Engineering guide · Updated May 24, 2026

Types of Beams & Beam Supports

Diagrams, support reactions, formulas and worked examples for common structural beam types. Pick a beam below and try it instantly in the free Optimal Beam calculator.

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Simply Supported beam — Full-span UDL
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Deflection scaled for clarity, not to true ratio

Beam type

Simply Supported beam

Supports
Pin + Roller
Determinacy
Statically determinate
End rotation
Allowed
Load case
m
kN/m
RA reaction

— kN

—

View shear diagram
RB reaction

— kN

—

View shear diagram
Mmax bending

— kN·m

—

View moment diagram
δmax deflection

— mm

—

View deflection diagram
Stiffness E·I — affects deflection only Defaults: steel, small section

Common uses: Floor beams, roof beams, lintels above openings, simple bridge spans, joists between secondary beams.

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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.

1

Load

External force applied to the beam.

2

Beam

Carries shear and bending across the span.

3

Supports

Restrain the beam at specific points.

4

Reactions

Forces and moments returned by supports.

Concrete structural beam example
Concrete beams transfer floor and roof loads into columns and foundations.

Definition

What is a support beam?

A support beam is a structural beam used to carry loads from floors, roofs, walls or other structural elements and transfer those loads to columns, posts, walls or foundations. In residential construction, the term often refers to a beam that supports floor joists, roof framing or an opening where a wall has been removed.

In engineering terms, a support beam is still analyzed as a beam. The important questions are where it is supported, what loads it carries, how long the span is, what material and section are used, and what deflection or stress limits apply.

At a glance

Beam types comparison

The support arrangement is one of the fastest ways to classify a beam. This table compares the common beam types used in introductory beam analysis and everyday structural design, using idealized pin, roller and fixed support models.

Beam type Supports Support rotation Idealized determinacy Common use
Simply supported Pin + roller Allowed at supports Statically determinate Floor beams, roof beams, lintels
Cantilever Fixed at one end, free at the other Restrained at fixed support Statically determinate Balconies, canopies, brackets
Fixed beam Fixed at both ends Restrained at both supports Statically indeterminate Rigid frames, monolithic concrete
Overhanging Supports inside beam length Usually allowed at simple supports Determinate or indeterminate Roof overhangs, balconies
Continuous Three or more supports Varies by support Statically indeterminate Multi-span floors and bridges

Determinacy here refers to the idealized beam model. Added restraints, releases, internal hinges or unusual support details can change the classification.

1

Simply supported beam

Pin at one end, roller at the other

A simply supported beam is supported at two points, commonly with a pin at one end and a roller at the other. The supports allow rotation, so the beam does not develop fixed-end moments at the supports.

Support model

Pin + roller
MA = 0MB = 0rotation allowedrotation allowedRARBHAPinRollerspan L

What to read from the figure

Vertical reactions

Loads resolve into RA and RB at the two supports.

Free rotation

The ends can rotate, so ideal end moments are zero.

Single span

L is measured between the pin and roller centerlines.

Support reactions

For a vertical loading case, a simply supported beam typically has a vertical reaction at each support. If one support is pinned, it can also resist horizontal force. For symmetrical loading, the two vertical reactions are often equal.

Common uses and loads

Simply supported beams are common in floors, roofs, bridges, lintels and basic framing members. Common loading examples include a point load at midspan, a uniform distributed load across the full span, or several point loads from joists or secondary beams.

In real life

Simply supported beam IRL

In real life, a simply supported beam is any beam that spans between two bearing points and is free to rotate at its supports, so the supports carry vertical (and sometimes horizontal) reactions but no end moments. Real connections often have some rotational stiffness, so engineers use the simply supported model whenever end rotation is close enough to the ideal pin-and-roller assumption.

  • Floor joist on bearing walls
  • Steel beam, shear-tab connection
  • Bridge girder on bearings
  • Lintel over an opening
  • Roof purlin between frames
Simply supported beam in real life: steel beams bolted to a column with shear-tab connections
Steel beams on shear-tab connections behave like simply supported beams.

Center point load

Symmetric point load placed at x = L/2.

