------------------ | ----------------- | ------------------- | ---------------------- | ------------------ | | Flexure (compact) | F2.1, phi=0.90 | Cl 5.1, phi=0.9 | Cl 6.2.5, gamma_M0=1.0 | Cl 13.5, phi=0.9 | | Deflection limits | IBC Table 1604.3 | BCA/AS 1170.0 App C | EN 1990 Table A1.4 | NBCC Annex D | | Live load deflection | L/360 (floors) | Span/250 (imposed) | L/250 to L/350 | L/360 (floors) | | Total load deflection | L/240 (floors) | Span/250 (total) | L/250 (total) | L/300 (total) | | Shear check | G2.1, phi=1.0 | Cl 5.11, phi=0.9 | Cl 6.2.6 | Cl 13.4.1, phi=0.9 | | Live load reduction | ASCE 7, Eq. 4.7-1 | AS 1170.1, Cl 3.4 | EN 1991-1-1, Cl 6.3.1 | NBCC 4.1.5.9 |

Key difference: AISC/IBC uses L/360 for live load and L/240 for total load on floor beams. Australian BCA uses span/250 for incremental (imposed) loads. Eurocode permits L/250 to L/350 depending on the finish type. Canadian NBCC uses L/360 for live and L/300 for total. These differences mean the same beam may pass in one code but fail in another for deflection.

Step-by-Step Example

Problem: Find the lightest W-shape for a 30-ft simply supported floor beam carrying wD = 0.8 kip/ft dead load and wL = 1.2 kip/ft live load. Fy = 50 ksi. Full lateral bracing. Limits: L/360 for live load, L/240 for total load.

Step 1 -- Factored load (LRFD): wu = 1.2 _ 0.8 + 1.6 _ 1.2 = 0.96 + 1.92 = 2.88 kip/ft.

Step 2 -- Required moment capacity: Mu = 2.88 _ 30^2 / 8 = 2.88 _ 900 / 8 = 324 kip-ft. Zx,req = 324 _ 12 / (0.90 _ 50) = 3888 / 45 = 86.4 in^3.

Step 3 -- Required moment of inertia (live load deflection, L/360): delta*allow = 30 * 12 / 360 = 1.0 in. Ix,req = 5 _ (1.2/12) _ (360)^4 / (384 _ 29000 _ 1.0) = 5 _ 0.1 _ 1.680 _ 10^10 / (384 _ 29000) = 8.398 _ 10^9 / 1.114 * 10^7 = 754 in^4.

Step 4 -- Required moment of inertia (total load deflection, L/240): delta*allow = 360/240 = 1.5 in. w_total = 0.8 + 1.2 = 2.0 kip/ft = 0.1667 kip/in. Ix,req = 5 * 0.1667 _ (360)^4 / (384 _ 29000 _ 1.5) = 839 in^4.

Step 5 -- Select lightest section: Need: Zx >= 86.4 in^3 AND Ix >= 839 in^4 (total load controls).

• W18x50: Zx = 101, Ix = 800 in^4. Ix < 839. FAILS deflection.
• W21x44: Zx = 95.4, Ix = 843 in^4. Both criteria met. Weight = 44 lb/ft.
• W18x55: Zx = 112, Ix = 890 in^4. OK but heavier at 55 lb/ft.

Result: W21x44 is the lightest adequate section (44 lb/ft). Controlling criterion: total load deflection (Ix governs). A W18x50 fails by 5% on deflection despite passing strength by a wide margin -- demonstrating why span tables check both criteria simultaneously.

Common Design Mistakes

• Selecting beams on strength alone without checking deflection: For spans over 25 ft, deflection almost always controls beam selection. A beam that passes strength with a comfortable margin can still fail L/360 deflection, requiring a heavier or deeper section.
• Not including beam self-weight in the dead load: A W21x44 adds 44 lb/ft = 0.044 kip/ft to the dead load. For lightly loaded beams, self-weight can represent 5-10% of the total dead load and should be included in the final check.
• Using total load for the L/360 check: L/360 is a live-load-only deflection limit. Using the total load (dead + live) against L/360 is overly conservative by 30-60% and selects heavier beams than necessary. Total load is checked against L/240.
• Ignoring LTB for unbraced roof beams: Span tables typically assume full lateral bracing (Cb factor benefit). Roof beams without a concrete deck may have unbraced lengths of 6-10 ft or more, reducing flexural capacity below the tabulated value. Always verify the LTB assumption.
• Not checking shear at heavily loaded short spans: For transfer beams and beams with span-to-depth ratios below 10, shear strength can control. Span tables that only check moment and deflection will miss shear-critical selections.
• Applying live load reduction without checking K_LL * AT: The ASCE 7 live load reduction factor only applies when K_LL * tributary area exceeds 400 ft^2. Floor beams with small tributary widths (under 10 ft for typical joists) may not qualify for any reduction.

