> ## Documentation Index
> Fetch the complete documentation index at: https://calcs.com/docs/llms.txt
> Use this file to discover all available pages before exploring further.

# Size a Beam from Deflection

> Worked examples in US and metric units for sizing a beam from a deflection limit.

On typical residential and light commercial spans, deflection sets the beam size, not strength. That means you size the section from a stiffness target and then confirm strength afterwards. Two worked examples follow, one in US units and one in metric.

## Example 1: a 20 ft span in US units

Take a simply supported 20 ft span carrying 1,000 plf.

**Moment.** M = wL² / 8 = 50 kip-ft. Almost any rolled section covers that.

**Stiffness.** Holding deflection to L/360, which is 0.67 in, needs I of at least 5wL⁴ / 384Eδ = 186 in⁴.

**Sections.** A W12x26 at I = 204 in⁴ clears the requirement. The W14x68 loaded by default in the beam calculator is far stiffer at 722 in⁴. It deflects 0.17 in, which is L/1,396.

Change the span, the load, or the deflection limit and the required I moves with them. Testing those combinations quickly is what the calculator is for.

## Example 2: a 4 m span in metric units

Take a simply supported 4 m span carrying 3 kN/m dead load and 3 kN/m live load. The section is a 150 UB 14.0, with I\_x = 6.66 x 10⁶ mm⁴.

**Serviceability.** The short-term case, 1.0G + 0.7Q, deflects 13.1 mm against the 16.0 mm allowed by L/250. The section works with about 20% to spare. Reaching that limit exactly needs I\_x of at least 5.44 x 10⁶ mm⁴.

**Strength.** Strength is not close. The moment demand of 16.5 kN·m sits at 56% of the 29.4 kN·m capacity to AS 4100.

**Heavier loads.** Raise the load and the section has to grow. A 180 UB 16.1 gives 10.6 x 10⁶ mm⁴, and a 200 UB 22.3 gives 21.0 x 10⁶ mm⁴.

Derive your own line load from the floor area and imposed action to AS/NZS 1170.1. The 6 kN/m used above is an illustrative residential case only.

## Confirm strength separately

Deflection sizing gives you a candidate section. Confirming it also needs a strength check and a lateral-torsional buckling check. Those run against the governing standard, for example AISC, NDS, ACI 318, or AS 4100. Those are design checks rather than analysis outputs.

Both examples are illustrations. Use your own loads, limits, and restraint conditions, and review the result before relying on it.