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The cross section of a beam is a T with the dimension shown in Figure. The moment at the section is M = 4 kip-ft. Determine the: Location of the internal axis of the cross section; Moment of inertia with respect to the neutral axis; Maximum tensile stress and the maximum compressive stress on the cross section. y_c = sigma y_ci A_i/sigma A_i, l =bh^3/12 + Ad^2 Solution M = moment = 4 kip-ft = 4000 lb-ft = 333.33 lb-in Area of flage = 1x5 = 5 in2 area of web = 1x5 = 5 in2 y for flange = 5+1/2 = 5.5in y for web = 5/2 = 2.5in yc = [5x5.5+5x2.5]/[5+5] yc = 4in yt = distance between centre of gravity of section to upper fibre = 5 + 1 - 4 = 2in I = (bd 3 /12) + Ah 2 moment of inertia for flange I = (5x1 3 /12) + 5x(5.5-4) 2 = 11.67 in4 moment of inertia for web I = (1x5 3 /12) + 5x(4-5/2) 2 = 21.67 in4 total moment of inertia = 11.67+21.67 = 33.34 in4 Maximum tensile stress occurs at lower extreme fibre tensile stress = (M/I) Yc = (333.33/21.67 )4 = 61.53 psi Maximum compression stress occurs at upper extreme fibre compression stress = (M/I) Yt = (333.33/21.67 )2 = 30.76 psi .

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Maximum tensile stress occurs at lower extreme fibre
tensile stress = (M/I) Yc = (333.33/21.67 )4 = 61.53 psi
Maximum compression stress occurs at upper extreme fibre
compression stress = (M/I) Yt = (333.33/21.67 )2 = 30.76 psi

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