STATICS & STRENGTH OF MATERIALS - Examples

A riveted butt joint is shown below. The diameter of the rivets is 7/8 inch. The width of the plates is 9 inches, and the thickness of the plates is 3/4 inch. The allowable stresses are as follows:
Rivets: t = 15, 000 psi st = 32, 000 psi sc = 34, 000 psi
Plate: t = 14,000 psi st = 28, 000 psi sc = 30, 000 psi

A.) Calculate the strength of the joint.
B.) Calculate the efficiency of the joint.

Part A:
1). P_shear = n(pd²/4)t_rivets = 16(p*(0.875 in)²/4)(15,000 psi) = 144,300 lb
2). P_bearing = n(d*t)s_C = 8(0.875 in* 0.75 in)(30,000 psi) = 157,500 lb
3). P_{plate,row 1} = (w - nd)t*s_T = (9 in - (2* 0.875 in))(0.75 in)(28,000 psi) = 152,250 lb
(6/8) P_{plate,row 2} = (w - nd)t*s_T = (9 in - (3* 0.875 in))(0.75 in)(28,000 psi) = 133,875 lb
P_{plate,row 2} = (8/6)(133,875 lb) = 178,500 lb

Then strength of joint equals lowest load causing failure = 144,300 lb

Part B:
efficiency = strength of joint/strength of solid plate = strength/(w*t)s_{T, plate} = 144,300 lb/ (9in*0.75in)(28,000 psi) = .763