Solve Axial Displacement: 80kN Load on Steel Rod Attached to Aluminum Tube

In summary, the conversation discusses a problem involving an assembly with an aluminum tube and a steel rod. The goal is to determine the displacement of point C when a tensile load of 80 kN is applied to the rod. The conversation also includes the equations and steps used to solve the problem, including the use of Hooke's Law and the superposition of displacements.
  • #1
mbaron
6
0
Please give me some guidance on this problem. I can attach the figure if it will help.

The assembly shown in the figure consists of an aluminum tube AB having a cross sectional area of 400mm2. A steel rod having a diameter of 10 mm is attached to a rigid collar and passes through the tube. If a tensile load of 80 kN is applied to the rod, determine the displacement of the end C of the rod. Take Est = 200 GPa, Eal = 70 GPa. [ΔL = 4.20 mm]


Here is what I have so far:

[tex] E_al = \frac{\sigma}{\epsilon} [/tex]

[tex] 70GPa = \frac{\frac{Force}{Area}}{\frac{\delta_length}{length_0}} [/tex]

[tex] 70GPa = \frac{\frac{80KN}{.0004m^2}}{\frac{\delta_length}{.4m}} [/tex]

[tex] \delta_length = \left[ \frac{80KN}{.0004m^2} \right] .4m [/tex]

[tex] \delta_length = 1.1428m[/tex]


The displacement is already to large for the given answer. This does not yet include the displacement of the steel bar.

I attached the image that was provided with the homework problem.
 

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  • #2
Can you post the picture?
 
  • #3
Hello again,

You have a superposition of displacements, which will give you the final the displacement of point C. First you have the displacement of the steel rod due to the tensile stress, and then the displacement of the aluminium tube due to compressive stress.

[tex] \delta_{aluminium} + \delta_{steel} = \delta_{C} [/tex]

Use: (displacement of a prismatic bar based on Hooke's Law)

[tex] \delta = \frac{PL}{EA} [/tex]

Becareful of your units.
 
  • #4
Thanks for the response. I worked it out.

-Morgan
 

1. What is axial displacement?

Axial displacement refers to the movement of a material or structure in the axial direction, which is the direction along its length. It is a measure of how much the material or structure has stretched or compressed under a load.

2. How is axial displacement calculated?

Axial displacement is calculated by dividing the applied load by the cross-sectional area of the material and multiplying by its length. This gives the amount of displacement in the axial direction.

3. What is the significance of a 80kN load on a steel rod attached to an aluminum tube?

The 80kN load is the amount of force applied to the steel rod, which is attached to the aluminum tube. This load can cause the materials to undergo axial displacement and potentially affect the overall strength and stability of the structure.

4. How does the material of the rod and tube affect the axial displacement?

The material of the rod and tube can greatly affect the axial displacement. Steel is a stronger and stiffer material compared to aluminum, so it may experience less displacement under the same load. However, aluminum is lighter and more flexible, so it may deform more easily under the load.

5. What factors can influence the accuracy of solving for axial displacement?

The accuracy of solving for axial displacement can be influenced by factors such as the properties of the materials, the applied load, the geometry of the structure, and any external forces or constraints acting on the system. It is important to consider all these factors when calculating axial displacement.

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