Shear and Moment Diagram Calculator

Calculate support reactions, shear force diagrams, bending moment diagrams, maximum shear, maximum moment, and values at any beam location.

Calculator is for informational purposes only. Terms and Conditions

\[ \sum F_y = 0,\qquad \sum M = 0,\qquad \frac{dV}{dx}=-w(x),\qquad \frac{dM}{dx}=V(x) \]
1

Choose the beam setup

Select the beam type, example case, result focus, unit preset, and sign convention.

This version solves statically determinate beams using equilibrium.
Choose a preset to quickly test a common shear and moment diagram case.
Choose which result appears as the main answer. All major results still appear in the result grid.
Changing presets preserves the same physical beam by converting existing values.
Default example: simple span beam with a center point load. Add or remove loads as needed.
2

Enter beam geometry and loads

Add point loads, distributed loads, and applied moments at any beam location.

Total beam length measured from the left end to the right end.
For simple span beams this is locked at the left end. Use overhanging mode for interior support locations.
For simple span beams this is locked at the right end. Use overhanging mode for interior support locations.
Used when Result Focus is set to “Shear and moment at x.” The calculator reports V(x) and M(x) at this location.
Sign convention: positive vertical loads act downward, negative loads act upward, positive point moments are counterclockwise, and positive bending moment is treated as sagging.

Loads and applied moments

Point loads, distributed loads, and applied moments can be added at multiple locations.

Advanced Options
3

Beam, Shear, and Moment Diagrams

The beam diagram, shear force diagram, and bending moment diagram update with each load.

Shear and moment diagram calculator visual A beam diagram with supports, loads, reactions, shear force diagram, and bending moment diagram generated from the calculator inputs.
Hover or tap the diagram to inspect x, V(x), and M(x).
4

Solution

Live reactions, maximum shear, maximum moment, key values, warnings, and solution steps.

Maximum Bending Moment
Real-time result updates as you type.

Quick checks

  • Check
Show key values table See values at supports, loads, zero shear points, and maximum locations
LocationEventV beforeV afterM beforeM after
Enter values to generate the key values table.
Show solution steps See reactions, equilibrium checks, unit conversions, assumptions, and diagram logic
  1. Enter values to see the full calculation steps and checks.
5

Source, Standards, and Assumptions

Calculation basis, sign convention, assumptions, and limitations.

Statics equilibrium method

Beam reactions are calculated from static equilibrium. Shear and moment diagrams are generated from the load-shear-moment relationships.

  • Final structural design must be verified by a qualified engineer using applicable codes and project-specific load combinations.
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Calculator Guide

How to Use the Shear and Moment Diagram Calculator

The Shear and Moment Diagram Calculator above calculates support reactions, shear force diagrams, bending moment diagrams, maximum shear, maximum moment, and values at a selected beam location. It is designed for statically determinate beams such as simple spans, overhanging beams, and cantilevers.

Use the calculator first to build the diagram, then use this guide to understand why the reactions, jumps, slopes, maximum values, and sign conventions appear the way they do. A shear and moment diagram is more than a graphic: it is the internal force map used to find critical beam sections for structural analysis and preliminary design checks.

Best for Simple span, overhanging, and cantilever beams with common load types
Main result Reactions, SFD, BMD, max shear, max moment, and key values
Most important inputs Beam type, support location, load magnitude, load location, and units

Quick Answer

A shear and moment diagram calculator uses static equilibrium to find reactions, then builds the shear force diagram \(V(x)\) and bending moment diagram \(M(x)\) along the beam. Point loads create jumps in shear, distributed loads create sloped or curved shear, and moment changes according to the area under the shear diagram.

Do not rely on a simplified calculator when…

Do not use this as the only basis for final structural design, code compliance, continuous multi-span beams, fixed-fixed beams, propped cantilevers, nonlinear supports, dynamic loading, buckling checks, or load-rated construction decisions. Final design must also check load combinations, material capacity, deflection, lateral bracing, connection forces, support bearing, and applicable structural codes.

Inputs and Outputs for Shear and Moment Diagrams

The calculator needs a beam type, beam length, support conditions, and one or more loads. The output is a complete statics summary: reactions, shear values, moment values, critical locations, and a diagram that shows how internal forces change along the beam.

