Question

The T shape is used as a post that supports a load of P- 50 kN. Note that the load P is applied 400 mm from the flange of the T shape. Determine the normal and shear stresses at point H. int: first, you must find A. the centroid, B. thev second moment of inertia about the z axis (not x axis), C. the internal forces and moments at the cross-section HK 6 150 mm 20 mm 0.8 m 400 mm 20 mm X 120 mm

Answer 1

at MK cross-section, the equivalent loading is: A = 130 times 20 + 120 times 20 = 5000 mm^2 x bar = A_1 x_1 + A_2 x_2/A_1 + A_2 = 130 times 20 times 140 + 120 times 20 times 65/5000 = 104 mm I_z = I_1, z + I_2, z I_2,z = I_2 + A_2 r_2^2 = 130^3 times 20/12 + 130 times 20 times (104 - 65)^2 = 2.738 times 10^7 mm^4 I_1 z = I_1 + A_1 r_21 ^2 = 20^3 times 120/12 + 120 times 20 times (140 - 104)^2 = 0.319 times 10^7 mm^4 Therefore I_z = 3.057 times 10^7 mm^4 Normal stress due to force rho sigma_A = rho/A = 20 times 10^3/5000 = 10 N/mm^2 = 10 MPa (compressive) Normal stress due to bending sigma_B = Mx bar/I_z = 50 times 10^3 times 400 times 10^4/3.057 times 10^7 = 68.04 MPa (tensile) Net Normal Stress of M, = sigma = sigma_B - sigma_A = 58.07 MPa (tensile)