P
P at midspanRARBHAVMδMmax = PL/4δmax
RA = RB Peak M at midspan Max sag at midspan
Support reactions
RA = RB = P / 2
Maximum moment
Mmax = PL / 4 at midspan
Maximum deflection
δmax = PL3 / 48EI at midspan
Open this point-load setup in the calculator

Full-span UDL

Uniform load w applied continuously from A to B.

w
w kN/m over full spanRARBHAVMδMmax = wL²/8δmax
Total load = wL Parabolic moment Max sag at midspan
Support reactions
RA = RB = wL / 2
Maximum moment
Mmax = wL2 / 8 at midspan
Maximum deflection
δmax = 5wL4 / 384EI at midspan
Open this UDL setup in the calculator
2

Cantilever beam

Fixed at one end, free at the other

A cantilever beam is fixed at one end and free at the other. The fixed support restrains translation and rotation, so it can resist vertical reaction, horizontal reaction and bending moment. The free tip is unsupported and carries the largest deflection.

Support model

Fixed at one end
MA ≠ 0free tiprotation restrainedfree to deflectRAHAMAspan L

What to read from the figure

Fixed-end reaction

The wall resists vertical force RA from the load.

Fixed-end moment

Rotation is restrained, so MA is non-zero and peaks at the wall.

Free tip

No support: maximum deflection occurs here.

Common uses and loads

Cantilever beams are used for balconies, canopies, crane arms, brackets, signs, retaining wall stems and projecting roof elements. The largest bending moment normally occurs at the fixed support.

End point load

Concentrated load P applied at the free tip.

P
P at tipRAHAMAVMδMmax = PLδmax
RA = P Peak M at fixed end Max sag at tip
Support reaction
RA = P
Maximum moment
Mmax = PL at fixed end
Maximum deflection
δmax = PL3 / 3EI at tip
Open this point-load setup in the calculator

Full-span UDL

Uniform load w applied along the entire cantilever span.

w
w kN/m over spanRAHAMAVMδMmax = wL²/2δmax
Total load = wL Parabolic moment Max sag at tip
Support reaction
RA = wL
Maximum moment
Mmax = wL2 / 2 at fixed end
Maximum deflection
δmax = wL4 / 8EI at tip
Open this UDL setup in the calculator
3

Fixed beam

Restrained at both ends

A fixed beam has both ends restrained against rotation. Because the ends cannot freely rotate, fixed beams usually develop negative bending moments at the supports and lower midspan deflection than a comparable simply supported beam.

The beam can still deflect along its span. What makes it fixed is the restraint at the ends, not the absence of deformation everywhere.

Support model

Fixed at both ends
MA ≠ 0MB ≠ 0rotation restrainedrotation restrainedRARBHAHBMAMBspan L

What to read from the figure

Two reactions

Both walls resist vertical force, so the load splits between RA and RB.

Fixed-end moments

Both ends develop non-zero moments because rotation is restrained.

Single span L

Fixed beams stiffen the same span by restraining the supports.

Full-span UDL

Uniform load w applied across the full span with both ends fixed.

w
w kN/m over full spanRARBHAHBMAMBVMδ|Mend| = wL²/12Mmid = wL²/24δmax
RA = RB = wL/2 Sign change in M Lower sag than pinned
Support reactions
RA = RB = wL / 2
End moments
|Mend| = wL2 / 12 at supports
Midspan moment
Mmid = wL2 / 24 at midspan
Maximum deflection
δmax = wL4 / 384EI at midspan
Open this UDL setup in the calculator

Center point load

Concentrated load P at midspan with both ends fixed.

P
P at midspanRARBHAHBMAMBVMδ|Mend| = PL/8Mmid = PL/8δmax
RA = RB = P/2 |Mend| = Mmid Quarter of pinned sag
Support reactions
RA = RB = P / 2
End moments
|Mend| = PL / 8 at supports
Midspan moment
Mmid = PL / 8 at midspan
Maximum deflection
δmax = PL3 / 192EI at midspan
Open this point-load setup in the calculator

End moments are negative (hogging) and the midspan moment is positive (sagging). For the same load and span, fixing both ends roughly halves the peak moment and quarters the midspan deflection compared with a simply supported beam.

4

Overhanging beam

Supports inside the beam length

An overhanging beam has at least one support located inside the total beam length, so part of the beam extends past a support. The span L runs between the two supports and the overhang a runs from the inner support to the free tip.

