{
  "$schema": "https://slfy.solidify.studio/schema/slfy-0.1.schema.json",
  "format": "slfy",
  "version": "0.1",
  "model": {
    "id": "beam-question",
    "title": "Simply supported beam: point load and UDL",
    "summary": "A 6 m simply supported beam with a 20 kN point load at 2 m from A and 5 kN/m over its whole span.",
    "units": "m",
    "question": {
      "text": "A simply supported beam of span 6 m carries a point load of 20 kN at 2 m from A and a uniformly distributed load of 5 kN/m over its whole length. Determine the reactions at A and B and the maximum bending moment.",
      "find": [
        "the reactions at A and B",
        "the maximum bending moment"
      ]
    },
    "parameters": [
      {
        "id": "L",
        "label": "Span",
        "symbol": "L",
        "value": 6,
        "min": 3,
        "max": 10,
        "step": 0.5,
        "unit": "m"
      },
      {
        "id": "P",
        "label": "Point load",
        "symbol": "P",
        "value": 20,
        "min": 0,
        "max": 50,
        "step": 1,
        "unit": "kN"
      },
      {
        "id": "a",
        "label": "Load position from A",
        "symbol": "a",
        "value": 2,
        "min": 0.5,
        "max": 5,
        "step": 0.5,
        "unit": "m"
      },
      {
        "id": "w",
        "label": "Distributed load",
        "symbol": "w",
        "value": 5,
        "min": 0,
        "max": 15,
        "step": 0.5,
        "unit": "kN/m"
      }
    ],
    "parts": [
      {
        "id": "beam",
        "name": "Beam",
        "material": "steel",
        "role": "static",
        "position": [
          0,
          0,
          0
        ],
        "explode": [
          0,
          0,
          0.1
        ],
        "shapes": [
          {
            "kind": "box",
            "sx": "L",
            "sy": 0.25,
            "sz": 0.15
          }
        ]
      },
      {
        "id": "support_a",
        "name": "Pin support A",
        "material": "castIron",
        "role": "static",
        "explode": [
          0,
          0,
          0.1
        ],
        "mount": {
          "kind": "against",
          "target": "beam",
          "face": "-y",
          "shift": [
            "-L / 2",
            0,
            0
          ]
        },
        "shapes": [
          {
            "kind": "box",
            "sx": 0.3,
            "sy": 0.25,
            "sz": 0.3
          }
        ]
      },
      {
        "id": "support_b",
        "name": "Roller support B",
        "material": "castIron",
        "role": "static",
        "explode": [
          0,
          0,
          0.1
        ],
        "mount": {
          "kind": "against",
          "target": "beam",
          "face": "-y",
          "shift": [
            "L / 2",
            0,
            0
          ]
        },
        "shapes": [
          {
            "kind": "cylinder",
            "rotation": [
              1.5708,
              0,
              0
            ],
            "r": 0.12,
            "h": 0.3
          }
        ]
      }
    ],
    "annotations": [
      {
        "id": "p",
        "kind": "force",
        "label": "P",
        "magnitude": "P",
        "unit": "kN",
        "anchor": {
          "part": "beam",
          "at": "+y",
          "along": 0.33
        }
      },
      {
        "id": "ra",
        "kind": "force",
        "label": "R_A",
        "magnitude": "R_A",
        "unit": "kN",
        "anchor": {
          "part": "support_a",
          "at": "-y"
        },
        "direction": "+y"
      },
      {
        "id": "rb",
        "kind": "force",
        "label": "R_B",
        "magnitude": "R_B",
        "unit": "kN",
        "anchor": {
          "part": "support_b",
          "at": "-y"
        },
        "direction": "+y"
      }
    ],
    "calculations": [
      {
        "id": "W",
        "label": "Total distributed load",
        "symbol": "W",
        "formula": "w * L",
        "unit": "kN",
        "latex": "W = wL",
        "step": "Replace the distributed load by its total, acting at mid-span."
      },
      {
        "id": "R_B",
        "label": "Reaction at B",
        "symbol": "R_B",
        "formula": "(P * a + W * L / 2) / L",
        "unit": "kN",
        "latex": "R_B = \\frac{Pa + W L/2}{L}",
        "step": "Take moments about A to find R_B.",
        "answer": true
      },
      {
        "id": "R_A",
        "label": "Reaction at A",
        "symbol": "R_A",
        "formula": "P + W - R_B",
        "unit": "kN",
        "latex": "R_A = P + W - R_B",
        "step": "Resolve vertically to find R_A.",
        "answer": true
      },
      {
        "id": "M_max",
        "label": "Maximum bending moment",
        "symbol": "M_{max}",
        "formula": "R_A * a - w * a ^ 2 / 2",
        "unit": "kN·m",
        "latex": "M_{max} = R_A a - \\frac{w a^2}{2}",
        "step": "The shear force changes sign under the point load, so the bending moment is greatest there.",
        "answer": true
      }
    ],
    "charts": [
      {
        "id": "bmd",
        "title": "Bending moment diagram",
        "x": {
          "label": "x",
          "unit": "m",
          "from": "0",
          "to": "L"
        },
        "y": {
          "label": "M",
          "unit": "kN·m"
        },
        "series": [
          {
            "id": "m",
            "label": "M",
            "formula": "R_A * x - w * x ^ 2 / 2 - P * mac(x - a, 1)"
          }
        ]
      }
    ]
  },
  "view": {
    "camera": {
      "position": [
        0.52,
        0.38,
        0.58
      ],
      "target": [
        0,
        0,
        0
      ]
    },
    "extent": 0.5,
    "floorY": -0.2,
    "cut": {
      "enabled": true,
      "normal": [
        0,
        0,
        1
      ],
      "pos": 0
    }
  },
  "meta": {
    "generator": "Solidify (solidify.studio)",
    "license": "CC-BY-4.0",
    "created": "2026-11-10"
  }
}