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Unformatted text preview: SECTION 10.3 DifferentialEquationsof theDeflectionCurve 635 SHEARFORCE AND BENDINGMOMENT DIAGRAMS v o M vi Problem 10.33 A cantilever beam AB of length L has a fixed support at A and ~see figure). The support at B is moved downward through a distance liB' Using the fourthorder differential equation of the deflection curve (the load eqU;UWn),deterririnethe reactions of the beam and the equation of the deflection curve. (Note: Express all results in terms of the imposed / displacement liB') ............................................................................................................................................................................................................................................................ _/.,8..olution 10.33 Cantilever beam with imposed displacement liB B,fUtUDII1AJ REAcnONS (FROMEQUILIBRIUM) SHEARFORCE(EQ. 4) RA = RB (1) MA = RBL (2) 3E/lis 3E/lis V= RA=V(O)= L3 L3 DIFFERENTIAL EQUATIONS SOLVE EQUATIONS (8) AND (9): 3E/lis 3E/lis C1=V C2=u REAcnONS(EQs. I AND2) 3E/lis 3E/lis RA =Rs=V MA =RsL=U + DEFLECTION (FROM EQ. 7): lis~ v= (3Lx) + 2L3 SLOPE (FROM EQ. 6): 3lisx v' =(2Lx) 2L3 \,1 , I 63& CHAPTER 10 StatlcaHyIndetenninateBeams J Problem 10.34 A cantilever beam AB of length L has a fixed support at A and a spring support at B (see figure). The spring behaves in a linearly elastic manner with stiffness k. If a uniform load of intensity q acts on the beam, what is the downward displacement BB of end B of the beam? (Use the secondorder .!lifferential equation of the deflection curve, that is, the bendingmoment equation.) Ve:!MtW't\tclowl7wa;tJ d1'spfqtp~ g B Solution 10.34 Beam with spring support q = intensity of uniform load 'J r of D 1ft ,M/lI7 K8 EQun.mRIUM RA = qL RB (1) ..A qL2 MA =T!!LL (2) SPRING RB = kBB (3) BB = downward displacement of point B....
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This note was uploaded on 03/15/2012 for the course CIVL 000 taught by Professor Kk during the Spring '10 term at HKUST.
 Spring '10
 KK

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