BIZOMAT MAKEOS · Strength
Compression Strut Sizing (Euler or Johnson, Round Bar or Tube)
What is the smallest round bar or tube that carries this compressive load with my safety factor against buckling, and how does my chosen size compare?
Sizing of a pin-ended or end-restrained compression strut in solid round bar or round tube: the slenderness ratio and transition slenderness, buckling by the Euler formula for slender struts or the Johnson parabola for intermediate ones (as the column buckling tool), the least outside diameter that meets the safety factor (found by search), and the safety factor, stress and mass per metre of the size you choose.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Compressive load | kN | Axial compressive load. |
| Length between supports | mm | Length between the end supports. |
| Effective length factor | Effective length factor for the end conditions (1 pinned–pinned, 0.7 fixed–pinned, 0.5 fixed–fixed, 2 fixed–free; designers often use larger practical values). | |
| Elastic modulus | GPa | Elastic modulus of the material. |
| Yield strength | MPa | Yield strength of the material. |
| Safety factor required | Safety factor against buckling you require. | |
| Section | choice | Solid bar or tube. |
| Tube outside diameter ÷ wall thickness | For a tube, the ratio of outside diameter to wall thickness (kept constant while sizing). | |
| Outside diameter chosen | mm | Outside diameter you intend to use. |
| Density | kg/m³ | Density for the mass per metre. |
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.
What this means: Compressive load
- What it is
- The axial force pushing along the strut’s centre line, from your load analysis.
- Units and format
- Enter a number in kN: kilonewtons (1 kN = 1000 N). The form accepts 0.000001 kN to 1000000 kN. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 kN as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The least diameter needed rises, and the chosen size’s safety factor falls in inverse proportion to the load.
- Get it right
- kN, not N; enter the working load and let the safety factor provide the margin.
What this means: Length between supports
- What it is
- The actual length of the strut between the points where it is held against sideways movement. The effective length factor is applied separately.
- 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 2000 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Do not multiply by the effective length factor here; enter it in its own field.
What this means: Effective length factor
- What it is
- A multiplier that converts the actual length into the buckling length according to how the ends are held (pinned, fixed or free).
- Units and format
- Enter a plain number with no unit. The form accepts 0.5 to 2.1. 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.
- Get it right
- Choose it from how the ends are really restrained; a nominally fixed end is rarely fully fixed.
What this means: Elastic modulus
- What it is
- The stiffness of the strut material in tension and compression (Young’s modulus), 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 500 GPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- GPa, not MPa: a value a thousand times too small makes the strut look far weaker in buckling.
What this means: Yield strength
- What it is
- The stress at which the strut material starts to yield, from the material standard or certificate. It governs short and intermediate struts.
- 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 250 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Safety factor required
- What it is
- The ratio of buckling load to working load 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 2.5 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher factor raises the least diameter needed.
What this means: Section
- What it is
- Whether the strut is a solid round bar or a round tube. For a tube the wall thickness follows the outside diameter ÷ wall ratio below.
- Units and format
- Choose one of 2 options from the list: Solid round bar; Round tube.
- Example
- The form opens with “Solid round bar” selected as a worked example. Choose the option that matches your case.
What this means: Tube outside diameter ÷ wall thickness
- What it is
- For a tube, the outside diameter divided by the wall thickness, held constant while the tool searches for the least size.
- Units and format
- Enter a plain number with no unit. The form accepts 4 to 100. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 15 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- It is ignored for a solid bar. A large ratio means a thin wall that can also buckle locally.
What this means: Outside diameter chosen
- What it is
- The outside diameter of the bar or tube you intend to use, checked for its own safety factor and mass per metre.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 5000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter the outside diameter, not the radius or the bore.
What this means: Density
- What it is
- The mass per unit volume of the strut material, used only to report the mass per metre of the chosen size.
- Units and format
- Enter a number in kg/m³: kilograms per cubic metre. The form accepts 0.000001 kg/m³ to 20000 kg/m³. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 7850 kg/m³ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Method and formulas
- Slenderness λ = K L ÷ r with r = √(I ÷ A); transition C_c = π √(2E ÷ S_y).
- Euler (λ ≥ C_c): σ_cr = π² E ÷ λ²; Johnson (λ < C_c): σ_cr = S_y − (S_y λ ÷ 2π)² ÷ E (as the column buckling tool).
- Safety factor = σ_cr A ÷ P; the least diameter is found by bisection for the required factor.
- Example: 50 kN over 2000 mm needs at least 47.661 mm; a 50 mm bar gives a factor of 3.028.
Limitations
- Concentric load; eccentric loads need the secant formula.
- Thin-walled tubes can also fail by local buckling.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size a push rod, brace or prop
- Compare bar and tube for weight
- Check a strut after a length change
Who it is for
- Design engineers
- Structural engineers
- Fabrication supervisors
What you get
- Least diameter for the safety factor
- Slenderness and buckling mode
- Safety factor, stress and mass of the chosen size
Interpreting the result
- For the same mass a tube is far stiffer against buckling than a solid bar.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 281–287. 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
Bracing: how stiff and how strong
What it covers: What a brace must do to hold a compression member: the stiffness it needs, the small force it carries, tension-only diagonals, sizing a strut, and what slack in the bracing does.
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 Compression Strut Sizing (Euler or Johnson, Round Bar or Tube) calculator