ELISHA MITCHELL SCIENTIFIC SOCIETY. 50 



On adding- the expressions (3), (7) and (8), we find 

 for the total elastic work of one truss, neg-lectino- con- 

 stants, 



1 r ^ 



[58960/ ^— 597250j^] j (9). 



2E L J • 



By the principle of least work, the derivative of this 

 with respect to p must be placed equal to zero in order to 



find A 



117920/)— 597250=0 



. •. /r=5.07. 



So that the chord, acting- as a beam, sustains a down- 

 ward force at the left po^t of about 5 thousand pounds 

 and an upward force at the rig-ht post of 9.5 — f> or about 

 4.5 thousand pounds, causing- the chord to bend dovvn- 

 at the left post and upward at the right post. This 

 reversed curve assumed by the chord causes it to be more 

 efficient as a beam than in the preceding- bridg-e exam- 

 ined. 



The value of the reactions of the chord, acting- as a 

 beam, at the ends, we have seen to be, 

 /— 3.17 = 1.90 and 

 6.33— ;5-1.26; 



thus g-iving" the greatest moment at the left post equal to 

 1900x15=28500 foot lbs. 

 If we allow, by the usual formula, 1200 pounds per 

 square inch fibre stress the chord, for a depth of 16 

 inches, should be 6.6 inches wide in place of the 6 inches 

 assumed. Certain chang*es of temperature will increase 

 this width still further as we shall see. 



INFLUENCE OF CHANGE OF TEMPERATURE. 



The linear expansion of iron, per unit of leng-th, for each 

 decree centig-rade (1°C), is 1-82500. 



Suppose the bridge put together at 10°C (50°F) and that 



