How Beams Work: Bending, Shear, and the Deflected Shape

A beam’s job is to carry load across a gap and deliver it to its supports. To do that it bends — and bending stretches one face while squeezing the other. The face that stretches is in tension; the face that squeezes is in compression. Designing a beam is mostly about knowing where those forces peak.

Play with the model below: change the support, the load, and where the load sits, and watch the three diagrams move together.

SupportSimply supportedCantilever (fixed at left)

Load typePoint loadUniform load (UDL)

Load magnitude: 4.0 kNLoad position: 3.0 m from left

Left reaction: 2.0 kN

Right reaction: 2.0 kN

Max moment: 6.0 kN·m @ 3.0 m

Tension on the: bottom fibre

Reading the three diagrams

• The beam (top): the dashed blue line is the exaggerated deflected shape. Under gravity a simply-supported beam sags — it curves down between the supports.
• Shear (V): how much the load is trying to “scissor” the beam vertically at each point. It’s largest near the supports.
• Moment (M): how hard the beam is being bent at each point. This is the one that sizes the beam. It’s drawn on the tension side, so for a sagging beam the curve hangs below the line — the bottom is in tension.

The key intuitions

1. Tension follows the sag. Where a beam curves like a smile (sagging), the bottom stretches → tension on the bottom. That’s why a simply-supported beam’s bottom fibre matters most.
2. A cantilever flips it. Fix one end and load the other and the beam curves the other way (hogging) — now the top is in tension, and the moment is biggest at the fixed end. Switch the support above to see the moment diagram jump to the other side of the line.
3. Midspan vs. support. A simply-supported beam bends most at midspan (largest moment) but shears most at the supports — different problems at different places.
4. Point vs. uniform. A point load makes a sharp peak in the moment diagram right under the load; a uniform load makes a smooth parabola.

The numbers here use simple textbook formulas (for example, a central point load gives a maximum moment of P·L/4; a uniform load gives w·L²/8) so the diagram shapes are exact — the goal is the feel, not a design check.

This is a teaching model, not an engineering calculation. Real beams need a licensed engineer, material properties, and code-based load combinations.