What Is a Beam in Structural Engineering?

Beams are the most fundamental structural element in engineering. This guide explains the different types of beams, how they work, where they are used in the real world, and how to choose the right beam type for your project. Try examples in the free beam calculator.

Definition of a Beam

A beam is a horizontal or inclined structural member that spans between two or more supports and primarily resists loads applied perpendicular to its longitudinal axis. When a beam is loaded, it develops internal forces — shear force acting perpendicular to the axis and bending moment causing curvature — that transfer the applied loads to the supports, and from there to columns, walls, or foundations.

Beams are distinguished from other structural elements by the way they carry loads. A column carries loads primarily through axial compression. A cable carries loads through tension. A truss member carries loads through axial force only. A beam, by contrast, carries loads through a combination of bending and shear. This bending action is what gives beams their characteristic curved deflected shape under load.

Beams can be made of virtually any structural material: steel, reinforced concrete, prestressed concrete, timber (solid or engineered), aluminum, fiber-reinforced polymers, or even stone (as in ancient Roman and Greek architecture). The material affects the beam’s strength, stiffness, weight, and cost, but the fundamental principles of beam behavior are the same regardless of material. The StructureCalcs Beam Calculator analyzes beams of any material — simply enter the appropriate Young’s modulus and cross-sectional properties.

Simply Supported Beams

A simply supported beam rests on two supports — typically a pin at one end and a roller at the other. The pin prevents vertical and horizontal movement, while the roller prevents only vertical movement, allowing the beam to expand and contract freely with temperature changes.

This is the simplest and most commonly analyzed beam type. It is statically determinate, meaning the support reactions can be found using the three equations of equilibrium alone (ΣFx = 0, ΣFy = 0, ΣM = 0). For a simply supported beam with a central point load P, the reactions are P/2 at each support, the maximum moment is PL/4 at mid-span, and the maximum deflection is PL³/(48EI).

Real-world examples: Steel floor beams resting on columns in a building frame. A timber joist spanning between two walls. A precast concrete plank sitting on bearing walls. A bridge girder resting on two abutments. In all these cases, the beam is free to rotate at its ends and is not designed to transfer moment to the supports.

When to use: Simply supported beams are the go-to choice for single-span situations. They are easy to fabricate, straightforward to analyze, and the connections (bearings) are simple. The trade-off is that deflections are larger than for continuous or fixed beams of the same span, so for long spans or strict deflection limits, other beam types may be more efficient.

Figure 1.A simply supported beam: 8 m, pinned one end, roller the other, 10 kN/m. The two reactions are equal, the moment is a sagging parabola peaking at 80.0 kN·m at mid-span, and the beam bows downward everywhere.

Cantilever Beams

A cantilever beam is fixed at one end and free at the other. The fixed end must resist not only the vertical reaction force but also a moment reaction, which makes the connection design more demanding than for a simply supported beam.

Cantilever beams have distinctive characteristics: the maximum bending moment occurs at the fixed end (not at mid-span), the maximum deflection occurs at the free end, and the entire beam is in hogging (the top fiber is in tension). For a cantilever with a point load P at the free end, the maximum moment is PL at the fixed support, and the maximum deflection is PL³/(3EI) — significantly larger than a simply supported beam of the same span.

Real-world examples: A balcony projecting from a building facade. A canopy over a building entrance. A diving board at a swimming pool. A sign bracket extending from a pole. A crane arm (jib). Retaining wall counterforts. The wing of an aircraft (fixed at the fuselage, free at the tip).

When to use: Cantilevers are essential when a structure must project beyond its support without a column at the far end. They are also used as part of more complex systems — for example, a beam that is continuous over a support and extends beyond it acts as a cantilever on the extension. Because cantilever deflections are large, they are typically limited to short projections (up to about one-quarter to one-third of the adjacent span in continuous beam systems).

Figure 2.A cantilever: fixed at the left, free at the right, 20 kN at the tip. The support returns a moment of 80.0 kN·m as well as a vertical force, the whole beam hogs, and the largest deflection is at the free end.

Continuous Beams

A continuous beam spans over three or more supports without any internal hinges. Unlike a series of individual simply supported beams, a continuous beam transfers bending moment across the intermediate supports, creating hogging (negative) moments at the supports and reduced sagging (positive) moments at mid-span.

This moment redistribution is the key advantage of continuous beams: the maximum bending moment in a continuous beam is significantly less than in a simply supported beam of the same span and load. For a two-span continuous beam with equal spans carrying a uniform load, the maximum moment is only wL²/8 at the interior support (hogging) compared to wL²/8 for a simply supported beam — but the mid-span moments are reduced to 9wL²/128 (sagging), allowing smaller beam sections.

Continuous beams are statically indeterminate, meaning they cannot be solved using equilibrium equations alone. Additional equations based on compatibility (the beam must be continuous at intermediate supports) are required. The StructureCalcs calculator uses the direct stiffness method, which handles indeterminate beams of any complexity automatically.

Real-world examples: A steel beam running over multiple columns in a building frame. A multi-span bridge girder supported on piers. A continuous concrete slab spanning across parallel walls. A conveyor belt support running across multiple trestles.

When to use: Continuous beams are the preferred choice when a beam spans over multiple supports, as they use material more efficiently than separate simply supported beams. However, they require more careful analysis (which the calculator handles) and are sensitive to support settlement — differential settlement of intermediate supports can induce significant additional bending moments.

Figure 3.A two-span continuous beam over three supports, 12 kN/m throughout. The middle support takes far more than its share, and a hogging moment of 54.0 kN·m appears over it — exactly the moment that does not exist if the two spans are built separately.

