Residual Stress Analysis - Mechanics of Materials by Hibbeler

[Hirams_bro]

In my Mechanics of Materials book by Hibbeler, it discusses residual stress loading diagrams.
I'm sure anyone who has taken a Strenths of Materials course will remember the classic problem in residual stress analysis of a statically indeterminate bar between two fixed supports with an external load acting somewhere along its length. Here is a crude diagram. Beam
______________________________________
Fb ---->|________|<---P________________|<----- FaFb and Fa are support forces, and P is external loading applied at some point along the member.
On every loading diagram of this sort it they first create a stress-strain diagram for the loading and unloading phase with one side of the member usually going plastic during loading while the other remains elastic.

Now, my book says to create the unloading part of the diagram and find the residual stress we remove the external load P "which is equivalent to reversing P in the opposite direction as it was during loading."

My question is, how does removing the external load equate to reversing it? How are those two the same thing? I asked my professor this, but he is literally a semester away from retirement and doesn't really answer questions of this sort too well.

Homework Statement

Homework Equations

The Attempt at a Solution

 

[Hirams_bro]

Sorry, that drawing came out a lot cruder once it posted. I could scan the page from my book, but I don't know html and wouldn't know how to post it.

 

[weezy.darwin!]

According to my knowledge i guess adding a load in the opposite direction cancels out the initial load in the other direction (note that this load to be added has to be of the same magnitude). And knowing from the definition of residual stress that it a stress or deformation caused after the external load applied to a structure has been removed, the two loads cancels out meaning the beam does not experience any load again since the loads have canceled each other out. Hope this helps a little as i am student in my final year myself and i am looking into residual stress effect on structures for my final year project.