Question

[3. (3 marks) Two steel plates each of 1.0 inch thickness (E-30 MPsi) are joined by SAE grade 8 bolt and no washers. Assume the bolt specification to be 34-10 UNC and bolt length of 2.75 inch. The joint is subjected to a fluctuating load from 1000 lbf to 9000 lbf. The yield strength of the plate material is 60 kpsi. Neglect the stress concentration in the threads of the bolt. Determ ine the following: [a]. whether the bolt is safe for continuous performance, if no pre-load is applied to the joint, [b]. whether the bolt is safe for continuous performance, if it is pre-loaded with 3000 lbf, and [cl. whether the bolt is safe for continuous performance, if it is pre-loaded with 9,000 lbf

Answer 1

Given thickness of plate, t = 1in For grade 8 bolt, d = 3/4 in = 0.75 in yield strength of plate, s_yt = 60 kpsi both length, L = 2.75 in For grade 8 bolt, F = 30 Mpsi For plate, E = 30 Mpsi Stiffness of bolt, k_b = pi/4 d^2 (E/l) = pi/4 (0.75)^2 30 times 10^6/2.75 = 4.817 times 10^6 lb/in stiffness of plate, k_c = (1 times 1) 30 times 10^6/2.75 = 10.909 times 10^6 lb/in Delta P = P (k_b/k_b + k_c) P = 1000 + 9000/2 = 5000 lbf = 5000 (4.817/4.817 + 10.909) = 1531.53 lb P_b = P_i + Delta P \r\n a) If P_i = 0 => P_b/A = S_yt/F_s 1531.5^3/pi/4 (0.75)^2 = 60 times 10^3/F S F S = 17.3 rightarrow Bolt is Safe b) If P_i = 3000 lbf => P_b = 3000 + 1531.53 = 4531.63 lbf