How to Design a Steel Beam
Designing a steel beam means picking the lightest shape that is strong enough and stiff enough for its loads. In the United States the strength checks come from the AISC Specification for Structural Steel Buildings (AISC 360), the loads from ASCE 7, and the deflection limits from the International Building Code (IBC). For most floor and roof beams the design comes down to four checks:
- Bending — can the beam carry the maximum moment without yielding?
- Lateral-torsional buckling — if the compression flange isn't braced, will the beam twist sideways first?
- Shear — can the web carry the reactions near the supports?
- Deflection — does the beam sag more than the code or the finishes allow?
This guide walks through those checks by hand on a real example, then shows how to run the same design in WebStructural's beam designer, which does the calculations for you.
The Steps to Design a Steel Beam
1. Find the loads
Floor and roof loads are given as area loads in pounds per square foot (psf). Multiply each one by the beam's tributary width — usually the beam spacing — to get a line load in pounds or kips per foot. Keep each load case separate:
- Dead load (D) — slab, deck, finishes, ceiling, mechanical, and the beam itself.
- Live load (L) — occupancy, from ASCE 7 Table 4.3-1 (for example 50 psf for offices, 40 psf for residential floors).
- Roof live (Lr), snow (S), wind (W) and others where they apply.
For more on load cases and how they are combined, see load cases and load combinations.
2. Combine the loads
Strength checks use factored load combinations from ASCE 7. With Load and Resistance Factor Design (LRFD), the two that usually govern a floor beam are:
wu = 1.4D or wu = 1.2D + 1.6L
With Allowable Strength Design (ASD) the loads are left unfactored (D + L) and the safety factor is applied to the beam's strength instead. Deflection is always checked with unfactored service loads.
3. Find the maximum moment and shear
For a simply supported beam with a uniform load w over a span L:
Mmax = wL² / 8 Vmax = wL / 2
Continuous beams, cantilevers and point loads need a shear and moment diagram. You can draw one with the free shear and moment diagram calculator.
4. Pick a trial shape
If the compression flange is braced along its length (for example by a metal deck welded to the top flange), the beam can reach its full plastic moment, Mp = FyZx. Solving the LRFD bending check for the plastic section modulus gives the size you need:
Zx,req = Mu / (φb Fy) with φb = 0.90
Wide-flange beams (W-shapes) are normally ASTM A992 steel with Fy = 50 ksi. Pick the lightest W-shape with Zx at least this large. The shape name gives its nominal depth and weight: a W16X26 is about 16 in. deep and weighs 26 lb/ft. Lighter usually means cheaper. The steel beam sizes chart lists Zx and the design bending strength of every W-shape, and the steel beam span chart gives a starting size for a span and load.
5. Check bending and lateral-torsional buckling
AISC 360 Section F2 gives the bending strength of a W-shape. It depends on the unbraced length Lb, the distance between points where the compression flange is held against moving sideways:
- Lb ≤ Lp: the beam yields before it buckles, and Mn = Mp.
- Lp < Lb ≤ Lr: inelastic lateral-torsional buckling; Mn drops in a straight line toward 0.7FySx.
- Lb > Lr: elastic lateral-torsional buckling, and Mn falls off quickly.
The factor Cb raises the strength when the moment isn't constant along the unbraced segment (1.14 for a simple span with uniform load and no intermediate bracing). The check passes when Mu ≤ φbMn.
6. Check shear
From AISC 360 Section G2, for most rolled W-shapes:
φvVn = φv × 0.6 Fy × d tw × Cv1
φv = 1.0 when h/tw ≤ 2.24√(E/Fy) (53.9 for 50 ksi steel), and 0.90 otherwise. Shear rarely governs uniformly loaded beams, but check it for short spans and heavy point loads near a support.
7. Check deflection
For a simple span with a uniform load:
Δ = 5wL⁴ / (384 E I)
IBC Table 1604.3 sets the maximum deflection for floor members at L/360 under live load and L/240 under dead plus live load. Deflections are given as a fraction of the span so that beams of different lengths can be compared: a 12 ft beam that deflects 0.5 in. is at L/288, and so is an 18 ft beam that deflects 0.75 in. Beams that support brittle finishes, masonry or sensitive equipment often need stricter limits. Deflection is a service check, so use unfactored loads.
