These lessons will focus on the design of the arch and trussed bridges and how they handle tension or compression. The primary concept students should understand is that an arch bridge relies primarily on compression while a truss bridge relies primarily on axially loaded members acting in tension and compression. An activity will follow the lecture to help students understand the strength of a triangle (the basic shape utilized in a truss).
Lecture
An arch bridge is a bridge that utilizes the arch as its main design as this bridge carries
its weight outward along the curve of the arch to the supports at each end. The supports, known as the abutments, carry the load. The abutments also keep the ends of the bridge from spreading out by creating two equal and opposite horizontal forces that push inward on the arch. (See NOVA's website http://www.pbs.org/wgbh/nova/bridge/meetarch.html for an activity that allows students to examine the importance of abutments.)
Arch bridges rely primarily on compression because as forces are carried outwards along the curve of the arch, the molecules of the material are compressed. When selecting a building material for an arch bridge, engineers must consider only materials that are strong under compression. These materials include stone, concrete, or steel.
Trusses are like a beam bridge because forces are transverse to the axis of the whole truss. A truss is identified by its series of triangles that are connected by a lower and upper chord or flange. Forces are carried along the axis of the assembled members that form the shape of a triangle. The members of the truss carry forces of tension or compression but not both.
As stated in Lesson Two, bending occurs when both tension and compression are acting on a member. Members which hold the deck for the cars, trains, people, bikes and other objects crossing the bridge are subjected to both tension and compression. Bending in theses members may combine with axial loads in truss members which adds some complexity to the analysis of this type of bridge.
The following Activity will help students understand why a triangle can sustain more force than a quadrilateral. It can also help them understand how members are axially loaded.
Activity
Students will compare two basic shapes: the triangle and the square. They should discover that the triangle can sustain more force than a square. In addition to this activity, you may want the students to find resultants of vectors.
Materials: Popsicle Sticks, rubber bands, and pins
Procedure:
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1. Create a rectangle using the popsicle sticks and pins.
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2. Apply a force to the pivot points and record what you observe about this structure.
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3. Now take a rubber band and attach it to two pins to create a diagonal in the rectangle. (This will now form 2 triangles.)
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4. Apply a load to the pivot points and record what you observe.
Analysis:
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1. Did your change help to make the structure stronger. Explain.
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2. How might this particular structure explain how a truss bridge carries the load of moving vehicles?
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3. Can you identify which members are in tension and which members are in compression?
Post Activity Lecture
As stated earlier, a truss is a series of triangles that consist of members and joints to form a stable configuration. A truss bridge must have two support nodes to sustain both vertical and horizontal forces. A fixed joint supports the horizontal and vertical direction while a rolling joint only supports the vertical direction. Loads on a truss bridge cause the members to be in either tension or compression. A stable structure or a structure in equilibrium has the weight of a static or dynamic load equal but opposite in direction to the support forces.
(figure available in print form)
A truss can be more efficient than a beam bridge. A truss uses only axial forces which means that a member is either in tension or compression, but not both. Each member will sustain forces along its axis. The compression members are short and thick while the tension members are typically longer and thinner. To further explore which members of a truss are in tension or compression you may want to go to the following website: John Hopkins University: What is Engineering? - Virtual Laboratory: "Bridge Designer", http://www.jhu.edu/~virtlab/bridge/truss.htm. On this website students are able to build a truss, apply loads, have the computer software calculate how much force each support applies, and visually see what members are in tension or compression. This is an excellent "hands on" interdisciplinary (science and math) activity for students in eleventh and twelfth grades.
When a trussed bridge is designed, strength and stiffness must be considered. The strength of a material determines the size of the member required to support the anticipated loads calculated by engineers. Since members of a truss can be in either tension or compression, steel is a material that is often selected for the construction of a truss because steel can sustain both tension and compression. In addition to the stress a material can sustain, engineers want every part of the bridge to behave elastically (the ability of a material to deform minimally during loading and return to its original length after the load is removed). As discussed in earlier lessons, the engineers rely on the Modulus of Elasticity to determine which alloy of steel (as each one will have its own stress-strain curve) is adequate for the function of the member. Engineers use their professional judgement to stay within allowable stress limits. It is important that the material of each member is not sustaining too much or too little stress.
Homework Activity
Students must identify at least three different truss bridges in Connecticut and bring in a picture of each type of truss bridge. They must explain to the class how each bridge carries the load and try to identify the members in compression and tension.
