Deformation Caused By Tightening A Nut

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In summary, the conversation discusses finding the deformation in CD and the equations and reasoning used to solve for it. The equation \delta = PL/AE is used, with P representing the force, L representing the length, A representing the area, and E representing the modulus of elasticity. The answer is supposed to be 9.73 kN, but the attempt at a solution resulted in 11.9^{kN}. The individual is unsure if the deformation is expressed correctly due to conflicting deformations caused by tightening and compressing the bolt.
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NinjaGodel
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Homework Statement



question.jpg


Homework Equations


[itex]\delta[/itex] = PL/AE


The Attempt at a Solution


attempt.jpg

As you can see I know that [itex]F_{cd}[/itex] is related to [itex]F_{be}[/itex]
and a second relationship can be found by the geometry of the deformations.
I end up with [itex]F_{cd}[/itex] = [itex]11.9^{kN}[/itex] but the answer is supposed to be
9.73 kN.

I am unsure when it comes to finding the deformation in CD. I'm not sure if the deformation is expressed correctly. My reasoning is: tightening the bolt causes a 'positive' deformation and a 'negative' deformation comes from compressing the bolt.
 
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The equation I use is \delta = PL/AE. Where P is the force, L is the length, A is the area and E is the modulus of elasticity. I then plug in the values for P, L, A and E and solve the equation to find the deformation.
 

1. What is deformation caused by tightening a nut?

The deformation caused by tightening a nut refers to the change in shape or size of a material that occurs when a nut is tightened onto a bolt or screw. This deformation can be both permanent and temporary, depending on the material and amount of force applied.

2. Why does deformation occur when tightening a nut?

Deformation occurs when tightening a nut because the force applied to the nut causes it to compress the material it is being tightened onto. This compression can result in a change in the material's shape or size, which is known as deformation.

3. What factors can contribute to deformation caused by tightening a nut?

There are several factors that can contribute to deformation when tightening a nut. These include the material properties of the nut and the material it is being tightened onto, the amount of force applied, and the design of the nut and bolt/screw.

4. Is deformation caused by tightening a nut always a problem?

No, deformation caused by tightening a nut is not always a problem. In fact, a certain amount of deformation is necessary for a secure and tight fit between the nut and bolt/screw. However, excessive deformation can lead to issues such as thread stripping or damage to the material being tightened onto.

5. How can deformation caused by tightening a nut be prevented?

To prevent excessive deformation when tightening a nut, it is important to use the appropriate amount of force and to make sure the nut and bolt/screw are properly matched in terms of size and material. Additionally, using lubrication on the threads can help reduce friction and minimize deformation. Proper tools and techniques should also be used to ensure even and controlled tightening.

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