CIV102-Structural-Analysis: Moving Load Bridge Simulation

A MATLAB-based structural engineering tool developed to simulate dynamic payload physics and analyze thin-walled matboard bridge structures under moving train configurations. This repository contains the complete numerical optimization and structural failure verification engine for the CIV102 design framework.

Project Purpose

The core objective of this project was to design, optimize, and validate a 1200 mm thin-walled matboard bridge structure capable of safely supporting a multi-car train configuration. This code acts as the analytical backbone of the design process, allowing our team to:

1. Track Dynamic Demands: Simulate a 3-car moving train across 1,200 spatial increments to compute localized live-load configurations.
2. Expose Failure Thresholds: Construct continuous Shear Force Envelopes (SFE) and Bending Moment Envelopes (BME).
3. Map Structural Capacities: Predict absolute structural failure loads by evaluating localized material limits, glue-line shear stresses, and thin-plate local buckling capacities (Euler & plate buckling theories).

Engineering Team Members

• Helen Huang – Structural Optimization, Mathematical Engine & Script Architecture, Iterative Design Decisions, Design Illustration
• XueQi Yang – Structural Optimization, Mathematical Engine & Script Architecture, Iterative Design Decisions

Code Architecture & Implementation

The program is structured into three unified modules executing the complete structural analysis pipeline:

1. Moving Load Solver (SFE & BME Generation)

• Localized Train Displacements: Evaluates reaction forces at each discrete longitudinal coordinate as the train model travels left-to-right from $x = -856\text{ mm}$ to $x = L$.
• Envelope Generation: Dynamically computes internal shear forces and bending moments at every point along the bridge span, extracting absolute maximum bounds across all load states.

2. Cross-Sectional Geometry Engine

• Centroid Analysis: Determines the structural neutral axis ($\bar{y}$, $y_{top}$, $y_{bot}$) for a custom thin-walled section defined by parameterized plate matrices.
• Second Moment of Area ($I$): Calculates the total structural moment of inertia using the Parallel Axis Theorem ($\sum I_0 + \sum Ad^2$).
• First Moment of Area ($Q$): Resolves $Q_{cent}$ at the neutral axis and $Q_{glue}$ at critical joint locations to compute horizontal and vertical shear flow metrics.

3. Factor of Safety (FOS) & Stability Predictor

• Material Yield Inquiries: Evaluates tension limits ($30\text{ MPa}$) against the bottom fibers and compression limits ($6\text{ MPa}$) against top fibers.
• Thin-Plate Local Buckling: Models flexural and shear plate buckling modes ($k_1, k_2, k_3, k_4$) using the thin-plate stability formulation: $$\sigma_{cr} = \frac{\pi^2 E}{12(1 - \nu^2)} \cdot k \cdot \left(\frac{t}{b}\right)^2$$
• Global Failure Output: Isolates the absolute minimum FOS across all failure paths, outputs multi-plot subplots comparing structural capacity vs. actual dynamic demand, and predicts the absolute failure load ($P_{fail}$) under Load Case 1 ($400\text{ N}$ baseline).