s chamber, as it is called, measures 34 feet by 17 feet and is 19 feet high, and in it is placed the sarcophagus of King Khufu. It is composed entirely of granite most exactly cut and fitted and beautifully polished. The construction of the roof is remarkable, as it is composed of nine great blocks “each nearly 19 feet long and 4 feet wide, which are laid side by side upon the walls so as to form a complete ceiling.” There is a singular feature of construction of this ceiling designed to remove all pressure from it and consisting of five alternate open spaces and blocks of granite placed in vertical series, the highest open space being roofed over with inclined granite slabs leaning or strutted against each other like the letter V inverted. This arrangement relieves the ceiling of the sepulchral chamber from all pressure; indeed only the inclined highest set of granite blocks or slabs carry any load besides their own weight. There are two small ventilating- or air-shafts running in about equally inclined directions upward from the king’s chamber to the north and south faces of the pyramid. These air-shafts are square and vary between 6 and 9 inches on a side. The age of this pyramid is probably not far from 5000 years.

Entrance to the Great Pyramid.

The second pyramid is not much inferior in size to the Great Pyramid, its base being a square of about 707 feet on a side, and its height about 454 feet. The remaining pyramids are much inferior in size, diminishing to comparatively small dimensions, and of materials much inferior to those used in the earlier and larger pyramids.

7. Obelisks, Labyrinths, and Temples.—Among other constructions of the Egyptians which may be called engineering in character, as well as architectural, are the obelisks, the “Labyrinth” so called, on the shore of Lake Mœris, and the magnificent temples at the ancient capital Thebes, which are the most remarkable architectural creations probably that the world has ever known. These latter were not completed by one king, as was each of the pyramids. They were sometimes despoiled and largely wrecked by invading hosts from Assyria, and then reconstructed in following periods by successive Egyptian kings and again added to by still subsequent monarchs, whose reigns were characterized by statesmanship, success in war, and prosperity in the country. Their construction conclusively indicates laborious operations and transportation of great blocks of stone characteristic of engineering development of the highest order for the days in which they took place. The dates of these constructions are by no means well defined, but they extend over the period running from probably about 2500 B.C. to about 400 B.C., with the summit of excellence about midway between.

Another class of ancient structures which can receive but a passing notice, although it deserves more, is the elaborate rock tombs of some of the old Egyptian monarchs in the rocks of the Libyan Hills. They were very extensive constructions and contained numerous successions of “passages, chambers, corridors, staircases, and pillared halls, each further removed from the entrance than the last, and all covered with an infinite number of brilliant paintings.” These tombs really constituted rock tunnels with complicated ramifications which must have added much to the difficulty of the work and required the exercise of engineering skill and resources of a high order.

8. Nile Irrigation.—The value of the waters of the Nile for irrigation and fertilization were fully appreciated by the ancient Egyptians. They also apparently realized the national value of some means of equalizing the overflow, although the annual régimen of the Nile was unusually uniform. There were, however, periods of great depression throughout the whole Nile valley consequent upon the phenomenal failure of overflow to the normal extent. One of the earliest monarchs who was actuated by a fine public spirit undertook to solve the problem of providing against such depressions by diverting a portion of the flood-waters of the Nile into an enormous reservoir, so that during seasons of insufficient inundation the reservoir-waters could be drawn upon for the purpose of irrigation. This monarch is known as the good Amenemhat, although the Greeks call him Mœris. In the Nile valley, less than a hundred miles above Memphis, on the left side or to the west of the river, there is a gap in the Libyan Hills leading to an immense depression, the lower parts of which are much below the level of the water in the Nile. This topographical depression, perhaps 50 miles in length by 30 in breadth, with an area between 600 and 700 square miles, now contains two bodies of water or lakes, one known as the Birket Keroun and the other as Lake Mœris. The vicinity of this depression is called the Fayoum. A narrow rocky gorge connects it with the west branch of the Nile, known as Bahr el Yousuf, and it is probable that during extreme high water in the Nile there was a natural overflow into the Fayoum. The good Amenemhat, with the judgment of an engineer, or guided by advisers who possessed that judgment, appreciated the potential value of this natural depression as a possible reservoir for the surplus Nile waters and excavated a channel, possibly a natural channel enlarged, of suitable depth from it to the Bahr el Yousuf. As a consequence he secured a storage-reservoir of enormous capacity and which proved of inestimable value to the lowlands along the Nile in times of shortage in the river-floods.

Investigators have differed much in their conclusions as to the extent of this reservoir. Some have maintained that only the lower depressions of the Fayoum were filled for reservoir purposes, while others, like Mr. Cope Whitehouse, believe that the entire depression of the Fayoum was utilized with the exception of a few very high points, and that the depth of water might have been as much as 300 feet in some places. In the latter case the circuit of the lake would have been from 300 to 500 miles. Whatever may have been the size of the lake, however, its construction and use with its regulating-works was a piece of hydraulic engineering of the highest type, and it indicates an extraordinary development of that class of operations for the period in which it was executed. The exact date of this construction cannot be determined, but it may have been as early as 2000 B.C., or perhaps earlier.

9. Prehistoric Bridge-building.—The development of the art of bridge-building seems to have lagged somewhat in the prehistoric period. The use of rafts and boats prevented the need of bridges for crossing streams from being pressing. It is not improbable that some small and crude pile or other timber structures of short spans were employed, but no remains of this class of construction have been found. Large quantities of timber and much of an excellent quality were used in the construction of buildings. That much is known, but there is practically no evidence leading to the belief that timber bridges of any magnitude were used by prehistoric people. It is highly probable that single-timber-beam crossings of small streams were used, but that must be considered the limit of ancient bridging until other evidence than that now available is found.

10. Ancient Brick-making.—It has already been seen that stone as a building material has been used since the most ancient periods, and the use of brick goes back almost as far. Fortunately it was frequently a custom of the ancient brick-makers to stamp proprietary marks upon their bricks, and we know by these marks that bricks were made in the Chaldean regions certainly from 3000 to 4000 years before the Christian era. In Egypt also the manufacture of brick dates back nearly or quite as far. Some of these Chaldean bricks, as well as those in other parts of the ancient world, were of poor quality, readily destroyed by water or even a heavy storm of rain when driving upon them. Other bricks, however, were manufactured of good quality of material and by such methods as to produce results which compare favorably with our modern building-bricks. The ruins of cities, at least in Assyria and Chaldea, show that enormous buildings, many of them palaces of kings, were constructed largely of these bricks, although they were elaborately decorated with other material. The walls were heavy, indeed so massive that many of the ruin-mounds are frequently formed almost entirely of the disintegrated brick of poorer quality. These old builders not only executed their work on a large scale, but did not hesitate to pile up practically an artificial mountain of earth, or other suitable material, on which to construct a palace or temple. The danger of water to these native bricks was so well known and recognized that elaborate and very excellent systems of subsurface drains or sewers were frequently constructed to carry off the storm-water as fast as it fell.

11. Ancient Arches.—In the practice of these building operations it became necessary to form many openings and to construct roofs for the sewers or drains, and the arch, both true and false, came to be used in the Euphrates valley, in that of the Nile, and in other portions of the ancient world. Pointed sewer-arches of brick have been found in what is supposed to be the palace of Nimrod on the Tigris River, possibly of the date about 1300 B.C. Excavations at Nippur have revealed a mud-brick pointed arch supposed to date back to possibly 4000 B.C. Also semicircular voussoir arches have been discovered at the ruins of Khorsabad near Nineveh with spans of 12 to 15 feet. These arches are supposed to belong to the reign of Sargon, an Assyrian king who flourished about 705 to 722 B.C. Again, the ancient so-called treasury of Atreus at Mycenæ in Greece, although a dome, exhibits an excellent example of the method of forming the false arch, the date of the construction being probably about 1000 B.C. The main portion of this structure consists of a pointed dome, the diameter of the base being 48 feet and the interior central height 49 feet. A central section shows a beehive shape, as in Fig. 6.

VAULTED DRAIN, KHORSABAD
Fig. 4.

VAULTED DRAINS, KHORSABAD.
Fig. 5.

The exterior approach is between two walls 20 feet apart, the intermediate entrance to the dome or main chamber being a passage 9 feet 6 inches wide at the bottom and 7 feet 10 inches at the top and about 19 feet high. At right angles to the entrance there is a chamber 27 feet by 20 feet cut into the adjacent rock, entered through a doorway about 4 feet 6 inches wide and 9 feet 6 inches high. Both the main entrance to the dome and the doorway to the adjacent chamber are covered or roofed with large flat lintel-stones, over which are the triangular relieving (false) arches, so common in ancient construction, by which the lintels are relieved of load, the triangular openings being closed by single, great upright flat stones. There are a considerable number of these in Greece. The stone used is a “hard and beautiful breccia” from the neighboring hills and Mount Eubora near by. The courses of stone are about two feet thick and closely fitted without cement.

Fig. 6.—Plan and Section of the Treasury of Atreus at Mycenæ.

The great majority, or perhaps all, of the Assyrian true arches, so far discovered, are formed of wedge-shaped bricks, most of them being semicircular, although some are pointed, the span being not over about 15 feet. The most of the arches found at Nineveh and Babylon belong to a period reaching possibly from 1300 to 800 B.C., but some of the Egyptian arches are still older. Egyptians, Assyrians, Greeks, and other ancient people used false arches formed by projecting each horizontal course of stones or bricks over that below it on either side of an opening. The repetition of this procedure at last brings both sides of the opening together at the top of the arch, and they are surmounted at that point with a single flat stone, brick, or tile. It has been supposed by some that these false arches, whose sides may be formed either straight or curved, exhibit the oldest form of the arch, and that the true arch with its ring or rings of wedge-shaped voussoirs was a subsequent development. It is possible that this is true, but the complete proof certainly is lacking. In Egypt and Chaldea both styles of arches were used concurrently, and it is probably impossible to determine which preceded the other. Again, some engineers have contended that two flat slabs of stone leaning against each other, each inclined like the rafters of a roof, was the original form of the arch, as found in the pyramids of Egypt; but it is probable that the true arch was used in Chaldea prior to the time of the pyramids. Indeed crude arches of brick have been found at Thebes in Egypt dating back possibly to 2500 B.C., or still earlier. Aside from that, however, such an arrangement of two stones is not an arch at all, either true or false. The arrangement is simply a combination of two beams. A condition of stress characteristic of that in the true arch is lacking.

The ancient character of the engineering works whose ruins are found in Chaldea and Assyria is shown by the simple facts that Babylon was destroyed about the year 690 B.C. and Nineveh about the year 606 B.C.

CHAPTER II.

12. The Beginnings of Engineering Works of Record.—In a later period of the world’s history we reach a stage in the development of engineering works of which we have both records and remains in such well-defined shape that the characteristics of the profession may be realized in a definite manner. This is particularly true of the civil-engineering works of the Romans. In their sturdy and unyielding character, with their limitless energy and resolution, the conditions requisite for the execution of engineering works of great magnitude are found. An effeminate or generally æsthetic nation like the Greeks would furnish but indifferent opportunity for the inception and development of great engineering works, but the resolute and vigorous Roman nation offered precisely the conditions needed. They appreciated among other things the absolute necessity of the freest possible communication with the countries which they conquered and made part of their own empire. They recognized water transportation as the most economical and effective, and used it wherever possible. They also realized the advantages of roads of the highest degree of solidity and excellence. No other roads have ever been constructed so direct, so solid, and so admirably adapted to their purposes as those built by the Romans. They virtually ignored all obstacles and built their highways in the most direct line practicable, making deep cuts and fills with apparently little regard for those features which we consider obstacles of sufficient magnitude to be avoided. They regarded this system of land communication so highly that they made it radiate from the Golden Mile-stone in the Roman Forum. The point from which radiated these roads was therefore in the very centre of Roman life and authority, and it fitly indicated the importance which the Roman government gave to the system of communication that bound together with the strongest bonds all parts of the republic and of the empire.

The design and construction of these roads must have been a matter to which their constructors gave the most careful attention and study. They were works involving principles deduced from the most careful thought and extended experience. There were incorporated in them the most effective materials of construction then known, and it was evidently the purpose of their constructors that they should possess indefinite endurance. The existence of some of them at the present time, with no other attention given to them than required for ordinary maintenance, demonstrates that the confidence of the builders was not misplaced.

Street Fountain and Watering-trough in Pompeii.
Called the Fountain of Plenty, from the figure
with Horn of Plenty on the perforated upright post.

13. The Appian Way and other Roman Roads.—Probably the oldest and most celebrated of these old Roman roads is the Appian Way. It was the most substantially built, and the breadth of roadway varied from 14 to 18 feet exclusive of the footwalks. Statius called it the Queen of Roads. It was begun by Appius Claudius Cæcus, 312 years before the Christian era. He carried its construction from the Roman gate called Porta Capena to Capua, but it was not entirely completed till about the year 30 B.C. Its total length was three hundred and fifty miles, and it formed a perfect highway from Rome to Brundisium, an important port on what may be called the southeastern point of Italy. It was built in such an enduring manner that it appears to have been in perfect repair as late as 500 to 565 A.D.

The plan of construction of these roads was so varied as to suit local conditions, but only as required by sound engineering judgment. They wisely employed local materials wherever possible, but did not hesitate to transport proper material from distant points wherever necessary. This seemed to be one of their fundamental principles of road construction. In this respect the old Romans exhibited more engineering and business wisdom than some of the American states in the beginnings of improved road construction in this country. An examination of the remains of some Roman roads now existing appears to indicate that in earth the bottom of the requisite excavation was first suitably compacted, apparently by ramming, although rollers may have been used. On this compacted subgrade were laid two or three courses of flat stones on their beds and generally in mortar. The second layer placed on the preceding was rubble masonry of small stones or of coarse concrete. On the latter was placed the third layer of finer concrete. The fourth or surface course, consisting of close and nicely jointed polygonal blocks, was then put in place, and formed an excellent unyielding pavement. This resulted in a most substantial roadway, sometimes exceeding 3 feet in total thickness. It is difficult to conceive of a more substantial and enduring type of road construction. The two lower layers were omitted when the road was constructed in rock. Obviously the finer concrete constituting the second layer from the top surface was a binder between the pavement surface and the foundation of the roadway structure.

The paved part of a great road was usually about 16 feet in width, and raised stone causeways or walls separated it from an unpaved way on each side having half the width of the main or paved portion. This seemed to be the type of the great or main Roman roads. Other highways of less important character were constructed of inferior materials, earth or clay sometimes being used instead of mortar; but in such cases greater crowning was employed, and the road was more elevated, possibly for better drainage. Then, as now, adequate drainage was considered one of the first features of good road design. City streets were paved with the nicely jointed polygonal blocks to which reference has already been made, while the footways were paved with rectangular slabs much like our modern sidewalks.

EXAMPLE OF EARLY BASALT ROAD.
BY THE TEMPLE OF SATURN ON
THE CLIVUS CAPITOLINUS.
Fig. 7.

The smooth polygonal pavements of the old Romans put to the keenest shame the barbarous cobblestone street surfaces with which the people of American cities have been and are still so tortured.

The beneficial influence of these old Roman highways has extended down even to the present time in France, where some of them were built. The unnecessarily elaborate construction has not been followed, but the recognition of the public benefits of excellent roads has been maintained. The lower course of the foundation-stones apparently began to be set on edge toward the latter part of the eighteenth century, the French engineer Tresaguet having adopted that practice in 1764. At the same time he reduced the thickness of the upper layers. His methods were but modifications of the old Roman system, and they prevailed in France until the influence of the English engineers Macadam and Telford began to be felt.

14. Natural Advantages of Rome in Structural Stones.—Although the ancient Romans were born engineers, possessing the mental qualities and sturdy character requisite for the analytic treatment and execution of engineering problems, it is doubtful whether they would have attained to such an advanced position in structural matters had not the city of Rome been so favorably located.

The geological character of the great Roman plain and the Roman hills certainly contributed most materially to the early development of some of the most prominent of the Roman engineering works. The plain surrounding the city of Rome is composed largely of alluvial and sandy deposits, or of the emissions of neighboring volcanoes, of which the Alban Hills form a group. While these and other volcanic hills in the vicinity are, and have been for a long period, quiescent, they were formerly in a very active state. The scoriæ, or matter emitted in volcanic eruptions, is found there in all possible degrees of coherence or solidity, from pulverulent masses to hard rock. The characteristic Roman material called tufa is a mixture of volcanic ash and sand, loose and friable, as dropped from the eruptions in large quantities or again compressed into masses with all degrees of hardness. The hard varieties of yellow or brown tufa form building material much used, although a considerable percentage of it would not be considered fit building material for structures of even moderate height at the present time. The most of it weathers easily, but forms a fairly good building-stone when protected by a coating of plaster or stucco.

Another class of building-stones found at or in the vicinity of Rome is the so-called “peperino,” consisting chiefly of two varieties of conglomerate of ash, gravel, broken pieces of lava, and pieces of limestone, some possessing good weathering qualities, while others do not. Ancient quarries of these stones exist whence millions of cubic yards have been removed, and are still being worked. The better varieties of “peperino” possess good resisting qualities, and were much used in those portions of masonry construction where high resistance was needed, as in the ring-stones of arches, heavily loaded points of foundations, and other similar situations.

Some of the prehistoric masonry remains of the Romans show that their earliest constructors appreciated intelligently the qualities of this stone for portions of works where the duty was most severe.

Lava from the extinct volcanoes of the Alban Hills called “silex” was used for paving roads and for making concrete. It was hard and of gray color. At times considerable quantities of this stone were employed. A species of pure limestone called “travertine,” of a creamy white color, was quarried at Tibur or Tivoli, and began to be used about the second century B.C. Vitruvius speaks of its having good weathering qualities, but naturally it is easily calcined. Its structure is crystalline, and it is strong in consequence of that quality only when it is laid on its bed.

15. Pozzuolana Hydraulic Cement.—The most valuable of all building materials of old Rome was the “pozzuolana,” as it furnished the basis of a strong, enduring, and economic concrete, and permitted almost an indefinite development of masonry construction. Had there not been at Rome the materials ready at hand to be manufactured into an excellent cementing product, it is highly probable that neither the structural advance nor the commercial supremacy of the Roman people could have been attained. It is at least certain that the majority of the great masonry works constructed by the Romans could not have been built without the hydraulic cementing material produced with so little difficulty and in such large quantities from the volcanic earth called pozzuolana. The name is believed to have its origin from the large masses of this material at Pozzuoli near Naples. Great beds are also found at and near Rome. The earliest date of its use cannot be determined, but it has given that strong and durable character to Roman concrete which has enabled Roman masonry to stand throughout centuries, to the admiration of engineers.

It is a volcanic ash, generally pulverulent, of a reddish color, but differs somewhat in appearance and texture according to the locality from which it is taken. It consists chiefly of silicate of alumina, but contains a little oxide of iron, alkali, and possibly other components. The Romans therefore pulverized the pozzuolana and mixed it with lime to make hydraulic cement. This in turn was mixed with sand and gravel and broken stone to form mortar and concrete, and that process is carried on to this day. The concrete was hand-mixed, and treated about as it is at present. After having been well mixed the Romans frequently deposited it in layers of 6 to 9 or 10 inches thick, and subjected it to ramming. In connection with this matter of mortar and concrete production, Vitruvius observes that pit-sand is preferable to either sea or river sand.

16. Roman Bricks and Masonry.—The Romans produced bricks both by sun-baking and by burning, although there are now remaining apparently no specimens of the former in Rome. Bricks were used very largely for facing purposes, such as a veneer for concrete work. The failure to recognize this fact has led some investigators and writers into error. As matter of fact bricks were used as a covering for concrete work, the latter performing all the structural functions.

The old Roman aqueducts were frequently lined with concrete, made of a mixture of pozzuolana, lime, and crushed (pounded) bricks or potsherds. The same material was also used for floors under the fine mortar in which the mosaics were imbedded.

Marble came into use in Rome about 100 B.C., from Luna, near modern Carrara, Mt. Hymettus, and Mt. Pentelicus, near Athens and the Isle of Paros, nearly all being for sculpture purposes. Colored and structural marbles were brought from quarries in various parts of Italy, Greece, Phrygia, Egypt, near Thebes (oriental alabaster or “onyx”), Arabia, and near Damascus.

From the latter part of the first century B.C. the hard building-stones like granites and basalts were brought to Rome in large quantities. Most of the granites came from Philæ on the Nile. The basalts came both from Lacedæmonia and Egypt. Both emery (from the island of Naxos in the Ægean Sea) and diamond-dust drills were used in quarrying or working these stones. Ships among the largest, if not the largest, of those days, were built to transport obelisks and other large monoliths.

The quality of ancient Roman mortar varies considerably as it is now found. That of the first and second centuries is remarkably hard, and made with red pozzuolana. In the third century it began to be inferior in quality, brown pozzuolana sometimes being used. The reason for this difference in quality cannot be confidently assigned. The deterioration noted in the third century work may be due to the introduction of bad materials, or to the wrong manipulation of material intrinsically good, or it is not unlikely the deterioration is due to a combination of these two influences. The use of mortar indicates a class of early construction; it is found in the Servian wall on the Aventine, of date 700 B.C., or possibly earlier.

Dovetail Wooden Tenon.Wooden Dowel.
Fig. 8.

Under the empire (27 B.C. to A.D. 475) large blocks of tufa, limestone (travertine), or marble were set with very close joints, with either no mortar or, if any, as thin as paper; end, top, and bottom clamps of iron were used to bond such stones together. It was also customary, in laying such large, nicely finished blocks of stone without mortar, to use double dovetailed wooden ties, or, as in the case of columns, a continuous central dowel of wood, as shown in the figures.

The joints were frequently so close as to give the impression that the stones might have been fitted by grinding together. In rectangular dimension stonework (ashlar) great care was taken, as at present, to secure a good bond by the use of judiciously proportioned headers and stretchers. Foundation courses were made thicker than the body of the superincumbent wall, apparently to distribute foundation weights precisely as done at present. Weaker stone was used in thicker portions of walls, and strong stone in thinner portions. Also at points of concentrated loading, piers or columns of strong stone are found built into the bodies of walls of softer or weaker stone. Quarry chips, broken lava, broken bricks, or other suitable refuse fragments were used for concrete in the interest of economy, the broken material always being so chosen as to possess a sharp surface to which the cement would attach itself in the strongest possible bond.

At the quarries where the stones were cut the latter were marked apparently to identify their places in the complete structure, or for other purposes. The remains of the quarries themselves as seen at present are remarkable both for their enormous extent and for the system on which the quarrying was conducted. It appears that the systems employed were admirably adapted to the character of the stone worked, and that the quarrying operations were executed as efficiently and with as sound engineering judgment as those employed in great modern quarries.

17. Roman Building Laws.—So much depended upon the excellence of the building in Rome, and upon the materials and methods employed, that building laws or municipal regulations were enacted in the ancient city, prescribing kind and quality of material, thickness of walls, maximum height of buildings, minimum width of streets, and many other provisions quite similar to those enacted in our modern cities. The differences appear to arise from the different local conditions to be dealt with, rather than from any failure on the part of the old Romans to reach an adequate conception of the general plans suitable for the masses of buildings in a great city. Prior to the great fire A.D. 64 in Nero’s reign, an act prescribing fire-proof exterior coverings of buildings was under consideration, and subsequently to that conflagration it was enacted into law. Many of the city roads or streets were paved with closely fitting irregular polygonal blocks of basalt, laid on concrete foundations, and with limestone (travertine) curbs and gutters, producing an effect not unlike our modern streets.

18. Old Roman Walls.—In no class of works did the ancient Romans show greater engineering skill or development than in the massive masonry structures that were built not only in and about the city of Rome, but also in distant provinces under Roman jurisdiction. Among the home structures various walls, constituting strong defences against the attacks of enemies, stand in particular prominence. Some of these great structures had their origin prior even to historic times. The so-called “Wall of Romulus,” around the famous Roma Quadrata of the Palentine, is among the latter. It is supposed by many that this wall formed the primitive circuit of the legendary city of Romulus. That, however, is an archæological and not an engineering question, and, whatever its correct answer may be, the wall itself is a great engineering work; it demonstrates that the early Romans, whatever may have been their origin, had attained no little skill in quarrying and in the building of dry masonry, no mortar being used in this ancient wall. Portions of it 40 feet high and 10 feet thick at bottom, built against a rocky hill, are still standing. The courses are 22 to 24 inches thick, and they are laid as alternate headers and stretchers; the lengths of the blocks being 3 to 5 feet, and the width from 19 to 22 inches. The ends of the blocks are carefully worked and true, as are the vertical joints in much of the wall, although some of the latter, on the other hand, are left as much as 2 inches open.

Civil engineers, who are familiar with the difficulties frequently experienced in laying up dry walls of considerable height, as evidenced by many instances of failure probably within the knowledge of every experienced engineer, will realize that this great dry masonry structure must have been put in place by men of no little engineering capacity. The rock is soft tufa, and marks on the blocks indicate that chisels from ¼ to ¾ inch in width were used, as well as sharp-pointed picks. In all cases the faces of the blocks were left undressed, i.e., in modern terms they were “quarry-faced.”

19. The Servian Wall.—Later in the history of Rome the great Servian Wall, built chiefly by Servius Tullius to enclose the seven hills of Rome, occupies a most prominent position as an engineering work. Part of the wall, all of which belongs to the regal period (753 to 509 B.C.), is supposed to be earlier than Servius, and may have been planned and executed by Tarquinius Priscus. A part only of the stones of this wall were laid in cement mortar, and concrete was used, to some extent at least, in its foundation and backing. The presence of cement mortar in this structure differentiates it radically from the wall of Romulus. Probably the discovery of pozzuolana cement, and the fabrication of mortar and concrete from it, had been made in the intervening period between the two constructions. Tufa, usually the softer varieties but of varying degrees of hardness, was mostly used in this wall, and the blocks were placed, as in the previous instance, as alternate headers and stretchers in courses about two feet thick. Portions of the wall 45 feet high and about 12 feet thick have been uncovered. At points it was pierced with arched openings of 11 feet 5 inches span, possibly as embrasures for catapults or other engines of war. The upper parts of these openings are circular arches with the usual wedge-like ring-stones. The voussoirs were cut from peperino stone. This wall, like that of Romulus, was constructed as a military work of defence, and at some points it was built up from the bottom of a wide foss 30 feet deep. At such places it was counterforted or buttressed, a portion of wall 11 feet 6 inches long being found between two counterforts, each of the latter being 9 feet wide and projecting 7 feet 9 inches out from the wall.

Fig. 9.—Part of Servian Wall on Aventine.

Fig. 10.—Wall and Agger of Servius.

20. Old Roman Sewers.—It is demonstrable by the writings of Vitruvius and others that the old Romans, or at any rate the better educated of them, possessed a correct general idea of some portions of the science of Sanitary Engineering, so far as anything of the nature of science could then be known. Their sanitary views were certainly abreast of the scientific knowledge of that early day. The existence of the “cloacæ,” or great sewers, of the ancient city of Rome showed that its people, or at least its rulers, not only appreciated the value of draining and sewering their city, but also that they knew how to secure the construction of efficient and enduring sewers or drains. It has been stated, and it is probably true, that this system of cloacæ, or sewers, was so complete that every street of the ancient city was drained through its members into the Tiber. They were undoubtedly the result of a gradual growth in sewer construction and did not spring at once into existence, but they date back certainly to the beginning of the period of the kings (753 B.C.). The famous Cloaca Maxima, as great as any sewer in the system, and certainly the most noted, is still in use, much of it being in good order. The mouth of the latter where it discharges into the Tiber is 11 feet wide and 12 feet high, constituting a large arch opening with three rings of voussoirs of peperino stone. Many other sewers of this system are also built with arch tops of the same stone, with neatly cut and closely fitting voussoirs. We do not find, unfortunately, any detailed accounts of the procedures involved in the design of these sewers, yet it is altogether probable that the old Roman civil engineers formed the cross-sections, grades, and other physical features of their sewer system by rational processes, although they would doubtless appear crude and elementary at the present time. It would not be strange if they made many failures in the course of their structural experiences, but they certainly left in the old Roman sewers examples of enduring work of its kind.

Some portions of this ancient sewer system are built with tops that are not true arches, and it is not impossible that they antedate the regal period. These tops are false arches formed of horizontal courses of tufa or peperino, each projecting over that below until the two sides thus formed meet at the top. The outline of the crowns of such sewers may therefore be triangular, curved, or polygonal; they were usually triangular. Smaller drains forming feeders to the larger members of the system were formed with tops composed of two flat stones laid with equal inclination to a vertical line so as to lean against each other at their upper edges and over the axis of the sewer. This method of forming the tops of the drains by two inclined flat stones was a crude but effective way of accomplishing the desired purpose.

The main members of this great sewer system seem to have followed the meandering courses of small rivers or streams, constituting the natural drainage-courses of the site of the city. The Cloaca Maxima has an exceedingly crooked course and it, along with others, was probably first formed by walling up the sides of a stream and subsequently closing in the top. Modern engineers know that such an alignment for a sewer is viciously bad, and while this complicated system of drains is admirably constructed in many ways for its date, it cannot be considered a perfect piece of engineering work in the light of present engineering knowledge. It is probable that the walling in of the sides of the original streams began to be done in Rome at least as early as the advent of the Tarquins, possibly as early as 800 B.C. or earlier.

We know little about the original outfalls or points of discharge into the Tiber, except that, as previously stated, these points were made through the massive quay-walls constructed during the period of the kings along both shores of the Tiber, probably largely for defence as originally built. The discharge of the old Roman sewers through the face of this quay-wall and into the river is precisely the manner in which the sewers of New York City in many places are discharged into the North, East, and Harlem rivers.

The Cloaca Maxima is not the only great ancient sewer thus far discovered. There are at least two others equal to it, and some of the single stones with which they are built contain as much as 45 cubic feet each. These cloacæ were not mere sewers; indeed they were more drains than sewers, for they carried off flood-waters and the natural drainage as well as the sewerage. They were therefore combined sewers and drains closely akin to the sewers of our “combined” systems. The openings into them were made along the streets of Rome and in public buildings or some other public places. There is no evidence that they were ventilated except through these openings, and from each noxious gases were constantly rising to be taken into the lungs of the passers-by. It is a rather curious as well as important fact that so far as excavations have been made there is practically no evidence that a private residence in Rome was connected with the sewers. The “latrines” were generally located adjacent to the Roman kitchens and discharged into the cloacæ.

