716_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 716_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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710 CHAPTER 9 Deflections of Beams Deflection Formulas Problems 9.3-1 through 9.3-7 require the calculation of deflections using the formulas derived in Examples 9-1, 9-2, and 9-3. All beams have constant flexural rigidity EI . Problem 9.3-1 A wide-flange beam (W 12 ± 35) supports a uniform load on a simple span of length L ² 14 ft (see figure). Calculate the maximum deflection d max at the midpoint and the angles of rotation u at the supports if q ² 1.8 k/ft and E ² 30 ± 10 6 psi. Use the formulas of Example 9-1. Probs. 9.3-1 through 9.3-3 L h q Solution 9.3-1 Simple beam (uniform load) W 12 ± 35 L ² 14 ft ² 168 in. q ² 1.8 k/ft ² 150 lb/in. E ² 30 ± 10 6 psi I ² 285 in. 4 M AXIMUM DEFLECTION (E Q . 9-18) ² 0.182 in. ; d max ² 5 qL 4 384 EI ² 5(150 lb/in.)(168 in.) 4 384(30 * 10 6 psi)(285 in. 4 ) A NGLE OF ROTATION AT THE SUPPORTS (E Q s. 9-19 AND 9-20) ² 0.003466 rad ² 0.199° ; ² (150 lb/in.)(168 in.) 3 24(30 * 10 6 psi)(285 in. 4 ) u ² u A ² u B ² qL 3 24 EI Problem 9.3-2 A uniformly loaded steel wide-flange beam with simple supports (see figure) has a downward deflection of 10 mm at the midpoint and angles of rotation equal to 0.01 radians at the ends.
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Unformatted text preview: Calculate the height h of the beam if the maximum bending stress is 90 MPa and the modulus of elasticity is 200 GPa. ( Hint : Use the formulas of Example 9-1.) Solution 9.3-2 Simple beam (uniform load) d ² d max ² 10 mm u ² u A ² u B ² 0.01 rad s ² s max ² 90 MPa E ² 200 GPa Calculate the height h of the beam. Flexure formula: s ² Mc I ² Mh 2 I Equate (1) and (2) and solve for L : L ² 16 d 5 u (3) Eq. (9-19): u ² u A ² qL 3 24 EI or q ² 24 EI u L 3 (2) Eq. (9- 18): d ² d max ² 5 qL 4 384 EI or q ² 384 EI d 5 L 4 (1) Maximum bending moment: (4) (5) Substitute for q from (2) and for L from (3): Substitute numerical values: h ² 32(90 MPa)(10 mm) 15(200 GPa)(0.01 rad) 2 ² 96 mm ; h ² 32 sd 15 E u 2 ; Solve Eq. (4) for h : h ² 16 I s qL 2 M ² qL 2 8 ‹ s ² qL 2 h 16 I 09Ch09.qxd 9/27/08 1:31 PM Page 710...
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