Source: https://guthlabs.ai/docs/instruments/shear-moment-diagram-plotter/mechanism/

instrument mechanism / verified-with-binding-errata

# Shear & Moment Diagram Plotter mechanism

The inspectable method record for Shear & Moment Diagram Plotter, kept separate from implementation and qualification.

Status: **VERIFIED_WITH_ERRATA**Lifecycle: **verified-with-binding-errata**

## Model scope

The governing differential equations are correct only with explicit sign conventions and distributional jump rules. The specification is not yet implementation-deterministic because it omits reaction-equilibrium details, numerical integration/step behavior, discontinuity handling, units schema, and extrema tie/one-sided conventions. Add these definitions before release.

- The differential relations dV/dx=-w(x) and dM/dx=V(x) are standard under a stated sign convention, but the specification does not define the signs of loads, reactions, shear, bending moment, or applied couples.

- Point loads and point moments are not represented by ordinary derivatives alone: a point load produces a jump in V, and an applied concentrated moment produces a jump in M. The jump magnitudes and signs must be explicitly defined.

- The specification does not state how support reactions are computed from equilibrium before integrating the diagrams. This is required for arbitrary support positions and load combinations.

- Numeric integration is underspecified: no integration method, step size, discontinuity handling, interpolation rule, or numerical tolerance is given. Exact piecewise integration or event-aligned integration is needed to avoid errors at point loads and moments.

- Mmax location/value is underspecified when the maximum occurs at a discontinuity, at a support, or over a flat interval. One-sided locations and tie handling should be defined.

- The honest label 'statically determinate beams only' is appropriate, but the input schema must reject mechanisms, indeterminate supports, invalid support locations, and geometrically unstable configurations.

## Units and conventions

- All distances are in metres, forces in kN, distributed loads in kN/m, and concentrated moments in kN·m unless explicitly converted.

- Positive distributed load w is downward; positive shear V is upward on the left face; positive bending moment M is sagging; positive applied concentrated moment is counterclockwise under the convention used in the test vectors.

- For a downward point load P, V jumps by -P. For a positive counterclockwise applied point moment C, M jumps by -C in the test-vector convention.

- Beam coordinates satisfy 0 <= x <= L, and supports and loads lie within the beam span.

- Reactions are calculated using static equilibrium before applying dV/dx=-w and dM/dx=V.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "beam_length_m": 6,
    "supports": [
      {
        "type": "pin",
        "position_m": 0
      },
      {
        "type": "roller",
        "position_m": 6
      }
    ],
    "loads": [
      {
        "type": "point_load",
        "position_m": 3,
        "magnitude_kN": 12,
        "direction": "downward"
      }
    ],
    "sign_convention": "sagging_M_positive",
    "integration": "exact_piecewise",
    "sampled_x_m": [
      0,
      2,
      3,
      "3+",
      "4",
      6
    ]
  },
  "expected_outputs": {
    "reactions": {
      "R_A_kN": 6,
      "R_B_kN": 6
    },
    "sampled_points": [
      {
        "x_m": 0,
        "V_kN": 6,
        "M_kNm": 0
      },
      {
        "x_m": 2,
        "V_kN": 6,
        "M_kNm": 12
      },
      {
        "x_m": "3-",
        "V_kN": 6,
        "M_kNm": 18
      },
      {
        "x_m": "3+",
        "V_kN": -6,
        "M_kNm": 18
      },
      {
        "x_m": 4,
        "V_kN": -6,
        "M_kNm": 12
      },
      {
        "x_m": 6,
        "V_kN": -6,
        "M_kNm": 0
      }
    ],
    "Mmax": {
      "location_m": 3,
      "value_kNm": 18,
      "location_note": "continuous M; V changes from +6 to -6 at x=3"
    }
  },
  "working": "Equilibrium: R_A+R_B-12=0. Taking moments about A: 6R_B-12(3)=0, so R_B=36/6=6 kN and R_A=12-6=6 kN. For 0<=x<3, w=0, so V=6 kN and M(x)=6x; M(2)=6(2)=12 kN·m and M(3-)=6(3)=18 kN·m. At x=3, the downward point load causes V(3+)=V(3-)-12=6-12=-6 kN, while M is continuous, so M(3+)=18 kN·m. For 3<x<=6, M(x)=18-6(x-3); M(4)=18-6(1)=12 kN·m and M(6)=18-6(3)=0. Since V is positive before x=3 and negative after it, Mmax=18 kN·m at x=3."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

A zero-length beam with coincident supports produces a 0/0 reaction calculation and has no determinate beam solution. The instrument must reject that input; accepting it would create undefined reactions and invalid diagrams.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/shear-moment-diagram-plotter/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/shear-moment-diagram-plotter/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/shear-moment-diagram-plotter/qualification/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json`

- `evidence-tranche6/tranche6-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`