Question

A horizontal bracket ABC consists of two perpendicular arms AB of a length 0.75 m and BC of a length 0.5 m. The bracket has a solid, circular cross section with a diameter equal to 65 mm. The bracket is inserted in a frictionless sleeve at A (which is slightly larger in diameter), so it is free to rotate about the z0 axis at A and is supported by a pin at C.

Moments are applied at point C M1= 1.5 kN m in the x direction and M2 =1.0 kN m acts in the -z direction. Considering only the moments M1 and M2, calculate the maximum tensile stress, the maximum compressive stress, and the maximum in-plane shear stress at point p, which is located at support A on the side of the bracket at mid-height.

0.75 m Frictionless sleeve embedded in support 20 0.5 m -65 mm Cross section at A

Answer 1

Given data: diameter (d) - 65mm = .065m Length of Arm CAB), b2= 0.75m Length of Arm CBC), by = 0.5m M, = 1.5 km M2 = :0 KN.M kom Analysis Step-19 The propereties of the Cros-section : d=65mm , as - 32.5mm A = 2 = 3652 = 3. 318 x 103 mm2 Is een dy = x 64 = 8.762 x 105 mma Ip = 21, : Ip = 1.752x106 com 4 Q = {re? - * (32-5')3 Q = 2.289x104mme? Step-21) Streess Resultants at lupporzt A N2=0 Axial force My so Mx = -M2 b + M, 3 Mx = 0 T:0 Torsional Fructionless Sleeve at support A (M2). Vy se mohou s = -2

0x=0 y=o 0 exy = 0 » Exy = Id -2x (2.289 x104) 8.762 x105 x.065 = -0.8038 mpa ~ -0.804 mpa Zmax = Vox-by) ?t zxył = Vzxy? = (-0.804² раги каал , мм = -8o4 мри stresses at point p on the side of the bracket. exy 117 og THANK YOU