48 STRESSES IN ROOF TRUSSES 



The loads are laid off, the reactions found, and the stresses calcu- 

 lated beginning at joint L , as explained in Fig. 27. The stress diagram 

 for the right half of the truss need not be drawn where the truss and 

 loads are symmetrical as in Fig. 30; however it gives a check on the 

 accuracy of the work and is well worth the extra time required. The 

 loads Pj_ on the abutments have no effect on the stresses in the truss 

 and may be omitted in this solution. 



In calculating the stresses at joint P 3 , the stresses in the members 

 3-4, 4-5 and .r-5 are unknown, and the solution appears to be in- 

 determinate. The solution is easily made by cutting out members 4-5 

 and 5-6, and replacing them with the dotted member shown. The 

 stresses in the members in the modified truss are now obtained up to 

 and including stresses >-x and 6-7. Since the stresses 6-,r and 

 6-7 are independent of the form of the framework to the left, as can 

 easily be seen by cutting a section through the members 6-jtr, 6-7 

 and 7-3', the solution can be carried back and the apparent ambiguity 

 removed. The ambiguity can also be removed by calculating the stress 

 in 7-3' by algebraic moments and substituting it in the stress diagram. 

 It will be noted that all top chord members are in compression and all 

 bottom chord members are in tension. 



The dead load stresses can also be calculated by any of the three 

 remaining methods, as previously described. 



Dead and Ceiling Load Stresses. The stresses in a triangular 

 Pratt truss due to dead and ceiling loads, are calculated by graphic 

 resolution in Fig. 31. 



For simplicity the stresses are shown for one side only. The re- 

 action R-L is equal to one-half of the entire load on the truss. The solu- 

 tion will appear more clear when it is noted that the stress diagram 

 shown consists of two diagrams, one due to loads on the upper chord 

 and the other due to loads on the lower chord, combined in one, the 

 loads in each case coming between the stresses in the members on each 

 side of the load. The top chord loads are laid off in order downward, 

 while the bottom chord loads are laid off in order upward. 



