Plane (2D) Stress Transform

Welcome to StressTransform 2D, your comprehensive tool for solving and visualizing 2D stress transformations. Follow these steps to make the most of this powerful app:

Input Stress Values

1. Enter the normal stresses (\(\sigma_x\), \(\sigma_y\)) and the shear stress (\(\tau_{xy}\)) at the point of interest.
2. Use the provided input fields to manually enter each value, or use the range input for the rotation angle (\(\theta\)) to control the transformation.

\(\sigma_x\), \(\sigma_y\) & \(\tau_{xy}\) : stresses on xy corrdinate system

\(\theta\) : the rotation angle of \(x^I\) in CCW direction measured from x axis

Real-Time Angle Adjustment

1. The angle (\(\theta\)) can be adjusted using either the input box or the range slider.
2. Any changes made will be automatically reflected in the calculated stresses, element views, and Mohr's Circle visualization, giving you immediate feedback on how stress transformation occurs.

View the Results

1. After entering the input values, the app will calculate the normal and shear stresses on the rotated plane.
2. In addition, it will display principal stresses, principal directions, maximum/minimum shear stresses, and their respective orientations.

\(\sigma_{x^I}\), \(\sigma_{y^I}\) & \(\tau_{x^Iy^I}\) : stresses on x'y' coordinate system

\(\sigma_{1}\) & \(\sigma_{2}\) : principal normal stresses

\(\theta_{P_1}\) & \(\theta_{P_2}\) : principal directions

\(\tau_{max}\) & \(\tau_{min}\) : maximum and minimum shear stresses

\(\theta_{P_1}\) & \(\theta_{P_2}\) : directions for maximum and minimum shear stresses

Visualize Stress Transformation

1. The app provides visual representations of the original element, the rotated element, principal directions, and maximum shear stress configuration.
2. A Mohr's Circle diagram is generated to give a comprehensive graphical overview of the stress states and transformations at the point.

Repeat with New Values

1. Change the input values or angle as needed, and watch the results update in real time to explore different stress scenarios.