{
  "title": "Beam Bending Stress Calculator",
  "author": "Carlos Acosta",
  "version": "1.0.0",
  "description": "Interactive calculator for maximum bending stress in rectangular wooden beams under uniform load. Implements classical beam theory: σ = M/S where M = wL²/8 and S = bh²/6.",
  "formulas": {
    "maximum_bending_moment": {
      "symbol": "M",
      "equation": "M = (w × L²) ÷ 8",
      "units": "ft-lbs",
      "description": "Maximum moment at mid-span for simply-supported beam with uniform distributed load"
    },
    "section_modulus": {
      "symbol": "S",
      "equation": "S = (b × h²) ÷ 6",
      "units": "in³",
      "description": "Geometric property of rectangular cross-section resisting bending"
    },
    "bending_stress": {
      "symbol": "σ",
      "equation": "σ = (M × 12) ÷ S",
      "units": "psi",
      "description": "Maximum tensile/compressive fiber stress at extreme fibers of beam"
    }
  },
  "inputs": {
    "beam_width": {
      "id": "beamWidth",
      "symbol": "b",
      "units": "inches",
      "default": 3.5,
      "range": [0.5, 24]
    },
    "beam_height": {
      "id": "beamHeight",
      "symbol": "h",
      "units": "inches",
      "default": 9.25,
      "range": [1.5, 36]
    },
    "span_length": {
      "id": "spanLength",
      "symbol": "L",
      "units": "feet",
      "default": 12,
      "range": [2, 100]
    },
    "uniform_load": {
      "id": "uniformLoad",
      "symbol": "w",
      "units": "lbs/ft",
      "default": 50,
      "range": [10, 5000]
    }
  },
  "outputs": {
    "moment_result": {
      "id": "momentResult",
      "symbol": "M",
      "units": "ft-lbs"
    },
    "section_modulus_result": {
      "id": "sectionModulus",
      "symbol": "S",
      "units": "in³"
    },
    "stress_result": {
      "id": "stressResult",
      "symbol": "σ",
      "units": "psi"
    }
  },
  "grounding": {
    "wikidata_entity": "Q49167267",
    "entity_slug": "bending-stress",
    "verification_urls": [
      "https://mechanicalc.com/reference/beam-analysis",
      "https://4ort.xyz/entity/bending-stress"
    ]
  },
  "worked_example": {
    "scenario": "2x10 Douglas Fir roof beam",
    "inputs": {
      "beam_width": 1.5,
      "beam_height": 9.25,
      "span_length": 12,
      "uniform_load": 50
    },
    "outputs": {
      "moment_result": 900.0,
      "section_modulus_result": 21.66,
      "stress_result": 503.0
    },
    "allowable_reference": "1000-1500 psi (species/grade dependent)"
  },
  "limitations": [
    "Assumes simply-supported boundary conditions",
    "Does not account for shear stress or deflection limits",
    "Material homogeneity assumed (no knots, defects)",
    "Linear elastic behavior only"
  ],
  "published_at": "2026-07-17T14:00:00Z",
  "location": "/load-calculator.html"
}