Deflection of Simply Supported Beam

What is this formula?

The Deflection of Simply Supported Beam formula calculates the maximum vertical deflection produced by a concentrated load applied at the center of a simply supported beam.

Deflection is often a governing design criterion because excessive deformation can affect serviceability even when stresses remain below allowable limits.

When to use it

Use this formula when analyzing:

- Steel beams

- Reinforced concrete beams

- Timber beams

- Floor joists

- Bridge girders

with a single concentrated load acting at midspan.

Example

A simply supported steel beam carries a centered load of 20 kN.

Data:

P = 20,000 N

L = 5 m

E = 200,000,000,000 Pa

I = 8×10⁻⁵ m⁴

Formula:

δ = PL³/(48EI)

Substitution:

δ = (20,000 × 5³)/(48 × 200,000,000,000 × 8×10⁻⁵)

δ = 0.003255 m

Result:

δ = 3.26 mm

Applications

- Structural serviceability checks

- Building floor design

- Bridge engineering

- Steel structures

- Concrete structures

- Timber engineering

Note

This equation applies to a simply supported beam subjected to a single concentrated load at midspan and assumes linear elastic behavior. Different loading conditions such as distributed loads, multiple loads, cantilevers, or continuous beams require different deflection equations.