Lesson: Designing BridgesContributed by: Integrated Teaching and Learning Program and Laboratory, University of Colorado Boulder
Educational Standards :
Pre-Req Knowledge (Return to Contents)
The students should have a familiarity with bridge types, as introduced in the first lesson of the Bridges unit, including area, and compressive and tensile forces.
Learning Objectives (Return to Contents)
After this lesson, students should be able to:
Introduction/Motivation (Return to Contents)
We know that bridges play an important part in our daily lives. We know they are essential components of cities and the roadways between populations of people. Some bridges are simple and straightforward; others are amazingly complex. What are some bridges that you know that might be called simple bridges? (Possible answers: Log over a creek, bridges over streams.) What are some bridges you know that might be considered more complicated? (Possible answers: Golden Gate Bridge, other large bridges, bridges that carry both highway traffic and train traffic.) What makes some bridges simple and other complex? (Possible answers: Their size, multiple purposes, environmental conditions, environmental forces, material maintenance requirements, etc.)
One amazing example of a bridge's contribution to connecting people to other populations and places for both social and commerce reasons is the Sky Gate Bridge connecting people to Japan's Kansai International Airport, located in Osaka Bay.
It all started when the nearby Osaka and Tokyo airports were unable to meet demand, nor be expanded. To solve the problem, the people of Japan took on one of the most challenging engineering projects the world has ever seen. Since they had no land for a new airport, they decided to create the Kansai International Airport by constructing an entire island! On this new, artificial island, they built the airport terminal and runways. Then, they needed a bridge to access it. Spanning 3.7 km from the mainland in Osaka to the airport in an ocean bay, the Sky Gate Bridge is one of the longest truss bridges in the world and has an upper deck for auto transport and a lower, internal deck for rail lines.
Considered a modern engineering marvel, the airport and bridge opened in 1994. Four months later, it survived a magnitude 6.7 earthquake with only minor damage. Because the airport site is built on compact soil, it sinks 2-4 cm per year — another condition for engineers to consider in the ongoing safety and maintenance of the airport and bridge.
It is not easy to create a bridge the size of the Sky Gate Bridge. Have you ever wondered how engineers actually go about designing an entire bridge? Bridges are often designed one piece at a time. Each pier (columns) and girder (beams) has to meet certain criteria for the success of the whole bridge. Structural engineers go through several steps before even coming up with ideas for their final designs.
Lesson Background & Concepts for Teachers (Return to Contents)
For designing safe bridge structures, the engineering design process includes the following steps: 1) developing a complete understanding of the problem, 2) determining potential bridge loads, 3) combining these loads to determine the highest potential load, and 4) computing mathematical relationships to determine the how much of a particular material is needed to resist the highest load.
Understanding the Problem
One of the most important steps in the design process is to understand the problem. Otherwise, the hard work of the design might turn out to be a waste. In designing a bridge, for instance, if the engineering design team does not understand the purpose of the bridge, then their design could be completely irrelevant to solving the problem. If they are told to design a bridge to cross a river, without knowing more, they could design the bridge for a train. But, if the bridge was supposed to be for only pedestrians and bicyclists, it would likely be grossly over-designed and unnecessarily expensive (or vice versa). So, for a design to be suitable, efficient and economical, the design team must first fully understand the problem before taking any action.
Determining the potential loads or forces that are anticipated to act on a bridge is related to the bridge location and purpose. Engineers consider three main types of loads: dead loads, live loads and environmental loads:
Values for these loads are dependent on the use and location of the bridge. Examples: The columns and beams of a multi-level bridge designed for trains, vehicles and pedestrians should be able to withstand the combined load all three bridge uses at the same time. The snow load anticipated for a bridge in Colorado would be much higher than that one in Georgia. A bridge in South Carolina should be designed to withstand earthquake loads and hurricane wind loads, while the same bridge in Nebraska should be designed for tornado wind loads.
During bridge design, combining the loads for a particular bridge is an important step. Engineers use several methods to accomplish this task. The two most popular methods are the UBC and ASCE methods.
