2025-08-21 14 min
Shear Force Calculator
Calculate shear force at any section of a beam with point loads or UDL. Includes shear force diagram values and maximum shear.
Calculator
Unit System
Beam Type
Point Load (P)(N)
N
Beam Span (L)(mm)
mm
Load Position (a)(mm) Help
mm
Distance from left support
UDL Intensity (w)(N/mm)
N/mm
Evaluate at Position (x)(mm) Help
mm
Distance from left support
Decimal Precision
Results update live as you type
Results
Normal
Shear at Position
10000.00N
Maximum Shear
10000.00N
Zero Shear Location
2500.00mm
Visualizations
Results Overview
10,000NShear at Position
10,000NMaximum Shear
2,500NZero Shear Location
Formula
Shear force at any section is the algebraic sum of all vertical forces acting to one side of that section.
V(x) = Sum of vertical forces to the left of section x
Alternative Form
dM/dx = V | tau = V*Q/(I*b)
Variables
| Symbol | Name | Unit | Description |
|---|---|---|---|
| V | Shear Force | N | Net vertical force at a cross-section |
| Ra | Left Reaction | N | Support reaction at left end |
| P | Point Load | N | Concentrated force on the beam |
| w | UDL Intensity | N/mm | Load per unit length |
Explanation
Shear force represents the tendency of one part of a beam to slide relative to the adjacent part. It is critical for designing connections and web members.
Derivation
From vertical equilibrium of a differential beam element, the change in shear equals the applied load: dV/dx = -w(x).
Step-by-Step Calculation
Follow each step to understand how the result is calculated from your inputs.
Step 1
Calculate support reactions using equilibrium equations
Result: Reactions determined
Step 2
Identify the section of interest along the beam
Result: Section location identified
Step 3
Sum all vertical forces to the left of the section
Result: Shear force calculated
Step 4
Determine maximum shear force for design
Result: Maximum shear identified
Step 5
Locate points of zero shear (where moment is maximum)
Result: Critical sections found
Final Answer
10000.00
Worked Examples
See how the calculator works with different scenarios.
Scenario
5 m beam with 20 kN at midspan.
Inputs
Beam Type:Simply Supported
Load (P):20000 N
Span (L):5000 mm
Load Position (a):2500 mm
Shear Position (x):1000 mm
Calculation
Ra = Rb = 10000 N. At x=1000: V = 10000 N (left of load). Vmax = 10000 N.
Result
V at x=1000 = 10000 N, Vmax = 10000 N
Interpretation
Shear is constant at 10 kN from support to midspan. It drops to -10 kN after the load. Zero shear at midspan indicates maximum moment.
Understanding Your Result
Your Result: Shear at Position: 10000.00 N
Typical range: Shear forces range from a few kN for light beams to several MN for heavy structural members. Design shear stress is typically 0.4-0.6 of yield strength.
What This Means
Shear force analysis determines the vertical sliding tendency at any section of a beam under applied loads.
Why It Matters
Shear failure can be sudden and catastrophic. Beams must have adequate shear capacity, especially near supports where shear is highest.
Professional Interpretation
Compare maximum shear against the beam's shear capacity. Check shear at supports, at point loads, and where concentrated moments change the diagram.
Recommendations
- •Always check shear at support locations
- •Use the correct sign convention consistently
- •Verify zero shear locations for maximum moment
Educational Content
Introduction
Shear force analysis is fundamental to beam design and structural analysis.
Concept Explanation
Shear force results from the imbalance of vertical forces. The shear diagram shows how this imbalance varies along the beam.
Applications
▸Structural steel design
▸Reinforced concrete beams
▸Machine tool structures
▸Aerospace structures
▸Bridge engineering
Benefits
- •Simple graphical method for force visualization
- •Identifies critical sections for design
- •Foundation for shear stress calculations
Limitations
- •Assumes linear elastic behavior
- •Does not account for stress concentrations
- •Valid only for slender beams (L/h > 4)
Best Practices
- •Draw the complete shear diagram before analyzing moments
- •Check equilibrium: sum of reactions equals total load
- •Use consistent sign convention throughout
Common Misconceptions
Myth: Shear is always maximum at midspan
Truth: Shear is typically maximum at supports, not midspan. Zero shear occurs at the point of maximum moment.
Practical Tips
- •Shear is constant between point loads
- •UDL causes linear shear variation
- •Zero shear marks the location of maximum bending moment
- •Shear at supports equals the reaction force
Common Mistakes
Confusing shear force with shear stress
Shear force (V) is the resultant force; shear stress (tau) is force per area. tau = V*Q/(I*b).
Wrong sign convention
Use standard convention: positive shear acts downward on the right face of a section.
Forgetting concentrated moments
Concentrated moments do not affect the shear diagram; they only change the moment diagram.
Assumptions
This calculator makes the following assumptions to provide estimates:
Slender Beam: Beam is long compared to depth (L/h > 4).
Linear Elastic: Material obeys Hooke's law throughout.
Small Deflections: Deflections do not significantly alter the loading geometry.
Limitations
Be aware of these limitations when using this calculator:
Deep Beams: Shear deformation becomes significant for L/h < 4.
Stress Concentrations: Not captured by beam theory near loads and supports.
Dynamic Loading: Static shear analysis does not apply to impact or vibration.
Frequently Asked Questions
Answers to common questions about this calculator.
What is shear force?
Shear force at any section of a beam is the algebraic sum of all vertical forces acting on one side of that section. It tends to slide one part of the beam relative to the adjacent part.
How is shear force calculated?
Shear force at a section equals the sum of all vertical forces to the left (or right) of the section. Upward forces are positive, downward forces are negative by convention.
