Engineering guide · Beam fundamentals · Reviewed July 30, 2026

Types of Beams and Beam Supports

Definitions, diagrams and comparison tables for five common beam configurations, idealized roller, pin and fixed supports, section properties and structural analysis classifications.

Interactive beam example Beam deflection formulas
Interactive example

Interactive beam explorer

Select a support arrangement and load case to compare reactions, bending moment and deflection. The calculation controls and unit systems are consistent with the corresponding individual beam guides.

Live beam, shear, moment & deflection

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Simply Supported beam diagramInteractive beam diagram loading.
Simply Supported beam — Full-span UDL
Bending M(x) Open full diagram →
Deflection y(x) Open full diagram →

Deflected shape is scaled for clarity.

Quick calculator

Simply Supported beam calculator

Support model
Pin + Roller
Analysis
Statically determinate
Choose a load case
m
kN/m

Left reaction RA

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View shear diagram →

Right reaction RB

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View shear diagram →

Maximum moment Mmax

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View moment diagram →

Maximum deflection δmax

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View deflection diagram →
Material and section stiffness E·I Used for deflection

Need a real load arrangement? Continue with these inputs, then add loads, move supports, choose a section and export full results.

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Quick cases are for comparison and hand checks. For multiple loads, partial UDLs, custom support locations or a selected cross-section, continue in the full beam calculator.

Definition

What is a structural beam?

A structural beam is a horizontal or sloped structural member that carries loads across a span. Loads applied to the beam are transferred to supports, columns, posts, walls, girders or foundations.

In most practical beam problems, the beam mainly resists two internal actions: shear force and bending moment.

Beams are commonly made from steel, wood, reinforced concrete, aluminum or engineered lumber. Real-world examples include floor beams, roof beams, bridge beams, lintels above openings, joists, girders, crane beams and balcony supports.

What a beam does Transfers load across a span to its supports
Shear force
Transfers transverse load through the member.
Bending moment
Produces curvature, tension and compression.
Reactions
Return the load to columns, walls or foundations.
Common applications
  • Floor & roof beams
  • Bridge girders
  • Lintels & joists
  • Crane beams
  • Balcony supports
Idealized boundary conditions

Beam support types

A beam support restrains one or more movements at a point. The restrained degrees of freedom determine the possible reaction forces and moments included in the structural model.

Degrees of freedom and reactions

Read the restraint before drawing the reaction

A node in a two-dimensional frame can translate horizontally, translate vertically and rotate. Restraining a degree of freedom introduces a corresponding possible reaction component.

  1. 1
    Identify the allowed movementAsk whether the node may translate or rotate.
  2. 2
    Mark the restrained movementA restraint imposes a displacement boundary condition.
  3. 3
    Add the possible reactionThe reaction may be zero for a particular load case.
Three possible movements at a two-dimensional beam nodeA beam-end node can translate horizontally, translate vertically and rotate. Restraining those movements creates horizontal reaction, vertical reaction and moment reaction respectively.ONE BEAM-END NODEuₓhorizontaluᵧverticalθrotationRESTRAINED MOVEMENT → POSSIBLE REACTIONrestrain uₓreaction Rₓrestrain uᵧreaction Rᵧrestrain θreaction M
Teal indicates an allowed movement. Amber indicates a restrained movement and its possible reaction.
Three common idealizations

Roller, pinned and fixed supports

Start with what the support lets the beam do. Each example pairs the analysis symbol with one typical physical connection.

Teal indicates an allowed movement. Amber indicates a restrained movement and its possible reaction.
01 · Roller

Roller support

Carries force normal to its bearing surface, but lets the beam slide along the bearing and rotate.

Idealized symbol
One physical realization Roller support application: bridge expansion bearingA bridge girder rests on a roller bearing over a concrete pier. The support carries vertical reaction while allowing thermal movement.BRIDGE EXPANSION BEARINGRᵧMOVEMENT ALLOWEDROTATION ALLOWED

Quick read

Moves freely
Movement along the bearing and rotation θ.
Reacts with
Rn
Typical use
Bridge expansion bearings and long members that need to move with temperature.
Compare all supports
02 · Pinned

Pinned support

Holds the beam end in place, but lets it rotate. It is also called a hinged support.

