Electronics πŸ”§ Mech ⚑ Renewable πŸ–¨οΈ 3D Print 🧱 Materials βš›οΈ Physics πŸ§ͺ Chemistry πŸ“ Math πŸ“Š Stats

πŸ”— Mechanical Suite

βš™οΈ Gear Ratio & Torque πŸ—οΈ Stress & Strain πŸ”© Spring Resolver πŸ“ Beam Deflection β­• Belt & Pulley 🌑️ Thermal Expansion πŸ’¨ Fluid Pressure

πŸ“ Beam Deflection Calculator

Estimate the structural bending of a simply supported beam under point loads for civil and mechanical engineering designs.

Force applied at center
Distance between supports
Steel β‰ˆ 200, Alu β‰ˆ 70
Moment of inertia (bhΒ³/12)

Structural Beam Bending

When a beam is loaded, it deforms. The amount of vertical displacement is called **Deflection**. Controlling deflection is critical for safety and user comfortβ€”you don't want a floor that feels bouncy!

Beam Deflection Diagram

Figure 1: Simply supported beam with a central load F and deflection delta.

The Deflection Formula

For a **simply supported beam** with a point load at the center, the maximum deflection (Ξ΄) occurs directly under the load:

Ξ΄ = (PΓ—LΒ³)/(48Γ—EΓ—I)

Where:

  • P: Applied load or force (N)
  • L: Span length of the beam (mm)
  • E: Modulus of elasticity (MPa, though we input GPa in the tool)
  • I: Area moment of inertia (mm⁴)

How to Reduce Deflection

If your beam bends too much, you have four options based on the physics:

  • Increase I (Shape): Use a taller beam. Since I depends on height cubed (hΒ³), small increases in height make the beam much stiffer.
  • Decrease L (Span): Shorten the distance between supports. Deflection grows with the cube of length (LΒ³).
  • Change E (Material): Switch to a stiffer material (e.g., from aluminum to steel).
  • Decrease P (Load): Reduce the weight on the beam.