Beam Deflection Calculator Simple Centre Point Load

A simply supported beam rests on two supports — typically modelled as a pin at one end and a roller at the other — free to rotate at each support but not to deflect vertically there. This calculator covers the common special case of a single point load applied exactly at mid-span, such as a beam supporting a central column load, or a test load applied at the centre of a span for a simple bending test. Because the load is symmetric, both support reactions are equal, and the maximum deflection and maximum bending stress both occur right at mid-span.

If your load sits somewhere other than dead centre, use our Simply Supported, Point Load (any position) calculator instead, which handles a load at any point along the span.

This calculator calculates the End Slopes, Support Reactions, Maximum Deflection and Maximum Stress in a simply supported beam with a centre point 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.

SIMPLY SUPPORTED BEAM - POINT LOAD AT CENTRE

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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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 STRESS:

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RELATED PAGES

• Simply Supported, Point Load (any position)
• Simply Supported, Twin Point Load
• Simply Supported, Uniform Load

FREQUENTLY ASKED QUESTIONS

Why are both support reactions equal for a centre point load?

Because the load is positioned symmetrically between the two supports, each support carries exactly half the total load, regardless of the beam's length or stiffness.

Where does maximum deflection occur for an off-centre load instead?

It occurs slightly toward the longer side of the span, not exactly under the load itself — for an asymmetric load position, use our general point load calculator rather than this centre-load-specific one.