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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Unformatted text preview: 06Ch06.qxd 9/24/08 514 5:34 AM Page 514 CHAPTER 6 Stresses in Beams (Advanced Topics) Solution 6.3-6 Plastic beam with aluminum strips (1) Plastic segments: b 3d 75 mm d 120 mm (2) Aluminum strips: b 75 mm Ea Ep 2c Plastic: I1 4t 5d M 3 mm 1.0 kN # m 212 mm 1 (75)(40)3 + (75)(40)(83)2 d 12 + 3 GPa 75 GPa h t All dimensions in millimeters. 40 mm 1 (75)(120)3 12 52.934 * 106 mm4 ALUMINUM: TRANSFORMED SECTION (PLASTIC) 2c 1 (1875)(3)3 + (1875)(3)(104.5)2 12 + I2 1 (1875)(3)3 + (1875)(3)(61.5)2 d 12 165.420 * 106 mm4 I1 + I2 IT 218.35 * 106 mm4 MAXIMUM STRESS IN THE PLASTIC (1) (EQ. 6-15) sp Plastic segments are not changed. n Ea Ep s1 25 (25)(75 mm) t) ; 0.47 MPa MAXIMUM STRESS IN THE ALUMINUM (2) (EQ. 6-17) sa s2 Width of aluminum strips nb M(h/2 IT M(h/2)n IT 12.14 MPa ; 1875 mm 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 the figure part a). The modulus of elasticity of the steel is 20 times that of the wood. (a) If the allowable stresses in the 4 in. steel and wood are 12,000 psi and 900 psi, respectively, what is the allowable load qallow? (Note: Disregard the weight of z the beam, and see Table E-5a 8 in. 6 in. of Appendix E for the dimensions and properties of the Steel angle angles.) (b) Repeat part a if a 1 in. 10 in. wood flange (actual dimensions) is added (see figure part b). (a) 4 in. yC y Wood flange C z Wood beam 2 in. Wood beam Steel angle 2 in. (b) ...
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