66 STRESSES IN BRIDGE TRUSSES 



It will be seen that the coefficients for the web stresses are equal 

 to the shear in the respective panels. Having found the shears in the 

 different panels of the truss, the remaining coefficients may be found 

 by resolution. Pass a section through any panel and the algebraic sum 

 of the coefficients will be equal to zero. Therefore, if two coefficients 

 are known, the third may be found by addition. 



Beginning with member i-x, which is known and equals 3; 

 coefficient of 2,-x = ( 3 3) = + 6 ; 

 coefficient of 3-3; = (+ 6 + 2) = 8; 

 coefficient of 4-* = ( 8 2) = + 10 ; 

 coefficient of 5-37 = (+ 10 + i) = n ; 

 coefficient of 6-x = ( n I ) = + 12 ; 

 coefficient of j-y = (+ 12 + 0) = 12 . 

 Loading for Maximum Stresses. The effect of different positions 

 of the loads on a Warren truss will now be investigated. 



Let the truss in Fig. 43 be loaded with a single load P as shown. 



Web Stresses 



Chord Stresses - Coefficients x Ptan0 



CoefxP 5 ec6^/ V^ -i/V* -4/V4 - 



-? -f -f 



Coefficients for One Load. 



FIG. 43. 



6 P 



The left reaction, R^ = ~P, and the right reaction, R 2 = -y . The 



stress in i-y = y- P tan 6, and stress in i-x = + -y F sec The 



6 1 



stress in 1-2 = -y- P sec and stress in 2-3 _ = -y- P sec 0, 



etc. The remaining coefficients are found as in the case of dead loads 

 by adding coefficients algebraically and changing the sign of the result. 

 In Fig. 44 the coefficients for a load applied at each joint in turn 

 are shown for the different members; the coefficients for the load on 

 left being given in the top line. 