The Uniform Building Code (UBC), the building code standard adopted by many states, defines five different load combinations. With this method, the load combination that produces the highest load or most critical effect is used for design planning. The five UBC load combinations are:
The American Society of Civil Engineers (ASCE) defines six different load combinations. As with the UBC method, the load combination that produces the highest load or most critical effect is used for design planning. However, the load calculations for ASCE are more complex than the UBC ones. For the purposes of this lesson and its associated activity, we will use the five UBC load combinations.
Determination of Member Size
After an engineer determines the highest or most critical load combination, s/he determines the size of the members. A bridge member is any individual main piece of the bridge structure, such as columns (piers) or beams (girders). Column and beam sizes are calculated independently.
To solve for the size of a column, engineers perform calculations using strengths of materials that have been pre-determined through testing. The Figure 1 sketch shows a load acting on a column. This force represents the highest or most critical load combination from above. This load acts on the cross-sectional area of the column.
The stress due to this load is σ = Force ÷ Area. In Figure 1, the area is unknown and hence the stress is unknown. Therefore, the use of the tensile and compressive strength of the material is used to size the member and the equation becomes Force = Fy x Area, where force is the highest or most critical load combination. Fy can be the tensile strength or compressive strength of the material. For common building steel, this value is typically 50,000 lb/in2. For concrete, this value is typically in the range of 3,500 lb/in2 to 5,000 lb/in2 for compression. Typically, engineers assume that the tensile strength of concrete is zero. Therefore, solving for the Area, Area = Force ÷ Fy. Keeping the units consistent is important: Force is measured in pounds (lbs) and Fy in pounds per square inches (lb/in2). The area is easily solved for and is measured in square inches (in2).
To solve for the size of a beam, engineers perform more calculations. The sketch in Figure 2 shows a beam with a load acting on it. This load is the highest or most critical load combination acting on the top of the beam at mid-span. Compressive forces usually act on the top of the beam and tensile forces act on the bottom of the beam due to this particular loading. For this example, the equation for calculating the area becomes a bit more complicated than for the size of a column. With a single load acting at the mid-span of a beam, the equation is Force x Length ÷ 4 = Fy x Zx. As before, force equals the highest or most critical load combination pounds (lbs). Length is the total length of the beam that is usually known. Usually, units of length are given in feet (ft) and often converted to inches. Fy is the tensile strength or compressive strength of the material as described above. Zx is a coefficient that involves the dimensions of the cross-sectional area of the member. Therefore, Zx = (Force x Length) ÷ (Fy x 4), where Zx has units of cubed inches (in3).
Every beam shape has its own cross sectional area calculations. Most beams actually have rectangular cross sections in reinforced concrete buildings, but the best cross-section design is an I-shaped beam for one direction of bending (up and down). For two directions of movement, a box, or hollow rectangular beam, works well (see Figure 3).
Vocabulary/Definitions (Return to Contents)
Associated Activities (Return to Contents)
Lesson Closure (Return to Contents)
Take a moment and think of all the bridges you know around your home and community. Maybe you see them on roadways, bike paths or walking paths. Think of those that have piers (columns) and girders (beams). What do they look like? Can you remember the sizes of the piers and girders? (Discussion point: Students may recall noticing that piers and girders for pedestrian and bicycle bridges are much smaller than those for highway or railway traffic.)
What are examples of load types? (Possible answers: Vehicles, people, snow, rain, wind, the weight of the bridge and its railings and signs, etc.) Why would the loads make a difference in how an engineer designed a bridge? (Answer: Engineers must figure out all of the loads that might affect bridges before they design them.) If you were an engineer, how would you go about designing a bridge to make sure it was safe? (Discussion points: First, fully understand the problem to be solved with the bridge, its requirements and purpose. Then figure out all the possible types of loads [forces] that the bridge might need to withstand. Then calculate the highest possible load the bridge might have to withstand at one time. Then figure out the amount of construction material required that can resist that projected load.)
