--------------------------------- | --------------- | | Floor beams (general) | L/360 | | Floor beams (sensitive to vibration) | L/480 | | Roof beams (no plaster) | L/240 | | Roof beams (with plaster) | L/360 | | Crane beams | L/600 to L/1000 |

AS 4100 (Australia)

AS 4100 Clause 5.4 provides serviceability load combinations but does not prescribe specific deflection limits. Limits are determined by the structural engineer based on the application:

EN 1993 (Eurocode)

EN 1993-1-1 Section 7 defers to EN 1990 Annex A1 and the National Annex:

CSA S16 (Canada)

CSA S16 Clause 5 refers to the National Building Code of Canada:

Worked example: W460x52 floor beam

Problem: A W460x52 spans 9 m and supports a service (unfactored) uniform load of 22 kN/m. Check deflection against L/360.

Section properties (W460x52):

• Ix = 213,000,000 mm^4
• E = 200,000 MPa

Step 1: Calculate maximum deflection

delta = 5 * w * L^4 / (384 * E * I)
delta = 5 * 22 * 9000^4 / (384 * 200000 * 213000000)
delta = 5 * 22 * 6.561e15 / 1.635e16
delta = 44.2 mm

Step 2: Check against limit

L/360 = 9000 / 360 = 25.0 mm
44.2 mm > 25.0 mm  -- FAILS

Step 3: Select larger section

Try W530x82 (Ix = 475,000,000 mm^4):

delta = 5 * 22 * 9000^4 / (384 * 200000 * 475000000)
delta = 19.8 mm  < 25.0 mm  -- OK

The W530x82 passes the deflection check with margin.

Key insight: The strength check for this beam (not shown) would pass with the W460x52. Deflection governed the design, requiring a section 58% heavier. This is common for medium-span floor beams.

How to reduce deflection

If the selected beam fails the deflection check, you have several options:

1. Use a deeper section: I increases roughly with h^3. Going from W460 to W530 nearly doubles I with modest weight increase.

2. Add a cover plate: Welding a plate to the flange increases I through the parallel axis theorem. A 300x20 plate on the bottom flange of a W460x52 adds approximately 46,000,000 mm^4 of Ix.

3. Use fixed or continuous supports: Fixed ends reduce deflection by 80% compared to simply supported. Continuous beams reduce it by about 20%.

4. Reduce the span: Adding an intermediate support cuts the effective span in half, reducing deflection by a factor of 16 (since deflection scales with L^4).

5. Use a stiffer material: Not usually practical for steel (all structural steel has E = 200,000 MPa), but composite action with a concrete slab increases the effective I significantly.

6. Pre-camber: For long-span beams, fabricate with a slight upward camber equal to the expected dead load deflection. This does not reduce live load deflection but prevents visual sag.

Using the beam deflection calculator

Our Beam Serviceability Limits Calculator handles:

1. Multiple support conditions: Simply supported, fixed, cantilever, continuous.
2. Any loading pattern: Uniform, point loads, partial loads, triangular loads.
3. Standard section database: Select W, HSS, C, and other shapes from built-in databases.
4. Instant code checks: Deflection compared against L/240, L/360, L/480 limits automatically.

Common mistakes in deflection calculations

1. Using factored loads: Deflection is a serviceability check. Use unfactored (working) loads, not LRFD factored loads.

2. Using the wrong moment of inertia: Make sure you are using Ix (strong axis) for beams bending about the strong axis. Using Iy gives deflections that are 10-50x too large.

3. Ignoring composite action: A beam with a concrete deck acting compositely has a much higher effective I. Ignoring composite action overestimates deflection.

4. Not checking cantilevers separately: Cantilever deflection limits are typically more lenient (L/180) but the deflections themselves are much larger per unit load.

5. Forgetting long-term effects: For sustained loads, consider creep effects in composite beams and relaxation in cables.

Related calculators

• Beam Capacity Calculator — bending, shear, and combined checks
• Beam Span Calculator — maximum allowable spans for steel sections
• Moment of Inertia Calculator — section properties for any steel shape
• Load Combinations Calculator — ASCE 7, AS 4100, EN 1990, CSA S16 combinations
• Section Properties Database — browse 500+ W, HSS, C, L, and WT sections with Ix values, dimensions, and classification limits

References

• AISC 360-22, Commentary Chapter B: Design Requirements
• AISC Design Guide 11: Vibrations of Steel-Framed Structural Systems
• AS 4100:2020, Clause 5.4: Serviceability
• EN 1993-1-1:2005, Section 7: Serviceability Limit States
• CSA S16:24, Clause 5: Design Requirements

Disclaimer: This content is for educational purposes only. Results must be verified by a licensed professional engineer. Steel Calculator provides preliminary design tools — NOT a substitute for professional engineering judgment.