6.2. Deflection

Try these first

1. 1.

   Define torsion in the context of structural engineering.

   Hint

   Think about how a corkscrew works.

2. 2.

   What is the formula for shear stress in a circular shaft?

   Hint

   Recall the relationship between torque and radius.

3. 3.

   What is the formula for shear stress in a circular shaft?

   • τ = Tr/J
   • τ = T/J
   • τ = T/πr^2

   Hint

   Remember the variables involved in the shear stress equation.

4. 4.

   True or False: The angle of twist increases with the length of the shaft.

   • True
   • False

   Hint

   Consider the relationship defined in the equation.

5. 5.

   A solid circular shaft of radius 0.05 m experiences torque of 1000 Nm. Calculate the maximum shear stress and angle of twist if the shaft is 2 m long and made of steel with a shear modulus of 80 GPa.

   Hint

   Break down the components: calculate J, shear stress, and then angle of twist.

6. 6.

   Design a hollow shaft for transmission that withstands a torque of 600 Nm. The available materials are aluminum (G=26 GPa) and steel (G=80 GPa). Determine the outer diameter if the inner diameter is 0.03 m.

   Hint

   Consider the trade-offs between strength and weight to determine the optimal diameter.