Calculate Euler and Johnson buckling loads, allowable compressive force and utilization of a hydraulic cylinder rod.
Set the inputs and run the calculation.
Compare compressive force with Euler or Johnson buckling load and safety factor.
Rod diameter, effective buckling length, end condition factor, Young's modulus, yield strength, compression force and safety.
Buckling length and support are often more decisive than rod material strength. Side load or a loose guide can reduce ideal Euler load substantially; check cylinder force at the most unfavorable stroke.
Effective length follows support conditions. Slender rods use Euler Fₖ = π²EI/Lₖ²; lower slenderness uses a Johnson approximation.
A pinned rod has greater effective length than a fixed-fixed rod and therefore lower buckling load.
Sources and limits: Euler/Johnson stability theory; ISO 4413 requires safe design; guides and side loads are project-specific.
Compare compressive force with Euler or Johnson buckling load and safety factor.
Hydraulic calculations link pressure difference, effective area and flow. Pressure determines force, flow determines speed, while line losses and efficiency reduce ideal values.
Effective length follows support conditions. Slender rods use Euler Fₖ = π²EI/Lₖ²; lower slenderness uses a Johnson approximation.
Rod diameter, effective buckling length, end condition factor, Young's modulus, yield strength, compression force and safety. Buckling length and support are often more decisive than rod material strength. Side load or a loose guide can reduce ideal Euler load substantially; check cylinder force at the most unfavorable stroke.
Enter rod diameter, effective buckling length (from support type and end-condition factor), Young's modulus, yield strength, the applied compressive force and required safety factor. The calculator automatically selects between Euler and Johnson approximation based on slenderness.
A pinned rod has greater effective length than a fixed-fixed rod and therefore lower buckling load.
Buckling length and support are often more decisive than rod material strength. Side load or a loose guide can reduce ideal Euler load substantially; check cylinder force at the most unfavorable stroke. The result is a pre-sizing point. Higher pressure raises cylinder force; more flow raises speed but usually also increases losses and heat.
Diameter and length in millimetres, Young's modulus and yield strength in MPa, force in kN.
Checking whether a piston rod is sufficiently safe against buckling at maximum operating pressure and extended stroke, especially for long-stroke or slender cylinders.
Euler/Johnson stability theory; ISO 4413 requires safe design; guides and side loads are project-specific.
Common mistake: Don't confuse the actual support type with a fixed-fixed rod – even one pinned instead of fixed end raises effective buckling length and noticeably lowers allowable compressive force. For stocky (non-slender) rods, the pure Euler formula gives unrealistically high values; the Johnson approximation is intended for that range.
At full rod extension, where effective free length and thus slenderness are greatest; the check should therefore be performed at maximum stroke.
Below a critical slenderness ratio that depends on the material, Euler gives overly optimistic values; the Johnson approximation then additionally accounts for the material's yield strength.
An additional intermediate guide substantially reduces effective buckling length by splitting the rod into shorter sections, and can correspondingly raise allowable compressive force significantly.
Check a compression-loaded cylinder rod for buckling reserve with Euler and Johnson column theory.
Results are preliminary engineering estimates. Component approval, safety functions, material, fatigue, installation checks and the complete system assessment remain separate.