Concept explainers
(a)
The force
(a)
Answer to Problem 73P
The force
Explanation of Solution
The figure below shows the free body diagram of pulley A.
Figure-(1)
The figure below shows the free body diagram of pulley B.
Figure-(2)
Convert the forces from
Calculate the force
Here, the force acting on pulley
Conclusion:
Substitute
Thus, the force
(b)
The bearing reaction forces, assuming the bearing act as simple supports.
(b)
Answer to Problem 73P
The bearing reaction forces, assuming the bearing act as simple supports at
Explanation of Solution
Write the expression for moment about bearing
Here, the reaction force at bearing
Write expression for the equation to balance the forces in
Here, the reaction force at bearing
Write expression for the moment about bearing
Here, the reaction force at bearing
Write expression for the equation to balance the forces in
Here, the reaction force at bearing
Calculate the reaction forces at bearing
Here, the reaction force at bearing
Calculate the reaction forces at bearing
Here, the reaction force at bearing
Conclusion:
Substitute
Convert
Substitute
Substitute
Substitute
Substitute
Substitute
Thus, the bearing reaction forces, assuming the bearing act as simple supports at
(c)
The shear force and bending moment diagram for the shaft.
(c)
Answer to Problem 73P
The shear force and bending moment diagram for the shaft in
Figure-(2)
The shear force and bending moment diagram for the shaft in
Figure-(3)
Explanation of Solution
The calculations for shear force and bending moment diagram in
Calculate the shear force at
Here, the shear force at
Calculate the shear force at
Here, the shear force at
Calculate the shear force at
Here, the shear force at
Calculate the shear force at
Here, the shear force at
Calculate the moment at
Here, the moment at
Calculate the moment at
Here, the moment at
Calculate the moment at
Here, the moment at
The calculations for shear force and bending moment diagram in
Calculate the shear force at
Here, the shear force at
Calculate the shear force at
Here, the shear force at
Calculate the shear force at
Here, the shear force at
Calculate the shear force at
Here, the shear force at
Calculate the moment at
Here, the moment at
Calculate the moment at
Here, the moment at
Calculate the moment at
Here, the moment at
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Thus, the shear force and bending moment diagram in
Figure-(4)
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Thus, the shear force and bending moment diagram in
Figure-(5)
(d)
The bending stress at point of maximum bending moment.
The shear stress at point of maximum bending moment.
(d)
Answer to Problem 73P
The bending stress at point of maximum bending moment is
The shear stress at point of maximum bending moment is
Explanation of Solution
Write the net moment at
Here, the net moment at
Write the net moment at
Here, the net moment at
Write the torque transmitted by shaft from
Here, the torque transmitted by shaft from
Calculate the bending stress.
Here, the bending stress is
Calculate the shear stress.
Here, the shear stress is
Conclusion:
Substitute
Substitute
Since,
Substitute
Substitute
Thus, the bending stress at point of maximum bending moment is
Substitute
Thus, the shear stress at point of maximum bending moment is
(e)
The principal stresses at point of maximum bending moment.
The maximum shear stress at point of maximum bending moment.
(e)
Answer to Problem 73P
The principal stresses at point of maximum bending moment are
The maximum shear stress at point of maximum bending moment is
Explanation of Solution
Calculate the maximum principal stress.
Here, the maximum principal stress is
Calculate the minimum principal stress.
Here, the minimum principal stress is
Calculate the maximum shear stress.
Here, maximum shear stress is
Conclusion:
Substitute
Substitute
Thus, the principal stresses at point of maximum bending moment are
Substitute
Thus, the maximum shear stress at point of maximum bending moment is
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Chapter 3 Solutions
Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)