Concept explainers
The principal stresses at any point located on the surface of the shaft.
Answer to Problem 9.89RP
The principal stresses at any point located on the surface of the shaft are
Explanation of Solution
Given information:
Rotation of the propeller is
The engine develops the power of 900 kW.
Thrust on the shaft is
The outer diameter of the shaft is 250 mm.
Calculation:
Find the power transmission as shown below.
Here, P is the power transmission and
Substitute 900 kW for P and
Sketch the internal torque and forces for the propeller shaft as shown in Figure 1.
Find the section properties as shown below.
Find the cross sectional area as shown below.
Here, d is the diameter of the shaft.
Substitute 250 mm for d.
Find the polar moment of inertia as shown below.
Substitute 250 mm for d.
Find the normal stress as shown below.
Here, N is the normal force and A is the cross sectional area.
Substitute
Convert the unit from
Find the shear stress as shown below.
Here, T is the torque, J is the polar moment of inertia, and c is the centroidal distance between the neutral axis and the extreme fibre.
Substitute
Convert the unit from
Sketch the state of stress as shown in Figure 2.
Refer to Figure 2.
Find the in-plane principal stresses as shown below.
Here,
Substitute
The principal stresses are,
Therefore, the principal stresses at any point located on the surface of the shaft are
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