45 6 PROBLEMS 



PROBLEM 22. WIND LOAD STRESSES IN A TRESTLE BENT. 



(a) Problem. Given a trestle bent, height 45'-o", width at the 

 base 3o'-o", width at the top 9'-o", wind loads P , P 2 , P 8 , P 4 , as shown. 

 Calculate the stresses in the members of the bent due to wind loads by 

 algebraic moments and check by calculating the stresses by graphic 

 resolution. Assume the diagonal members to be tension members, and 

 that the dotted members shown are not acting. Scale of truss, i" = 

 lo'-o". Scale of loads, i" = 2000 Ibs. 



(b) Methods. ( i ) Algebraic Moments : To calculate the stresses 

 in the diagonal members take center of moments about the point A, 

 the point of intersection of the inclined posts. Then to calculate stress 

 in 12, take section cutting 12, i X and 2 F; assume the external 

 force as acting from the outside toward the cut section, and we have 

 1-2 X 15.9 + 3000 X 19.3 = o and 1-2 = 3640 Ibs. Stresses in 3-4, 

 5-6, 2-3, 4-5 and 6-X are found in a similar manner. To obtain reac- 

 tion R 1 take moments about (h), and R t X 30 + 2000 X 15 + 2000 X 

 30 + 3000 X 45 = o and R 1 = --{- 7500 Ibs. = R^. To calculate 

 stresses in 2-Y, 4-F and 6-Y, take moments about (b), (c) and (d), 

 respectively. To calculate stresses in 3-X and 5-X, take moments 

 about (f) and (g), respectively. (2) Graphic Resolution: The loads 

 P , P 2 , P 3 and P 4 are laid off horizontally as shown, and with load P x 

 at (c) the stress triangle F-2-4 is drawn. The remainder of the solu- 

 tion can be easily followed. 



(c) Results. For the reason that the wind may blow from the 

 opposite direction, both sets of stresses must be considered in de- 

 signing each leg. 



PROBLEM 22a. WIND LOAD STRESSES IN A TRESTLE BENT. 



(a) Problem. Given a trestle bent, height 45'-o", width at the 

 base 3o'-o", width at the top g'-o", wind loads P x , P 2 , P 8 , P 4 , as shown, 

 and P = 3ooo Ibs. acting 8'-o" above top of trestle. Calculate the 

 stresses in the members of the bent due to wind loads by algebraic 

 moments and check by calculating the stresses by graphic resolution. 

 Assume the diagonal members to be tension members, and that the 

 dotted members shown are not acting. In solving the stresses by 

 graphic resolution continue the posts up to the line of P and substi- 

 tute an auxiliary panel to transfer P to the bent. Scale of truss, i" = 

 lo'-o". Scale of loads, 1^ = 3000 Ibs. 



