For the cantilever beam with L= 12 m and w = 50 kN/m, w a) M...

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For the cantilever beam with L= 12 m and w = 50 kN/m, w a) M = WL2 24 A B C L/2- L/2- 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) 0c = radian b) Determine the deflection at point C yc= mm (insert "-" sign if the deflection is downward) Beam and Loading y Appendix D Beam Deflections and Slopes Elastic Curve Maximum Deflection Slope at End X 2 w L x 4 M a 6 L W P b B A y B A a Equation of Elastic Curve PL PL P mux y (x-3x) 3 2EI 6EI WL max 8EI WL 6EI y= 24EI (x 4Lx + 6Lx) L 1 I ML ML M Ymax y 2EI EI 2EI L Ymax x PL 48EI For a b: Pb(L - b)3/2 9V3EIL L b Bx at xm = L - b 3 = PL 16EI - + Pb(L - b) 6EIL Pa(L - a) GEIL For x = L: y= P 48EI (4x- 31x) For xa: y = Pb 6EIL [x- (1 - b)x] Pab For xa: y- 3EIL L x 5WL 384EI + WL3 24EI y = 24EI (x2Lx + Lx) Ymax ML ML B x 6 = + 9V3EI 6EI M 6EIL (x- 1x) ML = 3EI For the cantilever beam with L= 12 m and w = 50 kN/m, w a) M = WL2 24 A B C L/2- L/2- 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) 0c = radian b) Determine the deflection at point C yc= mm (insert "-" sign if the deflection is downward) Beam and Loading y Appendix D Beam Deflections and Slopes Elastic Curve Maximum Deflection Slope at End X 2 w L x 4 M a 6 L W P b B A y B A a Equation of Elastic Curve PL PL P mux y (x-3x) 3 2EI 6EI WL max 8EI WL 6EI y= 24EI (x 4Lx + 6Lx) L 1 I ML ML M Ymax y 2EI EI 2EI L Ymax x PL 48EI For a b: Pb(L - b)3/2 9V3EIL L b Bx at xm = L - b 3 = PL 16EI - + Pb(L - b) 6EIL Pa(L - a) GEIL For x = L: y= P 48EI (4x- 31x) For xa: y = Pb 6EIL [x- (1 - b)x] Pab For xa: y- 3EIL L x 5WL 384EI + WL3 24EI y = 24EI (x2Lx + Lx) Ymax ML ML B x 6 = + 9V3EI 6EI M 6EIL (x- 1x) ML = 3EI