431_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

431_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 05Ch05.qxd 9/24/08 4:59 AM Page 425 425 SECTION 5.6 Design of Beams t Problem 5.6-18 A horizontal shelf AD of length L 915 mm, width b 305 mm, and thickness t 22 mm is supported by brackets at B and C [see part (a) of the figure]. The brackets are adjustable and may be placed in any desired positions between the ends of the shelf. A uniform load of intensity q, which includes the weight of the shelf itself, acts on the shelf [see part (b) of the figure]. Determine the maximum permissible value of the load q if the allowable bending stress in the shelf is sallow 7.5 MPa and the position of the supports is adjusted for maximum load-carrying capacity. A B D C b L (a) q A D B C L (b) Solution 5.6-18 NUMERICAL DATA L b 915 mm sallow 2 12) Substitute x into the equation for either M1 or |M2|: 305 mm t 22 mm Mmax Mmax 7.5 MPa MOMENT DIAGRAM qL2 (3 8 sallow S sallow a 2 12) Eq. (1) bt 2 b 6 Eq. (2) Equate Mmax from Eqs. (1) and (2) and solve for q: qmax 4bt2sallow 3L2(3 Substitute numerical values: For maximum load-carrying capacity, place the supports so that M1 |M2|. Let x M1 ‹ length of overhang qL (L 8 qL (L 8 4x) 4x) Solve for x: x |M2| L ( 12 2 qx2 2 1) qx2 2 qmax 10.28 kN/m ; ...
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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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