767_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

767_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 09Ch09.qxd 9/27/08 1:35 PM Page 761 761 SECTION 9.7 Nonprismatic Beams Solution 9.7-5 Simple beam with a rigid segment B.C. 2 n(L) 0 PLx2 6 EI PL3 + 3EIdB 54 ‹ C2 Px3 18 5PL2x 54 PL2 + 3EIdB 54 B.C. ‹ dB FROM A TO B uA 3dB x L L b 3 (1) 3dB L ¿ a0 … x … a0 … x … L b 3 L , (nB)Left 3 3 At x (2) 8PL3 729EI dB L/3 a M EI PLx 3 ¿ B.C. 1 At x ‹ C1 EI ¿ PLx 3 Px 3 (3) Px2 + C1 6 L/3, 8PL2 243EI ; Substitute for dB in Eq. (5) and simplify: P (7L3 486EI 61L2x + 81L x2 5PL2 54 Px2 6 5PL2 54 PLx2 6 Px3 18 a v¿ 3EIdB L 5PL2x 54 L … x … Lb 3 3EIdB x + C2 L a L … x … Lb 3 L … x … Lb 3 61L2 + 162Lx MAXIMUM DEFLECTION a EI P ( 486EI 3dB L 3EIdB L 27x3) (6) Also, ¿ ¿ (5) ; a PL 3 L … x … Lb 3 (nB)Right (Eqs. 1 and 5) FROM B TO C EI – 3EIdBx L L (9 9 40 15PL3 6561EI 0 gives x1 81x2) L … x … Lb 3 2 25) (7) 0.5031L Substitute x1 in Eq. (6) and simplify: (4) max dmax max 40 15PL3 6561EI 0.01363 PL3 EI ; ...
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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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