Strain, thermal strain and agle of twist

[Dell]

the cylindrical beam is attached to 2 walls and a torsion of Mo is applied 30cm from one end, the system is warmed ΔT, if point B is found at the coordinates (a,b) before deformation where will it be after the deformation? (a',b')

i found the reactions using equilibruim and the fact that the total angle of twist along the beam is 0, then i found the angle of twist at point B, but my problem is finding the effect of the warming on the point,
warming will cause a positive strain on the radial axis, giving me a larger radius, but will the point be stay in the same place and just grow?? is the torsion the only component i need to take into account, then using a triangle i can draw the new place of B

 

[Valkarie]

? Yes, warming will cause a positive strain on the radial axis, resulting in an increase in the radius of the beam. The point B will stay in the same place and just grow. The torsion is the only component you need to take into account. Using a triangle, you can calculate the new coordinates of point B (a', b').

 

[Mene]

I would like to clarify and provide an explanation to the concepts mentioned in the question. Strain refers to the change in shape or size of an object due to an applied force or temperature change. Thermal strain specifically refers to the change in shape or size of an object due to a change in temperature.

The angle of twist is a measure of the rotation or torsion of an object, in this case a cylindrical beam. It is important to note that the angle of twist is directly proportional to the applied torque, which is the twisting force.

In this scenario, the cylindrical beam is attached to two walls and a torsion of Mo is applied 30cm from one end. This means that the beam is experiencing both torsion and bending due to the applied torque. The system is then warmed by a change in temperature, resulting in a positive thermal strain on the radial axis. This will cause the beam to expand in size, resulting in a larger radius.

To determine the new coordinates of point B after the deformation, we need to consider both the effects of torsion and thermal strain. Using the principles of equilibrium and the fact that the total angle of twist along the beam is 0, we can determine the reactions at the two walls. This will help us calculate the angle of twist at point B.

However, the warming also affects the position of point B. The point will not stay in the same place and just grow, as the beam itself is rotating due to the applied torque. Therefore, we need to consider the effects of both torsion and thermal strain to accurately determine the new coordinates of point B, which can be done using a triangle method.

In conclusion, as a scientist, I would suggest taking into account both the torsion and thermal strain effects to accurately determine the new coordinates of point B after the deformation. This will provide a comprehensive understanding of the behavior of the cylindrical beam under the given conditions.