BIZOMAT MAKEOS · Strength
Two-Span Stringer Check (Continuous Beam, Deflection, Support Reactions)
Is a beam running continuously over three supports strong and stiff enough for this load, and can the middle support take its share?
Check of a stringer, rail or pipe-rack beam continuous over two spans with a uniform load plus its own weight: support reactions, the negative moment over the middle support, the span moments, the bending stress and the span deflections (as the continuous beam over two spans tool), against your allowable stress, deflection limit as a fraction of span, and the capacity of each support.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Span 1 | mm | Length of the first span. |
| Span 2 | mm | Length of the second span. |
| Applied uniform load | N/m | Uniform load on the beam (both spans). |
| Beam mass per metre | kg/m | Mass of the beam per metre (added to the load). |
| Elastic modulus | GPa | Elastic modulus. |
| Second moment of area | mm⁴ | Second moment of area of the beam about its bending axis. |
| Distance to extreme fibre | mm | Distance from the neutral axis to the extreme fibre. |
| Allowable bending stress | MPa | Allowable bending stress. |
| Deflection limit (span ÷ …) | Deflection limit as span divided by this number. | |
| Capacity of each support | kN | Load each support, bracket or column can take. |
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: Span 1
- What it is
- The length of the first span, from the end support to the middle support, measured between support centres.
- 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 spans raise moments, stresses and deflections sharply.
What this means: Span 2
- What it is
- The length of the second span, from the middle support to the other end support, between support centres.
- 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.
What this means: Applied uniform load
- What it is
- The applied load spread evenly along the beam over both spans, not counting the beam’s own weight, which is added separately.
- Units and format
- Enter a number in N/m: N/m. The form accepts 0 N/m or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2000 N/m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Moments, stresses, reactions and deflections rise in proportion to the total load.
- Get it right
- Enter newtons per metre run of beam; convert an area load by multiplying by the width the beam supports.
What this means: Beam mass per metre
- What it is
- The mass per metre of the beam itself, from section tables. The tool converts it to weight and adds it to the applied load.
- Units and format
- Enter a number in kg/m: kilograms per metre of length. The form accepts 0 kg/m to 100000 kg/m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 15 kg/m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter kilograms per metre, not newtons per metre.
What this means: Elastic modulus
- What it is
- The elastic (Young’s) modulus of the beam material, from the material data.
- 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.
- Effect on the result
- Deflection is inversely proportional to it; stress does not change.
- Get it right
- Enter gigapascals, not megapascals.
What this means: Second moment of area
- What it is
- The second moment of area of the beam section about the axis it bends about, from section tables.
- Units and format
- Enter a number in mm⁴: millimetres to the fourth power (second moment of area). The form accepts 0.000001 mm⁴ or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 8000000 mm⁴ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Stress (with fixed c) and deflection are inversely proportional to it.
- Get it right
- Use the value for the bending axis actually loaded, usually the strong axis, in mm⁴ (1 cm⁴ = 10⁴ mm⁴).
What this means: Distance to extreme fibre
- What it is
- The distance from the neutral axis of the section to its outermost fibre on the side being checked, usually half the depth for a symmetric section.
- 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 50 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Bending stress rises in proportion to it.
What this means: Allowable bending stress
- What it is
- The largest bending stress you accept in the beam, from your design code or the material supplier.
- 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 150 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Deflection limit (span ÷ …)
- What it is
- The divisor in the deflection limit: the largest deflection allowed is the span divided by this number, from your design code or the stringer’s use.
- Units and format
- Enter a plain number with no unit. The form accepts 50 to 5000. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 300 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter the divisor only (for span ÷ 300, enter 300); a larger number is a stricter limit.
What this means: Capacity of each support
- What it is
- The largest load each support, bracket or post can carry, from its rating or your strength check.
- 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 15 kN as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter kilonewtons; the middle support usually carries the most.
Method and formulas
- Total load per metre = applied + mass × g on both spans.
- Middle-support moment from the three-moment equation; reactions, span moments and deflections by superposition (as the continuous beam over two spans tool).
- Stress = largest moment × c ÷ I; deflection limit = span ÷ ratio.
- Example: the middle support carries 8.0516 kN; the beam is stressed to 15.097 MPa and deflects 0.58871 mm.
Limitations
- Prismatic beam on rigid supports at the same level; support settlement changes the moments.
- Uniform load on both spans; patterned live loads can raise span moments.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a conveyor stringer or rail over three supports
- Size a pipe-rack beam
- Find the load on a middle support
Who it is for
- Structural designers
- Design engineers
- Fabrication engineers
What you get
- Support reactions
- Moments and bending stress
- Span deflections against the limit
Interpreting the result
- The middle support of equal spans takes about 1¼ times the load of one span: check it first.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 264–267. Topic reference; no source tables or recommended settings are reproduced.
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Open the Two-Span Stringer Check (Continuous Beam, Deflection, Support Reactions) calculator