Idealized symbol
One physical realization Pinned support application: simple beam-to-column connectionA beam is connected to a column through a simple shear plate and pin. Translation is restrained while end rotation remains possible.SIMPLE SHEAR CONNECTIONRᵧRₓROTATION ALLOWED

Quick read

Moves freely
Rotation θ; no idealized moment reaction.
Reacts with
Rx, Ry
Typical use
Simple beam-to-column shear connections, truss joints and hinge details.
Compare all supports
03 · Fixed

Fixed support

Holds the beam end in place and prevents it from rotating.

Idealized symbol
One physical realization Fixed support application: cantilever cast into a wallA cantilever beam is embedded into a wall. Horizontal and vertical translation and end rotation are restrained.RIGID CANTILEVER CONNECTIONRᵧRₓM

Quick read

Moves freely
No translation or rotation in the idealized model.
Reacts with
Rx, Ry, M
Typical use
Cantilevers cast into walls and rigid moment-resisting beam connections.
Compare all supports
Support comparison

What each beam support allows

For a horizontal two-dimensional beam, compare the movement first and then add the possible reactions.

01

Roller support

Allowed movement
Slides along the bearing and rotates
Possible reactions
1 forceNormal to the bearing surface · Rn
02

Pinned support

Allowed movement
Rotates, but does not translate
Possible reactions
2 forcesHorizontal and vertical · Rx, Ry
03

Fixed support

Allowed movement
No translation or rotation
Possible reactions
2 forces + 1 momentHorizontal, vertical and moment · Rx, Ry, M
Advanced note: beam-end boundary conditions

Pin or roller at a beam end: vertical deflection is zero (v = 0), but rotation is allowed and the idealized support moment is zero (M = 0).

Fixed support at a beam end: vertical deflection and rotation are both zero (v = 0 and dv/dx = 0).

Continuous beam: a support beneath an unbroken member does not create an internal hinge. The beam can still carry bending moment across that support.

Support configurations

Types of structural beams

The five beam types below are classified by support arrangement and member extent. Use the support pattern to identify the corresponding idealized model.

1

Simply supported

Statically determinate

A single span carried by a pin and roller. Both ends can rotate, so the idealized support moments are zero.

Supports
Pin + Roller
Model cue
Two bearing points with free end rotation
Common use
Straightforward single spans and simple connections
Simply supported beam guide
2

Cantilever

Statically determinate

Fixed at one end and free at the other. The fixed connection supplies both force and moment resistance.

Supports
Fixed at one end
Model cue
One fixed end with an unsupported tip
Common use
Balconies, canopies, brackets and projecting members
Cantilever beam guide
3

Fixed beam

Statically indeterminate

Restrained against rotation at both ends. End fixity creates support moments and reduces midspan deflection.

Supports
Fixed at both ends
Model cue
Both ends reliably restrain rotation
Common use
Rigid frames and monolithic construction
Fixed beam beam guide
4

Overhanging beam

Statically determinate

Supported at two points with part of the member extending beyond a support. The projecting length changes reactions and moment distribution.

Supports
Pin + Roller (one end overhangs)
Model cue
A free segment extends past a support
Common use
Roof eaves, balcony edges and projecting beam ends
Overhanging beam beam guide
5

Continuous beam

Statically indeterminate

One uninterrupted member crossing three or more supports. Adjacent spans share load through continuity.

Supports
Three or more supports
Model cue
One member continues over three or more supports
Common use
Multi-span floors, roofs and bridge girders
Continuous beam beam guide
Summary table

Beam types comparison

Compare the restraint, analysis behavior and likely critical region before choosing a detailed guide.

