How It Works
Structural beam analysis determines internal forces, bending moments, and deflections that develop when loads are applied to horizontal structural members. These calculations form the foundation of safe structural design by ensuring beams can support applied loads without failure or excessive deflection.
Shear Force (V) represents the internal force tending to cut through the beam cross-section. For a simply supported beam with point load P at distance ‘a’ from the left support and distance ‘b’ from the right support:
- Left reaction: R_A = P x b / L
- Right reaction: R_B = P x a / L
- Shear force: Changes abruptly at load application points
Bending Moment (M) represents the internal moment that causes beam curvature. Maximum moment typically occurs where shear force equals zero:
- Simply supported beam, center load: M_max = P x L / 4
- Cantilever beam, end load: M_max = P x L
- Uniformly distributed load: M_max = w x L squared / 8 (simply supported)
Deflection quantifies beam bending under load. Deflection formulas depend on loading pattern and support conditions. Where E represents the modulus of elasticity and I represents the moment of inertia about the neutral axis.
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