Question on deformations of members under axial loading

In summary, the conversation discusses the deformation of a solid brass rod and an aluminum tube with threaded screw on covers. The calculations for the elongations of each part add up to a total deformation of 3.75E-4, which is found by multiplying the quarter turn and the pitch of the screw. There is confusion about why the total deformation is not the difference between the elongations of the two parts.
  • #1
jeash
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Homework Statement


N/A

A 250-mm long aluminum tube of 36mm outer diameter and 28mm inner diameter may be closed at both ends by means of single threaded screw on covers of 1.5mm pitch. With one cover screwed on tight, a solid brass rod of 25mm diameter is placed inside the tube and the second cover is screwed on. Since the rod is slightly longer than the tube it is observed that the cover must be forced against the rod by rotating it one-quarter turn before it can be tightly closed. Determine the deformation of the rod and of the tube.

Homework Equations

I have no problem calculating the elongations of each part, but wonder in the end why they add up to 3.75E-4 (the total deformation of the system as found from the threaded screw) when I thought the outer tube is in tension and the inner rod is in compression. Wouldn't this mean the total deformation of the system would be the difference between the two values? Our professor says no, but I am confused as to why.

Any help is appreciated/if you have more info as to the solution let me know.

The Attempt at a Solution



With other given values I calculated delta rod=0.1325mm and delta tube=0.1325, which adds up to delta total=3.75E-4 (found by multiplying .25 turn* the pitch of 1.5mm)
 
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  • #2
Can you explain your statement: "delta rod=0.1325mm and delta tube=0.1325, which adds up to delta total=3.75E-4"? The final length of both the tube and the rod is 250.1325 mm? Or not?
 

1. What is axial loading?

Axial loading refers to a type of force that acts along the longitudinal axis of a member, causing it to either compress or stretch in the direction of the force.

2. What are the different types of deformations that can occur under axial loading?

The two main types of deformations that can occur under axial loading are compression and tension. Compression occurs when a member is pushed together, causing it to shorten in length. Tension occurs when a member is pulled apart, causing it to lengthen.

3. What factors affect the deformation of a member under axial loading?

The deformation of a member under axial loading is affected by several factors, including the material properties of the member, the magnitude and direction of the applied force, and the length and cross-sectional area of the member.

4. How is the deformation of a member under axial loading calculated?

The deformation of a member under axial loading can be calculated using the formula δ = PL/AE, where δ is the deformation, P is the applied force, L is the length of the member, A is the cross-sectional area, and E is the modulus of elasticity of the material.

5. What are some common applications of understanding deformations under axial loading?

Understanding deformations under axial loading is important in the design and analysis of structures such as buildings, bridges, and other load-bearing structures. It also has applications in mechanical engineering, such as in the design of machine parts and mechanical systems.

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