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12_5 - 12.5 A tee-shaped flexural member(Fig P12.5b is...

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12.5 A tee-shaped flexural member (Fig. P12.5 b ) is subjected to an internal axial force of 2,200 lb, an internal shear force of 1,600 lb, and an internal bending moment of 4,000 lb-ft, as shown in Fig. P12.5 a . Determine the normal and shear stresses at point H , which is located 1.5 in. below the top surface of the tee shape. Show these stresses on a stress element. Fig. P12.5 a Fig. P12.5 b Solution Centroid location in y direction: (reference axis at bottom of tee shape) Shape Width b Height h Area A i y i (from bottom) y i A i (in.) (in.) (in. 2 ) (in.) (in. 3 ) top flange 6 1 6.000 6.500 39.000 stem 1 6 6.000 3.000 18.000 12.000 in. 2 57.000 in. 3 3 2 57.0 in. 4.750 in. 12.0 in. i i i y A y A Σ = = = Σ (measured upward from bottom edge of stem) Moment of inertia about the z axis: (i.e., horizontal axis) Shape I C d = y i y d²A I C + d²A (in. 4 ) (in.) (in. 4 ) (in.
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