Common inputs and outputs for a shear and moment diagram calculator
TypeValueWhat It MeansCommon Unit
InputBeam lengthTotal distance from the left end to the right end of the beam.ft, in, m, mm
InputBeam typeSupport arrangement such as simple span, overhanging beam, or cantilever.
InputSupport locationsLocations where vertical reactions occur for simple or overhanging beams.ft, m
InputPoint loadA concentrated force applied at a specific beam location.lb, kip, N, kN
InputDistributed loadA load spread over a length, including uniform, triangular, or trapezoidal loading.lb/ft, kip/ft, N/m, kN/m
InputApplied momentA concentrated couple applied at a beam location.lb-ft, kip-ft, N-m, kN-m
InputCheck location \(x\)A specific beam location where the calculator reports \(V(x)\) and \(M(x)\).ft, in, m, mm
OutputSupport reactionsForces or fixed-end moments required to keep the beam in equilibrium.lb, kip, N, kN; moment units for fixed ends
OutputShear force diagramGraph of internal vertical shear force along the beam.lb, kip, N, kN
OutputBending moment diagramGraph of internal bending moment along the beam.lb-ft, kip-ft, N-m, kN-m
OutputKey values tableValues before and after supports, point loads, applied moments, zero-shear points, and maximum locations.varies

Formula Used for Shear and Moment Diagrams

Shear and moment diagrams are built from equilibrium and the relationship between load, shear, and bending moment. Reactions come from force and moment balance, while the diagram shape comes from how load changes shear and how shear changes moment.

Static Equilibrium

\[ \sum F_y=0,\qquad \sum M=0 \]

These equations are used first to calculate the support reactions for statically determinate beams.

Load, Shear, and Moment Relationships

\[ \frac{dV}{dx}=-w(x),\qquad \frac{dM}{dx}=V(x) \]

A distributed load \(w(x)\) changes shear, and shear \(V(x)\) changes bending moment \(M(x)\).

Area Relationships

\[ \Delta V=-\int_{a}^{b}w(x)\,dx,\qquad \Delta M=\int_{a}^{b}V(x)\,dx \]

The change in shear equals the negative area under the distributed load, while the change in moment equals the area under the shear diagram.

Maximum Moment Condition

\[ \frac{dM}{dx}=V(x)=0 \]

A local maximum or minimum bending moment often occurs where the shear diagram crosses zero, unless a boundary, fixed support, or applied moment jump controls.

Variables Used in Shear and Moment Calculations

Every shear and moment calculation depends on consistent sign convention and distance measured from a reference point. In this calculator, locations are measured from the left end of the beam.

Variable definitions for shear and moment diagram formulas
SymbolMeaningHow to Enter or Interpret It
\(L\)Beam lengthEnter the total beam length in one consistent length unit.
\(x\)Location along the beamMeasured from the left end. Use \(x=0\) at the left end and \(x=L\) at the right end.
\(R_A, R_B\)Support reactionsCalculated by equilibrium. Positive reaction values typically act upward in the reaction result.
\(P\)Point load magnitudeEnter force magnitude and location. Positive downward loads reduce shear.
\(w(x)\)Distributed load intensityEnter start and end intensity for uniform, triangular, or trapezoidal loads.
\(V(x)\)Shear force at location \(x\)Read from the shear force diagram or key values table.
\(M(x)\)Bending moment at location \(x\)Read from the bending moment diagram or key values table.
\(M_0\)Applied point momentCreates a jump in the bending moment diagram but does not create a shear jump.

How to Use This Calculator Step by Step

Start with the physical beam setup, then add loads one at a time. After each change, check that the reaction values, diagram shapes, and maximum locations make engineering sense.

1

Select the beam type

Choose simple span, overhanging beam, cantilever fixed at left, or cantilever fixed at right. This determines which reactions are available.

2

Enter beam geometry

Enter the beam length and, when applicable, support locations. For a simple span, supports are typically at \(x=0\) and \(x=L\).

3

Add loads and moments

Add point loads, distributed loads, and applied moments. Use distributed load start and end intensities to model uniform, triangular, or trapezoidal loads.

4

Choose the result focus

Select maximum moment, maximum shear, reactions, full summary, or values at a specific \(x\)-location. Use the check location input to find \(V(x)\) and \(M(x)\) at a chosen point.

5

Check the diagram and solution table

Review support reactions, jump locations, zero-shear points, maximum moment locations, diagram readout values, and the key values table before using the result.

