Beam Deflection Calculator Fixed Supported Uniform Load

A fixed (or "built-in") supported beam is rigidly fixed at both ends, resisting rotation as well as vertical deflection at each support — think of a beam cast into concrete at both ends, or welded rigidly into a surrounding steel frame. This calculator covers a fixed beam carrying a uniformly distributed load along its full span. Because both ends resist rotation, a fixed beam deflects considerably less, and distributes bending moment differently, than the same beam and load simply supported — with negative (hogging) moment at each support and positive (sagging) moment at mid-span.

For the same loading on a beam that's free to rotate at its supports instead, see our Simply Supported, Uniform Load calculator, which will show noticeably greater deflection for the same load and span.

This calculator calculates the End Slopes, Support Reactions, Maximum Deflection and Maximum Stress in a fixed supported beam with a uniform load.

Enter your values as required and press SOLVE, your results will be displayed. If you change any unit types or values please press SOLVE again.

CLEAR ALL clears all fields.

FIXED AND SUPPORTED - UNIFORM LOAD

MATERIAL: Aluminium 2024-T4Aluminium 6061-T6Aluminium 7075-T3BrassCast IronCopperLeadMagnesiumPhosphur BronzeStainless Steel, 304Stainless Steel, 316Steel, S235Steel, S275Steel, S355Steel, 4130Steel, ASTM A36Steel, ASTM A441Titanium, Grade 2Titanium, Grade 5

MOMENT OF INERTIA:

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TOTAL LENGTH: (L)

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LOAD LENGTH: (A)

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DISTANCE TO NEUTRAL PLANE: (Z)

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POINT LOAD: (P)

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END SLOPE A: (A°)

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END SLOPE: (B°)

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SUPPORT REACTION: (WA)

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SUPPORT REACTION: (WB)

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MAXIMUM DEFLECTION: (y)

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MAXIMUM DEFLECTION LENGTH: (B)

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MAXIMUM STRESS:

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RELATED PAGES

• Simply Supported, Uniform Load
• Cantilever, Uniform Load

FREQUENTLY ASKED QUESTIONS

Why does a fixed beam deflect less than a simply supported beam under the same load?

Because the fixed supports resist rotation as well as vertical movement, effectively stiffening the beam's response — for a UDL, a fixed-fixed beam deflects at only a fraction (around 1/5) of the maximum deflection of the same beam simply supported.

What does "hogging" moment mean at the supports?

It means the beam curves concave-downward near the fixed supports (the opposite curvature to the sagging, concave-upward shape at mid-span), which puts the top fibre of the beam in tension near the supports rather than compression — important to account for when checking stress at those locations, particularly for materials or sections that behave differently in tension versus compression.

Are true "fixed" supports achievable in practice?

Perfectly rigid fixity is an idealisation — real connections (welds, deep concrete encasement, rigid frame joints) can approach it closely, but some small rotation typically still occurs. Engineering judgement is needed on how closely a real support matches the fixed-end assumption for a given calculation.