. The strength of materials; a text-book for engineers and architects. - w cover a span a b (Fig. 198) of length /. The free curve is in this case a parabola a c b, with maximum IV l~ordinate -^• o Therefore, since the area of a parabola is two-thirds of the. Fig. 198.—Fixed Beam with Uniform Load. area of the circumscribing rectangle, area of free curve 2 , w P w P= 3 -J- --12 End = wP12 J IV P IV P 12 Then setting u^^ a e and b f equal to , ^ and joining e f we get the end diagram, and the effective curve isthe difference as sho^Ti shaded. At the points G and h theB.
. The strength of materials; a text-book for engineers and architects. - w cover a span a b (Fig. 198) of length /. The free curve is in this case a parabola a c b, with maximum IV l~ordinate -^• o Therefore, since the area of a parabola is two-thirds of the. Fig. 198.—Fixed Beam with Uniform Load. area of the circumscribing rectangle, area of free curve 2 , w P w P= 3 -J- --12 End = wP12 J IV P IV P 12 Then setting u^^ a e and b f equal to , ^ and joining e f we get the end diagram, and the effective curve isthe difference as sho^Ti shaded. At the points G and h is zero, and these points are called the points of contra-flexure, the curvature of the elastic line changing sign at thesepoints. FIXED AND CONTINUOUS BEAMS 419 Suppose the point g is at distance x from the centre of thebeam, then the ordinate of the parabola must be equal to -,^ XjLI 10 /P o\. w P 1-e. 2 1^4 ^j - 12 w X- X IV P 24 12 I X = 2V3 Distance of g from e = ^ — x 2 ^ 2 2V3 = -211 Z Shear Diagram.—With symmetrical loading the sheardiagram will be the same as for the simply supported is because the shear at any point of a beam is equal tothe slope of the curve at that point, and the slope of is not altered in the ca
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