Calculator-specific tip

Use the Example Case dropdown to test standard beam cases, then edit the loads to match your actual beam. Use the Key Values Table to inspect values immediately before and after point loads, supports, and applied moments.

Sign Convention Used by the Calculator

Sign convention is one of the most common reasons a shear or moment diagram appears different from a textbook answer. The magnitudes can be correct even when a diagram is drawn with the opposite sign convention.

Calculator sign convention for shear and moment diagrams
QuantityPositive ConventionPractical Meaning
Vertical loadPositive downwardA positive point load or distributed load acts downward on the beam.
Uplift loadNegative vertical loadUse a negative load value for upward loads.
Support reactionPositive upward in the reaction resultA negative reaction can indicate uplift at that support.
Applied point momentPositive counterclockwiseA point moment creates a jump in the bending moment diagram.
Bending momentPositive saggingSagging is commonly visualized as a smile-shaped curvature.
Negative bending momentHoggingHogging commonly occurs near fixed supports or over supports in overhanging/continuous behavior.

Textbook convention warning

If your textbook or class uses the opposite convention, your signs may appear reversed even when the absolute values are correct. Always compare the stated sign convention before deciding a shear or moment result is wrong.

How Each Load Type Changes the Shear and Moment Diagrams

A top-quality shear and moment diagram is built by understanding how each type of load changes the diagram. Point loads, distributed loads, support reactions, and point moments each affect the diagram differently.

Load behavior rules for shear and moment diagrams
Load or EventEffect on Shear DiagramEffect on Moment Diagram
Support reactionVertical jump in shearChanges the slope of the moment diagram after that point
Point loadVertical jump equal to load magnitudeMoment remains continuous, but slope changes
Uniform distributed loadLinear slopeParabolic curve
Triangular distributed loadCurved shearHigher-order curved moment
Trapezoidal distributed loadCurved shearHigher-order curved moment
Applied point momentNo shear jumpVertical jump in moment
No load between pointsConstant shearLinear moment
Zero shear pointShear crosses or touches zeroPossible local maximum or minimum moment

Why before-and-after values matter

At a support or point load, shear can be discontinuous, so \(V\) just before the point and \(V\) just after the point are different. Moment is usually continuous through a point load, but it jumps at an applied point moment. This is why the calculator’s key values table separates “before” and “after” values.

How to Read a Shear and Moment Diagram from Left to Right

Reading a diagram from left to right is the easiest way to catch mistakes. Start at \(x=0\), track every support and load event, and confirm the diagram closes correctly at the end of the beam.

1

Start at the left end

Begin at \(x=0\). If there is a support reaction at the left end, the shear diagram jumps by that reaction.

2

Move across point loads and supports

Point loads and reactions cause shear jumps. Downward point loads reduce shear; upward reactions increase shear.

3

Handle distributed loads

Distributed loads change shear gradually. A uniform distributed load creates a straight sloped shear line.

4

Build moment from shear

Moment increases when shear is positive and decreases when shear is negative. The change in moment equals the area under the shear diagram.

5

Check the right end

For a simple span with no applied end moment, the moment should return to zero at the right support. If it does not, check reactions, loads, and moments.

How to Interpret the Results

The shear diagram tells you where vertical internal force is largest. The moment diagram tells you where bending demand is largest. These locations often control member sizing, reinforcement, connection forces, or the next design check.

How to interpret common shear and moment diagram features
Result or Diagram FeatureWhat It MeansWhat to Check Next
Shear jumps upwardAn upward reaction or upward point force occurs at that location.Confirm support location and reaction sign.
Shear jumps downwardA downward point load occurs at that location.Confirm load magnitude and load location.
Sloped shear lineA distributed load is acting over that span.Check whether the load is uniform, triangular, or trapezoidal.
Linear moment diagramShear is constant over that region.Check the area under the shear diagram.
Curved moment diagramA distributed load is causing shear to vary.Check maximum moment at zero-shear locations.
Moment jumpAn applied point moment is present.Confirm moment sign convention and magnitude.
Moment reversalThe bending moment changes sign from sagging to hogging or vice versa.Check both positive and negative moment demands.
Negative reactionA support may be in uplift for the selected loading.Check overhangs, load placement, hold-downs, and support assumptions.

