463_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

463_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 05Ch05.qxd 9/25/08 2:29 PM Page 457 SECTION 5.10 Shear Stresses in Beams with Flanges Shear Stresses in Beams with Flanges Problem 5.10-1 through 5.10-6 A wide-flange beam (see figure) having y the cross section described below is subjected to a shear force V. Using the dimensions of the cross section, calculate the moment of inertia and then determine the following quantites: (a) The maximum shear stress tmax in the web. (b) The minimum shear stress tmin in the web. (c) The average shear stress taver (obtained by dividing the shear force by the area of the web) and the ratio tmax/taver. (d) The shear force Vweb carried in the web and the ratio Vweb /V. z h 12 in., h1 10.5 in., and V 6 in., t h t b NOTE: Disregard the fillets at the junctions of the web and flanges and determine all quantities, including the moment of inertia, by considering the cross section to consist of three rectangles. Problem 5.10-1 Dimensions of cross section: b O h1 Probs 5.10.1through 5.-10.6 0.5 in., 30 k. Solution 5.10-1 Wide-flange beam b t 0.5 in. h (b) MINIMUM SHEAR STRESS IN THE WEB (Eq. 5-48b) 6.0 in. 12.0 in. tmin Vb 2 (h 8It 10.5 in. V 30 k taver V th1 MOMENT OF INERTIA (Eq.5-47) tmax taver 1.014 1 (bh3 12 bh3 + th3) 1 1 333.4 in.4 V (bh2 8It bh2 + th2) 1 1 ; 5795 psi 5714 psi ; ; (d) SHEAR FORCE IN THE WEB (Eq. 5-49) (a) MAXIMUM SHEAR STRESS IN THE WEB (Eq. 5-48a) tmax 4555 psi (c) AVERAGE SHEAR STREAR IN THE WEB (Eq. 5-50) h1 I h12) ; Vweb th1 (2tmax + tmin) 3 Vweb V 0.942 ; 28.25 k ; 457 ...
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