Short Answer:

A fixed beam is a type of beam whose both ends are rigidly fixed into supports, preventing any rotation or vertical movement at the supports. It can resist vertical loads, bending moments, and shear forces. The fixed ends develop reaction moments that reduce bending and deflection in the beam.

In simple words, a fixed beam is a restrained beam with both ends firmly built into walls or supports. This type of beam has higher stiffness and lesser deflection compared to a simply supported beam. Fixed beams are commonly used in bridges, frames, and continuous structures where rigidity and stability are important.

Detailed Explanation :

Fixed Beam

A fixed beam (also known as a restrained beam or built-in beam) is a structural member whose both ends are rigidly fixed to supports. The fixing is such that the beam cannot rotate or translate at the ends. This restriction prevents angular movement, thereby introducing reaction moments in addition to the shear forces and vertical reactions at the supports.

When a load acts on a fixed beam, bending moments develop not only at the midspan but also at the supports. These moments counteract the external load, resulting in a reduction in the maximum bending moment and deflection compared to a simply supported beam. Because of this, fixed beams are more efficient and stronger for resisting transverse loads.

Characteristics of Fixed Beam

Both Ends Rigidly Fixed:
The ends of the beam are firmly built into the supports, so neither rotation nor translation is allowed.
Develops Reaction Moments:
The fixed supports develop moments to resist bending caused by the loads acting on the beam.
Less Deflection:
Due to restraint at both ends, the beam shows less deflection than a simply supported beam under the same load.
Indeterminate Structure:
A fixed beam is statically indeterminate, meaning the support reactions cannot be determined using only equilibrium equations. Additional compatibility equations are required.
Higher Rigidity:
Fixed beams offer more stiffness and strength and are suitable for structures requiring stability.
Internal Stress Distribution:
Internal stresses are distributed more evenly because of restraint at both ends.

Bending Moment and Shear Force in Fixed Beam

When loads act on a fixed beam, bending moments and shear forces develop throughout the beam. The bending moment distribution depends on the type of loading.

For a Fixed Beam with Central Point Load (W):
- Bending moment at supports (Mₐ = Mᵦ):

- Maximum bending moment at center:

- Reaction at each support:

Here, the negative moment at supports (hogging moment) helps in reducing the maximum positive bending moment at midspan.
For a Fixed Beam with Uniformly Distributed Load (UDL, w):
- Bending moment at supports:

- Maximum bending moment at center:

- Reaction at each support:

From these equations, it is clear that the maximum bending moment in a fixed beam is half of that in a simply supported beam with the same loading.

Deflection in Fixed Beam

The fixed ends of the beam prevent excessive bending, which reduces the maximum deflection. The deflection depends on the type of loading.

For a Point Load (W) at Midspan:

For a Uniformly Distributed Load (w):

Where,

= maximum deflection,
= modulus of elasticity,
= moment of inertia of beam section,
= length of the beam.

The deflection of a fixed beam is only one-fourth that of a simply supported beam under the same load and conditions, showing its superior stiffness.

Advantages of Fixed Beam

Less Deflection:
Due to the rigid supports, deflection is much smaller than in simply supported beams.
Smaller Bending Moment:
The bending moments are reduced because the fixed ends share the moment with the span.
Higher Strength:
The beam can carry heavier loads for the same span compared to a simply supported beam.
Greater Rigidity:
The fixed supports prevent rotation, increasing the overall stiffness of the structure.
Better Aesthetics and Economy:
Requires smaller depth for the same span, leading to a compact design.

Disadvantages of Fixed Beam

Difficult Construction:
Achieving a perfectly rigid connection at both ends is complicated and costly.
High Stress at Supports:
The fixed ends experience large reaction moments that may cause cracking in concrete or stress concentration in steel beams.
Thermal Stresses:
Fixed beams cannot expand or contract freely, causing temperature-induced stresses.
Sensitive to Settlement:
Any differential settlement of supports introduces large additional stresses.
Indeterminate Analysis:
Requires more complex calculations because it is statically indeterminate.

Applications of Fixed Beam

Fixed beams are used in structures where rigidity and reduced deflection are essential. Some common applications include:

Bridges: To reduce bending under vehicle loads.
Building Frames: In reinforced concrete and steel structures.
Cantilever Extensions: Where overhangs need fixed stability.
Industrial Floors and Roofs: To support heavy equipment.
Machine Foundations: For high stiffness and low vibration performance.

Fixed beams are especially preferred in continuous and multi-span structures where both ends can be rigidly embedded.

Behavior of Fixed Beam under Load

The top fibers of the beam are under compression, while the bottom fibers are under tension for downward loads.
The maximum bending moment occurs at both supports as negative moments (hogging).
The maximum shear force occurs near the supports.
The neutral axis passes through the centroid of the beam’s cross-section.

This combination of moments and shear gives the beam high stiffness and load-carrying capacity.

Conclusion

In conclusion, a fixed beam is a beam whose both ends are rigidly fixed to supports, preventing any rotation or movement. It can resist bending moments, shear forces, and deflection more effectively than other beam types. Because of its high rigidity and strength, it is widely used in bridges, buildings, and frames. However, due to complex construction and sensitivity to temperature and settlement, careful design is essential to ensure safety and durability.