398_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

398_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Normal Stresses in Beams Problem 5.5-1 A thin strip of hard copper ( E ± 16,000 ksi) having length L ± 90 in. and thickness t ± 3/32 in. is bent into a circle and held with the ends just touching (see figure). (a) Calculate the maximum bending stress s max in the strip. (b) By what percent does the stress increase or decrease if the thickness of the strip is increased by 1/32 in.? 392 CHAPTER 5 Stresses in Beams (Basic Topics) Solution 5.5-1 (a) M AXIMUM BENDING STREES (b) % C HANGE IN STRESS t new ± 4 32 s maxnew ± Et new 2 r ; s max ± 52.4 ksi r ± 14.324 inches s max ± Et 2 r s ± E P t 2 r Q r ± L 2 p t ± 3 32 inches E ± 16000 ksi L ± 90 inches 33% increase (linear) in max.stress due to increase in t ; same as % increase in thickness
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Unformatted text preview: t 4 32 3 32 3 32 (100) 33.3 ; s maxnew s max s max (100) 33.3 s maxnew 69.813 ksi Solution 5.4-6 N UMERICAL DATA N ORMAL STRAIN AT TOP OF BAR : tensile strain, radius of curvature SMALL DEFLECTION SO SMALL ANGLE sin( u ) L 2 r u L 2 r u r h 2 r h 2 r d 3.0 mm L 1.5 m h 120 mm numerical solution for radius of curvature strain at top (compressive): ; h 2 r 640 * 10 6 r 93.749 m r gives r a 1 cos a L 2 r bb d d r a 1 cos a L 2 r bb 3 32 t = in. 05Ch05.qxd 9/24/08 4:59 AM Page 392...
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