What's the difference between deflection and stress?
Deflection measures how much the beam bends (in mm). Stress measures internal material resistance (in MPa). Both must stay within acceptable limits.
Engineering
Beam Deflection Calculator
Calculate deflection and forces for simply supported beams under point loads.
Structural Beam Analysis
Analyze beam behavior with precise calculations for deflection, reactions, and bending moments.
What this calculator does
A beam deflection calculator determines how much a structural beam bends under load. This is critical in engineering because excessive deflection can cause discomfort, affect machinery alignment, or indicate failure risk. Engineers verify beams meet code requirements (typically span/240 or span/360).
How it works
The calculator takes beam properties (length, width, height), material stiffness (Young's modulus), and load information. It computes moment of inertia from dimensions, then uses beam theory formulas to determine reaction forces, bending moments, and deflection.
Formula
Maximum Deflection = (P×a×b×(L+a))/(3×E×I×L), where P = load, a and b = distance terms, L = length, E = Young's modulus, I = moment of inertia. I = (b×h³)/12 for rectangular sections.
Tips for using this calculator
- Verify beam material and orientation—placing on its side dramatically increases deflection
- Check deflection limits against code requirements
- Young's modulus varies by material: steel ~200 GPa, aluminum ~70 GPa, wood ~12 GPa
- Deflection ratio above L/200 signals undersizing
- Consider dynamic loads in real applications
Frequently asked questions
Why does load position matter?
Loads near supports cause less deflection; centered loads cause maximum deflection. Position significantly affects structural behavior.
What does Young's modulus represent?
Young's modulus measures material stiffness. Higher values mean stiffer materials that deflect less under the same load.