HomeCalculatorsMechanicalBeams & DeflectionShear and Moment Calculator
Mechanical calculator

Shear and Moment Calculator

Shear and bending moment at a cut in a simply supported span. Point forces and concentrated moments only. Runs locally. Not beam deflection.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary CVP VERIFIED · production STALE · CVP protocol 1.0.0-proposed · Engineering assurance
Input interpretation
Enter values to calculate.
Result
—
Assurance
Engineering
Declared partition coverage
PASS · 2/2 declared partitions (domain, invalid-domain) · Matrix
Known limitations
  • Physics L1 gap capability
  • Core CVP does not include live graph, viewport, or pointer interaction.
Model
Support reactions and the shear and bending moment at one cut of a simply supported span.
Scope
Calculation runs locally in the browser; values are not uploaded.
Verification
Engine tested · Source checked · v1.0.0 · CVP VERIFIED · production STALE · CVP protocol 1.0.0-proposed · Engineering assurance· View Manifest · CVP overview · Specification
Versions
Calculation 1.0.0 · CVP protocol 1.0.0-proposed
CVP identity
0/0 property · digest 97eb4991dc8d
Legacy regression
6/6 tests · Production surface contract 6/6
Trust layers
Verification VERIFIED · Production STALE · overall VERIFIED_STALE
CVP status
STALE · Capability production binding: STALE · Site report: STALE · Evidence changed after the last successful production attestation. Re-attestation required.
Reference
O1 model · O2 expected_values · O2 numerical_behavior
Interfaces
PASS · UI (SSR) / REST / MCP — ui-ssr is query-result HTML, not a live browser session.
Supplemental domain review
Not performed
Named expert review
Not performed
CVP suite
1/1 golden · 4/4 CVP boundary · 3/3 invalid · 1/1 cross-interface · 6/6 CVP contract · Manifest
Sources
  • Hibbeler, Engineering Mechanics: Statics — Internal loadings
  • Gere and Goodno, Mechanics of Materials — Internal loadings
Sources
Evidence
2 legacy golden · 4 legacy boundary · legacy regression suite · 1/1 oracle-backed golden · 3/3 invalid · Artifact integrity PASS
STALE · Last attested schema matched 1.0.0 snapshot / local build · Semantic contract ✓ · Last attestation PASS · current evidence changed · re-attestation required · CVP STALE · attestation STALE — Production CURRENT withheld · Public/cache ✓ · Origin ✓
Semantic contract
PASS
Full verification

Manifest identity, reference classes, interfaces, suite, and production records.

Formulas

Core equations used by this calculator.

ReactionsAy + By + ΣFy = 0, By L + Σ(Fy x) + ΣM = 0
SectionV and M balance the left side of the cut
iA load exactly at the cut stays on the right. This page does not integrate a distributed load and does not compute deflection.

How to use

1

Enter the span and the section

L is the distance between supports. s is measured from the left support and must lie strictly between them.

2

Enter point forces as Fy, x

Upward is positive. x is measured from the left support.

3

Read V and M on the left face

CCW moment is positive. Ay and By are the support reactions.

Example calculations

Common configurations with formula and result.

