Beam Bending and Deflection simulation
What's on screen
Two panels stacked. Top panel shows the beam with supports, applied load, the original straight position (dashed gray), and the deflected curve (solid blue) with δmax labeled. Bottom panel shows the Bending Moment Diagram (BMD) on the left with Mmax marked, and a cross-section stress distribution diagram on the right showing σ = My/I with compression on top and tension on bottom.
4 sliders, each teaches a key relationship:
Load P (1 to 50 kN): Deflection is linear with P. Double the load, double the deflection.
Span L (1 to 10 m): Deflection is cubic (L³) or quartic (L⁴). This is the most powerful slider. Going from 3m to 6m span increases deflection 8× for point loads.
E (10 to 400 GPa): Material stiffness. Steel = 200, aluminum = 69, wood = 12. Lower E = more deflection. Inversely proportional.
I (1 to 200 × 10⁶ mm⁴): Moment of inertia. Bigger I = stiffer beam. This is why I-beams exist. Inversely proportional to deflection.
The stress distribution visualization (bottom right):
A rectangular cross-section shows:
Color gradient from light at NA (zero stress) to dark at extreme fibers (max stress)
Red dashed neutral axis line
Triangular stress distribution: σ = My/I, linear from zero at NA to σmax at top/bottom
Compression labeled on top, tension on bottom
σmax value calculated and displayed
Key slider experiments::
Switch from SS to cantilever with same P and L. Watch δmax jump from ~2mm to ~32mm. The 1/48 vs 1/3 coefficient difference is massive.
Drag the span slider from 3m to 6m on SS + point load. Deflection goes from ~0.9mm to ~7.5mm. That's the L³ relationship made visible.
Drag I from 50 to 200. Deflection drops by 4×. This is why selecting the right cross-section matters more than adding more material.
Switch to UDL and compare with point load at same total force. UDL deflects less because the load is spread.