What to do with the result

Use the maximum shear to check shear strength and support or connection forces. Use the maximum moment to check bending stress, section modulus, reinforcement, or member capacity. Use the shape of the diagrams to locate critical sections rather than checking only the beam midpoint.

When maximum moment is not at midspan

Maximum moment is not always at the center of the beam. It may occur where shear equals zero, at a fixed support, at a point moment jump, near a heavy unsymmetrical load, or at a support in an overhanging beam. Always check the full diagram and key values table.

Quick sanity check

For a simple span with only downward loads, the sum of upward reactions should equal the total downward load. Also, the bending moment at simple supports should usually be zero unless an applied point moment is located at the support.

How to Check the Calculator Results by Hand

A hand check helps confirm that the calculator inputs match the beam you intended to model. You do not need to redraw the full diagram to catch most errors.

  1. Add all downward loads. Include point loads and the resultants of all distributed loads.
  2. Check vertical equilibrium. For a simple span, confirm \(R_A+R_B\) equals the total downward load, adjusted for any upward loads.
  3. Take moments about one support. Confirm the other reaction balances the load moments and applied point moments.
  4. Check shear jumps. A support reaction should jump shear upward; a downward point load should jump shear downward.
  5. Check distributed load areas. The area under \(w(x)\) should match the change in shear across that loaded region.
  6. Check moment by shear area. The change in moment between two points should equal the area under the shear diagram.
  7. Check maximum moment locations. Look at zero-shear points, fixed supports, point moment jumps, and beam boundaries.
  8. Check end conditions. A simple support usually has zero moment; a fixed end usually has a fixed-end moment.

Self-weight reminder

Beam self-weight is not automatically included unless a calculator has a specific self-weight option. If self-weight matters, add it as a distributed load using the appropriate force-per-length value.

Input Quality Checklist

Small input mistakes can completely change the diagram. Before using the output, verify the beam model matches the real support and loading condition.

Check support type

Make sure the selected beam type matches the physical condition. A cantilever fixed end is not the same as a pin or roller support.

Check load direction

Use the calculator sign convention consistently. Positive downward loads and negative uplift loads should not be mixed accidentally.

Check load location

A point load at \(x=10\) ft is very different from a point load at \(x=10\) in. Confirm the location unit selector.

Check distributed load length

For partial distributed loads, verify both the start and end locations. Reversing them or using the wrong length changes the resultant.

Check units

Do not mix kip with lb or ft with in unless the unit selectors are set correctly.

Check assumptions

Use this statics-based calculator for determinate beams. Continuous beams and fixed-fixed beams need additional compatibility analysis.

Worked Examples for Common Shear and Moment Diagrams

Worked examples are useful for checking whether the calculator is behaving as expected. The examples below use common textbook-style beam cases.

Example 1: Simple Span with Center Point Load

Beam length
\(L=20\,ft\)
Point load
\(P=10\,kip\) at midspan
Beam type
Simply supported

Support Reactions

\[ R_A=R_B=\frac{P}{2}=\frac{10\,kip}{2}=5\,kip \]

Maximum Moment

\[ M_{max}=R_A\left(\frac{L}{2}\right)=5\,kip(10\,ft)=50\,kip\cdot ft \]

Final Answer

Reactions: \(R_A=5\,kip\), \(R_B=5\,kip\). Maximum shear: \(5\,kip\). Maximum moment: \(50\,kip\cdot ft\) at midspan.

Example 2: Simple Span with Uniform Distributed Load

Beam length
\(L=20\,ft\)
Uniform load
\(w=1\,kip/ft\)
Beam type
Simply supported

Total Load and Reactions

\[ W=wL=1(20)=20\,kip,\qquad R_A=R_B=\frac{W}{2}=10\,kip \]

Maximum Moment

\[ M_{max}=\frac{wL^2}{8}=\frac{1(20)^2}{8}=50\,kip\cdot ft \]

Final Answer

Reactions: \(10\,kip\) at each support. Maximum shear: \(10\,kip\). Maximum moment: \(50\,kip\cdot ft\) at midspan.