21. Early Roman Bridges.—The early Romans were excellent bridge-builders as well as constructors in other lines of engineering work. Although the ancient city was first located on the left bank of the Tiber, apparently it was but a comparatively short time before the need of means for readily crossing from bank to bank was felt. The capacity of the Roman engineers was equal to the demands of the occasion, and it is now known that seven or eight ancient bridges connected the two shores of the river Tiber. The oldest bridge is that known as Pons Sublicius. No iron was used in its construction, as bronze was the chief metal employed in that early day. The structure was probably all of timber except possibly the abutments and the piers. A French engineer, Colonel Emy, has exhibited in his “Traité de l’Art de la Charpenterie” a plan of this structure restored as an all-timber bridge with pile foundations. Lanciani, on the other hand, believes that the abutments and piers must have been of masonry. The masonry structures, however, known to exist at a later day may have been parts of the work of rebuilding after the two destructions by floods. The date of its construction is not known, but tradition places it in the time of Ancus Marcius. This may or may not be correct. A flood destroyed the bridge in 23 B.C., and again in the time of Antoninus Pius, but on both occasions it was rebuilt. The structure has long since disappeared. The piers only remained for a number of centuries, and the last traces of them were removed in 1877 in order to clear the bed of the river.

Fig. 11 shows Colonel Emy’s restoration of the plan for the pile bridge which Julius Cæsar built across the Rhine in ten days for military purposes. This plan may or may not include accurate features of the structure, but it is certain that such a timber bridge was built, and well preserved pieces of the piles have been taken from under water at the site little the worse for wear after two thousand years of submersion.

The censor Ælius Scaurus built a masonry arch across the Tiber about a mile and a half from Rome in the year 100 B.C. This bridge is now known as the Ponte Molle, and some parts of the original structure are supposed to be included in it, having been retained in the repeated alterations. The arches vary in span from 51 to 79 feet, and the width of the structure is a little less than 29 feet.

In or about the year 104 A.D. the emperor Trajan constructed what is supposed to be a wooden arch bridge with masonry piers across the Danube just below the rapids of the Iron Gate.

Cross-section at Pier.

Plan at Pier.

Fig. 11.—Bridge thrown across the Rhine by Julius Cæsar.

A bas relief on the Trajan Column at Rome exhibits the timber arches, but fails to give the span lengths, which have been the subject of much controversy, some supposing them to have been as much as 170 feet.

The ancient Pons Fabricius, now known as Ponte Quattiro Capi, still exists, and it is the only one which remains intact after an expiration of nearly two thousand years. It has three arches, the fourth being concealed by the modern embankment at one end; a small arch pierces the pier between the other two arches. This structure is divided into two parts by the island of Æsculapius. It is known that a wooden bridge must have joined that island with the left bank of the Tiber as early as 192 B.C., and a similar structure on the other side of the island is supposed to have completed the structure. While Lucius Fabricius was Commissioner of Roads in the year 62 B.C. he reconstructed the first-named portion into a masonry structure of arches. An engraved inscription below the parapets shows that the work was duly and satisfactorily completed, and further that it was the custom to require the constructors or builders of bridges to guarantee their work for the period of forty years. Possession of the last deposit, made in advance as a guarantee of the satisfactory fulfilment of the contract, could not be regained until the forty-first year after completion.

Fig. 12.—Trajan’s Bridge.

The Pons Cestius is a bridge since known as the Pons Gratianus and Ponte di S. Bartolomeo. Its first construction is supposed to have been completed in or about 46 B.C., and it was rebuilt for the first time in A.D. 365. A third restoration took place in the eleventh century. The modern reconstruction in 1886-89 was so complete that only the middle arch remains as an ancient portion of the structure. The island divides the bridge into two parts, the Ship of Æsculapius lying between the two, but it is not known when or by whom the island was turned into that form.

Another old Roman bridge, of which but a small portion is now standing, is Pons Æmilius, the piers of which were founded in 181 B.C., but the arches were added and the bridge completed only in 143 B.C. It was badly placed, so that the current of the river in times of high water exerted a heavy pressure upon the piers, and in consequence it was at least four times carried away by floods, the first time in the year A.D. 280.

The discovery of what appears to be a row of three or four ruins of piers nearly 340 feet up-stream from the Ponte Sisto seems to indicate that a bridge was once located at that point, although little or nothing is known of it as a bridge structure. Some suppose it to be the bridge of Agrippa.

The most historical of all the old Roman bridges is that which was called Pons Ælius, now known as Ponte S. Angelo, built by Hadrian A.D. 136. Before the reconstruction of the bridge in 1892 six masonry arches were visible, and the discovery of two more since that date makes a total of eight, of which it is supposed that only three were needed in a dry season. The pavement of the approach to this bridge as it existed in 1892 was the ancient roadway surface. Its condition at that time was an evidence of the substantial character of the old Roman pavement.

Below the latter bridge remains of another can be seen at low water. It is supposed that this structure was the work of Nero, although its name is not known.

The modern Ponte Sisto is a reconstruction of the old Pons Valentinianus or bridge of Valentinian I. The latter was an old Roman bridge, and it was regarded as one of the most impressive of all the structures crossing the river. It was rebuilt in A.D. 366-67.

The most of these bridges were built of masonry and are of the usual substantial type characteristic of the early Romans. They were ornamented by masonry features in the main portions and by ornate balustrades along either side of the roadway and sidewalks. The roadway pavements were of the usual irregular polygonal old Roman type, the sidewalk surfaces being composed of the large slabs or stones commonly used in the early days of Rome for that purpose.

22. Bridge of Alcantara.—Among the old Roman bridges should be mentioned that constructed at Alcantara in Spain, supposedly by Trajan, about A.D. 105. It is 670 feet long and its greatest height is 210 feet. One of its spans is partially destroyed. The structure is built of blocks of stone without cementing material. In this case the number of arches is even, there being six in all, the central two having larger spans than those which flank them. It is a bridge of no little impressiveness and beauty and is a most successful design.

23. Military Bridges of the Romans.—In the old Roman military expeditions the art of constructing temporary timber structures along lines of communication was well known and practised with a high degree of ability. Just what system of construction was employed cannot be determined, but piles were constantly used. At least some of these timber military bridges, and possibly all, were constructed with comparatively short spans, the trusses being composed of such braces and beams as might be put in place between bents of piles. As already observed, some of the sticks of these bridges have been found in the beds of German rivers, and at other places, perfectly preserved after an immersion of about two thousand years. These instances furnish conclusive evidence of the enduring qualities of timber always saturated with water.

24. The Roman Arch.—The Romans developed the semicircular arch to a high degree of excellence, and used it most extensively in many sewers, roads, and aqueducts. While the aqueduct spans were usually made with a length of about 18 or 20 feet, they built arches with span lengths as much as 120 feet or more, comparing favorably with our modern arch-bridge work. They seldom used any other curve for their arches than the circular, and when they built bridges an odd number of spans was usually employed, with the central opening the largest, possibly in obedience to the well-known esthetic law that an odd number of openings is more agreeable to the eye than an even number. Apparently they were apprehensive of the safety of the piers from which their arches sprang, and it was not an uncommon rule to make the thickness of the piers one third of the clear span. Nearly one fourth of the entire length of the structure would thus be occupied by the pier thicknesses. Although the use of mortar, both lime and cement, early came into use with the Romans, they usually laid up the ring-stones of their arches dry, i.e., with out the interposition of mortar joints.

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CHAPTER III.

25. The Roman Water-supply.—There is no stronger evidence of engineering development in ancient Rome, nor of the advanced state of civilization which characterized its people, than its famous system of water-supply, which was remarkable both for the volume of water daily supplied to the city and for the extensive aqueducts, many of whose ruins still stand, as impressive monuments of the vast public works completed by the Romans. These ruins, and those of many other works, would of themselves assure us of the elaborate system of supply, but fortunately there has been preserved a most admirable description of it, the laws regulating consumption, the manner of administering the water department of the government of the ancient city, and much other collateral information of a most interesting character. In the work entitled, in English, “The Two Books on the Water-supply of the City of Rome,” by (Sextus) Julius Frontinus, an eminent old Roman citizen, who, besides having filled the office of water commissioner[1] of the city, was governor of Britain and three times consul, as well as having enjoyed the dignity of being augur. He may properly be called a Roman engineer, although he evidently was a man of many public affairs, and so esteemed by the emperors who ruled during his time that he accompanied them in various wars as a military man of high rank. He wrote seven books at least, viz., “A Treatise on Surveying,” “Art of War,” “Strategematics,” “Essays on Farming,” “Treatise on Boundaries, Roads, etc.,” “A Work on Roman Colonies,” and his account of the water-works of Rome, entitled “De Aquis.” It is the latter book in which engineers are particularly interested. The translation of this book from the original Latin is made from what is termed the “Montecassino Manuscript,” an account of which with the translation is given by Mr. Clemens Herschel in his entertaining work, “Frontinus, and the Water-supply of the City of Rome.”

As near as can be determined Frontinus lived from about A.D. 35 to A.D. 103 or 104. Judging from the offices which Frontinus held and the honors which he enjoyed throughout his life, it would appear that he was a patrician; he was certainly a man of excellent executive capacity, of intellectual vigor and refined taste, and a conscientious public servant. The water-supply of the city was held by the Romans to be one of the most important of all its public works, and its administration during the life of Frontinus was entrusted to what we should call a water commissioner, appointed by the emperor. It was considered to be an office of dignity and honor, and the proper discharge of its responsibilities was a public duty which required a high order of talent, as well as great integrity of character.

26. The Roman Aqueducts.—Frontinus states that from the foundation of the city of Rome until 313 B.C., i.e., for a period of 441 years, the only water-supply was that drawn either from the river Tiber or from wells or springs. The veneration of the Romans for springs is a well-known feature of their religious tenets. They were preserved with the greatest care, and hedged about with careful safeguards against irreverent treatment or polluting conditions. Apparently after this date the people of Rome began to feel the need of a public water-supply adequate to meet the requirements of a great city. At any rate, in the year 313 B.C. the first aqueduct, called the Appia, for bringing public water into the city of Rome was attempted by Censors Appius Claudius, Crassus, and C. Plautius, the former having constructed the aqueduct, and the latter having found the springs. Appius must have been an engineer of no mean capacity, for it was he who constructed the first portion of the Appian Way. The origin of this water-supply is some springs about 10 miles from Rome, and they may now be seen at the bottom of stone quarries in the valley of the Anio River. This aqueduct, Aqua Appia, is mostly an underground waterway, only about 300 feet of it being carried on masonry arches. At the point where it enters the city it was over 50 feet below the surface; its clear cross-section is given as 2½ feet wide by 5 feet high. The elevation of its water surface in Rome was probably under 60 feet above sea-level.

Claudia, of dimension stone, and Anio Novus,
of brick and concrete, on top of it.

27. Anio Vetus.—The next aqueduct built for the water-supply of Rome was called Anio Vetus. It was built 272-269 B.C., and is about 43 miles long; it took its water from the river Anio. About 1100 feet of its length was carried above ground on an artificial structure. It also was a low-level aqueduct, the elevation at which it delivered water at Rome being about 150 feet above sea-level. It was built of heavy blocks of masonry, laid in cement, and the cross-section of its channel was about 3.7 feet wide by 8 feet high. In the year 144 B.C. the Roman senate made an appropriation equal to about $400,000 of our money to repair the two aqueducts already constructed, and to construct a new one called Aqua Marcia, to deliver water to the city at an elevation of about 195 feet above sea-level. This aqueduct was finished 140 B.C.; it is nearly 58 miles long, and carried water of most excellent quality through a channel which, at the head of the aqueduct, was 5⅞ feet wide by 8³/₁₀ feet high, but farther down the structure was reduced to 3 feet wide by 5⁷/₁₀ feet high. The excellent water of these springs is used for the present supply of Rome, and is brought in the Aqua Pia, built in 1869, as a reconstruction of the old Aqua Marcia. This aqueduct, like its two predecessors, is built of dimension stone, 18 inches by 18 inches by 42 inches, or larger, laid in cement; but concrete and brick were used in the later aqueducts, with the exception of Claudia.

28. Tepula.—The aqueduct called Aqua Tepula, about 11 miles in length, and completed 125 B.C., was constructed to bring into the city of Rome a slightly warm water from the volcanic springs situated on the hill called Monte Albani (Alban Hills) southeast of Rome. The temperature of these springs is about 63° Fahr. In the year B.C. 33 Agrippa caused the water from some springs high up the same valley to be brought in over the aqueduct Aqua Julia, 14 miles long. This latter water was considerably colder than that of the Tepula Springs. The two waters were united before reaching Rome and allowed to flow together far enough to be thoroughly mixed. They were then divided and carried into Rome in two conduits. The volume of water carried in the Aqua Julia was about three times that taken from the Tepula Springs, the cross-section of the latter being only 2.7 feet wide by 3.3 feet high, while that of Julia was 2.3 feet by 4.6 feet. The water from Aqua Julia entered Rome at an elevation of about 212 feet above sea-level, and that from Aqua Tepula about 11 feet lower.

29. Virgo.—The sixth aqueduct in chronological order was called Virgo, and it was completed 19 B.C. It takes water from springs about 8 miles from Rome and only about 80 feet above sea-level, but the length of the aqueduct is about 13 miles. The delivery of water in the city by this aqueduct is about 67 feet above that level. The cross-section of this channel is about 1.6 feet wide and 6.6 feet high.

30. Alsietina.—The preceding aqueducts are all located on the left or easterly bank of the Tiber, but one early structure was located on the right bank of the Tiber to supply what was called the Trans-Tiberine section of the city, and it was known as Aqua Alsietina. The emperor Augustus had this aqueduct constructed during his reign, and it was finished in the year A.D. 10. Its source is a small lake of the same name with itself, about 20 miles from Rome. The elevation of this lake is about 680 feet above sea-level, while the water was delivered at an elevation of about 55 feet above the same level. The water carried by this aqueduct was of such a poor quality that Frontinus could not “conceive why such a wise prince as Augustus should have brought to Rome such a discreditable and unwholesome water as the Alsietina, unless it was for the use of Naumachia.” The latter was a small artificial lake or pond in which sham naval fights were conducted.

Sand and Pebble Catch-tanks near Tivoli.
Dimension-stone aqueducts of Marcia at either end
of the tank built of small stone; opus incretum.
The arches are chambers of the tanks.

31. Claudia.—The eighth aqueduct described by Frontinus is the Aqua Claudia, built of dimension stone, which he calls a magnificent work on account of the large volume of water which it supplied, its good quality, and the impressive character of considerable portions of the aqueduct itself, between 9 and 10 miles being carried on arches. It was built in 38-52 A.D. and is forty-three miles long. The sources of its supply are found in the valley of the Anio, and consequently it belongs to the system on the left bank of the Tiber. The cross-section of its channel was about 3.3 feet wide by 6.6 feet high. It was a work greatly admired by the Roman people, as is evidenced by the praise “given to it by Roman authors who wrote at that time.” It delivered water at the Palatine 185 feet above sea-level. According to Pliny, the combined cost of it and the Aqua Anio Novus was 55,500,000 sestertii, or nearly $3,000,000. This aqueduct probably belongs to the highest type of Roman hydraulic engineering. It follows closely the location of the Aqua Marcia, although its alignment now includes a cut-off tunnel about 3 miles long, the latter having been constructed about thirty-six years after the aqueduct was opened. Mr. Clemens Herschel observes that the total sum expended for these two aqueducts makes a cost of about $6 per lineal foot for the two. The arches of this aqueduct and those of the Anio Novus have clear spans of 18 to 20 feet, with a thickness at the crown of about 3 feet.

32. Anio Novus.—The ninth aqueduct described by Frontinus is called Anio Novus. It was also constructed in the years A.D. 38-52. This aqueduct has a length of about 54 miles and takes its supply from artificial reservoirs constructed by Nero at his country-seat in the valley of the Anio near modern Subiaco. This structure is built of brick masonry lined with concrete. That portion of the Aqua Claudia which is located on the Campagna carries for 7 miles the Anio Novus, and it forms the long line of aqueduct ruins near Roma Vecchia. The upper surface of the arch-ring at the crown forms the bottom of the channel of the aqueduct. The cross-section of the channel of the Anio Novus was 3.3 feet wide by 9 feet high. The elevation of the water in this, as in the Claudia, when it reached the Palatine was about 185 feet above sea-level. The Anio Novus in some respects would seem to be a scarcely less notable work than the Claudia. About 8 miles of its length is carried on arches, some of them reaching a height of about 105 feet from the ground.

33. Lengths and Dates of Aqueducts.—These nine aqueducts constituted all those described by Frontinus, as no others were completed prior to his time. Five others were, however, subsequently completed between the years 109 A.D. and 306 A.D., but enough has already been shown in connection with the older structures to show the character of the water-supply of ancient Rome.

The following tabular statement is a part of that given by Mr. F. W. Blackford in “The Journal of the Association of Engineering Societies,” December, 1896. It shows the dates and lengths of the ancient aqueducts of Rome between the years 312 B.C. and 226 A.D., with the length of the arch portions. The list includes those built up to the end of the Empire. It will be observed that the total length of the aqueducts is 346 miles, and that of the arch portions 44 miles. The figures vary a little from those given by Lanciani and others, but they are essentially accurate.

34. Intakes and Settling-basins.—The preceding brief descriptions of the old Roman aqueducts give but a superficial idea of the real features of those great works and of the system of water-supply of which they were such essential portions. Enough has been shown, however, to demonstrate conclusively that the engineers and constructors of old Rome were men who, on the one hand, possessed a high order of engineering talent and, on the other, ability to put in place great structures whose proportions and physical characteristics have commanded the admiration of engineers and others from the time of their completion to the present day. If a detailed statement were to be made in regard to the water-supply of ancient Rome, it would appear that much care was taken to insure wholesome and potable water. At the intakes of a number of the aqueducts, reservoirs or basins were constructed in which the waters were first received and which acted as settling-basins, so that as much sedimentation as possible might take place. Similar basins (picinæ) were also constructed at different points along the aqueducts for the same purpose and for such other purposes as the preservation of the water in a portion of the aqueduct in case another portion had to be repaired or met with an accident which for the time being might put it out of use. These basins were usually constructed of a number of apartments, the water flowing from one to the other, very much as sewage in some sewage-disposal works flows at the present time through a series of settling-basins. The object of these picinæ was the clearing of the water by sedimentation. Indeed there was in some cases a use of salt in the water to aid in clarifying it. This is an early type of the modern process of clarifying water by chemical precipitation, not the best of potable water practice, but one that is sometimes permissible.

35. Delivery-tanks.—The aqueducts brought the water to castellæ or delivery-tanks, i.e., small reservoirs, both inside the city and outside of it, and from these users were obliged by law to take their supplies; that is, for baths, for fountains, for public uses, for irrigation, and for private uses. When Frontinus wrote his “De Aquis” a little less than three tenths of all the water brought to Rome by the aqueducts was used outside of the city. The remainder was distributed in the city from 247 delivery-tanks or small reservoirs, about one sixth of it being consumed by 39 ornamental fountains and 591 water-basins.

36. Leakage and Lining of Aqueducts.—These aqueducts were by no means water-tight. Indeed they were subject to serious leakage, and Frontinus shows that forces of laborers were constantly employed in maintaining and repairing them. As has been stated, the older aqueducts were built of dimension stones, while the later were constructed of concrete or bricks and concrete. The channels of these aqueducts, as well as reservoirs and other similar structures, were made as nearly water-tight as possible by lining them with a concrete in which pottery, broken into fine fragments, was mixed with mortar.

Claudia and Anio Novus near Porta Furba.
Repairs in brickwork and in a composite
of concrete and brickwork.

37. Grade of Aqueduct Channels.—The fall of the water surface in these aqueducts cannot be exactly determined. The levelling-instruments used by the Romans were simple and, as we should regard them, crude, although they served fairly well the purposes to which they were applied. They were not sufficiently accurate to determine closely the slope or grade of the water surface in the aqueduct channels. The deposition of the lime from the water along the water surface on the sides of the channels in many cases would enable that slope to be determined at the present time, but sufficiently careful examinations have not yet been made for that purpose. Lanciani states that the slopes in the Aqua Anio Vetus vary from about one in one thousand to four in one thousand. An examination of the incrustation on the sides of the Aqua Marcia near its intake makes it appear that the slope of the surface was about .06 foot per 100 feet, which would produce a velocity, according to the formula of Darcy, of about 3.3 feet per second. In some aqueducts built in Roman provinces it would appear that slopes have been found ranging from one in six hundred to one in three thousand.

38. Qualities of Roman Waters.—The chief characteristic in most of the old Roman waters was their extreme hardness. They range from 11° to 48° of hardness, the latter belonging to the water of the Anio, while the potable waters in this country scarcely reach 5°. The old Romans recognized these characteristics of their waters and, as has been intimated, used the best of them for table purposes, while the less wholesome were employed for fountains, flushing sewers, and other purposes not affected by undesirable qualities. The water from Claudia, for instance, was used for the imperial table. The water from the Aqua Marcia was also of excellent quality, while that brought in by the Aqua Alsietina was probably not used for potable purposes at all.

39. Combined Aqueducts.—In several cases a number of aqueduct channels were carried in one aqueduct. A marked instance of this kind was that of Julia, Tepula, and Marcia, all being carried in vertical series in one structure. Numerous instances of this sort occurred.

40. Property Rights in Roman Waters.—In reading the two books of Frontinus one will be impressed by the property values which the old Romans created in water rights. The laws of Rome were exceedingly explicit as to the rights of water-users and as to the manner in which water should be taken from the aqueducts and from the pipes leading from the reservoirs in and about the city. The proper methods for taking the water and using it were carefully set forth, and penalties were prescribed for violations of the laws pertaining to the use of water. There were many abuses in old Rome in the administration of the public water-supply, and one of the most troublesome duties which Frontinus had to perform lay in reforming those abuses and preventing the stealing of water. The unit of use of water (a “quinaria,” whose value is not now determinable) was the volume which would flow from an orifice .907 inch in diameter and having an area of about .63 of a square inch. Mr. Herschel shows that in consequence of the failure of the Romans to understand the laws of the discharge of water under varying heads, the quinaria may have ranged from .0143 cubic foot to .0044 cubic foot per second or between even wider limits.

41. Ajutages and Unit of Measurement.—Frontinus describes twenty-five ajutages of different diameter, officially approved in connection with the Roman system of public water-supply; but only fifteen of these were actually used in his day. All of these were circular in form, although two others had been used prior to that time. They varied in diameter from .907 to 8.964 English inches and were originally made of lead, but that soft metal lent itself too easily to the efforts of unscrupulous water-users to enlarge them by thinning the metal. In his time they were made of bronze, which was a hard metal and could not be tampered with so as to enlarge its cross-section. The discharge through the smallest of these ajutages was the quinaria, the unit in the scale of water rights. The largest of the above ajutages had a capacity of a little over 97 quinariæ.

This unit (the quinaria) was based wholly on superficial area, and had no relation whatever to the head over the orifice or to the velocity corresponding to that head. Although Frontinus refers in several cases to the fact that the deeper the ajutage is placed below the water surface the greater will be the discharge through it, also to the fact that a channel or pipe of a given area of cross-section will pass more water when the latter flows through it with a high velocity, he and other Roman engineers seem to have failed completely to connect the idea of volume of discharge to the product of area of section by velocity. In the Roman mind of his day, and for perhaps several hundred years after that, the area of the cross-section of the prism of water in motion was the only measure of the volume of discharge. This seems actually preposterous at the present time, and yet, as observed by Mr. Herschel, possibly a majority of people now living have no clearer idea of the volume of water flowing in either a closed or open channel. Existing statutes even respecting water rights bear out this statement, improbable as it may at first sight appear. This early Roman view of the discharge is, however, in some respects inexplicable, for Hero of Alexandria wrote, probably in the period 100-50 B.C., that the section of flow only was not sufficient to determine the quantity of water furnished by a spring. He proceeded to set forth that it was also necessary to know the velocity of the current, and further explained that by forming a reservoir into which a stream would discharge for an hour the flow or discharge of that stream for the same length of time would be equal to the volume of water received by the reservoir. His ideas as to the discharge of a stream of water were apparently as clear as those of a hydraulic engineer of the present time. Indeed the method which he outlines is one which is now used wherever practicable.

It has been a question with some whether Frontinus and other Roman engineers were acquainted with the fact that a flaring or outward ajutage would increase the flow or discharge through the orifice. The evidence seems insufficient to establish completely that degree of knowledge on their part. At the same time, in the CXII chapter of Frontinus’ book on the “Water-supply of the City of Rome,” he states that in some cases pipes of greater diameter than that of the orifice were improperly attached to legal ajutages. He then states: “As a consequence the water, not being held together for the lawful distance, and being on the contrary forced through the short restricted distance, easily filled the adjoining larger pipe.” He was convinced that the use of a pipe with increased diameter under such circumstances would give the user of the water a larger supply than that to which he was entitled, and he was certainly right in at least most cases.

The actual unit orifice through which the unit volume of water called the quinaria was discharged was usually of bronze stamped by a proper official, thus making its use legal for a given amount of water. The Roman engineers understood that such an orifice should be inserted accurately at right angles to the side of the vessel or orifice, and that was the only legal way to make the insertion. Furthermore, the law required that there should be no change in the diameter of the pipe within 50 feet of the orifice. It was well known that a flaring pipe of increased diameter applied immediately at the orifice would largely increase the discharge, and unscrupulous people resorted to that means for increasing the amount of water to be obtained for a given price.

42. The Stealing of Water.—It appears also that Frontinus experienced much trouble from clandestine abstraction of water from reservoirs and water-pipes. The administration of the water commissioner’s office had been exceedingly corrupt prior to his induction into office, and some of his most troublesome official work arose from his efforts to detect water-thieves, and to guard the supply system from being tapped irregularly or illegally. We occasionally hear of similar instances of water-stealing at the present time, which shows that human nature has not altogether changed since the time of Frontinus.

43. Aqueduct Alignment and Design of Siphons.—The alignment of some of the Roman aqueducts followed closely the contours of the hills around the heads of valleys, while others took a more direct line across the valleys on suitable structures, frequently series of arches. Judging from our own point of view it may not be clear at first sight why such extensive masonry constructions were used when the aqueduct could have been kept in excavation by following more closely the topography of the country. There is little doubt that the Romans knew perfectly well what they were about. Indeed it is definitely stated in some of the old Roman writings that the structures were built across valleys for the specific purpose of saving distance which, in most instances at least, meant saving in cost.

These masonry structures, it must be remembered, were built of material immediately at hand. Furthermore, these aqueducts were generally only made of sufficient width for the purpose of carrying water-channels. They were not wide structures. In some cases they were not more than 8 feet or 9 feet wide for a height of nearly 100 feet. The cost of construction was thus largely reduced below that of wide structures.

Old Roman Lead and Terra-cotta Pipe.

The Romans were perfectly familiar with the construction of inverted siphons. As a matter of fact Vitruvius, in Chapter VII of his Eighth book, describes in detail how they should be designed. His specific descriptions relate to lead pipes, but it is clear from what he states at other points that he considered earthenware pipes equally available. He sets forth how the pipes should be carried down one slope, along the bottom of the valley, and up the other slope, the lowest portion being called the “venter.” He realized the necessity of guarding all elbows in the pipe by using a single piece of stone as a detail for the elbow, a hole being cut in it in each direction in which the adjoining sections of pipe should be inserted, the sections of lead pipe being 10 feet long, and even goes so far as to describe the stand-pipes that should be inserted for the purpose of allowing air to escape. Vitruvius also advises that the water should not only be admitted to inverted siphons in a gradual manner, but that ashes should be thrown into the water when the siphon is first used in order that they may settle into the joints or open places so as to close any existing leaks. Lead pipe siphons, 12 to 18 inches in diameter, with 1 inch thickness of metal under 200 feet head, built in ancient times, have been found at Lyons in France. Also a drain-pipe siphon with masonry reinforcement was built at Alatri in Italy 125 B.C. to carry water under a head of about 340 feet. There are other notable instances of inverted siphons constructed and used during the ancient Roman period, some of them being of lead pipe imbedded in concrete.

CHAPTER IV.

44. Antiquity of Masonry Aqueducts.—Masonry aqueducts, either solid or with open arches, were not first constructed by the city of Rome; their origin was much farther back in antiquity than that. The Greeks at least used them before the Roman engineers, and it is not unlikely that the latter drew their original ideas from the former, if indeed they were not instructed by them. Nor during the times of the Romans was the construction of aqueducts confined to Rome. Wherever Roman colonies were created it would appear that vast sums were expended in the construction of aqueducts for the purpose of suitably supplying cities with water. Such constructions are found at many points in Spain, France, and other countries which were in ancient times Roman colonies. It is probable that there are not less than one hundred, and perhaps many more, of such structures in existence at the present time.

45. Pont du Gard.—Among the more prominent aqueducts constructed during the old Roman period and outside of Italy were the Pont du Gard at Nismes in the south of France, and those at Segovia and Tarragona in Spain. The Pont du Gard has three tiers of arches with a single channel at the top. The greatest height above the river Gardon is about 180 feet, and the length of the structure along the second tier of arches is 885 feet. The arches in the lowest tier are 51 feet, 63 feet, and 80.5 feet in span, while the arches in the highest tier are uniformly 15 feet 9 inches in span. The thickness of the masonry at the top of the structure from face to face is 11 feet 9 inches, and 20 feet 9 inches at the lower tier of arches, the thickness at the intermediate tier being 15 feet.

