Strain, thermal strain and agle of twist

In summary, when a cylindrical beam is attached to 2 walls and a torsion of Mo is applied 30cm from one end, and the system is warmed ΔT, the point B at coordinates (a,b) will experience a positive strain on the radial axis, causing an increase in the radius of the beam. However, the point B will remain in the same location and only grow. The only component to consider is the torsion, and using a triangle, the new coordinates of point B (a',b') can be calculated.
  • #1
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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')

Capture.JPG


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
 

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  • #2
? 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').
 
  • #3


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.
 

What is strain?

Strain is a measure of the deformation of a material in response to an applied force. It is defined as the change in length or shape of a material relative to its original length or shape.

What is thermal strain?

Thermal strain is a type of strain that occurs when a material is exposed to changes in temperature. It is caused by the expansion or contraction of the material due to thermal energy.

What factors affect strain?

The amount of strain experienced by a material is influenced by its composition, shape, and the magnitude and direction of the applied force. Temperature changes can also cause thermal strain.

What is the relationship between strain and stress?

Strain and stress are closely related concepts. Stress is the force applied to a material, while strain is the resulting deformation. In other words, stress causes strain.

What is the angle of twist?

The angle of twist is a measure of the amount of rotation that occurs in a material due to an applied torque or twisting force. It is a measure of the flexibility or stiffness of a material.

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