README.md

metadata

title: Beam UDL Calculator — Deterministic + Explainable
emoji: 🧮
colorFrom: blue
colorTo: green
sdk: gradio
sdk_version: 5.48.0
app_file: app.py
pinned: false
license: mit

Beam UDL Calculator — Deterministic + Explainable

A transparent, first‑principles simply supported beam calculator under a uniformly distributed load (UDL).
The math is deterministic; an optional LLM produces a plain‑English explanation grounded purely in the computed numbers.

• Deterministic backend returns a structured record (JSON) with inputs, units, equations (LaTeX), results, and pass/fail checks — so users can see the math.
• Gradio UI shows (i) Numerical results and (ii) Explain the results.
• Optional LLM explanation (Hugging Face Transformers). When disabled, a deterministic template explainer is used.

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Scope & Assumptions

• Euler–Bernoulli beam, small deflections; linear elastic material.
• Uniformly distributed load across the entire span; simply supported ends.
• Educational helper; not a design code. Use engineering judgment and applicable standards.

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Inputs, Units, and Valid Ranges

Name	Unit	Range	Default	Notes
L	m	0.5–30	6.0	Span length
w_kN_per_m	kN/m	0–50	10.0	Uniformly distributed load
E_GPa	GPa	50–210	200	Young’s modulus (steel ≈ 200)
I_m4	m⁴	1e−7–1e−2	5.0e−5	Second moment of area
S_m3	m³	1e−6–1e−1	5.0e−4	Section modulus
Fy_MPa	MPa	150–700 (opt)	250	Yield strength (optional stress check)
defl_ratio	L/–	180–1000	360	Allowable deflection limit

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Governing Equations (first principles)

• Max bending moment: ( M_{\max} = \dfrac{w L^2}{8} )
• Max shear: ( V_{\max} = \dfrac{w L}{2} )
• Max elastic deflection: ( \delta_{\max} = \dfrac{5 w L^4}{384 E I} )
• Bending stress: ( \sigma_{\max} = \dfrac{M_{\max}}{S} )

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What the app returns (structured record)

Example (abridged):

{
  "meta": {"calc_name": "Simply supported beam under UDL", "version": "1.0.0", "timestamp_utc": "…"},
  "assumptions": ["Euler–Bernoulli…", "UDL over full span…", "No partial factors…"],
  "equations_TeX": {
    "M_max": "M_{\\max} = \\frac{w L^2}{8}",
    "V_max": "V_{\\max} = \\frac{w L}{2}",
    "delta": "\\delta_{\\max} = \\frac{5 w L^4}{384 E I}",
    "sigma": "\\sigma_{\\max} = \\frac{M_{\\max}}{S}"
  },
  "units": {
    "inputs": {"L": "m", "w_kN_per_m": "kN/m", "E_GPa": "GPa", "I_m4": "m^4", "S_m3": "m^3", "Fy_MPa": "MPa", "defl_ratio": "L/ratio"},
    "outputs": {"M_max_kN_m": "kN·m", "V_max_kN": "kN", "delta_mm": "mm", "sigma_MPa": "MPa"}
  },
  "inputs": { "L": 6.0, "w_kN_per_m": 10.0, "E_GPa": 200.0, "I_m4": 5e-5, "S_m3": 5e-4, "Fy_MPa": 250.0, "defl_ratio": 360 },
  "results": { "M_max_kN_m": 45.0, "V_max_kN": 30.0, "delta_mm": 16.9, "sigma_MPa": 90.0 },
  "checks": {
    "stress": {"criterion": "sigma <= Fy", "utilization": 0.36, "status": "OK"},
    "deflection": {"criterion": "delta <= L/360", "allowable_mm": 16.67, "utilization": 1.01, "status": "NG"}
  },
  "validation": {"passed": true, "messages": []},
  "notes": "Educational tool; not a substitute for design codes or professional judgement."
}

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References

1. Gere, J.M., & Timoshenko, S.P. Mechanics of Materials.
2. Roark, R.J., & Young, W.C. Roark’s Formulas for Stress and Strain.
3. Beer, F.P., & Johnston, E.R. Mechanics of Materials.
   (Used to confirm the standard UDL formulas and assumptions.)

License

• MIT

Acknowledgments

• GenAI usage: Explanatory text and repo scaffolding were assisted by ChatGPT.
• All engineering formulas and outputs are deterministic and were verified against standard references.