8. Pick the final size
If any check fails, try the next heavier or deeper shape and repeat. On short spans strength usually governs; on longer spans deflection usually does, and a deeper shape of the same weight is often the cheapest fix.
Worked Example: A 24 ft Steel Floor Beam
Loads
wD = 60 psf × 10 ft = 0.60 k/ft wL = 50 psf × 10 ft = 0.50 k/ft
wu = 1.2(0.60) + 1.6(0.50) = 1.52 k/ft (1.4D = 0.84 k/ft is smaller)
ASCE 7 would allow a small live load reduction here (about 7%, since the tributary area is 240 ft²). We skip it, which is conservative.
Moment, shear and required size
Mu = 1.52 × 24² / 8 = 109.4 kip-ft Vu = 1.52 × 24 / 2 = 18.2 kips
Zx,req = 109.4 × 12 / (0.90 × 50) = 29.2 in³
Deflection sets its own minimum. The live load limit is L/360 = 288 in. / 360 = 0.80 in., and the dead plus live limit is L/240 = 1.20 in. Rearranging Δ = 5wL⁴/(384EI):
Ireq = 161 in⁴ for live load Ireq = 236 in⁴ for dead plus live
So strength alone points to a W12X22 (Zx = 29.3 in³), but the dead plus live deflection limit needs a moment of inertia about 50% higher than that shape has.
Checking trial shapes
Each row below includes the beam's own weight. The numbers are demand divided by capacity, so anything above 1.00 fails. Click a shape to open it in the beam designer.
| Shape | Zx (in³) | Ix (in⁴) | Bending | Live load deflection (L/360) | Dead + live deflection (L/240) | Result |
|---|---|---|---|---|---|---|
| W12X22 | 29.3 | 156 | 1.01 | 1.03 | 1.54 | Fails |
| W14X22 | 33.2 | 199 | 0.89 | 0.81 | 1.21 | Fails deflection |
| W14X26 | 40.2 | 245 | 0.74 | 0.66 | 0.99 | Passes, barely |
| W16X26 | 44.2 | 301 | 0.67 | 0.53 | 0.80 | Passes |
The W14X26 and W16X26 weigh the same, but the deeper W16X26 is 23% stiffer, so it is the better choice.
Final checks for the W16X26
Bending. With self weight, wu = 1.2(0.60 + 0.026) + 1.6(0.50) = 1.55 k/ft and Mu = 111.7 kip-ft. With the top flange braced continuously, φMn = 0.90 × 50 × 44.2 / 12 = 166 kip-ft. Ratio 0.67. OK.
Shear. Vu = 1.55 × 24 / 2 = 18.6 kips. The W16X26 web has h/tw = 56.8, just over 53.9, so φv = 0.90 (Cv1 is still 1.0). φvVn = 0.90 × 0.6 × 50 × 15.7 × 0.250 = 106 kips. Ratio 0.18. OK.
Deflection. Live load: Δ = 0.43 in. ≤ 0.80 in. Dead plus live (1.13 k/ft): Δ = 0.96 in. ≤ 1.20 in. OK.
Use a W16X26. Deflection, not strength, decided the size.
How Bracing Changes the Answer
When a beam bends, one flange is in compression. Like a long ruler pushed from both ends, a slender compression flange can buckle sideways and twist the beam with it. This is lateral-torsional buckling, and bracing the compression flange is what prevents it. For a simple span the compression flange is the top one; over the interior support of a continuous beam or along a cantilever, it's the bottom one.
Here is the same W16X26 with the same 111.7 kip-ft demand, under three bracing conditions. For this shape Lp = 3.96 ft and Lr = 11.2 ft. Click a row to open that case in the beam designer.
| Bracing | Lb | Cb | φMn (kip-ft) | Bending ratio |
|---|---|---|---|---|
| Deck welded to top flange | 0 | — | 166 | 0.67 |
| Braced at third points (filler beams) | 8 ft | 1.01 | 131 | 0.85 |
| Unbraced between supports | 24 ft | 1.14 | 34 | 3.26 |
Without bracing the beam carries about a fifth of its braced strength. If you aren't sure how a beam is braced, design it as unbraced; that is always conservative.
