96 SIMPLE GIRDERS. [CHAP. VH. 



easily found according to the preceding Art., while the maxi- 

 mum moments will be given by the ordinates to the parabola 

 for full live and dead load [Fig. 30, Art. 44]. For a framed 

 structure, we have simply to multiply the shear at any point 

 by the secant of the angle which the brace at that point 

 makes with the vertical, in order to find the strain in that 

 brace. The moment, divided by the depth of truss at the point 

 in question, gives the strain in the flanges. For & plate girder, 

 the moment being found as above, and one dimension as the 

 depth given, we can, from Art. 52, so proportion the other di- 

 mension as that the strain in the outer fibre shall not exceed 

 the amount allowable in practice. The preceding Art. as also 

 Arts. 78 and 44 and 52 are all that we need to refer to for all 

 practical cases of parallel flange girders of large span. 



The preceding will complete our discussion of the simple 

 girder. We have only to remark here that the strains due to 

 rolling load will, in general, be most satisfactorily found by the 

 method of resolution of forces, as illustrated in Art. 12. By 

 this method we first find the reactions at the supports for a sin- 

 gle apex load, either graphically or by a simple calculation 



, and then follow this reaction through the 



girder, and find the resulting strains. We can thus find and 

 tabulate the strains in every piece due to a weight at each and 

 every apex. The maximum strains can, then, be easily taken 

 from the table thus formed. When the live load is supposed 

 thus concentrated at each apex, it is, as we have seen in Art. 12, 

 unnecessary to follow through every reaction. The reactions 

 due to the first and last weights are sufficient to fill out the 

 table. For solid-built beams or plate girders, the principles of 

 the present Chap., therefore, come more especially into play. 

 (See also remarks at close of Chap. Y.) * 



The preceding principles will, it is hoped, be found sufficient 

 to enable the reader to find the maximum moments and shear 

 at each and every cross-section of a beam of given span rest- 

 ing simply upon two supports, and acted upon by any given 

 forces or system of forces in any given position. The reader 

 will do well to take examples of simple trusses, and check the 

 results obtained by the method given in Chap. I. by the above 

 principles. The method of tabulation of single apex loads 



