---
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

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