What is a Fixed Beam?

A fixed beam, also known as a built-in or encastré beam, is a structural element where both ends are rigidly fixed into supports. Unlike a simply supported beam, the ends of a fixed beam cannot rotate. This constraint induces "Fixed End Moments" (FEM) which significantly reduce the maximum bending moment at the center, making the structure stiffer and capable of carrying higher loads with less deflection.

How to Use the Fixed Beam Calculator

To use this online engineering tool, simply follow these steps:

1. Select Load Type: Choose between a Uniformly Distributed Load (UDL), a central point load, or an eccentric point load.
2. Enter Beam Length: Input the total span of the beam in meters.
3. Input Load Magnitude: Enter the force in kN (for point loads) or kN/m (for UDL).
4. Eccentricity: If you selected an eccentric load, specify the distance from the left support to the application point.
5. Results: Click calculate to instantly see the vertical reactions and fixed-end moments.

Key Engineering Formulas

This calculator utilizes standard structural analysis formulas. For a UDL, the fixed end moments are calculated as M = wL²/12. For a central point load, the moments are M = PL/8. In the case of an eccentric point load at distance 'a' from the left and 'b' from the right, the moments are M_A = Pab²/L² and M_B = Pa²b/L². These formulas are essential for civil and mechanical engineers during the preliminary design phase of buildings and bridges.

Frequently Asked Questions

Why are fixed beams used? They are used to reduce the mid-span deflection and provide higher structural stability compared to simply supported beams.

What is the degree of indeterminacy? A fixed beam is statically indeterminate to the second degree, meaning basic equilibrium equations are not enough to find reactions without considering deformations.