What is the deformation of a shaft under axial loading?

In summary, the displacement of the shaft is equal to the summation of the displacement of each individual piece. The deformation at AB is 0.0024 in and at BC is 0.0026 in. The internal load at CD is 1 Kip and the deformation at CD is 0.042 in. There may have been a mistake in the calculations for the last two calculations, resulting in a difference of 10 in the power.
  • #1
MrJoseBravo
10
0

Homework Statement


http://prntscr.com/7rw2hj

Homework Equations


deformation = PL/AE
A= pi/4 (d^2)

The Attempt at a Solution


The displacement of the shaft is equal to the summation of the displacement of each individual piece. I started on end A, and got the internal force to be 6kips
then
deformation at AB ~ 6x50/(9pi/4 x 18x10^3)
= .0024 in

for the middle shaft i got the internal force to be 2 Kips ( this could be where i am wrong, I am not completely sure I am doing these FBD's right.

deformation at BC ~ 2x75/(pi x 18x10^3) ( the 4's cancel out)
= .026

internal load at CD is 1Kip

deformation at CD ~ 60/(pi/4 x 18x10^3)
= .042

for the last two calculations, i believe they are off by a power of 10...and i can't figure out why.
I have attached my FBD's also, thanks in advance
 

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  • #2
You just did the math wrong; 2*75/(pi*18000)=.0026 not .026
 
  • #3
thats ridiculous.
Did i have the fBD's correct?
 

1. What is MoM axial loading deformation?

MoM axial loading deformation refers to the deformation or bending that occurs in a material when it is subjected to an axial or compressive force along its length. This type of loading is commonly seen in structures such as columns and beams.

2. How is MoM axial loading deformation calculated?

The amount of deformation caused by axial loading can be calculated using the equation δ = PL/AE, where δ is the deformation, P is the applied force, L is the length of the material, A is the cross-sectional area, and E is the material's Young's modulus. This equation is known as Hooke's law.

3. What factors affect MoM axial loading deformation?

The amount of deformation caused by axial loading is affected by various factors, including the material properties (such as Young's modulus and yield strength), the cross-sectional area of the material, and the length of the material. Other factors such as the type of loading and the support conditions of the material also play a role.

4. How does MoM axial loading deformation differ from lateral loading deformation?

MoM axial loading deformation and lateral loading deformation are two different types of deformation that occur in materials. Axial loading deformation refers to the bending that occurs when a material is subjected to an axial or compressive force, while lateral loading deformation refers to the bending that occurs when a material is subjected to a transverse or bending force.

5. How can MoM axial loading deformation be minimized?

To minimize MoM axial loading deformation, engineers and designers can use materials with higher Young's modulus and yield strength, increase the cross-sectional area of the material, or shorten the length of the material. Properly designing the structure and using appropriate supports can also help to reduce the amount of deformation caused by axial loading.

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