Essentials in the theory of framed structures . Fig. 60a. Fig. 606. over the left-half of the beam, decreasing to zero at the center;hence the bending moment curve has a positive slope at U,which decreases to zero at K, where the tangent to the curve ishorizontal. Beyond K the curve has an increasing negativeslope. Any ordinate in the bending moment diagram is easilydetermined from the area of the shear diagram; thus IJ = area SABF = 4,800 = area SAC = 6,400 The bending-moment curve is a parabola, as will be shown in thefollowing article. SQ. The Structural Engineers Parabola
Essentials in the theory of framed structures . Fig. 60a. Fig. 606. over the left-half of the beam, decreasing to zero at the center;hence the bending moment curve has a positive slope at U,which decreases to zero at K, where the tangent to the curve ishorizontal. Beyond K the curve has an increasing negativeslope. Any ordinate in the bending moment diagram is easilydetermined from the area of the shear diagram; thus IJ = area SABF = 4,800 = area SAC = 6,400 The bending-moment curve is a parabola, as will be shown in thefollowing article. SQ. The Structural Engineers Parabola.—The mathemati-cian usually derives the equation of the parabola with the 92 THEORY OF FRAMED STRUCTURES Chap. II origin at the vertex and the axis of symmetry horizontal, asshown in Fig. 6oa. Under these conditions the general equationof the parabola is 72 = kX (i) where X and Y are variables and ^ is a constant. The structural engineer finds it more convenient to choosesome point not at the vertex for the origin, with the axis ofsymmetry
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