428 PROBLEMS 



PROBLEM 8. STRESSES IN A ROOF TRUSS BY GRAPHIC AND ALGEBRAIC 



RESOLUTION. 



(a) Problem. Given a Fink truss, span 4o'-o", pitch 30 ; trusses 

 spaced i2'-o"; load 40 Ibs. per sq. ft. of horizontal projection. Calcu- 

 late the reactions by means of force and equilibrium polygons. Cal- 

 culate the stresses by graphic resolution, and check by algebraic resolu- 

 tion. Scale of truss, i" = 8'-o". Scale of loads, i" = 6ooo Ibs. 



(b) Methods. Start force polygon at (6.25", 5.6"). Lay off 

 the loads in the order P , P 2 , P\, from the top downward. Construct 

 a force polygon, and draw an equilibrium polygon as in Fig. 14, and 

 calculate the reactions R^ and R 2 by means of the closing line as in 

 Fig. 15. Construct stress diagram beginning at L and analyzing the 

 joints in the order, L , U lt L^ U 2 , etc., checking at L' . Arrows acting 

 toward joints in the truss and toward the ends of the lines in the 

 stress diagram indicate compression, while arrows acting away from 

 the joints and ends of lines respectively, indicate tension. Use one 

 arrow in the stress diagram the first time a force is used, and two 

 arrows the second time. In algebraic resolution the sum of the hori- 

 zontal components at any joint are placed equal to zero, and the sum 

 of the vertical components are placed equal to zero, and the solution 

 of these two sets of equations gives the required stresses. 



(c) Results. The top chord is in compression, while the bottom 

 chord is in tension. In the Fink truss it will be seen that the long web 

 members are in tension, while the short web members are in com- 

 pression. This makes the truss a very economical one. 



PROBLEM 8a. STRESSES IN A ROOF TRUSS BY GRAPHIC AND ALGEBRAIC 



RESOLUTION. 



(a) Problem. Given a Fink truss, span 4o'-o", pitch ^3 ; trusses 

 spaced i4'-o" ; load 40 Ibs. per sq. ft. of horizontal projection. Calcu- 

 late the reactions by means of force and equilibrium polygons. Cal- 

 culate the stresses by graphic resolution, and check by algebraic resolu- 

 tion. Scale of truss, i" = 8'-o". Scale of loads, i" = 5ooo Ibs. 



