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Rod buckling check

Select the mounting type, enter the rod diameter and lengths, and see whether the cylinder is safe against buckling under thrust force, along with the recommended minimum rod diameter.

Mounting type (Euler case)
Safe

Allowable push force (Fk / ν) 0 kN ≈ 0 ton
Recommended minimum rod diameter Ø 0 mm Calculated: Ø 0 mm
Critical buckling load Fk
0 kN
Buckling length Lk = K × (L + S)
0 mm
Slenderness λ = 4·Lk / d
0
Method
Euler
Moment of inertia I
0 cm⁴
Actual safety
0
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This is a theoretical preliminary check using Euler/Tetmajer (E = 210,000 N/mm², St52/S355 rod material). Side loads, misalignment and body deflection are not considered; the final design needs an engineering review.

Formulas used

Buckling length: Lk = K × (retracted length + stroke). K: Case 1 = 2 · Case 2 = 1 · Case 3 = 0.7 · Case 4 = 0.5

Moment of inertia: I = π × d⁴ / 64  ·  Slenderness: λ = 4 × Lk / d

Euler (λ ≥ 89): Fk = π² × E × I / Lk²  ·  Tetmajer (20 < λ < 89, St52): σk = 589 − 3,82 × λ (N/mm²), Fk = σk × A

Allowable force: Fallow = Fk / ν — a safety factor of 3.5 is commonly used for hydraulic cylinders.

What is buckling in a hydraulic cylinder?

Buckling is the sideways bending of a slender, long rod under compressive load before the material's strength limit is reached. In long-stroke cylinders, it is often buckling rather than pressure that determines the rod diameter, so once the piston diameter has been selected, the rod diameter must always be checked against buckling.

Why does the mounting type matter?

How the cylinder is attached to the machine changes the effective buckling length. For a cylinder pinned at both ends (Euler case 2), the buckling length equals the mounted length; for a cylinder with a flange-mounted body and a free rod end (case 1), it doubles and the allowable force drops to one quarter.

How should you interpret the result?

A safety factor of 3.5 is generally used for buckling in hydraulic cylinders. If the tool shows "borderline" or "risky," you need to increase the rod diameter, stiffen the mounting type, or guide the rod. In final design, lateral loads and axis misalignment are also taken into account.

Frequently asked questions

How is the rod diameter of a hydraulic cylinder determined?
First, the piston diameter is selected based on the required force and pressure. The rod diameter is then verified with a buckling calculation based on stroke, mounting length and connection type. For long strokes, buckling is usually the deciding factor.
What safety factor should be used in buckling calculations?
A safety factor of 3.5 is common practice for hydraulic cylinders. For applications with shock loads or side loads, a higher value may be selected.
What is the difference between Euler and Tetmajer?
The Euler formula gives elastic buckling for rods with a high slenderness ratio (thin and long). When the slenderness ratio is low (approximately λ < 89 for steel), the Tetmajer relation is used; otherwise, Euler overstates the actual strength.
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