Arche 3 Theory Of Structures Simulations
A collection of interactive 3D visualizations and simulations to help you master concepts in arche 3 theory of structures.
Module 1: Introduction to Structural Analysis and Loads - Theory & Concepts
Classification of structures, design loads per NSCP, load path and tributary areas.
LRFD Load Combinations Simulator (NSCP 2015)
Input Loads (kN)
Factored Combinations
Governing Load Combination:
Combo 5: 1.2D + 1.0E + 1.0L = 250.0 kN
Module 2: Stability and Determinacy - Theory & Concepts
Conditions for stability, external and internal determinacy, degree of indeterminacy.
Truss Determinacy Calculator
Equation: m + r = 2j
m + r = 5 + 3 = 8
2j = 2(4) = 8
Assumes internal arrangement is stable and reactions are non-concurrent/non-parallel.
Module 3: Analysis of Statically Determinate Structures - Theory & Concepts
Reactions of multi-span beams, complex roof trusses, and three-hinged arches.
Module 4: Moving Loads and Influence Lines - Theory & Concepts
Concept of moving loads, influence lines for determinate beams, maximum shear and moment.
Truss Influence Line Simulator
Move the load across the bottom chord of the Pratt truss to see how the force in the selected member changes. Negative values indicate compression, and positive values indicate tension.
Approximate Analysis of Statically Indeterminate Structures - Theory & Concepts
Simplified methods for analyzing complex indeterminate frames under vertical and lateral loads, including the Portal and Cantilever methods.
Exact Analysis of Indeterminate Structures: Force Methods - Theory & Concepts
The Method of Consistent Deformations, Maxwell-Betti theorem, and the Three-Moment Equation for analyzing statically indeterminate structures.
Force Method: Propped Cantilever Simulation
Observe how the method of consistent deformations solves for the redundant reaction $R_B$. The primary structure (a simple cantilever) deflects downwards due to the uniform load. The redundant force $R_B$ must push upwards exactly enough to bring the net deflection at support B back to zero.
Calculations
- Length ($L$): 10 m
- Flexural Rigidity ($EI$): 10000 kN·m²
- Primary Deflection at B (): 1250.00 mm (down)
- Flexibility Coefficient (): 33.33 mm/kN
- Redundant Reaction ($R_B$): 37.50 kN (up)
Exact Analysis of Indeterminate Structures: Displacement Methods - Theory & Concepts
The Slope-Deflection Method and the Moment Distribution Method for analyzing indeterminate beams and frames.
Moment Distribution Method Simulator
Uniform Load: 20 kN/m on spans AB and BC (L = 10m)
| Joint | A | B | C | |
|---|---|---|---|---|
| Member | AB | BA | BC | CB |
| DF | 0 | 0.5 | 0.5 | 0 |
| Initial FEMs | -166.67 | 166.67 | -166.67 | 166.67 |
| Cycle 1 (Dist) | 0.00 | 0.00 | ||
| Cycle 1 (CO) | 0.00 | 0.00 | ||
| Cycle 2 (Dist) | 0.00 | 0.00 | ||
| Cycle 2 (CO) | 0.00 | 0.00 | ||
| Cycle 3 (Dist) | 0.00 | 0.00 | ||
| Cycle 3 (CO) | 0.00 | 0.00 | ||
| Cycle 4 (Dist) | 0.00 | 0.00 | ||
| Cycle 4 (CO) | 0.00 | 0.00 | ||
| Cycle 5 (Dist) | 0.00 | 0.00 | ||
| Cycle 5 (CO) | 0.00 | 0.00 | ||
| Final Moments | -166.67 | 166.67 | -166.67 | 166.67 |
Note how the unbalanced moment at joint B is distributed (multiplied by DF and reversed in sign), and then half of that distributed moment is carried over to the fixed ends A and C.
Module 9: Matrix Stiffness Method - Theory & Concepts
Introduction to matrix methods, local vs. global coordinates, and assembly of the global stiffness matrix.
Direct Stiffness Assembly Simulation
Walk through the core concept of matrix structural analysis: assembling local stiffness matrices into a global matrix.
1. Define the Structure
Consider a 1D axial structure with two spring members (Member 1 and Member 2) connected in series at three nodes (Node 1, Node 2, Node 3).