A couple of magnitude M is applied to a square bar of side a. For each of the orientations shown, determine the maximum stress of the bar. M |ª| (a) M The maximum stress in orientation a is The maximum stress in orientation bis (b) M q³ M

The solid steel rod (1) shown in the figure has an allowable shear stress of 18 ksi. The brass tube (2) has an allowable shear stress of 6 ksi. The outside diameter of the tube is D2 = 1.50 in., and its wall thickness is t2 = 0.125 in. The tube is attached to a fixed plate at C, and both the rod and the tube are welded to a rigid end plate at B. Calculate (a) the largest torque T that can be applied at the upper end of the steel rod if the allowable shear stress in tube (2) is not to be exceeded. (b) the corresponding minimum diameter d1 required for steel rod (1). Rod (1) Tube (2) B D₂ IT -d₁ Fixed plate End plate

The d = 16-mm-diameter solid rod passes through a D = 21-mm-diameter hole in the support plate. When a load P is applied to the rod, the rod head rests on the support plate. The support plate has a thickness of b = 11 mm. The rod head has a diameter of a = 32 mm, and the head has a thickness of t = 10 mm. The shear stress in the rod head cannot exceed 130 MPa, the punching shear stress in the support plate cannot exceed 90 MPa, and the bearing stress between the rod head and the support plate cannot exceed 145 MPa. Determine the maximum value of Pmax that can be supported by the structure. P Support Plate Rod Answer: Pmax i Hole diameter D Head KN

Consider the state of plane stress shown. (Hint: Consider both in-plane and out-of-plane shearing stresses.) 7 ksi Determine the maximum shearing stress when ox- 18 ksi and ay = 8 ksl. The maximum shearing stress is ksi.