2.1. Shear Stress Formula

Try these first

1. 1.

   Define shear stress.

   Hint

   Think about how the forces are applied.

2. 2.

   What is the formula for the polar moment of inertia for a solid shaft?

   Hint

   Remember the equation for solid shafts.

3. 3.

   What is the formula to calculate shear stress in a circular shaft?

   • τ = Tr/J
   • τ = J/(Tr)
   • τ = TL/(GJ)

   Hint

   Focus on how torque relates to shear.

4. 4.

   True or False: The polar moment of inertia for a solid shaft is J = πd^4/32.

   • True
   • False

   Hint

   Recall the formula you learned.

5. 5.

   A circular shaft of 0.08 m diameter and length 1.5 m is subjected to a torque of 300 Nm. Calculate the shear stress at a distance of 0.04 m from the center and the angle of twist. Shear modulus is 70 GPa.

   Hint

   Utilize the correct formulas in steps.

6. 6.

   Design a hollow shaft that can safely handle a torque of 1000 Nm without exceeding a shear stress of 50 MPa. Determine the outer and inner diameters, assuming a material with a shear modulus of 75 GPa.

   Hint

   Remember to rearrange the formula to find the necessary diameters.