Table of Contents
1. Introduction to Steel Sections
Structural steel is a versatile and widely used construction material offering high strength-to-weight ratio, ductility, and ease of fabrication. Steel beams are the primary horizontal framing elements in steel structures, transferring floor and roof loads to columns. The AISC Manual of Steel Construction provides design tables and section properties for all standard hot-rolled shapes produced in North America.
The selection of an economical steel beam section balances strength (moment and shear capacity), stiffness (deflection control), stability (lateral-torsional buckling), and constructability (connection details, camber, and composite action with concrete slabs). The most economical section is typically the lightest section that satisfies all design criteria, as steel is priced by weight.
Standard steel grades include ASTM A992 (50 ksi yield, used for W-shapes), ASTM A572 Grade 50 (50 ksi, for plates and miscellaneous shapes), and ASTM A36 (36 ksi, for angles and channels). Higher-strength grades like A913 (65 ksi) are available for special applications requiring lighter sections.
2. Steel Beam Shape Types
W-shapes (wide flange) are the most common beam sections, with parallel inner and outer flange surfaces. The designation W24×62 indicates a nominal depth of 24 inches weighing 62 lbs/ft. W-shapes are efficient in bending due to the concentration of material in the flanges, where flexural stresses are highest. They are available from W4×13 to W44×335, providing a wide range of capacities.
S-shapes (American Standard beams) have tapered flanges (1:6 slope) and are primarily used in lighter applications, crane rails, and where the tapered flange provides practical benefits. C-shapes (channels) have a single web with two flanges on the same side, used for purlins, girts, bracing, and beam attachments. The shear center of channels is outside the section, causing torsion under eccentric loading.
Hollow Structural Sections (HSS) are closed shapes (rectangular, square, or circular) with high torsional resistance and aesthetic appeal. HSS beams are less efficient in simple bending than W-shapes (material is farther from the neutral axis) but excel where torsion, biaxial bending, or exposed architecture is involved. HSS is defined by outside dimensions and wall thickness, e.g., HSS8×4×⅜.
The Steel Beam Section Properties Calculator provides section properties for all standard shapes, enabling rapid comparison.
3. Key Section Properties
Moment of inertia I (in⁴ or cm⁴) measures the geometric resistance to bending deflection. A larger I produces smaller deflections under a given moment. The elastic section modulus S = I/c (in³ or cm³) relates directly to bending strength: the nominal moment capacity Mn = Fy × S (for compact sections at the plastic moment). The plastic section modulus Z accounts for the full plastification of the section and is 10-20% larger than S for typical W-shapes.
The radius of gyration r = √(I/A) measures the distribution of area around the centroidal axis and governs buckling resistance. The torsional constant J and warping constant Cw are important for torsional analysis. For most steel beams, the section properties are tabulated in the AISC Manual—direct calculation is rarely needed.
The Moment of Inertia Calculator computes I, S, r, and other section properties for custom shapes, while the Section Properties Calculator covers all standard AISC shapes.
4. Design Process per AISC 360
The AISC 360 Specification for Structural Steel Buildings (ANSI/AISC 360-22) governs steel beam design in LRFD (Load and Resistance Factor Design) or ASD (Allowable Strength Design) formats. The LRFD method applies load factors (1.2D + 1.6L typical) and resistance factors (φb = 0.90 for flexure, φv = 1.00 for shear) with the design check φRn ≥ Ru.
The design process begins with determining factored loads and computing the required flexural strength Mu, shear strength Vu, and deflection Δ. Trial sections are selected from the AISC Manual beam tables, which provide φbMp values for each compact section based on unbraced length Lb. The available moment φbMn decreases as Lb increases due to lateral-torsional buckling (LTB), shown in the moment capacity versus unbraced length curves.
Three LTB zones are distinguished: plastic (Lb ≤ Lp, full plastic capacity), inelastic (Lp < Lb ≤ Lr, reduced capacity), and elastic (Lb > Lr, Euler-type buckling). Providing intermediate lateral bracing at Lb ≤ Lp ensures that the full plastic moment is achieved. Composite beams (steel beam with concrete slab connected by shear studs) significantly increase strength and stiffness. The effective transformed section accounts for the concrete compression zone.
The Section Properties Calculator and Load Calculator support initial sizing, and the Cantilever Beam Calculator handles specialized beam configurations.
5. Economy and Optimization
The most economical steel beam is typically the lightest section meeting all design criteria. However, other factors influence overall cost: the number of different section sizes used (standardization reduces procurement and fabrication costs), depth constraints affecting floor-to-floor height (taller beams require deeper spandrel beams and more cladding), and connection complexity (deeper beams require stiffer connections for moment frames).
