What is the deflection of a simply supported beam with a central point load?

For a central point load P: δ_max = PL³/(48EI) at mid-span. The maximum bending moment is M_max = PL/4 at the center.

How does UDL deflection compare to point load?

For equal total load (q×L = P): UDL deflection δ = 5qL⁴/384EI = 5PL³/384EI, while center point load gives PL³/48EI. UDL causes 62.5% of the point load deflection.

How do I reduce beam deflection?

Increase EI (deeper section or stiffer material), reduce span L (most effective since δ ∝ L³ or L⁴), add intermediate supports, or use continuous beam construction.

Simply Supported Beam Deflection Calculator

Calculate maximum deflection for simply supported beams. Center point load: δ_max = PL³/(48EI). Uniformly distributed load: δ_max = 5qL⁴/(384EI). Maximum moments: PL/4 and qL²/8.

2D stress state at a point. All stresses in MPa.

σx — Normal Stress X (MPa)

σy — Normal Stress Y (MPa)

τxy — Shear Stress (MPa)

⚙ Mechanical Note: Results are based on standard textbook formulas and ISO/AASHTO references. Always verify critical designs with applicable codes (ISO 898, AASHTO 1993, AISC, Eurocode 3) and a qualified engineer.

How to Use

Enter the values for the patient or scenario you are assessing. Calculate maximum deflection for simply supported beams. Center point load: δ_max = PL³/(48EI). Uniformly distributed load: δ_max = 5qL⁴/(384EI). Maximum moments: PL/4 and qL²/8. Use the simply supported deflection result to inform your clinical assessment.

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Simply Supported Beam Deflection Calculator

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Frequently Asked Questions

What is the deflection of a simply supported beam with a central point load?

How does UDL deflection compare to point load?

How do I reduce beam deflection?