Finding Average Normal Stress in Rod

[rugerts]

Homework Statement

Here's a snapshot of the problem:

Homework Equations

+ Newton's 2nd Law.

The Attempt at a Solution

My question is: why does the delta P term have only a single 40 kN force considered, whereas for delta EF there's an F/2?
Thanks for your time.

 

[Chestermiller]

I can't figure out what they did, but this is definitely not how I would have solved this problem. I would have written $$F=\frac{\frac{\pi}{4}(0.03^2)(101)(10^9)}{300}\delta_p$$and $$F_{EF}=\frac{\frac{\pi}{4}(0.04^2)(193)(10^9)}{450}\delta_p$$where $\delta_p$ in mm is the displacement that the plate shifts to the left. Then I would have substituted for F and $F_{EF}$ into Eqn. 1 to solve for $\delta_p$.

This gives $\delta_p=0.0874\ mm$, $F_{EF}=38380 N$, and $F=20810 N$. So the answer given in your book doesn't agree with this.