792CHAPTER 9Deflections of BeamsProblem 9.11-3An overhanging beam ABCof height hhas a guided support at Aand a roller at B. The beam is heated to a temperature T1on the top and T2on the bottom (see figure).Determine the equation of the deflection curve of the beam, the angle of rotation uCat end C, and the deflection dCat end C.xyALBCT1T2T1T2ahSolution 9.11-3B.C.n±(0)²0C1²0B.C. n(L)²0³(x)²a(T2´T1)(x2´L2)2hC2²´a(T2´T1)L22h³²a(T2´T1)x22h+C1x+C2v¿²a(T2´T1)xhµC1³–²d2dx2a(T2´T1)hUpwardCounter ClockwiseuC²v¿(Lµa)²a(T2´T1Lµa)h;²a(T2´T1)(2La+a2)2h;dC²³(L+a)²a(T2´T1)[(L+a)2´L2]2hProblem 9.11-4A simple beam ABof length Land height h(see figure) is heated in such a manner that the temperature difference T2´T1between the bottom and top of the beam is proportional to the distance from support A; that is, assume the temperature difference varies
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