engineering

Beam Bending Calculator

Calculate maximum deflection, bending moment, and reactions for simply supported, cantilever, and fixed-fixed beams

Beam Bending Calculator

Maximum deflection, bending moment, and support reactions for common beam configurations.

Results

Max Deflection δ

1.0004 mm

= 1.0004e-3 m

Max Bending Moment M_max

5000.00 N·m

= 5.0000 kN·m

Support Reactions

R_A = R_B = P/2 = 5000.00 N

Formulas Used

δ = PL³ / (48EI)
M_max = PL / 4 (at center)
E = 200 GPa · I = 8.330e-6 m⁴ · EI = 1.6660e+6 N·m²

How to Use This Calculator

1

Select the beam support condition

Choose from simply supported, cantilever, or fixed-fixed beam configurations.

2

Enter beam geometry and loading

Input the beam length, cross-section moment of inertia (I), modulus of elasticity (E), and load type and magnitude.

3

Read deflection, moment, and reactions

The calculator applies the appropriate beam formula to compute maximum deflection, maximum bending moment, and support reactions.

Formula Reference

Simply Supported — Midpoint Deflection (UDL)

δmax = 5wL⁴ / (384EI)

Variables: w = distributed load per unit length, L = beam span, E = elastic modulus, I = area moment of inertia

Cantilever — Tip Deflection (Point Load)

δmax = PL³ / (3EI)

Variables: P = point load, L = beam length

When to Use This Calculator

  • •Use the Beam Bending Calculator when solving homework or exam problems that require quick numerical verification of your hand calculations.
  • •Use it during the design phase to rapidly iterate on parameters before running detailed finite element simulations.
  • •Use it when reviewing a colleague's calculation or checking a vendor's data sheet for plausibility.
  • •Use it to generate reference data for a technical report or presentation without manual computation.

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