TRUSSED BEAMS, ETC. 



635« 



because the deflection at B, due to W in Fig-. 13, corresponds to the 

 deflection at C, due to W in Fig. 14 — 



^ W 6/ Ei ^ 



and, putting {1 -a) for a, in order to transfer the origin to the right 

 hand end, or, what is the same thing, to obtain a formula applicable^ 

 to Fio-. 14- 



W 



= ^^'^ ^. 2/ (I - '0 - ?/ - (^- '^y ^> 



6/Ei C ^ 3 



and, as in previous calculation — 



„ 4_„i_= ^^' (3Z — 4/,) 

 ^K^ R OEI ^ '^ 



■ ■ J^.2— 2// (3/ - 4./ J 



This equation for Kj? combined with the ordinary statical 

 equations, enables us to calculate the bending moment at any point 

 between an abutment and a post, as the load moves from one of these 

 jjoints to another. 



The diagram. Fig. 16, shows portions of a few cui-ves, each of 

 which corresponds to a certain value of /i, i.e., to a cei'tain spacing- 

 of the posts. The abscissae represent different distances of the load 

 from an abutment : ordinates represent bending moments. In this 

 way, we ascertain, graphicallv, Avhat position the load on one of 

 the end bays corresponds to a maximum value of the bending 

 moment at the point of application of the load. 



This diag-ram has to be considered simultaneously with that in 

 Fig. 13. Comparing them, Avith the object of finding what spacing of 

 the posts would corresjiond to equalitv' of bending moment at mid- 

 span and in end bay, under a moving load, Ave find that, when li = 

 0247/, these two bending moments are equal. This is found in Fig. 

 16 by interpolation between the curves for 'i="24/ and I^ = "25l. The- 

 load is at about two-thirds of the length of the end bay, i.e., | of h, 

 from the end of the beam, when the maximum bending- moment 

 occurs in the end bay. The common A^alue of the bending moments, 

 here referred to, is 0'079 W/. Fig. 13 shows that any lesser value of 

 /[ than 0'247 I^ corresponds to a greater bending moment at mid- 

 span than 0'079 WI, while Fig. 16 shows that any greater value of l-^ 

 than 0'247 I corresponds to a greater bending- moment in the end 

 bay than 0"079 W/. The diagram in Fig. 13 also shows that the 

 bending moment at a post, when the load is there, is, for the said 

 spacing of the posts, much less than the bending- moment at mid- 

 span or the maximum one in the end bay when the load is at these 

 latter points. We conclude, therefore, that the best positions for 



