Question

Calculate the peak principal stress for the bracket and its location. Calculate the maximum deflection for the bracket. Use the stress concentration and nominal stress to calculate the the stress at the fillet and hole. Please show all work for the hand calculations.

Assume material is AISI 1020. The left face of the bracket is fixed. A load of 3500 lb. is applied to the face as shown.

Answer 1

3500lb 1ft = 0.3048 metrial rightarrow Hole is Subjected to bending - stress, as well as axial-compressive - stress Now, bending occurs in the whole plate so, 6 = MY/I = (3500) times (2.25) times (0.75/2)/(0.75)^3 times 4/12 1 rightarrow 6 = 21000 lb^2/ft^2 (along z-direction) direct-compressive-stress = land/area = 3500/(4.25 - 1.50) times (4.0 - 1.50) = 509.09 rightarrow k_t = stress concentration factor = 1 + 2 times (1/1) [1 + 2(9/0)]] = 3 (Therefore it is circle) S0, Net-axial compressive stress = (Stress can factor) times 509.09 = 3 times 509.09 = 1529.7 lb/ft^2 (along-y) Now, talking about fillet, it is subjected to tasile stress sly. So, We need to calculate size of fillet so, 6tasile = land/1heat times length of fillet = 3500/1heat times 4.00 so, 6(tensile MAX) = 3500/0.707 times h times 4 (for fillet) rightarrow h need to be calculated only rightarrow 0.707 is because max stress will be at 45 degree