Fixed Beams (Encastré)

A fixed beam (also called an encastré beam or built-in beam) is restrained against rotation at both ends. Both supports provide vertical reactions, horizontal reactions, and moment reactions. This is the highest degree of restraint for a single-span beam.

Fixed beams have smaller deflections and bending moments than simply supported beams of the same span. For a fixed beam with a uniform load, the maximum mid-span moment is wL²/24 (compared to wL²/8 for simply supported) and the end moments are wL²/12. The maximum deflection is wL⁴/(384EI), five times less than the simply supported case.

Real-world examples: A steel beam with full-moment connections (welded flanges) to columns at both ends. A concrete beam monolithically cast with columns. A lintel built into masonry walls on both sides.

When to use: Fixed beams are used when you need to minimize deflection and mid-span moment, and when the supports (columns or walls) can resist the end moments. The trade-off is that the connections are more expensive to fabricate (full-moment connections versus simple shear connections). Fixed beams are also sensitive to support settlement and rotation — if the “fixed” end actually rotates slightly, the moment distribution changes significantly.

Figure 4.A fixed-ended beam, same span and load as Figure 1. End moments of 53.3 kN·m appear, the mid-span sagging drops to a third of the simply supported value, and the peak moment in the beam falls from 80.0 to 53.3 kN·m.

Overhanging Beams

An overhanging beam extends beyond one or both of its supports. The portion beyond the support acts as a cantilever, while the portion between supports acts similarly to a simply supported beam but with modified moments due to the overhang.

The overhang creates a hogging moment at the support, which reduces the sagging moment in the main span. A well-proportioned overhang can significantly reduce the maximum bending moment in the beam, leading to a more efficient design. For a beam with equal overhangs of about 0.35L on each side (where L is the main span), the bending moments can be almost perfectly balanced.

Real-world examples: A roof beam extending beyond the building wall to form eaves. A loading dock canopy. A bridge with approach spans. A diving platform with a projecting board.

When to use: Overhanging beams are used when the structure must extend beyond the support line. The overhang is particularly efficient when it carries a significant load, as this reduces mid-span moments. However, the support at the base of the overhang must resist a larger reaction (the support is being “pulled up” by the overhang), which needs to be checked.

Figure 5.An overhanging beam: 6 m between supports with a 2 m tail, 10 kN/m throughout. The overhang produces 20.0 kN·m of hogging over the right support — hogging in a perfectly determinate beam — and pulls the mid-span sagging down with it.

Propped Cantilevers

A propped cantilever is fixed at one end and supported by a roller or pin at the other. It is statically indeterminate to the first degree — it has one more reaction than can be determined by equilibrium alone.

The prop (roller) prevents the free end from deflecting, creating a reaction at that end. This significantly reduces both the maximum bending moment and the maximum deflection compared to a pure cantilever. For a propped cantilever with a uniform load, the maximum moment is wL²/8 at the fixed end, and the prop reaction is 3wL/8.

Real-world examples: A balcony slab that is not only fixed at the building wall but also supported by a column at the edge. A retaining wall with a prop or anchor at the top. A scaffold platform fixed at the wall and propped at the outer edge.

When to use: Propped cantilevers are a good compromise when a pure cantilever would deflect too much but a full simply supported arrangement is not possible due to the geometry. They provide better performance than cantilevers while requiring only one fixed connection.

Figure 6.A propped cantilever: fixed at the left, propped on a roller at the right, 10 kN/m. One redundant reaction, so it is indeterminate — the fixed end carries 80.0 kN·m and 50.0 kN of the 80 kN total, against 30.0 kN at the prop.

How Beam Behavior Differs by Material

While the principles of beam analysis are universal, different materials bring different considerations:

  • Steel beams have high strength and stiffness relative to weight. They behave elastically up to the yield stress, then develop a plastic hinge. Standard steel sections (I-beams, channels, hollow sections) are available from the steel section library.
  • Reinforced concrete beams use steel reinforcing bars embedded in concrete to resist tension. Concrete is strong in compression but weak in tension, so the steel rebar handles tensile stresses. RC beams are heavier but fireproof and durable.
  • Timber beams are lightweight and renewable but have lower strength and stiffness than steel. Engineered timber products (LVL, glulam, CLT) can span longer distances. Timber beams are common in residential construction.
  • Aluminum beams are used in lightweight structures and where corrosion resistance is important. Aluminum has about one-third the stiffness of steel (E ≈ 70 GPa), so deflection often governs.

The beam calculator works with any material — select a standard steel section or enter custom values of E and I for any material.

Choosing the Right Beam Type for Your Project

Selecting the appropriate beam type depends on the structural requirements, architectural constraints, and economic considerations:

  • Single span, simple connections: Simply supported beam. Easiest to fabricate and erect.
  • Projection beyond support: Cantilever or overhanging beam. Keep overhangs short relative to the main span.
  • Multiple supports available: Continuous beam. Most material-efficient for multi-span situations.
  • Strict deflection limits: Fixed beam or continuous beam. Both significantly reduce deflection compared to simply supported.
  • Uncertain foundation conditions: Simply supported beam. Determinate beams are not affected by differential settlement.
  • Seismic design: Moment frames use fixed beams (rigid connections) to resist lateral loads. The beam-column joint must be detailed for ductility.

Use the StructureCalcs Beam Calculator to compare different configurations. Set up your beam as simply supported, then change to fixed or continuous and observe how the moments, shear forces, and deflections change.

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