21. Method of Sections. A. Ritter's Method.—In the case of braced structures the following method is convenient: When a section of a girder can be taken cutting only three bars, the stresses in the bars can be found by taking moments. In fig. 38 m n cuts three bars, and the forces in the three bars cut by the section are C, S and T. There are to the left of the section the external forces, R, W1, W2. Let s be the perpendicular from O, the join of C and T on the direction of S; t the perpendicular from A, the join of C and S on the direction of T; and c the perpendicular from B, the join of S and T on the direction of C. Taking moments about O,
Rx-W1(x+a)-W2(x+2a) = Ss;
taking moments about A,
R3a-W12a-W2a = Tt;
and taking moments about B,
R2a-W1a = Cc
Or generally, if M1 M2 M3 are the moments of the external forces to the left of O, A, and B respectively, and s, t and c the perpendiculars from O, A and B on the directions of the forces cut by the section, then
Ss = M1; Tt = M2 and Cc = M3.
Still more generally if H is the stress on any bar, h the perpendicular distance from the join of the other two bars cut by the section, and M is the moment of the forces on one side of that join,