Mechanical Engineering
Column / Rod Buckling (Euler)
Calculate the critical buckling load for pneumatic and hydraulic cylinder rods, columns and struts under compressive loading.
Units:
Cylinder rods in compression (pushing loads) must be checked for buckling — the rod may buckle before reaching the cylinder force limit. Use a safety factor of at least 3.5 for cylinder rods. Rule of thumb: L/d > 10 requires buckling check.
F_crit = π² × E × I / (β × L)² | I = π/64 × d⁴ [solid rod]
Input
Rod diameter iDiameter of the cylindrical rod or column in mm.
mm
Free buckling length iFree buckling length in mm. Depends on end conditions — see bearing type below.
mm
End condition (β factor) iEnd conditions affect the effective length. Cylinder rods: typically β=1.0 to 2.0.
Material iMaterial with Young's modulus E.
Safety factor iSafety factor applied to critical load. Recommended for cylinder rods: 3.5. Structural columns: 2.0–4.0.
Result
Slenderness ratio L/d
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Second moment of area I [mm⁴]
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Critical buckling load F_crit [kN]
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Allowable load (with SF) [kN]
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Assessment
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