TRUSSED BEAMS, ETC. 641 



The writer is indebted to Professor Nanson for this simple 

 formula expressing the relation between S// and %, when the loading 

 is symmetrical. 



As an example of unsymmetrical loading, take the case when the 

 load, W, is at B : then, if we neglect squares and higher powers of 

 small quantities, it will be found that d will rise as much as b will 

 fall, and c will remain nearly unchanged in height. Reasoning, 

 similar to that given above, shows that this will not be far from the 

 truth when the deflections are small. This whole matter has still, 

 however, to be worked out. Perhaps a closer approximation may be 

 found necessary. 



It is evident that the maximum tension in the rods — -in fact, the 

 maxima longitudinal stresses throughout — occur when the isolated 

 load is at C, because, then, no portion of the load is transmitted to 

 the abutments by the beam, acting as a beam. 



An Ex-perirtiental Method of Determining Stresses in Trussed 

 Beams, similar to that frequently employed in solving problems con- 

 nected with ordinary continuous beams, gives a sufficiently close 

 approximation to the stresses in definite cases. Possibly, when there 

 are three, or more, posts, this method may prove more convenient 

 than the mathematical one. As an illustration, a description may be 

 given of the way in which the forces, Ri, R2, and R3, have been 

 determined in the case of a triple-post trussed beam, loaded with a 

 central load. For this method, one requires, in the first place, a 

 imiform, flexible bar; secondly, a firm, level surface to work on; 

 thirdly, a number of short columns of equal height; fourthly, a 

 number of weights; and fifthly, several accurate spring balances. 



The bar requires to be flexible, because, in most cases, the 

 accuracy of our work depends upon our measurement of the heights 

 of various parts of it above tlie level surface, and, the more flexible 

 the bar is, the less effect upon the result will a small error in this 

 measurement have. A steel straight-edge, about 6 ft. long, such as 

 is used in a drawing office, answers the purpose well. The writer has 

 also seen a long, straight-grained strip of wood used for a similar 

 pui-pose. 



Referring to the curved lines in Figs. 27 and 28, where the 

 deflections of the beam are shown on an exaggerated scale, it will 

 be seen that, under the central load, there assumed, the points A 

 and E, only, will remain at their original level ; C will fall below 

 tliat level ; B and D will rise above it. 



We may, first, determine values of Rj, Ro, and R3, corresponding 

 to diffei'ent values of W, without allowing for the weight of the beam, 

 and, afterwards, modify our results in such a way as to allow for this. 



We have R^ ( = R3) and W, acting downwards, and Ro acting 



e . 



upwards at C, R2 cos ^ acting upwards at B and D (Fig. 28). 



We apply weights at A, C, and E, and support the points B, C, 

 and D by means of spring balances. 



The weights applied at A and E are equal in each experiment, 

 wliile the weight at C is adjusted, relatively to them, until the spring 

 balances at B, C, and D show upward forces acting there, nearly in 



a Q . . 



the proportion cos „ : 1 ^ cos -* 