The largest arch has a depth of keystone of 5 feet 3 inches, while the other arches of the lower tier have a depth of keystone of 5 feet. The depth of the ring-stones of the small upper arches is 2 feet 7 inches. This structure forms a sort of composite construction, the lower arches constituting four separate arch-rings placed side by side, making a total thickness of 20 feet 9 inches. The intermediate arches consist of three similar series of narrow arches placed side by side, but the masonry of the upper tier is continuous throughout from face to face. The three and four parallel series of arches of the middle and lowest tiers are in no way bonded or connected with each other. There is no cementing material in any of the arch-rings, but cement mortar was used in rubble masonry or concrete around the channel through which the water flowed above the upper tier of small arches. This structure is supposed to have been built between the years 31 B.C. and 14 A.D.

46. Aqueducts at Segovia, Metz, and Other Places.—The Segovia aqueduct was built by the emperor Trajan about A.D. 100-115. It is built without mortar, and has 109 arches, but 30 are modern, being reproductions of the old. It has a length of over 2400 feet, and in places its height is about 100 feet. The old Tarragona aqueduct is built with two series of arches, 25 being in the upper series and 11 in the lower. It is 876 feet long and has a maximum height of over 80 feet. At Mayence there are ruins of an aqueduct about 16,000 feet long. In Dacia, Africa, and Greece there are other similar ruins. Near Metz are the remains of a large old Roman aqueduct. It consisted of a single row of arches, and had no features of particular prominence. This latter observation, however, could not be made of one of the bridges in the aqueduct at Antioch. Although the masonry and design of this latter structure were crude, its greatest height is 200 feet, and its length 700 feet. The lower portion of this structure was a solid wall with the exception of two openings, the arches extending in a single row along its upper portion. On the island of Mytilene are the ruins of another old aqueduct about 500 feet long, with a maximum height of about 80 feet.

The building of these remarkable aqueducts was practised at least down to the later periods of the Roman empire, that of Pyrgos, near Constantinople,—built not earlier than the tenth century,—being an excellent example. It consists of two branches at right angles to each other. The greater branch is 670 feet long, and its greatest height 106 feet. There are three tiers of arches, the two upper being of semicircular and the lower of Gothic outline. The number in each tier for a given height is the same, but with an increasing length of span in rising from the lowest to the highest tier. Thus the highest tier of piers is the lightest, relieving the top of the structure of weight. The lowest row of piers is reinforced by counterforts or buttresses. At the top of the structure the width or thickness is 11 feet, but the thickness increases uniformly to 21 feet at the bottom. The smaller branch of the aqueduct is 300 feet long, and was built with twelve semicircular arches.

47. Tunnels.—The construction of tunnels, especially in connection with the building of aqueducts, constituting a branch of engineering procedure, was frequently practised by the ancient nations. Large tunnel-works were executed many times by the ancient Greeks and Romans. It would seem that the Greeks were the instructors of the Romans in this line of engineering operations. As early as B.C. 625 we are told that the Greek engineer Eupalinus constructed a tunnel 8 feet broad, 8 feet high, and 4200 feet long, through which was built a channel for carrying water to the city of Athens.

Sixty-five years later a similar work was constructed for the same Grecian city. Indeed it appears that tunnels were constructed in the time of the earliest history of aqueducts built to supply ancient Greek and Roman cities with water.

It is certain that at the beginning of the Christian era tunnelling processes were well known among the Romans. Vitruvius writes, in speaking of the construction of aqueducts, in Chapter VII of the Eighth Book: “If hills intervene between the city wall and spring head, tunnels underground must be made, preserving the fall above assigned; if the ground cut through be sandstone or stone, the channel may be cut therein; but if the soil be earth or gravel, side walls must be built, and an arch turned over, and through this the water may be conducted. The distance between the shafts over the tunnelled part is to be 120 feet.”

The Romans pierced rock in their tunnel-work, not only by chiselling, but sometimes by building fire against the rock so as to heat it as hot as possible. The heated rock was then drenched with cold water, so that it might be cracked and disintegrated to as great an extent as practicable. According to Pliny vinegar was used instead of water in some cases, under the impression that it was more efficacious.

Roman water-pipe made of bored-out blocks of stone.

One of the methods mentioned by Vitruvius is plainly “the cut and cover” procedure of the present day. In Duruy’s history of Rome a tunnel over three miles long is mentioned on a line of an aqueduct at Antibes in France, as well as another constructed to drain Lake Fucinus in Italy, about A.D. 50. It is there stated that the latter required eleven years’ labor of 30,000 men to build a rock tunnel with a section of 86 to 96 square feet 18,000 feet long.

Lanciani, in his “Ancient Rome,” states that about A.D. 152 a Roman engineer (Nonius Datus) began the construction of a tunnel in Algeria, and after having carefully laid out the axis of the tunnel across the ridge “by surveying, and taking the levels of the mountains,” left the progress of the work in the hands of the contractor and his workmen. After the rather long absence from such a work of four years he was called back by the Roman governor to ascertain why the two opposite sections of the tunnel, as constructed, would not meet, and to take the requisite measures for the completion of the work through which water was to be conducted to Saldæ in a suitable channel. He explains that there should have been no difficulty, and that the failure of the two headings to meet was due to the negligence of the contractor and his assistant, whom he states “had committed blunder upon blunder,” although he writes, “As always happens in these cases, the fault was attributed to the engineer.” He solved the problem by connecting the two approximately parallel tunnels by a transverse tunnel, so that water was finally brought to the city of Saldæ.

The art of tunnel construction has been one of the most widely practised branches of Civil-Engineering from the times of the ancient Assyrians, Egyptians, Greeks, Romans, and other ancient nations down to the present.

48. Ostia, the Harbor of Rome.—The capacity of the ancient Romans to build harbor-works is shown by what they did at Ostia, which was then at the mouth of the Tiber, but is now not less than four miles inland from the present shore line. At the Ostia mouth of the river the present annual average advance seaward is not less than 30 feet, and at the Fiumicino mouth about one third of that amount.

Fig. 13.—Plan of Ostia and Porto.

The ancient port of Ostia is supposed to have been founded during the reign of the fourth king Ancus Marcius, but it attained its period of greatest importance during the reign of Claudius and Trajanus. At that time the fertile portions of the Campania had been so largely taken up by the country-places of the wealthy Romans that it was no longer possible for the peasantry to cultivate sufficient ground to yield the grain required by the home market of the Romans. Large fleets were consequently engaged in the foreign grain-trade of Rome. The wheat and other grain required in great quantities was grown mostly in Egypt, although Carthage and other countries supplied large amounts. The great fleets occupied in this trade made ancient Ostia their Roman port. At the present time it has no inhabitants, but is a group of complete ruins, with its streets of tombs, baths, palaces, and temples, deeply covered with the accumulations of many centuries. Enough excavations have been made along the shores of the Tiber at this point to show that the river was bordered with continuous and substantial masonry quays, flanked on the land side by successions of great warehouses, obviously designed to receive grain, wine, oil, and other products of the time. The entrance to this harbor was difficult, as the mouth of the river was shallow, with bars apparently obstructing its approach. There were no jetties, or other seaward works for the protection of vessels desiring to make the harbor. It is stated that during one storm nearly or quite two hundred vessels were destroyed while they were actually in the harbor.

49. Harbors of Claudius and Trajan.—The difficulty in entering the mouth of the Tiber prompted the emperor Claudius to construct another harbor to accommodate the vast commerce then centring at the port of Rome. Instead of increasing the capacity of Ostia and opening the mouth of the river by deepening it, he constructed a new harbor on what was then the seashore, a short distance from Ostia, and connected it with the Tiber by a canal, the extension of which by the natural forces of the river has become the Fiumicino, the only present navigable entrance to the river. This harbor was enclosed by two walls stretching out from the shore, and converging on the sea side to a suitable opening left for the entrance of ships. The superficial area of this harbor was about 175 acres, but it became insufficient during the time of Trajan. He then proceeded to excavate inland a hexagonal harbor with a superficial area of about 100 acres, which was connected both with the harbor of Claudius and the canal connecting the latter with the Tiber. These harbor-works were elaborate in their fittings for the accommodation of ships, and were built most substantially of masonry. They showed that at least in some branches of harbor-work the old Romans were as good engineers as in the construction of aqueducts, bridges, and other internal public works. The harbors at ancient Ostia, including those of Claudius and Trajan, were not the only works of their class constructed by the Romans, but they are sufficient to show as great advancement in harbor and dock work as in other lines of engineering.

These harbors were practically defenceless and exposed to the incursions of pirates, which came to be frequently and successfully made in the days of the declining power of Rome. It was therefore rather early in the Christian era that these attacks discouraged, and ultimately drove away, first, the maritime business of the Romans and, subsequently, all the inhabitants of these ports, leaving the pillaged remnants of the vast harbor-works, warehouses, palaces, temples, and other buildings in the ruined condition in which they are now found.

CHAPTER V.

50. Ancient Engineering Science.—The state of what may be called the philosophy or science of engineering construction in ancient Rome is admirably illustrated by the work on Architecture by Marcus Vitruvius Pollio, who is ordinarily known as Vitruvius, and who wrote probably a little more than two thousand years ago. He calls himself an architect, and his work is a classic in that profession of which he claims to be a member. Although much of his work was purely architectural, a great portion of it, on the other hand, was not architecture as we now know it, but civil-engineering in the best sense of the term. It must be remembered, therefore, that what is here written applies to that large portion of his work which is purely civil-engineering.

It will be seen that although he understood really little or nothing about the science of civil-engineering as we now comprehend it, he perceived many of the general and fundamental principles of the best practice of that profession and frequently applied them in a manner which would do credit to a modern civil engineer. He not only laid down axioms to govern the design of civil-engineering structures and machinery for the transmission of power, but he also set forth many considerations bearing upon public and private health and the practice of sanitary engineering in a way that was highly creditable to the state of scientific knowledge in his day. Speaking of the general qualifications of an architect, remembering that that word as he understood it includes the civil engineer, he states: “An architect should be ingenious, and apt in the acquisition of knowledge; ... he should be a good writer, a skilful draughtsman, versed in geometry and optics, expert at figures, acquainted with history, informed on the principles of natural and moral philosophy, somewhat of a musician, not ignorant of the sciences both of law and physics, nor of the motions, laws, and relations to each other of the heavenly bodies.” Again he adds: “Moral philosophy will teach the architect to be above meanness in his dealings and to avoid arrogance; it will make him just, compliant, and faithful to his employer; and, what is of the highest importance, it will prevent avarice gaining an ascendency over him; for he should not be occupied with the thoughts of filling his coffers, nor with the desire of grasping everything in the shape of gain, but by the gravity of his manners and a good character should be careful to preserve his dignity.”

These quaint statements of the desirable qualities of a professional man are worthy to be considered rules of good professional living at this time fully as much as they were in the days of old Rome. His esteem for his profession was evidently high, but not higher than the value which every civil engineer should put upon his professional life. The need of a general education for a civil engineer is greater now even than in his day, although musical accomplishments need not be considered as essential in modern engineering practice. That qualification, it is interesting to observe in passing, was inserted by Vitruvius in order to illustrate the wide range of engineering practice in those days when the architect-engineer was called upon, among other things, to construct catapults and other engines of war, in which a nice adjustment of gut ropes was determined by the musical tones emitted under the desired tension.

51. Ancient Views of the Physical Properties of Materials.—When it is remembered that the chemical constitution of materials used in engineering was absolutely unknown, that no quantitative determination of physical qualities had been made, and that the first correct conception of engineering science had yet to be acquired, it is a matter of wonder that there had been attained the engineering development evidenced both by ancient writings like those of Vitruvius and great engineering works like those of Rome, in the Babylonian Plain and in Egypt. In discussing the problem of water-supply, he mentions that certain learned ancients, “physiologists and philosophers, maintained that there are four elements—air, fire, water, and earth—and that their mixture, according to the difference of the species, formed a natural mode of different qualities. We must recollect that not only from these elements are all things generated, but that they can neither be nourished nor grow without their assistance.” This view of the construction of material things was not conducive to a clear comprehension of those physical laws which lie at the foundation of engineering science, and it is absolutely essential that these elementary considerations be kept constantly in view in considering the engineering attainments of the Romans and other ancient peoples.

52. Roman Civil Engineers Searching for Water.—In ancient times, as at present, it was very important in many cases to know where to look for water, and how to make what might promise to be a successful search for it. Vitruvius states that the sources of water for a supply may easily be found “if the springs are open and flowing above ground.” If the sources are not so evident, but are more obscure, he recommends that “before sunrise one must lie down prostrate in the spot where he seeks to find it, and, with his chin placed on the ground and fixed, look around the place; for, the chin being fixed, the eye cannot range upwards further than it ought and is confined to the level of the place. Then where the vapors are seen curling together and rising into the air, there dig, because those appearances are not discovered in dry places.” This method of discovering water-supply would be considered by modern engineers at least somewhat awkward as well as damp and disagreeable in the early morning hours. It is not more fantastic, however, or less philosophical than the use of the divining-rod, which has been practised in modern times as well as ancient, and is used even in some country districts at the present time.

Vitruvius does not forget that the local features, including both those of soil and of an artificial character, may affect the quality of the water and possibly make it dangerous. He, therefore, sets forth general directions by which good potable water may be found and that of a dangerous nature avoided. The necessity of distinguishing between good and bad water was as present to his mind and to the minds of the old Roman engineers as to civil engineers of the present day, but the means for making a successful discrimination were crude and obviously faulty, and very often unsuccessful. He set forth, what is well known, that rain-water when collected from an uncontaminated atmosphere is most wholesome, but proceeds to give reasons which would not now be considered in the highest degree scientific.

In Chapter V of his Eighth Book there are described some “means of judging water” so quaint and amusing that they may now well be quoted even though no civil engineer would be bold enough to cite them in modern hydraulic practice. He says: “If it be of an open and running stream, before we lay it on, the shape of the limbs of the inhabitants of the neighborhood should be looked to and considered. If they are strongly formed, of fresh color, with sound legs and without blear eyes, the supply is of good quality.” At another point he comes rather closely to our modern requirements which look to the exclusion of minute and elementary vegetable growths, when he says: “Moreover, if the water itself, when in the spring, is limpid and transparent, and the places over which it runs do not generate moss, nor reeds, nor other filth be near it, everything about it having a clean appearance, it will be manifest by these signs that such water is light and exceedingly wholesome.”

53. Locating and Designing Conduits.—In treating of the manner of conducting water in pipes or other conduits, he adverts to the necessity of accurate levelling and the instruments that were used for that purpose. The three instruments which he mentions as being used are called the dioptra, the level (libra aquaria), and the chorobates, the latter consisting of a rod about 20 feet in length, having two legs at its extremities of equal length and at right angles to it. Cross-pieces were fastened between the rod and the legs with vertical lines accurately marked on them. These vertical lines were placed in a truly vertical position by means of plumb-lines so that the top of the rod was perfectly level, and the work could thus be made level in reference to it.

In Rome the water was generally conducted either by means of open channels, usually built in masonry for the purpose, or in lead pipes, or in “earthen tubes.” Vitruvius states that the open channels should be as solid as possible, and have a fall of not less than one half a foot in 100 feet. The open channels were covered with an arch top, so that the sun might be kept from striking the water. After bringing the water to the city it was divided into three parts. One was for the supply of pools and fountains, another for the supply of baths, and a third for the supply of private houses. A charge was made for the use of water for the pools, fountains, and baths, and in this way a yearly revenue was obtained. A further charge was also made for the water used in private houses, the revenue from which was applied for the maintenance of the aqueduct which supplied the water. The treatment to be given to the different soils, rocks, and other materials through which the conduit was built which brought the supply to Rome is duly set forth by Vitruvius, and he describes the conditions under which tunnels were constructed. He also described the methods of classifying the lead pipes through which water was conducted from the reservoirs to the various points in the city after stating that they must be made in lengths of not less than 10 feet. The sheets of lead employed in the manufacture of the pipes he describes as ranging in width from 5 inches to 100 inches. The diameter of the pipe would obviously equal very closely the width of the sheet divided by the ratio between the circumference and the diameter of the corresponding circle.

54. Siphons.—He speaks of passing valleys in the construction of the conduits by means of what we now call siphons, and prescribes a method for relieving it of the accumulated air. In speaking of earthen tubes or pipes he says that they are to be provided not less than 2 inches thick and “tongued at one end so that they may fit into one another,” the joints being coated with quicklime and oil. He further observes that water conducted through earthen pipes is more wholesome than that through lead, and that water conveyed in lead must be injurious because from it white lead is obtained, which is said to be injurious to the human system. Indeed the effects of lead-poisoning were recognized in those early days, and its avoidance was attempted. In the digging of wells he wisely states that “the utmost ingenuity and discrimination” must be used in the examination of the conditions under which wells were to be dug. He also appreciated the advantage of sedimentation, for he advises that reservoirs be made in compartments so that, as the water flows from one to another, sedimentation may take place and the water be made more wholesome.

55. Healthful Sites for Cities.—In the location of cities, as well as of private residences, Vitruvius lays down the general principle that the greatest care should be taken to select sites which are healthy and subject only to clean and sanitary surroundings. Marshy places and those subject to fogs, especially those “charged with the exhalations of the fenny animals,” are to be avoided. Apparently this reference to “fenny animals” may have beneath it the fundamental idea of bacteria, but that is not certain. The main point of all these directions for the securing of sanitary conditions of living is that, so far as his technical knowledge permitted him to go, he insists on the same class of wholesome conditions that would be prescribed by a modern sanitary engineer.

56. Foundations of Structures.—Similarly in Chapter V of his First Book, on “Foundations of Walls and Towers,” Vitruvius shows a realization of the principal conditions needful and requisite for the suitable founding of heavy buildings. After a sanitary site for a city is determined and one that can be put in communication with other people “by good roads, and river or sea navigation for the transportation of merchandise,” he proceeds to state that “foundations should be carried down to solid bottom, if such can be found, and that they should be built thereon of such thickness as may be necessary for the proper support of that part of the wall standing above the natural level of the ground. They should be of the soundest workmanship, and materials of greater thickness than the walls above.” Again, in speaking of the foundations supporting columns, he states: “The intervals between the foundations brought up under the columns should be either rammed down hard, or arched, so as to prevent the foundation-piers from swerving. If solid ground cannot be come to, and the ground be loose or marshy, the place must be excavated, cleared, and either alder, olive, or oak piles, previously charred, must be driven with a machine as close to each other as possible and the intervals between the piles filled with ashes. The heaviest foundations may be laid on such a base.” It is thus seen that pile foundations were used by the Romans, and that the piles were driven with a machine. It would be difficult to give sounder general rules of practice even after more than two thousand years’ additional experience.

57. Pozzuolana and Sand.—Of all the materials which were useful to the Romans in their various classes of construction, including the foundations of roads, “pozzuolana” must have been the most useful, and that which contributed more to the development of successful construction in Rome than any other single agent. Vitruvius speaks of it frequently and gives rules not only for the use of it in the production of mortar and concrete, but also lays down at considerable length the treatment which should be given to lime in order to produce the best results. It was common, according to his statements, to use two measures of “pozzuolana” with one of lime in order to obtain a suitable cementing material. This mixture was used in varying proportions with sand and gravel or broken stone to produce concrete. He describes the various grades of sands to be found about Rome and the manner of using them. The statement is made that sand should be free of earth and that the best of it was such as to yield a “grating sound” when “rubbed between the fingers.” This is certainly a good engineering test of sand. He prefers pit-sand to either river- or sea-sand; indeed throughout all his directions regarding this particular class of construction his rules might be used at the present time with perfect propriety.

58. Lime Mortar.—The old Romans had also discovered the advisability of allowing lime to stand for a considerable period of time after slaking. This insured the slaking of all those small portions which were possibly a little hydraulic and therefore slaked very slowly. He prescribes as a good proportion two parts of sand to one of lime, and also mentions the proportion of three to one. He attempts to explain the setting, as we term it, of lime, but his explanation in obscure terms, involving qualities of the elements of fire and air, is not very satisfactory.

59. Roman Bricks according to Vitruvius.—As is well known, the Romans were good brick-makers, and they were well aware that bricks made from “ductile and cohesive” “red or white chalky” earth were far preferable to those made of more gravelly or sandy clay. The Roman bricks were both sun-dried and kiln-burned.

60. Roman Timber.—Timber was a material much used by the Romans, and the greater part of that which they used probably was grown in Italy, although considerable quantities were imported from other localities. Vitruvius writes in considerable detail concerning the selection of timber while standing, as well as in reference to its treatment before being used in structures. Like every material used by the old Romans in construction, the various kinds and qualities of timber received careful study from them, and they were by no means novices in the art of producing the best results from those kinds of timber with which they were familiar.

61. The Rules of Vitruvius for Harbors.—In Chapter XII of his Fifth Book Vitruvius lays down certain general rules for the selection and formation of harbors, and it is known that the Romans were familiar with elaborate and effective harbor construction, as is shown by that at Ostia. He appreciates that a natural harbor is one which has “rocks or long promontories jutting out, which from the shape of the place form curves or angles,” and that in such places “nothing more is necessary than to construct portices and arsenals around them, or passages to the markets.” He then proceeds to state that if such a natural formation is not to be found, and that if “on one side there is a more proper shore than on the other, by means of building or of heaps of stones, a projection is run out, and in this the enclosures of harbors are formed.” He then proceeds to explain how “pozzuolana” and lime, in the proportion of two of the former to one of the latter, are used in subaqueous construction. He also prescribed a mode of building a masonry wall up from the bottom of an excavation made within what we should call a coffer-dam, formed, among other things, “of oaken piles tied together with chain pieces.” The Romans knew well how to select harbors and how to construct in an effective manner the artificial works connected with them, although it appears that the effects of tidal and river currents in estuaries were neither well understood in themselves nor in their transporting power of the solid material which those currents eroded.

62. The Thrusts of Arches and Earth; Retaining-walls and Pavements.—Although the Romans possessed little or no knowledge of analytical mechanics they attained to some good qualitative mechanical conceptions. Among other things they understood fairly well the general character of the thrust of an arch and the tendency of the earth to overthrow a retaining-wall. They knew that a massive abutment was needed to receive safely the thrust of an arch, and they counterforted or buttressed retaining-walls in order to hold them firmly in place. They also realized the danger of wet earth pressing against a retaining-wall, and even made a series of offsets or teeth on the inside of the wall on which the earth rested in order to aid in holding the wall in place. Vitruvius recommends as a safeguard against the pressure of earth wet by winter rains that “the thickness of the wall must be proportioned to the weight of earth against it,” and that counterforts or buttresses be employed “at a distance from each other equal to the height of the foundations, and of the same width as the foundations,” the projections at the bottom being equal in thickness to that of the wall, and diminishing toward the top.

He gives in considerable detail instructions for the forming of pavements and stucco work, so many examples of which are still existing in Rome. These rules are in many respects precisely the same as would govern the construction of similar work at the present time. There are also described in a general way the methods of producing white and red lead, as pigments of paints, and a considerable number of other pigments of different colors.

63. The Professional Spirit of Vitruvius.—It is evident, from many passages in the writings of this Roman architect-engineer, that the ways of the professional men in old Rome were not always such as led to his peace of mind. Vitruvius utters bitter complaints which show that he did not consider purely professional knowledge and service to be adequately recognized or appreciated by his countrymen. He writes that in the city of Ephesus an ancient law provided that if the cost of a given work completed under the plans and specifications of an architect did not exceed the estimate, he was commended “with decrees and honors,” but if the cost exceeded the estimate with 25 per cent added thereto, he “was required to pay that excess out of his own pocket.” Then he exclaims, “Would to God that such a law existed among the Roman people, not only in respect to their public but also to their private buildings, for then the unskilful could not commit their depredations with impunity, and those who were the most skilful in the intricacies of the art would follow the profession!”

64. Mechanical Appliances of the Ancients.—It is well known that the ancients possessed at least some simple types of machines, for the reason that they raised many great stones to a considerable height in completed works after having transported them great distances from the quarries whence they were taken. Undoubtedly these machines were of a simple and crude character and were made effective largely by the power of great numbers of men. We are not acquainted with all the details of these machines, although the general types are fairly well known. The elementary machines, including the lever, the inclined plane, the pulley, and the screw, which is only an application of the inclined plane, were all used not only by the Romans, but probably by every civilized ancient nation. Vitruvius describes a considerable number of these machines, and from his descriptions it is clear that they had wide application in the structural works of the Romans. The block and fall, as we term the pulley at the present time, was a common machine in the plant of a Roman constructor, as were also various modifications and applications of the lever, the roller, and the inclined plane.

65. Unlimited Forces and Time.—It is neither surprising nor very remarkable that with the use of these simple machines, aided by a practically unlimited number of men, the necessary raising or other movement of heavy weights was accomplished by the Romans and other ancient peoples. It is to be borne in mind that the element of time was of far less consequence in those days than at present, and that the rate of progress made in the construction of most if not all ancient engineering works was what we should consider intolerably slow.

PART II. BRIDGES. — CHAPTER VI.

66. Introductory.—Although the bridge structures of to-day serve the same general purposes as those served by the most ancient structures, they are very different engineering products. It is not long, in comparison with the historic and prehistoric periods during which bridges have been built, since the science of mechanics has been sufficiently developed to make bridge design a rational procedure; and it is scarcely more than a century since the principles of mechanics were first applied to the design of bridge structures in such a way as to determine even approximately the amount of stress produced in any member by the imposed load. Naturally the first efforts made toward a truly rational bridge design were in fact simple and crude and only loosely approximate in their results. Probably the first analytic treatment of bridges was given to the design of arches in masonry and then in cast-iron. As the action of forces in structures became better known through the development of mechanical science, the applications of the latter became less crude and approximate and the approach to the refined accuracy of the present day was begun.

67. First Cast-iron Arch.—These older structures, nearly all of them arches or more or less related to the arch, first appeared in cast-iron in the latter part of the eighteenth century, when nothing like an accurate analysis of forces developed by the application of a given load was known. The first cast-iron arch was erected over the Severn in England near Coalbrookdale in the year 1779. This bridge had a span of 100 feet, and the under surface of the arch or soffit at the crown was 45 feet above the points at the abutment from which the arch sprang, or, as civil engineers put it, the arch had a span of 100 feet and a rise or versine of 45 feet. Other cast-iron arches were built in England soon after.

68. Early Timber Bridges in America.—Timber bridges have been built since the earliest historic periods and even earlier, but the widest and boldest applications of timber to bridge structures have been made in this country, beginning near the end of the eighteenth century and running to the middle of the nineteenth century, when timber began to be displaced by iron. Timber bridges and those of combined iron and timber are built to some extent even at the present day, but the most extended work of this class is to be found in the period just named.

In 1660 what was called the “Great Bridge” was built across the Charles River near Boston, and was a structure on piles. Other similar structures followed, but the first long-span timber bridge, where genuine bridge trussing or framing was used, appears to have been completed in 1792, when Colonel William P. Riddle constructed the Amoskeag Bridge across the Merrimac River at Manchester, N. H., in six spans of a little over 92 feet from centre to centre of piers. From that time timber bridges, mostly on the combined arch and truss principle, were built, many of them examples of remarkably excellent engineering structures for their day. Among these the most prominent were the Bellows Falls Bridge, in two spans of 184 feet each from centre to centre of piers, over the Connecticut River, built in 1785-92 by Colonel Enoch Hale; the Essex-Merrimac Bridge over the Merrimac River, three miles above Newburyport, Mass., built by Timothy Palmer in 1792, consisting actually of two bridges with Deer Island between them, the principal feature of each being a kind of arched truss of 160 feet span on one side of the island and 113 feet span on the other; the Piscataqua Bridge, seven miles above Portsmouth, N. H., in which a “stupendous arch of 244 feet cord is allowed to be a masterly piece of architecture, planned and built by the ingenious Timothy Palmer of Newburyport, Mass.,” in 1794; the so-called “Permanent Bridge” over the Schuylkill River at Philadelphia, built in 1804-06 in two arches of 150 feet and one of 195 feet, all in the clear, after the design of Timothy Palmer; the Waterford Bridge over the Hudson River, built in 1804 by Theodore Burr, in four combined arch and truss spans, one of 154 feet, one of 161 feet, one of 176 feet, and the fourth of 180 feet, all in the clear; the Trenton Bridge, built in 1804-06 over the Delaware River at Trenton, N. J., by Theodore Burr, in five arch spans of the bowstring type, ranging from 161 feet to 203 feet in the clear; a remarkable kind of wooden suspension bridge built by Theodore Burr in 1808 across the Mohawk River at Schenectady, N. Y., in spans ranging in length from 157 feet to 190 feet; the Susquehanna Bridge at Harrisburg, Pa., built by Theodore Burr in 1812-16 in twelve spans of about 210 feet each; the so-called Colossus Bridge, built in 1812 by Lewis Wernwag over the Schuylkill River at Fairmount, Pa., with a clear span of 340 feet 3¾ inches; the New Hope Bridge, built in 1814 over the Delaware River, in six 175 feet combined arch and truss spans, and a considerable number of others built by the same engineer.

Some of these wooden bridges, like those at Easton, Pa., and at Waterford, N. Y., remained in use for over ninety years with only ordinary repairs and with nearly all of the timber in good condition. In such cases the arches and trusses have been housed and covered with boards, so as to make what has been commonly called a covered bridge. The curious timber suspension bridge built by Theodore Burr at Schenectady was used twenty years as originally built, but its excessive deflection under loads made it necessary to build up a pier under the middle of each span so as to support the bridge structure at those points. These bridges were all constructed to carry highway traffic, but timber bridges to carry railroad traffic were subsequently built on similar plans, except that Burr’s plan of wooden suspension bridge at Schenectady was never repeated.

MOHAWK BRIDGE AT SCHENECTADY N.Y.
Built by Theodore Burr.

Fig. 1.

PATENT BRIDGE “COLOSSUS”
Across the River Schuylkill at Philadelphia.
Built by Lewis Wernwag.

Single Arch 340 feet 3¾ inches.

Fig. 2.

