Compound shaft-axial force,internal force

[chandran]

There is a compound solid shaft. Outer shaft is made of material A and inner shaft is made of material B. One end of the shaft is fixed and another end has a force of F.

Will the internal force in each of the shaft members vary? why. If i pull with a force F, I think the internal force F will be same each of the solid members.

Similarly if a torque is applied at one end and the other end is fixed, will the internal torque differ in the two shafts

 

[Astronuc]

The stiffer material will bear greater load.

In a compound shaft, the displacements of the different materials are equal.

In the case of a torque, the shear stresses will also be different. For one, the torsional stress at radius r is given by,

$$\tau\,=\,\frac{Tr}{J}$$

where T is applied Torque, r is radius and J is torsional moment of inertia.

 

[piercas]

?

I would respond by saying that the internal forces and torques in each of the shaft members will indeed vary. This is because each material has its own unique properties, such as strength and stiffness, which will affect how it responds to external forces and torques.

In the case of the compound shaft, the outer shaft made of material A may be able to withstand more force before deforming compared to the inner shaft made of material B. This means that the internal force in the outer shaft will be greater than that in the inner shaft. Similarly, the internal torque in each shaft will also differ due to the difference in their material properties.

Additionally, the distribution of the external force or torque along the length of the shaft may also affect the internal forces and torques. For example, if the force or torque is applied at one end of the shaft, the internal force and torque will be highest at that end and decrease gradually along the length of the shaft.

As a result, it is important to consider the material properties and distribution of external forces and torques when analyzing the internal forces and torques in a compound shaft. This understanding can help engineers design more efficient and reliable shaft systems for various applications.