tutorial(4th and 7th May)

tutorial(4th and 7th May) - SECTION 10.3 Differential...

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SECTION 10.3 DifferentialEquationsoftheDeflectionCurve 635 SHEAR-FORCE AND BENDING-MOMENT DIAGRAMS v o M vi Problem 10.3-3 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 fourth-order 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 10.3-3 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= --(3L-x) +- 2L3 SLOPE (FROM EQ. 6): 3lisx v' = --(2L -x) 2L3 \,1 } , I
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63& CHAPTER 10 StatlcaHyIndetenninateBeams J Problem 10.3-4 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 second-order .!lifferential equation of the deflection curve, that is, the bending-moment equation.) Ve:!MtW't\-tclowl7wa;tJ d1'spfqtp~ g B 0 Solution 10.3-4 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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