Plate Girder Flexural Capacity Calculator
This calculator determines the plastic moment capacity Mp of a symmetric doubly-symmetric plate girder (built-up I-section) from its cross-section dimensions. Mp = Fy * Z, where the plastic section modulus Z is computed from the flange and web plate dimensions. This is the upper bound flexural capacity, applicable to fully braced, compact sections. For sections with slender webs or with inadequate lateral bracing, the actual capacity is reduced by flange local buckling, lateral-torsional buckling, or bend-buckling factors per AISC 360 Chapter F. Those reductions require detailed analysis beyond this calculator.
Plate girder plastic moment formula
Zflange = 2 × bf × tf × (hw/2 + tf/2)
Zweb = tw × hw² / 4
Z = Zflange + Zweb
Mp = Fy × Z (kip-in)
phi Mn = 0.90 × Mp
This is the upper-bound capacity for a compact, laterally braced section. Slender webs (h/tw greater than 5.70 sqrt(E/Fy)) require the RPG bend-buckling reduction per AISC 360 Section F5.
Web slenderness and capacity reduction
- Compact web limit: h/tw less than or equal to 3.76 sqrt(E/Fy) = 90.6 (A572-50). Below this, no web reduction applies.
- For h/tw greater than 5.70 sqrt(E/Fy) = 137 (A572-50), AISC 360 Section F5 applies an RPG reduction factor: Rpc = Mp/My * (1 - (h/tw)/(5.7*sqrt(E/Fy))).
- Lateral-torsional buckling also reduces capacity for unbraced lengths exceeding Lp = 1.76 ry sqrt(E/Fy). Check per AISC 360 Section F5.
- Web stiffeners: intermediate transverse stiffeners are typically needed when h/tw exceeds 2.24 sqrt(E/Fy) = 53.9 for shear per AISC 360 Section G2.
Frequently asked questions
What is a plate girder?
A plate girder is a built-up I-shaped flexural member fabricated by welding flat steel plates together to form flanges and a web. Plate girders are used when the required capacity exceeds what rolled wide-flange sections can provide, typically for spans over 60-80 ft or very heavy loads.
How is the plastic moment capacity Mp calculated?
Mp = Fy * Z, where Fy is the yield strength and Z is the plastic section modulus. The plastic section modulus Z = (Af * (hw + tf)) for each flange's contribution plus (0.25 * hw^2 * tw) for the web. This calculator builds up Z from the plate dimensions you enter.
What limits the flexural capacity of a plate girder?
Three limit states can reduce capacity below Mp: lateral-torsional buckling (LTB) if the compression flange is not braced; flange local buckling (FLB) if the flange slenderness bf/(2tf) exceeds the compact limit; and web local buckling or bend-buckling, which reduces the nominal moment for slender webs using the RPG factor.
What is the compact web slenderness limit for plate girders?
AISC 360 Table B4.1b sets the compact web limit as h/tw less than or equal to 3.76 * sqrt(E/Fy). For A572-50 steel: 3.76 * sqrt(29,000/50) = 90.6. Plate girder webs are often slender (h/tw = 100-250), triggering the bend-buckling reduction.
Do I need transverse stiffeners on a plate girder web?
Intermediate transverse stiffeners are required when the web shear exceeds the shear buckling capacity. AISC 360 Section G2 governs shear; bearing stiffeners at supports are almost always required for plate girders to prevent local crippling of the web under concentrated reactions.
Official sources
- American Institute of Steel Construction: AISC 360-22 Specification, Chapter F Flexure and Chapter G Shear.
- American Society of Civil Engineers: ASCE 7 Load requirements for structural design.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.