General Bending

The General Bending Solver GUI is a user-friendly MATLAB app designed to simplify structural beam analysis. It supports symbolic and numeric

GUI Description for the General Bending Solver

The General Bending Solver GUI is a user-friendly MATLAB app designed to simplify structural beam analysis. It supports symbolic and numeric calculations for bending moments, shear forces, and deflections in both single- and multi-plane loading scenarios. Below is a detailed breakdown of its features and workflow:

Key Features

• Multi-Plane Analysis: Handles bending in the X-Z and Y-Z planes.
• Symbolic Computation: Derives analytical expressions for deflections, moments, and shear forces using MATLAB’s Symbolic Math Toolbox.
• Real-Time Visualization: Generates plots for shear force, bending moment, and deflection.
• Support for Complex Loads:

1. Distributed loads (rectangular, triangular, trapezoidal).
2. Concentrated forces and moments.

• Interactive Input: Intuitive interface for defining beam properties, supports, and loads.
• LaTeX Integration: Displays equations in LaTeX for easy verification.

GUI Workflow

1. Mode Selection

Choose the analysis mode:

- Symbolic Mode: Solve using symbolic stiffness coefficients (\(k_{xx}, k_{yy}, k_{xy}\)).

- I-Coefficients Mode: Input second moments of area (\(I_{xx}, I_{yy}, I_{xy}\)).

- k-Coefficients Mode: Directly input stiffness coefficients.

2. Beam Setup

- Beam Length: Define the beam length symbolically (e.g., `3*L`) or numerically.

- Initial Plot: Click "Begin" to initialize the beam visualization (neutral axis).

3. Defining Supports and Loads

- **Supports** (Figure 5.3):

- **Fixed**, **Simple**, or **Roller** supports.

- Specify position (e.g., `0` for the left end or `2*L` for a mid-point).

- Loads:

- Distributed Loads:

- Rectangular (`rec`), Triangular (`n_tri`, `rev_tri`), or Trapezoidal (`trap`).

- Define start/end positions and magnitude.

- Concentrated Loads:

- Forces (`con_f`) and Moments (`con_m`).

- Specify position and magnitude.

- Preview Option: Visualize loads with correction terms (for distributed loads) before finalizing.

4. Solving and Results

1.Solve:

- Click the "Solve" button to compute reactions, moments, shear forces, and deflections.

- The solver uses equilibrium equations and boundary conditions to resolve unknowns.

2. Plots :

- Shear Force Diagram: Shows shear distribution along the beam.

- Bending Moment Diagram: Displays moment variation.

- Deflection Curve: Plots beam deflection in the Y-Z and/or X-Z planes.

3. Equations Tab:

- View symbolic equations for reactions, moments, shear forces, and deflections in LaTeX.

- Copy equations for reports or further analysis.

4. Custom Calculator:

- Input unitless values to compute deflections at specific beam positions.