Documentation

Getting Started

SAS2D uses the displacement method (also known as the stiffness method) to analyze 2D frame structures. The analysis considers both axial and bending deformations.

Basic Workflow

1. Define nodes (joints) with coordinates
2. Connect nodes with bars (elements)
3. Apply support conditions
4. Add loads (nodal or distributed)
5. Run analysis
6. View results and diagrams

Defining Nodes

Nodes are the connection points in your structure. Each node has:

• Coordinates (x, y): Position in the 2D plane
• Joint type: Rigid or hinged connection
• Support condition: 0 (free) to 9 (various restraints)
• Loads: Forces and moments applied at the node

Creating Bars

Bars (or elements) connect nodes and transfer forces. Each bar requires:

• Initial and final nodes: Connection points
• Material properties: Young's modulus (E)
• Section properties: Area (A), Moment of inertia (I)
• End releases: Optional hinges at bar ends

Support Conditions

Available support types:

• 0: Free (no restraint)
• 1: Fixed (u=v=θ=0)
• 2: Pinned (u=v=0, θ free)
• 3: Roller X (v=0, u and θ free)
• 4: Roller Y (u=0, v and θ free)
• 5-9: Specialized conditions

Applying Loads

Nodal Loads

Applied directly at nodes:

• Forces: magnitude and angle
• Moments: magnitude (positive = counterclockwise)

Distributed Loads on Bars

12 load types available including:

• Uniform transverse loads
• Triangular/trapezoidal loads
• Axial loads
• End moments

Running Analysis

The displacement method follows these steps:

1. Calculate element stiffness matrices (local coordinates)
2. Transform to global coordinates
3. Assemble global stiffness matrix [K]
4. Apply boundary conditions
5. Solve KU = F for displacements {U}
6. Calculate element forces and reactions

Interpreting Results

After analysis, you can view:

• Support Reactions: Forces and moments at supports
• Nodal Displacements: u, v, θ at each node
• Internal Force Diagrams:
  • Normal force (N)
  • Shear force (V)
  • Bending moment (M)