Shear Force & Bending Moment Diagrams • Reactions • Equilibrium — Simulate • Explore • Practice • Quiz
Beam bending analysis is a fundamental topic in structural mechanics and strength of materials. Engineers use Shear Force Diagrams (SFD) and Bending Moment Diagrams (BMD) to visualise how internal forces vary along a beam under various loading conditions. Understanding these diagrams is essential for designing safe structures, selecting appropriate beam cross-sections, and preventing structural failure.
A beam is a structural element that resists loads primarily through bending. The most common beam types are simply supported beams (resting on two supports), cantilever beams (fixed at one end, free at the other), and overhanging beams (extending beyond one or both supports). Each type responds differently to applied loads, producing unique SFD and BMD shapes that engineers must understand to predict structural behaviour.
The shear force at any section of a beam equals the algebraic sum of all vertical forces to one side of that section. For a simply supported beam with a central point load P, the reactions are each P/2. The SFD shows a constant positive shear from the left support to the load, then a step change to negative shear from the load to the right support. The bending moment at any section equals the sum of moments about that section from all forces on one side. The BMD for this case is triangular, with maximum moment M = PL/4 at the centre. Under a uniformly distributed load (UDL), the SFD is linear and the BMD is parabolic, with maximum moment M = wL²/8.
There is a fundamental mathematical relationship: dM/dx = V (the slope of the BMD equals the shear force) and dV/dx = −w (the slope of the SFD equals the negative of the distributed load intensity). This means that where the shear force is zero, the bending moment reaches a maximum or minimum. A point of contraflexure occurs where the bending moment changes sign — the beam transitions from sagging (concave up) to hogging (concave down). These relationships allow engineers to quickly sketch diagrams and verify calculations.
In Simulate mode, select a beam type (Simply Supported, Cantilever, or Overhanging), then add point loads and UDL using the sliders and action buttons. The canvas displays the beam diagram with supports and loads at the top, the SFD in the middle, and the BMD at the bottom — all updating in real time. Use presets for common loading cases. Switch to Explore mode to study 12 concepts across Beam Basics, Forces & Moments, and Diagrams with worked examples. Practice mode generates random beam problems, and Quiz tests your knowledge with 5 randomised questions.
This simulator is designed for civil and mechanical engineering students, structural analysis trainees, strength of materials students, and instructors teaching beam bending, SFD/BMD construction, and structural design. It provides visual, hands-on understanding of internal forces in beams without requiring laboratory equipment or complex software.