In continuation of Lesson Two, this lesson will focus on the three types of stress caused by tensile and compressive forces, strain, and the tests that scientists perform on materials so that engineers have accurate data to refer to when selecting the materials for a bridge. Students will also be expected to define and calculate the stress on different samples of wood.
Lecture
A bridge member under tension, compression or both forces at the same time experiences what engineers define as stress. J. E. Gordon states "stress is a measure of how hard the atoms and molecules which make up the material are being pushed together or pulled apart as a result of external forces. Stress is not associated with any particular length or cross-section therefore testing multiple shapes and sizes of the same material will yield the same stress limit. (Gordon, 46) To calculate the stress, you must take the force exerted on a material sample divided by the cross-sectional area of the sample.
The elongation or shortening of a material under stress is defined as strain. Strain is a measure of how far a material is being pulled apart or pushed together and like stress, it is not associated with any particular length or cross-section of a material. (Gordon, 49-50) Strain is calculated using the following formula:
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(Strain ) e = (Change in Length ) D L / (Original Length) L
To be of use to engineers, the values of stress and strain are plotted on a graph. The stress is plotted on the y-axis and strain is plotted on the x-axis. Gordon explains the stress-strain curve as follows: "The slope of this curve is usually a straight line and when this happens it is said that the material is 'obeying Hooke's Law'. The slope of the line varies for different materials. Engineer's use the slope of a stress-strain curve to measure how readily a material strains elastically (deforms temporarily and returns to its original shape after a load has been removed) under a given stress."(Gordon 1978, pg. 52) Hooke's Law is the amount of restoring force needed to bring a spring back to it's original position after a force has been applied to it. It is important that a material behave much like a spring because engineers do not want permanent deformation of a structure to occur every time a load is applied. Therefore, the slope (Ds/De), also known as the Young's Modulus of Elasticity of a stress-strain curve measures the elastic stiffness of a material or the point at which the maximum elastic deformation will occur. Engineers might desire a material with a low Modulus of Elasticity such as rubber or a material with very high Modulus of Elasticity such as steel depending upon the designed application of the member.
When referring to stresses, materials can experience different types. Forces pulling on a member will cause tensile stress, forces pushing on a member will result in compression stress, and when both forces push and pull on a member and the lines of forces are not directly across from each other, a shear stress is produced. (Avaikian, 482) Figure 2b explains how compression and tension affect a member to cause shearing. This type of stress can cause bending or twisting of a material.
The amount of stress a member can tolerate is crucial when selecting materials for a bridge. Engineers analyze every component of a bridge to determine what members will be in tension, compression, or both. Engineers must keep in mind that certain materials are better under compression rather than tension. These include concrete, brick, hard woods, and steel. Some materials such as steel, flexible yet strong can carry tensile forces. There are also materials that can carry both tensile and compressive forces. Pre-stressed concrete is one of these materials. Pre-stressed concrete has steel rods running through it so it can withstand not only a compression force but a tension force as well.
After engineers have determined the forces acting on members of a bridge, they refer to engineering reference books for the stress-strain limits of specific materials. As stated above, the required stiffness of a material will depend on the function of the member.
The following lab activity is designed to help students understand how scientists perform tests on materials to obtain stress limits. This particular test is a compression test in which they can calculate the stress of a material utilizing the formula:
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(Stress) s = (Force) F / (Cross Sectional Area) A (Units of Measure are lb/in2 or N/m2)
Today, scientists can test materials with a test machine. When an engineer wants a particular material tested, they create a test piece that is put into a testing machine. This machine can simulate a load of tension or compression. The machine measures the strain with an extensometer. From this data, a stress-strain curve can be obtained.
Lab Activity
Objectives
To help students understand how scientists test materials, calculate stress, determine maximum compression loads of different types of wood, and understand why different wood can tolerate more stress.
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Materials:
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2 pieces of pre-cut balsa wood (4" x 4" x ¼" and 4" x 4" x 5/32")
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2 pieces of pre-cut pine wood (4" x 4" x ¼" and 4" x 4" x 5/32")
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2 pieces of pre-cut oak wood (4" x 4" x ¼" and 4" x 4" x 5/32")
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20 Bricks or Weights of 50 N or more
Procedure:
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1. Record the weight of 1 brick in Newtons.
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2. Calculate the cross-sectional area of the two different samples of wood. (Multiply the length x height)
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2. To begin the test, place 2 bricks on a table.
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3. Lay one specimen of wood at a time across the two bricks.
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4. Slowly add a weight or brick on top of the wood and observe what happens. Students will be expected to continue until the material begins to deform or fail.
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5. Record the maximum amount of weight before a failure or deformation in the material occurs.
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6. Calculate the stress of that particular sample.
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7. Repeat with the other samples.
Assessment: Students should draw a force diagram to illustrate what forces are acting on the wood. They should compare the values of stress for each pair of wood and explain what they have observed.
Post-Lab Discussion
Students should discuss their observations, hypothesize why certain materials can withstand more stress than others, and realize that the different cross-sectional areas of the same material do not affect the amount the material can tolerate. You can discuss the molecular structure of hardwood versus softwood to explain why hardwoods can tolerate more stress. Since the next lesson focuses on arch bridges you can explain that arch bridges, which experience mostly compression forces, are built from materials such as concrete, stone, and brick because these materials are very good in compression.
In conclusion to the post-lab discussion, you could discuss the other tests scientists conduct on materials such as the hardness and tensile tests. It is also important to note that the test results are published in material reference books available to engineers who use this data to select the desired materials for a structure.
