# Physical Significance of Max Shear Stress in a Rod in Compression

For a rod in compression, the max shear stress at a point is $$\pm\sigma_x/2$$, i.e. half the compressive stress applied at either end.

This value is obtained using the equation for $$\sigma_\theta$$, the longitudinal stress at any point in a material if it is subjected to a set of stresses (equivalently represented by normal and shear stresses), then rotated through an angle $$\theta$$, while these same stresses remain in place.

So, does this max shear stress in a rod in compression refer to when the rod is rotated by 45 degrees such that it experiences max shear stress under the same compressive load? Or is this a value that the rod experiences at all times as a result of weaknesses in the material along different axes? Because at an angle of 0 degrees, there wouldn't be any shear stress in a perfectly homogeneous rod under compression, would there?

What you are referring to is the shear stress in Mohr circle at a plane rotated counterclockwise 45 degrees from the horizontal $$\sigma_n$$ axis.
It means if we consider a differential small cube of the rod under just plane compression, normal stress, at a plane with an angle of 45 the average $$\sigma_n = \frac{ (o+\sigma_{n\ max})}{2 }= \tau_{xy\ max}$$.