Shear & Moment Diagram Plotter mechanism

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

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