387_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

387_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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) ...
View Full Document

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.

Ask a homework question - tutors are online