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