A bracket ABCD having a hollow circular cross section consists of a vertical arm
ID: 1851808 • Letter: A
Question
A bracket ABCD having a hollow circular cross section consists of a vertical arm AB (L = 6 ft), a horizontal arm BC parallel to the x0 axis, and a horizontal arm CD parallel to the z0 axis (sec figure). The arms BC and CD have lengths b1 = 3.6 ft and b2 = 2.2 ft, respectively. The outer and inner diameters of the bracket are d2 = 7.5 in. and d1 = 6.8 in. An inclined load P = 2200 lb acts at point D along line DH. Determine the maximum tensile, compressive, and shear stresses in the vertical arm.sExplanation / Answer
tan(HDC) = 6/2.2 =
HDC = 69.863 deg =
Pcos component will cause torsion
T = Pcos*b1 = 220cos*3.6 = 272.6496 lb-ft
M = P*(3.6^2 + 2.2^2)1/2 = 928.181 lb-ft
I = /64*(d2^4 - d1^4) = 50.3599 in^4
J = /32*(d2^4 - d1^4) = 100.7198 in^4
Area = 7.861 in^2
Tensile
= -Psin/A + Mc/I = -220sin69.863*12/7.861 + 928.181*12*3.75/50.3599 = 514.0852 psi
Compressive
= -Psin/A - Mc/I = -220sin69.863*12/7.861 - 928.181*12*3.75/50.3599 = -855.668 psi
Shear
= Tr/J = 272.6496*12*3.75/100.7198 = 121.815 psi
Max Shear Stress max = ((x/2)^2 + xy^2)^0.5 = ((855.668/2)^2 + 121.815^2)^0.5 = 444.837 psi
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