Custom Steel Section — Built-Up Section Properties Calculator

Q: How are bolt holes accounted for in built-up section net section calculations?

Per AISC 360 B4.3b and D3, bolt hole deductions reduce the gross section area to a net section area for tension checks. The reduction accounts for: (1) standard hole diameter = bolt diameter + 1/16 inch, (2) oversize and slotted holes use larger deductions per AISC Table J3.3, (3) for staggered bolt patterns, the net width = gross width - sum(dh) + sum(s²/(4g)), where s is the longitudinal pitch and g is the transverse gauge. The calculator identifies the critical net section path (the one with minimum net area) and applies the appropriate shear lag factor U per AISC D3.

Q: What is the minimum weld size for web-to-flange connections in built-up beams?

Per AISC Table J2-4 and AWS D1.1, minimum fillet weld sizes for web-to-flange connections depend on the thicker part joined: for material thickness up to 1/2 inch, minimum weld = 1/8 inch; for 1/2 to 3/4 inch, minimum = 3/16 inch; for 3/4 to 1-1/2 inches, minimum = 1/4 inch. The weld size must also satisfy strength requirements for horizontal shear per AISC I6-2: VQ/I. Intermittent welds are permitted when the calculated required continuous weld size is less than the minimum, and must be at least 1.5 inches long with maximum spacing of 24 times the thinner plate thickness.

Calculate section properties for custom built-up steel sections. Design welded plate girders, box columns, built-up channels, and other fabricated sections. Supports any combination of plates and standard rolled shapes.

Quick links: Beam capacity → | Section properties → | All beam sizes →

Core calculations run via WebAssembly in your browser with step-by-step derivations across AISC 360, AS 4100, EN 1993, and CSA S16 design codes. Results are preliminary and must be verified by a licensed engineer.

Overview of Built-Up Steel Sections

Built-up steel sections are fabricated by welding or bolting together individual plates, rolled shapes, or a combination of both. Unlike standard rolled sections (W-shapes, channels, angles), built-up sections can be optimized for specific structural requirements: deeper girders for longer spans, variable flange sizes for non-uniform moment envelopes, or box sections for torsional resistance. They are commonly used in plate girders, crane runway beams, heavy column construction, bridge girders, and special architectural applications.

The Custom Section calculator computes the full set of section properties for any built-up assembly, enabling the designer to verify that the fabricated section meets strength, stiffness, and stability requirements without manual hand calculations.

Section Property Calculations

The calculator computes the following properties using the parallel axis theorem and first principles:

Cross-sectional area (A) — The sum of each component area. For plates: A = b × t. For rolled shapes: A is retrieved from the embedded shape database.

Centroid location (x̄, ȳ) — Computed as the weighted average of component centroids: ȳ = Σ(Ai × yi)/Σ(Ai), where yi is the distance from a reference axis to the centroid of component i.

Moment of inertia (Ix, Iy) — Using the parallel axis theorem: Ix = Σ(Ix,i + Ai × di²), where Ix,i is the centroidal moment of inertia of component i and di is the distance from the component centroid to the section centroid.

Section modulus (Sx, Sy) — Elastic section modulus: Sx = Ix/c, where c is the distance from the neutral axis to the extreme fiber. Both positive and negative Sx are reported for unsymmetric sections.

Radius of gyration (rx, ry) — rx = √(Ix/A), ry = √(Iy/A). Used for slenderness calculations in compression and LTB.

Plastic modulus (Zx, Zy) — Computed by dividing the section into a finite number of fibers about the plastic neutral axis (PNA). The PNA divides the section into equal tension and compression areas. Zx = Σ(Ai × |yi - yPNA|).

Torsional constant (J) — For open sections: J = Σ(1/3 × bi × ti³). For closed sections (box sections): J = 4A² / Σ(Δs/t).

Warping constant (Cw) — For doubly symmetric I-sections: Cw = Iy × (d - tf)²/4. For unsymmetric sections, the calculator uses a general finite element approach.

Built-Up Section Configurations

Welded Plate I-Girders

The most common built-up configuration — two flange plates welded to a web plate. The calculator requires: web depth × thickness, top flange width × thickness, bottom flange width × thickness, and web-to-flange weld size. Both symmetric and unsymmetric (different top and bottom flange sizes) sections are supported. The calculator checks width-thickness ratios for flange and web elements per AISC B4.1 and provides slenderness classification (compact, non-compact, slender).

Design example — A plate girder with web 60×3/8 inches, top flange 16×1 inch, bottom flange 16×1-1/4 inches. A = 60×0.375 + 16×1.0 + 16×1.25 = 22.5 + 16 + 20 = 58.5 in². Ix ≈ 34,500 in⁴ (web: bh³/12 + 2 × flange contributions with parallel axis). Sx,top = Ix/31.5, Sx,bot = Ix/32.0. Zx ≈ 2,100 in³ for this asymmetric section.

Box Sections (Rectangular HSS and Built-Up)

Box sections consist of four plates welded to form a closed tube. The calculator supports: (1) welded box girders — two flange plates and two web plates with complete joint penetration (CJP) welds, (2) multi-cell boxes — multiple adjacent box cells separated by web plates, and (3) battened boxes — flange plates connected by batten plates at intervals (for reduced weight).