Attachments (Return to Contents)
Assessment (Return to Contents)
Pairs Drawing: Divide the class into teams of three students each. Have each engineering team sketch a bridge to carry a train across a river that is 100-meters wide. Have them describe the type of bridge and where the compressive and tensile forces are acting on it.
Complete the Design/Presentation: Have student teams return to their bridge design from the pre-lesson assessment and think about the potential loads on their bridge, given the just-discussed engineering design process steps. Have them draw in the loads and the direction that they would act on the bridge. What do they think the highest load combination would be (how many of these loads could actually happen at the same time)? Then, ask for one or two engineering teams to volunteer to present the details of their bridge design to the class.
Lesson Summary Assessment
Human Bridge: Have students use themselves as the raw construction material to create a bridge that spans the classroom and is strong enough that a cat could walk across it. Encourage them to be creative and design it however they want, with the requirement that each person must be in direct contact with another class member. How many places can you identify tension and compression? How would you change the design if the human bridge had to be strong enough for a child to walk across it? What other loads might act upon your bridge?
Concluding Discussion: Wrap up the lesson and gauge students' comprehension of the learning objectives by leading a class discussion using the questions provided in the Lesson Closure section.
Math Worksheet: Assign students the attached Load Combinations Worksheet as homework. After using the five UBC load combinations to calculate the highest or most critical load on the first page, they use that information to solve three problems on subsequent pages, determining the required size of bridge members of specified shapes and materials. The three problem questions increase in difficulty: younger students should complete only problem 1; older students should complete problems 1 and 2; advanced math students should complete all three problems.
Lesson Extension Activities (Return to Contents)
Have students build and test the load-carrying capacity of balsa wood bridges. Begin by looking at Peter L. Vogel's website on his Balsa Bridge Building Contest at http://www.balsabridge.com/
Accidents happen! Assign students to investigate and report on what went wrong when a steel beam from a highway viaduct fell onto a moving vehicle. Read the May 2004 National Transportation Safety Board highway accident brief with photos. See NTSB Abstract HAB-06/01, Passenger Vehicle Collision with a Fallen Overhead Bridge Girder at: http://www.ntsb.gov/news/events/2006/golden_co/presentations.html
Have the class participate in the yearly West Point Bridge Design Contest. Access excellent and free downloadable bridge design software and other educational resources at the US Military Academy at West Point website: bridgecontest.usma.edu/
Additional Multimedia Support (Return to Contents)
Use the online Bridge Designer software (no downloading required!) provided by Virtual Laboratories, Whiting School of Engineering, Johns Hopkins University: http://www.jhu.edu/virtlab/bridge/truss.htm
References (Return to Contents)
ACI Committee 318, Building Code Requirements for Structural Concrete (ACI 318-02) and Commentary (ACI 318R-02): An ACI Standard. American Concrete Institute: Farmington Hills, MI, 2002.
AISC Committee on Manuals and Textbooks, Manual of Steel Construction: Load and Resistance Factor Design, Third Edition. American Institute of Steel Construction, 2001.
Hibbeler, R.C. Mechanics of Materials, Third Edition. Prentice Hall: Upper Saddle River, NJ, 1997.
Kansai Airport. Earth Observatory Newsroom, National Aeronautics and Space Administration.
Uniform Building Code. International Conference of Building Officials: Whittier, CA, 1991.
ContributorsJonathan S. Goode, Joe Friedrichsen, Natalie Mach, Christopher Valenti, Denali Lander, Denise W. Carlson, Malinda Schaefer Zarske
Copyright© 2007 by Regents of the University of Colorado.
Supporting Program (Return to Contents)Integrated Teaching and Learning Program and Laboratory, University of Colorado Boulder
Acknowledgements (Return to Contents)
The contents of this digital library curriculum were developed under a grant from the Fund for the Improvement of Postsecondary Education (FIPSE), U.S. Department of Education and National Science Foundation GK-12 grant no. 0338326. However, these contents do not necessarily represent the policies of the Department of Education or National Science Foundation, and you should not assume endorsement by the federal government.