Encyclopaedia Britannica, 11th Edition, Volume 4, Part 3 / "Brescia" to "Bulgaria"

where the summation extends to all the loads to the left of a b. If the loads on the right of the section are considered the expressions are similar and give the same results.

If A_t A_c are the cross sections of the tension and compression flanges or chords, and h the distance between their mass centres, then on the assumption that they resist all the direct horizontal forces the total stress on each flange is

H_t = H_c = M/h

and the intensity of stress of tension or compression is

f_t = M/A_th,

f_c = M/A_ch.

If A is the area of the plate web in a vertical section, the intensity of shearing stress is

f_x = S/A

and the intensity on horizontal sections is the same. If the web is a braced web, then the vertical component of the stress in the web bars cut by the section must be equal to S.

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,

R_x-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,

Hh = M.