Support model

Pin + roller, free tip
MA = 0MB = 0free tipRARBHAspan Loverhang a

What to read from the figure

Two reactions

Pin at A, roller at B; both develop vertical reactions but no end moments.

Span L

Distance between the two supports where the beam mostly sags.

Overhang a

Beam projecting past the roller; loads here cause hogging at support B.

Common loading cases

Overhanging beams appear in roof eaves, balcony edges, canopies and framing where a beam must project beyond a column or wall. Depending on the geometry and loading, the overhang can create negative bending near the support.

UDL on full length

Uniform load w applied across both the span L and the overhang a.

w
w over full length (L+a)RARBHAVMδ|MB| = wa²/2
Total load = w(L+a) Negative M at roller Sag inside, lift at tip
Reaction at pin
RA = w(L2 − a2) / 2L
Reaction at roller
RB = w(L + a)2 / 2L
Negative peak moment
|MB| = wa2 / 2 at roller
Open this UDL setup in the calculator

Point load at free tip

Concentrated load P at the free tip levers the beam over the roller.

P
P at free tipRARBHAVMδ|MB| = Paδtip
RA = −Pa/L RB = P(1 + a/L) Max sag at tip
Reaction at pin
RA = −Pa / L downward
Reaction at roller
RB = P(1 + a / L)
Negative peak moment
|MB| = Pa at roller
Tip deflection
δtip = Pa2(L + a) / 3EI at tip
Open this tip-load setup in the calculator
5

Continuous beam

Three or more supports

A continuous beam extends over more than two supports. It is common in floor systems, bridges and multi-span framing. Because the internal support creates additional reaction forces, continuous beams are usually statically indeterminate and are better solved using structural analysis software.

Support model

Three or more supports
MA = 0MB < 0MC = 0positive bending in each spannegative bending over support BRARBRCHAspan Lspan L

What to read from the figure

Three reactions

Loads share between the end supports and the interior support.

Multiple spans

Each span L is measured between adjacent supports.

Negative bending over support B

The interior support causes hogging, so MB is negative even though MA = MC = 0.

Continuous beams can be efficient because the load path is shared across multiple supports. They also create negative bending moments over interior supports, which means reinforcement, connection detailing and stress checks often need more care.

Use the free beam calculator to calculate reactions, shear force, bending moment and deflection for multi-span beams.

Idealized supports

Beam support types

Beam supports transfer loads from the beam into the rest of the structure. The support type determines what reaction forces can develop. In idealized beam analysis, the most common support types are roller, pinned and fixed supports.

This roller, pinned and fixed support grouping is widely used in introductory structural analysis because each support maps directly to the reaction components it can resist.

Support type Resists vertical force Resists horizontal force Resists moment Allows rotation?
Roller Yes No No Yes
Pinned Yes Yes No Yes
Fixed Yes Yes Yes No

A simple support is usually a modeling term for a support that allows rotation and does not resist moment. Depending on whether horizontal movement is restrained, it is commonly represented as a roller or pinned support.

R

Roller support

Allows rotation and horizontal movement, while resisting vertical movement for a horizontal beam.

Reaction components shown

Ry

Rotation

Allows rotation and movement along the support

Roller support reaction diagram
Reaction diagram
Bridge bearing as a roller support analogy
Bridge bearing — roller analogy
P

Pinned support

Restrains horizontal and vertical movement, but allows rotation. A pinned support can resist two force components, but not moment.

Reaction components shown

Rx, Ry

Rotation

Allows rotation

Pinned support reaction diagram
Reaction diagram
Door hinge as a pinned support analogy
Door hinge — pinned analogy
F

Fixed support

Restrains horizontal movement, vertical movement, and rotation. A fixed support can resist horizontal force, vertical force, and bending moment.

Reaction components shown

Rx, Ry, M

Rotation

Restrains rotation

Fixed support reaction diagram
Reaction diagram
Anchored light pole acting as a fixed support
Anchored base — fixed support

To compare how these restraints change reactions, shear, moment and deflection, model roller, pinned and fixed supports in the free beam calculator.

Engineering diagrams

Beam diagrams

Beam diagrams turn a structural problem into something engineers can check. The same simply supported beam under a uniform distributed load is broken down below into the five diagrams an engineer reads in order — free body, reactions, shear, moment and deflection.

