Spring force due to Axial and Torque load?

In summary, the first theory discusses a spring under an axial load where the torque is given as WRcos(a), and the second theory discusses a spring under axial torque where T is given as Wsin(a). It is important to note that in Fig 12.5, alpha is the angle between T and the Y axis, not between T and the X axis. Additionally, the bending moment is equal to Tcos(alpha) and the axial torque is equal to Tsin(alpha), with the torque being around the X axis.
  • #1
Mechaman
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Homework Statement


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The first theory shows a spring under an axial load where the Torque is given as WRcos(a)

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The second theory shows a spring under axial Torque. T is given as Wsin(a)

Homework Equations


Given in links

The Attempt at a Solution


A torque T would be at full strength along the X axis, where cos(0) = 1. Where a bending moment would be at full strength along Y where sin(90) = 1.

It seems to be other way around though, what am I missing?
 
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  • #2
Mechaman said:
It seems to be other way around though, what am I missing?
In Fig 12.5, alpha is the angle between T and the Y axis, not between T and the X axis.
 
  • #3
haruspex said:
In Fig 12.5, alpha is the angle between T and the Y axis, not between T and the X axis.

Ok I see now how the axis has has rotated and has the same angle relative to the Y axis. So that means X axis is 0 degrees and Y is 90 degrees.

Why is the bending moment = Tcos(alpha) and axial Torque = TSin(alpha). Wouldn't measuring Torque be TCos(alpha) as Cos(0) = 1?
 
  • #4
Mechaman said:
Why is the bending moment = Tcos(alpha) and axial Torque = TSin(alpha). Wouldn't measuring Torque be TCos(alpha) as Cos(0) = 1?
The torque is around the X axis, so the vector is along the X axis, i.e. where alpha is zero. So yes, it is cos because cos(0)=1.
 
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  • #5
haruspex said:
The torque is around the X axis, so the vector is along the X axis, i.e. where alpha is zero. So yes, it is cos because cos(0)=1.
Thanks for response sorry for late reply. I see now.
 

1. What is the spring force due to axial and torque load?

The spring force due to axial and torque load is the force exerted by a spring when it is stretched or compressed due to an applied axial or torque load. This force is directly proportional to the displacement of the spring from its equilibrium position.

2. How do you calculate the spring force due to axial and torque load?

The formula for calculating the spring force due to axial and torque load is F = kx, where F is the spring force, k is the spring constant, and x is the displacement of the spring from its equilibrium position. This formula applies to both axial and torque loads.

3. What factors affect the spring force due to axial and torque load?

The spring force due to axial and torque load is affected by several factors including the spring's material, diameter, and length, as well as the magnitude and direction of the applied load. These factors can impact the spring's stiffness and its ability to resist deformation under a load.

4. How does the spring force change with increasing axial and torque load?

The spring force due to axial and torque load increases proportionally with the applied load. This means that as the load increases, the spring will stretch or compress further, resulting in a greater force exerted by the spring. However, if the load exceeds the spring's elastic limit, the force will no longer increase proportionally and the spring may become permanently deformed.

5. What is the difference between axial and torque load on a spring?

Axial load is a force applied along the axis of a spring, while torque load is a rotational force applied to the spring. Both types of loads cause the spring to compress or stretch, but the direction of the force and the resulting displacement of the spring will differ. Additionally, the formula for calculating the spring force will also differ depending on whether it is an axial or torque load.

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