Example 3: Cantilever with End Point Load

Beam length
\(L=10\,ft\)
End load
\(P=4\,kip\)
Beam type
Cantilever fixed at left

Fixed Reaction

\[ R=P=4\,kip \]

Fixed-End Moment

\[ M_{max}=PL=4(10)=40\,kip\cdot ft \]

Final Answer

Fixed reaction: \(4\,kip\). Maximum shear: \(4\,kip\). Maximum moment: \(40\,kip\cdot ft\) at the fixed support.

Example 4: Beam with an Applied Point Moment

Beam type
Simply supported
Applied moment
\(M_0\) at a specified location
Important behavior
Moment jump without shear jump

Diagram Behavior

\[ \Delta V=0,\qquad \Delta M=M_0 \]

Key Point

A point moment changes the bending moment diagram suddenly, but it does not add vertical force. Therefore, it does not create a shear jump. This is one of the most common mistakes when drawing beam diagrams by hand.

Engineering Diagram: How Loads Create Shear and Moment

The live diagram above is the main visual for this calculator. The static reference below shows the same core idea without requiring any external image file: loads create reactions, reactions and point loads create shear jumps, and the bending moment diagram is shaped by the area under the shear diagram.

Shear and moment diagram concept for a simply supported beam A simply supported beam with a center point load, equal reactions, a shear diagram with jumps, and a triangular bending moment diagram. Beam Load → Shear Force Diagram → Bending Moment Diagram Point loads and reactions create shear jumps; moment changes with the area under shear. Point Load P RA RBShear Force Diagram +V -VBending Moment Diagram Max M where V changes sign
A point load causes a jump in the shear force diagram. The bending moment diagram reaches its maximum where the shear diagram changes from positive to negative for this symmetric simple-span case.

How to read the diagram quickly

Start at the left end. Reactions and point loads create vertical shear jumps. Distributed loads create sloped shear. The moment diagram rises when shear is positive, falls when shear is negative, and reaches a local maximum or minimum where shear crosses zero.

Reference Values and Common Beam Cases

Reference cases are useful for checking whether the calculator output is reasonable. These formulas apply only to idealized cases with the specific support and loading conditions shown.

Common shear and moment reference cases
Beam CaseReaction ResultMaximum MomentWhere Maximum Moment Occurs
Simple span, center point load \(P\)\(R_A=R_B=P/2\)\(M_{max}=PL/4\)Midspan
Simple span, full uniform load \(w\)\(R_A=R_B=wL/2\)\(M_{max}=wL^2/8\)Midspan
Cantilever, end point load \(P\)\(R=P\)\(M_{max}=PL\)Fixed support
Cantilever, full uniform load \(w\)\(R=wL\)\(M_{max}=wL^2/2\)Fixed support
Simple span with applied point momentDepends on moment location and signMoment diagram contains a jumpOften near the applied moment or support region
Common diagram shape rules
Loading ConditionShear Diagram ShapeMoment Diagram Shape
No distributed loadConstant shearLinear moment
Point loadVertical jumpSlope changes, usually continuous
Uniform distributed loadLinear slopeParabolic curve
Linearly varying distributed loadCurved shearHigher-order curved moment
Applied point momentNo changeVertical jump

Beam Types Supported by This Calculator

The beam type determines what reactions are available and where the maximum moment is likely to occur. Use the correct beam model before interpreting the diagrams.

Supported statically determinate beam types
Beam TypeBest ForMain Reaction BehaviorImportant Note
Simple spanBasic beam checks and homework examplesTwo vertical reactionsMoment is typically zero at ideal pin/roller supports.
Overhanging beamLoads extending beyond supportsTwo vertical reactionsCan create uplift, hogging moment, and maximum moment away from midspan.
Cantilever fixed at leftBalcony, bracket, or projecting beam behaviorVertical reaction plus fixed-end momentMaximum moment often occurs at the fixed support.
Cantilever fixed at rightReverse cantilever layoutVertical reaction plus fixed-end momentLoad distance from the fixed end strongly affects moment.

Special Notes for Overhanging Beams

A load outside the support span can create uplift at the opposite support. Negative reaction is not automatically an error; it may indicate that a hold-down or different support assumption is needed.

Special Notes for Cantilevers

A cantilever fixed support resists both vertical force and moment. Load distance from the fixed end matters because bending moment grows with lever arm, often making the fixed end the controlling location.

Indeterminate Beam Warning

Fixed-fixed beams, propped cantilevers, and continuous beams require compatibility or stiffness-based analysis. They cannot be solved by equilibrium alone.

