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09-01ChapGere.0004

# 09-01ChapGere.0004 - Calculate the height h of the beam if...

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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 3 35) supports a uniform load on a simple span of length L 5 14 ft (see figure). Calculate the maximum deflection d max at the midpoint and the angles of rotation u at the supports if q 5 1.8 k/ft and E 5 30 3 10 6 psi. Use the formulas of Example 9-1. Solution 9.3-1 Simple beam (uniform load) 550 CHAPTER 9 Deflections of Beams W 12 3 35 L 5 14 ft 5 168 in. q 5 1.8 k / ft 5 150 lb / in. E 5 30 3 10 6 psi I 5 285 in. 4 M AXIMUM DEFLECTION (E Q . 9-18) 5 0.182 in. d max 5 5 qL 4 384 EI 5 5(150 lb / in.)(168 in.) 4 384(30 3 10 6 psi)(285 in. 4 ) A NGLE OF ROTATION AT THE SUPPORTS (E Q s. 9-19 AND 9-20) 5 0.003466 rad 5 0.199º u 5 u A 5 u B 5 qL 3 24 EI 5 (150 lb / in.)(168 in.) 3 24(30 3 10 6 psi)(285 in. 4 ) 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 5 d max 5 10 mm u 5 u A 5 u B 5 0.01 rad s 5 s max 5 90 MPa E 5 200 GPa Calculate the height h of the beam. Eq. (9-18): or (1) Eq. (9-19): or (2) Equate (1) and (2) and solve for L : (3) Flexure formula: s 5 Mc I 5 Mh 2 I L 5 16 d 5 u q 5 24 EI u L 3 u 5 u A 5 qL 3 24 EI q 5 384 EI d 5 L 4 d 5 d max 5 5 qL 4 384 EI Maximum bending moment: (4) Solve Eq. (4) for h : (5) Substitute for q from (2) and for L from (3): Substitute numerical values: h 5 32(90 MPa)(10 mm) 15(200 GPa)(0.01 rad) 2 5 96 mm h 5 32 s d 15 E u 2 h 5 16 I s qL 2 ∴ s 5 qL 2 h 16 I M 5 qL 2 8 L h q Probs. 9.3-1, 9.3-2 and 9.3-3 A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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