734_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 734_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 09Ch09.qxd 728 9/27/08 1:31 PM Page 728 CHAPTER 9 Deflections of Beams EI –¿ q x + C5 a L … x … EI – q x3 3qL x2 + 6 4 q x2 3L + C5 x + C6 a L … x … b 2 2 Va 3L b 2 0 C5 3qL 2 3L b 2 Ma 3L b 2 0 C6 B.C. –a EI – q x2 3qL x + 2 2 EI ¿ q x3 3qL x2 + 6 4 n L(L) C7 + 9 qL2 8 9 qL2 x + C7 8 EI 9 qL3 + C7 8 5 qL3 12 B.C. n(L) 20 xL3 + 27 L2 x2 aL … x … 12 L x3 + 2 x4 + 3 L42 dC a uC 5 qL3 12 14 qL 16 C8 0 q 1 48 EI (x) 9 qL2 x2 16 5 qL3 x + C8 12 + n R(L) qL3 3qL3 + 6 4 9 qL2 x 8 3 qL x3 q x4 + 24 12 9 qL2 8 –¿ a qL3 8 EI ¿ 3L b 2 B.C. B.C. 3L b 2 ¿a Problem 9.4-10 Derive the equations of the deflection curve for beam AB, 9 qL4 128 EI 3L b 2 ; (Clockwise) y MA with guided support at A and roller support at B, supporting a distributed load of maximum intensity q0 acting on the right-hand half of the beam (see figure). Also, determine deflection dA, angle of rotation uB, and deflection dC at the midpoint. Use the fourth-order differential equation of the deflection curve (the load equation). ; ; 7 qL3 48 EI 3L b 2 3L b 2 q0 x A L/2 C L/2 B RB Solution 9.4-10 LOAD EQUATION EI –– q B.C. 0 L a0 … x … b 2 EI –¿ C1 a 0 … x … L b 2 EI – C1 x + C2 a 0 … x … n (0) V(0) C1 0 2 B.C. – (0) M(0) EI – L b 2 0 q0 L2 12 EI ¿ q0 L2 x + C3 12 q0 L 12 a0 … x … C2 q0 L2 12 L b 2 a0 … x … L b 2 ...
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