Beam Deflection Calculator | Supported Beams

Quick Start Guide

  1. Select beam type: Choose from simply supported, cantilever, fixed-fixed, or overhanging.
  2. Choose load type: Select point load, uniform distributed load, triangular, or moment.
  3. Enter beam dimensions: Input length and specify the unit (meters, feet, inches, or millimeters).
  4. Input load value: Enter the magnitude and unit of the applied load.
  5. Specify material properties: Enter Young's modulus and moment of inertia, or select a predefined material.
  6. View results: See maximum deflection, slope, and bending stress results.

Understanding Beam Deflection

Why support type changes the formula entirely

A simply-supported beam (resting on two supports) deflects far more than a cantilever (fixed at one end) or a fixed-fixed beam (rigidly clamped at both ends) under the same load — the support conditions change which formula applies, not just the numbers going into it. Overhanging beams add a third condition: part of the beam extends past a support.

Flexural rigidity: EI

Deflection is inversely proportional to EI — the product of Young's Modulus (E, material stiffness) and moment of inertia (I, cross-section shape). Doubling either one halves the deflection. A stiffer material or a deeper/wider cross-section both resist bending more.

Point, distributed, triangular, and moment loads

A point load acts at a single location; a uniformly distributed load (UDL) spreads evenly across a span; a triangular load ramps from zero to a peak (common for wind or hydrostatic pressure); an applied moment twists the end of the beam directly rather than pushing on it. Each has its own deflection formula — not every beam type supports every load type (for example, an applied end moment is only modeled for simply-supported beams here).

Reading reaction forces and bending moment

Reaction forces are what the supports push back with to hold the beam in equilibrium — for a simply-supported beam these split predictably based on load position; for cantilevers, the single fixed end carries the whole load plus a resisting moment. Maximum bending moment tells you where internal stress is highest, which is what you would combine with the beam's section modulus to check if it will actually yield.

How much deflection is acceptable

Building codes commonly limit deflection to a fraction of the span — L/360 for floors under live load, L/240 for roofs, tighter still (L/600 or less) for sensitive finishes like plaster. Compare your calculated maximum deflection against the relevant limit for your span length before finalizing a design.

Features

Multiple Beam Types: Support simply supported, cantilever, fixed-fixed, and overhanging beam configurations.

Load Types: Analyze point loads, uniformly distributed loads, and triangular loads across all beam types, plus applied end moments for simply-supported beams.

Material Library: Predefined materials (steel, aluminum, concrete, wood) with standard properties.

Comprehensive Results: Get deflection, slope, and bending stress at critical points.

Common Use Cases

Bridge Design: calculate deflection under traffic loads, verify the beam meets serviceability limits, and compare different span configurations.

Building Structures: analyze floor beam deflection under live loads, check compliance with building codes, and design optimal beam sections.

Cantilever Analysis: calculate deflection of overhanging structures, analyze balcony or bracket deflection, and determine safe load limits.

Material Comparison: compare deflection across different materials (steel, aluminum, concrete), evaluate cost vs. performance trade-offs, and select the optimal material for the application.

Frequently Asked Questions

Excessive deflection can crack finishes, jam doors, or be visually unsettling. Building codes limit deflection (e.g., L/360) to ensure serviceability and safety.
Moment of Inertia (I) represents a beam geometry's resistance to bending. A higher "I" value (deeper beam) significantly reduces deflection. Doubling beam depth reduces deflection by a factor of 8.
Simply supported beams are supported at both ends and free to rotate. Cantilever beams are fixed at one end and free at the other (more deflection for the same load). Fixed-fixed beams are constrained at both ends (least deflection). Choose the type that matches your physical setup.
A point load (concentrated force) acts at a single location. A uniformly distributed load (UDL) spreads evenly over the beam length, like the weight of flooring. A distributed load causes roughly half the maximum deflection of an equivalent point load at mid-span.

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