Question

Рkip W kip/ft Problem No. 6 (30 points) The cantilever beam of length L and constant modulus of rigidity El is supported at B and subjected to uniformly distributed load w (kip/ft) throughout and a concentrated load P (kip) at A. (a) Using the method of integration, determine deflection at A (as fraction; do not use decimal). (b) Determine the rotation at A (as fraction; do not use decimal) (c) List two major assumptions used in solving this problem. El = constant KL

Answer 1

Solution x. is dus-lance from ter distributed load of "kep - w kiplit EI=constant wie doel - L- - 2L2 111111- Er du = - Mae = 10 (1-2) en dat (+x2–21x) gutegoeting 7 Joz erably top [ex + grey -Lz?]+1 of x=0, duso whence G=0 Es diye (1x + -LX2) theo 10 nuo [ *x+mi-12] By entegooting fwrothers Esya uches en terme la 3] +62 at x=0 , yoo Hence C2=0 1g, det et 13 ] - for concentrated food p og ETDP= - My PCL-x) Integration - Et des PC 12 -) +57 ctx=0 de co 950 de Scan CS CamScanna

ET Y = Pl Integrating sontegroting ga = p [1.22- 6 23 a) Deflection at a r'using supres position theorem) YA = y + y2 you tre ) + mai (17**] Jom [ LD6x2 + 4x 3 7 ( + 64,33 + P23 )+ sor any ya tate ( cente + PL ]**+ (p-wedged + mozek ] by Rotation at A (using supes position thcorem ) DAT 're + PLX) +(- page + bogel BAC { const +PL)x - (none +] + + words ] e Tuo marox assumptions used in solving this problem. it stress is pooportional to strain re hooks low is applicable 27 The curvature is always small 32 plane section before bending remains plain after bending 97 Any deflection from shear stress mate wal is neglected Scanned with CamScanner