CHAPTER 6 BUILT-IN BEAMS Summary The maximum bending moments and maximum deflections for built-in beams with standard loading cases are as follows: MAXIMUM B.M.AND DEFLECTION FOR BUILT-IN BEAMS Loading case Maximum B.M. Maximum deflection Central concentrated WL WL3 load w 8 192EI Uniformly distributed wL2 WL WL4 WL load w/metre (total load W) 12=12 384Ei=384E Concentrated load W not at mid-span Wab2 Wa'b 2Wab2 2aL d or D 3E1(L+2a2 at x= (L+2a) where a< L Wab3 3EIL under load Distributed load w' varying in intensity MA=- w儿-对k between x =x1 and L X =X2 X2 w'(亿-x)x2 M8=- dx 140CHAPTER 6 BUILT-IN BEAMS Summary The maximum bending moments and maximum deflections for built-in beams with standard loading cases are as follows: MAXIMUM B.M. AND DEFLECTION FOR BUILT-IN BEAMS Loading case Central concentrated load W Uniformly distributed load w/metre (total load W) Concentrated load W not at mid-span Distributed load w’ varying in intensity between x = x, and x = x2 Maximum B.M. WL 8 - wL2 WL 12 12 _-- Wab2 Wa2b ~ or - L2 L2 w‘(L -x)Z MA= - dx Maximum deflection WL3 192EI __ wL4 WL3 38481 384EI __=- 2 Wa3b2 2aL at x=- 3EI(L + 2a)2 (L + 2a) where a < - Wa3b3 3EIL3 =- under load 140