CIV102 Bridge Project

Note

🎉 We were top 1 in our cohort and 2nd in the class of 2025. A blog post is available here.

📑 Docs are available as Wiki.

If you find our work helpful to you, you do not have to cite our design report, but perhaps star our repository, thanks.

Project Description

The CIV102 course has a term project where we build a bridge with a matboard that aims to survive under various load cases. It is actually one of the requirements that we need to implement some sort of automated analysis procedure. Our team decide to take this one step further and make these features possible:

• Composition of complex cross-sections using basic shapes
• Automatic calculation of (x̄, ȳ) (the centroid), I (the moment of inertia), and Q(y) (the first moment of area about a given axis)
• Visualization of cross-sections
• Support beam bridges with either uniform cross-sections or varying cross-sections
• Automatic calculation of shear forces (pivot points) and expanded shear forces
• Shear force diagram
• Automatic calculation of bending moments (pivot points) and expanded bending moments
• Bending moment diagram
• Automatic calculation of axial and shear stresses
• Safe factor diagram
• Automatic calculation of curvatures, slopes, and displacements
• Displaced shape
• Simulation of the train passing the bridge
• Finding the maximum load
• Optimization of the cross-section dimensions
• Extendability to other types of bridges
• Extremely easy to use

Installation

pip install git+https://github.com/ATATC/CIV102-Bridge-Project.git

Quick Start

All dimensions are measured in millimeters. All loads are measured in Newtons. All angles are measured in radians. All complex units are combinations of these fundamental units.

Deliverable 1 as an Example

You can find the definition of Deliverable 1 and its objectives in the project handout.

It is quite obvious that you need to have a bridge before analyzing it. To create a BeamBridge, you need to know the following parameters. The checked ones are defaulted to what we are given this year as the base case in load case 2.

• Total train load in Newtons
• Cross-section profile
• Length of the bridge (1200 mm)
• Wheel positions ([172 348 512 688 852 1028], which is the center)
• Load distribution (1.35 1.35 1 1 1 1)

The following case uses the default cross-section.

from bridger import *

cross_section = CIV102Beam()
material = Material()
bridge = BeamBridge(452, cross_section)
bridge.plot_sfd(save_as="assets/images/sfd.png")
bridge.plot_bmd(save_as="assets/images/bmd.png")
print(f"(x_bar, y_bar): {cross_section.centroid()} mm")
print(f"I_x: {cross_section.moment_of_inertia()} mm4")
print(f"Ultimate applied stress: {bridge.ultimate_stress()} MPa")
print(f"FOS: {bridge.safety_factor((material.compressive_strength, material.tensile_strength))}")

You will see output like this:

(x_bar, y_bar): (49.99999999999999, 41.43109435192319) mm
I_x: 418352.20899942354 mm4
Ultimate applied stress: (6.384059301633374, 7.592045684386937) MPa
FOS: (0.9398408937813106, 3.9515041462006852)

Plot the Displaced Shape

Furthermore, we can plot the displaced shape.

from bridger import *

cross_section = CIV102Beam()
material = Material()
bridge = BeamBridge(452, cross_section)
bridge.plot_displaced_shape(material, save_as="assets/images/displaced_shape.png")

Predict the Maximum Load

from bridger import *

cross_section = CIV102Beam()
material = Material()
bridge = BeamBridge(452, cross_section)
evaluator = Evaluator(bridge, material)
print(evaluator.maximum_load())  # (240.0889550207032, 'flexural buckling')

Plot the Factors of Safety at the Maximum Load

from bridger import *

cross_section = CIV102Beam()
material = Material()
bridge = BeamBridge(452, cross_section)
evaluator = Evaluator(bridge, material)
bridge.train_load(train_load=evaluator.maximum_load()[0])
evaluator.plot_safety_factors(save_as="assets/images/safety_factors_d1.png")

Team 602

Authors

Sorting follows alphabetic order of the first name initials and does not reflect contributions. The hyperlinks refer to portfolios.

D. Chan, J. Zhou, N. Saxena, and T. Fu

Team Name: Beam Everyone

"Beat everyone" but "beam".

Bridge Name: Highway 102

We picked this name not only because the course name is CIV102, but also because Ontario highways are named such that Highway 404 means there are four lanes. Our bridge only had one lane, so it made perfect sense.

Citation

@techreport{team602civ102,
    title = {CIV102 Bridge Project Design Report},
    author = {Chan, D. and Zhou, J. and Saxena, N. and Fu, T.},
    institution = {Faculty of Applied Science and Engineering, University of Toronto},
    year = {2025},
    month = {November},
    type = {Course Project Report},
    course = {CIV102: Structures and Materials},
    note = {Team 602}
}