Rationale

These experiments will test samples in compression. For slender samples, the applied load can cause two different responses: an elastic/plastic response analogous to that obtained in a tensile test, or a buckling instability before the
sample reaches its elastic limit (yield point) in compression.
This last deformation mode is called Euler Buckling and is
illustrated in the diagram. The force, P_cr , is the critical force
for the buckling response. At a force level below P_cr , the
rod is stable to infinitesimal transverse displacements. For
forces equal to or greater than P_cr , the rod will buckle.

For a rod of length, L, free to rotate at each end, with a
Young's modulus, E, a second moment of area, I :
P_cr = {P² E I} / L² .
For a rod with circular cross section of radius, r :
I = { P r⁴ / 4}

From: Hibbeler,
"Statics and Mechanics of Materials,"
Macmillan, (1993)