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Engineering · Statics & Structural Analysis

Beam Deflection and Slope Workbench Calculator

Calculate elastic beam rotation and maximum deflection for four common determinate support-and-load cases using explicitly entered E and I.

Engineering · Statics & Structural Analysis

Enter the engineering model

Explicit properties, geometry, units and assumptions
  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
Try an example
Visual modelSchematic · not to scale
Statics & Structural Analysis: simplePoint visual explanationA simplified diagram showing the relationship represented by the selected calculator mode. It is explanatory and not a fabrication, safety or scale drawing.point load → elastic curvemovement is governed by load, span and EI
The diagram explains the selected relationship only. Dimensions, symbols and proportions are illustrative; use the entered values and stated assumptions for the calculation.

Keep every unit basis, sign convention, property source and idealization consistent. Values stay in this browser.

Engineering calculation result

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Enter valid values to see the result.

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Understand the structural model

How beam stiffness controls movement

Beam deflection is the elastic movement produced by loading. This tool keeps load, span and flexural rigidity visible so you can see why length has such a strong influence on movement.

Relationship used

Simple center point: δmax=PL³/(48EI); simple UDL: δmax=5wL⁴/(384EI); cantilever end point: δmax=PL³/(3EI); cantilever UDL: δmax=wL⁴/(8EI).

Worked scenario: A 6 m simple beam with a 10 kN center load, E=200 GPa and I=8×10⁻⁵ m⁴ deflects about 2.813 mm.

Keep the boundary visible: It evaluates four declared textbook cases; it does not determine whether the resulting movement is acceptable.

Quick guide

How to use this calculator

  1. Choose the analysis mode that matches the physical model before entering values.
  2. Enter properties, geometry, loads, states and coefficients from one consistent unit and sign convention.
  3. Use the intermediate outputs to audit the relationship, then retain the stated idealization before applying it.

Calculation method

Transparent engineering model

Simple center point: δmax=PL³/(48EI); simple UDL: δmax=5wL⁴/(384EI); cantilever end point: δmax=PL³/(3EI); cantilever UDL: δmax=wL⁴/(8EI).

The calculator evaluates only the declared relationship and preserves visitor-entered assumptions rather than selecting materials, factors, components or standards.

Worked example

Worked example

A 6 m simple beam with a 10 kN center load, E=200 GPa and I=8×10⁻⁵ m⁴ deflects about 2.813 mm.

Simple center point: δmax=PL³/(48EI); simple UDL: δmax=5wL⁴/(384EI); cantilever end point: δmax=PL³/(3EI); cantilever UDL: δmax=wL⁴/(8EI).

Supported inputs

Precision and limits

Analysis, not approval

Small-deflection Euler–Bernoulli relationships only. The calculator does not select section properties, loads, combinations, limits, bracing or material values.

Standards and properties

Material properties, allowable values, load combinations, safety factors, correlations, manufacturer data, codes and jurisdictional requirements are not supplied automatically.

Units and precision

Use one consistent unit basis. Results retain working precision but cannot be more accurate than the entered measurements and properties.

Privacy

Entered engineering values and results stay in this browser and are not sent to analytics or third parties.