733_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

733_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 09Ch09.qxd 9/27/08 1:31 PM Page 727 SECTION 9.4 Deflections by Integration of the Shear Force and Load Equations 727 Solution 9.4-8 q0 L2 x q0 x4 q0 x3 + + C3 + 6 24 L 3 LOAD EQUATION E I –– q q0 + EI ¿ q0 x L q0 x + EI –¿ B.C. n (0) V(0) q0 x + C1 2L 0 + C3 x + C4 C1 0 B.C. EI – n (0) 0 C3 B.C. E I –¿ q0 x2 q0 x + 2L n(L) 0 C4 q0 x3 q0 x2 + + C2 2 6L B.C. n (L) M(L) 0 q0 1 120 EIL (x) q0 L2 3 C2 0 2 q0 L4 15 5 x4 L + x5 16 L52 + 20L3 x2 q0 x2 q0 x3 q0 L2 + + 2 6L 3 EI – q0 x5 q0 L2 x2 q0 x4 + + 24 120 L 6 EI 2 ; MAXIMUM DEFLECTION dmax (0) Problem 9.4-9 Derive the equations of the deflection curve for beam ABC, with guided support at A and roller support at B, supporting a uniform load of intensity q acting on the over-hang portion of the beam (see figure). Also, determine deflection dC and angle of rotation uC. Use the fourth-order differential equation of the deflection curve (the load equation). 2 q0 L4 15EI ; y MA q x A L B L/2 C RB Solution 9.4-9 LOAD EQUATION E I –– B.C. n (0) 0 (0 … x … L) q 0 C3 qL x + C4 16 EI E I –¿ C1 (0 … x … L) EI – C1 x + C2 (0 … x … L) B.C. n (0) V(0) 0 C1 – (0) M(0) EI – q L2 8 EI ¿ q L2x + C3 8 qL 8 B.C. 0 2 B.C. 0 22 C2 q L2 8 n(L) (x) 0 C4 qL2 2 1x 16 E I q L4 16 L22 (0 … x … L) LOAD EQUATION EI –– q aL … x … 3L b 2 ; ...
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This note was uploaded on 12/22/2011 for the course MEEG 310 taught by Professor Staff during the Fall '11 term at University of Delaware.

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