677_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

677_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 08Ch08.qxd 9/18/08 11:04 AM Page 671 671 SECTION 8.4 Maximum Stresses in Beams VQ I tw txy A txy sx + sy s1 + 2 s1 A 8.27 MPa sx + sy s2 2 tmax A tmax 23.061 MPa 2 ; 2 sy sx 2 2 b + txy 2 0 Q h h ba b a b 2 4 2.19 sy 0 txy 26.69 MPa ƒ txy ƒ s2 s1 txy s1 s2 tmax 2 2 b + txy h1 h1 ba b 2 4 105 mm3 VQ I tw txy t w2 a 1b Pure shear: s1 ; 64.3 MPa a sy sx a 36.3 MPa s2 2 b + txy sx Q sy 2 sx a (c) NEUTRAL AXIS (POINT C) tmax ; 26.7 Mpa ; 26.7 Mpa 26.7 Mpa ; 7.5 k 7.5 k ; Problem 8.4-9 A W 12 14 wide-flange beam (see Table E-1(a), Appendix E) is simply supported with a span length of 120 in. (see figure). The beam supports two anti-symmetrically placed concentrated loads of 7.5 k each. At a cross section located 20 in. from the right-hand support, determine the principal stresses s1 and s2 and the maximum shear stress tmax at each of the following locations: (a) the top of the beam, (b) the top of the web, and (c) the neutral axis. W 12 × 14 D 40 in. 40 in. 20 in. 20 in. 120 in. Solution 8.4-9 RB RA 7.5 # 80 7.5 # 40 120 RB RA RB k 2.5 k (upward) 2.5 k (downward) At Section C-C M V RB # 20 in. RB V M (a) TOP OF THE BEAM (POINT A) sx sy 50 k # in. 2.5 k h Ma b 2 sx I 0 txy 14 I 88.6 in.4 b sy s1 s2 ; 0 103 psi 0 Uniaxial stress: s1 W12 3.361 s2 sx 3361 psi tmax ; 3.970 in. tmax 1680 psi ; tw 0.200 in. (b) TOP OF THE WEB (POINT B) tf 0.225 in. h 11.91 in. Ma h1 h h1 11.46 in. sx I 2tf sy h1 b 2 0 sx 3.234 103 psi ` sx ` 2 ...
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