Beam type & schematic Support arrangement Rotation Determinacy Typical critical region
Simply supported
Pin + Roller Allowed Statically determinate Usually inside the span
Cantilever FREE END
Fixed at one end Restrained at fixed end Statically determinate At the fixed support
Fixed beam
Fixed at both ends Restrained at both ends Statically indeterminate At supports and within the span
Overhanging beam OVERHANG
Pin + Roller (one end overhangs) Allowed at supports Statically determinate At the inboard support and in the main span
Continuous beam
Three or more supports Varies along the span Statically indeterminate Over interior supports and within each span

Determinacy refers to the idealized model shown. Added restraints, releases, internal hinges or different support details can change the classification.

Reference equations · 12 verified cases

Beam Deflection Formulas & Equations

Identify the support arrangement and load case before selecting the corresponding reaction, shear, moment, slope and deflection equations.

Complete formula reference Beam calculator for combined or partial loads
1 Match the supports 2 Match the load and position 3 Check the assumptions
These are quick reference cases. The formula library also includes eccentric point loads, overhangs and two-span continuous beams.
Complete formula index
Cross-section geometry

Beam cross-sections and section properties

Support type controls the boundary conditions. Cross-section controls how efficiently the member turns material into bending stiffness, stress resistance and stability about each axis.

Why shape matters
Deflection and curvature flexural rigidity = EI

For the same material and loading, increasing the relevant second moment of area I reduces elastic curvature and deflection.

Elastic bending stress σmax = M / S

Elastic section modulus S = I/c relates the bending moment to stress at the extreme fibre.

A
AreaAxial stress, self-weight and material quantity.
C
CentroidLocates the elastic neutral axis for a homogeneous section.
Ix, Iy
Second moment of areaBending stiffness about the selected axis; units are length4.
Sx, Sy
Elastic section modulusConnects bending moment to extreme-fibre elastic stress.
Zx, Zy
Plastic section modulusUsed in suitable ductile-section plastic resistance checks.
r = √(I/A)
Radius of gyrationUsed with effective length in member slenderness and buckling checks.
xy

I and H sections

Place most material in the flanges, far from the neutral axis, for efficient strong-axis bending.

Often used for: Steel floor beams, girders and columns
xy

RHS and box sections

Closed walls provide useful stiffness about both axes and better torsional behavior than open sections.

Often used for: Architectural beams, frames and edge members
xy

CHS and pipe

A symmetric closed shape gives the same geometric properties in every bending direction through its center.

Often used for: Exposed structures, posts and curved framing
xy

Channels

An open, unsymmetric section that is convenient at edges but can twist when load misses the shear center.

Often used for: Purlins, lintels, stringers and built-up members
xy

T sections

An unsymmetric shape with different top and bottom elastic section moduli and a shifted centroid.

Often used for: Split tees, concrete stems and edge details
xy

Rectangular sections

Simple solid geometry; turning the deep dimension toward bending greatly increases moment of inertia.

Often used for: Timber, concrete and plate-built members
Section properties calculator Steel section tables Reference calculations include A, centroid, Ix/Iy, S, Z and radius of gyration.
Additional classification systems

Beam classification by material, geometry and analysis

A complete beam description combines its support condition with its material, longitudinal geometry and analysis behavior. Each label answers a different engineering question.

01 · Material system

Classification by material

Young’s modulus E tells us how resistant a material is to elastic deformation. For two otherwise identical beams, the material with the higher E bends less.

Typical elastic modulus and conceptual deflection comparison for common beam materialsStructural steel has a modulus near 200 gigapascals, aluminum near 69, normal-weight concrete commonly 24 to 35, solid-sawn wood commonly 7 to 14, and glulam commonly 10 to 13. With the same beam geometry and load, lower modulus produces greater elastic deflection.ELASTIC MATERIAL STIFFNESS Esteel is the 100% referenceSTRUCTURAL STEEL200 GPa100% of steelALUMINUM69 GPa35% of steelNORMAL-WEIGHT CONCRETE24–35 GPa12–18% of steelSOLID-SAWN WOOD7–14 GPa4–7% of steelGLULAM10–13 GPa5–7% of steelSAME LOAD · SPAN · CROSS-SECTIONHIGHER E = LESS BENDINGhigher E = bends lesslower E = bends moreConceptual elastic curves; not to scale.
Elastic material stiffness E Steel = 100%
Structural steel200 GPa
100% of steel
Aluminum69 GPa
35% of steel
Normal-weight concrete24–35 GPa
12–18% of steel
Solid-sawn wood7–14 GPa
4–7% of steel
Glulam10–13 GPa
5–7% of steel
Same load, span and sectionHigher E means less bending
Higher E: bends lessLower E: bends more
Steel is the 100% reference for elastic material stiffness. The bars do not compare strength or allowable load. The beam curves assume the same load, span, supports and cross-section.
How to read the comparison
Higher E

