397_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 397_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Problem 5.4-5 A thin strip of steel of length and thickness is bent by couples (see figure). The deflection at the midpoint of the strip (measured from a line joining its end points) is found to be 0.20 in. Determine the longitudinal normal strain at the top surface of the strip. â M 0 t ± 0.2 in. L ± 20 in. SECTION 5.4 Longitudinal Strains in Beams 391 Solution 5.4-5 N UMERICAL DATA L ONGITUDINAL NORMAL STRAIN AT TOP SURFACE assume angle is small so that d ± r a 1 ² cos a L 2 r bb u ± L 2 r d ± r (1 ² cos( u )) sin( u ) ± L 2 r sin( u ) ± L 2 r â ± ² t 2 r â ± ² t 2 r d ± 0.20 inches L ± 28 inches t ± 0.25 inches insert numerical data: numerical solution for radius of curvature strain at top (compressive):
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Unformatted text preview: ; â ± 255 1 10 ² 6 2 â ± t 2 r â ± 2.552 * 10 ² 4 r ± 489.719 inches r gives r ± 0.20 1 ² cos a 14 r b solving for r : r ± d 1 ² cos a L 2 r b t M M d L 2 — L 2 — Problem 5.4-6 A bar of rectangular cross section is loaded and supported as shown in the figure. The distance between supports is and the height of the bar is The deflection at the midpoint is measured as 3.0 mm. What is the maximum normal strain at the top and bottom of the bar? â h ± 120 mm. L ± 1.5 m P h P a a d L 2 — L 2 — 05Ch05.qxd 9/24/08 4:59 AM Page 391...
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