Beam Lab
Explore loading, shear, bending moment, angle, and deflection.
Click to add a force. Drag an arrow left/right to move it and up/down to change its strength. Drag below the beam for an upward force.
Shear force
Bending moment
Angle / slope
Deflection
How to play
Start with the point force, then move it toward the free end. Compare the curves. Fix the other end to see how another wall changes the reactions and bending. Combine multiple point forces, a uniform patch, and your own drawn distribution.
- Point force: click to add, then drag the arrow. Horizontal motion moves the force; vertical motion changes its magnitude. Up to 12 forces can act together.
- Uniform load: drag across the span to set its extent; drag higher or lower to change intensity. A tap applies a uniform load across the whole beam. A new gesture replaces this layer.
- Draw load: sketch above the beam for downward loading and below it for upward loading. Draw along the beam to erase a region. New strokes edit the existing shape.
- Inspect: move across any curve to compare all four quantities at the same position. The green tangent in the deflection view shows the local angle.
What the curves mean
Shear changes where a distributed load acts and jumps at a point force. Moment’s slope is shear. Curvature is proportional to bending moment; integrating curvature gives the angle, and integrating angle gives displacement. Each panel uses its own labeled vertical scale. Deflection is exaggerated for visibility, while the readouts show the calculated displacement in millimeters.
Sign convention: x increases from the left wall. Applied load, deflection, and slope are positive downward; positive moment is sagging. This gives dV/dx = −q, dM/dx = V, dθ/dx = −M/EI, and dy/dx = θ. Positive shear and moment plot upward; positive angle and deflection plot downward. Wall forces are positive upward; wall couples are positive counterclockwise. At a point-force jump the readout uses the value immediately to the right.
The model is a uniform, linearly elastic Euler–Bernoulli beam with constant EI and small deflection. A fixed wall enforces zero displacement and zero rotation. A free end has zero end moment and shear unless an end force acts there. The two-wall case solves the extra reactions using both end constraints. Drawn loading is represented by 65 linearly connected samples; load integrals are evaluated analytically. Beam weight, shear deformation, yielding, vibration, and buckling are omitted. Large predicted bending is flagged because it exceeds this model’s assumptions. This is an educational simulation.
Reference: University of Illinois — Deflection of Beams. The signs above define this lab’s coordinate convention.