Why does pure axial loading cause shear stress?

[zachdr1]

I just found that applying an axial load of magnitude σ on both sides of a ductile rod will produce a max in plane shear stress of magnitude σ/2. Why is this? How can there be shear stress if only a normal force is applied?

 

[Dr.D]

Do you know about Mohr's Circle? If so, there is the answer. The state of stress at a point consists of all the stress components at that point. Which component you see depends upon the plane in which you look at the stresses. You see the pure axial stress only when you look at a section aligned normal to the load direction.

 

[Chestermiller]

I just found that applying an axial load of magnitude σ on both sides of a ductile rod will produce a max in plane shear stress of magnitude σ/2. Why is this? How can there be shear stress if only a normal force is applied?

For a plane oriented at an angle of 45 degrees to the rod axis, the stress vector acting on the plane has components in both the normal direction and the tangential (shear) direction (of the plane).