768_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

768_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 09Ch09.qxd 9/27/08 762 1:35 PM Page 762 CHAPTER 9 Deflections of Beams Problem 9.7-6 A simple beam ABC has moment of inertia 1.5I from A to B and I from P B to C (see figure). A concentrated load P acts at point B. Obtain the equations of the deflection curves for both parts of the beam. From the equations, determine the angles of rotation uA and uC at the supports and the deflection dB at point B. 1.5I I A C B L — 3 2L — 3 Solution 9.7-6 Simple beam (nonprismatic) PLx2 6 Use the bending-moment equation (Eq. 9-12a). EI DEFLECTION CURVE B.C. 0 B.C. Ea 3I b– 2 EI – 2Px 3 M Px 3 PL 3 M a0 … x … From Eq. (6): 0 From Eq. (7): ¿ 4Px2 + C1 18 EI ¿ PLx 3 B.C. (2) 4P L 3 L a b + C1 a b 54 3 3 a L b 3 PL L 2 ab 63 L … x … Lb 3 C1L (4) C2 C1 C1 C4 PL2 a b + C2 63 11PL2 162 4Px3 + C1x + C3 54 P L3 ab 18 3 (5) a0 … x … L b 3 38PL2 729 C2 175PL2 1458 (10) C3 0 13PL3 1458 SLOPES OF THE BEAM (FROM EQS. 3 AND 4) INTEGRATE EQS. (3) AND (4) EI (9) SOLVE EQS. (5), (8), (9), AND (10) From Eqs. (3) and (4): PL L ab 33 C2L 10PL3 + C2L + 3C4 243 (3) (n B)Right 4P L 2 a b + C1 18 3 PL3 9 From Eqs. (6), (8), and (7): 1 Continuity of slopes at point B (n B)Left (8) L + C2 a b + C4 3 a0 … x … Px2 + C2 2 0 (nB)Right INTEGRATE EACH EQUATION EI C3 C4 (1) L a … x … Lb 3 (7) 4 Continuity of deflections at point B (nB)Left L b 3 L … x … Lb 3 3 Deflection at support C v(L) BENDING-MOMENT EQUATIONS a 2 Deflection at support A n (0) B.C. Px3 + C2x + C4 18 (6) ¿ 2P (19L2 729EI 81x2) a 0 … x … L b 3 (11) ...
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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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