ϟ

Downward 10 N at midspan

L = 4 m, section at 1 m

Ay = By = 5 N
V = −5 N, M = 5 N·m
ϟ

Section at the load

The 10 N load stays on the right of s = 2 m

M = P L / 4
M = 10 N·m

Shear and Moment calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
Vertical reactions of a simple span, then the shear and bending moment on the left face of a cut. Upward force and CCW moment are positive.
What it calculates
Support reactions and the shear and bending moment at one cut of a simply supported span.
Inputs
  • L
  • s
  • forces?
  • moments?
Outputs
  • Ay
  • By
  • V
  • M
Formula
ΣFy = 0 and ΣM about the left support = 0, then the left-face V and M
Assumptions
  • Calculation runs locally in the browser; values are not uploaded.
  • Keep units consistent with the labels on each field.
  • A load exactly at the cut stays on the right. This page does not integrate a distributed load and does not compute deflection.
Units
  • Length in m, force in N, moment in N·m. Upward and CCW are positive.
Boundary conditions
  • missing L or s → MISSING_REQUIRED_INPUT
  • L ≤ 0 → VALUE_MUST_BE_POSITIVE
  • s outside (0, L) → VALUE_OUT_OF_RANGE
  • a load outside the span → INVALID_INPUT
Example
L=4, s=1, forces=-10,2 → V=-5 N, M=5 N·m
Validation cases

3 published on this page · 6/6 tests · Production surface contract 6/6 · View evidence

  • L=4 s=1 forces=-10,2 → Ay=5, By=5, V=-5, M=5
  • L=4 s=2 forces=-10,2 → V=-5, M=10
  • L=4 s=4 forces=-10,2 → VALUE_OUT_OF_RANGE
Sources
  • Hibbeler, Engineering Mechanics: Statics — Internal loadings
    Supports: Shear and bending moment from equilibrium of a cut segment
  • Gere and Goodno, Mechanics of Materials — Internal loadings
    Supports: Supports the page formula: Ay + By + ΣFy = 0, By L + Σ(Fy x) + ΣM = 0
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Find the shear and bending moment at one cut of a simply supported span.

Supported and not supported

Supported: point forces, concentrated moments, the two vertical reactions, and V and M on the left face of the cut.

Not supported: distributed loads, beam deflection, and indeterminate supports. /calc/mechanical is not open.

Agent / API notes

Capability id: mechanical.statics.shear_moment · tool id: shear-moment · pin 1.0.0.

{ "L": 4, "s": 1, "forces": "-10,2" }

A force row is Fy,x, with upward positive and x measured from the left support. Share the link with L, s, forces, and moments when used. The result is not written into the link.

Other calculators in this family: Beam Deflection Calculator, Beam Moment Deflection Calculator, Beam Moment Maximum Deflection Calculator, Cantilever Deflection Calculator, Cantilever Intermediate Deflection Calculator, Cantilever Load at a Station Calculator, Cantilever Moment at the Couple Calculator, Cantilever Moment Deflection Calculator . Explore all Beams & Deflection.

→ Beam Deflection Calculator Midspan deflection of a simply supported span with one concentrated load. δ = P L³/(48 E I). I is an input. Runs locally. › → Beam Moment Deflection Calculator Midspan deflection of a simply supported span with one end moment. δ = M L²/(16 E I). I is an input. Runs locally. › → Beam Moment Maximum Deflection Calculator Largest deflection of a simply supported span with one end moment. δ = M L²/(9√3 E I) at x = L/√3. I is an input. Runs locally. › → Cantilever Deflection Calculator Free-end deflection of a cantilever with one concentrated load at the tip. δ = P L³/(3 E I). I is an input. Runs locally. › → Cantilever Intermediate Deflection Calculator Deflection at a concentrated load on a cantilever. δ = P a³ / (3 E I). a is measured from the fixed end. Runs locally. › → Cantilever Load at a Station Calculator Deflection at station x for a cantilever load at a. x = a is the load page. x = L is the free-end page. Runs locally. › → Cantilever Moment at the Couple Calculator Deflection at a concentrated moment on a cantilever. δ = M a² / (2 E I). a is measured from the fixed end. Runs locally. › → Cantilever Moment Deflection Calculator Free-end deflection of a cantilever with one concentrated moment. δ = M L²/(2 E I). I is an input. Runs locally. ›

Frequently asked questions

Key distinctions behind the calculation.

Does this compute deflection?

No. It returns the shear and bending moment at one cut, plus the two vertical reactions. Slope, deflection, and distributed loads are out of scope.

What does a negative shear mean?

Upward force is positive. V is the vertical force on the left face of the cut. For a downward midspan load, V is negative to the left of the load and positive to the right.