What is a shear force diagram?
A shear force diagram (SFD) plots the variation of shear force along the beam length. Horizontal lines indicate constant shear, sloped lines indicate UDL regions, and steps indicate point loads.
What is the maximum shear force?
Maximum shear force typically occurs at the supports. For a simply supported beam with central point load, Vmax = P/2. For UDL, Vmax = w*L/2 at the supports.
How does a point load affect the shear diagram?
A point load causes an instantaneous step change in the shear diagram. The magnitude of the step equals the load. The shear remains constant between point loads.
How does a UDL affect the shear diagram?
A uniformly distributed load causes a linearly sloped shear diagram. The slope equals -w (the load intensity). The shear decreases by w*L over the UDL span.
Where is shear force zero?
Shear force is zero where the shear diagram crosses the horizontal axis. This typically occurs under point loads or at the center of symmetric beams. Zero shear corresponds to maximum bending moment.
What is the relationship between shear and moment?
The derivative of bending moment equals shear force: dM/dx = V. Where shear is zero, the moment is at a local maximum or minimum. Where shear changes sign, the moment peaks.
How do you calculate shear at a specific point?
Sum all vertical forces to the left of the point. Positive forces (upward) add to shear, negative forces (downward) subtract. The result is the shear force at that section.
What is the sign convention for shear force?
Standard convention: positive shear acts downward on the right face of a section (or upward on the left face). This causes clockwise rotation of the section element.
How does an eccentric load affect shear?
An eccentric load creates both shear and torsion. The shear component follows standard beam theory; the torsion must be analyzed separately using torsion formulas.
What is the shear force at a support?
The shear force at a support equals the reaction force at that support. For the left support, shear starts at +Ra. For the right support, shear ends at -Rb.
How do multiple loads affect shear?
Multiple loads create a series of steps and slopes in the shear diagram. Each point load creates a step, each UDL creates a sloped region. Superposition applies for linear elastic behavior.
What is the shear force for a cantilever beam?
For a cantilever with end point load P, the shear is constant at V = P throughout. For UDL w, the shear varies linearly from w*L at the fixed end to 0 at the free end.
How does self-weight affect shear?
Self-weight acts as a UDL and adds to the shear diagram as a linear slope. For a simply supported beam, self-weight w adds w*L/2 to each support reaction.
What is the maximum shear stress in a beam?
Maximum shear stress occurs at the neutral axis: tau_max = V*Q/(I*b). For a rectangular section, tau_max = 3*V/(2*A), which is 1.5 times the average shear stress.
How do you handle concentrated moments in shear?
Concentrated moments do not affect the shear force diagram. They cause a step change in the bending moment diagram but have no effect on shear at any section.
What is the shear force at the point of maximum moment?
At the point of maximum bending moment, the shear force is zero. This is because dM/dx = V, and the derivative is zero at a local maximum.
How do support conditions affect shear?
Support conditions determine the reaction forces, which set the boundary values of the shear diagram. Fixed supports can carry shear plus moment; pins and rollers carry only shear.
What is the shear force for a beam with overhang?
For an overhanging beam, the shear diagram extends beyond the supports. The overhang creates additional shear that may cause uplift (negative reaction) at the adjacent support.
How do you verify a shear force diagram?
Check that the shear at the right end equals the negative of the right reaction. Verify that steps match point loads and slopes match UDL intensities.
What is the difference between shear force and shear stress?
Shear force is the resultant vertical force at a section. Shear stress is the force per unit area acting on the cross-section. They are related by tau = V*Q/(I*b).
How does shear force relate to beam design?
Shear force determines the required shear capacity of the beam. Beams must resist both bending and shear. Shear is often critical near supports.
What is the shear force diagram for a simply supported beam with two point loads?
The diagram shows constant shear segments between loads and supports. Each load creates a step. The shear is maximum near the heavier load or closer support.
How do you calculate shear force from a distributed load?
For UDL of intensity w, shear at distance x from left support: V(x) = Ra - w*x for x less than the UDL extent. The shear decreases linearly.
What is the shear force at the center of a simply supported beam?
For a central point load P, the shear at center is Ra - P/2 = 0 (just left of load) or -P/2 (just right of load). For UDL, V at center = 0 for symmetric loading.
What is the typical shear force range for steel beams?
Shear forces in steel beams range from a few kN for light floor joists to several MN for heavy bridge girders. Typical design shear ranges from 10 to 500 kN.
How do you handle point loads on shear diagrams?
Point loads create discontinuities (steps) in the shear diagram. Plot constant shear between loads, with vertical jumps at each load location.
What is the shear force for a propped cantilever?
A propped cantilever is indeterminate. The shear diagram depends on both the support reaction and applied loads. Use compatibility methods to find the prop reaction first.
How does load position affect maximum shear?
Moving a point load toward a support increases the shear at that support. Maximum shear occurs when the load is directly adjacent to the support.
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Glossary
Technical terms used in mortgage calculations explained in plain language.
- Shear Force
- The algebraic sum of vertical forces at a cross-section of a beam.
- Shear Diagram
- A plot showing shear force variation along the beam length.
- Sign Convention
- Standard convention defining positive and negative shear directions.
- Zero Shear
- The location where shear force equals zero, typically at maximum bending moment.
Authoritative References
Trusted sources and standards referenced by this calculator.
Applicable Standards
AISC 360 - Shear DesignEurocode 3 - Shear ResistanceACI 318 - Shear in Concrete
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Page Information
Last Updated:
2025-08-21
Version:
2.0.0
References:
License:
Free to use for educational and professional purposes.