eci130-s09-final_soln

eci130-s09-final_soln - ECI 130 - Spring 09 - Holland Final...

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ECI 130 - Spring 09 - Holland 1/10 Final (Open Book, Open Notes) Name: 1. A cantilever beam is fixed at point A and carries concentrated opposing moments at points B and C as shown. EI is constant across the length, L. Using the Direct Integration Method write the equation for deflection for beam segments AB and BC. (25 pts) (hint: use boundary conditions to define constants) Elastic Curve Statics Moment-Deflection Equations AB 0 EI 2 2 = dx v d 1 EI C dx dv = 2 1 EI C x C v + = BC 0 2 2 M EI = dx v d 3 0 M EI C x dx dv + = 4 3 2 0 2 M EI C x C x v + + = Boundary Conditions AB 0 ; 0 : 0 x 1 = = = C dx dv 0 ; 0 : 0 x 2 = = = C v BC 2 M 0 2 M ; 0 : 2 x 0 3 3 0 L C C L dx dv L = = + = = 8 M 0 2 2 M 2 2 M ; 0 : 2 x 2 0 4 4 0 2 0 L C C L L L v L = = + = = Deflection Equations AB 0 = v BC + = 8 M 2 M 2 M 1 2 0 0 2 0 L x L x EI v x A L/2 L/2 B C M 0 M 0 x A L/2 L/2 B C M A = 0 A x = 0 A y = 0 M 0 M 0 M(x) M 0 FBD A B C M 0 M 0
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ECI 130 - Spring 09 - Holland 2/10 Final (Open Book, Open Notes) Name: Alternative Coordinate Systems Moment-Deflection Equations - BC 0 2 2 2 M EI = dx v d 3 2 0 2 M EI C x dx dv + = 4 2 3 2 2 0 2 M EI C x C x v + + = Boundary Conditions - BC 0 ; 0 : 0 x 3 2 2 = = = C dx dv 0 ; 0 : 0 x 4 2 = = = C v Deflection Equations - BC EI x v 2 M 2 2 0 = Moment-Deflection Equations - BC 0 2 2 2 M EI = dx v d 3 2 0 2 M EI C x dx dv + = 4 2 3 2 2 0 2 M EI C x C x v + + = Boundary Conditions - BC 2 M 0 2 M ; 0 : 2 x 0 3 3 0 2 2 L C C L dx dv L = = + = = 8 M 0 2 2 M 2 2 M ; 0 : 2 x 2 0 4 4 0 2 0 2 L C C L L L v L = = + = = Deflection Equations - BC
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eci130-s09-final_soln - ECI 130 - Spring 09 - Holland Final...

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