69. Town Lattice Bridge.—A later type of timber bridge which was most extensively used in this country was invented by Ithiel Town in January, 1820, which was known as the Town lattice bridge. This timber bridge was among those used for railroad structures. As shown by the plan it was composed of a close timber lattice, heavy plank being used as the lattice members, and they were all joined by wooden pins at their intersections. This type of timber structure was comparatively common not longer ago than twenty-five years, and probably some structures of its kind are still in use. The close latticework with its many pinned intersections made a very safe and strong frame-work, and it enjoyed deserved popularity. It was the forerunner in timber of the modern all-riveted iron and steel lattice truss. It is of sufficient significance to state, in connection with the Town lattice, that its inventor claimed that his trusses could be made of wrought or cast-iron as well as timber. In many cases timber arches were combined with them.

Fig. 3.

70. Howe Truss.—The next distinct advance made in the development of bridge construction in the United States was made by brevet Lieutenant-Colonel Long of the Corps of Engineers, U.S.A., in 1830-39, and by William Howe, who patented the bridge known as the Howe truss, although the structure more lately known under that name is a modification of Howe’s original truss. Long’s truss was entirely of timber, including the keys, pins, or treenails required, and it was frequently built in combination with the wooden arch. The truss was considerably used, but it was not sufficiently popular to remain in use.

Howe Truss-Bridge.

Fig. 4.

The Howe truss was not an all-wooden bridge. The top and bottom horizontal members, known as “chords,” the inclined braces between them and the vertical end braces, all connecting the two chords, were of timber, and they were bolted at all intersections; but the vertical braces were of round iron with screw ends. These rods extended through both chords and received nuts at both ends pressing on cast-iron washers through which the rods extended. These wrought-iron round rods were in groups at each panel-point, numbering as many as existing stresses required. The ends of the timber braces abutted against cast-iron joint-boxes. The railroad floor was carried on heavy timber ties running entirely across the bridge and resting upon the lower chord members. It was a structure simple in character, easily framed, and of materials readily secured. It was also easily erected and could quickly be constructed for any reasonable length of span. It possessed so many merits that it became widely adopted and is used in modified form at the present day, particularly on lines where the first cost of construction must be kept as low as possible. The large amount of timber in it and the simple character of its wrought-iron or steel members greatly reduces its first cost.

71. Pratt Truss.—In 1844 the two Pratts, Thomas W. and Caleb, patented the truss, largely of timber, which has since been perpetuated in form by probably the largest number of iron and steel spans ever constructed on a single type. The original Pratt trusses had timber upper and lower chords, but the vertical braces were also made of timber instead of iron, while the inclined braces were of round wrought-iron with screw ends, the reverse of the web arrangement in the Howe type. This truss had the great advantage of making the longest braces (of iron) resist tension only, while the shorter vertical braces resist compression. As a partially timber bridge it could not compete with the Howe truss, because it contained materially more iron and consequently was more costly. This structure practically closed the period of development of timber bridges.

72. Squire Whipple’s Work.—What amounted to a new epoch in the development of bridge construction in this country practically began in 1840 when Squire Whipple built his first bowstring truss with wrought-iron tension and cast-iron compression members. While the Pratts and Howe had begun to employ to some extent the analysis of stresses in the design of their bridge members, the era of exact bridge analysis began with Squire Whipple. He subjected his bridge designs to the exacting requirements of a rational analysis, and to him belongs the honor of placing the design of bridges upon the firm foundation of a systematic mathematical analysis.

73. Character of Work of Early Builders.—The names of Palmer, Burr, and Wernwag were connected with an era of admirable engineering works, but, with bridge analysis practically unknown, and with the simplest and crudest materials at their disposal, their resources were largely constituted of an intuitive engineering judgment of high quality and remarkable force in the execution of their designs never excelled in American engineering. They occasionally made failures, it is true, but it is not recorded that they ever made the same error twice, and the works which they constructed form a series of precedents which have made themselves felt in the entire development of American bridge-building.

CHAPTER VII.

74. Modern Bridge Theory.—The evolution of bridge design having reached that point where necessity of accurate analysis began to make itself felt, it is necessary to recognize some of the fundamental theoretical considerations which lie at the base of modern bridge theory, and which involve to a considerable extent that branch of engineering science known as the elasticity or strength of the materials used in engineering construction.

The entire group of modern bridge structures may be divided into simple beams or girders, trusses, arches, suspension bridges, and arched ribs, each class being adapted to carry either highway or railway traffic. That class of structure known as beams or girders is characterized by very few features. There are solid beams like those of timber, with square or rectangular cross-sections, and the so-called flanged girders which are constituted of two horizontal pieces, one at the top and the other at the bottom, connected by a vertical plate running the entire length of the beam. The fundamental theory is identically the same for both and is known as the “common theory of flexure,” i.e., the theory of beams carrying loads.

If an ordinary scantling or piece of timber of square or rectangular cross-section, like a plank or a timber joist, so commonly used for floors, be supported at each end, it is a matter of common observation that it will sustain an amount of load depending upon the dimensions of the stick and length of span. When such a bar or piece is loaded certain forces or stresses, as they are called, are brought into action in its interior. The word “stress” is used simply to indicate a force that exists in the interior of any piece of material. It is a force and nothing else. It is treated and analyzed in every way precisely as a force. If the stresses or forces set up by the loading in the interior of the bar become greater than the material can resist, it begins to break, and the breaking of that portion of the timber in which the stresses or forces are greatest constitutes its failure. The load which produces this failure in a beam is called the breaking load of the beam. In engineering practice all beams are so designed or proportioned that the greatest load placed on them shall be only a safe percentage of the breaking load; the safe load usually being found between ⅓ and ⅙ of the breaking load. In most buildings the safe or working load, as it is called, is probably about ¼ of the breaking load.

Fig. 5.

Fig. 6.

Fig. 7.

75. The Stresses in Beams.—The proper design of beams or girders to carry prescribed loads is based upon the stresses which are developed or brought into action by them. It can easily be observed that if a beam supported at each end be composed of a number of thin planks or boards placed one upon the other, it will carry very little load. Each plank or board acts independently of the others and a very small load will cause a sag, as shown in Fig. 6. If there be taken, on the other hand, a beam made of a single stick of timber of the same width and depth as the number of planks shown in Fig. 6, so as to secure the solid beam shown in Fig. 7, it is a further common observation that this latter beam may carry many times the load which the laminated beam, shown in Fig. 6, sustains. The thin planks or boards readily slide over each other, so that the ends present the serrated form shown in Fig. 6. The preventing of this sliding is the sole cause of the greatly increased stiffness of the solid beam shown in Fig. 7, for there is thus developed along the imaginary horizontal sections in the solid beam of Fig. 7 what are called shearing forces or stresses; and since they exist on horizontal sections or planes running throughout the entire length of the beam, they are called horizontal shears.

At each end of the beam shown in Fig. 7 there will be an upward or supporting force exerted by the abutments on which the ends of the beam rest. Those upward or supporting forces are shown at R and R′ and are called reactions, because the abutments, so to speak, react against the ends of the beam when the latter is loaded. These reactions depend for their value on the amount and the location of the loading which the beam carries. Obviously these upward forces or reactions tend to cut or shear off the ends of the beam immediately above them, and if the loads were sufficiently large and the beam kept from bending, the reactions would actually shear off those ends, just as punches or shears in a machine-shop actually shear off the metal when the rivet-hole is punched, or when a plate is cut by shearing into two parts. The beam, however, bends or sags before shearing apart actually takes place.

Fig. 8.

Fig. 9.

76. Vertical and Horizontal Shearing Stresses.—If it be supposed that the length of the beam is divided into a great number of parts by imaginary vertical lines, like those shown in Fig. 8, then vertical shearing forces will be developed in those vertical planes and sometimes, though not often, they are enough to cause failure. It is not an uncommon thing, on the other hand, in timber to have actual shearing failure take place along a horizontal plane through the centre of the beam. Indeed this is recognized frequently as the principal method of failure in very short spans. When this horizontal shearing failure takes place, the upper and lower parts of the beam slide over each other and act precisely like the group of planks shown in Fig. 6.

If, then, the loaded beam be divided by vertical and horizontal planes into the small rectangular portions shown in Figs. 8 and 9, on each such vertical and horizontal imaginary plane there will be respectively vertical and horizontal shearing forces, which are shown by arrows in Fig. 9. It will be noticed in that figure that in each corner of the rectangle the two shearing forces act either toward or from each other; in no case do the two adjacent shearing forces act around the rectangle in the same direction. This is a condition of shearing stresses peculiar to the bent beam. It can be demonstrated by theory and is confirmed by experiment. There is a further peculiarity about these shearing forces which act in pairs either toward or from the same angle in any rectangle, and it is that the two stresses adjacent to each other have precisely the same value per square inch (or any square unit that may be used) of the surface on which they act. These stresses per square inch vary, however, either along the length of the beam or as the centre line of any normal cross-section is departed from. They are greatest along the centre line or central horizontal plane represented by AB, and they are zero at the top and bottom surfaces of the beam.

Inasmuch as the horizontal shear along the plane AʹBʹ is less than that along AB in Fig. 9, a part of the latter has been taken up by the horizontal fibres of the beam lying between the two planes. In other words, the horizontal layer of fibres at AʹBʹ is subjected to a greater stress or force along its length than at AB. The same general observation can be made in reference to any horizontal layer of fibres that is farther away from the centre than another. Hence the farther any fibre is from the centre the greater will be the stress or force to which it is subjected in the direction of its length. It results, then, that the horizontal layers of fibres which are farthest from the centre line of the beam, i.e., those at the exterior surfaces, will be subjected to the greatest force or stress, and that is precisely what exists in a loaded beam whatever the material may be.

77. Law of Variation of Stresses of Tension and Compression.—Since a horizontal beam supported at each end is deflected or bent downward when loaded, it will take a curved form like that shown in either Fig. 7 or Fig. 10; but this deflection can only take place by the shortening of the top of the beam and the lengthening of its bottom. This shows that the upper part of the beam is compressed throughout its entire length, while the lower part is stretched. In engineering language, it is stated that the upper part of the beam is thus subjected to compression and the lower part to tension. The horizontal layers or fibres receive their tension and compression from the vertical and horizontal shearing forces in the manner already explained. If the conditions of loading of the bent beam should be subjected to mathematical analysis, it would be found that throughout the originally horizontal plane AB, Fig. 7, passing through the centre of each section there would be no stress of either tension or compression, although the horizontal shearing stress there would be a maximum. Further, as this central plane is departed from the stress of tension or compression per square inch in any vertical section would be found to increase directly as the distance from it. This is a very simple law, but one of the greatest importance in the design of all beams and girders, whatever may be the form or size of cross-section. It is a law, which applies equally to the solid timber beam and to the flanged steel girder, whether that girder be rolled in the mill or built up of plates and angles or other sections in the shop. It is a fundamental law of what is called the common theory of flexure, and is the very foundation of all beam and girder design. The horizontal plane represented by the line AB in Fig. 8, along which there is neither tension nor compression, is called the “neutral plane,” and its intersection with any normal cross-section of the beam is called the “neutral axis” of that section. Mathematical analysis shows that the neutral plane passes through the centres of gravity of all the normal sections of the beam and, hence, that the neutral axis passes through the passes through the centre of gravity of the section to which it belongs.

78. Fundamental Formulæ of Theory of Beams.—The fundamental formulæ of the theory of loaded beams may be quite simply written. Fig. 10 exhibits in a much exaggerated manner a bent beam supporting any system of loads W₁, W₂, W₃, etc., while Fig. 11 shows a normal cross-section of the same beam. In Fig. 10 AB is the neutral line, and in Fig. 11 CD is the neutral axis passing through the centre of gravity, c.g., of the section.

Fig. 10.

Fig. 11.

If a is the amount of force or stress on a square inch (or other square unit), i.e., the intensity of stress, at the distance of unity from the neutral axis CD of the section, then, by the fundamental law already stated, the amount acting on another square inch at any other distance z from the neutral axis will be az. This quantity is called the “intensity of stress” (tension or compression) at the distance z from the neutral axis. Evidently it has its greatest values in the extreme fibres of the section, i.e., ad and ad₁. At the neutral axis az becomes equal to zero. FG in Fig. 11 represents the same line as FG in Fig. 10. If the line FH in Fig. 11 be laid down equal to ad and at right angles to FG, and if O represent the centre of gravity, c.g., of the section, then let the straight line LH be drawn. Any line drawn parallel to FH from FG to LH will represent the intensity of stress in the corresponding part of the beam’s cross-section. Obviously, as these lines are drawn in opposite directions from FG, those above O will indicate stress of one kind, and those below that point stress of another kind, i.e., if that above be tension, that below will be compression. It can be demonstrated by a simple process that the total tension on one side of the neutral axis is just equal to the total compression on the other side, and from that condition it follows that the neutral axis must pass through the centre of gravity or centroid of the section.

Returning to the left-hand portion of Fig. 11, let dA represent a very small portion of the cross-section; then will az. dA be the amount of stress acting on it. The moment of this stress or force about the neutral axis will be

azdA·z = az²· dA.

If this expression be applied to every small portion of the entire section, the aggregate or total sum of the small moments so found will be the moment of all the stresses in the section about the neutral axis. That moment will have the value

In equation (1) the symbol ∫ means that the sum of all the small quantities to the right of it is taken, and I stands for that sum which, in the science of mechanics, is called the moment of inertia of the cross-section about its neutral axis. The value of the quantity I may easily be computed for all forms of section. Numerical values belonging to all the usual forms employed in engineering practice are found in extended tables in the handbooks of the large iron and steel companies of the country, so that its use ordinarily involves no computations of its value.

Equation (1) may readily be changed into two other forms for convenient practical use. In Fig. 10 mn is supposed to be a very short portion of the centre line of the beam represented by dl. Before the beam is bent the section FG is supposed to have the position MN parallel to PQ. Also let u be the small amount of stretching or compression (shortening) of a unit’s length of fibre at unit’s distance from the centre line AB of the beam, then will udl and uzdl be the short lines parallel to GN in the triangle GmN shown in the figure. The point C is the centre of curvature of the line mn, and Cn = Cm is the radius. The two triangles Cnm and mNG are therefore similar, hence

If the quantity called the coefficient or modulus of elasticity be represented by E, then, by the fundamental law of the theory of elasticity in solid bodies,

a = Eu.      (3)

As has already been shown, the greatest stresses (intensities) in the section are +ad (tension) and -ad₁ (compression). If K represent that greatest intensity of stress, then

If the value of a from equation (4) be substituted in equation (1),

79. Practical Applications.—Equation (5) is a formula constantly used in engineering practice. All quantities in the second member are known in any given case. K is prescribed in the specifications, and is known as the “working resistance” in the design of beams and girders. For rolled steel beams in buildings it is frequently taken at 16,000 pounds, i.e., 16,000 pounds per square inch, about one fourth the breaking strength of the steel. In railroad-bridge work it may be found between 10,000 and 12,000 pounds, or approximately one fifth of the breaking strength of the steel. The quantities I and d depend upon the form and dimensions of the cross-section, and are either known or may be determined. The quotient I ÷ d is now known as the “section modulus,” and its numerical values for all forms of rolled beams can be found in published tables. The use of equation (5) is therefore in the highest degree convenient and practicable.

80. Deflection.—It is frequently necessary, both in the design of beams and framed bridges, to ascertain how much the given loading will cause the beam or truss to sag, or, in engineering language, to deflect below the position occupied when unloaded. The deflection is determined by the sagging in the vertical plane of the neutral line below its position when the structure carries no load. In Fig. 10 the curved line AB is the neutral line of the beam when supporting loads. If the loads should be removed, the line AB would return to a horizontal position. The line drawn horizontally through A and indicated by x is the position of the centre line of the beam before being bent. The vertical distance w below this horizontal line shows the amount by which the point at the end of the line x is dropped in consequence of the flexure of the beam. The vertical distance w is therefore called the deflection. Evidently the deflection varies with the amount of loading and with the distance from the end of the beam. The curved line AB in one special case only is a circle. The general character of that curve is determined by the loading and the length of span.

In order that the deflection may be properly considered it is necessary that the relation between x and w shall be established for all conditions of loading and length of span. If the value of u from equation (2) be placed in equation (3), there will result

If the value of a from equation (6) be substituted in the last member of equation (1), there will at once result

It is established by a very simple process in differential calculus that

Hence, substituting from equation (8) in equation (7),

Equation (9) may be used by means of some very simple operations in integral calculus to determine the value of w in terms of x and the loads on the beam when the value of the bending moment M is known, and the procedures for determining that quantity will presently be given.

Using the processes of the calculus, the two following equations will immediately be found:

As already explained, numerical values for both E and I may be taken at once from tables already prepared for all materials and for all shapes of beams ordinarily employed in structural work, so that equation (11) enables the deflection or sag of the bent beam to be computed in any case. The expression dw/dx is the tangent of the angle made by the neutral line of a bent beam with a horizontal line at any given point, and it is a quantity that it is sometimes necessary to determine. dw and dx are indefinitely short vertical and horizontal lines respectively, as shown immediately to the left of B in Fig. 10.

Equation (11) is not used in structural work nearly as much as equation (5), but both of them are of practical value and involve only simple operations in their use.

81. Bending Moments and Shears with Single Load.—The second members of equations (5) and (9) exhibit values of the moments of the internal forces or stresses in any normal cross-section of a bent beam about the neutral axis of the section, while the values of Mmust be expressed in terms of the external forces or loading. Inasmuch as the latter moment develops just the internal moment, it is obvious that the two must be equal. In order to write the value of the external moment in terms of any loading, it is probably the simplest procedure to consider a beam carrying a single load. In Fig. 12, AB is such a beam, and W is a load which may be placed anywhere in the span, whose length is l. The distances of the load from the abutments are represented by x₁ and x₂. The reactions or supporting forces exerted under the ends of the beam at the abutments are shown by R and R′. The reactions, determined by the simple law of the lever, are

The greatest bending moment in the beam will occur at the point of application of the load, and its value will be

M₁	= Rx₁	= - Rʹx₂	= W	x₁x₂
				l

Fig. 12.

The bending moments at the end of the beam are obviously zero, and the second and fourth members of equation (13) show that the moment increases directly as the distance from either end. Hence in the lower portion of Fig. 12, at D, immediately under the load W, the line DC is laid off at any convenient scale to represent the moment M₁. The straight lines AC and CB are then drawn. Any vertical intercept, as FH or KL, between AB and either AC or CB will represent the bending moment at the corresponding point in the beam. The simple triangular diagram ACB therefore represents the complete condition of bending of the beam under the single load W placed at any point in the span.

The beam AB is supposed for the moment to have no weight. Consequently the only force acting upon the portion of the beam AO is the reaction R, and, similarly, Rʹ is the only force acting upon the portion OB. Obviously so far as the simple action of these two forces or reactions is concerned, the tendency of each is to cause vertical slices of the beam, so to speak, to slide over each other. In other words, in engineering language, the portion AO of the beam is subjected to the shear S = R, while OB is subjected to the shear Sʹ = -Rʹ. The cross-sectional area of the beam must be sufficient to resist the shear S or Sʹ. The upper part of Fig. 13 shaded with broken vertical lines indicates this condition of shear. It is evident from this simple case that the total vertical shears at the ends of any beam will be the reactions or supporting forces exerted at those ends, and that each will remain constant for the adjoining portion of the beam.

The third member of equation (13) shows that the greatest bending moment M₁ in the beam varies as the product x₁x₂ of the segments of the span. That product will have its greatest value when x₁ = x₂. Hence a simple beam loaded by a single weight will be subjected to the greatest possible bending moment when the weight is placed at the middle of the span, at which point also that moment will be found.

82. Bending Moments and Shears with any System of Loads.—The general case of a simple beam loaded with any system of weights whatever may be represented in Fig. 13, in which the beam of Fig. 12 is supposed to carry three loads, w₁, w₂, w₃. The spacing of the loads is as shown. The reactions or supporting forces Rʹ are determined precisely as in Fig. 12, each reaction in this case being the resultant of three loads instead of one. Applying the law of the lever as before, the reaction R will have the value

A similar value may be written for Rʹ, but it is probably simpler, after having found one reaction, to write

R′ = W₁ + W₂ + W₃ - R.(15)

As the beam is supposed to have no weight, no load will act upon the beam between the given weights. The bending moments at the points of application of the three weights or loads will be

M₁ = Ra,		(16)
M₂ = R(a + b) - W₁b,
M₃ = R(a + b + c) - W₁(b + c) - W₂c.

After substituting the value of R from equation (14) in equations (16) the values of the latter are at once known.

Fig. 13.

The bending produced by each weight will also be represented precisely like that in Fig. 12. The triangle ANB represents the bending produced by W₁; AOB the bending produced by W₂; and APB the bending produced by W₃. The resultant bending effect produced by the three loads or weights acting simultaneously is simply the summation of the three effects each due to a single load. Hence DC is erected vertically through the point of application of W₁, so as to equal DN added to the two vertical intercepts between AB and AP, and AB and AO. Similarly, HF is equal to HO added to the intercepts between AB and AP, and AB and BN. Finally, KL is equal to PL added to the other two intercepts, one between AB and BN, and the other between AB and BO. Straight lines then are drawn through A, C, F, K, and B. Any vertical intercept between AB and ACFKB will represent the bending moment in the beam at the corresponding point. Obviously any number of loads of any magnitude, or a uniform load, may be treated in precisely the same way.

An important practical rule can readily be deduced from the equations (16), each one of which may be regarded as a general equation of moments. If the system of three, or any other number of loads, be moved a small distance Δx, while they all remain separated by the same distances as before, the bending moment M will be changed by the amount shown in equation (16a):

ΔM = RΔx - W₁Δx - W₂Δx - etc.(16a)

If the notation of the differential calculus be used by writing the letter d instead of Δ, and if both members of equation (16a) be then divided by dx, equation (16b) will result:

The second member of this equation shows the sum of all the external forces acting on one portion of the beam, that portion being limited by the section about which the moment M acts. That sum of all the external forces, as given by the second member of equation (16b), is evidently the total transverse shear at the section considered. Equation (16b) then shows, in the language of the differential calculus, that the first derivative of M in respect to x is equal to the total transverse shear. It is further established in the differential calculus that whenever a function, such as M, the bending moment, is a maximum or a minimum, the first derivative is equal to zero. The application of this principle to equation (16b) shows that the bending moment in any beam or truss has its greatest value wherever the shear is zero. Hence, in order to determine at what section the bending moment has its greatest value in any loaded beam carrying a given system of loads, it is only necessary to sum up all the forces or loads, including the reaction R, on that beam from one end to the point where that sum or shear is zero; at this latter point the greatest moment sought will be found. This is a very simple method of determining the section at which the greatest moment in the beam exists.

The preceding formulæ and diagrams may be extended to include any number of loads, and they are constantly used in engineering practice, not only for beams and girders in buildings, but also for bridges carrying railroad trains. Whatever may be the number of loads, the expressions for the bending moments at the various points of application of those loads are to be written precisely as indicated in equations (16). When the number of loads becomes great the number of terms in the equations correspondingly increase, but in reality they are just as simple as those for a smaller number of loads.

The diagram for the vertical shear in this beam is the lower part of Fig. 13. As in the case of Fig. 12 the shear at A is the reaction R, as it is Rʹ at the other end of the beam. The shear in the portion AD of the beam has the value R, but in passing the point D to the right the weight W₁ represented by OT must be subtracted from R, so that the shear over the section b of the span is R - W₁ or QV in the diagram. Similarly, in passing the point H toward the right, both W₂ and W₁ must be subtracted from R, giving the negative shear (the previous shear being taken positive) VW. The negative shear VW remains constant throughout the distance c, but is increased by W₃ at the point L, so that throughout the distance d the shear Sʹ = -Rʹ. These shear values are all shown in the lower portion of Fig. 13 by the vertical shaded lines. Obviously it is a matter of indifference whether the shear above the straight line GJ is made positive or negative; it is only necessary to recognize that the signs are different.

In the case of heavy beams, either built or rolled, as in railroad structures, it is of the greatest importance to determine both the bending moments and the shears, as represented in the preceding equations and diagrams, and to provide sufficient metal to resist them.

The case of Fig. 13 is perfectly general for moments and shears, and the methods developed are applicable to any amount or any system of loading whatever.

83. Bending Moments and Shears with Uniform Loads.—Fig. 14 represents what is really a special case of Fig. 13, in which the loading is uniform for each unit of length of the beam throughout the whole span l. Inasmuch as the load is uniformly distributed, it is evident that the reaction at each end of the beam will be one half the total load, or

Fig. 14.

The general expression for the bending moment at any point G in the span, and located at the distance x from the end A, will take the form

This equation, giving the value of M, is the equation of a parabola with the vertex over the middle of the span. The bending moment at the latter point will be found by placing x = l/2 in equation (18), which will give

Hence, in Fig. 14, if the vertical line DC be erected at D, so as to represent the value of M in equation (19) to a convenient scale, the parabola ACB may be at once drawn. Any vertical intercept, as GF between AB and the curve AFCB, will represent by the same scale the bending moment in the beam at the point indicated by the intercept. Equation (19), giving the greatest external bending moment in a simple beam due to a uniform load, is constantly employed in structural work, and shows that that moment is equal to the total load multiplied by one eighth of the span.

It has already been shown, in connection with Fig. 12, that when a single centre weight rests on a beam the centre bending moment is equal to that weight multiplied by one fourth the span. If the total uniform load in the one case is equal to the single load in the other, these equations show that the single centre load will produce just double the bending moment due to the same load uniformly distributed over the span. Wherever it is feasible, therefore, the load should be distributed rather than concentrated at the centre of the span.

That portion of Fig. 14 shaded with vertical lines shows the shear existing in the beam. Evidently the shear at each end is equal to the reaction, or one half the total load on the span. The expression for the shear at any point, as G, distant x from A will be

If x = l/2 in equation (20), S becomes equal to zero. In other words, there is no shear at the centre of the span of a beam uniformly loaded. Hence, if at each end of the span a vertical line AK or BL be laid off downward, and if straight lines KD and DL be drawn, any vertical intercept, as GH, between these lines and AB will represent the shear at the corresponding point. Equation (20) also shows that the shear S at any point is equal to the load resting on the beam between the centre D and that point. Although this case of uniform loading is a special one it finds wide application in practical operations.

84. Greatest Shear for Uniform Moving Load.—The preceding loads have been treated as if they were occupying fixed positions on the beams considered. This is not always the case. Many of the most important problems in connection with the loading of beams and bridges arise under the supposition that the load is movable, like that of a passing railroad train. One of the simplest of these problems, although of much importance, consists in finding the location of a uniform moving load, like that of a train of cars, which will produce the greatest shear at a given point of a simple beam, such as that represented in Fig. 15, in which a moving load is supposed to pass continuously over the span from the left-hand end A. It is required to determine what position of this uniform load will produce the greatest shear at the section C.

Fig. 15.

Let the moving load extend from A to any point D to the right of C. The two reactions R and Rʹ may be found by the methods already indicated. Let W represent the uniform load resting on the portion CD of the span. The shear S′ existing at C will be

Sʹ = Rʹ - W.(21)

Let R‴ be that part of Rʹ which is due to W, and Rʺ that part due to the load on AC. Evidently R‴ is less than W; then

Sʹ = Rʺ + R‴ - W.(22)

Since the negative quantity W is greater than the positive quantity R‴, S′ will have its greatest value when both W and R‴ are zero. Hence the greatest shear at the point C will exist when

Sʹ = Rʺ.(23)

Obviously the loading must extend at least from A to C in order that Rʺ may have its maximum value. Hence the greatest shear at any section will exist when the uniform load extends from the end of the span to that section, whatever may be the density of the load.

If the segment of the span covered by the moving load is greater than one half the span, the maximum shear is called the main shear; but if that segment is less than one half the span, the maximum shear is called the counter-shear. The reason for these two names will be apparent later in the discussion of bridge-trusses.

This rule for determining the maximum shear at any section of a beam is equally applicable to bridge-trusses under certain conditions, and has an important bearing upon the determination of the greatest stresses in some of the members of bridge-frames, although it has less importance now than it had in the earlier days of bridge-building.

85. Bending Moments and Shears for Cantilever Beams.—The case of a loaded overhanging beam or cantilever bracket, as shown in Fig. 16, is sometimes found. In that figure a single weight W is supposed to be applied at the end, while a uniform load w per unit of length extends over its length l. The bending moment at any point C distant x from the end will obviously be

Fig. 16.

The greatest value of the bending moment will be found by placing x equal to l in equation (24), and it will have the value

The shear at any point and at the end A respectively will be

S = W + wx and S₁ = W + wl.      (26)

The shear due to W is equal to itself and is constant throughout the whole length of the beam.

The second term of the second member of equation (24) is the equation of a parabola with its vertex at B, Fig. 16. Hence if AF be laid off equal to (wl²) /2, and if the parabola FHB be drawn, any vertical intercept, as HK, between that curve and AB will represent the bending moment at the corresponding point. On the other hand, the first term of the second member of equation (24) shows that the bending moment due to W varies directly as the distance from B. Hence if AG be laid off vertically downward from A equal to Wl to any convenient scale, then any intercept, as KL, between AB and BG will represent the bending moment due to W at the corresponding point of the beam.

86. Greatest Bending Moment with any System of Loading.—One of the most important positions of loading to be established either for simple beams or for bridge-trusses is that at which any given system of loading whatever is to be placed on any span so as to produce the maximum bending moment at any prescribed point in that span. In order to make the case perfectly general a system of arbitrary loads, like that shown in Fig. 17, is assumed and the system is supposed to be a moving one.

Fig. 17.

The separate loads are placed at fixed distances apart, indicated by the letters a, b, c, d, etc., W₁ being supposed to be at the head of the train, while W₏ is the last load having a variable distance x between it and the end of the span. In Fig. 17 this system of moving loads or train is supposed to pass over the span l from right to left. The problem is to determine the position of the loading, so that the bending moment at the section C of the beam or truss will be a maximum, the section C being at the distance lʹ from the left-hand end of the span. The complete analysis of this problem is comparatively simple and may readily be found, but it is not necessary for the accomplishment of the present purpose to give it here. In order to exhibit the formula which expresses the desired condition, let Wₙʹ be that weight which is really placed at C, but which is assumed to be an indefinitely short distance to the left of that point, for a reason which will presently be explained. The equation of condition or criterion sought will then be the following:

If the loads are so placed as to fulfil the condition expressed in equation (27), the bending moment at section C will be a maximum. If the variation in the train weights is very great, it is possible that there may be more than one position of the train which will satisfy that equation. It is necessary, therefore, frequently to try different positions of the loading by that criterion and then ascertain which of the resulting maximum moments is the greatest. It is not usually necessary to make more than one or two such trials. The application of the equation is therefore simple and involves but little labor.

