05-04 Chap Gere

# 05-04 Chap Gere - SECTION 5.10 Shear Stresses in Circular Beams with Flanges Problem 5.10-2 Dimensions of cross section b ϭ 180 mm t ϭ 12 mm h ϭ

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Shear Stresses in Circular Beams Problem 5.9-1 A wood pole of solid circular cross section ( d 5 diameter) is subjected to a horizontal force P 5 450 lb (see figure). The length of the pole is L 5 6 ft, and the allowable stresses in the wood are 1900 psi in bending and 120 psi in shear. Determine the minimum required diameter of the pole based upon (a) the allowable bending stress, and (b) the allowable shear stress. Solution 5.9-1 Wood pole of circular cross section 338 CHAPTER 5 Stresses in Beams L P d d P 5 450 lb L 5 6 ft 5 72 in. s allow 5 1900 psi t allow 5 120 psi Find diameter d (a) Based upon bending stress M max 5 PL 5 (450 lb)(72 in.) 5 32,400 lb-in. d min 5 5.58 in. (b) Based upon shear stress V max 5 450 lb d min 5 2.52 in. (Bending stress governs.) t 5 4 V 3 A 5 16 V 3 p d 2 Ê d 2 5 16 V max 3 p t allow 5 6.366 in. 2 s 5 M S 5 32 M p d 3 Ê d 3 5 32 M max p s allow 5 173.7 in. 3 L P d d Problem 5.9-2 A simple log bridge in a remote area consists of two parallel logs with planks across them (see figure). The logs are Douglas fir with average diameter 300 mm. A truck moves slowly across the bridge, which spans 2.5 m. Assume that the weight of the truck is equally distributed between the two logs. Because the wheelbase of the truck is greater than 2.5 m, only one set of wheels is on the bridge at a time. Thus, the wheel load on one log is equivalent to a concentrated load W acting at any position along the span. In addition, the weight of one log and the planks it supports is equivalent to a uniform load of 850 N/m acting on the log. Determine the maximum permissible wheel load W based upon (a) an allowable bending stress of 7.0 MPa, and (b) an allowable shear stress of 0.75 MPa.

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Problem 5.10-2 Dimensions of cross section: b 5 180 mm, t 5 12 mm, h 5 420 mm, h 1 5 380 mm, and V 5 125 kN. Solution 5.10-2 Wide-flange beam SECTION 5.10 Shear Stresses in Circular Beams with Flanges 343 b 5 180 mm t 5 12 mm h 5 420 mm h 1 5 380 mm V 5 125 kN M OMENT OF INERTIA (Eq. 5-47) (a) M AXIMUM SHEAR STRESS IN THE WEB (Eq. 5-48a) t max 5 V 8 It ( bh 2 2 bh 1 2 1 th 1 2 ) 5 28.43 MPa I 5 1 12 ( bh 3 2 bh 1 3 1 th 1 3 ) 5 343.1 3 10 6 mm 4 (b) M INIMUM SHEAR STRESS IN THE WEB (Eq. 5-48b) (c) A VERAGE SHEAR STRESS IN THE WEB (Eq. 5-50) (d) S HEAR FORCE IN THE WEB (Eq. 5-49) V web V 5 0.957 V web 5 th 1 3 (2 t max 1 t min ) 5 119.7 kN t max t aver 5 1.037 t aver 5 V th 1 5 27.41 MPa t min 5 Vb 8 It ( h 2 2 h 1 2 ) 5 21.86 MPa t h 1 b h Problem 5.10-3 Wide-flange shape, W 8 3 28 (see Table E-1, Appendix E); V 5 10 k. Solution 5.10-3 Wide-flange beam W 8 3 28 b 5 6.535 in. t 5 0.285 in. h 5 8.06 in. h 1 5 7.13 in. V 5 10 k M OMENT OF INERTIA (Eq. 5-47) (a) M AXIMUM SHEAR STRESS IN THE WEB (Eq. 5-48a) (b) M INIMUM SHEAR STRESS IN THE WEB (Eq. 5-48b) t min 5 Vb 8 It ( h 2 2 h 2 1 ) 5 4202 psi t max 5 V 8 It ( bh 2 2 bh 2 1 1 th 1 2 ) 5 4861 psi I 5 1 12 ( bh 3 2 bh 3 1 1 th 3 1 ) 5 96.36 in. 4 (c) A VERAGE SHEAR STRESS IN THE WEB (Eq. 5-50) (d) Shear force in the web (Eq. 5-49) V web V 5 0.943 V web 5 th 1 3 t max 1 t min ) 5 9.432 k t max t aver 5 0.988 t aver 5 V th 1 5 4921 psi t h 1
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## This note was uploaded on 10/01/2009 for the course MEGR 2144 taught by Professor Sharpe during the Fall '08 term at UNC Charlotte.

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05-04 Chap Gere - SECTION 5.10 Shear Stresses in Circular Beams with Flanges Problem 5.10-2 Dimensions of cross section b ϭ 180 mm t ϭ 12 mm h ϭ

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