Stresses in structural steel angles : with special tables . , is indicated in Fig. 7. Forsuch a condition the restraint which each angle exerts uponthe other may be assumed to produce a deflection in the planeof bending and the neutral axis may be assumed to be per-pendicular to the connected legs. The loading for each anglewill then be equivalent to some loading in a plane passingthrough 0, the center of area of the section, and through thevertices bc and de of the section modulus polygon, which isindicated for each angle in Fig. 8. Let m denote the bendingmoment for one angle, which if actin
Stresses in structural steel angles : with special tables . , is indicated in Fig. 7. Forsuch a condition the restraint which each angle exerts uponthe other may be assumed to produce a deflection in the planeof bending and the neutral axis may be assumed to be per-pendicular to the connected legs. The loading for each anglewill then be equivalent to some loading in a plane passingthrough 0, the center of area of the section, and through thevertices bc and de of the section modulus polygon, which isindicated for each angle in Fig. 8. Let m denote the bendingmoment for one angle, which if acting in the plane of 0, bc,and de would produce the same deformations as those whichresult from the actual loading for the pair of angles. The 16 STRESSES IN STRUCTURAL STEEL ANGLES actual moment must be equal to the resultant of the twomoments m, or M = 2m sin 6, . . (29) in which M = actual bending moment for the pair of angles;m = equivalent bending moment for one angle;6 = angle which the plane for m makes with theneutral axis for the pair of angles,. Fig. 8. The bending stress for each angle is equal to m divided bythe section modulus in its plane, or /= M2s sin d (30) in which / = unit stress at the extreme fiber; s = section modulus for the plane of m. In Eq. (30), the value of s sin 6 may be considered as theequivalent section modulus for one angle of the pair for halfof the total vertical load. For the case illustrated, this valueis equal to the y-coordinate of be, for the edge BC of the angle,or to the ^-coordinate of de for the edge DE of the angle. THEORY AND DISCUSSION 17 Thus, for angles in pairs, the equivalent section modulus forone angle can be obtained directly from a table of coordinatesof section modulus polygons. However, even this is unnec-essary if a table of properties of sections is at hand, for thevalues of the coordinates in question are each obtained bydividing the moment of inertia by the distance from theneutral axis to the extreme fiber. In other wor
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