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09-01ChapGere.0006

# 09-01ChapGere.0006 - figure The beam has length L 5 27.5 m...

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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 wide- flange section with E 28 10 6 psi and an allowable bending stress of 17,500 psi in both tension and compression. Calculate the ratio / 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.) Solution 9.3-5 Cantilever beam (uniform load) 552 CHAPTER 9 Deflections of Beams L h q E 28 10 6 psi 17,500 psi Calculate the ratio L. Maximum deflection (Eq. 9-26): (1) (2) Flexure formula with s Mc I ¢ qL 2 2 ¢ h 2 I qL 2 h 4 I M qL 2 2 : L qL 3 8 EI max qL 4 8 EI h L 1 8 Solve for q : (3) Substitute q from (3) into (2): Substitute numerical values: L 17,500 psi 2(28 10 6 psi) (8) 1 400 d L s 2 E ¢ L h 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 (see
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Unformatted text preview: figure). The beam has length L 5 27.5 m m and rectangular cross section of width b 5 4.0 m m and thickness t 5 0.88 m m. The total load on the beam is 17.2 m N. If the deflection at the end of the beam is 2.46 m 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 t L q b Cantilever beam with a uniform load. L 5 27.5 m m b 5 4.0 m m t 5 0.88 m m qL 5 17.2 m N d max 5 2.46 m m Determine Eq. Eq. (9-26): or E q 5 3 qL 4 2 bt 3 d max I 5 bt 3 12 E q 5 qL 4 8 I d max d 5 qL 4 8 E q I Substitute numerical values: 5 80.02 3 10 9 N / m 2 or E q 5 80.0 GPa E q 5 3(17.2 m N)(27.5 m m) 3 2(4.0 m m)(0.88 m m) 3 (2.46 m m) A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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