Structural Load Distribution: Beams & Supports

simulator intermediate ~10 min
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M_max = 30.0 kN·m at midspan

A 20 kN point load at the center of a 6m simply supported beam produces equal reactions of 10 kN at each support and a maximum bending moment of 30 kN·m at midspan.

Formula

R_left = P × (L − a) / L for simply supported beam
R_right = P × a / L
M_max = P × a × (L − a) / L at the load point

How Buildings Stand Up

Every structure on earth must transfer loads — gravity, wind, occupants, snow — safely to the ground. The beam is the most fundamental structural element: a horizontal member that spans between supports and resists loads through internal shear forces and bending moments. Understanding how loads flow through a beam is the first step in structural engineering, whether you're designing a bridge or a bookshelf.

Reactions, Shear, and Moment

When a load pushes down on a beam, the supports push back with reaction forces. For a simply supported beam, these reactions follow a simple lever rule: the closer the load is to a support, the more force that support carries. Between the supports, the beam develops internal shear forces (vertical sliding tendency) and bending moments (rotational stress) that vary along its length. This simulation draws those diagrams in real time as you move the load.

Support Conditions Matter

How a beam is attached to its supports dramatically changes the force distribution. A simply supported beam is free to rotate at both ends — like a plank resting on two sawhorses. A cantilever is rigidly fixed at one end, concentrating all the moment there. A fixed-fixed beam clamps both ends, reducing the midspan moment but creating moments at the supports. Each condition suits different architectural situations.

From Diagrams to Design

Shear and moment diagrams are not abstract exercises — they directly determine the size of every beam in a building. The maximum bending moment tells the engineer the minimum cross-section needed to prevent failure. The maximum shear force determines whether the beam needs web stiffeners. Every skyscraper, bridge, and house is designed by computing these diagrams for every load combination the structure might face.

FAQ

How do loads distribute through a simply supported beam?

A simply supported beam transfers loads to its two supports through shear forces and bending moments. The reactions at the supports are inversely proportional to their distance from the load — a load closer to the left support puts more force on that support.

What is a bending moment diagram?

A bending moment diagram shows how the internal bending moment varies along a beam's length. It peaks where the beam is most stressed and is zero at simple supports. Engineers use it to determine the required beam size and to locate the critical cross-section.

What is the difference between a cantilever and a simply supported beam?

A simply supported beam rests on two supports and is free to rotate at each end. A cantilever is fixed at one end and free at the other, like a diving board. Cantilevers have maximum moment at the fixed support, while simply supported beams have maximum moment somewhere along the span.

How do you calculate beam reactions?

For a simply supported beam with a point load P at distance a from the left support (span L), the left reaction is P×(L−a)/L and the right reaction is P×a/L. This comes from equilibrium: sum of forces = 0 and sum of moments = 0.

Sources

Embed

<iframe src="https://homo-deus.com/lab/architecture/structural-loads/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub