466_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

466_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 05Ch05.qxd 9/25/08 460 2:29 PM Page 460 CHAPTER 5 Stresses in Beams (Basic Topics) Problem 5.10-6 Dimensions of cross section: b h 350 mm, h1 330 mm, and V 120 mm, t 7 mm, 60 kN Solution 5.10-6 Wide-flange beam (b) MINIMUM SHEAR STRESS IN THE WEB (Eq. 5-48) b 120 mm t 7 mm h 350 mm h1 60 kN taver 1 (bh3 12 bh3 + th3) 1 1 90.34 * 106 mm4 V (bh2 8It bh2 + th2) 1 1 19.35 MPa ; 1.093 25.97 MPa ; ; (d) SHEAR FORCE IN THE WEB (Eq. 5-49) Vweb 28.40 MPa th1 (2tmax + tmin) 3 Vweb V (a) MAXIMUM SHEAR STRESS IN THE WEB (Eq. 5-48a) tmax V th1 tmax taver MOMENT OF INERTIA (Eq. 5-47) I h2) 1 (c) AVERAGE SHEAR STRESS IN THE WEB (Eq. 5-50) 330 mm V Vb 2 (h 8It tmin 0.977 58.63 kN ; ; ; Problem 5.10-7 A cantilever beam AB of length L 6.5 ft supports a trapezoidal distributed load of peak intensity q, and minimum intensity q/2, that includes the weight of the beam (see figure). The beam is a steel W 12 14 wide-flange shape (see Table E-1(a), Appendix E). Calculate the maximum permissible load q based upon (a) an allowable bending stress sallow 18 ksi and (b) an allowable shear stress tallow 7.5 ksi. (Note: Obtain the moment of inertia and section modulus of the beam from Table E-1(a)) q — 2 q B A L = 6.5 ft Solution 5.10-7 b 3.97 in. t tf h h1 6.5 ft 11.9 in. 18 ksi q + qbL 2 2 Vmax t allow 7.5 ksi 1q 2 1 q 2L L+ L 22 22 3 Mmax 2 tf s allow a Mmax 11.45 in. L 14.9 in.3 h Vmax 0.225 in. S h1 88.6 # in.4 0.2 in. I 5 qL2 12 3 qL 4 W 12 14 ...
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