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519_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 519_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 06Ch06.qxd 9/24/08 5:34 AM Page 513 SECTION 6.3 Transformed-Section Method 513 Solution 6.3-5 Plastic beam with aluminum strips (1) Plastic segments: b 3.0 in. 3d 3.6 in. Ep 440 (2) Aluminum strips: b d 1.2 in. All dimensions in inches. 2c 103 psi 3.0 in. t 0.1 in. 1 (3.0)(1.2)3 + (3.0)(1.2)(2.50)2 d 12 + Plastic: I1 1 (3.0)(3.6)3 12 6 Ea 11 10 psi h 4t 5d 6.4 in. 57.528 in.4 Aluminum: 6.0 k-in. I2 2c 1 (75)(0.1)3 + (75)(0.1)(3.15)2 12 + M 1 (75)(0.1)3 + (75)(0.1)(1.85)2 d 12 TRANSFORMED SECTION (PLASTIC) 200.2 in.4 IT I1 + I2 257.73 in.4 MAXIMUM STRESS IN THE PLASTIC (1) (EQ. 6-15) sp s1 M(h/2 IT t) 72 psi ; MAXIMUM STRESS IN THE ALUMINUM (2) (EQ. 6-17) Plastic segments are not changed. n Ea Ep 25 sa s2 M(h/2)n IT 1860 psi ; Width of aluminum strips nb (25)(3.0 in.) 75 in. Problem 6.3-6 Consider the preceding problem if the beam has width b 75 mm, the aluminum strips have thickness t 3 mm, the plastic segments have heights d 40 mm and 3d 120 mm, and the total height of the beam is h 212 mm. Also, the moduli of elasticity are Ea 75 GPa and Ep 3 GPa, respectively. Determine the maximum stresses sa and sp in the aluminum and plastic, respectively, due to a bending moment of 1.0 kN m. ...
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