ASD vs. LRFD
AISC 360 allows either method, and for typical floor loads they give similar sizes. LRFD factors the loads up and the strength down (φ = 0.90 for bending). ASD uses service loads and divides the strength by a safety factor (Ω = 1.67 for bending). For the W16X26 above, ASD gives Ma = 1.13 × 24² / 8 = 81.1 kip-ft against Mn/Ω = 184.2 / 1.67 = 110.3 kip-ft, a ratio of 0.74 versus 0.67 for LRFD (open the ASD design). LRFD tends to come out a little lighter when live load is small compared to dead load.
Design a Steel Beam in WebStructural
The hand calculation above takes a few iterations. WebStructural's beam designer runs every check from AISC 360 as you change the beam, including load combinations, lateral-torsional buckling with Cb, shear and deflection, for single spans, continuous beams and cantilevers. The interface follows six steps:
- Select a shape
- Choose a material grade
- Select a design method and deflection limits
- Add spans and configure supports
- Add loads
- Configure bracing
In this walkthrough we'll design a two-span continuous beam (a 12 ft span and a 4 ft span on pinned supports) carrying a uniform load. To skip ahead, open the finished beam.
Step 1: Select a Shape
Let's select a W shape from WebStructural's shape library, which is built from the AISC shapes database.
This beam is roughly 8 inches deep and weighs 15 pounds per foot. After we enter the loads, we can change the shape if this one isn't adequate.
Step 2: Choose a Material Grade
Step 3: Select a Design Method — ASD, LRFD or Capacity
With ASD or LRFD, WebStructural builds the load combinations and applies the matching AISC 360 equations. You can view the equations and click any of them to leave it out of the analysis.
Unchecking Use LRFD/ASD Equations shows capacity ratios based on service loads only, which is useful for preliminary sizing or teaching. The Capacity option shows capacity ratios for the loads you enter with no load factors or design equations applied.
This dialog also sets the deflection limits, such as L/360 for live load and L/240 for total load. Change them for your use case.
Step 4: Add Spans and Configure Supports
A span is the distance between supports. To add or edit spans, click the Spans button or click a span dimension on the drawing. You can add spans to the left or right of the existing ones.
Clicking a support (the gray triangle under the beam) cycles it through Pinned, Fixed and Free. Setting an end support to Free turns that span into a cantilever. For this example, leave all three supports pinned.
Your model should now look like this:
Step 5: Add Loads
WebStructural supports four load types:
- Uniform loads (kips per foot by default) — joists, rafters or a slab framing into the beam, found by multiplying the area load in psf by the tributary width.
- Linear loads — loads that vary along their length, such as snow drifts or joists framing in at a skew.
- Point loads (kips) — a beam or column bearing on the beam.
- Moments (kip-feet) — for example from a column welded to the top of the beam with a horizontal force on it. Torsion can't be entered.
Each load can have a magnitude for every load case: dead, live, roof live, snow, wind, seismic and others. For this example we'll use a dead load D = 0.63 k/ft and a live load L = 1.5 k/ft over the whole beam, and Include Self Weight.
Enter service (unfactored) loads. WebStructural applies the LRFD or ASD load factors for you.
Your model should now look like this:
Step 6: Configure Bracing
As the bracing example above shows, the unbraced length can change a beam's bending strength several times over. WebStructural treats supports as brace points and lets you add bracing in common configurations. Continuous bracing means the compression flange is braced along its whole length. To find the compression side, look at the moment diagram: positive moment puts the top flange in compression, negative moment (over interior supports and on cantilevers) the bottom flange.
Review the Results
WebStructural recalculates as you go. It runs a finite element analysis of the beam, then checks bending, shear and deflection against AISC 360 for every load combination. Each result is a demand-to-capacity ratio: "Bending 0.87" means the beam is at 87% of its design bending strength. Green means every ratio is below 1.0.
If a ratio is above 1.0 the result turns red and you need a larger beam. Pick a deeper or heavier shape and the results update.
For our example the W8X15 passes: bending 0.87 (at the interior support, where the moment is −44.4 kip-ft), shear 0.38 and deflection 0.97.
Scroll down for reactions and the moment, shear and deflection diagrams for each load case.