It will usually happen that Wₙʹ in equation (27) is not to be taken as the whole of that weight, but only so much of it as may be necessary to satisfy the equation. This is simply assuming that any weight, W, may be considered as made up of two separate weights placed indefinitely near to each other, which is permissible.

After having found the position of loading which satisfies equation (27), the resulting maximum bending moment will take the following form:

In this equation x corresponds to the position of loading for maximum bending, while the sign (?) represents the distance between the concentrations W₍ₙʹ₋₁₎ and Wₙʹ. This equation has a very formidable appearance, but its composition is simple and it is constantly used in making computations for the design of railroad bridges. The loads W₁, W₂, W₃, etc., represent the actual weights on the driving-axles and other axles of locomotives, tenders, and cars, and the spacings a, b, c, etc., are the actual spacings found between those axles. In other words, these quantities are the actual weights and dimensions of the different portions of moving railroad trains.

The computations indicated by equation (28) are not made anew in every instance. Concentrated weights of typical locomotives, tenders, and cars are prescribed by different railroad companies for their different classes of trains, ranging from the heaviest freight traffic to the lightest passenger train. A tabulation is then made from equation (28) for each such typical train, and it is used as frequently as is necessary to design a bridge to carry the prescribed traffic. The tabulations thus made are never changed for a given or prescribed loading.

87. Applications to Rolled Beams.—It is to be remembered that these last observations do not limit the use of equations (27) and (28) to railroad-bridge trusses only; they are equally applicable to solid and rolled beams and are frequently used in connection with their design. Great quantities of these beams and various rolled steel shapes are used in the construction of large modern city buildings, as well as in railroad and highway bridge structures. The steel frames of the great office buildings, so many of which are seen in New York and Chicago as well as in other cities, which carry the entire weight of the building, are formed wholly of these steel shapes. The so-called handbooks published by steel-producing companies exhibit the various shapes rolled in each mill. These books also give in tabular statements many numerical values of the moment of inertia, the section modulus, and other elements of all these sections, so that the formulæ which have been established in the preceding pages may be applied in practical work with great convenience and little labor. Tables are also given showing the sizes of rolled beams required to sustain the loads named in them. Such tables are formed for practical use, so that, knowing the distance apart of the beams, their span, and the load per square foot which they carry, the required size of beam may be selected without even computation. Such labor-saving tables are quite common at the present time, and they reduce greatly the labor of numerical computations.

CHAPTER VIII.

88. The Truss Element or Triangle of Bracing.—A number of the preceding formulæ find their applications to bridge-trusses, as well as to beams; hence it is necessary to give attention at least to some simple forms of those trusses.

Fig. 18.

Fig. 18a.

The skeleton of every bridge-truss properly designed to carry its load is an assemblage of triangles. In other words, the truss element, i.e., the simplest possible truss, is the triangular frame, such as is shown in skeleton in Figs. 18 and 18a. These simple triangular frames are sometimes called the King-post Truss. The action of such a triangular frame in carrying a vertical load is extremely simple. In Fig. 18 let the weight W be suspended from the apex C of the triangle. The line CF represents that weight, and if the latter be resolved into its two components parallel to the two upper members of the triangular frame, the two component forces CG and CD will result. If from D and G the horizontal lines DH and GO be drawn, those two lines will represent the horizontal components of the forces or stresses in the two bars CA and CB. The force HD will act to the left at the point A, and the force CG will act to the right at B, and as these two forces are equal and opposite to each other, equilibrium will result. Either of the horizontal forces will represent the magnitude of the tension in AB. Both AC and CB will be in compression, the former being compressed by the force CD, and the latter by the force CG. The manner of drawing a parallelogram of forces makes the triangle COG similar to CNB, and CHD similar to CNA; hence HW divided by CH will be equal to AN divided by NB. But HW is the vertical component of the stress in CB, while CH is the vertical component of the stress in AC, the latter being represented by the reaction R and the former by the reaction R′. It is seen, therefore, that the weight W is carried by the frame to the two abutment supports A and B, precisely as if it were a solid beam. In other words, the important principle is established that when weights rest upon a simple truss supported at each end they will produce reactions at the ends in accordance with the principle of the lever, precisely as in the case of a solid beam. In engineering parlance it is stated that the weight W is divided according to the principle of the lever, and that each portion travels to its proper abutment through the members of the triangular frame. If the two inclined members of the triangular frame are equally inclined to a vertical, the case of Fig. 18a results, in which one half of the weight goes to each abutment.

The triangular frame, with equally inclined sides, shown in Fig. 18a, is evidently the simplest form of roof-truss, constituting two equally inclined members with a horizontal tie.

89. Simple Trusses.—The simplest forms of trussing used for bridge purposes are those shown in Figs. 19, 20, and 21. There are many other forms which are exhibited in complete treatises on bridge structures, but these three are as simple as any, and they have been far more used than any other types. The horizontal members af and AB are called the “chords,” the former being the upper chord and the latter the lower chord. The vertical and inclined members connecting the two chords are called the web members or braces. When a bridge is loaded, either by its own weight only, or by its own weight added to that of a moving train of cars, the upper chord will evidently be in compression, while the lower chord is in tension. A portion, which may be called a half, of the web members will be in tension and the other portion, or half, will be in compression.

The function of the upper and lower chords is to take up or resist the horizontal tension and compression which correspond to the direct stresses of tension and compression existing in the longitudinal fibres of a loaded solid or flanged beam. The metal designed to take these so-called direct stresses is concentrated in the chords of trusses, whereas it is distributed throughout the entire section of a beam, whether that beam be solid or flanged. The function of the web members of a truss is to resist the transverse or vertical shear which is represented by the algebraic sum of the reactions and loads. The total section of a solid beam resists these vertical shears, while the web only of a flanged beam is estimated to perform that duty. The horizontal shears, which have already been recognized as existing along the horizontal planes in a bent beam, are resisted by the inclined web members of a truss, the horizontal stress components being the horizontal shears, whereas the vertical shears are resisted by the vertical web members of a truss. If the web members are all inclined, as shown in Fig. 21, each web member resists both horizontal and vertical shear. It is thus seen that the members of a truss perform precisely the same duties as the various portions of either solid or flanged beams. Inasmuch as the chords of bridge-trusses resist the direct or horizontal stresses of tension and compression produced by the bending in the truss, it is obvious that the greatest chord stresses will be found at the centre of the span, and that they will be the smallest at the ends of the span. In the web members, on the contrary, since the vertical shear is the greatest at the ends of the span and equal to the reactions at those points, decreasing towards the centre precisely as in solid beams, the greatest web stresses will be found at the ends of the span and the least near the centre. It is obvious that the areas of cross-sections of either chords or web members must be proportioned to the stresses which they carry. Hence the distribution of stresses just described tends to a uniform distribution of the truss weights over the span.

90. The Pratt Truss Type.—In the discussion of these three simple types of trusses, the simplest possible loading of a perfectly uniform train will be assumed. The portions into which the trusses are divided by the vertical or inclined bracing are called panels. In Fig. 19, for instance, the points 1, 2, 3, 4, 5, and 6 of the lower chord and a, b, c, d, e, and f of the upper chord are called panel-points. The distance between each consecutive two of these points is called a panel length. The uniform train-load which is to be assumed will be represented by the weight W at each panel-point. This is called the “moving load” or “live load.” The own weight of the structure is called the “dead load” or the “fixed load.” The dead load per upper-chord panel will be taken as Wʹ, and W₁ for the lower chord. The loads to be used will, therefore, be as follows:

There will also be used the length of panel and depth of truss as follows:

• Panel length = p;
• Depth of truss = d.

In these simple trusses with horizontal upper and lower chords the stress in any inclined web members is equal to the shear multiplied by the secant of the inclination of the members to a vertical line. Also, at each panel-point every inclined web member, in passing from the end to the centre of the span, adds to either chord stress at that point an amount represented by the horizontal component of the stress which it carries; or, what is the same thing, an amount equal to the shear at the panel in question multiplied by the tangent of its angle of inclination to a vertical line.

It has already been shown in discussing solid beams that the greatest shear at any section will be found when the uniform moving load covers one of the segments of the span. This principle holds equally true for trusses carrying uniform panel-loads like those under consideration. In determining the stresses in these trusses, therefore, the inclined web members will take their greatest stresses when the moving train or load extends from the farthest end of the span up to the foot of the member in question. In this connection it is to be observed also that any two web members meeting in the chord which does not carry the moving load take their greatest stresses for the same position of the latter. The so-called “counter web members” take no stresses from the dead load.

Inasmuch as every load placed upon a truss will produce compression in the upper chord and tension in the lower, the greatest chord stresses will obviously exist when the moving load covers the entire span, and that condition of loading is to be used for the stresses in the following cases.

Bearing these general observations in mind, the ordinary simple method of truss analysis yields the tabulated statement of stresses given below for the three types selected for consideration. The first case to be treated is that of Fig. 19, which represents the Pratt truss type. The moving load is supposed to pass across the bridge from right to left. The plus sign indicates tension and the minus sign compression.

Fig. 19.

It is easy to check any of the chord stresses by the method of moments. As an example, let moments first be taken about the panel-point 5 in the lower chord, and then about the panel-point c in the upper chord. The following expressions for the chord members U₁ and L₄ will be found, and it will be noticed that they are identical with the stresses for the same members given in the preceding tabulation, the counter-members, shown in broken lines, being omitted from consideration as they are not needed.

Fig. 20.

91. The Howe Truss Type.—The truss shown in Fig. 20 is the skeleton of the Howe truss, to which reference has already been made. The inclined web members are all in compression, while the vertical web members are all in tension. In the Howe truss all compression members are composed of timber. It has the disadvantage of subjecting the longest web members to compression. It thus makes the truss, if built all in iron or steel, heavier and more expensive than the trusses of the Pratt type. As in the preceding case, the moving train or load is supposed to pass across the bridge from B to A. Also, as before, the + sign indicates tension and the - sign compression. The greatest stresses, given in the tabulated statement below, can be computed or checked by the method of moments in this case, precisely as in the preceding.

It will be noticed in the cases of Figs. 19 and 20 that upper and lower chord panels in the same lozenge or oblique panel have identically the same stresses, but with opposite signs. For instance, in Fig. 20 the stress in U₂ is equal in amount to that in L₂; and the same observation can be made in reference to the stresses in U₂ and L₄ of Fig. 19. This must necessarily always be the case in trusses having vertical web members.

In making computations for these forms of trusses it is very essential to observe where the first counter-member, as c₁, must be used. These counter-members may be omitted if the proper main web members near the centre of the span are designed to take both tension and compression.

92. The Simple Triangular Truss.—The truss shown in Fig. 21, in which all the web members have equal inclination to a vertical line, is sometimes called the Warren Truss, although that term has also been applied specially to this type of truss so proportioned as to make the depth just equal to the panel length. As before, the moving train is supposed to pass over the bridge from B toward A, while the + sign represents tension and the - sign compression. The greatest stresses are the following.

Fig. 21.

The chord stresses may be checked or found by the method of moments, precisely as in the case of Fig. 19. If, for instance, it is desired to determine the stresses in the upper chord member U₂, moments must be taken about the lower-chord panel-point 5, and about the upper-chord panel-point d for the lower-chord stress in L₄. Taking moments about those points, results given in equations (31) and (32) will at once follow, which it will be observed are identical with the values previously found for the same members.

93. Through- and Deck-Bridges.—These simple trusses have all been taken as belonging to the “through” type, i.e., the moving load passes along their lower chords. It is quite common to have the moving load pass along the upper chords, in which cases the bridges are said to be “deck” structures. The general methods of computation are precisely the same whether the trusses be deck or through. It is only necessary carefully to observe that the application of the methods of analysis depends upon the position of each panel-load as it passes across the structure.

Fig. 22.

94. Multiple Systems of Triangulation.—Figs. 19, 20, and 21 exhibit what are called single systems of triangulation or single systems of bracing, but in each of those types the system of web members may be double or triple; in other words, they may be manifold. There have been many bridges built in which two or more systems of bracing are employed. Fig. 22 represents a truss with a double system of triangulation, known at one time as the Whipple truss. Fig. 23, again, exhibits a quadruple system of triangulation with all inclined web members. The method of computation for such manifold systems is precisely the same as for a single system, each system in the compound truss being treated as carrying those loads only which rest at its panel-points. This procedure is not quite accurate. The complete consideration of an exact method of computation would take the treatment into a region of rather complicated analysis beyond the purposes of these lectures, but its outlines will be set forth on a later page. The exact method of treatment of two or more web systems involves the elastic properties of the material of which the trusses are composed. In the best modern bridge practice engineers prefer to design trusses of all lengths with single web systems, although the panels are frequently subdivided to avoid stringers and floor-beams of too great weight.

Fig. 23.

95. Influence of Mill and Shop Capacity on Length of Span.—In the early years of iron and steel bridge-building the sizes of individual members were limited by the shop capacity for handling and manufacturing, and by the relatively small dimensions of bars of various shapes, and of plates which could be produced by rolling-mills. As both mill and shop processes have advanced and their capacities increased, corresponding progress has been made in bridge design. Civil engineers have availed themselves of those advances, so that at the present time single system trusses with depths as great as 85 feet or more and spans of over 550 feet are not considered specially remarkable.

96. Trusses with Broken or Inclined Chords.—As the lengths of spans have increased certain substantial advantages have been gained in design by no longer making the upper chords horizontal in the case of long through-spans, or indeed in the cases of through-spans of moderate length. The greatest bending moments and the greatest chord stresses have been shown to exist at the centre of the span, while the greatest web stresses are found near the ends. Trusses may be lightened in view of those considerations by making their depths less at the ends than at the centre. This not only decreases the sectional areas of the heaviest web members near the ends of the truss, but also shortens them. It adds somewhat to the sectional area of the end upper-chord members, but the resultant effect is a decrease in total weight of material and increased stability against wind pressure by the decreased height and less exposure near the ends. It has therefore come to be the ruling practice at the present time to make through-trusses with inclined upper chords for practically all spans from about 200 feet upward. A skeleton diagram of such a truss is given in Fig. 24.

Fig. 24.

97. Position of any Moving Load for Greatest Web Stress.—In the preceding treatment of bridge-trusses with parallel and horizontal chords a moving or live load has been taken as a series of uniform weights concentrated at the panel-points. This simple procedure was formerly generally used, and at the present time it is occasionally employed, but it is now almost universal practice to assume for railroad bridges a moving load consisting of a series of concentrations, which represent both in amount and distribution the weights on the axles of an actual railroad train. If a bridge is supposed to be traversed by such a train, it becomes necessary to determine a method for ascertaining the positions of the train causing the greatest stresses in the various members of the bridge-truss. The mathematical demonstration of the formulæ determining those positions of loading need not be given here, but it can be found in almost any standard work on bridges.

In order to show concisely the results of such a demonstration let it be desired to find the position of a moving load which will give the greatest stress to any web member, as S in Fig. 24. Let the point of intersection of GK and DC be found in the point O, then let CK be extended, and on its extension let the perpendicular h be dropped from O. The distance of the point O from A, the end of the span, is i, while m is the distance AD. Using the same notation which has been employed in the discussion of beams, together with that shown in Fig. 24, equation (33) expresses the condition to be fulfilled by the train-loads in order that S shall have its greatest stress. The first parenthesis in the second member of that equation represents the load between the panel p and the left end of the span, while the second parenthesis represents the load in panel p itself.

It will be noticed in equation (33) that the quantity m shows in what panel the inclined web member whose greatest stress is desired is located, and it is important to observe that panel carefully. If, for instance, the vertical member KD were in question, the point O would be located at the intersection of the panel NK and the lower chord of the bridge. In other words, the point O must be at the intersection of the two chord members belonging to the same panel in which the web member is located.

98. Application of Criterions for both Chord and Web Stresses.—The criterion, equation (33), belongs to web members only. If it is desired to find the position of moving load which will give the greatest chord stresses in any panel, equation (27), already established for beams, is to be used precisely as it stands, the quantity l′ representing the distance from one end of the span to the panel-point about which moments are taken.

If the desired positions of the moving load for greatest stresses have been found by equations (27) and (33), those stresses themselves are readily found by taking moments about panel-points for chord members and about the intersection-points O, Fig. 24, for web members. These operations are simple in character and are performed with great facility. Tabulations and diagrams are made for given systems of loading by which these computations are much shortened and which enable the numerical work of any special case to be performed quickly and with little liability to error. These tabulations and diagrams and other shortening processes may be found set forth in detail in many publications and works on bridge structures. They constitute a part of the office outfit of civil engineers engaged in structural work.

The criterion, equation (27), for the greatest bending moments in a bridge is applicable to any truss whatever, whether the chords are parallel or inclined, but it is not so with equation (33). If the chords of the trusses are parallel, the quantity i in equation (33) becomes infinitely great, and the equation takes the following form:

Ordinarily the span l divided by the panel length p is equal to the number of panels in the span. Hence equation (34) shows, in the case of parallel or horizontal chords, that when the moving load is placed for the greatest web stress in any panel, the total load on the bridge is equal to the load in that panel multiplied by the total number of panels.

99. Influence Lines.—A graphical method, known as that of “influence lines,” is used for determining the greatest shears and bending moments caused by a train of concentrated weights passing along a beam or bridge-truss. Obviously it must express in essence that which has already been shown by the formulæ which determine positions of moving loads for the greatest shears and bending moments. In reality it is the application of graphical methods which have become so popular to the determination of the greatest stresses in beams and bridges.

100. Influence Lines for Moments both for Beams and Trusses.—It is convenient to construct these influence lines for an arbitrary load which may be considered a unit load; the effect of any other load will then be in proportion to its magnitude. The results determined from influence lines drawn for a load which may be considered a unit can, therefore, be made available for other loads by multiplying the former by the ratio between any desired load and that for which the influence lines are found.

Fig. 25.—Bending Moment in a Simple Beam.

AB in Fig. 25 represents a beam simply supported at each end, so that any load g resting upon it will be divided between the points of support, according to the law of the lever. Let it be desired to determine the bending moment at the section X produced by the load g in all of its positions as it passes across the span from A to B. Two expressions for the bending moment must be written, one for the load g at any point in AX, and the other for the load at any point in BX. The expression for the first bending moment is

and that for the latter

As shown in the figure, z and x, the latter locating the section at which the bending moments are to be found, are measured to the right from A. Equation (a) shows that if the quantity g(l-x) be laid off, by any convenient scale, as BK at right angles to AB, XC will represent the moment M by the same scale when x = z or when z has any value between 0 and x. Similarly will AD be laid off at right angles to AB by the same scale as before, to represent gx. Then when x = z the expression for M′ will have the same value XC as before. Hence if the lines AC and CB be drawn as parts of AK and DB, any vertical intercept between AB and ACB will represent the bending at X produced by the load g when placed at the point from which the intercept is drawn. The lines AC and CB are the influence lines for the bending moments produced by the load g in its passage across the span AB. It is to be observed that the influence lines are continuous only when the positions of the moving load are consecutive. In case those positions are not consecutive the influence lines are polygonal in form.

If there are a number of loads g resting on the span at the same time, the total bending moments produced at X will be found by taking the sum of all the vertical intercepts between AB and ACB, drawn at the various points where those loads rest. The influence lines drawn for a single load, therefore, may be at once used for any number of loads.

The load g is considered as a unit load. If the vertical intercepts representing the bending moments by the scale used are themselves represented by y, and if W represent any load whatever, the general expression for the bending moment at X, produced by any system of loads, will be

If this expression be written as a series, the general value of the bending moment will be the following:

The effect of a moving train upon the bending moment at any given section is thus easily made apparent by means of influence lines. It is obvious that there will be as many influence lines to be drawn as there are sections to be considered. In the case of a truss-bridge there will be such a section at every panel-point.

A slight modification of the preceding results is to be made when the loads are applied to the beam or truss at panel-points only.

In Fig. 25 let 1, 2, 3, 4, 5, 6, and 7 be panel-points at which loads are applied, and let the load g be located at the distance z′ to the right of panel-point 5, also let the panel length be p. The reactions at 5 and 6 will then be

The reactions at A will then be

Hence the moment at any section X in the panel in question will be

Remembering that z-z′ is a constant quantity, it is at once clear that the preceding expression is the equation of a straight line, with M and z or z′ the variables. If z′ = 0, equation (e) becomes identical with equation (a), while if z′ = p, it becomes identical with equation (b). Hence the influence line for the panel in which the load is placed, as 5-6, is the straight line KL. It is manifest that when the load g is in any other panel than that in which the section X is located, the effect of the two reactions at the extremities of that panel will be precisely the same at the section as the weight itself acting along its own line of action. Hence the two portions AK and BL of the influence line are to be constructed as if the load were applied directly to the beam or truss, and in the manner already shown. The complete influence line will then be AKLB, and it shows that the existence of the panel slightly reduces the bending at any section within its limits. The panel 5-6, as treated, is that of a beam in which the bending moment will, in general, vary from point to point. If AB were a truss, however, X would always be taken at a panel-point, and no intercept between panel-points, as 5 and 6, would be considered.

101. Influence Lines for Shears both for Beams and Trusses.—The influence lines for shears in a simple beam, supported at each end, can be drawn in the manner shown in Fig. 25a. In that figure AB represents a non-continuous beam with span l supported from A. The reaction at A will be

Fig. 25a.—Shear in a Simple Beam.

Let X be the section at which the shear for various positions of g is to be found. When g is placed at any point between A and X the shear S at the latter point will be

but when the load is placed between B and X the shear becomes

Obviously these two values of the shear are equations of two parallel straight lines, that represented by equation (f) passing through A, and that represented by equation (h) passing through B, the constant vertical distance between them being g. Hence let BF be laid off negatively downward and AG positively upward, each being equal to g by any convenient scale. The ordinates drawn from the various positions 1, 2, 3 ... 6 of g on AB to AD and BC will be the shears at X produced by the load g at any point of the span, and determined by equations (f) and (h). The influence line, therefore, for the section X will be the broken line ADCB. When g is at X the sign of the shear changes, since the latter passes through a zero value.

If a train of weights W₁, W₂, W₃, etc., passes across the span, the total shear at X will be found by taking the sum of the vertical intercepts between AB and ADCB, drawn at the positions occupied by the various single weights of the train. If those single weights are expressed in terms of the unit load g, the shear S will have the value

y being the general value of the intercept between AB and the influence line. The latter shows that the greatest negative shear at X will exist when the greatest possible amount of loading is placed on AX only, while the greatest positive shear at the same section will exist when BX only is loaded. If BX is the smaller segment of span, the latter shear is called the “counter-shear,” and the former the “main shear.”

If the loads are applied at panel-points of the span only, the treatment is the same in general character as that employed for bending moments. In Fig. 25a let 4 and 5 be the panel-points between which the load g is found, and let the panel length be p. Also, let z′ be the distance of the weight g from panel-point 4. The reactions at A and 4 will then be

The shear at the section X for any position of the weight g will then be

As this is the equation of a straight line, with S and z or z′ for the coordinates, the influence line for the panel in which the section X is located will be the straight line represented by KL in Fig. 25a.

If z′ is placed equal to 0 and p successively, then will equation (k) become identical with equations (f) and (h) in succession. The shears at points 4 and 5 will therefore take the same values as if the loads were applied directly to the beam. For the reasons stated in connection with the consideration of bending moments, loads in other panels than that containing the section for which the influence line is drawn will have the same effect on that section as if they were applied directly to the beam or truss. Hence AKLB is the complete influence line for this case.

It is evident that there must be as many influence lines drawn as there are sections to be discussed. Also, if g is taken as some convenient unit, i.e., 1000 or 10,000 pounds, it is clear that the labors of computation will be much reduced.

102. Application of Influence-line Method to Trusses.—In considering both the bending moments and shears when the loads are applied at panel-points, it has been assumed, as would be the case in an ordinary beam, that the bending moments as well as the shears may vary in the panel; but this latter condition does not hold in a bridge-truss. Neither bending moment nor shear varies in any one panel. Yet the influence lines for moments and shears are to be drawn precisely as shown in Figs. 25 and 25a. The section X will always be found at a panel-point, and no intercept drawn within the limits of the panel adjacent to that section carrying the load g is to be used. This method will be illustrated by the aid of Fig. 25b.

The employment of influence lines may be illustrated by determining the moment and shear in a single section of the truss shown in Fig. 24, which is reproduced in Fig. 25c, when carrying the moving load exhibited in Fig. 25b, although its use may be much extended beyond this simple procedure.

The moving load shown in Fig. 25b is that of a railroad train consisting of a uniform train-load of 4000 pounds per linear foot drawn by two locomotives with the wheel concentrations shown; it is a train-load frequently used in the design of the heaviest class of railroad structures. If the criterion of equation (27) be applied to this moving load, passing along the truss shown in Fig. 25c, from left to right, it will be found that the greatest bending moment is produced at the section Q when the second driving-axle of the second locomotive is placed at the truss section in question, as shown in Fig. 25c.

The unit load to be used in connection with the influence lines will be taken at 10,000 pounds. Remembering that the panel lengths are each 30 feet, it will be seen that the panel-point Q is 150 feet from A. Hence the product gx will be 1,500,000 foot-pounds. Similarly the product g(l - x) will be 900,000 foot-pounds. Laying off the first of these quantities, as AD, at a scale of 1,000,000 foot-pounds per linear inch, and the second quantity, as BK, by the same scale, the influence line ACB can at once be completed. Vertical lines are next to be drawn through the positions of the various weights, including one through the centre of the uniform train-load 110 feet in length resting on the truss. The vertical line through the centre of the uniform train-load is shown at O. By carefully scaling the vertical intercepts between AB and ACB, and remembering that each of the loads on the truss must be divided by 10,000, the following tabulated statement will be obtained, the sum of the intercepts for each set of equal weights being added into one item, and all the items of intercepts being multiplied by 1,000,000:

The lever-arm of ef, i.e., the normal distance from Q to ef, is 39.7 feet. Hence the stress in ef is

All the chord stresses can obviously be found in the same manner.

In order to place the same moving load so as to produce the greatest shear at the same section Q, the criterion of equation (33) must be employed. The dimensions of the truss shown in connection with Fig. 29 give the following data to be used in that equation: i = 210 feet, m = 60 feet, and p = 30 feet.

Fig. 25b.

Fig. 25c.

Fig. 25d.

Introducing these quantities into equation (33), and remembering that the train moves on to the bridge from A, it would be found that the second axle of the first locomotive must be placed at the section Q, as shown in Fig. 25d, which exhibits the lower-chord panel-points numbered from 1 to 7. The conventional unit load g will be taken in this case at 20,000 pounds. It is represented as AG and BF (Fig. 25d), laid off at a scale of 10,000 pounds per inch. K is immediately under panel-point 5 and L is immediately above panel-point 6, hence the broken line AKLB is the influence line desired. The vertical lines are then drawn from each train concentration in its proper position, all as shown, including the vertical line through the centre of the 54 feet of uniform train-load on the left. The summation of all the vertical intercepts between AB and the influence line AKL, having regard to the scale and to the ratio between the various loads and the unit load g, will give the following tabular statement:

These simple operations illustrate the main principles of the method of influence lines from which numerous and useful extensions may be made.

CHAPTER IX.

103. Lateral Wind Pressure on Trusses.—The duties of a bridge structure are not confined entirely to the supporting of vertical loads. There are some horizontal or lateral loads of considerable magnitude which must be resisted; these are the wind loads resulting from wind pressure against both structure and moving train. In order to determine the magnitudes of these loads it is assumed in the first place that the direction of the wind is practically or exactly at right angles to the planes of the trusses and the sides of the cars. This assumption is essentially correct. There is probably nothing else so variable as both the direction and pressure of the wind. These variations are not so apparent in the exposure of our bodies to the wind, for the reason that we cannot readily appreciate even considerable changes either in direction or pressure. As a matter of fact suitable measuring apparatus shows that there is nothing steady or continued in connection with the wind unless it be its incessant variability. Its direction may be either horizontal or inclined, or even vertical, while within a few seconds its pressure may vary between wide limits. Under such circumstances the wind is as likely to blow directly against both bridge and train as in any other direction, and inasmuch as such a condition would subject the structure to its most severe duty against lateral forces, it is only safe and proper that the assumption should be made. The open work of bridge-trusses enables the wind to exert practically its full pressure against both trusses of a single-track bridge, or against even three trusses if they are used for a double-track structure. Hence it is customary to take the exposed surface of bridge-trusses as the total projected area on a plane throughout the bridge axis of both trusses if there are two, or of three trusses if there are three. Inasmuch as the floor of a bridge from its lowest point to the top of the rails or other highest point of the floor is practically closed against the passage of the wind, all that surface between the lowest point and the top of the rail or highest floor-member is considered area on which wind pressure may act.

Many experimental observations show that on large surfaces, greater perhaps than 400 or 500 square feet in area, the pressure of the wind seldom exceeds 20 or 25 pounds per square foot, while it may reach 80 or 90 pounds, or possibly more on small surfaces of from 2 to 40 or 50 square feet in area. This distinction between small and large exposed areas in the treatment of wind pressures is fundamental and should never be neglected.

This whole subject of wind pressures has not yet been brought into a completely definite or well-defined condition through lack of sufficient experimental observations, but in order to be at least reasonably safe civil engineers frequently, and perhaps usually, assume a wind pressure acting simultaneously on both bridge and train at 30 pounds per square foot of exposed surface and 50 pounds per square foot of the total exposed surface of a bridge structure which carries no moving load. This distinction arises chiefly from the fact that a wind pressure of 30 pounds per square foot on the side of many railroad trains, particularly light ones, will overturn them, and it would be useless to use a larger pressure for a loaded structure. There have been wind pressures in this country so great as to blow unloaded bridges off their piers; indeed in one case a locomotive was overturned which must have resisted a wind pressure on its exposed surface of not less than 90 pounds and possibly more than 100 pounds per square foot.

