A slender limb fails by buckling before bending
Supplied working report; original verdicts not validated.
Review status: Blogger published. This is an archival source note, not a passed proof.
README.md
# A slender limb fails by buckling before bending **XXII, Theory 46 / Organism / Limb design** · verdict: **supported** Claim (verbatim): > Maximum limb length is set by the ratio of bending strength to buckling load, so a slender limb fails by buckling before it fails in bending. ## Result With cortical-bone constants the crossover slenderness is 38; above it the Euler buckling stress falls below the bending yield stress, so a slender limb buckles first. ## Headline Slender limbs (lambda > 38) buckle before they yield in bending. ## Design Euler buckling stress was compared to bending yield stress across slenderness ratios for cortical bone (E = 18 GPa, yield = 120 MPa). ## Key statistics - crossover_slenderness = 38.4765 dimensionless ## Predictions - **P1** (supported): for lambda > 38, buckling stress < yield stress ## Limitations - Euler buckling assumes a perfectly straight, axially loaded column; real limbs are tapered and load at an angle. - The crossover value depends on the material constants chosen. - This is an idealised stability analysis, not a measurement on an actual limb. Provenance: Euler column formula with cortical-bone elastic constants. *Working paper — not peer reviewed. AI-assisted. Not medical, clinical, financial or safety advice.*