1. Introduction
Beams are structural elements designed to resist loads primarily by bending. They are a critical component in aerospace structures such as wings, fuselages, and frames. The classification of beams is based on the type of supports they have and the nature of loads applied to them. Understanding beam types and loading scenarios is essential for accurate structural analysis.
2. Classification of Beams by Support Conditions
2.1 Cantilever Beam
- Fixed at one end and free at the other.
- All reactions (horizontal, vertical, and moment) occur at the fixed end.
- Common in aircraft wings attached rigidly to the fuselage.
2.2 Simply Supported Beam
- Supported at both ends: one with a pin (resists both vertical and horizontal) and the other with a roller (resists vertical only).
- No moment resistance at supports.
2.3 Overhanging Beam
- Extends beyond its support on one or both sides.
- Combines features of simply supported and cantilever beams.
2.4 Fixed-Fixed Beam
- Both ends are fixed.
- Can carry higher loads with smaller deflections.
- Statistically indeterminate.
2.5 Continuous Beam
- Spans over more than two supports.
- Indeterminate but more efficient structurally.
3. Types of Loads
3.1 Point Load (Concentrated Load)
- Acts at a single point.
- Produces abrupt changes in shear force, and linear variation in bending moment between loads.
3.2 Uniformly Distributed Load (UDL)
- Spread evenly over a length.
- Causes linear variation in shear and quadratic variation in bending moment.
3.3 Uniformly Varying Load (UVL)
- Load intensity varies linearly or nonlinearly along the length.
- Leads to nonlinear shear and cubic bending moment curves.
3.4 Moment Load (Couple)
- A pure moment applied at a point.
- Produces a constant shift in bending moment without affecting shear.
4. Loading Configurations in Aerospace Applications
- Wing Loads: Typically experience distributed lift (UDL) and point loads at engine mountings.
- Fuselage Structures: Subjected to point loads from payloads and distributed loads from internal pressurization.
- Control Surfaces: Experience varying loads due to aerodynamic pressure distribution.
5. Load Effects
- Loads induce internal shear forces and bending moments in beams.
- Understanding loading is the first step toward constructing shear force and bending moment diagrams, essential for further analysis.
6. Governing Equilibrium Equations
For 2D analysis of a loaded beam:
These equations help compute support reactions and internal forces.
