Designing Bridges
Associated Worksheet
Lesson 2 Worksheet.pdfIntroduction/Motivation
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? What are some bridges you know that might be considered more complicated?What makes some bridges simple and other complex?
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.
First and foremost, engineers must understand the problem completely. To do this, they ask a lot of questions. What are some questions the engineers might ask? (Possible answers: How strong would you need to make the bridge? What materials would you use? How would you anchor the pier foundations? What natural phenomena might your bridge need to be capable of withstanding?)
Next, engineers must determine what types of loads or forces they expect the bridge to carry. Loads might include traffic such as trains, trucks, bikes, people and cars. Other loads might be from the natural environment. For example, bridges in Florida must be able to withstand hurricane forces. So, engineers consider loads such as winds, hurricanes, tornadoes, snow, earthquakes, rushing river water, and sometimes standing water. Can you think of any other loads that may act on a bridge of any kind?
The next step is to determine if these loads can occur at the same time and what combination of loads provides the highest possible force (stress) on the bridge. For example, a train crossing a bridge and an earthquake in the vicinity of the bridge could occur at the same time. However, many vehicles crossing a bridge and a tornado passing close to the bridge probably would not occur at the same time.
After having calculated the largest anticipated force from all the possible load combinations, engineers use mathematical equations to calculate the amount of material required to resist the loads in that design. (For simplicity, we will not consider how these forces act on the bridge; just knowing that they do act on the bridge is sufficient.)
After they have considered all of these calculations, engineers brainstorm different design ideas that would accommodate the anticipated loads and amount of material needed. They split their design into smaller parts and work on the design criteria for all the components of the bridge.
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.
Load Determination
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:
Dead loads include the weight of the bridge itself plus any other permanent object affixed to the bridge, such as toll booths, highway signs, guardrails, gates or a concrete road surface.
Live loads are temporary loads that act on a bridge, such as cars, trucks, trains or pedestrians.
Environmental loads are temporary loads that act on a bridge and that are due to weather or other environmental influences, such as wind from hurricanes, tornadoes or high gusts; snow; and earthquakes. Rainwater collecting might also be a factor if proper drainage is not provided.
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.
Load Combinations
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:
Dead Load + Live Load + Snow Load
Dead Load + Live Load + Wind Load (or Earthquake Load)
Dead Load + Live Load + Wind Load + (Snow Load ÷ 2)
Dead Load + Live Load + Snow Load + (Wind Load ÷ 2)
Dead Load + Live Load + Snow Load + Earthquake Load
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.
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).