What is a Cantilever Beam?

A cantilever beam is a structural element that is anchored at only one end, with the other end extending horizontally into space. This configuration is common in balconies, bridges, and various mechanical arms. Because only one end is fixed, the beam must be able to resist both shear stress and bending moments at the support point.

How to Use This Cantilever Beam Calculator

This online tool helps engineers and students determine the critical values for a cantilever beam under a single point load. To use the calculator, follow these steps:

• Total Length (L): Enter the total length of the beam in meters.
• Point Load (P): Enter the downward force applied to the beam in kiloNewtons (kN).
• Load Distance (a): Enter the distance from the fixed support to the point where the load is applied. If the load is at the very tip, 'a' equals 'L'.
• Elasticity (E): Provide the Young's Modulus of the material (e.g., 210 GPa for steel).
• Moment of Inertia (I): Provide the area moment of inertia of the beam's cross-section in cm⁴.

Understanding the Formulas

The calculations are based on standard structural engineering formulas for static analysis:

1. Bending Moment: The maximum moment occurs at the fixed support and is calculated as M = P × a.

2. Maximum Deflection: If the load is at the free end, the deflection is calculated using δ = (P × L³) / (3 × E × I). If the load is at distance 'a', the deflection at the tip is calculated using the superposition of the slope and the deflection at point 'a'.

Frequently Asked Questions

What units should I use?

The calculator is designed for Metric units: meters for length, kN for force, GPa for elasticity, and cm⁴ for inertia. The output results provide deflection in millimeters (mm) for better precision.

Does this account for the beam's own weight?

No, this specific tool calculates the effects of a single point load. In real-world applications, you must also add the Distributed Load (UDL) caused by the beam's self-weight.