s5.2 Slope and Deflection of Beams 99 Again,when =0andA=wL x=L dx x=L y=0 and B=wL4wLi wL4 24 6、 8 y= wx4 wL3x wL4 24+ (5.9) EI 68 wL4 dy wL3 Atx=0, and (5.10) 8EI dx m 6EI (c)Simply-supported beam with uniformly distributed load(Fig.5.7) w/metre xbecccoxceecc wL Fig.5.7. M=E1=wLx、w dr= 2 2 El dywLx2 wx dx 4 6+A Ely =WLx3 wxt 1224+Ax+B At x=0,y=0 ∴.B=0 At x=L,y=0 0=WL4 wL4 1224+AL A=、wL3 24 1「wLx3wx4wL3x7 y=El12-24-24 (5.11) In this case the maximum deflection will occur at the centre of the beam where x=L/2. ()-()()】 5wL+ (5.12) 384EI Similarly dy WL3 dx 4E at the ends of the beam. (5.13)$5.2 Again, when Slope and Deflection of Beams dY w13 x=L, -=0 and A=- dx 6 .. At x = 0, wL4 w13 y,= -__ and (2) =- 8El rmx 6El (c) Simply-supported beam with uniformly distributed load (Fig. 5.7) I' w/metre - WL - WL 2 2 Fig. 5.1. d2y wLx wx2 dx2 2 2. M =El-=--- xx dy wLx2 wx3 dx 4 6 wLx3 wx4 12 24 EI- = __ +A - ~ Ely = ~ - __ +Ax+B At x=O, y=O .'. B=O At 99 (5.9) (5.10) (5.11) In this case the maximum deflection will occur at the centre of the beam where x = L/2. .. - 5wL4 - -__ 384El WL3 , 24EI Similarly (2) =*- at the ends of the beam. (5.12) (5.13)