Beam Deflection Info

Beam deflection basics:

Measures how much a beam bends under load
Measured in length units (mm, inches)
Depends on beam properties and loading
Common limit: L/360 for live loads
Maximum allowable values in building codes

Key parameters:

Length (L): Span of the beam
Load (P): Force applied to the beam
Young's modulus (E): Material stiffness
Moment of inertia (I): Cross-section property

Simply Supported Beam:

Point load (middle): δ = PL³/(48EI)

Uniform load: δ = 5wL⁴/(384EI)

Cantilever Beam:

Point load (end): δ = PL³/(3EI)

Uniform load: δ = wL⁴/(8EI)

Fixed-Fixed Beam:

Point load (middle): δ = PL³/(192EI)

Uniform load: δ = wL⁴/(384EI)

Structural Engineering:

Building beam design
Floor vibration analysis
Bridge deflection verification
Compliance with building codes

Mechanical Engineering:

Machine component design
Shaft deflection analysis
Spring design
Equipment support structures

Other Applications:

Aerospace: Wing deflection
Civil: Foundation design
Materials testing and validation

Beam Deflection Calculator

Calculate Beam Deflection

Beam Type

Load Type

Beam Length (L):

Load (P):

Young's Modulus (E):

Moment of Inertia (I):

Maximum Deflection

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Select beam and load types to see the formula

What is Beam Deflection?

Beam deflection is the displacement of a beam from its original position when subjected to a load. The amount of deflection depends on the beam's material properties, geometry, support conditions, and applied loads.

In structural engineering, controlling beam deflection is crucial for safety, serviceability, and aesthetics. Excessive deflection can cause cracking in connected elements, affect the functionality of the structure, and create a perception of instability even when the structure is safe.

Most building codes specify maximum allowable deflections, typically expressed as a fraction of the span length (such as L/360 or L/240). These limits ensure that structures remain serviceable throughout their design life.

Educational Resource

This educational video explains beam deflection concepts with clear explanations of the bending behavior of structural beams under various loading conditions. It covers essential principles that engineers need to understand when designing structures.

Beam Deflection Calculator: Common Questions

Beam deflection refers to the degree to which a structural element bends under a load. It's important in engineering because: 1) Excessive deflection can cause discomfort for building occupants, 2) It can damage connected non-structural elements, 3) It can affect the functionality of machines or structures, 4) It indicates the stiffness and strength of structures, and 5) Building codes set maximum allowable deflection limits.

A simply supported beam is supported at both ends with freedom to rotate at the supports but not to translate. A cantilever beam is fixed at only one end while the other end is free. Simply supported beams typically have maximum deflection at the center, while cantilever beams have maximum deflection at the free end. Cantilever beams experience larger deflections for the same load and material properties.

The moment of inertia (I) is a geometric property of a beam's cross-section that represents its resistance to bending. It depends on the cross-sectional shape and dimensions, not the material. For rectangular sections, I = bh³/12 (where b is width and h is height). For circular sections, I = πd⁴/64 (where d is diameter). Increasing the height of a beam dramatically increases its moment of inertia and reduces deflection.