Beam Deflection Calculator

Calculate structural beam bending and deflection for various load configurations

Beam Properties

Beam Support Type

Beam Length (m)

Beam Width (mm)

Beam Height (mm)

Material Type

Elastic Modulus (GPa)

Load Configuration

Load Type

Load Value (kN or kN/m)

Load Position from Left Support (m)

Beam diagram will appear here after calculation

Important: This calculator is for preliminary design purposes only. Always consult a qualified structural engineer for critical structural applications and verify calculations according to relevant British Standards (BS EN 1993, BS EN 1992).

What is Beam Deflection?

Beam deflection refers to the vertical displacement of a structural beam when subjected to loads. It occurs when external forces cause the beam to bend from its original straight position. In construction and engineering, controlling deflection is crucial for both structural integrity and serviceability.

Key Factors Affecting Beam Deflection

Load magnitude and type – Heavier loads cause greater deflection
Beam span – Longer beams deflect more than shorter ones
Material properties – Higher elastic modulus reduces deflection
Cross-sectional properties – Larger moment of inertia reduces deflection
Support conditions – Different support types affect deflection patterns

UK Building Standards for Deflection

According to British Standards, typical deflection limits are:

Beam Type	Deflection Limit	Application
Cantilever beams	Length/180	General construction
Simply supported beams	Span/200 to Span/360	Depends on finish materials
Beams with brittle finishes	Span/360	Plaster ceilings
Floor beams	Span/250	Residential and office

Beam Deflection Formulas

The deflection of a beam depends on its support conditions and loading pattern. Here are the fundamental formulas used in structural calculations:

Simply Supported Beam

Point Load at Centre:

δ = PL³ / (48EI)

Uniformly Distributed Load:

δ = 5wL⁴ / (384EI)

Cantilever Beam

Point Load at End:

δ = PL³ / (3EI)

Uniformly Distributed Load:

δ = wL⁴ / (8EI)

Where:

δ = Maximum deflection (mm)
P = Point load (N)
w = Distributed load per unit length (N/m)
L = Beam length (mm)
E = Elastic modulus (N/mm²)
I = Second moment of area (mm⁴)

Moment of Inertia Calculation

For rectangular cross-sections, the second moment of area about the neutral axis is:

I = bh³ / 12

Where b = width and h = height of the beam cross-section

Common Materials in UK Construction

Material	Elastic Modulus (GPa)	Typical Applications
Structural Steel (S355)	200	Steel frame construction, bridges
Reinforced Concrete (C30/37)	30-32	Building frames, slabs
Softwood Timber (C24)	11-13	Roof structures, floor joists
Hardwood Timber	14-16	Heavy timber construction
Aluminium Alloy	70	Lightweight structures

Frequently Asked Questions

What is acceptable deflection for a beam?

Acceptable deflection limits vary by application. For general construction in the UK, simply supported beams typically should not exceed span/250 under total load, while cantilevers should not exceed length/180. Beams supporting brittle finishes have stricter limits of span/360.

How does beam depth affect deflection?

Beam depth has a dramatic effect on deflection because the moment of inertia increases with the cube of the depth (I ∝ h³). Doubling the beam depth reduces deflection by approximately 8 times, making depth the most effective way to control deflection.

What’s the difference between deflection and bending stress?

Deflection is the physical displacement of the beam from its original position, measured in millimetres. Bending stress is the internal force per unit area within the beam material, measured in MPa. Both must be checked to ensure structural adequacy.

Should I consider dynamic loads?

Yes, for structures subject to moving loads, vibration, or impact forces. This calculator considers static loads only. Dynamic loads require additional factors and should be assessed by a structural engineer according to relevant design codes.

How accurate is this calculator?

This calculator uses established engineering formulas and provides accurate results for simple beam configurations under static loads. However, it’s intended for preliminary design only. Complex loading, continuous beams, and critical applications require detailed structural analysis.