BIZOMAT MAKEOS · Strength
Tube Post with Eccentric Load (Section, Secant Formula, Load Factor)
Is this round tube post or column safe under a load applied off its centreline, and how much more load would bring it to yield?
Check of a round tube post or strut carrying an axial load at an eccentricity (a bracket, a sign arm or an offset beam seat): area, second moment, radius of gyration and slenderness of the tube, Euler buckling load, and the secant-formula peak stress and load factor to first yield (as the eccentrically loaded column tool), checked against your load factor and slenderness limit.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Tube outside diameter | mm | Outside diameter of the tube. |
| Wall thickness | mm | Wall thickness of the tube. |
| Length | mm | Length of the post or strut. |
| Effective length factor | Effective length factor for the end fixity (2 for a free-standing post fixed at the base). | |
| Axial load | N | Axial compressive load. |
| Eccentricity of load | mm | Distance from the tube centreline to the line of the load. |
| Elastic modulus | GPa | Elastic modulus. |
| Yield strength | MPa | Yield strength of the tube. |
| Required load factor | Factor on load you need before first yield. | |
| Largest slenderness KL/r | Largest slenderness ratio your code allows. |
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: Tube outside diameter
- What it is
- The outside diameter of the round tube used as the post or strut.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 3000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 114.3 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger diameter greatly increases the second moment of area and radius of gyration.
What this means: Wall thickness
- What it is
- The wall thickness of the tube.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 200 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 6 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 increases area and stiffness, lowering stress.
- Get it right
- Use the actual or minimum wall, not a nominal schedule name.
What this means: Length
- What it is
- The actual length of the post or strut between its supports, or from the base to the free top for a free-standing post.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3000 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Longer posts are more slender and more sensitive to the eccentric load.
What this means: Effective length factor
- What it is
- The effective length factor, which converts the actual length to an equivalent pin-ended length according to how the ends are held, from your structural code or design reference.
- Units and format
- Enter a plain number with no unit. The form accepts 0.1 to 5. 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.
- Effect on the result
- Effective length is K × L, so a higher factor increases slenderness and the secant effect.
- Get it right
- A post fixed at the base and free at the top is much more slender than one held at both ends.
What this means: Axial load
- What it is
- The compressive load acting along the post, applied at the eccentricity entered below.
- Units and format
- Enter a number in N: newtons. The form accepts 0.000001 N or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20000 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter newtons; 1 kN = 1000 N.
What this means: Eccentricity of load
- What it is
- The offset of the line of the load from the tube’s centreline, such as the distance to a bracket or the load on a cantilever arm.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 100000 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.
- Effect on the result
- Larger eccentricity adds bending and reduces the load factor to yield.
- Get it right
- Measure from the tube centreline, not from its outer surface.
What this means: Elastic modulus
- What it is
- The elastic (Young’s) modulus of the tube material, 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 1000 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
- Enter gigapascals, not megapascals.
What this means: Yield strength
- What it is
- The yield strength of the tube material, from the mill certificate or material standard.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 100000 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.
- Effect on the result
- The load factor is the multiple of the load at which the peak stress reaches this value.
What this means: Required load factor
- What it is
- The least multiple of the applied load you accept before the tube first yields, from your design code or rules.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 20. 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: Largest slenderness KL/r
- What it is
- The largest slenderness ratio (effective length ÷ radius of gyration) your structural code allows for a compression member.
- Units and format
- Enter a plain number with no unit. The form accepts 10 to 1000. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Method and formulas
- A = π (D² − d²) ÷ 4; I = π (D⁴ − d⁴) ÷ 64; r = √(I ÷ A); slenderness = K L ÷ r.
- σ_max = P ÷ A [1 + (e c ÷ r²) sec(K L ÷ 2r × √(P ÷ A E))] (as the eccentrically loaded column tool).
- Load factor = the multiple of P at which σ_max reaches yield.
- Example: the tube peaks at 32.093 MPa; yield comes at 4.4217 × the load; KL/r = 156.46.
Limitations
- Elastic secant formula to first yield; it does not include residual stresses or initial crookedness beyond the eccentricity.
- Local buckling of thin walls is not checked.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a pipe post carrying a bracket load
- Size a column with an offset beam seat
- Check a cantilever sign post in compression
Who it is for
- Structural designers
- Design engineers
- Fabrication engineers
What you get
- Section properties and slenderness
- Euler load and peak stress
- Load factor to yield
Interpreting the result
- Eccentricity, not slenderness, usually controls short posts: move the load line closer to the centre if you can.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 281–287, 234–246. Topic reference; no source tables or recommended settings are reproduced.
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Open the Tube Post with Eccentric Load (Section, Secant Formula, Load Factor) calculator