724CHAPTER 9Deflections of BeamsProblem 9.4-4A beam with a uniform load has a guided support at oneend and spring support at the other. The spring has stiffness k48EI/L3.Derive the equation of the deflection curve by starting with the third-orderdifferential equation (the shear-force equation). Also, determine the angle ofrotation uBat support B.RB= kdBMAk= 48EI/L3ABqyxLSolution 9.4-4SHEAR-FORCE EQUATIONB.C.n(L)M(L)0EIqL2x24qx424+C2x+C3EI¿qL2x2qx36 +C2EI–qL22qx22 C1qL22 EI–qx22+C1 EI–¿VqxB.C.n(0)0C20B.C.uB¿(L)qL33EI(Counterclockwise);(2x412x2L211L4);(x)q48EIC311qL448 (L)qLkqL448EIProblem 9.4-5
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