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 supported. Unlike a simply supported beam, a fixed beam is restrained against both rotation and translation at its supports. This redundancy makes the beam statically indeterminate, meaning the internal forces and reactions cannot be determined by simple equilibrium equations alone.

How to Use This Fixed Beam Calculator

To use this calculator, follow these simple steps to analyze your structural beam design:

• Beam Length (L): Enter the total span of the beam in meters.
• Load Magnitude (P): Specify the concentrated point load applied to the beam in kiloNewtons (kN).
• Load Position (a): Distance from the left support (A) to the point where the load is applied.
• Elastic Modulus (E): The material stiffness, typically 200 GPa for structural steel.
• Moment of Inertia (I): The cross-sectional property in cm⁴.

Key Structural Formulas

For a fixed beam with a point load at distance a from the left and b from the right (where b = L - a), the fixed-end moments are calculated as:

MA = (P * a * b²) / L²
MB = (P * a² * b) / L²

These moments counteract the bending caused by the load, leading to significantly lower maximum deflections compared to simply supported beams of the same span and loading. This increased stiffness is why fixed beams are preferred in high-rise buildings and continuous bridge spans.

Frequently Asked Questions

Why are the moments negative? In structural engineering, fixed-end moments are often considered negative because they cause tension on the top fibers of the beam near the supports (hogging).

What happens if the load is at the center? When a = b = L/2, the moments at both ends are equal (PL/8) and the central deflection is minimized.