Harder to deform elastically less beam deflection.

Lower E

Easier to deform elastically more beam deflection.

Common beam material Typical E What affects the stiffness used in design?
Structural steel 200 GPa29,000 ksi Stable elastic modulus across common structural grades; yielding and local buckling are separate strength limits.
Aluminum 69 GPa10,000 ksi Alloy and temper strongly affect strength, but common wrought alloys have similar E.
Normal-weight concrete 24–35 GPa3,500–5,100 ksi Compressive strength and density affect Ec; cracking, reinforcement and creep govern effective member stiffness.
Solid-sawn wood 7–14 GPa1,000–2,000 ksi Species, grade, grain direction and moisture condition affect E; shear deformation and load duration can increase service deflection.
Glulam 10–13 GPa1,500–1,900 ksi Species combination, layup and stress class govern the tabulated value; moisture, shear deformation and load duration affect service response.
EMaterial stiffnessA property of the material. Steel has a higher E than aluminum, concrete or wood.
ICross-section stiffnessA property of the beam shape and size. Deeper sections usually have a much larger I.
EIBeam bending stiffnessThe material and cross-section work together. Increasing either E or I reduces elastic deflection.
Show the beam-deflection relationship

δ ∝ 1 / (EI) means deflection δ decreases when material stiffness E or cross-section stiffness I increases. For the same beam geometry and load, doubling E halves elastic deflection.

Typical reference values only. Use the project code, specified grade and manufacturer data. References: AISC 360, ACI 318, NASA material constants, USDA Wood Handbook and the AWC NDS Supplement.

Steel beam sizes Section properties calculator
02 · Longitudinal geometry

Classification by longitudinal geometry

A prismatic beam can use one EI value along the span. Tapers, haunches, curves and built-up construction introduce variable stiffness, local axes or connection-dependent composite action.

How prismatic, tapered, curved and built-up geometry changes beam stiffness and modelingA prismatic member has constant flexural rigidity. Tapered and haunched members have a varying second moment of area. Curved members use rotating local axes, and built-up members depend on connection shear transfer.GEOMETRY CHANGES I(x) AND EI(x)I = bd³ / 12PRISMATIC · CONSTANT EII(x)One section property setBasis of most closed-form formulas.TAPERED MEMBER · VARIABLE EI(x)d₁d₂I(x)xSegment or integrate stiffnessDepth changes dominate because d is cubed.CURVED · ROTATING LOCAL AXESx′ tangenty′Axial and bending response interactResolve forces in the changing local system.BUILT-UP · CONNECTION-DEPENDENTfasteners transfer interface shearSlip reduces composite stiffnessConnection spacing and rigidity matter.
Geometry changes I(x) and EI(x) I = bd3 / 12

Prismatic Constant EI

One section property set

Basis of most closed-form formulas.

Tapered member Variable EI(x)

Segment or integrate stiffness

Depth changes dominate because d is cubed.

Curved member Rotating local axes

Axial and bending response interact

Resolve forces in the changing local system.

Built-up member Connection-dependent

Slip reduces composite stiffness

Connection spacing and rigidity matter.

The member profile changes the second moment of area I(x). Curvature and built-up interfaces add modeling effects beyond a simple change in depth.
Rectangular sectionI = bd3 / 12

Depth is cubed: if width stays constant, doubling the depth increases I eightfold. This is why haunches can add substantial stiffness with localized material.

