644_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

644_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 07Ch07.qxd 9/27/08 638 1:24 PM Page 638 CHAPTER 7 Analysis of Stress and Strain Problem 7.7-18 A cantilever beam of rectangular cross h b section (width b 25 mm, height h 100 mm) is loaded by a force P that acts at the midheight of the beam and is inclined at an angle a to the vertical (see figure). Two strain gages are placed at point C, which also is at the midheight of the beam. Gage A measures the strain in the horizontal direction and gage B measures the strain at an angle b = 60° to the horizontal. The measured strains are Pa 125 * 10 6 375 * 10 6. and Pb Determine the force P and the angle a, assuming the material is steel with E 200 GPa and 1/3. h C a P b B b A C Probs. 7.7-18 and 7.7-19 Solution 7.7-18 Cantilever beam (plane stress) HOOKE’S LAW Beam loaded by a force P acting at an angle a. E h 1/3 200 GPa b 25 mm sx E 100 mm Axial force F P sin a Shear force V âx P cos a (At the neutral axis, the bending moment produces no stresses.) At u âA 0°: At u 60°: sx âx âB P sin a bh txy 125 * 10 375 * 10 125 * 10 sy 6 ây 9 ) P cos a ây âx + 2 âx1 (1) (2) 60°: âx + ây âx1 6 2 âB 375 * 10 gxy cos 2u + 6 2u 2 sin 2u (3) 120° Substitute into Eq. (3): 0 375 * 10 6 41.67 * 10 6 (3.464 * 10 3P cos a 2bh 3V 2A âx (8.0 * 10 6 ELEMENT IN PLANE STRESS F A P sin a bhEâx 62,500 N txy 3(1 + ) P cos a 3P cos a gxy G 2bhG bhE FOR u STRAIN GAGES P sin a bhE or P cos a âx 41.67 * 10 6 9 6 )P cos a (4) 108,260 N SOLVE EQS. (1) AND (4): tan a P a 0.5773 266 * 10 30° ; ; 125 kN Problem 7.7-19 Solve the preceding problem if the cross-sectional dimensions are b angle is b = 75°, the measure strains are Pa 171 * 10 6 and Pb with modulus E 6.0 * 106 psi and Poisson’s ratio 0.35. 41.67 * 10 6 1.0 in. and h 3.0 in., the gage , and the material is a magnesium alloy ...
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This note was uploaded on 12/22/2011 for the course MEEG 310 taught by Professor Staff during the Fall '11 term at University of Delaware.

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