# Bridge Analysis

## built, bridges, truss, trusses, fig and arch

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BRIDGE ANALYSIS Introduction. The following treatment of the subject of Bridge Analysis, while not exhaustive, is regarded as sufficiently elaborate to develop and instill the principal theoretical considera tions, to illustrate the most convenient and practical methods of analyzing the common forms of trusses and girders, and also to lay a sufficient foundation for the analysis of such other trusses as are not specifically mentioned or treated herein.

The necessary steps and operations required for a proper analysis of the several types of bridges are fully demonstrated by sketches and computations, the numerical values being mechanically obtained by the use of a slide rule, which is a handy instrument for quickly performing the operations of multiplication and division, and for squaring and extracting the roots of numbers. The values given may differ from the exact value by one unit in the second decimal place (seldom more) and are sufficiently accurate for the purpose of design. All bridge computers should be proficient in the use of the slide rule.

The problems given in the back of this Instruction Paper, exemplifying the practical application of the subject-matter treated in the various articles, should be solved by the student as each article is mastered.

Early Bridges. Early bridges were not bridges according to the present conception of the term. They were simple pile trestle bents placed at frequent intervals and connected by wooden beams on which the floor was placed. The Pans sublicius, built over the Tiber, at Rome, about 650 years before Christ was born, was of this trestle type. Also the famous bridge Built by Cæsar across the Rhine in 55 B. C. was of the same kind of construction. As civiliza tion progressed, the arch type was developed; and in 1390 the great Copyright, 19o3, by Amencan School of Coreapondence.

bridge at Trezzo over the River Adda was built of one span of 251 feet, which has never been eclipsed or equaled.

3. Truss Bridge Development. The first truss bridge is sup

posed to have been originated by Palladio, an Italian, who used the king-post truss (Fig. 1) about 1570. Its importance was not recog nized, and it became entirely for gotten until it was rediscovered in 1798 by Theodore Burr, an Ameri can, who used it in his construction.

About the same time, Burr invented the truss that bears his name, which was in reality a series of king-post trusses (see Fig. 8). This was found to be unstable under moving loads, and was therefore stiffened by the use of an arch (Fig. 2), or was built somewhat as an arch, there being considerable rise at the center of the span (Fig. 3). By 1830 the principle of the double cross-bracing in the panel was understood; and in quick succession came the patents of Long, Howe, Pratt, and Whipple on forms of trusses which bear their respective names.

It remained for Squire Whipple in 1847 to place the science of bridge building on a rational and exact mathematical basis such as is now used. Previous to this time, and indeed several years afterwards—for Whipple's work did not become generally known until a much later date—bridges were built, not from previously computed strains, but by "judgment." All parts of a bridge were made of the same size, and if one started to fail it was replaced by a larger one; or small models were made and loaded proportionally, broken metnbcrs being replaced by larger ones. There is no doubt that many of the bridges built at this period were very weak as well as very strong. The failures are not remembered; but the sound judgment of many of our earlier bridge engineers is recorded in the wooden structures they left behind them, some of which have stood the demands of traffic for over a century. After 1850, bridges were built from computed stresses; wood was discarded; and the develop ment became rapid, until about 1870, when the introduction of sub diagonal systems brought the truss system to practically what it is to-day.

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