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Steel Column Safe Stress (Classic AISC Formulas)
What safe unit stress and load do the classic AISC column formulas give for this slenderness?
Safe unit stress for steel compression members by the classic AISC working-stress formulas quoted in the handbook — parabolic up to l/r 120, and the secant-type formula above 120 for bracing and secondary members, reduced for main members — with the safe concentric load for a given section area.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Effective length | mm | Effective (unbraced) length of the member. |
| Least radius of gyration | mm | Least radius of gyration of the section. |
| Cross-section area | mm² | Gross area of the section. |
| Member type | choice | Main members above l/r 120 take a further reduction. |
| Applied concentric load | kN | Axial load to check. |
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: Effective length
- What it is
- The effective length of the compression member: the unbraced length between points of lateral support, adjusted for how its ends are held.
- 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 2500 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A longer member raises the slenderness ratio and lowers the safe stress.
- Get it right
- Use the effective length the steel design standard gives for your end conditions, not just the overall member length.
What this means: Least radius of gyration
- What it is
- The least radius of gyration of the cross-section: the square root of the smaller second moment of area divided by the area. Section tables list it.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 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
- A larger radius lowers the slenderness ratio and raises the safe stress.
- Get it right
- Use the least value (about the weak axis) unless the member is braced so it cannot buckle that way.
What this means: Cross-section area
- What it is
- The gross cross-sectional area of the member, from the section table or calculated from its dimensions.
- Units and format
- Enter a number in mm²: square millimetres. The form accepts 0.000001 mm² to 100000000 mm². Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1500 mm² as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The safe concentric load is directly proportional to the area.
- Get it right
- Use the gross area of the whole section, not just the web or one flange.
What this means: Member type
- What it is
- Whether the member is a main load-carrying member or a bracing or secondary member. Above a slenderness of 120 the formula for main members applies a further reduction.
- Units and format
- Choose one of 2 options from the list: Main member; Bracing or secondary member.
- Example
- The form opens with “Main member” selected as a worked example. Choose the option that matches your case.
- Get it right
- Main members above a slenderness of 200 are outside these formulas and are refused.
What this means: Applied concentric load
- What it is
- The axial load the member must carry, applied through the centroid of the section, to compare with the safe concentric load.
- Units and format
- Enter a number in kN: kilonewtons (1 kN = 1000 N). The form accepts 0 kN to 10000000 kN. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 kN as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- It changes only the utilisation and verdict, not the safe stress or safe load.
- Get it right
- Use the total working load on this one member, not a factored limit-state load; these are working-stress formulas.
Method and formulas
- l/r ≤ 120: safe stress = 17,000 − 0.485 (l/r)² psi.
- l/r > 120, bracing and secondary members: 18,000 ÷ [1 + (l/r)² ÷ 18,000] psi; main members: that value × (1.6 − l/r ÷ 200).
- Converted to MPa (1 psi = 0.0068948 MPa); safe load = stress × area.
- Example: l/r = 100 gives a safe stress of 83.772 MPa.
Limitations
- Historic working-stress formulas for mild structural steel; current design uses AISC 360 or the local steel code.
- Concentric loads only; main members are limited to l/r 200 here.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check an existing or historic steel strut or column
- Compare older design calculations with current methods
- Quick sizing of light bracing
Who it is for
- Structural engineers
- Maintenance engineers
- Design engineers
What you get
- Slenderness ratio
- Safe unit stress
- Safe concentric load
Interpreting the result
- Use for comparison and older structures; confirm new work to the current code.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 281–285. Topic reference; no source tables or recommended settings are reproduced.
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