Art. 58. 



STRESSES IN TRUSSES. 



77 



~~-i L 1 



moment of the stresses at the section; or the bending moment at 

 the section = the moment of resistance at the section. 



The distribution of the shearing and bending stresses over 

 the cross section is discussed . 



under the theory of flexure, Chap- 



I * Mr 



ter VI. 



Fig. 55 shows a similar case 

 with a uniform load. 



2 vert, comps. =0=R l wa 

 shearing stress at the sec- 

 tion pq] or the shear at the section = the shearing stress at the 

 section =R 1 wa. 



3 moments about C = Q = R 1 a waXVi^ mome nt of the 

 stresses at the section ; or the bending moment at the section = 

 the moment of resistance at the section. M = M & = R 1 ay 2 wa". 



The uniform load to the left of the section is wa; it is treated 

 as a concentrated load at its center of gravity ; hence its lever arm 

 is l / 2 a and in the bending moment for uniform load there will al- 

 ways be a term of the form y 2 wa 2 . 



58. Stresses in Trusses. Algebraic Solution. In a truss 

 it is also often convenient to speak of the shear at a section (in a 

 panel since this is constant) and the bending moment at a section 

 (at a joint since this is the most convenient point in finding the 

 resisting stresses), but these are resisted by members in direct 

 tension and compression. 



In Fig. 56, for >A 



example, the part to 

 the left of the section 

 which cuts the 

 stresses U, D, and L 

 is considered. The 

 shear in the panel 

 resisted by the ver- 

 tical components of 

 U and D (2 vert, comps. 0). The bending moment at any 

 point is resisted by the sum of the moments of U, D, and L about 

 the same point. 



In Fig. 33, the chords being parallel they take no shear, so 

 that, taking successive sections, the vertical component of aB = 



