A fixed beam is a structural element characterized by having both of its ends rigidly supported, or fixed. This means the beam is constrained against rotation and vertical displacement at its supports, unlike simply supported beams where rotation is permitted. These beams are also referred to as fixed-end beams, built-in beams, or restrained beams.
Key Characteristics of a Fixed Beam
Here are the fundamental features that define a fixed beam:
- Fixed Ends: Both ends of the beam are rigidly attached to supports, preventing any movement or rotation.
- Statically Indeterminate: Fixed beams are classified as statically indeterminate, meaning the equilibrium equations of statics alone are insufficient to determine all the support reactions. There are more than three unknowns (reactions) involved, and more complex methods of structural analysis are required to find the support reactions.
Implications of Fixed Supports
The nature of the fixed support has significant structural implications:
- Reduced Deflection: Compared to simply supported beams, fixed beams exhibit less deflection under the same loading conditions, making them suitable for applications requiring limited deformation.
- Increased Bending Moment: Fixed supports generate significant bending moments at the supports which is quite different from the zero moment at the supports for a simply supported beam. These support moments require the beam to have suitable reinforcement in the areas where the support moments occur.
- Enhanced Stability: The fixed ends provide a higher degree of stability to the structure.
Comparison Table: Fixed Beam vs. Simply Supported Beam
| Feature | Fixed Beam | Simply Supported Beam |
|---|---|---|
| Support Type | Both ends fixed, no rotation or movement allowed | Both ends have simple supports; rotation is allowed |
| Deflection | Less deflection under the same loading | More deflection under the same loading |
| Bending Moment | High bending moments at supports | Zero bending moment at supports |
| Static Determinate | Statically Indeterminate | Statically Determinate |
Examples of Fixed Beam Applications
Fixed beams find applications in various engineering structures, including:
- Building Frames: Beams within rigid building frames which are often cast integrally with the columns to create fixed end conditions.
- Bridge Structures: Certain bridge designs incorporate beams with fixed ends to achieve increased stiffness and stability.
- Machine Parts: Components within machinery, where rigidity and dimensional stability are crucial.
Analysis of Fixed Beams
Because fixed beams are statically indeterminate, their analysis is more complex compared to simply supported beams. Methods like the moment distribution method, the slope deflection method, or finite element analysis are often employed to determine support reactions and internal stresses. These methods take into account the rotational constraints at the supports.
