Long bones like the femur behave biomechanically as hollow cylindrical columns under compressive loads. Euler's formula gives the critical buckling load:
Where I = π(r_o⁴ − r_i⁴)/4 is the second moment of area, E ≈ 17 GPa for cortical bone, and K is the end-condition factor (K=1 for pinned ends).
The hollow tubular design minimizes weight while maximizing bending stiffness — trabecular bone fills the medullary canal to resist buckling modes.
Stress fractures, osteoporosis (reduced E), and impact loading all affect P_cr. Normal femur: P_cr ≈ 7,000–9,000 N.