# Axial Force and Normal Stress in Mechanics

A couple of questions about the behavior of normal stress.

For both of these, assume that the axial force applied is ideal, meaning distributed along the whole face of the member on both sides, and perfectly perpendicular to the face of the member, so that average normal stress is guaranteed to be equivalent to the exact stress on any point on the cross section. (This is opposed to having the axial force targeted at part of the face on both sides, so certain places on the cross-sectional area would be experiencing more stress.)

For simplicity, also assume we are dealing with an ordinary cylindrical member.

1. Is the normal stress identical no matter where along the beam you take a cross-section? Or is it larger the closer you get to the sides of the member, where the axial force is applied?

2. If it is, how would the member start deforming once the stress became too large? Where in the member would the material start to give.

I understand that these scenarios are ideal and never possible in the real world but hypothetically, if they were to happen, the member would still undergo deformation so I was curious what that would look like. Thank you!