Frequently Asked Questions

How does a span table differ from a full beam capacity check? A span table pre-screens sections against simplified load cases — typically a uniform load on a simply supported span — and returns sections that pass both strength and deflection limits under those assumptions. A full capacity check uses your actual factored loads, tributary widths, load combinations, and checks all limit states including lateral-torsional buckling, shear, and web crippling. Use the span table to narrow your shortlist to two or three candidate sections, then confirm the governing section with a complete design check.

What does "lightest adequate section" mean in the span table results? The lightest adequate section is the W-shape with the smallest weight per foot (lb/ft or kg/m) that satisfies both the moment capacity and deflection criteria for the entered span and load. Selecting the lightest section minimizes material cost and self-weight dead load. However, lighter sections are typically shallower, which means higher deflection-to-span ratios, so verify that the controlling criterion matches your project requirements before finalising the selection.

What is the span-to-depth ratio rule of thumb for steel beams? A commonly used preliminary rule is L/20 for the total depth of a steel beam under typical floor loading, where L is the span in consistent units. For a 9 m span this gives a trial depth of roughly 450 mm, pointing to a W460 or W450 range. This ratio is a starting point only; heavily loaded beams, long spans, or tight deflection limits (L/360 or stricter) will require a deeper or heavier section than the rule suggests.

How do live load and dead load affect section selection differently? Dead load is permanent and applies to all load combinations; it governs total (long-term) deflection, which is checked against limits such as L/240. Live load is transient and governed by limits such as L/360 for floors to prevent perception of vibration and cracking of non-structural elements. Because live-load deflection and strength are checked separately, a beam may pass strength under the combined factored load but fail live-load deflection — or vice versa. Enter dead and live loads separately in the tool to see which criterion controls.

When should I check deflection rather than strength, and when does strength govern? For typical floor beams with spans up to about 10 m (33 ft), deflection under service live load frequently controls selection, especially with L/360 limits. For heavily loaded short-span transfer beams, roof beams with large snow loads, or beams with concentrated loads, strength (flexure or shear) tends to govern. As a quick check: if the span-to-depth ratio is near or exceeding L/20, expect deflection to control; if the load intensity is high relative to span, expect strength to control.

What does the K_LL tributary area reduction factor do and when does it apply? K_LL is a live-load element factor used with ASCE 7 to determine whether the tributary area is large enough to justify reducing the code-specified live load. For members with K_LL × A_T ≥ 400 ft² (37.2 m²), the design live load may be reduced by up to 50% for members supporting large areas. The reduction recognises that it is statistically unlikely for the full code live load to act simultaneously over a large area. Span tables that do not apply this reduction are conservative for multi-bay or large-floor-plate structures.

Related pages

• Steel beam sizes reference
• Section properties database
• Beam capacity calculator
• Beam Serviceability Limits Calculator
• Unit converter
• Tools directory
• Reference tables directory
• Guides and checklists
• How to verify calculator results
• Disclaimer (educational use only)
• beam analysis with SFD and BMD
• Beam Design Workflow
• Deflection Limits

Disclaimer (educational use only)

This page is provided for general technical information and educational use only. It does not constitute professional engineering advice, a design service, or a substitute for an independent review by a qualified structural engineer. Any calculations, outputs, examples, and workflows discussed here are simplified descriptions intended to support understanding and preliminary estimation.

All real-world structural design depends on project-specific factors (loads, combinations, stability, detailing, fabrication, erection, tolerances, site conditions, and the governing standard and project specification). You are responsible for verifying inputs, validating results with an independent method, checking constructability and code compliance, and obtaining professional sign-off where required.

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