Beam Deflection Simulator
Interactive beam bending visualization for simply supported and cantilever beams
About this Simulator
This interactive simulator visualizes beam bending behavior in real-time. Watch how beams deflect under load with accurate deflection curves, reaction forces, and bending moments displayed. The deflection is magnified for visibility while showing actual calculated values.
Physics & Formulas
Simply Supported (Center Load):
$$\delta_{max} = \frac{P L^3}{48 E I}$$
Cantilever (End Load):
$$\delta_{max} = \frac{P L^3}{3 E I}$$
Bending Moment:
$$M_{simply} = \frac{PL}{4}, \quad M_{cantilever} = PL$$
How to Use
- Adjust the Applied Load slider to see how deflection changes with force
- Change Beam Length to visualize different span scenarios
- Modify Elastic Modulus for different materials (Steel ~200 GPa, Aluminum ~70 GPa)
- Adjust Moment of Inertia to simulate different cross-sections
- Switch between Simply Supported and Cantilever beam types
- Toggle Show Deflection Curve to highlight the neutral axis
- Toggle Show Forces to see reaction forces and moments
- Click Animate to see dynamic loading behavior
Frequently Asked Questions
What is an acceptable deflection?
Typical limits: L/360 for floor beams, L/240 for roof beams, L/180 for cantilevers. More stringent limits (L/500) may apply for precision equipment or sensitive finishes.
How do I find moment of inertia?
Use steel section tables (AISC, Eurocode). For rectangular sections: I = bh³/12. For circular sections: I = πd⁴/64. I-beams have much higher I values for the same weight.
Why is deflection important?
Excessive deflection causes serviceability issues: cracked finishes, sagging appearance, door/window binding, and equipment malfunction. Deflection limits ensure structural adequacy.