Prismatic
Constant section and EI.Closed-form beam equations normally assume a straight member, constant material and constant cross-section.
Tapered or haunched
I(x) changes along the length.Depth is placed where moment, shear or connection demand is high; use segmented properties, numerical integration or frame elements that support variable sections.
Curved
Local axes rotate with the member.Axial force, bending and sometimes torsion interact. A straight-beam formula may miss important local-axis effects.
Built-up or composite
Connection shear transfer controls composite action.Welds, bolts, fasteners, adhesive or shear connectors must transfer interface force; slip reduces effective stiffness.
Non-prismatic frame analysis Section inertia reference
03 · Analysis behavior

Beam classification by analysis behavior

Answer two separate questions: can equilibrium find every reaction, and does the beam keep the same stiffness as it deforms?

Question 1

Can equilibrium alone determine every reaction?

Compare the reaction unknowns with the three independent equilibrium equations available for a stable two-dimensional free body.

YesDeterminate
3 reaction unknowns 3 equilibrium equations

Equilibrium is enough

NoIndeterminate
6 reaction unknowns Only 3 equilibrium equations

Use an indeterminate analysis method

Question 2

Does stiffness stay constant during loading?

This is a different classification from determinacy. Check the response assumptions after the support model is established.

Yes
Linear elastic model

Small displacements, an approximately linear material response and unchanged supports allow one constant stiffness model. Superposition is valid.

No
Nonlinear or inelastic model

Yielding, cracking, large displacement, uplift or changing contact alters stiffness. The analysis must update the model incrementally.

Beam analysis calculator 2D frame analysis

Engineering calculators

Put the beam concepts to work

Analyze the member, calculate its section properties, or look up a standard steel shape with the tool that fits your next step.
Beam Calculator Calculate reactions, shear, bending moment, slope, deflection and stress for a straight beam. Open Beam Calculator 2D Frame & Truss Analysis Model and analyze frames and trusses with member releases, load cases and combinations. Open Frame Calculator Section Properties Calculate area, centroid, moments of inertia, section modulus and radius of gyration. Calculate Section Properties Section Builder Draw or import a custom or arbitrary cross-section and calculate its geometric properties. Open the free Custom Section Builder Steel Beam Sizes Find dimensions and properties for AISC, CISC, UK, European and Australian steel shapes. Browse Steel Beam Sizes
Questions and answers

Beam types and supports FAQ

Short answers to the questions that commonly decide which idealized beam model to use.

What are the five main beam types?

The five common beam types classified by support arrangement are simply supported, cantilever, fixed, overhanging and continuous beams. Other classifications describe the material, cross-section or geometry instead.

What are the three main beam support types?

The main idealized supports are roller, pinned and fixed supports. A roller provides one force reaction, a pin provides two force reactions, and a fixed support provides force reactions plus a moment reaction.

What is the difference between a pin and a roller support?

Both allow rotation and do not resist moment. A pin restrains horizontal and vertical translation, while a roller normally restrains movement in only one direction and allows movement along its supporting surface.

What is the difference between a cantilever and an overhanging beam?

A cantilever has one fixed support and a free end. An overhanging beam has two or more supports, with part of the beam extending beyond at least one support.

What makes a beam statically indeterminate?

A beam is statically indeterminate when equilibrium equations alone cannot determine all reactions. Fixed and continuous beams normally require deformation compatibility and stiffness information in addition to equilibrium.

Is a pin support the same as an internal hinge?

No. A pin support restrains a node relative to the supporting structure while allowing rotation. An internal hinge connects two member segments, allows relative rotation between them and transfers axial and shear force but no bending moment.

What is the difference between a beam support and a support beam?

A beam support is a restraint such as a roller, pin or fixed connection. A support beam is a load-bearing structural member. The terms describe different parts of a structural system.

Engineering authorship

Prepared and reviewed by

The support restraints, reaction components, determinacy labels and model-selection guidance were technically reviewed for the idealized two-dimensional beam models presented on this page. Last technical review: July 30, 2026.

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