527_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

527_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 6.4 Beams with Inclined Loads 521 Problem 6.4-2 A wood beam of rectangular cross section (see figure) is simply supported on a span of length L . The longitudinal axis of the beam is horizontal, and the cross section is tilted at an angle a . The load on the beam is a vertical uniform load of intensity q acting through the centroid C . Determine the orientation of the neutral axis and calculate the maximum tensile stress s max if b 80 mm, h 140 mm, L 1.75 m, a 22.5°, and q 7.5 kN/m. Probs. 6.4-2 and 6.4-3 Problem 6.4-3 Solve the preceding problem for the following data: b 6 in., h 10 in., L 12.0 ft, tan a 1/3, and q 325 lb/ft. Solution 6.4-3 B ENDING MOMENTS M y q sin( a ) L 2 8 M
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Unformatted text preview: q ± 325 lb/ft b ± 6 in. C z y q h b a Solution 6.4-2 B ENDING MOMENTS M OMENT OF INERTIA I y ± hb 3 12 I y ± 5.973 * 10 6 mm 4 M z ± q cos( a ) L 2 8 M z ± 2653 N # m M y ± q sin( a ) L 2 8 M y ± 1099 N # m h ± 140 mm a ± 22.5 deg L ± 1.75 m q ± 7.5 kN/m b ± 80 mm N EUTRAL AXIS nn M AXIMUM TENSILE STRESS ( AT POINT A) s max ± 17.5 MPa ; s max ± M y a b 2 b I y ² M z a ² h 2 b I z b ± a tan a I z I y tan( a ) b b ± 51.8° ; I z ± bh 3 12 I z ± 18.293 * 10 6 mm 4 M OMENT OF INERTIA I z ± bh 3 12 I z ± 500 in. 4 I y ± hb 3 12 I y ± 180 in. 4 M z ± q cos( a ) L 2 8 M z ± 66598 lb-in. 06Ch06.qxd 9/24/08 5:54 AM Page 521...
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