Bending Under Load
When a beam carries transverse loads, internal stresses develop to maintain equilibrium. The top fibers compress, the bottom fibers stretch in tension, and somewhere between lies the neutral axis where stress is zero. This fundamental mechanism — beam bending — governs the design of every floor joist, bridge girder, and roof rafter in the built world. The simulation visualizes these internal forces as they develop along the beam's length.
Shear & Moment Diagrams
Shear force and bending moment diagrams are the structural engineer's primary tools. For a simply supported beam with uniform load, shear varies linearly from +qL/2 at the left support to −qL/2 at the right, passing through zero at midspan. The bending moment follows a parabolic curve, peaking at M = qL²/8 at the center. These diagrams reveal where the beam is most stressed and where reinforcement or larger sections are needed.
Deflection & Serviceability
Beyond strength, beams must satisfy stiffness requirements. Excessive deflection causes cracking in plaster ceilings, misalignment of partition walls, and occupant discomfort from perceptible bounce. Building codes typically limit deflection to L/360 for floors and L/240 for roofs. The classical formula δ = 5qL⁴/(384EI) shows that deflection grows with the fourth power of span — doubling the span increases deflection sixteen-fold, which is why long-span design demands deep beams or trusses.
Material & Section Choice
The elastic modulus E and moment of inertia I together define a beam's flexural rigidity EI. Steel (E ≈ 200 GPa) is roughly seven times stiffer than timber (E ≈ 12 GPa) per unit area, but timber can be competitive in light loads due to lower self-weight. Increasing the section depth is far more efficient than adding width — doubling depth increases I (and thus stiffness) by a factor of eight, explaining why I-beams and deep trusses dominate structural engineering.