1 2 3 4 Appendix D Beam Deflections and Slopes Maximum Deflection Slope at End Equation of Elastic Curve Beam and Loading Elastic Curve L X PL PL Yux 3 2EI W L x y L I L M O L 5 L P b y 6 A M A A BY P 6EI y = (x - 3Lx) WL max 8EI WL 6EI w y= 24EI max ML 2EI PL 48EI ML M - EI 2EI PL 16EI (x - 4Lx + 6Lx) For x =L: y = P 48EI (4x- 31x) b a Ymax For a b: Pb(L - b)3/2 93EIL Pb(L - b) For xa: Pb BA = y = [x- (12-h)x] 6EIL 6EIL B x - L2 b Pa(L - a) Pab at xm For xa: y- 3 GEIL 3EIL X 5WL 384EI + WL3 y = 24EI W 24EI (x4 - 2Lx + Lx) y L ML ML Bx = + y 9V3EI 6EI M 6EIL (x - 1x) Ymax ML 3EI For the cantilever beam with L= 12 m and w = 50 kN/m, w M WL2 24 A B C L/2 L/2- a) Determine the slope at C of the beam. Use / = 7.500x109 mm and E =200GPa. (Hint: Use the Beam Deflections and Slopes Table on page A29, Beer et al., Textbook or the Table shown below) ec = radian b) Determine the deflection at point C Yc= mm (insert "-" sign if the deflection is downward)