. The strength of materials; a text-book for engineers and architects. = 1012 ft. tons, the shaded portion being the resulting curve for the central and over-hanging portions of the uniform load. Combining thesediagrams we get the resulting curve as shown, themax. occurring at B, and being equal to 165 ft. tons. Relation between Load, Shear and Diagrams.—Let A c T> B, Fig. 66, represent the load curve on a span a any point p along the span, and consider a shortpiece c D of the load, the centre of which is at distance xfrom p. Then the shear at p due to this piece of th
. The strength of materials; a text-book for engineers and architects. = 1012 ft. tons, the shaded portion being the resulting curve for the central and over-hanging portions of the uniform load. Combining thesediagrams we get the resulting curve as shown, themax. occurring at B, and being equal to 165 ft. tons. Relation between Load, Shear and Diagrams.—Let A c T> B, Fig. 66, represent the load curve on a span a any point p along the span, and consider a shortpiece c D of the load, the centre of which is at distance xfrom p. Then the shear at p due to this piece of the load will be equalto the area of the portion c d of the load curve. Therefore thetotal shear S,. at p will be equal to the area of the load curveup to that point. But a sum curve * is such that its ordinate at any point * See p. 162. 148 THE STRENGTH OF MATERIALS represents the area of the primitive curve up to that the shear curve is the sum curve of the load curve. Suppose b F E G a is the sum curve of the load consider the at Fig. 66.—Relation between Load, Shear and Diagrams. The at p due to the portion c d of the load= given portion of load x x. Now if E and r are the corresponding points on the shearcurve, the difference of the ordinates at E and f gives theload on the portion c d. •. Load on portion c d = e f^. •. at p due to portion c d = e f^ x a:. .. Shaded portion e f Fg e^ represents the at p dueto the portion c d of the load. BENDING MOMENTS AND SHEARING FORCES 149 .•. Total at p = M,. = area of shear diagram up to p. Thus the curve is the sum curve of the shear curve. So that by drawing the sum curve B J H of the shear curvewe get the curve. Scales.—If V ^ x tons per foot is the scale of the loadcurve, and p-^ is the polar distance measured on the spacescale for obtaining the shear curve, then the scale of theshear curve V ^ Pi ^ tons. If P2 is the polar distance fromwhich the
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