Step 1 of 5

Free body diagram
w kN/m over full span

Defines the model: supports, spans, loads and the unknown reactions you need to find.

Applied load

A uniform load w is drawn as red down-arrows over the full span.

Supports

Pin at A allows rotation; roller at B allows rotation and horizontal sliding.

Step 2 of 5

Reaction diagram
RARBHA

Shows the support forces and moments after equilibrium or analysis.

Vertical reactions

RA and RB balance the total vertical load wL.

Horizontal reaction

HA exists only at the pin — the roller cannot resist horizontal force.

Step 3 of 5

Shear force diagram
V|V|max = wL/2

Shows where vertical force changes and where shear demand is highest.

Linear V

V starts at +wL/2 at A and drops linearly to −wL/2 at B.

Zero crossing

V crosses zero at midspan, exactly where the bending moment peaks.

Step 4 of 5

Bending moment diagram
MMmax = wL²/8

Shows sagging and hogging regions used for strength design.

Parabolic M

M(x) = wx(L − x) / 2 — sagging across the full span.

Strength check

Design uses the peak Mmax = wL2/8 at midspan.

Step 5 of 5

Deflection diagram
δδmax

Shows serviceability behavior and the maximum displacement.

Sagging shape

The deformed shape dips below the original beam line, peaking at midspan.

Serviceability

δmax = 5wL4 / 384EI — checked against deflection limits.

Instead of drawing these diagrams by hand, enter your span, supports and loads into the Optimal Beam calculator to generate reactions, shear force, bending moment and deflection diagrams.

Open the calculator

Quick reference

Beam formulas

Beam formulas are useful for quick checks and common loading cases. Use consistent units: if loads are in kN and spans are in m, moments are usually in kN·m. Deflection formulas require elastic modulus E and moment of inertia I.

P point load w distributed load L span a overhang EI flexural rigidity RA, RB support reactions M bending moment δ deflection

Subscripts identify the support or location: A and B are the supports shown in each schematic, max means maximum value, mid means midspan and fixed means the fixed support. Moment values are shown as magnitudes unless noted.

Configuration Schematic Key formulas
Simply supported

Center point load

Pin + roller, load at midspan.

Calculator → 		PLAB
RA = RB
= P / 2
Mmax
= PL / 4 at midspan
δmax
= PL3 / 48EI at midspan

Full-span UDL

Pin + roller, uniform load over L.

Calculator → 		wLAB
RA = RB
= wL / 2
Mmax
= wL2 / 8 at midspan
δmax
= 5wL4 / 384EI at midspan
Cantilever

End point load

Fixed end, load at free tip.

Calculator → 		PLA
RA
= P
Mfixed
= PL at fixed end
δmax
= PL3 / 3EI at tip

Full-span UDL

Fixed end, uniform load over L.

Calculator → 		wLA
RA
= wL
Mfixed
= wL2 / 2 at fixed end
δmax
= wL4 / 8EI at tip
Fixed beam

Full-span UDL

Both ends fixed, uniform load over L.

Calculator → 		wLAB
RA = RB
= wL / 2
|Mend|
= wL2 / 12 at supports
Mmid
= wL2 / 24 at midspan
δmax
= wL4 / 384EI at midspan

Center point load

Both ends fixed, load at midspan.

Calculator → 		PLAB
RA = RB
= P / 2
|Mend|
= PL / 8 at supports
Mmid
= PL / 8 at midspan
δmax
= PL3 / 192EI at midspan
Overhanging

Full-length UDL

Pin + roller with right overhang a.

Calculator → 		wLaAB
RA
= w(L2 − a2) / 2L
RB
= w(L + a)2 / 2L
|MB|
= wa2 / 2 at roller

Tip point load

Point load at free overhanging tip.

Calculator → 		PLaAB
RA
= −Pa / L downward
RB
= P(1 + a / L)
|MB|
= Pa at roller
δtip
= Pa2(L + a) / 3EI at tip

Need another load case, mixed loading, custom supports or section stiffness? Use the calculator to generate reactions, shear, moment and deflection diagrams from the same model.

