What is the deformation of a shaft under axial loading?

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AI Thread Summary
The discussion focuses on calculating the deformation of a shaft under axial loading using the formula deformation = PL/AE. The user initially calculated the deformation for different segments of the shaft, obtaining values of 0.0024 inches for segment AB, 0.026 for segment BC, and 0.042 for segment CD, but expressed uncertainty about the internal forces and Free Body Diagrams (FBDs). A response pointed out a significant error in the calculation for segment BC, correcting it to 0.0026 inches. The user seeks confirmation on the accuracy of their FBDs and calculations. Overall, the thread highlights the importance of accurate calculations and understanding of FBDs in determining shaft deformation.
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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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You just did the math wrong; 2*75/(pi*18000)=.0026 not .026
 
thats ridiculous.
Did i have the fBD's correct?
 

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