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520_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 520_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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514 CHAPTER 6 Stresses in Beams (Advanced Topics) Solution 6.3-6 Plastic beam with aluminum strips (1) Plastic segments: b 75 mm d 40 mm 3 d 120 mm E p 3 GPa (2) Aluminum strips: b 75 mm t 3 mm E a 75 GPa h 4 t 5 d 212 mm M 1.0 kN m T RANSFORMED SECTION ( PLASTIC ) # All dimensions in millimeters. A LUMINUM : M AXIMUM STRESS IN THE PLASTIC (1) (E Q . 6-15) M AXIMUM STRESS IN THE ALUMINUM (2) (E Q . 6-17) s a s 2 M ( h /2) n I T 12.14 MPa ; s p s 1 M ( h /2 t ) I T 0.47 MPa ; I T I 1 + I 2 218.35 * 10 6 mm 4 165.420 * 10 6 mm 4 + 1 12 (1875)(3) 3 + (1875)(3)(61.5) 2 d I 2 2 c 1 12 (1875)(3) 3 + (1875)(3)(104.5) 2 52.934 * 10 6 mm 4 + 1 12 (75)(120) 3 Plastic: I 1 2 c 1 12 (75)(40) 3 + (75)(40)(83) 2 d Plastic segments are not changed. Width of aluminum strips nb (25)(75 mm) 1875 mm n E a E p 25 Problem 6.3-7 A simple beam that is 18 ft long supports a uniform load of intensity q . The beam is constructed of two angle sections, each L 6 4 1/2, on either side of a 2 in. 8 in. (actual dimensions) wood beam (see the cross section shown in

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