BIZOMAT MAKEOS · Strength
Combined Axial and Biaxial Bending Stress
What are the corner stresses in this rectangular section under axial load and bending about both axes?
Stresses at the four corners of a rectangular section under an axial force and bending moments about both axes, with the peak tension and compression against an allowable stress.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Axial force (+ tension, − compression) | kN | Axial force at the section (tension positive). |
| Moment about X (bends in depth direction) | kN·m | Bending moment about the X axis (the width axis), from your load analysis. |
| Moment about Y (bends in width direction) | kN·m | Bending moment about the Y axis. |
| Section width (along X) | mm | Width of the rectangle along X. |
| Section depth (along Y) | mm | Depth of the rectangle along Y. |
| Allowable stress | MPa | Allowable stress from your design code. |
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: Axial force (+ tension, − compression)
- What it is
- The axial force acting along the member at the section, with tension entered as a positive number and compression as negative.
- Units and format
- Enter a number in kN: kilonewtons (1 kN = 1000 N). The form accepts -10000000 kN to 10000000 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.
- Get it right
- Watch the sign: compression must be entered with a minus sign. Enter kilonewtons, not newtons.
What this means: Moment about X (bends in depth direction)
- What it is
- The bending moment about the X axis (the width axis), which bends the section in its depth direction and stresses the top and bottom faces.
- Units and format
- Enter a number in kN·m: kN·m. The form accepts -10000000 kN·m to 10000000 kN·m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5 kN·m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Corner stresses change by this moment divided by b h² ÷ 6.
- Get it right
- Enter kN·m from your load analysis; the tool converts to N·mm.
What this means: Moment about Y (bends in width direction)
- What it is
- The bending moment about the Y axis (the depth axis), which bends the section in its width direction and stresses the two side faces.
- Units and format
- Enter a number in kN·m: kN·m. The form accepts -10000000 kN·m to 10000000 kN·m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 kN·m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Corner stresses change by this moment divided by h b² ÷ 6.
- Get it right
- Make sure the moments are paired with the right section dimensions: My works across the width b.
What this means: Section width (along X)
- What it is
- The width of the solid rectangular section, measured along the X axis.
- 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 150 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The section modulus for My rises with the square of the width.
What this means: Section depth (along Y)
- What it is
- The depth of the solid rectangular section, measured along the Y axis.
- 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 250 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The section modulus for Mx rises with the square of the depth.
What this means: Allowable stress
- What it is
- The highest stress magnitude your design code permits in tension or compression; the largest corner stress, of either sign, is compared with it.
- 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 165 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Compression members may also need a buckling check, which this tool does not make.
Method and formulas
- A = b h; Zx = b h² ÷ 6; Zy = h b² ÷ 6.
- Corner stress σ = P/A ± Mx ÷ Zx ± My ÷ Zy.
- Peak magnitude compared with the allowable.
- Example: the default loads give corner stresses from -6.6667 to 4 MPa.
Limitations
- Solid rectangular section, elastic; buckling of compression members is checked separately.
- For base plates on concrete or soil, a negative (tension) corner means lift-off and a different analysis.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check brackets, posts and machine legs with offset loads
- Find whether a base plate lifts (tension)
- Check a section under combined loads
Who it is for
- Design engineers
- Structural and mechanical engineers
- Engineering students
What you get
- Stress at each corner
- Peak tension and compression
- Whether the whole section stays in compression
Interpreting the result
- If any corner is in tension on a bearing surface, the contact area shrinks and the simple formula no longer applies.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 212–218. Topic reference; no source tables or recommended settings are reproduced.
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Open the Combined Axial and Biaxial Bending Stress calculator