BIZOMAT MAKEOS · Hydraulics
Hydraulic Cylinder Structure (Barrel, End Cap and Rod Buckling)
Is this hydraulic cylinder’s barrel thick enough, will the end cap hold the pressure, and will the rod buckle when it pushes fully extended?
Structural check of a hydraulic cylinder: barrel stresses by the thick-wall (Lamé) equations with closed ends and the von Mises stress at the bore (as the pressure cylinder tool), the least wall for your safety factor, the bore expansion under pressure (which affects the piston seal), the flat end cap thickness as a clamped plate (as the circular plate tool), the push force, and buckling of the fully extended rod by Euler or Johnson (as the column buckling tool).
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Barrel | ||
| Bore | mm | Bore of the barrel. |
| Barrel wall thickness | mm | Wall thickness of the barrel. |
| Working pressure | bar | Highest working pressure. |
| Barrel yield strength | MPa | Yield strength of the barrel tube. |
| Barrel safety factor required | Safety factor against yield you require for the barrel. | |
| Elastic modulus | GPa | Elastic modulus of the barrel and rod steel. |
| Poisson’s ratio | Poisson’s ratio. | |
| End cap | ||
| End cap thickness | mm | Thickness of the flat end cap (treated as clamped at the bore). |
| End cap allowable stress | MPa | Allowable bending stress of the end cap (your design value). |
| Rod | ||
| Rod diameter | mm | Diameter of the piston rod. |
| Mount to rod end, fully extended | mm | Length from the cylinder mounting point to the rod end with the rod fully extended. |
| Effective length factor for the mounting | Effective length factor for the mounting (1 for pivoted at both ends; 2 for a fixed body with a free rod end; follow the cylinder maker’s mounting factors). | |
| Rod yield strength | MPa | Yield strength of the rod. |
| Rod buckling safety factor required | Safety factor against buckling you require for the rod. | |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
Barrel
What this means: Bore
- What it is
- The inside diameter of the cylinder barrel, which is also the piston diameter. It sets the pressure force on the end cap and the push force on the rod.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 2000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 80 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Push force rises with the square of the bore.
- Get it right
- Enter the bore diameter, not the barrel outside diameter.
What this means: Barrel wall thickness
- What it is
- The wall thickness of the barrel tube: outside diameter minus bore, divided by two.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 500 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 8 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A thicker wall lowers the barrel stresses and raises its safety factor.
- Get it right
- Use the thinnest wall, allowing for tube tolerance and any honing.
What this means: Working pressure
- What it is
- The highest pressure in the cylinder in normal service, as gauge pressure.
- Units and format
- Enter a number in bar: bar (1 bar = 100 kPa). The form accepts 0.000001 bar to 2000 bar. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 160 bar as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Barrel and end cap stresses rise in proportion; the rod buckling factor falls in inverse proportion.
- Get it right
- bar, not MPa: 10 bar = 1 MPa. Include pressure peaks the relief valve allows.
What this means: Barrel yield strength
- What it is
- The yield strength of the barrel tube material, from the tube standard or mill certificate.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 3000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 355 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Barrel safety factor required
- What it is
- The ratio of yield strength to the barrel’s von Mises stress you require, from your design code or practice.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 10. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Elastic modulus
- What it is
- The stiffness of the steel (Young’s modulus), used for both the barrel expansion and the rod buckling, from the material data sheet.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 300 GPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 206 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- One value serves both barrel and rod; GPa, not MPa.
What this means: Poisson’s ratio
- What it is
- The ratio of sideways contraction to lengthwise stretch for the barrel steel. It is used only for the bore expansion.
- Units and format
- Enter a plain number with no unit. The form accepts 0.1 to 0.5. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.3 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
End cap
What this means: End cap thickness
- What it is
- The thickness of the flat end cap that closes the barrel, treated as a plate clamped at the bore.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 500 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 25 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- End cap stress falls with the square of its thickness.
What this means: End cap allowable stress
- What it is
- The bending stress you allow in the end cap, from your design code or material data with your margin included.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 2000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 150 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Rod
What this means: Rod diameter
- What it is
- The diameter of the piston rod, which must carry the full push force without buckling.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 56 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- It must be smaller than the bore, or the tool stops.
What this means: Mount to rod end, fully extended
- What it is
- The length from the cylinder’s mounting point to the end of the rod with the rod fully extended, the length that buckles under the push force.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1200 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Rod slenderness rises in proportion, lowering the buckling safety factor.
- Get it right
- Measure with the rod fully out, from the mounting pivot or flange, not just the rod length.
What this means: Effective length factor for the mounting
- What it is
- A multiplier that turns the mounted length into the buckling length according to how the body and rod end are held, from the cylinder maker’s mounting factors.
- Units and format
- Enter a plain number with no unit. The form accepts 0.5 to 4. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Rod slenderness rises in proportion.
What this means: Rod yield strength
- What it is
- The yield strength of the piston rod material, from the bar supplier’s data. It governs buckling of short, stocky rods.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 3000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 500 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Rod buckling safety factor required
- What it is
- The ratio of rod buckling load to push force you require, from your design code or the cylinder maker’s practice.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 10. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3.5 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Method and formulas
- Lamé at the bore: σ_θ = p (r_o² + r_i²) ÷ (r_o² − r_i²), σ_r = −p, σ_z = p r_i² ÷ (r_o² − r_i²) (closed ends); von Mises from the three (as the pressure cylinder tool); least wall found by bisection.
- Bore expansion Δd = 2 r_i [σ_θ − ν(σ_r + σ_z)] ÷ E.
- End cap (clamped plate) t = a √(0.75 p ÷ σ_a) with a = bore ÷ 2 (as the circular plate tool).
- Push force F = p π D² ÷ 4; rod buckling by Euler or Johnson with length K L_b (as the column buckling tool).
- Example: at 160 bar the barrel has a factor of 3.9142, the bore grows 32.085 µm, and the rod’s buckling factor is 8.3959.
Limitations
- Rod buckling uses a concentric load; side loads and mounting misalignment lower it.
- Welds, ports and thread roots need their own checks.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Design a custom hydraulic cylinder
- Check a cylinder for a higher pressure
- Check rod buckling for a longer stroke
Who it is for
- Hydraulic engineers
- Machine designers
- Design engineers
What you get
- Barrel stresses, safety factor, least wall and bore expansion
- End cap thickness needed
- Push force and rod buckling safety factor
Interpreting the result
- Rod buckling often limits long-stroke cylinders before pressure does: a larger rod or a better mounting style helps most.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 290–294, 281–288, 3421–3425. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Rods in machines: cylinders and screws
What it covers: Buckling of hydraulic cylinder rods and screws: the length and mounting that count, why the rod must survive the relief valve's force rather than the duty, and the same check for ball screws.
BIZOMAT tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
Open the Hydraulic Cylinder Structure (Barrel, End Cap and Rod Buckling) calculator