Interactive Stress State Explorer

An interactive visualization tool for plane stress transformation in solid mechanics built with Streamlit, NumPy, and Plotly.

This app lets you explore how stress components change with rotation angle, see principal stresses, and visualize Mohr’s Circle — all in a clean, responsive UI.

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📌 Features

✔ Visualizes stress transformation equations
✔ Shows σₓ', σᵧ', and τₓᵧ' vs rotation angle θ
✔ Computes principal stresses and max shear
✔ Plots Mohr’s Circle
✔ Purple-pink dark theme
✔ No heavy dependencies

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🎓 What It Does

The app computes the stress transformation equations:

🔹 Normal Stress on Rotated Face

$$ \sigma_{x'} = \frac{\sigma_x + \sigma_y}{2} + \frac{\sigma_x - \sigma_y}{2}\cos(2\theta) + \tau_{xy}\sin(2\theta) $$

🔹 Shear Stress on Rotated Face

$$ \tau_{x'y'} = -\frac{\sigma_x - \sigma_y}{2}\sin(2\theta) + \tau_{xy}\cos(2\theta) $$

It also computes:

• Principal stresses
• Maximum shear stress
• Mohr’s Circle representation

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🚀 How to Run

Clone the repository:

git clone https://github.com/LASTHALFBLOODPRINCE/Assignments.git
cd Assignments
Install dependencies:

pip install -r requirements.txt
Run the app:

streamlit run app.py
Open your browser to view the interactive UI.

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🧠 Usage
Use the sidebar sliders to adjust:

σₓ (normal stress in x direction)

σᵧ (normal stress in y direction)

τₓᵧ (shear stress)

θ (rotation angle)

Real-time plots update to show the resulting stress state.

🛠 Built With
Streamlit

NumPy

Plotly

📌 Author
Hemant Nagar
Roll No: 2024UCS0093