76 



STRESSES IN SOLID BEAMS. 



Art. 57. 



the remaining joints. If joints 6 and 7 be next used, the tenta- 

 tive stress diagrams DEQ'P'D and P'Q'R'O'P' may be drawn, 

 using any value for EQ'. This will give the true value of PQ, 

 as it lies between the parallel lines DP' and EQ'. Now if joint 

 5 be considered, it is seen that must lie on a line parallel to 

 ON of the truss, from N of the stress diagram, and that also 

 it must lie at the apex of the triangle O'P'Q', which has its base 

 P'Q' in the lines DP' and EQ' . "From this the true locations of 

 the other parts of the stress diagram are evident. 



The stresses will be the same in symmetrical members of 

 the truss, as the loads are symmetrical, but both halves of the 



Fig. 53. 



stress diagram should be drawn, in order to check the work. 

 The completed diagram should close. 



57. Stresses in Solid Beams. The method of sec- 

 tions must be used for finding the stresses in solid beams and 



girders (49). Fig. 54 shows a 

 solid beam (stick of timber or 

 girder) cut by a section pq. Either 

 the part to the left or to the right 

 of pq may be considered, but not 

 both. Considering the part to the 

 left of pq, and writing equations 

 Fig 54 of equilibrium between the forces 



acting on this part, we have 



2 vert, comps. =0=R l P l P 2 shearing stress at section: 

 or the shear at the section = the shearing stress at the section. 



2 moments about C =0=R 1 a-P l (a-l l ) -P 2 (a-l 1 -l 2 ) - 



