Plate Girder Design Calculator
Design steel plate girders: check moment capacity, shear capacity, web and flange slenderness, and compactness.
About this calculator
A plate girder is a fabricated I-shaped steel beam built from separately welded web and flange plates rather than rolled as a single piece, letting engineers proportion each element independently for very long spans or heavy loads beyond what standard rolled sections can handle. This calculator builds up the section's moment of inertia from your web and flange dimensions (I = web contribution + parallel-axis-adjusted flange contribution), converts that to a section modulus, and multiplies by the steel's yield strength (Fy) and a 0.9 resistance factor to report the design moment capacity (φMn) — the maximum bending moment the section can safely resist. Shear capacity (φVn) follows a similar approach using the web area and yield strength, but is reduced by a shear buckling coefficient (Cv) whenever the web's height-to-thickness ratio exceeds a slenderness limit tied to the steel grade — thin, deep webs buckle in shear before reaching full yield strength, which is precisely why plate girders often need transverse stiffeners that this simplified calculator does not model.
The tool also reports web slenderness (h/tw) and flange slenderness (bf/2tf), the two ratios AISC uses to classify a section as compact, noncompact, or slender, and combines both checks into a single compact/non-compact flag. A compact section can reach its full plastic moment capacity without local buckling; a non-compact one cannot and needs a reduced capacity calculation this tool doesn't perform. Treat these results as a preliminary sizing check only — a complete plate girder design also needs stiffener spacing, lateral-torsional buckling checks, and deflection verification under AISC 360 before construction.
Inputs
ASTM: A572 Gr.50 Fy=345 MPa (common); A36 Fy=250 MPa; A709 Gr.50W for bridge plate girders
Results
Moment Capacity (φMn)
3,310,459,821 N·mm
Shear Capacity (φVn)
1,446,868 N
How to Use This Calculator
- Enter the span length and uniform load carried by the girder.
- Set the web height-to-thickness ratio and flange dimensions.
- Input the steel yield strength (Fy) for the plate girder material.
- Review the Moment Capacity, Flange Slenderness ratio, and Web Slenderness check.
- Verify the Shear Capacity and Compact Section classification to confirm the section is adequate.
How the result changes with Web Depth
| Web Depth | Moment Capacity (φMn) | Shear Capacity (φVn) |
|---|---|---|
| 500 | 1,503,690,341 N·mm | 1,117,800 N |
| 750 | 2,367,966,797 N·mm | 1,446,868 N |
| 1,500 | 5,428,950,605 N·mm | 1,446,868 N |
| 2,500 | 10,598,222,426 N·mm | 1,446,868 N |
What each input means
- Span Length
- Clear span of the plate girder.
- Uniform Load
- Total uniformly distributed load on the girder.
- Web Depth
- Clear depth of the web plate between flanges.
- Web Thickness
- Thickness of the web plate.
- Flange Width
- Width of each flange plate.
- Flange Thickness
- Thickness of each flange plate.
- Steel Yield Strength (Fy)
- Yield strength of the steel plate per AISC 360 §F13 (plate girders). ASTM A572 Grade 50: Fy=345 MPa (most common for plate girders); ASTM A36: Fy=250 MPa; ASTM A709 Gr.50W (weathering): Fy=345 MPa for bridges.
How this is calculated
Worked example, using the default values
- Identify Input Parameters4 parametersSpan Length = 15, Uniform Load = 100, Web Depth = 1000, Web Thickness = 12 = 7 input(s) provided
- Calculate Moment CapacityMoment Capacity3310459821 = 3310459821
- Calculate Shear CapacityShear Capacity1446868 = 1446868
- Calculate Web SlendernessWeb Slenderness83.3 = 83.3
- Calculate Flange SlendernessFlange Slenderness7 = 7
Engine last updated . Checked against 2 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
What exactly does the Compact Section flag check?
It compares your web slenderness (h/tw) against a limit of 3.76√(200000/Fy) and your flange slenderness (bf/2tf) against a limit of 0.38√(200000/Fy) — both derived from the steel's yield strength. The section is only flagged compact (isCompact = 1) if both ratios pass their respective limits; failing either one flags it non-compact.
Why does shear capacity drop for a deep, thin web even at the same yield strength?
The calculator computes a web slenderness limit of 2.24√(200000/Fy), and once your web's height-to-thickness ratio exceeds that, the shear buckling coefficient (Cv) drops below 1.0 and directly reduces the shear capacity result. Thin, deep webs buckle in shear before reaching full yield, which is exactly why real plate girders in that range need transverse stiffeners this calculator doesn't model.
How is the moment capacity actually built from my web and flange dimensions?
The calculator computes the web's own moment of inertia, then adds each flange's contribution using the parallel-axis theorem (accounting for how far the flange sits from the section's center), sums them into a total moment of inertia, converts that to a section modulus, and multiplies by yield strength and a 0.9 resistance factor.
Does raising the steel yield strength (Fy) always make the design better?
It increases both moment and shear capacity directly, but it also tightens the flange and web slenderness limits (both scale with √(200000/Fy)), making it harder for the same physical dimensions to qualify as compact. A higher-strength steel section can end up non-compact where a lower-strength one of identical geometry would pass.
Do the Span Length and Uniform Load inputs affect the results?
No. Span Length and Uniform Load are collected but not currently used anywhere in the moment capacity, shear capacity, or slenderness calculations, which are derived entirely from the web/flange dimensions and steel yield strength.
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