798CHAPTER 10Statically Indeterminate BeamsREACTIONS(EQS. 1AND2)MA±RBL±3EIdBL2;RA±RB±3EIdBL3DEFLECTION(FROM EQ. 7):SLOPE(FROM EQ. 6):²¿±³3dBx2L3(2L³x)²± ³dBx22L3(3L³x);Problem 10.3-4A cantilever beam of length Land loaded by uniform load of intensity qhas a fixed support at Aand spring support at Bwithrotational stiffness kR. A rotation at B, , results in a reaction moment MB= kR.Find rotation and displacement at end B. Use the second-orderdifferential equation of the deflection curve to solve for displacements atend B.dBuB*uBuByxALBkRqMARAMBSolution 10.3-4q= intensity of uniform loadEQUILIBRIUM(1)(2)(3)BENDING MOMENTDIFFERENTIAL EQUATIONEIv¿±RAx22³MAx³qx36+C1EIv–±M±RAx³MA
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