The allowable shear stress in the shaft is 70 MPa and the allowable angle of twist of end A relative to end D is 0.01 rad. What is the required minimum diameter d of the shaft if it ha a solid cross section? The shear modulus of elasticity of the shaft is 80 GPa. 900 N · m 2000 N m 400 N · m 700 N · m A 2 m 2 m D 2 m B,

The solid shaft is made of an elastic-perfectly plastic material as shown in Figure 5. Determine the torque T needed to form an elastic core in the shaft having a radius of py = 20 mm. If the shaft is 3 m long, through what angle does one end of the shaft twist with respect to the other end? When the torque is removed, determine the residual stress distribution in the shaft and the permanent angle of twist. T (MPa) 160 0.004 80 mm Figure 5 T y (rad)

Find the max shear stress in a 200mm tall, 150mm wide rectangular cross section using the appropriate reduced shear stress equation. Assume Vmax = 12kN. Find the max shear stress in a W12x50 cross-section using the appropriate estimated shear stress equation. Assume Vmax = 236kips. Find the max shear stress in bending in the cross section below if Vmax = 10 kips. 10" Flange 2" Web 2" 8" Flange 2" 10" • Identify where in the cross section the max shear will occur. • Determine the thickness of the cross-section at the location you wish to find shear stress. • Calculate the Ix for the shape (assume bending in the x with most basic beams). • Calculate Q by dividing the section into two pieces at the point you want shear stress. Select one of the pieces (either will work), I picked the top piece. • Use the Shear Stress equation to determine the requested stress. • Compare you answer: Max shear stress = at the center of the cross section.

Calculate the normal stress and the shear Stress at Points C and D The shaft is hollow; inner and outer radlus values are shown below on paper. N = 1000N M = -900N V = -650N Torque = 90N - Mr = 13Mm