The consideration of wind pressure is of the greatest importance in connection with the high trusses of long spans, as well as in long suspension and cantilever bridges, and in the design of high viaducts, all of which structures receive lateral wind pressures of great magnitude.

Some engineers, instead of deducing the lateral wind loads from the area of the projected truss surfaces, specify a certain amount for each linear foot of span, as in ”The General Specifications for Steel Railroad Bridges and Viaducts” by Mr. Theodore Cooper it is prescribed that a lateral force of 150 pounds for each foot of span shall be taken along the upper chords of through-bridges and the lower chords of deck-bridges for all spans up to 300 feet in length; and that for the same spans a lateral force of 450 pounds for each foot of span shall be taken for the lower chords of through-spans and the upper chords of deck-spans, 300 pounds of this to be treated as a moving load and as acting on a train of cars at a line 8⁵/₁₀ feet above the base of rail.

When the span exceeds 300 feet in length each of the above amounts of load per linear foot is to be increased by 10 pounds for each additional 30 feet of span.

Special wind-loadings and conditions under which they are to be used are also prescribed for viaducts.

These wind loads are resisted in the bridges on which they act by a truss formed between each two upper chords for the upper portion of the bridge, and between each two lower chords for the lower portion of the structure.

Fig. 26.

104. Upper and Lower Lateral Bracing.—Fig. 26 shows what are called the upper and lower lateral bracing for such trusses as are shown in the preceding figures. The wind is supposed to act in the direction shown by the arrow. DERA and KLBC are the two portals at the ends of the structure, braced so as to resist the lateral wind pressures. It will be observed that the systems of bracing between the chords make an ordinary truss, but in a horizontal plane, except in the case of inclined chords like that of Fig. 24. In the latter case the lateral trusses are obviously not in horizontal planes, but they may be considered in computations precisely as if they were. These lateral trusses are then treated with their horizontal panel wind loads just as the vertical trusses are treated for their corresponding vertical loads, and the resulting stresses are employed in designing web and chord members precisely as in vertical trusses. The wind stresses in the chords, in some cases, are to be added to those due to vertical loading, and in some cases subtracted. In other words, the resultant stresses are recognized and the chord members are so designed as properly to resist them. At the present time it is the tendency in the best structural work to make all the web members of these lateral trusses of such section that they can resist both tension and compression, as this contributes to the general stiffness of the structure. On account of the great variability of the wind pressures and the liability of the blows of greatest intensity to vary suddenly, some engineers regard all the wind load on structure or train as a moving load and make their computations accordingly. It is an excellent practice and is probably at least as close an approximation to actual wind effects as the assumption of a uniform wind pressure on a structure.

Both the lateral and transverse wind bracing of railroad bridges have other essential duties to perform than the resistance of lateral wind pressures. Rapidly moving railroad trains produce a swaying effect on a bridge, in consequence of unavoidable unevenness of tracks, lack of balance of locomotive driving-wheels, and other similar influences. These must be resisted wholly by the lateral and transverse bracing, and these results constitute an important part of the duties of that bracing. These peculiar demands, in connection with the lateral stability of bridges, make it the more desirable that the lateral and transverse bracing should be as stiff as practicable.

105. Bridge Plans and Shopwork.—After the computations for a bridge design are completed in a civil engineer’s office they are placed in the drawing-room, where the most detailed and exact plans of every piece which enters the bridge are made. The numerical computations connected with this part of bridge construction are of a laborious nature and must be made with absolute accuracy, otherwise it would be quite impossible to put the bridge together in the field. The various quantities of bars, plates, angles, and other shapes required are then ordered from the rolling-mill by means of these plans or drawings. On receipt of the material at the shop the shopwork of manufacture is begun, and it involves a great variety of operations. The bridge-shop is filled with tools and engines of the heaviest description. Punches, lathes, planers, riveters, forges, boring and other machines of the largest dimensions are all brought to bear in the manufacture of the completed bridge.

106. Erection of Bridges.—When the shop operations are completed the bridge members are shipped to the site where the bridge is to be erected or put in place for final use. A timber staging, frequently of the heaviest timbers for large spans, called false works, is first erected in a temporary but very substantial manner. The top of this false work, or timber staging, is of such height that it will receive the steelwork of the bridge at exactly the right elevation. The bridge members are then brought onto the staging and each put in place and joined with pins and rivets. If the shopwork has not been done with mathematical accuracy, the bridge will not go together. On the accuracy of the shopwork, therefore, depends the possibility of properly fitting and joining the structure in its final position. The operations of the shop are so nicely disposed and so accurately performed that it is not an exaggeration to state that the serious misfit of a bridge member in American engineering practice at the present time is practically impossible. This leads to rapid erection so that the steelwork of a pin-connected railroad bridge 500 feet long can be put in place on the timber staging, or false works, and made safe in less than four days, although such a feat would have been considered impossible twenty years ago.

Fig. 27.

107. Statically Determinate Trusses.—The bridge structures which have been treated require but the simplest analysis, based only on statical equations of equilibrium of forces acting in one plane, i.e., the plane of the truss. It is known from the science of mechanics that the number of those equations is at most but three for any system of forces or loads, viz., two equations of forces and one of moments. This may be simply illustrated by the system of forces F₁, F₂, etc., in Fig. 27. Let each force be resolved into its vertical and horizontal components V and H. Also let l₁, l₂, etc. (not shown in the figure), be the normals or lever-arms dropped from any point A on the lines of action of the forces F₁, F₂, etc., so that the moments of the forces about that point will be F₁l₁, F₂l₂, etc. The conditions of purely statical equilibrium are expressed by the three general equations

• H₁ + H₂ + etc. = F₁ cos a₁ + F₂ cos a₂ + etc. = 0; (35)
• V₁ + V₂ + etc. = F₁ sin a₁ + F₂ sin a₂ + etc.   = 0; (36)
• Fl = F₁l₁ + F₂l₂ + etc. = 0.                                       (37)

If all the forces except three are known, obviously those three can be found by the three preceding equations; but if more than three are unknown, those three equations are not sufficient to find them. Other equations must be available or the unknown forces cannot be found. In modern methods of stress determinations those other needed equations express known elastic relations or values, such as deflections or the work performed in stressing the different members of structures under loads. A few fundamental equations of these methods will be given.

In Figs. 19, 20, and 21 let the truss be cut or divided by the imaginary sections QS. Each section cuts but three members, and as the loads and reactions are known, the stresses in the cut members will yield but three unknown forces, which may be found by the three equations of equilibrium (35), (36), (37). If more than three members are cut, however, as in the section TV of Figs. 22 and 23, making more than three unknown equations to be found, other equations than the three of statical equilibrium must be available. Hence the general principle that if it is possible to cut not more than three members by a section through the truss, it is statically determinate, but if it is not possible to cut less than four or more, the stresses are statically indeterminate.

At each joint in the truss the stresses in the members meeting there constitute, with the external forces or loads acting at the same point, a system in equilibrium represented by the two equations (35) and (36). If there are m such joints in the entire structure, there will be 2m such equations by which the same number of unknown quantities may be found. Since equilibrium exists at every joint in the truss, the entire truss will be in equilibrium, and that is equivalent to the equilibrium of all the external forces acting on it. This latter condition is expressed by the three equations (35), (36), and (37), and they are essentially included in the number 2m. Hence there will remain but 2m - 3 equations available for the determination of unknown stresses or external forces.

If, therefore, all the external forces (loads and reactions) are known, the 2m - 3 equations of static equilibrium can be applied to the determination of stresses in the bars of the truss or other structure. It follows, therefore, that the greatest number of bars that a statically determinate truss can have is

n = 2m - 3. (38)

In Fig. 19 there are twelve joints and twenty-one members, omitting counter web members and the verticals ab and fl, which are, statically speaking, either superfluous or not really bars of the truss. Hence

m = 12 and 2m - 3 = 21. (39)

Again, in Fig. 21 there are fifteen joints. Hence

m = 15, 2m - 3 = 27,

and there are twenty-seven bars or members of the truss. The number of joints and bars in actual, statically determinate trusses, therefore, confirm the results.

108. Continuous Beams and Trusses—Theorem of Three Moments.—These considerations find direct application to what are known as ”continuous beams,” i.e., beams (or trusses) which reach continuously over two or more spans, as shown in Fig. 28.

Fig. 28.

The beam shown is continuous over three spans, but a beam or truss may be continuous over any number of spans. In general the ends of the beam or girder may be fixed or held at the ends A and D, so that bending moments M and M₃ at the same points may have value. The bending moments at the other points of support are represented by M₁, M₂, etc. The points of support may or may not be at the same elevation, but they are usually assumed to be so in engineering practice. Finally, it is ordinarily assumed that the continuous structure is straight before being loaded, and that in that condition it simply touches the points of support. Whether the preceding assumptions are made or not, a perfectly general equation can be written expressing the relation between the bending moments over each set of three consecutive points of support, as M, M₁, and M₂, or M₁, M₂, and M₃. Such an equation expresses what is called the ”Theorem of Three Moments.” It is not necessary to give the most general form of this theorem, as that which is ordinarily used embodies the simplifying assumptions already described. This simplified form of the ”Theorem of Three Moments” applied to the case of Fig. 28 will yield the following two equations:

The figure over the sign of summation shows the span to which the summation belongs. If there is but one weight or load W in each span, the sign of summation is to be omitted. In an ordinary bridge structure or beam the ends are simply supported and M = M₃ = 0. In any case if the number of supports be n, there will be n - 2 equations like the preceding.

If the end moments M and M₃ are not zero, they will be determinable by the local conditions in each instance. In any event, therefore, they will be known, and there will be but n - 2 unknown moments to be found by the same number of equations. When the moments are known the reactions follow from simple formulæ.

109. Application to Draw- or Swing-bridges.—In general the reactions or supporting forces of the beams and trusses of ordinary civil-engineering practice are vertical, and all their points of application are known. Hence there are but two equations of equilibrium, equations (36) and (37), for external forces. These two equations for the external forces and the n - 2 equations derived from the theorem of three moments are therefore always sufficient to determine the n reactions. After the reactions are known all the stresses in the bars or members of the trusses can at once be found. The preceding equations and methods as described are constantly employed in the design and construction of swing- or drawbridges.

110. Special Method for Deflection of Trusses.—The method of finding the elastic deflections produced by the bending of solid beams has already been shown, but it is frequently necessary to determine the elastic deflections of bridge-trusses or other jointed or so-called articulate frames or structures. It is not practicable to use the same formulæ for the latter class of structures as for the former. The elastic deflection of a bridge- or roof-truss depends upon the stretching or compressions of its various members in consequence of the tensile or compressive forces to which they are subjected. Any method by which the deflection is found, therefore, must involve these elastic changes of length. There are a number of methods which give the desired expressions, but probably the simplest as well as the most elegant procedure is that which reaches the desired expression through the consideration of the work performed in the truss members in producing their elastic lengthenings and shortenings.

The general features of this method can readily be shown by reference to Fig. 29. It may be supposed that it is desired to find the deflection of any point, as J, of the lower chord produced both by the dead and live load which it carries. It is known from what has preceded that every member of the upper chord will be shortened and that every member of the lower chord will be lengthened; and also that generally the vertical web members will be shortened and the inclined web members lengthened. If there can be obtained an expression giving that part of the deflection of J which is due to the change of length of any one member of the truss independently of the others, then that expression may be applied to every other member in the entire truss, and by taking the sum of all those effects the desired deflection will at once result. While this expression will be found for some one particular truss member, it will be of such a general form that it may be used for any truss member whatever; it will be written for the upper-chord member BC in Fig. 29.

Fig. 29.

The general problem is to determine the deflection of the point J when the bridge carries both dead and moving load over the entire span, as shown in Fig. 29. The general plan of procedure is first to find the stresses due to this combined load in every member of the truss, so that the corresponding lengthening or shortening is at once shown. The effect of this lengthening and shortening for any single member BC in producing deflection at J is then determined; the sum of all such effects for every member of the truss is next taken, and that sum is the deflection sought. In this case the vertical deflection will be found, because that is the deflection generally desired in connection with bridge structures, but precisely the same method and essentially the same formulæ are used to find the deflection in any direction whatever. The following notation will be employed:

S or Z may be either tension or compression, and the formulæ will be so expressed that tension will be made positive and compression negative.

The change of length of the chord member BC produced by a stress gradually increasing from zero to S is

If it be supposed that BC is a spring of such stiffness that it will be compressed by the gradual application of Z exactly as much as the shortening of the actual member by the stress S, the deflection of the point 4 with the weight P hung from it, and due to that compression alone, will be precisely the same as that due to the actual shortening of BC by the combined dead and moving loads.

It is known by one of the elementary principles of mechanics that, since P acts along the direction of the vertical deflection w, the work performed by the weight P over that deflection is equal to the work performed by Z over the change of length l. Hence

The quantity Z÷P is the stress produced in the member by a unit load applied at the joint or point where the deflection is desired. Again, S÷A is the stress per unit of area, i.e., intensity of stress, in the member considered by the actual dead and moving loads. For brevity let these be written

then

If the influence of every member of the truss is similarly expressed, the value of the total deflection produced by the dead and moving loads will be

The sign of summation ∑ indicates that the summation is to extend over all the web and chord members of the truss.

111. Application of Method for Deflection to Triangular Frame.—Before applying those equations to the case of Fig. 29 it is best to consider a simpler case, i.e., that of the triangular frame shown in Fig. 18. The reactions are

The stresses in the various members are:

• Also: CB = h sec α; area of section = A₁.
•  CA = h sec β;  ” ” ”  = A₂.
•  AB = l; ” ” ”  = A₃.

In this instance it is simplest to take P = W. Equation (44) then gives

Let it be supposed that

If the bars are all supposed to be of yellow-pine timber, there may be taken

The insertion of these quantities in equation (46) gives the deflection

w = .01042 + .01253 + .01111 = 0.034. (47)

Equation (47) is so written as to show the portion of the deflection due to each member of the frame.

In applying either equation (43) or equation (44) care must be taken to give each stress and its corresponding strain (lengthening or shortening) the proper sign. As the formulæ have been written and used, a tensile stress and its resulting stretch must each be written positive, while a compressive stress must be written negative. This holds true for both the stresses Z and S (or z and s). The magnitude of the assumed load P is a matter of indifference, since the stress Z will always be proportional to it and the ratio P ÷ Z will therefore be constant. P is frequently taken as unity; or, as in the case just given, it may have any value that the conditions of the problem make most convenient.

112. Application of Method for Deflection to Truss.—In making application of the deflection formulæ to any steel railroad truss similar to that shown in Fig. 29, it will first be necessary to determine the stresses in all its members due to the dead and moving loads, since the deflection under the moving load is sought. These loads will be considered uniform, and that is sufficiently accurate for any railroad bridge. The moving train-load will be taken as covering the entire span, assumed, for a single-track railroad, 240 feet in length between centres of end pins. There are eight panels of 30 feet each, and the depth of truss at centre is 40 feet. Other truss dimensions are as shown in Fig. 29. The dead loads, or own weight, are taken at 400 pounds per linear foot of span for the rails and other pieces that constitute the track; at 400 pounds per linear foot for the steel floor-beams and stringers, and 1600 pounds per linear foot for the weight of trusses and bracing. The moving train-load will be taken at 4000 pounds per linear foot. This will make the panel-loads for each truss as follows:

The structure is a “through” bridge, hence all moving loads rest on the lower chord.

Fig. 30.

The stresses in the truss members due to the combined uniform dead and moving load are best found by the graphical method. One diagram only is needed to determine all the stresses, and it is shown in Fig. 30. This diagram is drawn accurately to scale, and the stresses measured from it are shown in the table on page 136.

The stresses in all the truss members due to the unit load hung at J are readily found by the single diagram shown in Fig. 31, also carefully drawn to scale. These stresses measured from the diagram are given in the table as indicated by the column z; they are also represented in equation (44) by the letter z. The quantity s in equation (44) is the intensity of the stress (pounds per square inch of cross-section of member) produced by the combined dead and moving loads in each member. As shown, these stresses are least in the web members near the centre of the span, and greatest in the chord members. The lengths in inches of the truss members are shown in the proper column of the table. It will be observed that all counter web members are omitted, as they are not needed for the uniform load. The coefficient of elasticity (E) is taken at 28,000,000 pounds. The quantities represented by the second member of equation (44) are computed from these data, and they appear in the last column of the table, the sum of which gives the desired deflection in inches. The elements of the table show how much of the deflection is due to the chords and to the web members, and they show that disregarding the latter would lead to a considerable error.

Fig. 31.

As the deflection is usually desired in inches, the lengths of members must be taken in the same unit.

113. Method of Least Work.—The so-called theorem or principle of “Least Work” is closely related to the subject of elastic deflections just considered in its availability for furnishing equations of condition in addition to those of a purely statical character in cases where indetermination would result without them. This principle of least work is expressed in the simple statement that when any structure supports external loading the work performed in producing elastic deformation of all the members will be the least possible. Although this principle may not be susceptible of a complete and general demonstration, it may be shown to hold true in many cases if not all. The hypothesis is most reasonable and furnishes elegant solutions in many useful problems.

The application of this principle requires the determination of expressions for the work performed in the elastic lengthening and shortening of pieces subjected either to tension or compression, and for the work performed in the elastic bending of beams carrying loads at right angles to their axes. Both of these expressions can be very simply found.

Let it be supposed that a piece of material whose length is L and the area of whose cross-section is A is either stretched or compressed by the weight or load S applied so as to increase gradually from zero to its full value. The elastic change of length will be SL/AE, E being the coefficient of elasticity. The average force acting will be ½S, hence the work performed in producing the strain will be

It will generally be best, although not necessary, to take L in inches. The expression (48) applies either to tension or compression precisely as it stands.

To obtain the expression for the work performed by the stresses in a beam bent by loads acting at right angles to its axis, a differential length (dL) of the beam is considered at any normal section in which the bending moment is M, the total length being L. Let I be the moment of inertia of the normal section, A, about an axis passing through the centre of gravity of the latter, and let k be the intensity of stress (usually the stress per square inch) at any point distant d from the axis about which I is taken. The elastic change produced in the indefinitely short length dL when the intensity k exists is (k/E)dL. If dA is an indefinitely small portion of the normal section, the average force or stress, either of tension or compression, acting through the small elastic change of length just given, can be written by the aid of equation (5) as

Hence the work performed in any normal section of the member, for which M remains unchanged, will be, since ∫k. dA. d = M,

The work performed throughout the entire piece will then be

Each of the expressions (48) and (51) belongs to a single piece or member of the structure. The total work performed in all the pieces subjected either to direct stress or to bending, and which, according to the principle of least work, must be a minimum, is found by taking the summation of the two preceding expressions:

In making an application of equation (52) it is to be remembered that S is the direct stress of tension or compression in any member, and that M is the general value of the bending moment in any bent member expressed in terms of the length L.

114. Application of Method of Least Work to General Problem.—The problem which generally presents itself in the use of equation (52) is the finding of an equation which expresses the condition that the work expended in producing elastic deformation shall be a minimum, some particular stress in the structure or some external load or force being the variable. If t represent that variable, then the desired equation of condition will be found simply by placing the first differential coefficient of e in equation (52) equal to zero:

The solution of equation (53) will give a value of t which will make the work performed as expressed in equation (52) a minimum. This method is not a difficult one to employ in such cases as those of drawbridges and stiffened suspension bridges. In the latter case particularly it is of great practical value.

115. Application of Method of Least Work to Trussed Beam.—The method of least work may be illustrated by the application of the preceding equations to the simple truss shown in Fig. 32. The pieces BC and GD are supposed to be of yellow-pine timber, the former 10 inches by 14 inches (vertical) in section and the latter 8 inches by 10 inches, while each of the pieces BD and DC are two 1⅝-inch round steel bars. The coefficient of elasticity E will be taken at 1,000,000 pounds for the timber and 28,000,000 for the steel. The length of BC is 360 inches; GD 96 inches; BD = 96 × 2.13 = 204.5 inches.

tan α = 1.875 and sec α = 2.13.

The weight W resting at G is 20,000 pounds. A part of this weight is carried by BC as a simple timber beam, while the remainder of the load will be carried on the triangular frame BCD acting as a truss, the elastic deflection of the latter throwing a part of the load on BC acting as a beam. According to the principle of least work the division of the load will be such as to make the work performed in straining the different members of the system a minimum.

That part of W which rests on BC as a simple beam may be represented by W₁, while W₂ represents the remaining portion carried by the triangular frame. As G is at the centre of the span, the beam reaction at either B or C is ½W₁. Hence the general value of the bending moment in either half of the beam at any distance x from either B or C is

M = ½W₁x. Hence M²dL = ¼W₁²x²dx.

As there is but one member acting as a beam, whose moment of inertia I is constant, the second term of the second member of equation (52) becomes, by the aid of the preceding equation,

Fig. 32.

The numerical elements of the expression for the work done in the members of the triangular frame are:

The substitution of those quantities in the first term of the second member of equation (52) will give

The substitution of numerical quantities in equation (54) gives

Or, since W - W₂ = W₁,

e = .000,003,73W₂² + .000,213(W - W₂)².      (55)

Hence

The solution of this equation gives

W₂ = .893W = 19,660 pounds.
  W₁ = 340 ”

It is interesting to observe that the first term of the second member of equation (56) is the deflection of the point of application of W₂ as a point in the frame, while the second term is the deflection of the point of application of W₁ considered as a point of the beam. In other words, the condition resulting from the application of the principle of least work is equivalent to making the elastic deflections by W₁ and W₂ equal. Indeed equation (53) expresses the equivalence of deflections whenever the features of the problem are such as to involve concurrent deflections of two different parts of the structure.

116. Removal of Indetermination by Methods of Least Work and Deflection.—The indetermination existing in connection with the computations for such trusses as those shown in Fig. 22 and Fig. 23 can be removed by finding equations of condition by the aid of the method of least work or of deflections. It is evident that the component systems of bracing of which such trusses are composed must all deflect equally. Hence expressions may be found for the deflections of those component trusses, each under its own load. Since these deflections must be equal, equations of condition at once result. A sufficient number of such equations, taken with those required by statical equilibrium, can be found to solve completely the problem. Such methods, however, are laborious, and the ordinary assumption of each system carrying wholly the loads resting at its panel-points is sufficiently near for all ordinary purposes.

The method of least work can be very conveniently used for the solution of a great number of simple problems, like that which requires the determination of the four reactions under the four legs of a table, carrying a single weight or a number of weights, and many others of the same character.

CHAPTER X.

117. The Arched Rib, of both Steel and Masonry.—During the past ten or fifteen years the type of bridge structure called the arched rib has come into much use, and its merits insure for it a wider application in the future. It partakes somewhat of the nature of both truss and arch; or it may be considered a curved beam or girder. The ordinary beam or truss when placed in a horizontal position and loaded vertically yields only vertical reactions. Under the same conditions, however, the arched rib will produce both vertical and horizontal reactions, and the latter must either be resisted by abutments of sufficient mass, or by a tie-rod, usually horizontal, connecting the springing points of the rib.

The arched rib may be built solid, as was done in the early days of bridge-building in this country when engineers like Palmer, Burr, and Wernwag introduced timber arches in combination with their wooden trusses, or as a curved plate girder, one of the most prominent examples of which is the Washington Bridge across the Harlem River in the city of New York; or, again, as a braced frame or curved truss, like the 800 feet arched rib carrying the roadway traffic and trolley cars across the Niagara gorge, or like those used in such great railroad train-sheds as the Grand Central Station, New York, the Pennsylvania stations at Jersey City and Philadelphia, and the Philadelphia and Reading station in Philadelphia. Those are all admirable examples of steel arched ribs, and they are built to sustain not only vertical loads but, in the case of station roofs, the normal or horizontal wind pressures.

Within a few years, less than ten, another type of arched rib has been brought into use and promises to be one of the most beautiful as well as the most substantial applications of this type of structure; that is, the arched rib of combined steel and concrete. Many examples of this type of structure already exist both in this country and in Europe, probably the most prominent of which in this country is that at Topeka, Kansas, across the Kansas River.

Fig. 33.

Fig. 34.

Fig. 35.

The characteristic feature of this type of structure, so far as the stresses developed in it are concerned, is the thrust throughout its length, more or less nearly parallel to its axis, which is combined with the bending moments and shears similar to those found in ordinary bridge-trusses. This thrust is the arch characteristic and differentiates it in a measure from the ordinary bridge-truss, while the bending moments and shears to which it is subjected differentiate it, on the other hand, from the pure arch type or a series of blocks in which thrust only exists. The thrust, bending moments, and shears in arched ribs are all affected by certain principal features of design. Those features are either fixedness of the ends of the ribs or the presence of pin-joints at those ends or at the crown. Fig. 33 represents an arched rib with its ends D and F supposed to be rigidly fixed in masonry or by other effective means.

118. Arched Rib with Ends Fixed.—The railroad steel arched bridge at St. Louis, built by Captain Eads between 1868 and 1874, is a structure of this character. The three spans (two each 537 feet 3 inches and one 552 feet 6 inches in length from centre to centre of piers) consist of ribs the main members of which are composed of chrome steel. It was a structure of unprecedented span when it was built, and constituted one of the boldest pieces of engineering in its day. The chords of the ribs are tubes made of steel staves, and their ends are rigidly anchored to the masonry piers on which they rest. It is exceedingly difficult, indeed impossible, to fix rigidly the ends of such a structure, and observations in this particular instance have shown that the extremities of the ribs are not truly fixed, for the piers themselves yield a little, giving elastic motion under some conditions of loading.

119. Arched Rib with Ends Jointed.—The rib shown in Fig. 34 is different from the preceding in that pin-joints are supplied at each end, so that the rib may experience elastic distortion or strain by small rotations about the pins at A and B. In the computations for such a design it is assumed that the ends of the rib may freely change their inclination at those points. As a matter of fact the friction is so great, even if no corrosion exists, as to prevent motion, but the presence of the pins makes no bending moment possible at the end joints, and the failure to move freely probably produces no serious effect upon the stresses in the ribs. The presence of these pin-joints simplifies the computations of stresses and renders them better defined, so that there is less doubt as to the actual condition of stress under a given load than in the type shown in Fig. 33 with ends fixed more or less stiffly. In Fig. 34, if the horizontal force H exerted by the ends of the rib against the points of support is known, the remaining stresses in the structure can readily be computed; but neither in Fig. 34 nor in Fig. 33 are statical equations sufficient for the determination of stresses. Equations of condition, depending upon the elastic properties of the material, are required before solutions of the problems arising can be made.

120. Arched Rib with Crown and Ends Jointed.—The rib shown in Fig. 35 possesses one characteristic radically different from any found in the ribs of Figs. 33 and 34, in that it is three-jointed, one pin-joint being at the crown and one at each end. So far as the conditions of stress are concerned, this is the simplest rib of all. Since there is a pin-joint at the crown as well as at the ends, the bending moments must be zero at each of those three points whatever may be the condition of loading. The point of application of the force or thrust at the crown, therefore, is always known, as well as the points of application at the ends of the joints. As will presently be seen, this condition makes equations of statical equilibrium sufficient for the determination of all stresses in the rib, and no equations depending upon the elastic properties of the material are required. The stresses in this class of ribs, therefore, are more easily determined than in the other two, and they are better defined. These qualities have insured for it a somewhat more popular position than either of the other two classes. The ribs of the great train-sheds of the Pennsylvania and Reading railroads in Jersey City and in Philadelphia belong to this class, while those of the Grand Central Station at New York City belong to the class shown in Fig. 34, as does the arched rib across the Niagara gorge, to which reference has already been made.

121. Relative Stiffness of Arch Ribs.—Obviously the three-hinged ribs are less stiff than the two-hinged ribs or those with fixed ends. This is a matter of less consequence for station roofs than for structures carrying railroad loads. The joints of the two-hinged rib being at the ends of the structure, there is but little difference in stiffness between that class of ribs and those with ends fixed. Indeed the difference is so slight, and the uncertainty as to the degree of fixedness of the fixed ends of the rib is so great, that the latter type of rib possesses no real advantage over that with hinged ends.

122. General Conditions of Analysis of Arched Ribs.—In each of the three types of arched ribs shown in Figs. 33, 34, and 35 it is supposed that all external forces act in the vertical planes which contain the centre lines of the various members of the rib. There are, therefore, the three conditions of statical equilibrium expressed by the three equations (35), (36), and (37). In practically all cases, except those of arched ribs employed in roof construction, all the external loads are vertical. In such cases the equations of statical equilibrium of the entire structure may be reduced to two only, viz., equations (36) and (37). These features of the problems connected with the design of arched ribs will always make necessary, except in the case of the three-hinged rib (Fig. 35), equations of condition depending upon the elastic properties of the structure.

The rib represented by Fig. 33 is supposed to have its ends so fixed that the inclinations of the centre line at F and D will never change whatever may be the loading or the variation of temperature. This requires the application at each of those points of a couple whose moment varies in value, but which is always equal and opposite to the bending moment at the same point produced by the loads imposed on the rib. It is also to be observed that the loads resting upon the rib are not divided between the points of support F and D in accordance with the law of the lever, since the conditions of fixedness at the ends are equivalent to continuity. There are then to be found, as acting external to the rib, the two vertical reactions and the two moments at F and D, as well as the horizontal thrust exerted at the ends of the structure, which is sometimes resisted by the tie-rod, making five unknown quantities. Inasmuch as all external loading is supposed to be vertical, equations (36) and (37) are the only statical equations available, and three others, depending upon the elastic properties of the structure, must be supplied in order to obtain the total of five equations of condition to determine the five unknown quantities. Inasmuch as the end inclinations remain unchanged, the total extension or compression of the material at any given constant distance from the axis of the rib taken between the two end sections F and D must be equal to zero. Similarly, whatever may be the amount or condition of loading, the vertical and horizontal deflections of either of the ends F or D in relation to the other must be zero, since no relative motion between these two points can take place. It is not necessary in these lectures to give the demonstration of the equations which express the three preceding elastic conditions, but if M is the general value of the bending moment for any point of the rib, and if x and y are the horizontal and vertical coordinates of the centre line of the rib, taking the central point of the section at either F or D as an origin, those equations, taken in the order in which the elastic conditions have been named, will be the following, in which n represents a short length of rib within which the bending moment M is supposed to remain unchanged.

