Cortical Bone Fracture Stress Calculator
Orthopedic biomechanics: Evaluate cross-sectional bending stress, torsional shear, second moment of area, and yield fracture safety factor for long bone diaphyses.
Bone Diaphysis Geometry (Hollow Ellipse)
Femur midshaft anterior-posterior
Dense cortical cortex shell
Applied Biomechanical Loads
Impact / stumble bending load
Body weight axial thrust (~3 × BW)
Twisting moment during pivot
Bone Beam Stress Mechanics
Superposition of axial compression and bending stress:
$$\sigma_{\text{max}} = \frac{P}{A} + \frac{M \cdot y}{I}$$
Torsional shear stress: $\tau = \frac{T \cdot r}{J}$. Cortical bone is anisotropic and weakest in shear and tension, failing in oblique or spiral fracture modes.
Peak Cortical Stresses
Max Compressive Stress
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Max Tensile Stress
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Shear & Combined Von Mises
Torsional Shear Stress (τ)
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T · r / J
Equivalent Von Mises Stress
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√(σ² + 3τ²)
Fracture Risk & Safety Factor
Factor of Safety (FS):
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Cortical Area / Medullary Cavity:
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Predicted Failure Mode:
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