PREFACE. The following pages are divided into three chapters. The first presents by way of intro-, duction some of the elementary principles of continuous girders, and the fundamental ideas relating to the calculation of strains. The second gives the theory of dexure as applied to the continuous t I sogf constant cross section, and exhibits it infbfbi. hplze I to VI, ready for application to any particular case and the third gives an example of the computation of strains in a continuous truss of five unequal spans, with some useful hints concerning the practical building of such bridges. The theory of flexure. indicates that, by the use of continuous instead of single span bridges, a saving in material of from twenty to forty per cent. may be effected. . It is easy in deed to say that thisadvantage will be entirely swallowed up by the effect of changes of temperature, increased labor of erection, or additional cost of workmanship, but by no amount of reasoning can such disadvantages be estimated. Theory indicates a large saving, whether or not it can be realized. may only be determined by trial. Other nations have built and are building continuous bridges, and their experience has not yet shown that the system is inferior to that of single spans. The interest now prevailing among American engineers in the subject, and the fact that at some recent bridge lettings plans have been offered for a continuous structure, seem to indicate that the system will also be tried here. This little book may then perhaps be of value to bridge engineers, as well as to students in general. 11. M. New Haven, Conn., July 10,1876. THEORY AND CALCULATION CONTINUOUS BRIDGES, W IEN a straight bridge consists of several spans, each entirely independent of the others, it is said to be composed of simnple girders. If, on the other hand, it consists of a single truss extending from one abutment to the other without any disconnection of parts over the piers it is called a continuous girder. A load placed upon any span of a continuous beam influences, to some extent, each of the other spans, and hence its complete theory is much more complex than that of the simple one. This very complexity however has rendered the subject an attractive one to mathematicians, who, pursuing science for sciences sake, have investigated the laws of equilibrium which govern it. These laws with the many beautiful consequences attending them form one of the most interesting chapters of mathematical analysis, and as such have interest and value independent of their application in engineering art. It is the object of the present paper to present in as simple a form as possible some of the main principles and lams most needed by the engineer, and to illustrate their application as fully as space will permit to the practical designing of continuous bridges. . The first point to be observed in considering either a simple or continnous girder is that all the exterior forces which act npon it are in equilibrinm. The exterior forces embrace the weight of the girder and the loads npon it which act clownnrard, and the pressures or re actions of the supports which . act np ward. In order that these may be in equilibrium, it is necessary that the sum of the reactions of all the twpports musfi 6e equal to the total weiqht of the girder am-2 its load. Thus, if a simple girder of uniform section and weight rest at its ends upon two supports, the reaction of each sup port will be one-half the weight. Exactly in the center between the two supports or abntments, let us suppose a pier to be placed just touching, but not pressing against the beam, which, at that point, has a deflection below ... --This text refers to the Paperback edition.