45 JOURNAIv OF THE 



the chord, depending- on the depth of the notch where the 

 rafter joins the chord, and thus not only causes a uniform 

 stress, in the chord but one due to the moment H/^. The 

 maximum fibre stress in the lower chord at a panel point 

 is that due to the above forces combined with that due to 

 the weigfht of the chord, for all of these influences cause 

 tension in the top fibre of the chord at a panel point. 



With a full live load W at each end of both suspended 

 beams, the stresses in the verticals are W as before. So that 

 the stresses in rods, rafters and upper chord are precise- 

 ly the same as for the eccentric load first considered. In 

 this case, the stress in the vertical rods =W, is exactly 

 balanced by the load W held at foot of rod, so there is 

 force tendincr to bend the chord. The dead load stresses 

 are of course to be found and added to those caused by 

 the live load. 



The above theor\' is upon the supposition that the 

 "suspended beams" are not fastened to the lower chords. 

 If they are fastened, a load at one suspended beam only, 

 is partly carried by the chord "acting- as a beam" and 

 partly by the vertical tics. Reasoning- as before, the 

 stresses in the verticals at the other joint are the same as 

 those of the first, giving- an upward pull on the chord 

 where the suspension beams meet it. The lower chord 

 in this case, is bent 'downward at the load and upwards 

 at the other panel points, thus giving- a reverse curva- 

 ture to the chord, so that it can resist bending- much 

 more effectively than in the former case, where it was 

 compelled to act as a lieam with a span equal to the span 

 of the bridge and was acted on b}^ a full panel load. The 

 exact solution for this case cannot be effected by statics 

 alone. Another principle has to be made use of and I have 

 availed m^^self of the "principle of least work, for which 

 see an article by the writer in the Transactions of the 

 American Society of Civil Engineers for April, 1891. 



In this article, the writer deduced the principle of least 

 work, with effect of temperature changes included, by 