Units for Shear and Moment Diagrams

Shear has force units, while bending moment has force times length units. Most incorrect answers come from mixing feet and inches, pounds and kips, or metric and U.S. customary values.

Common unit conversions for shear and moment calculations
QuantityCommon UnitsConversion Reminder
Lengthin, ft, mm, m\(1\,ft=12\,in\), \(1\,m=1000\,mm\)
Forcelb, kip, N, kN\(1\,kip=1000\,lb\), \(1\,kN=1000\,N\)
Distributed loadlb/ft, kip/ft, N/m, kN/mMultiply by loaded length to get resultant force.
Momentlb-in, lb-ft, kip-ft, N-m, kN-mMoment equals force times lever arm.
Stress follow-uppsi, ksi, Pa, MPaRequires section properties such as \(I\), \(S\), or \(c\).

Hidden unit trap

A moment of \(50\,kip\cdot ft\) is not the same as \(50\,kip\cdot in\). If you use the moment in a bending stress formula with section modulus in \(in^3\), convert \(kip\cdot ft\) to \(kip\cdot in\) first.

Shear Diagram vs. Moment Diagram vs. Deflection Diagram

Shear and moment diagrams show internal force demand. A deflection diagram shows displacement. All three are related, but they answer different engineering questions.

Comparison of common beam diagrams and related calculations
Tool or DiagramWhat It ShowsBest Used ForMain Limitation
Shear force diagramInternal vertical shear force \(V(x)\)Support force, web shear, and connection checksDoes not directly show bending stress or deflection
Bending moment diagramInternal bending moment \(M(x)\)Flexural strength and section sizingRequires section properties for stress checks
Deflection calculationBeam displacement under loadServiceability and stiffness checksRequires material stiffness and moment of inertia
Bending stress calculationStress from moment and section geometryChecking whether a member has enough flexural capacityRequires \(M\), section modulus, and allowable or design stress

Common Mistakes When Drawing Shear and Moment Diagrams

Most diagram errors come from skipped reactions, wrong sign convention, wrong load placement, or misunderstanding how point loads and point moments affect the diagrams.

Common Mistakes

  • Drawing the shear diagram before solving support reactions.
  • Treating a point load like a distributed load.
  • Forgetting that point moments jump the moment diagram but not the shear diagram.
  • Assuming maximum moment is always at midspan.
  • Mixing ft and in when using moment or section properties.
  • Forgetting to include self-weight as a distributed load when it matters.
  • Using a simple-span model for a fixed, propped, or continuous beam.

Better Practice

  • Solve reactions first using \(\sum F_y=0\) and \(\sum M=0\).
  • Mark every load, support, distributed load start/end, and applied moment location.
  • Use the key values table to check values immediately before and after jumps.
  • Look for maximum moment where shear crosses zero or where the moment diagram jumps.
  • Convert all force and length units before doing manual checks.
  • Use indeterminate analysis for fixed-fixed, propped cantilever, or continuous beams.

Troubleshooting Unexpected Results

If the diagram looks wrong, first check the beam model, load direction, load location, and units. The math may be correct for the inputs even if the inputs do not match the real beam.

Common shear and moment calculator problems and fixes
ProblemLikely CauseFix
Support reaction is negativeOverhanging load or uplift condition is causing one support to lift.Check support assumptions, load placement, and whether hold-downs are required.
Moment is not zero at a simple supportAn applied point moment may be located at the support, or the beam model is not a simple pin/roller span.Check applied moments and beam type.
Diagram jumps at an unexpected locationA point load, support, or applied moment may be entered at the wrong \(x\)-coordinate.Review every load location and unit selector.
Distributed load result seems too largeLoad intensity or loaded length may be wrong.Multiply intensity by loaded length manually to check the equivalent resultant.
Maximum moment location seems wrongZero shear may occur away from midspan, especially with unsymmetrical loads.Use the key values table and zero-shear markers.
Cantilever moment is much larger than expectedLoad is far from the fixed support, increasing the lever arm.Check \(M=P x\) or \(M=wL^2/2\) style hand estimates.

Suspicious result examples

Be cautious if a simple beam shows reactions that do not add up to the total load, if a large point load does not create a shear jump, if a point moment changes shear, or if the moment units do not match the force and length units used in your manual check.

