Beams

Beams are classified based on four criteria: geometry (straight, tapered, or curved), cross-section shape (I-beam, T-beam, L-beam, C-beam, or rectangular), support type (simply supported, overhanging, continuous, cantilever, or fixed), and equilibrium condition (statically determinate or indeterminate). Each classification affects how the beam performs under load.

Support type determines how a beam carries loads and resists forces. A simply supported beam has supports at both ends, while a cantilever beam is fixed at one end and extends outward. Continuous beams have support at more than two points, and fixed beams are anchored at both ends or one end. Each configuration creates different internal stress patterns and load-bearing capabilities.

Beam span is the distance between supports. It directly influences the beam's ability to support loads and resist bending. Longer spans require stronger beams or different cross-section designs to maintain structural integrity. Understanding span is essential for calculating internal forces and designing beams that safely support applied loads.

A statically determinate beam has reactions at supports involving only three unknowns, allowing engineers to solve for all forces using equilibrium equations alone. A statically indeterminate beam has additional unknowns beyond three, requiring supplementary equations or methods to analyze. This distinction affects how engineers calculate internal loadings in structural members and design the beam.

Cross-section geometry determines how a beam distributes stress and resists bending. I-beams and T-beams provide high strength-to-weight ratios by concentrating material away from the neutral axis. Rectangular and C-beams offer different load-bearing capabilities suited to specific applications. Engineers select cross-sections based on the loads the beam must support and structural requirements.

An overhanging beam extends beyond one of its supports, creating a cantilever section. This configuration allows loads to be applied beyond the support point, generating different internal stress patterns than simply supported beams. Overhanging beams require careful analysis to ensure the extended portion doesn't cause excessive deflection or failure.

Beam geometry—whether straight, tapered, or curved—affects how internal forces develop and distribute along the member. Straight beams with constant cross-sections are easiest to analyze, while tapered beams have varying cross-sections that change stress distribution. Curved beams introduce additional complexity. Proper geometric understanding enables accurate calculation of shear and bending moment diagram problem solving.