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387_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 387_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 04Ch04.qxd 9/25/08 12:43 PM Page 381 SECTION 4.5 Shear-Force and Bending-Moment Diagrams Problem 4.5-36 A simple beam AB supports two connected wheel loads P and 2P that are distance d apart (see figure). The wheels may be placed at any distance x from the left-hand support of the beam. P Solution 4.5-36 2P x (a) Determine the distance x that will produce the maximum shear force in the beam, and also determine the maximum shear force Vmax. (b) Determine the distance x that will produce the maximum bending moment in the beam, and also draw the corresponding bendingmoment diagram. (Assume P 10 kN, d 2.4 m, and L 12 m.) d A B L Moving loads on a beam P d L 10 kN 2.4 m 12 m Reaction at support B: 2P P x+ (x + d) L L Bending moment at D: (a) MAXIMUM SHEAR FORCE By inspection, the maximum shear force occurs at support B when the larger load is placed close to, but not directly over, that support. P (2d + 3x) L RB MD RB (L x d) P (2d + 3x) (L L P [ L dMD dx P ( L Solve for x: x 3x2 + (3L 6x + 3L x d) 5d)x + 2d(L 5d) L a3 6 d)] 0 5d b L 4.0 m ; 5d 2 b + (3L L 5d) Substitute x into Eq (1): Mmax x Vmax L RB d 381 ; 9.6 m P a3 P c L d b L 28 kN L2 3a b a3 6 L * a b a3 6 ; 5d b + 2d(L L d) d d2 b L 78.4 kN # m ; PL a3 12 (b) MAXIMUM BENDING MOMENT By inspection, the maximum bending moment occurs at point D, under the larger load 2P. Note: RA P d a3 + b 2 L 16 kN RB P a3 2 14 kN d b L Eq.(1) ...
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