Assumptions, Sources, and Limitations

This calculator is intended for educational use, preliminary beam checks, and statically determinate structural analysis. It uses equilibrium and standard load-shear-moment relationships.

Determinate Beam Assumption

The calculator is intended for simple span, overhanging, and cantilever beams that can be solved using static equilibrium.

Load Assumption

Loads are idealized as point loads, distributed loads, and applied point moments at specified locations.

Support Assumption

Supports are idealized. Real supports, bearings, fixity, settlement, and connection flexibility can change behavior.

Design Limitation

The calculator does not check material strength, section capacity, deflection, buckling, fatigue, load combinations, or code compliance.

What this calculator does not verify
Not CheckedWhy It Matters
Shear capacityThe maximum shear must be compared with member and connection capacity.
Bending capacityThe maximum moment must be compared with allowable or design flexural strength.
DeflectionA beam can pass strength checks and still fail serviceability limits.
Load combinationsDead, live, roof, snow, wind, seismic, and construction loads may need code-specific combinations.
Self-weightSelf-weight must be entered as a distributed load if it is not separately included.
Partial fixity or connection flexibilityReal supports may not behave as perfect pins, rollers, or fixed ends.
Moving loadsVehicles, cranes, and bridge loads may require influence lines or load position envelopes.
Lateral-torsional bucklingUnbraced beams may fail by instability before reaching basic bending capacity.

Calculation basis and source note

The diagram logic is based on standard engineering mechanics relationships for internal shear and bending moment, including \(\sum F_y=0\), \(\sum M=0\), \(\frac{dV}{dx}=-w(x)\), and \(\frac{dM}{dx}=V(x)\). For additional background, see the open engineering mechanics reference on shear and moment diagrams from Engineering LibreTexts.

For final structural design, verify the beam against applicable codes, project load combinations, material properties, serviceability limits, connection requirements, and professional engineering judgment.

Related Calculators and Next Steps

After finding shear and moment, the next step is usually to check stress, stiffness, geometry, or section properties. Verify that these linked tools are live on your site before publishing.

Glossary of Shear and Moment Diagram Terms

These definitions explain the main terms used in the calculator and diagram output.

Shear Force

Internal vertical force in a beam section, commonly shown as \(V(x)\).

Bending Moment

Internal bending effect in a beam section, commonly shown as \(M(x)\).

Support Reaction

Force or moment provided by a support to keep the beam in equilibrium.

Point Load

A concentrated force applied at one location on the beam.

Distributed Load

A load spread over a length of beam, such as uniform, triangular, or trapezoidal loading.

Applied Moment

A concentrated couple that causes a jump in the moment diagram without changing the shear diagram.

Sagging Moment

Positive bending moment convention commonly associated with sagging curvature, often visualized as a smile shape.

Hogging Moment

Negative bending moment convention commonly associated with reverse curvature over or near a support.

Frequently Asked Questions

What does a shear and moment diagram calculator calculate?

It calculates support reactions, shear force values, bending moment values, maximum shear, maximum moment, values at selected beam locations, and key discontinuities for statically determinate beams.

Why does the shear diagram jump at a point load?

A point load changes the internal vertical force instantly at its location, so the shear diagram jumps by the magnitude of that point load.

Why does the bending moment diagram slope change?

The slope of the bending moment diagram equals the shear force, so when shear changes, the slope of the moment diagram changes.

Why is maximum bending moment often where shear equals zero?

Because \(\frac{dM}{dx}=V\), a zero-shear location is where the moment diagram has a local maximum or minimum, unless a boundary, fixed support, or applied moment jump controls.

Does an applied point moment affect the shear diagram?

No. An applied point moment creates a jump in the bending moment diagram but does not create a jump in the shear force diagram.

Can the calculator handle distributed loads and point moments?

Yes. The calculator can be used with point loads, uniform distributed loads, linearly varying distributed loads, and applied point moments at different beam locations.

Does this calculator solve indeterminate beams?

No. It is intended for statically determinate beams such as simple spans, overhanging beams, and cantilevers. Fixed-fixed, propped cantilever, and continuous beams require indeterminate analysis.

Can shear and moment diagrams be used for final beam design?

Shear and moment diagrams are essential for beam design checks, but final design also requires load combinations, material properties, member capacity, deflection limits, connection checks, bracing checks, code requirements, and professional engineering judgment.

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