The second and third of these equations express the condition that the vertical and horizontal deflections respectively of the two ends in reference to each other shall be zero. The conditions expressed by equation (57) are constantly used in engineering practice to determine the bending moments and stresses which exist in the arched rib with fixed ends. The graphical method is ordinarily used for that purpose, as its employment is a comparatively simple procedure for a rib whose curvature is any whatever.

If the rib has hinged joints at the ends, as in Fig. 34, obviously there can be no bending moment at either of those two points, and hence the two equations of condition which were required in connection with Fig. 33 to determine them will not be needed. There is, therefore, no restriction as to the angle of inclination of the centre line of the rib at those two points. Again, it is obvious that either end A or B may have vertical movement, i.e., deflection in reference to the other, without affecting the condition of stress in any member of the rib; but it is equally obvious that neither A nor B can be moved horizontally, i.e., deflected in reference to the other, without producing bending in the rib and developing stresses in the various members. The unknown quantities in this case are, therefore, only the horizontal thrust H exerted at the two springing points A and B, and the two vertical reactions, making a total of three unknown quantities, equations for two of which will be given by equations (36) and (37). The other equation required is the third expression in equation (57), expressing the condition that the horizontal deflection of either of the points A or B in respect to the other is zero, since the span AB is supposed to remain unchanged. By the application of the graphical method to this case, as to the preceding, the employment of equations (36), (37), and (58) will afford an easy and quick determination of the three unknown quantities, whatever may be the curvature of the rib.

If the reactions and horizontal thrust H are found, stresses in every member may readily be computed and the complete design made.

If the arch is three-hinged, as in Fig. 35, the condition that the bending moment must be zero at the crown C under all conditions of loading gives a third statical equation independent of the elastic properties of the structure which, in connection with equations (36) and (37), give three equations of condition sufficient to determine the two vertical reactions and the horizontal thrust H. In this case, as has already been stated, no elastic equations of condition are required.

The determination of the end reactions, bending moments, and horizontal thrust H, in these various cases, is all that is necessary in order to compute with ease and immediately the stresses in every member of the rib. These computations are obviously the final numerical work required for the complete design of the structure. These procedures are always followed, and in precisely the manner indicated, in the design of arched ribs by civil engineers, whether the rib be articulated, i.e., with open bracing, or with a solid plate web, like those of the Washington Bridge across the Harlem River.

CHAPTER XI.

123. Beams of Combined Steel and Concrete.[2]—A reference has already been made to a class of beams and arches recently come into use and now quite widely employed, composed of steel and concrete, the former being completely surrounded by and imbedded in the latter. These composite beams are very extensively used in the floors of fire-proof buildings as well as for other purposes. Arches of combined concrete and steel were probably first built in Germany and but a comparatively few years ago. During the past ten years they have been largely introduced into this country, and many such structures have not only been designed but built. The most prominent design of arches of combined concrete and steel are those of the proposed memorial bridge across the Potomac River at Washington, for which a first prize was awarded as the result of a national competition in the early part of 1900. So far as the bending or flexure of these composite beams and arches is concerned, the theory is identically the same for both, the formulæ for each of which are given below. In order to express these formulæ the following notation will be needed:

MEMORIAL BRIDGE ACROSS THE POTOMAC
AT WASHINGTON D.C.

PLAN NO. 2.

Wm. H. Burr, Civil Engineer.

E. P. Casey, Associated Architect.
Plan Awarded First Prize in National Competition.
River spans 192 feet clear.
Total length of structure 3615 feet.

PLAN NO. 1.

Wm. H. Burr, Civil Engineer.

E. P. Casey, Associated Architect.

The Towers of this Plan were Recommended by Board of Award
to be Substituted for Those in Plan No. 2.

River spans 283 feet clear. Total length of structure 3437 feet.

P is the thrust along the arch determined by the methods explained in the consideration of arched ribs.

l is the distance of the line of the thrust P from the axis of the arched rib.

E₁ and E₂ are coefficients of elasticity for the two materials.

A₁ and A₂ are areas of normal section of the two materials.

I₁ and I₂ are moments of inertia of A₁ and A₂ about the neutral axes of the composite beam or arch sections.

k₁ and k₂ are intensities of bending stress in the extreme fibres of the two materials.

h₁ and h₂ are total depths of the two materials.

d₁ and d₂ are distances from the neutral axes to farthest fibres of the two materials; distances to other extreme fibres would be (h₁-d₁) and (h₂-d₂).

W₁ and W₂ are loads, either distributed or concentrated, carried by the two portions.

W = W₁ + W₂ is total load on the beam or arch.

The application of the theory of flexure to the case of a beam or arch of two different materials, steel and concrete in this case, will give the following results:

M = Pl; hence M₁ = q₁Pl and M₂ = q₂Pl.    (59)

These formulæ exhibit some of the main features of the analysis which must be used in designing either beams or arches of combined steel and concrete. In the use of these equations care must be taken to give the proper sign to the bending moment M. They obviously apply to the combination of any two materials, although at the present time the only two used in such composite structures are steel and concrete. If the subscript 1 belongs to the concrete portion, and the subscript 2 to the steel portion, there may be taken E₁ = 1,500,000 to 3,000,000 and E₂ = 30,000,000. Hence e = 20 to 10.

The purpose of introducing the steel into the concrete is to make available in the composite structure the high tensile resistance of that metal. A very small steel cross-section is sufficient to satisfactorily accomplish that purpose. The percentage of the total composite section represented by the steel will vary somewhat with the dimensions of the structure and the mode of using the material; it will usually range from 0.75 per cent to 1.5 per cent of the total section. The large mass of concrete in which the steel should be completely imbedded serves not only to afford a large portion of the compressive resistance required in both arches and beams, but also to preserve the steel effectively from corrosion. Many experiments have shown that it requires but a small per cent of steel section to give great tensile resistance to the composite mass.

CHAPTER XII.

124. The Masonry Arch.—The masonry arch is so old that its origin is lost in antiquity, but its complete theory has been developed with that of other bridge structures only within the latest period. It is only possible here to give some of the main features of that theory and a few of the fundamental ideas on which it is based. It is customary among engineers to regard the masonry arch as an assemblage of blocks finely cut to accurate dimensions, so that the assumption of either a uniform or uniformly varying pressure in the surface of contact between any two may be at least sufficiently near the truth for all practical purposes. Although care is taken to make joints between ring-stones or voussoirs completely cemented or filled with a rich cement mortar, it is usually the implicit assumption that such joints do not resist tension. As a matter of fact many arch joints are capable of resisting considerable tension, but, in consequence of settlement or shrinkage, cracks in them that may be almost or quite imperceptible frequently prevent complete continuity. It is, therefore, considered judicious to determine the stability of the ordinary masonry arch on the assumption that the joints do not resist tension.

In these observations it is not intended to convey the impression that no analysts treat the ordinary arch as a continuous elastic masonry mass, like the composite arches of steel and concrete. Although much may be said in favor of such treatment for all arches, it is believed that prolonged experience with arch structures makes it advisable to neglect any small capacity of resistance to tension which an ordinary cut-stone masonry joint may possess, in the interests of reasonable security.

The ring-stones or voussoirs of an arch are usually cut to form circular or elliptic curves, or to lines which do not differ sensibly from those curves. The arch-ring may make a complete semicircle, as in the old Roman arches, or a segment of a semicircle; or the stones may be arranged to make a pointed arch, like the Gothic; or, again, a complete semiellipse may be formed, or possibly a segment of that curve. When a complete semiellipse or complete semicircle is formed, the arches are said to be full-centred, and in those cases they spring from a horizontal joint at each end. On the other hand, segmental arches spring from inclined joints at each end called skew-backs.

125. Old and New Theories of the Arch.—In the older theories of the arch, considered as a series of blocks simply abutting against each other, the resultant loading on each block was assumed to be vertical. In the modern theories, on the other hand, the resultant loading on any block is taken precisely as it is, either vertical or inclined, as the case may be. Many arches are loaded with earth over their arch-rings. This earth loading produces a horizontal pressure against each of the stones, as well as a vertical loading due to its own weight. In such cases it is necessary to recognize this horizontal or lateral pressure of the earth, as it is called, as a part of the arch loading.

It is known from the theory of earth pressure that the amount of that pressure per square foot or any other square unit may vary between rather wide limits, the upper of which is called the abutting power of earth, and the latter the conjugate pressure due to its own weight only. If w is the weight per cubic unit of earth and x the depth considered, and if φ be the angle of repose of the earth, the abutting power per square unit will have the value:

while the horizontal or conjugate pressure due to the weight of earth only will be:

The use of these formulæ will be illustrated by actual arch computations.

Fig. 36.

Fig. 37.

Fig. 36 is supposed to show a set of ring-stones for an arch of any curvature whatever. The joints LM and ON represent the skew-backs or springing joints, while R and R₁ represent the supporting forces or reactions with centres of action at aʹ and a₁. The ring is divided into blocks or pieces by the joints at a, b, c, d, and e, the resultant loading or force on each block being given by the lines with arrow-heads and numbered 1, 2, 3, 4, 5, 6, and 7. Fig. 37 represents a force polygon constructed in the ordinary manner by laying off carefully to scale the two reactions R and R₁, together with the loads or forces numbered 1 to 7, inclusive. By constructing the so-called polygonal frame in the ring-stones of Fig. 36 in the usual manner with its lines or sides parallel to the radiating lines in Fig. 37, as shown by the broken lines, the points a, b, c, etc., are found where the resultant forces cut each joint. The line drawn through those points thus determined is called the line of resistance of the arch. Obviously, if that line of resistance be determined, the complete stability or instability of the arch, as the case may be, will be established. Furthermore, the complete determination of the force polygon in Fig. 37, and the corresponding polygonal frame drawn in the arch-ring, constitute all the computations involved in the design of an arch.

The thrust T₀ at the crown, shown both in Fig. 36 and Fig. 37, is frequently horizontal, although not necessarily so; its value is shown by Fig. 37. In the older arch theories a principle was enunciated called the “principle of least resistance.” The thrust T₀ is a fundamental and so-called passive force. That is, its magnitude depends not only upon its position, but also largely upon the magnitude of the active forces which represent the loading on the arch-ring. Under the principle of least resistance it was laid down as a fundamental proposition, in making arch computations, that this passive force T₀ must be the least possible consistent with the stability of the structure. While this provisional proposition answered its purpose well enough, there are other clearer methods of procedure which are thoroughly rational and involve the employment of no extraneous considerations other than those attached to the determination of statical equilibrium.

A scrutiny of the conditions existing in Fig. 36 will show that if the external forces or loadings on the individual blocks of the ring are given, four quantities are to be determined, viz., the two reactions R and R₁ and their lines of action. Inasmuch as no elastic features of the structure are to be considered, there are available for the determination of these four quantities the three equations of equilibrium, equations (35), (36), and (37), which are not sufficient for the purpose. If one line of action, such as that of R, be located by assuming its point of application aʹ, the three equations just named will be sufficient for the determination of the remaining three equations; and that is precisely the method employed. It is tentative, but perfectly practicable. If, instead of assuming one of the points of application of the reactions, we assume both of those points and construct a trial polygonal frame, it will be necessary to use but two of the three equations of statical equilibrium. For that purpose there are employed equations (35) and (36), but in a graphical manner, which will presently be illustrated.

126. Stress Conditions in the Arch-ring.—Before proceeding to the construction of an actual line of resistance, a little consideration must be given to the stress conditions in the arch-ring. As the joints are considered capable of resisting no tension, the dimensions of the arch-ring must be finally so proportioned that pressure only will exist in each and every joint. If each centre of pressure, as a, b, etc., in Fig. 36, is found in the middle third of the joint, it is known from a very simple demonstration in mechanics that no tension will ever exist in that joint, although the pressure may be zero at one extremity and a maximum at the other. This is the condition usually imposed in designing an arch-ring to carry given dead or live loads. It is usually specified that “the line of resistance of the ring must lie in the middle third.” It must be borne in mind, however, that the stability of the ring is perfectly consistent with the location of the line of resistance outside of the limits of the middle third, provided it is not so far outside as to induce crushing of the ring-stones. Whenever that crushing begins the arch is in serious danger and complete failure is likely to result.

127. Applications to an Actual Arch.—These principles will be applied to the arch-ring shown in Fig. 38, in which the clear span TU is 90 feet. The radius CO of the soffit (as the under surface of the arch is called) is 50 feet, the ring being circular and segmental. The uniform thickness of the ring shown at the various joints is assumed at 4 feet as a trial value. The loading above the ring to the level of the line EʹO is assumed to be dry earth weighing, when well rammed in place, 100 pounds per cubic foot. The depth of this earth filling at the crown n of the arch is taken at 4 feet. The ring-stones are assumed to be of granite or best quality of limestone, weighing 160 pounds per cubic foot. The thickness or width of arch-ring of one foot is assumed, as each foot in width is like every other foot, and the loads are taken for that width of ring. The rectangle EJJʹEʹ is supposed to represent a moving load covering one half of the span and averaging 500 pounds per linear foot; in other words, averaging 500 pounds per square foot of upper surface projected in the line EʹO. The total length of the arch-ring, measured on the soffit, is about 113 feet, and it is divided into ten equal portions for the purpose of convenient computation. The radial joints so located are as shown at de, fg, hk. From the points where these joints cut the extrados (as the upper surface of the arch-ring is called) vertical broken lines are erected, as shown in Fig. 38.

Fig. 38.

The horizontal line drawn to the left from f gives the vertical projection of that part of the extrados between d and f, and the horizontal earth pressure on df will be precisely the same in amount as that on the vertical projection of df, as just found. In the same manner the horizontal earth pressure on that part of the extrados between any two adjacent joints may be found. The mid-depths of these vertical projections below the line E′O are to be carefully measured by scale and then used for the values of x in equations (64) and (65), which now become equations (66) and (67), as the angle of repose φ is taken to correspond to a slope of earth surface of 1 vertical on 1½ horizontal.

p = 3.51wx. (66)

pʹ = 0.285wx.(67)

The horizontal earth pressures thus found are as follows:

These quantities h₁, etc., are found by multiplying the two intensities p and p′ by the vertical projections of the surface on which they act. The larger values are found by equation (66) and represent the abutting power of the earth, while the smaller values are found by equation (67), and represent the horizontal or conjugate pressure of the earth due to its own weight only. The actual horizontal earth pressure against the arch-ring may lie anywhere between these limits.

The weights of the moving load, earth, and ring-stones between each pair of vertical lines and radial joints shown in Fig. 38 are next to be determined, and they are as follows:

The centres of gravity of these various vertical forces are shown in Fig. 38 at the points W₁, W₂, etc. The triangles of forces shown in that figure and composed, each one, of a vertical and horizontal force as described, are laid down in actual position on the arch-ring, as shown. All data are thus secured for completing the force polygon and polygonal frame or line of resistance. It will be assumed that the reactions R and R′ cut the springing joints at c and a, respectively, one third of the width of the joint from the soffit, and it will further be assumed that b, the mid-point of the joint at the crown, is also in the line of resistance. The assumption of the location of these three points is made for the reason, as is well known, that with a given system of forces a polygonal frame may be found which will pass through any three points in the ring.

Fig. 39.

The force polygon B, 1, 2, 3, ..., 10, A, Fig. 39, is then drawn with the loadings on each ring segment found as already explained. The horizontal forces are taken as represented by the smaller values of h₁, h₂, h₃, h₄. Other force polygons with larger values of these horizontal forces were tried and not found satisfactory. Having constructed the force polygon and assumed the trial pole Pʹ, the radial lines are drawn from it as shown in Fig. 39. The polygonal frame shown in broken lines in Fig. 38 results from this trial pole. The frame practically passes through b and c, but leaves the ring, passing outside of it, above the joint VU. The point q in this frame is vertically above a. The “three-point” method of finding the frame that will pass through a, b, and c was then employed. The line A6, Fig. 39, was drawn; then P′D was drawn parallel to qb, Fig. 38 (not shown); after which PD was drawn parallel to ab, until it intercepted the horizontal line PQ, the line PʹQ having previously been drawn parallel to qc (not shown). The final pole P was thus found. The polygonal frame shown in full lines in the arch-ring was then drawn with sides parallel to the lines radiating from P, all in accordance with the usual methods for such graphic analysis. That polygonal frame lies within the middle third of the arch-ring, although at three points it touches the limit of the middle third. The arch, therefore, is stable.

This construction shows that, with the actual loading of the ring, a line of resistance can be found lying within the middle third; its stability under the conditions assumed is, therefore, demonstrated. It does not follow that the line of resistance as determined must necessarily exist, since there may be others located still more favorably for stability. This indetermination results from the fact already observed that the equations of statical equilibrium are not sufficient in number to determine the four unknown quantities (the two horizontal and the two vertical reactions); but the process of demonstrating the stability of the arch-ring is simple and sufficient for all ordinary purposes. The line of resistance found, if not the true one, is so near to it that no sensible waste of material is involved in employing it. This indetermination has prompted some engineers and other analysts to consider all arch-rings as elastic, thus obtaining other equations of condition. While such a procedure may be permissible, it is scarcely necessary, and perhaps not advisable, in view of the fact that many joints of cut-stone arches become slightly open by very small cracks, resulting possibly from unequal settlement, quite harmless in themselves, having practically no effect upon the stability of the structure.

128. Intensities of Pressure in the Arch-ring.—It still remains to ascertain whether the actual pressures of masonry in the arch-ring are too high or not. The greatest single force shown in the force polygon in Fig. 39 is the reaction R, having a value by scale of 122,000 pounds, under the left end of the arch, and it is supposed to act at the limit of the middle third of the joint. Hence the average pressure on that joint will be

This value may be taken as satisfactory for granite or the best quality of limestone.

Again, it is necessary in bridges, as in some other structures, to determine whether there is any liability of stones to slip on each other. In order that motion shall take place the resultant forces acting on the surface of a stone joint must have an inclination to that surface less than a value which is not well determined and which depends upon the condition of the surface of the stone; it certainly must be less than 70°. The inclination of every resultant force in Fig. 38 to the surface on which it acts is considerably greater than that value and, hence, the stability of friction is certainly secured.

129. Permissible Working Pressures.—The working values of pressures permissible on cut-stone and brick or other masonry must be inferred from the results of the actual tests of such classes of masonry in connection with the results of experience with structures in which the actual pressures existing are known. It is safe to state that with such classes of material as are used in the best grade of engineering structures these pressures will generally be found not to exceed the following limits:

Concrete, 20,000 to 40,000 pounds per square foot.

Cement rubble, same values.

Hard-burned brick, cement mortar joints, 30,000 to 50,000 pounds per square foot.

Limestone ashlar, 40,000 to 60,000 pounds per square foot.

Granite ashlar, 50,000 to 70,000 pounds per square foot.

The masonry arch is at the same time the most graceful and the most substantial and durable of all bridge structures, and it is deservedly coming to be more and more used in modern bridge practice. One of the greatest railroad corporations in the United States has, for a number of years, been substituting, wherever practicable, masonry arches for the iron and steel structures replaced. The high degree of excellence already developed in this country in the manufacture of the best grades of hydraulic cement at reasonable prices, and the abundance of cut stone, has brought this type of structure within the limits of a sound economy where cost but a few years ago would have excluded it. It is obviously limited in use to spans that are not very great but yet considerably longer than any hitherto constructed.

Fig. 40.—Elevation of Luxemburg Bridge
and Sections of Main Span.

130. Largest Arch Spans.—The longest arch span yet built has been but recently completed in Germany at the city of Luxemburg. This bridge has a span of 275.5 feet and a rise of 101.8 feet. It is rather peculiarly built in two parallel parts separated 19.5 feet in the clear, the space between being spanned by slabs or beams of combined concrete and steel. The arch-ring is 4.75 feet thick at the crown and 7.18 feet thick at a point 53.14 feet vertically below the crown where it joins the spandrel masonry. The roadway is about 52.5 feet wide and 144.5 feet above the water in the Petrusse River, which it spans.

Cabin John Bridge, near Washington, D. C.

The longest arch in this country is known as the Cabin John Bridge of 220 feet span and 57.5 feet rise. It is a segmental arch and is located a short distance from the city of Washington, carrying the aqueduct for the water-supply of that city. These lengths of span may be exceeded in good ordinary masonry construction, but the high degree of strength and comparative lightness which characterize the combination of steel and concrete will enable bridges to be built in considerably greater spans than any yet contemplated in cut-stone masonry.

CHAPTER XIII.

131. Cantilever and Stiffened Suspension Bridges.—There are two other types of bridges of later development which have, in recent years, become prominent by remarkable examples of both completed structure and design; they are known as the cantilever and stiffened suspension bridges. Both are adapted to long spans, although the latter may be applied to much longer spans than the former. A cantilever structure, with a main span of 1800 feet between centres of piers, is now in process of construction across the St. Lawrence River at Quebec, while the well-known Forth Bridge across the Firth of Forth in Scotland has a main span of 1710 feet. The longest stiffened suspension bridge yet constructed is the New York and Brooklyn Bridge, with a river span of about 1595.5 feet between centres of towers, but the stiffened suspension system has been shown by actual design to be applicable to spans of more than 3200 feet, with material now commercially produced.

Fig. 41.

Fig. 42.—Monongahela Bridge—Pittsburgh,
Carnegie & Western Railroad (Wabash), at Pittsburgh.

132. Cantilever Bridges.—Figs. 41 and 42 exhibit in skeleton outline two prominent cantilever designs for structures in this country. That shown in Fig. 41 was intended for a bridge across the Hudson River between Sixtieth and Seventieth streets, New York City. The main central opening has a span of 1800 feet, and a length of 2000 feet between centres of towers. Fig. 42 shows the Monongahela River cantilever bridge,[3] now being built at Pittsburgh, Penn. Both figures exhibit the prominent features of the cantilever system. The main parts are the towers, at each end of the centre span, which are 534.5 feet high in the North River Bridge and 135 feet high in the Monongahela River structure, and the central main or river span with its simple non-continuous truss hung from the ends of the cantilever brackets or arms which flank it on both sides. These cantilever arms are simply projecting trusses continuous with the shore- or anchor-arms. They rest on the piers at either end of the main span, as a lever rests on its fulcrum. This arrangement requires the shore extremities or the anchor-arms to be anchored down by a heavy weight formed by the masonry piers at those points. Recapitulating and starting from the two shore ends of the structure, there are the anchor-spans, continuous at the towers, with the cantilever arms projecting outward toward the centre of the main opening and supporting at their ends the suspended truss, which is a simple, non-continuous one. It is thus evident that the cantilever bridge is a structure composed of continuous trusses with points of contraflexure permanently fixed at the ends of the suspended span. The greatest bending moments are at the towers, and the great depth at that point is given for the purpose of affording adequate resistance to those moments by the members of the structure. The following statement shows some elements of the more prominent cantilever bridges of this country and of the Forth Bridge:

The arrangement of web members of cantilever structures is designed to be such as will transfer the loads from the points of application to the points of support in the shortest and most direct paths. Both Figs. 41 and 42 show these general results accomplished by an advantageous arrangement of web members.

It is interesting to note that the first cantilever bridge designed and built in this country was constructed in 1871. This structure was designed and erected by the late C. Shaler Smith, a prominent civil engineer of his day.

133. Stiffened Suspension Bridges.—The stiffened suspension bridge is a structure radically different in its main features and its mode of transferring load to points of support from any heretofore considered, except arched ribs. When a load is supported by a beam or truss, the stresses, either in the web members of the truss or in the solid web of the beams, travel up and down those members in zigzag directions with a relatively large amount of metal required for that kind of transference. That metal is represented by the weight of the web members of the truss and of the solid web of the beam. Again, there are two sets of truss members—the chords or flanges, one of which sustains tension and the other an equal amount of compression. The greater part of this metal must be so placed and used that the working intensities of stress are comparatively small. This is particularly the case in compression members of both chords and webs which constitute the greater portion of the weight of the truss. All compression members are known as long columns which sustain not only direct compression but bending, and the amount of stress or load which they carry per square inch is relatively small, decreasing as the length increases. For all these reasons the amount of metal required for both beams and trusses is comparatively large. In suspension bridges, however, the conditions requiring the employment of a relatively large amount of metal with relatively small unit stresses are absent. The main members of a suspension bridge are the cables and the stiffening trusses, the latter being light in reference to the length of span. The cables are subjected to tension only, which is the most economical of all methods of using metal. A member in tension tends to straighten itself, so that it is never subjected to bending by the load which it carries. The opposite condition exists with compression members. Again, grades of steel possessing the highest ultimate resistance may be used in the manufacture of cables. It is well known that wire is the strongest form in which either wrought-iron or steel can be manufactured. While the ultimate tensile resistance of ordinary structural steel will seldom rise above 70,000 pounds per square inch, steel wire, suitable to be used in suspension-bridge cables, may be depended upon, at the present time, to give an ultimate resistance of at least 180,000 pounds per square inch. The elastic limit of ordinary structural steel is but little above half its ultimate resistance, while the elastic limit of the steel used in suspension-bridge cables is probably not less than three fourths of its ultimate resistance. It is seen, therefore, that the high resistance of steel wire makes the steel cable of the suspension bridge a remarkably economical application of metal to structural purposes.

The latest example of stiffened suspension-bridge is the new East River Bridge reaching across the East River from Broadway in Brooklyn to Delancey Street, New York City, now being built, with a main span of 1600 feet between centres of towers. The entire length of the metal structure is 7200 feet, and the elevation of the centres of cable at the tops of the towers is 333 feet above mean high water.

Fig. 43 shows a view of this bridge. Its three principal divisions are the cables, the stiffening trusses, and the towers. The latter afford suitable points of support for the cables, which not only extend over the river span, but are carried back to points on the land where they are securely attached to a heavy mass of anchorage masonry. These anchorages must be sufficiently heavy to prevent any load which may come upon the bridge from moving them by the pull of the cables. It is usual to make these masses so great that they are capable of resisting from two to two and a half times the pull of the cables.

Fig. 43.—New East River Bridge.

134. The Stiffening Truss.—The function of the stiffening trusses is peculiar and imperatively essential to the proper action of the whole system. If they are absent and a weight should be placed upon the cable at any point, a deep sag at that point would result. If a moving load should attempt to pass along a roadway supported by a cable only, the latter would be greatly distorted, and it would be impossible to use such a structure for ordinary traffic. Some means must then be employed by which the cable shall maintain essentially the same shape and position, whatever may be the amount of loading. It can be readily shown that if any perfectly flexible suspension-bridge cable carries a load of uniform intensity over the span from one tower to the other, the curve of the cable will be a parabola, with its vertex at the lowest point. Furthermore, it can also be shown that if any portion of the span be subjected to a uniform load, the corresponding portion of the cable will also assume a parabolic curve. It is assumed in all ordinary suspension-bridge design that the total weight of the structure, including the cables and the suspension-rods which connect the stiffening trusses to the cable, is uniformly distributed over the span, and that assumption is essentially correct. So far as the weight of the structure is concerned, therefore, the curve of the cable will always be parabolic. It only remains, therefore, to devise such stiffening trusses as will cause any moving load passing on or over the bridge to be carried uniformly to the cables throughout the entire span. This condition means that if any moving load whatever covers any portion of the span, the corresponding pull of the suspension-rods on the cables must be uniform from one tower to the other, and that result can be practically accomplished by the proper design of stiffening trusses; it is the complete function of those trusses to perform just that duty.

135. Location and Arrangement of Stiffening Trusses.—It has been, and is at the present time to a considerable extent, an open question as to the best location and arrangement of the stiffening trusses. The more common method in structures built is that illustrated by the New York and Brooklyn and the new East River bridges. Those stiffening trusses are uniform in depth, extending from one tower to the other, or into the land spans, and connected with the cables by suspension-rods running from the latter down to the lower chords of the trusses. It is obvious that the floor along which the moving load is carried must have considerable transverse stiffness, and hence it may appear advisable to place the stiffening trusses so that the floor may be carried by them. On the other hand, some civil engineers maintain that it is a better distribution of stiffening metal to place it where the cables themselves may form members of the stiffening trusses, with a view to greater economy of material.

Figs. 44, 45, and 46 illustrate some of the principal proposed methods of constructing stiffening trusses in direct connection with the cables. The structure shown in Fig. 44 illustrates the skeleton design of the Point Bridge at Pittsburgh. The curved member is a parabolic cable composed of eye-bars. This parabolic cable carries the entire weight of the structure and moving load when uniformly distributed. If a single weight rests at the centre, the two straight members of the upper chord may be assumed to carry it. If a single weight rests at any other point of the span, it will be distributed by the bracing between the straight and curved members of the stiffening truss. Obviously the most unbalanced loading will occur when one half of the span is covered with moving load. In that case the bowstring stiffening truss in either half of Fig. 44 will make the required distribution and prevent the parabolic tension member from changing its form.

Fig. 44.

Fig. 45.

Fig. 46.

The type of bracing shown in Fig. 45 possesses some advantages of a peculiar nature. Each curved lower chord of the stiffening truss corresponds to the position of the perfectly flexible cable with the moving load covering that half of the span which belongs to the greatest sag of the cable. The two parabolic cables thus cross each other in a symmetrical manner at the centre of the span. If the moving load covers the entire span, the line of resistance or centre line of imaginary cable will be the parabola, shown by the broken line midway along each crescent stiffening truss. The diagonal bracing placed between the cables is so distributed and applied as to maintain the positions of cables under all conditions of loading.

