. Graphic statics, with applications to trusses, beams, and arches. 1 See Trans. Am. Soc. C. E., Aug., 1895. ROOF-TRUSSES. 73 gravity o) the section. In addition, F is the direct compression stress and F the shearing stress at the section. We thus see that the stress at the section is made up of: i. A bending stress, the bending moment (M) being the moment of the resultant external force on either side of the section, taken about the centre of gravity of the section. If we let / =. Fig. 44. moment of inertia of the section about the neutral axis throughthe centre of gravity, and y the distance
. Graphic statics, with applications to trusses, beams, and arches. 1 See Trans. Am. Soc. C. E., Aug., 1895. ROOF-TRUSSES. 73 gravity o) the section. In addition, F is the direct compression stress and F the shearing stress at the section. We thus see that the stress at the section is made up of: i. A bending stress, the bending moment (M) being the moment of the resultant external force on either side of the section, taken about the centre of gravity of the section. If we let / =. Fig. 44. moment of inertia of the section about the neutral axis throughthe centre of gravity, and y the distance from this neutral axis tothe most compressed fibre, we have for the maximum intensityof the bending (compression) stress M (1) 2. A uniformly distributed compression stress, F = Dx,whose intensity is F u= A (2) 74 GRAPHIC STATICS. 4= area of section. Combining (i) and (2), the maximumintensity of the compression stress will be t t . M F (3) 3. A transverse shearing stress, F = xP. This last stresswill usually be comparatively small in the case of arches. 55. Bending Moments Proportional to Vertical the case of vertical loads, the bending moments are propor-tional to the vertical intercepts between the line of pressure andthe centre line of the arch ring. Proof: Let RS (Fig. 45) be a portion of the centre line of an arch, the corresponding por-tions of the force diagram anda line of pressure being n be any section of thearch, nx being drawn perpen-di
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