Rule-of-thumb depths for preliminary sizing: simple beams L/20, continuous beams L/24, composite beams L/24 to L/28. These provide initial estimates before detailed analysis. Girder depths are typically L/12 to L/15. The AISC Manual includes design aids for rapid selection, such as beam selection charts plotting flexural strength versus unbraced length for each section.
Camber is a pre-fabricated upward curvature in the beam (typically L/360 to L/480) that offsets dead load deflection, ensuring a level floor under permanent loads. Camber is specified for longer spans (L > 40 ft) where deflection is visually significant. The Steel Structures Calculator hub provides access to all steel design tools.
6. Worked Example
Select a W-Shape for a Simply Supported Beam
Given: Span L = 40 ft. Floor framing at 10 ft spacing. Dead load = 60 psf (slab + steel + finishes), live load = 50 psf. A992 steel (Fy = 50 ksi). Unbraced length Lb = 10 ft (joists provide top flange bracing). Deflection limit L/360 for live load.
Step 1: Tributary width = 10 ft. wD = 60 × 10 = 600 plf. wL = 50 × 10 = 500 plf. wu = 1.2(600) + 1.6(500) = 1520 plf = 1.52 k/ft.
Step 2: Mu = wuL²/8 = 1.52(40²)/8 = 304 k-ft. Vu = wuL/2 = 1.52(40)/2 = 30.4 kips.
Step 3: Required φbMn ≥ 304 k-ft at Lb = 10 ft. From AISC beam tables, try W21×55: φbMp = 459 k-ft at Lp = 7.5 ft, φbMn at 10 ft = 445 k-ft (LTB reduction). φbMn = 445 > 304. Check shear: φvVn = 254 kips (Q), > 30.4. OK.
Step 4: Deflection. Δ_L = 5wLL⁴/(384EI) = 5(0.5)(40⁴×1728)/(384×29000×1140) = 1.36 in. L/360 = 40×12/360 = 1.33 in. Δ = 1.36 > 1.33. Deflection governs.
Step 5: Try W21×62: I = 1550 in⁴. Δ_L = 1.36 × 1140/1550 = 1.00 in < 1.33 in. φbMp = 516 k-ft, φbMn at 10 ft ≈ 505 k-ft > 304. OK. Weight: 62 plf vs 55 plf — 13% heavier but needed for deflection.
Result: Select W21×62 (A992). Verify with the Steel Beam Section Properties Calculator and consult AISC Manual for full design checks.
Steel Beam Cross-Section
[SVG Diagram: W-shape cross-section with labeled dimensions. Flange width bf, flange thickness tf, web depth h, web thickness tw, overall depth d. Neutral axis marked at mid-depth. Compression flange (top) and tension flange (bottom) indicated. Stress distribution shown: linear elastic (triangular) and fully plastic (rectangular) with plastic neutral axis.]
7. Frequently Asked Questions
What is lateral-torsional buckling?
Lateral-torsional buckling (LTB) is a limit state where a beams compression flange buckles laterally, twisting the entire cross-section. It reduces the moment capacity below the plastic moment. LTB capacity depends on unbraced length, section geometry (Z, ry, J, Cw), and material yield strength.
When should composite beams be used?
Composite action between steel beams and concrete slabs (via welded shear studs) increases flexural strength by 30-50% and stiffness by 20-40% compared to non-composite design. Composite beams are economical for spans of 20-50 ft where floor depth is constrained and vibration control is important.
What is the difference between LRFD and ASD?
LRFD (Load and Resistance Factor Design) applies load factors (>1.0) to service loads and resistance factors (<1.0) to nominal strengths. ASD (Allowable Strength Design) applies a single safety factor (Ω) to nominal strength and compares with service loads. Both methods produce equivalent designs when properly calibrated.
How is beam camber specified?
Camber is specified on structural drawings as the upward deflection at midspan, typically ranging from L/360 to L/480. It is fabricated by cold-bending at the mill. Camber is provided only for dead load—the beam flattens under permanent loads, remaining level for sensitive floor applications.
References & Standards
- ANSI/AISC 360-22. Specification for Structural Steel Buildings. AISC, 2022.
- AISC. Steel Construction Manual. 16th ed., AISC, 2023.
- ASCE 7-22. Minimum Design Loads for Buildings and Other Structures.
- Salmon, C.G., Johnson, J.E., and Malhas, F.A. Steel Structures: Design and Behavior. 5th ed., Pearson, 2009.
- McCormac, J.C. and Csernak, S.F. Structural Steel Design. 6th ed., Pearson, 2017.
- Civil Engineering Handbook — Steel Design chapter.
- Engineering Formula Library — Steel section formulas.
- Engineering Glossary — Steel structures definitions.