How Is Maximum Shear Stress Calculated for a Solid Circular Shaft?

[Solidsam]

Homework Statement

A solid circular steel drive shaft is 4 m long and 60 mm diameter. The modulus of
rigidity of the steel is 85 GPa and its maximum allowable shear strength is 150 MPa.
The shaft is used to transmit a power of 30 kW while rotating at 500 rev/min.
Calculate the following:

a) the torque carried by the rotating shaft [2 marks]

Homework Equations

J=pi(R^4)/2=1.272*10^6 mm^4

T=(J*maximum shear stress)/r

Homework Statement

How do i get the maximum shear stress?

 

[SteamKing]

You haven't shown any equations or work to determine the amount of torque acting on the shaft at the rated conditions.

 

[Solidsam]

You haven't shown any equations or work to determine the amount of torque acting on the shaft at the rated conditions.

ok well could u tell me what i should do

 

[Solidsam]

oh T=30000/(500*(pi/30))

 

[DeeNos]

To calculate the maximum shear stress on the solid shaft, you can use the formula T = (J*maximum shear stress)/r, where T is the torque carried by the shaft, J is the polar moment of inertia, and r is the radius of the shaft. In this case, we have the values for T (30 kW), J (1.272*10^6 mm^4), and r (30 mm). Therefore, we can rearrange the formula to solve for the maximum shear stress, which gives us a value of 0.785 MPa. This value is well within the maximum allowable shear strength of 150 MPa, indicating that the shaft is suitable for transmitting the given power at the specified rotational speed.