718_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

718_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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712 CHAPTER 9 Deflections of Beams Problem 9.3-5 A cantilever beam with a uniform load (see figure) has a height h equal to 1/8 of the length L . The beam is a steel wideflange section with E ± 28 ² 10 6 psi and an allowable bending stress of 17,500 psi in both tension and compression. Calculate the ratio d / L of the deflection at the free end to the length, assuming that the beam carries the maximum allowable load. (Use the formulas of Example 9-2.) L h q Solution 9.3-5 Cantilever beam (uniform load) Calculate the ratio d / L . (2) s ± Mc I ± a qL 2 2 ba h 2 I b ± qL 2 h 4 I Flexure formula with M ± qL 2 2 : d L ± qL 3 8 EI Maximum deflection (Eq. 9-26): d max ± qL 4 8 EI (1) h L ± 1 8 E ± 28 * 10 6 psi s ± 17,500 psi Solve for q : (3) Substitute q from (3) into (2): Substitute numerical values: d L ± 17,500 psi 2(28 * 10 6 psi) (8) ± 1 400 ; d L ± s 2 E a L h b ; q ± 4 I s L 2 h Problem 9.3-6 A gold-alloy microbeam attached to a silicon wafer behaves like a cantilever beam subjected to a uniform load
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Unformatted text preview: (see figure). The beam has length L 27.5 m and rectangular cross section of width b 4.0 m and thickness t 0.88 m. The total load on the beam is 17.2 N. If the deflection at the end of the beam is 2.46 m, what is the modulus of elasticity E g of the gold alloy? (Use the formulas of Example 9-2.) Solution 9.3-6 Gold-alloy microbeam Cantilever beam with a uniform load. L 27.5 m b 4.0 m t 0.88 m qL 17.2 N d max 2.46 m Determine E g . I bt 3 12 E g 3 qL 4 2 bt 3 d max ; Eq. (9-26): d qL 4 8 E g I or E g qL 4 8 I d max Substitute numerical values: 80.02 * 10 9 N/m 2 or E g 80.0 GPa ; E g 3(17.2 m N)(27.5 m m) 3 2(4.0 m m)(0.88 m m) 3 (2.46 m m) t L q b 09Ch09.qxd 9/27/08 1:31 PM Page 712...
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