The mode of constructing the stiffening truss between two cables, shown in Fig. 46, is that adopted by Mr. G. Lindenthal in his design for a proposed stiffened suspension bridge across the Hudson River with a span of about 3000 feet. The two cables are parabolic in curvature and may be either concentric or parallel. This system of stiffening bracing possesses some advantages of uniformity and is well placed to secure efficient results. The same system has been used in suspension bridges of short span by Mr. Lindenthal at both St. Louis and Pittsburgh. The stiffening bracing produces practically a continuous stiffening truss from one tower to the other, whereas the systems shown in Figs. 44 and 45 involve practically a joint at the centre of the span.

In all these three types of vertical stiffness the floor is designed to meet only the exigencies of local loading, being connected with the stiffening truss above by suspension bars or rods, preferably of stiff section.

When stiffening trusses are placed along the line of the floor, as in the case of the two East River bridges, to which reference has already been made, those trusses need not necessarily be of uniform depth, and they may be continuous from tower to tower or jointed at the centre, like those of the New York and Brooklyn suspension bridge. This centre joint detracts a little from the stiffness of the structure, but in a proper design this is not serious.

136. Division of Load between Cables and Stiffening Truss.—In a case where continuous stiffening trusses are employed it is obvious that they may carry some portion of the moving load as ordinary trusses. The portion so carried will be that which is required to make the deflection of the stiffening truss equal to that of the cable added to the stretch of the suspension-rods. In the old theory of the stiffening truss constructed along the floor of the bridge this effect was ignored, and the computations for the stresses in those trusses were made by the aid of equations of statical equilibrium only. That assumption, that the cable carried the entire load, was necessary to remove the ambiguity which would otherwise exist. In modern suspension-bridge design those trusses may be assumed continuous from tower to tower with their ends anchored at the towers, or they may be designed to be carried continuously through portions of the land spans and held at their extremities by struts reaching down to anchorages, so that those ends may never rise nor fall, but move horizontally if required. If there are no pin-joints in the trusses at the centre and ends of the main span, equations of statical equilibrium are not sufficient to enable the reactions under the trusses and the horizontal component of cable tension to be found.

One of the best methods of procedure for such cases is that of least work, in which the horizontal component of cable tension is so found that the total work performed in the elastic deflection of the stiffening trusses, suspension-rods, cables, and towers is a minimum. After having found this horizontal component of the cable tension and the reactions under the stiffening trusses, the stresses in all the members of the entire structure can be at once determined. It is obvious that the stiffening truss and the cables must deflect together. It is equally evident that the deeper the stiffening trusses are the more load will be required to deflect them to any given amount, and hence that the deeper they are the more load they will carry independently of the cable. It is desirable to throw as much of the duty of carrying loads upon the cables as possible. It therefore follows that the stiffening trusses should be made as shallow as the proper discharge of their stiffening duties will permit.

137. Stresses in Cables and Moments and Shears in Trusses.—The necessary limits of this discussion will not permit even the simplest analyses to be given. It is evident, however, that the greatest cable stresses will exist at the tops of the towers, and that if the horizontal component of cable tension be found by any proper method, the stress at any other point will be equal to that horizontal component multiplied by the secant of cable inclination to a horizontal line, it being supposed that the suspenders are found in a vertical plane.

If the stiffening trusses are jointed at the centre of the main span, as well as at the ends, the simple equations of statical equilibrium are sufficient in number to make all computations, for the reason that the centre pin-joint gives the additional condition that, whatever may be the amount or distribution of loading, the centre moment must be zero. If l is the length of main or centre span and p the moving load per linear foot of span, and if the stiffening trusses run from tower to tower, the following equations will give their greatest moments and shears both by the old and new theory of the stiffening truss.

	p = load per lin. ft., Old theory.	l = length of span in ft., New theory.
Max. moment	M = 0.01856pl²	M = 0.01652pl²		no centre
Max. shear	S  =  ⅛pl	S  = ⅛pl		hinge.
With centre hinge	M = 0.01883pl² and	S  = ⅛pl

The details of the theory of stiffening trusses for suspension bridges have been well developed during the past few years and are fully exhibited in modern engineering literature. The long spans requiring stiffened suspension bridges are usually found over navigable streams, and hence those bridges must be placed at comparatively high elevations. This is illustrated by the clear height of 135 feet required under the East River suspension-bridge structures already completed and in progress. Furthermore, the heights of towers above the lowest points of the cables usually run from one eighth to one twelfth of the span. These features expose the entire structure to comparatively high wind pressures, which must be carefully provided against. This is done by the requisite lateral bracing between the stiffening trusses and by what is called the cradling of the cables. The latter expression simply means that the cables as they are built are swung out of a vertical plane and toward the axis of the structure, being held in that position by suitable details. The cables on opposite sides of the bridge are thus moved in toward each other so as to produce increased stability against lateral movement. Occasionally horizontal cables are stretched between the towers in parabolic curves in order to resist horizontal pressures, just as the main cables carry vertical loads. This matter of stability against lateral wind pressures requires and receives the same degree of careful consideration in design as that accorded to the effects of vertical loading. The same general observation applies also to the design of the towers.

138. Thermal Stresses and Moments in Stiffened Suspension Bridges.—All material used in engineering structures expands and contracts with rising and falling temperatures to such an extent that the resulting motions must be provided for in structures of considerable magnitude. In ordinary truss-bridges one end is supported upon rollers, so that as the span changes its length the truss ends move the required amount upon the rollers. In the case of stiffened suspension bridges, however, the ends of the cables at the anchorages are rigidly fixed, so that any adjustment required by change of temperature must be consistent with the change of length of cable between the anchorages. The backstays, which are those portions of the cables extending from the anchorages to the tops of the towers, expand and contract precisely as do the portions of the cable between the tops of the towers. As the cables lengthen, therefore, the sag or rise at the centre of the main span will be due to the change in the entire length of cable from anchorage to anchorage. In order to meet this condition it is usual to support the cables at the tops of the towers on seats called saddles which rest upon rollers, so as to afford any motion that may be required. Designs have been made in which the cables are fixed to the tops of steel towers. In such cases changes of temperature would subject the towers to considerable bending which would be provided for in the design.

The rise and fall at the centres of long spans of stiffened suspension bridges is considerable; indeed, for a variation of 120° Fahr. the centre of the New York and Brooklyn Bridge changes its elevation by 4.6 feet if the saddles are free to move, as intended. In the case of a stiffened suspension bridge designed to cross the North River at New York City with a main span of 3200 feet a variation of 120° Fahr. in temperature would produce a change of elevation of the centre of the span of 6.36 feet. Such thermal motions in the structure obviously will produce stresses of considerable magnitude in various parts of the stiffening trusses, all of which are invariably recognized and provided for in good design.

139. Formation of the Cables.—At the present time suspension-bridge cables are made by grouping together in one cylindrical mass a large number of so-called strands or individual small cables, each composed of a large number of parallel wires about one sixth of an inch in diameter. The four cables of the New York and Brooklyn Bridge are each composed of 19 strands, each of the latter containing 332 parallel wires, making a total of 6308 wires, the cables themselves being 15½ inches in diameter. The wire is No. 7 gauge, i.e., 0.18 inch in diameter. In the new East River Bridge each of the four cables is 18¼ inches in diameter and contains 37 strands, each strand being composed of 208 wires all laid parallel to each other, or a total of 7696 wires. The size of the wire is No. 6 (Roebling) gauge, i.e., 0.192 inch in diameter. These strands are formed by laying wire by wire, each in its proper place. The strands are then bound together into a single cable, around which is tightly wound a sheathing or casing of smaller wire, 0.134 inch in diameter for the New York and Brooklyn Bridge. The tightness of this binding wire insures the unity of the whole cable, each wire having been placed in its original position so as to take a tension equal to that of each of the other wires. The suspension-rods are usually of wire cables and are attached by suitable details to the lower chords of the stiffening truss, also by specially designed clamps to the cable. The stiffening trusses are usually built with all riveted joints, so as to secure the greatest possible stiffness from end to end. The stiffened suspension bridge has been shown by experience, as well as by theory, to be well adapted to carry railroad traffic over long spans.

140. Economical Limits of Spans.—In the past, suspension bridges have, in a number of cases, been built for comparatively short spans, but it is well recognized among engineers that their economical use must be found for spans of comparatively great length. While definite lower limits cannot now be assigned to such spans, it is probable that with present materials of construction and with available shop and mill capacities the ordinary truss-bridge may be economically used up to spans approximately 700 to 800 feet, and that above that limit the cantilever system is economically applicable to lengths of span not yet determined but probably between 1600 and 2000 feet. The special field of economical employment of the long-span stiffened suspension bridge will be found at the upper limit of the cantilever system. So far as present investigations indicate, the stiffened suspension type of structure may be employed to advantage from about 1800 feet up to the maximum practicable length of span not yet assignable, but perhaps in the vicinity of 4000 feet. Obviously such limits are approximate only and may be pushed upward by further improvements in the production of material and in the enlargement of both shop and mill capacity.

PART III. WATER-WORKS FOR CITIES AND TOWNS. — CHAPTER XIV.

141. Introductory.—A preceding lecture in this course has shown to what an advanced state the public supply of water to large cities was developed in ancient times. The old Romans, Greeks, Egyptians, and other ancient peoples evidently possessed an adequate appreciation of the value of efficient systems of public water-supply. Very curiously that appreciation diminished so greatly as almost to disappear during the middle ages. The demoralization of public spirit and the decrease of national power which followed the fall of Rome induced, in their turn, among other things, a neglect of the works of the great water system of Rome, entailing their partial destruction. The same retrogression in civilization seemed to affect other ancient nations as well, until probably the lowest state of the use of public waters and the construction of public water systems was reached somewhere between A.D. 1000 and A.D. 1300 or 1400. Without reasonable doubt the terrible epidemics or plagues of the middle ages can be charged to the absence of suitable water-supplies and affiliated consequences. During that middle period of the absence of scientific knowledge and any apparent desire to acquire it, sanitary works and consequently sanitary conditions of life were absolutely neglected. No progress whatever was made toward reaching those conditions so imperative in large centres of population for the well-being of the community. Grossly polluted waters were constantly used for public and private supplies, and no efforts whatever were made among the masses toward the suitable disposition of refuse matters or, in a word, to attain to sanitary conditions of living.

A few important works were completed, particularly in Spain, but nothing indicative of general relief from the depths of ignorance and sanitary demoralization to which the greater portion of the civilized world had sunk at that time. The city of Paris took all its water from the Seine, except that which was supplied by a small aqueduct built in 1183. So small was the supply, aside from the water obtained from the river, that in 1550 it is estimated that the former amounted to about one quart only per head of population per day. The situation in London was equally bad, for it was only in the first half of the thirteenth century that spring-water was brought to the city by means of lead pipes and masonry conduits. Public water-works began to be constructed in Germany on a small scale in the early part of the fifteenth century. Obviously no pumps were available in those early days of water-supply, so that the small systems which have been mentioned were of the gravity class; that is, the water flowed naturally in open or closed channels from its sources to the points of consumption. Pumps of a simple and crude type first began to be used at a point on the old London Bridge in 1582, and in Hanover in 1527. Subsequently to those dates other pumps were set up on London Bridge, and installations of the same class of machinery were made in Paris in 1608, usually operated by water-power in some simple manner, as by the force of the water-currents. In 1624 the Paris supply received a reinforcement of 200,000 gallons per day by the completion of the aqueduct Arcueil. The New River Company was incorporated in 1619 for the partial supply of the city of London, and it began to lay its pipes at that time. As its name indicates, it took its supply from New River, and the inception of its business is believed to mark the first application of the principle of supplying each house with water. This company is still in existence and furnishes a considerable portion of the present London supply.

142. First Steam-pumps.—The application of steam to the creation or development of power by Watt, near the end of the eighteenth century, stimulated greatly the construction of water-works, as it offered a very convenient and economical system of pumping. It seems probable that the first steam-pumps were used in London in 1761. Twenty years later a steam-pump was erected in Paris, while another was installed in 1783. The second steam-pump in London was probably constructed in 1787. In all these earlier instances of the use of steam-pumps river supplies were naturally used.

143. Water-supply of Paris and London.—After the early employment of steam pumping-machinery demonstrated its great efficiency for public water-supplies, the extension of the latter became more rapid, and since 1800 the supplies of the two great cities of London and Paris have been greatly increased. As late as 1890 the Paris supply amounted to about 65 gallons per head of population, one fourth of which was used as potable, being drawn from springs, while three fourths, drawn from rivers, was used for street-cleaning or other public purposes. This supply, however, was found inadequate and was re-enforced in 1892 by an addition of 30,000,000 gallons per day of potable water brought to the city by an aqueduct 63 miles long. Another addition of about 15,000,000 gallons has been provided more recently.

Rather curiously the water-supply of London is afforded by eight private companies, one of which is the old New River Company already mentioned. These companies, with one exception, draw their supply mainly from the rivers Thames and Lea, all such water being filtered. The remaining company draws its water from deep wells driven into the chalk. The total population supplied amounts to about 5,500,000, the rate of supply being thus less than 45 gallons per head per day.

144. Early Water-pipes.—Inasmuch as the use of cast-iron for pipes was only begun about the year 1800, other materials were used prior to that date. As is well known, the pipes used in ancient water-works were either of lead or earthenware. In the eighteenth century wooden pipes made of logs with their centres bored out were used, sometimes 6 or 7 inches in diameter. As many lines of these log pipes were used as needed to conduct a single line of supply. In the earlier portion of the nineteenth century such log pipes, usually of pine or spruce, were used by the old Manhattan Company for the supply of New York City. A section of such a wooden pipe, with a bore of about 2½ inches is preserved in the museum of the Department of Civil-Engineering of Columbia University. Large quantities of such pipes were formerly used.

145. Earliest Water-supplies in the United States.—The earliest system of public water-supply in this country was completed for the city of Boston in 1652. This was a gravity system. It is believed that the first pumping-machinery for such a supply was set up for the town of Bethlehem, Pa., and put in operation in 1754. Subsequently water-supplies were completed for Providence, R. I., 1772, and for Morristown, N. J., in 1791; the latter has maintained a continuous existence since that date. The first use of steam pumping-machinery in this country was in Philadelphia in 1800. This machinery, curiously enough, was largely of wood, including some portions of the boiler; it was necessarily very crude and would perform with 100 pounds of coal only about one twenty-fifth or one thirtieth of what may be expected from first-class pumping-machinery at the present time. Other cities and towns soon began to follow the lead of these earlier municipalities in the construction of public water-supplies, but the principal development in this class of public works has taken place since about 1850.

It is estimated that the total population supplied in 1880 was about 12,000,000, which rose to about 23,000,000 in 1890, and it is probably not less than 50,000,000 at the present time.

146. Quality and Uses of Public Water-supply.—Advances in the public supplies in this country have been made rather in the line of quantity than quality. Insufficient attention has been given both to the quality of the original supply and to the character of the reservoirs in which it is gathered until within possibly the past decade. A few cities like Boston have scrutinized with care both the quality of the water and the character of the bottom and banks of reservoirs, and have spared neither means nor expense to acquire a high degree of excellence in their potable water. The same observations can be applied to a few other large cities, but to a few only. The realization of the dependence of public health upon the character of water-supply, however, has been rapidly extending, and it will doubtless be but a short time before the care exercised in collecting and preparing water for public use will be as great in this country as in Europe, where few large cities omit the filtration of public waters.

The distribution of water supplied for public use is not limited to domestic purposes, although that class of consumption controls public health so far as it is affected by the consumption of water. The applications of water to such public purposes as street-cleaning and the extinguishing of fires are of the greatest importance and must receive most careful consideration. Again, the so-called system of water-carriage in the disposal of domestic and manufacturing wastes, constituting the field of sewage-disposal, depends wholly upon the efficiency of the water-supply.

147. Amount of Public Water-supply.—The first question confronting an engineer in the design of public water-supply is the amount which should be provided, usually stated on the basis of an estimated quantity per head of population. This is not in all cases completely rational, but it is by far the best basis available. If the water-supply is designed for a small city or town previously supplied by wells or other individual sources, the first year’s consumption will be low per head of population for the reason that many people will retain their own sources instead of taking a share of the public supply. As time elapses that portion of population decreases quite rapidly in numbers, and in a comparatively few years practically the whole population will use the public supply. In communities, therefore, where public systems have long existed and it is desired either to add to the old supply or to install new ones, the only safe basis of estimate is the entire population.

148. Increase of Daily Consumption and the Division of that Consumption.—The amount of water required per head of population might naturally be assumed identical with the past consumption, but that would frequently be incorrect. It is one of the most prominent features of the history of public water-supplies in this country that the consumption per head of population has increased with great rapidity from the early years of the installation of the different systems, for reasons both legitimate and illegitimate. The daily average consumption of water from the Cochituate Works of the Boston supply increased from 42 gallons per head of population in 1850 to 107 gallons in 1893, and in the Mystic Works of the same supply the increase was from 27 gallons in 1865 to 89 gallons in 1894. Again, the daily average consumption in Chicago rose from 43 gallons per head per day in 1860 to 147 gallons in 1893, while in Philadelphia during the same period the increase was from 36 gallons per head per day to 150 gallons. In Cambridge, Mass., the increase in daily average consumption per head of population was from 44 gallons in 1870 to 70 gallons in 1894. These instances are sufficient to show that, under existing conditions, the daily consumption was increased at a rapid rate in the cities named, and they have been selected as fairly representative of the whole field. Civil engineers have made extended studies in connection with this question in a great number of cities, for it bears upon one of the most important lines of public works. It is absolutely essential to the health and business prosperity of every city that the water-supply should be abundant, safe, and adapted to the industrial and commercial pursuits of its population. It is imperative, therefore, that the division of the daily supply should be carefully analyzed. For this purpose the water-supply of a city may be, and frequently is, divided into four parts:

• (1) That used for domestic purposes;
• (2) That used for commercial and industrial purposes;
• (3) That used for public purposes;
• (4) That part of the supply which is wasted.

1. That portion of the supply consumed for domestic purposes includes not only the water used in private residences, but in those branches of consumption which may be considered of a household character found in hotels, clubs, stores, markets, laundries, and stables, or for any other residential service. As might be expected, this branch of consumption varies largely from one city to another. The results of one of the most interesting and suggestive studies ever made in connection with this subject are given by Mr. Dexter Brackett, M. Am. Soc. C. E., in the Transactions of the American Society of Civil Engineers for 1895. In Boston the purely domestic consumption varied in different houses and apartments from 59 gallons per head per day in costly apartments down to 16.6 gallons per head per day in the poorest class of apartment. In Brookline, one of the finest suburbs of Boston, the quantity was 44.3 gallons per day. In some other cities of Massachusetts, as Newton, Fall River, and Worcester, this class of consumption varied from 6.6 gallons to 26.5 gallons per day, the latter quantity being found at Newton in some of the best residences, and the former at houses also in Newton having but one faucet each. In Yonkers, N. Y., where the system was metered, the amount was 21.4 gallons per head of population per day, while in portions of London, England, it varied from 18.6 to 25.5 gallons per head per day. The average of these figures gives a result of 18.2 gallons per head per day, which, in round numbers, may be put at 20 gallons.

2. It is obvious that the rate of consumption for commercial and industrial purposes in any city must vary far more than that for domestic purposes, for the reason that some cities may be essentially residential in character while others may be essentially manufacturing. At the same time, it is to be remembered that many manufacturing establishments may have their own water-supply. The city of Fall River, Mass., is eminently a manufacturing city, yet Mr. Brackett found that the manufacturing demand on the public water-supply amounted to 2 gallons only per inhabitant per day, as the manufacturers draw the most of their supply from the river, but that where the manufacturers depend upon the public supply for all their water the amount rises to a value between 20 and 30 gallons per inhabitant. In Boston in 1892 the water consumed for all manufacturing and industrial purposes, including railroads, gas-works, elevators, breweries, etc., amounted to 9.24 gallons per head of population per day, while in Yonkers in 1897 the total consumption for commercial purposes was 27.4 gallons per head per day. In the city of New York, as nearly as can be estimated, the consumption for commercial purposes is probably not far from 25 gallons per inhabitant per day. Reviewing all these results, it may be stated that the water consumption for commercial and industrial purposes will generally range from 10 to 30 gallons per inhabitant per day.

3. The consumption of water for public purposes is a smaller amount than either of the two preceding. It covers such uses as public buildings, schools, street-sprinkling, sewer-flushing, fountains, fires, and other miscellaneous objects, more or less similar to those just named. The total use of this character was 3.75 gallons per inhabitant per day for Boston in 1892, and 5.57 gallons per inhabitant per day for Fall River in 1899. A few other cities give the following results: Minneapolis in 1897, 5 gallons; Indianapolis, 3 gallons; Rochester, N. Y., 3 gallons; Newton, Mass., 4 gallons; Madison, Wis., 10 gallons. In Paris it is estimated that not far from 2.5 gallons per head of population per day are used. It is probable, therefore, that an amount of 5 gallons per day per inhabitant will cover this particular line of consumption.

4. A substantial portion of the water-supply of every city fails to serve any useful purpose, for the reason that it runs to waste either by intention or by neglect. The sources of this waste are defective plumbing, including leaky faucets and cocks; deliberate omission to close faucets and cocks, constituting wilful waste; defective or broken mains, including leaky joints; and waste to prevent freezing.

149. Waste of Public Water.—All these wastes except the last are inexcusable. There is no difficulty in detecting defective plumbing, and its existence is generally known to the householder; but if the wasted water is not measured and paid for, it is far too frequently considered more economical to continue the waste than to pay for the plumber’s services. In a multitude of cases cocks are left open indefinitely for all sorts of insignificant reasons; in closets, under the erroneous impression that the continuous running of the stream will materially aid in a more effective cleansing of soil- and sewer-pipes, failing completely to appreciate that a far more powerful stream is required for that purpose; sometimes in sinks, for refrigerating purposes, and in many other inexcusably wrong ways. These sources of wilful waste lead to large losses and constitute one of the most unsatisfactory phases of administration of a public water system. Such losses result in a vicious waste of public money. The amount of water flowing from leaky joints and from leaks in pipes and mains is necessarily indeterminate because it escapes without evidence at the surface except in rare cases. In every instance where examinations have been made and a careful record kept of the amount of water supplied to a city, it has been found that the aggregate of the measured amounts consumed fail nearly to equal the total supply. There are probable errors both in the measurement of the quantities supplied and in the quantities consumed, but the large discrepancy cannot be accounted for in this manner. In many cases consumed water has even been carefully measured by meters, as at Yonkers, New York, Newton, Milton, and Fall River, Mass., Madison, Wis., and at other places, but yet the discrepancy appears to be nearly as wide as ever. Again, in 1893 observations were carefully made on the consumption of the water received by the Mystic supply of the Boston system at all hours of the twenty-four. Obviously between 1 and 4 A.M. the useful consumption should be nearly nothing, but, on the contrary, it was found to be nearly 60 per cent of the average hourly consumption for the entire twenty-four hours. The waste at Buffalo, N. Y., in 1894 was estimated at 70 per cent of the total supply. Similar observations in other places have given practically the same results. It has also been found that, in a number of instances, where old watercourses have been completely obliterated by considerable depths of filling required by the adopted grades of city streets and lots, and excavations for buildings have subsequently been opened practically the full volume of the former streams are flowing along the original but filled channel. This result has been observed under a practically impervious paved city surface. It is difficult to imagine the source of such a supply except from defective pipe systems or sewers. A flow of a least 100,000 gallons per day from a broken pipe which found its way into a sewer has also been discovered without surface evidence. These and many other results of experience conclusively demonstrate that much water flows to waste unobserved from leaky joints and defective or broken pipes.

Inasmuch as cast-iron water-pipes are produced in lengths which net 12 feet as laid, there will be at least 440 joints per mile. Furthermore, as leaky joints and broken pipes are as likely to occur at one place as another, it seems reasonable to estimate leakage through them as proportionate to the length of the pipe-line in a system; and that conventional law is frequently assumed. New pipe-lines have sometimes shown a leakage of 500 to 1200 gallons per mile of line per day. Civil engineers have sometimes specified the maximum permissible leakage of a new pipe-line at 60 to 80 gallons per mile of line per day for each inch in diameter of pipe, thus permitting 600 to 800 gallons to escape from a 10-inch pipe. In 1888 the late Mr. Chas. B. Brush reported a leakage of about 6400 gallons per mile per day from a practically new 24-inch cast-iron main, 11 miles long, of the Hackensack Water Company, the pressure being 110 pounds per square inch. Tests of water-pipes in German and Dutch cities have been reported as showing less waste than 300 gallons per mile per day, but such low results, unless for very low pressures and short lines, may reasonably be doubted. Obviously losses of this character will probably increase with the age of the pipe. By a very ingenious procedure based upon his own experience, Mr. Emil Kuichling of Rochester, N. Y., reaches the conclusion that a reasonable allowance for the waste from leaky joints and defective pipes is 2500 to 3000 gallons per mile of cast-iron pipe-line per day. If, as is frequently the case, the population per mile of pipe ranges from 300 to 1000, the preceding allowance amounts to 3 to 10 gallons per head of population per day. The loss or waste due to running cocks or faucets to prevent freezing cannot be estimated with sufficient accuracy to receive a definite valuation, but it must be considered an element of the total item of waste.

150. Analysis of Reasonable Daily Supply per Head of Population.—It has repeatedly been found that the losses or wastes set forth in the preceding statements amount apparently to quantities varying from 30 to 50 per cent of the total supply; or, to put it a little differently, the water unaccounted for in even the best systems now constructed apparently may reach one third to one half of the total supply. This is an exceedingly wasteful and unbusinesslike showing. It is probable that the statement is, to some extent at least, an exaggeration. It is practically certain that either the amount supplied or the amounts consumed, or both, are never measured with the greatest accuracy, and that the errors are such as generally swell the apparent quantity wasted. After making judicious use of the data thus afforded by experience, it is probable that the following tabular statement given by Messrs. Turneaure and Russell represents limits within which should be found the daily average supply of water in a well-constructed and well-administered system.

The values given in the preceding table are reasonable and sufficient to supply the legitimate needs of any community, but, as will be shown in the succeeding table, there are cities in this country whose average consumption is more than twice the maximum rate given above.

151. Actual Daily Consumption in Cities of the United States.—The following table exhibits the average daily consumption of water throughout the entire year for the cities given, as determined for the years indicated in the table.

The city of Buffalo shows a daily consumption of 271 gallons per inhabitant, and Allegheny, Pa., 247 gallons per inhabitant. There are a considerable number showing an average daily consumption per inhabitant of 160 gallons or more. All such high averages exhibit extravagant use of water, or otherwise inefficient administration of the water-supply. The reduction of such high rates of consumption is one of the most difficult problems confronting the administration of public works. The use of the meter has proved most efficient in preventing wastes or other extravagant consumption, as in that case every consumer pays a prescribed rate for the amount which he takes.

TABLE I.

• LEGEND:
• (A) = Population per Tap.
• (B) = Per Cent of Taps Metered
• (C) = Consumption per Inhabitant Daily, Gallons.

152. Actual Daily Consumption in Foreign Cities.—It has been for a long time a well recognized fact that the daily use of water in American municipalities is far greater per inhabitant than in European cities. It is difficult to explain the marked difference, but it is probably due in large part to the more extravagant general habits of the American people. Examinations in a number of cases have shown that the actual domestic use of water, at least in some of the American cities, is not very different from that found in corresponding foreign cities. Table II exhibits the consumption of water in European cities, as compiled from various sources and given by Turneaure and Russell.

TABLE II.

These foreign averages, with three exceptions, represent reasonable quantities of water used, and they have been confirmed as reasonable by many special investigations made in this country.

153. Variations in Rate of Daily Consumption.—The preceding observations are all based upon an average total consumption found by dividing the total annual consumption by the number of days in the year. This is obviously sufficient in a determination of the total supply needed, but it is not sufficient in those matters which involve a rate of supply during the different hours of the day, or the amount of the supply for the summer months as compared with those of the winter. As a general rule the greatest supply will be required during the hot summer months when lawn- and street-sprinkling is most active. It appears from observations made in a considerable number of the large cities of the United States that the maximum monthly average consumption may run from about 110 to nearly 140 per cent of the monthly average throughout the year. As an approximate value only, it may be assumed for ordinary purposes that the maximum monthly demand will be 125 per cent of the average.

The daily rate taken throughout the year is considerably more variable than the monthly. There are days in some portions of the year when consumption by hotels and industrial activities is at a minimum. On the other hand, there are other days when those activities are at a maximum and the total draft will be correspondingly high. Experience has shown that the maximum total draft may vary from about 115 to nearly 200 per cent of the average. It is permissible, therefore, to take approximately for general purposes the maximum total daily consumption as 150 per cent of the average. Manifestly any total consumption will have an hourly rate which may vary greatly from the early morning hours, when the draft should be almost nothing, to the forenoon hours on certain days of the week, when the draft is a maximum. These variations have frequently been investigated, and it has been shown that the maximum rate per hour of a maximum day may sometimes rise higher than 300 per cent of the average hourly rate for the year. These considerations obviously attain their greatest importance in connection with the capacity of the plant, either power or gravity, from which the city directly draws its supply. The hourly capacity of the pumps or steam-plant furnishing the supply need not necessarily be equal to the maximum, since storage-reservoirs may be and usually are used; but the capacity of the pipe system leading from such storage-reservoirs must be equal to the maximum hourly rate required.

154. Supply of Fire-streams.—The draft on a water-supply for fire-extinguishing purposes may have an important influence upon the hourly rate of consumption. These observations are particularly pertinent in connection with the water-supply of small cities where the draft of fire-engines may be considered a large percentage of the total hourly consumption. It is obviously impossible to assign precisely the number of fire-streams which may be required simultaneously in a city having a given population, but experiences of a considerable number of civil engineers furnish reasonable bases on which such estimates may be made. Table III exhibits such estimates as made by the civil engineers indicated. It is given by Mr. Emil Kuichling in the Transactions of the American Society of Civil Engineers for December, 1897. Probably no more reasonable estimate can be now presented.

TABLE III.

TABLE EXHIBITING ESTIMATED NUMBER OF
FIRE-STREAMS REQUIRED SIMULTANEOUSLY
IN AMERICAN CITIES OF VARIOUS
MAGNITUDES.