The torque applied to the A992 steel shaft causes it to twist, leading to shear stress within the material. Given the diameter of 75 mm and the shear modulus of elasticity of 75 GPa, we can analyze the shaft’s response to this torque.
First, we need to understand how shear stress is calculated in a solid circular shaft subjected to torque. The formula for shear stress (C2) is:
Where:
- T is the applied torque.
- r is the radius of the shaft (which is half the diameter).
- J is the polar moment of inertia for a circular cross-section, calculated as , where d is the diameter.
Since the shaft is fixed at both ends, we can expect that the maximum shear stress occurs at the center of the shaft. Depending on the amount of torque applied, we could determine whether the stresses exceed the material’s yield strength, leading to potential failure.
In summary, when torque is applied to the fixed A992 steel shaft, it induces shear stress proportional to the magnitude of the torque and inversely proportional to the polar moment of inertia. Proper design and analysis are necessary to ensure the shaft can withstand the applied loads without failing.