. Applied calculus; principles and applications . t the quantities to be depicted bythe curves. The fundamental curve is the curve for L, theload; the Shear S is represented by the first integral curve;the Moment M by the second integral curve; EI upon theSlope m, by the third integral curve; and EI upon the De-flection (?, by the fourth integral curve, where E and / areconstants denoting the Modulus of Elasticity and Momentof Inertia, respectively. Example 1. — Let a beam of length I between supportsbe simply supported at each end and loaded with a uniformload of w lbs. per hnear ft. L = y =
. Applied calculus; principles and applications . t the quantities to be depicted bythe curves. The fundamental curve is the curve for L, theload; the Shear S is represented by the first integral curve;the Moment M by the second integral curve; EI upon theSlope m, by the third integral curve; and EI upon the De-flection (?, by the fourth integral curve, where E and / areconstants denoting the Modulus of Elasticity and Momentof Inertia, respectively. Example 1. — Let a beam of length I between supportsbe simply supported at each end and loaded with a uniformload of w lbs. per hnear ft. L = y = —w, w taken with negative sign as a downwardforce. S = y = I —wdx = —wx -\- (Sq = -^,S being zero when ^^ = o) • M = y= I (-^ - wxjdx = Y^ — ^ + (^0 = 0, ikf when x = 0). wl „ wx^ M (m - 2/) = J (|-x - ^j da; = + f mo = ~ 24^^^ ^ when x = 0, m being zero at rr = ^J EI id = y)-f(^ APPLICATION TO BEAMS 231 6 24. dx 12 wx^ wlH - 24 - -24 + (^0 = 0, d at a; = 0). EXAMPLE 1. LoadLine IlilllllliniMiriniiiri^^ --^niminiixQjjjj^^ ShearLine. Inflexion Poini d=-^^,mca:. Inflexion Point XDefleciionCurve 384 EI ^^^^liillLlllllilMlllllllimilLUU-^ J,/i\i/ rnilllllMMIIIinTTTnT-r. i^ -ysV5i= -y^ii-yj-yfj/i ; ^-rrmTTTTTTTrmTTT^ ^■^^^ J ■XSlopeCiiTue
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Keywords: ., bookcentury1900, bookdecade1910, bookpublishernewyo, bookyear1919
