Steel Beam Selection Calculator
Determine required section modulus, moment of inertia, and approximate beam weight for steel beam design with uniform and point loads.
About this calculator
This calculator sizes a simply-supported steel beam carrying both a uniform load and a midspan point load at once, combining the two standard moment formulas — wL²/8 for the distributed load and PL/4 for the concentrated one — into a single required moment. From that moment it backs into a required section modulus using allowable stress design at 0.66 × Fy, the classic ASD bending allowable for compact steel sections. It then works the deflection problem in reverse: rather than checking a given section's deflection, it solves the standard uniform- and point-load deflection formulas (5wL⁴/384EI and PL³/48EI) for the moment of inertia I that would just barely satisfy your chosen deflection limit (span/360, span/240, etc.), using a fixed steel modulus of 200,000 MPa.
The "Max Deflection" output it then reports is deflection recomputed at that just-adequate I, so it will land at or very near your limit by construction — it is a confirmation of the target, not an independent check. The estimated weight per foot is a rough empirical correlation from section modulus, not a real steel shape lookup, so treat it as a ballpark for material estimating rather than a spec. Because this only enforces bending stress and deflection, you still need a separate shear check at the supports and a real W-shape table lookup to pick an actual rolled section that meets or exceeds both required properties.
Inputs
AISC/IBC: floor live load L/360; floor total load L/240; roof L/180; long-term L/480
ASTM: A992 W-shapes Fy=345 MPa; A36 plates Fy=250 MPa; A572 Gr.50 Fy=345 MPa
Results
Required Moment Capacity
165 kN·m
Required Section Modulus
724,638 mm³
How to Use This Calculator
- Enter the beam span in feet and the tributary width in feet.
- Input the dead load and live load in psf, including any point loads.
- Set the allowable deflection limit (span/240 or span/360) and the steel yield strength.
- Review the Required Plastic Section Modulus (Zx) and the Recommended Wide-Flange Section.
- Verify the selected section against shear capacity and deflection limits before finalizing.
How the result changes with Span Length
| Span Length | Required Moment Capacity | Required Section Modulus |
|---|---|---|
| 3 | 60 kN·m | 263,505 mm³ |
| 4.5 | 106.88 kN·m | 469,368 mm³ |
| 9 | 315 kN·m | 1,383,399 mm³ |
| 15 | 750 kN·m | 3,293,808 mm³ |
What each input means
- Span Length
- Clear span length of the beam between supports.
- Uniform Load
- Distributed load along the entire beam length in kN per meter.
- Point Load at Midspan
- Concentrated load applied at the center of the beam span.
- Deflection Limit (L/...)
- Deflection limit divisor per AISC 360 Design Guide and IBC. L/360 for floors with plaster ceilings; L/240 for floors without brittle finishes; L/180 for roofs with no ceiling. AISC Design Guide 3 recommends L/360 for walking vibration.
- Steel Yield Strength (Fy)
- Yield strength of the steel per ASTM standard. ASTM A992 (W-shapes, Grade 50): Fy=345 MPa (standard for wide-flange); ASTM A36: Fy=250 MPa (plates, angles); ASTM A572 Gr. 50: Fy=345 MPa; A588 weathering: Fy=345 MPa.
How this is calculated
Worked example, using the default values
- Identify Input Parameters4 parametersSpan Length = 6, Uniform Load = 20, Point Load at Midspan = 50, Deflection Limit (L/...) = 360 = 5 input(s) provided
- Calculate Required Moment CapacityRequired Moment Capacity165 = 165
- Calculate Required Section ModulusRequired Section Modulus724638 = 724638
- Calculate Required Moment of InertiaRequired Moment of Inertia168750000 = 168750000
- Calculate Max DeflectionMax Deflection16.67 = 16.67
Engine last updated . Checked against 1 independently-derived test — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
Why does 'Max Deflection' come out almost exactly equal to my deflection limit?
Because it's computed in reverse: the calculator first solves the standard deflection formulas (5wL⁴/384EI and PL³/48EI) for the moment of inertia I that would just barely satisfy your chosen limit, then plugs that same I back in to report the resulting deflection. The two numbers landing close together is by construction, confirming the target rather than independently checking a real section's stiffness.
How is the required moment of inertia calculated if I haven't picked an actual steel section yet?
The calculator isolates I algebraically from the uniform-load and point-load deflection formulas using your span, loads, the fixed steel modulus of 200,000 MPa, and your deflection limit (span/360, span/240, etc.), then adds the uniform-load and point-load contributions together. This gives you the minimum I a real W-shape needs to meet your stiffness target — you'd then look up a rolled section with I at or above that value.
Is the estimated weight per foot accurate enough to select an actual W-shape?
No — it's a rough empirical correlation from the required section modulus (roughly S/1000 × 3.4), not a lookup against real AISC W-shape tables. Use it only as a ballpark for early material and cost estimating; the actual section you select should come from matching required section modulus and moment of inertia against a real steel manual.
Why does the calculator use 0.66 × Fy instead of Fy directly when finding required section modulus?
0.66 × Fy is the classic allowable stress design (ASD) bending allowable for compact steel sections, representing a safety margin below the material's actual yield strength. Dividing the required moment by this reduced allowable stress, rather than by the full yield strength, is what keeps the resulting section modulus conservative.
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