Worked examples

From formulas to numbers

Two short worked examples showing how the formulas above become design numbers. Each example starts with the physical model, then traces the load path into reactions and peak bending moment.

Example 1 · Simply supported beam

Simply supported beam, span L = 6 m, UDL w = 10 kN/m

Open in calculator
Model + diagrams UDL over full span
10 kN/m over 6 mRA = 30 kNRB = 30 kNVMδVmax = 30 kNMmax = 45 kN·mδmax = 42.2 mm
60 kN total load 30 kN at each support 45 kN·m at midspan 42.2 mm max deflection
Span
L = 6 m
Uniform load
w = 10 kN/m
Deflection stiffness used
E = 200 GPa, I = 100 × 106 mm4

Total load

wL = 10 × 660 kN

Support reactions

RA = RB = 60 / 230 kN each

Maximum moment at midspan

Mmax = 10 × 62 / 845 kN·m

Maximum deflection at midspan

δmax = 5wL4 / 384EI42.2 mm

Because the load is symmetric, the reactions split evenly and the shear diagram crosses zero at midspan, exactly where the bending moment peaks.

Example 2 · Cantilever beam

Cantilever beam, span L = 2 m, end point load P = 5 kN

Open in calculator
Model + diagrams Point load at free tip
P = 5 kN at tipRA = 5 kNMA = -10 kN·mVMδVmax = 5 kNMmax = -10 kN·mδmax = 0.67 mm
5 kN tip load 5 kN wall reaction -10 kN·m at fixed end 0.67 mm tip deflection
Span
L = 2 m
Point load
P = 5 kN
Deflection stiffness used
E = 200 GPa, I = 100 × 106 mm4

Fixed-end vertical reaction

VA = P5 kN

Maximum moment at fixed end

Mmax = -PL = -(5 × 2)-10 kN·m

Tip deflection

δmax = PL3 / 3EI0.67 mm

For a cantilever with a tip load, the fixed support is the critical section: shear is constant along the span and bending moment grows linearly back to the wall.

Questions & answers

Beam types and supports FAQ

What is a beam?

A beam is a structural member that carries loads across a span and transfers those loads to supports such as columns, walls, posts or foundations. Beams mainly resist shear force and bending moment.

What is a structural beam?

A structural beam is a member that carries loads across a span and transfers those loads to supports such as columns, walls, posts, girders or foundations. Structural beams mainly resist shear force and bending moment.

What are the main types of structural beams?

The main structural beam types used in basic beam analysis are simply supported beams, cantilever beams, fixed beams, overhanging beams and continuous beams. These types are mainly classified by their support conditions.

What is a support beam?

A support beam is a structural beam used to carry floor, roof, wall or framing loads and transfer them to columns, posts, walls or foundations. In residential work, people often use the term when referring to beams under floor joists or above wall openings.

What are the main types of beams?

The main types are simply supported beams, cantilever beams, fixed beams, overhanging beams and continuous beams.

What are the main types of beam supports?

The main idealized support types are roller, pin and fixed supports. Roller supports usually resist one force direction, pins resist vertical and horizontal force, and fixed supports resist force plus moment.

What does a simply supported beam look like in real life?

In real life a simply supported beam is any member that spans between two bearing points and is free to rotate at its supports. Common examples include floor joists on bearing walls, steel beams on shear-tab connections, bridge girders on bearings, lintels over openings and roof purlins between frames. See the simply supported beam IRL section for a photo and more examples.

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

A simply supported beam can rotate at its supports and does not develop fixed-end support moments in the ideal model. A fixed beam has ends restrained against rotation and normally develops negative support moments.

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

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

What beam type has the lowest deflection?

For the same load, span, material and section, a fixed-ended beam usually has lower maximum deflection than a simply supported beam because end rotation is restrained.

What is a shear force diagram?

A shear force diagram shows how internal shear changes along the beam. It helps locate critical shear demands and supports bending moment diagram construction.

What is a bending moment diagram?

A bending moment diagram shows bending moment along the beam. It is used to find maximum positive and negative bending demands for design checks.

How do I calculate beam reactions?

For statically determinate beams, use equilibrium equations such as sum of vertical forces equals zero and sum of moments equals zero. For fixed, continuous and other indeterminate beams, use a structural analysis method or a beam calculator.

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