README.md

metadata

title: Cantilever Beam Calculator with AI Explanations
emoji: 🏗️
colorFrom: blue
colorTo: green
sdk: gradio
sdk_version: 4.44.0
app_file: app.py
pinned: false
license: mit

🏗️ Cantilever Beam Calculator with AI Explanations

Overview

An engineering analysis tool that calculates stress, deflection, and safety factors for cantilever beams, enhanced with AI-generated explanations to make results accessible to non-engineers.

Features

Engineering Calculations

• Stress Analysis: Maximum bending stress at fixed support
• Deflection Analysis: Maximum deflection at free end
• Safety Factors: Both yield and serviceability checks
• Dynamic Properties: First natural frequency calculation
• Mass Estimation: Total beam mass based on geometry and material

AI Integration

• Natural language explanations of numerical results
• Context-aware safety assessments
• Plain-English interpretation of engineering metrics
• Educational insights for non-technical users

Technical Scope

Beam Configuration

• Type: Cantilever beam with fixed support
• Loading: Concentrated force at free end
• Cross-section: Rectangular (uniform)
• Analysis Method: Linear elastic, small deflection theory

Input Parameters

1. Geometry:

   • Length: 0.1 - 10 meters
   • Width: 5 - 1000 mm
   • Height: 5 - 1000 mm

2. Loading:

   • Force: 0.001 - 1000 kN (at free end)

3. Material Properties:

   • Young's Modulus: 1 - 500 GPa
   • Yield Strength: 10 - 2000 MPa
   • Density: 100 - 20000 kg/m³

Calculations

Stress Analysis

σ_max = Mc/I where: M = FL (moment at fixed end) c = h/2 (distance to neutral axis) I = wh³/12 (second moment of area)

Deflection Analysis

δ_max = FL³/(3EI) where: F = applied force L = beam length E = Young's modulus

Safety Factors

• Yield: FoS = Sy/σ_max (should be > 1.5)
• Deflection: FoS = δ_allow/δ_max (where δ_allow = L/200)

Validation & Assumptions

Assumptions

• Homogeneous, isotropic material
• Linear elastic behavior (Hooke's Law)
• No buckling considerations
• Neglecting self-weight effects
• Perfect fixity at support

Valid Ranges

• Aspect ratio (L/h): 5 to 50
• Deflection/Length: < 5% (small deflection theory)
• Stress level: Below yield strength

Example Use Cases

1. Structural Design: Preliminary sizing of cantilever structures
2. Education: Teaching beam theory and structural mechanics
3. Quick Checks: Rapid verification of beam adequacy
4. Material Selection: Comparing different materials for same geometry

AI Model

• Model: SmolLM2-135M-Instruct
• Purpose: Generate accessible explanations of engineering results
• Temperature: 0.7 for balanced creativity and accuracy

Safety Notes

⚠️ Important: This tool is for educational and preliminary design purposes only. Professional structural analysis software and engineering judgment should be used for actual design work.

Technical Stack

• Backend: Python with engineering calculations
• Interface: Gradio for web UI
• AI: HuggingFace Transformers for natural language generation
• Deployment: HuggingFace Spaces

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Created for CMU 24-679 Course - Engineering Calculations with Natural Language Explanations