1. Introduction
In structural analysis, supports are constraints provided to structural members to maintain equilibrium under loads. These supports prevent certain types of movement—translations and/or rotations—and accordingly generate reaction forces or moments. Understanding support types and how they produce reactions is essential for analyzing the internal forces in beams, trusses, and frames.
2. Types of Supports
2.1 Fixed Support
- Restrains all degrees of freedom: vertical and horizontal translations, and rotation.
- Produces three reactions in 2D:
Example: Wall end of a fixed cantilever beam.
2.2 Pinned or Hinge Support
- Restrains translation in both x and y directions but allows rotation.
- Produces two reactions in 2D:
Common in trusses and simply supported beams.
2.3 Roller Support
- Restrains translation only in one direction (typically vertical).
- Allows movement in the other direction and free rotation.
- Produces one reaction in 2D:
Used when a structure needs to expand due to temperature or settlement.
2.4 Link or Cable Support
- Can only carry tensile or compressive forces along its length.
- The reaction is along the direction of the link.
3. Reaction Forces and Equilibrium
To find the reactions at supports, we apply the equations of static equilibrium in 2D:
- Sum of horizontal forces:
Sum of vertical forces:
Sum of moments about any point:
These allow solving for unknown reaction forces/moments provided the system is statically determinate.
4. Examples of Support Configurations
| Structure Type | Support A | Support B | Reactions Total |
|---|---|---|---|
| Simply Supported Beam | Pin | Roller | 3 |
| Cantilever Beam | Fixed | Free | 3 |
| Overhanging Beam | Pin | Roller | 3 |
| Fixed-Fixed Beam | Fixed | Fixed | 6 (indeterminate) |
5. Idealization in Analysis
In real-world structures, supports are not perfectly rigid or frictionless. However, for analytical simplicity, they are modeled as:
- Perfect hinges with no moment resistance,
- Perfect rollers with zero horizontal reaction,
- Perfectly rigid fixed ends.
This idealization makes solving for reactions feasible using equilibrium principles.
6. Practical Relevance in Aerospace Structures
Aircraft structures, while lightweight and complex, are often modeled using ideal supports for preliminary design and analysis. For instance:
- The wing root is considered a fixed support.
- Riveted joints may behave like pins.
- Landing gear reactions during touchdown are treated as external reaction forces at supports.
