Statistical Analysis of Methods to Repair Cracked Steel
A cracked steel beam in a highway bridge.Copyright Hoan-Bridge Investigation, Federal Highway Administration, U.S. Department of Transportation http://www.fhwa.dot.gov/bridge/steel/010710.cfm
Students apply pre-requisite statistics knowledge and concepts learned in an associated lesson to a real-world state-of-the-art research problem that asks them to quantitatively analyze the effectiveness of different cracked steel repair methods. As if they are civil engineers, students statistically analyze and compare 12 sets of experimental data from seven research centers around the world using measurements of central tendency, five-number summaries, box-and-whisker plots and bar graphs. The data consists of the results from carbon-fiber-reinforced polymer patched and unpatched cracked steel specimens tested under the same stress conditions. Based on their findings, students determine the most effective cracked steel repair method, create a report, and present their results, conclusions and recommended methods to the class as if they were presenting to the mayor and city council. This activity and its associated lesson are suitable for use during the last six weeks of the AP Statistics course; see the topics and timing note for details.
The maintenance and repair of civil infrastructure is an important task for governments around the world, and it is critical to get it right. Structural failure can have mortal, disastrous consequences, such as the I-35 bridge collapse in Minneapolis (see Figure 1) and the Alexander Kielland Norwegian North Sea rig disaster. Engineers continue to devise alternative repair methods that are more efficient, easier to perform, and less expensive than traditional methods. Composites with strength and durability similar or superior to that of steel have been successfully used to rehabilitate infrastructures. Carbon-fiber-reinforced polymers (CFRP) and epoxy adhesive patches are good solutions to stop crack propagation and extend the mean fatigue life of steel; they are also easy to apply and do not corrode, modify or overload the structure (see Figure 2). With the design of CFRP, engineers have provided a material that is as strong as steel, but lighter, corrosion resistant and simple to work with. Through this activity, students see and experience a real-world applied use for statistical analysis.
Figure 1. Structural fatigue failures may have tragic consequences, as shown by this bridge disaster, so it is very important to rehabilitate structures and avoid crack propagation, extending the mean fatigue life.Copyright 2007 Tony Webster, Wikimedia Commons https://commons.wikimedia.org/wiki/File:Minneapolis_I-35W_Bridge_Collapse_(1011531544).jpg
Figure 2. Patches made of a composite of carbon-fiber-reinforced polymers and epoxy adhesive successfully repair cracked steel structures.Copyright 2015 Environmental and Civil Engineering Department, Cullen College of Engineering, University of Houston
After this activity, students should be able to:
- Use box-and-whisker plots to analyze various data sets.
- Use bar graphs to compare and make conclusions about multiple data sets.
- Use technology to efficiently perform statistical analyses and graph data.
- Use PowerPoint® to present results and conclusions.
- Describe the statistical analyses performed on experimental data.
- Clearly state final conclusions resulting from statistical analyses.