Team A
The A-36 steel shaft is subjected to the torques shown.
The shaft diameter is 40 mm, J = 2.51 × 10−7 m4 , and
the modulus of rigidity is G = 75 GPa.
Use the x-axis shown in the figure when summing torques.
a. 2 minutes: Draw a diagram showing torques within the shaft.
Is the torque in region CD positive or negative?
Positive
Negative
Compare your answer with that of the other team.
Does the sign of the torque depend on your choice for the direction of x? Yes No
b. 2 minutes: Draw the torque in region CD into the section cut. Make
sure the direction is indicated correctly (consistent with your x-axis).
Compare your answer with that of the other team.
Does the torque have the same orientation as the other team’s? Yes No
c. Find the angle of twist 𝜙𝐶/𝐷
=
𝑇𝐿
𝐽𝐺
. Use the sign convention used for angle of twist calculations
(consult p. 209).
Questions: do you count the torque as positive or negative? Positive
Compare your answer with that of the other team.
Negative
Same Different
Summary:
1. Often we are only interested in the magnitude of the maximum shear stress and, therefore, the sign
of the torque is not a major concern. In these situations, a degree of ‘sloppiness’ is acceptable.
2. However, for angle of twist calculations we have to be more careful, especially when the geometry
gets more involved and our intuition becomes shaky.
3. When you calculate the internal torque, the sign depends on the orientation of the x-axis relative to
the cross-section, i.e. does it point away from or towards the cross-section. Both are acceptable choices
and both give the same physical orientation of the torque.
4. When we calculate the angle of twist, it is strongly recommended to use the sign convention, i.e. have
the x-axis point away from the cross-section and use the right-hand rule to determine the orientation of
a positive torque (and thereby a positive angle of twist).
Team B
The A-36 steel shaft is subjected to the torques shown.
The shaft diameter is 40 mm, J = 2.51 × 10−7 m4 , and
the modulus of rigidity is G = 75 GPa.
Use the x-axis shown in the figure when summing torques.
a. 2 minutes: Draw a diagram showing torques within the shaft.
Is the torque in region CD positive or negative?
Positive
Negative
Compare your answer with that of the other team.
Does the sign of the torque depend on your choice for the direction of x? Yes No
b. 2 minutes: Draw the torque in region CD into the section cut. Make
sure the direction is indicated correctly (consistent with your x-axis).
Compare your answer with that of the other team.
Does the torque have the same orientation as the other team’s? Yes No
c. Find the angle of twist 𝜙𝐶/𝐷
=
𝑇𝐿
𝐽𝐺
. Use the sign convention used for angle of twist calculations
(consult p. 209).
Questions: do you count the torque as positive or negative? Positive
Compare your answer with that of the other team.
Negative
Same Different
Summary:
1. Often we are only interested in the magnitude of the maximum shear stress and, therefore, the sign
of the torque is not a major concern. In these situations, a degree of ‘sloppiness’ is acceptable.
2. However, for angle of twist calculations we have to be more careful, especially when the geometry
gets more involved and our intuition becomes shaky.
3. When you calculate the internal torque, the sign depends on the orientation of the x-axis relative to
the cross-section, i.e. does it point away from or towards the cross-section. Both are acceptable choices
and both give the same physical orientation of the torque.
4. When we calculate the angle of twist, it is strongly recommended to use the sign convention, i.e. have
the x-axis point away from the cross-section and use the right-hand rule to determine the orientation of
a positive torque (and thereby a positive angle of twist).