Box sections offer superior torsional stiffness compared to open I-sections. The torsional constant J for a closed box is typically 10-100 times larger than an equivalent I-section, making box sections ideal for curved girders and torsionally loaded members.

Built-Up Columns (Laced and Battened)

For heavy column loads, built-up columns with lacing or batten plates provide an efficient alternative to single rolled sections. The calculator computes:

Modified slenderness — Per AISC E6, the modified slenderness (KL/r)m accounts for shear deformation in the lacing or battens
Lacing design — The lacing bars are designed per AISC E6-2 for the required shear force of 2% of the column axial capacity
Batten plate design — Batten plates are designed for the shear and moment from the 2% lateral force, with minimum thickness per E6-2

Local Buckling Checks

Per AISC 360 B4.1 and Table B4.1a, each plate element is classified based on its width-thickness ratio (λ):

Flange compact limit — λpf = 0.38√(E/Fy) for flanges of I-shaped sections. For Fy = 50 ksi: λpf = 0.38√(29,000/50) = 9.15. Flange overhang bf/(2tf) must be ≤ 9.15 for compact classification.

Web compact limit — λpw = 3.76√(E/Fy) for webs of I-shaped sections. For Fy = 50 ksi: λpw = 3.76√(29,000/50) = 90.6. Web h/tw must be ≤ 90.6 for compact classification.

Slender element reduction — For elements exceeding λr (slender limit), the effective width is reduced per E7-2: be = 1.92 × t × √(E/f) × [1 - 0.34/(b/t) × √(E/f)], where f is the computed stress in the element. The reduced section properties (using effective widths) are then used for strength calculations.

Welding Design for Built-Up Sections

Per AWS D1.1/D1.1M and AISC 360 Chapter J2:

Flange-to-web welds — Must develop the full horizontal shear at the interface. Per AISC B3.6, the required weld strength per unit length is VQI, where V is the factored shear, Q is the first moment of the flange about the neutral axis, and I is the moment of inertia about the neutral axis.

Minimum weld size — Per AISC Table J2-4: for a 3/4-inch thick flange plate welded to a 3/8-inch web, the minimum fillet weld size is 1/4 inch.

Intermittent welds — Permitted for non-seismic applications. Minimum segment length: 1.5 inches (40 mm). Maximum center-to-center spacing: 24 × tmin (thinner part thickness), not to exceed 12 inches.

Groove weld requirements — Full penetration groove welds (CJP) are required for tension flange splices in plate girders. Partial joint penetration (PJP) welds are permitted for compression flange splices if properly detailed.

Frequently Asked Questions

What built-up section types are supported? The calculator supports: (1) welded plate I-sections (symmetrical and unsymmetrical), (2) box sections (square, rectangular, and multi-cell), (3) built-up channels (C-shapes and MC-shapes with cover plates), (4) tee sections cut from W-shapes, (5) built-up columns with lacing or battens, and (6) custom polygon sections defined by coordinate input. Each shape type has specific local buckling and slenderness checks.

How are local buckling checks performed for built-up sections? Per AISC 360 B4.1 and Table B4.1a, each plate element (flange, web, cover plate) is classified as compact, non-compact, or slender based on its width-thickness ratio. Elements exceeding the slender limit (λr) require reduced effective widths per E7-2: be = 1.92t√(E/f) × [1 - 0.34/(b/t)√(E/f)]. The reduced section properties are then recomputed using effective widths.

What welding requirements apply to built-up sections? Per AWS D1.1/D1.1M Clause 4 and AISC 360 Chapter J2: (1) fillet welds connecting flanges to webs must develop the full shear strength at the interface, (2) intermittent welds are permitted for non-seismic applications with minimum length 1.5 inches and maximum spacing 24 times the thinner part thickness, (3) groove welds in built-up sections require complete joint penetration (CJP) for tension flanges, and (4) minimum weld size per AISC Table J2-4.

How are bolt holes accounted for in built-up section net section calculations? For bolted built-up sections, the net section properties must account for bolt hole reductions per AISC B4.3b. The net area An = Ag - Σ(dh × t) + Σ(s² × t / 4g), where dh is the hole diameter, s is the staggered pitch, and g is the gage. For holes larger than standard (oversized, slotted), additional reductions apply. The calculator allows the user to specify bolt hole patterns and automatically computes the net section properties for tension and shear checks.

What is the minimum weld size for web-to-flange connections in built-up beams? The minimum fillet weld size for web-to-flange welds in built-up beams is governed by two criteria: (1) the minimum required size per AISC Table J2-4 based on the thicker part joined (e.g., 1/4 inch for 3/4 to 1-1/2 inch thick parts), and (2) the required strength to develop the horizontal shear at the web-flange interface. The design shear flow is computed as q = VQ/I. The required weld throat thickness = q/(0.6 × FEXX × 0.707 × 2 welds). For a typical bridge plate girder, 5/16-inch fillet welds (E70) on each side of the web satisfy both minimum size and strength requirements.

Disclaimer (educational use only)

This page is provided for general technical information and educational use only. It does not constitute professional engineering advice. All results must be independently verified by a licensed Professional Engineer.