EVERYDAY ENGINEERING EXAMPLES FOR SIMPLE CONCEPTS

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1 EVERYDAY ENGINEERING EXAMPLES FOR SIMPLE CONCEPTS Simple Method to Calculate Young s Modulus Elasticity MECN Mechanical Measurement and Instrumentation Dr. Omar Meza Copyright 2015

2 MSEIP Engineering Everyday Engineering Examples Simple Method to Calculate Young s Modulus Elasticity Engage: Show the video The elastic modulus is one of the most vital properties involved in various aspects of material engineering for design purposes. Every material undergoes elastic deformation. Elastic deformation is mostly defined as temporary deformation of its physical shape and will able to return to its original state. For elastic deformation, the material undergoes an amount of stress without exceeding the elastic limit. Any deformation caused by further increases in load or stress beyond the yield point of a certain material will be plastic permanent. The Young s modulus (elastic modulus) is the measurement of the stiffness of a given material. It is defined as the limit for small strains of the rate of change of stress with strain. Besides using the stress and strain graphs, the Young s Modulus of any material can also be determined by using the deflection of the material (beam) when subjected to load. Page 1

3 1. Did you ever wonder how flexible is a Wooden Meter Ruler? 2. What is the relationship between load, span, width, height and the deflection of a beam that placed on two stands and affected by a concentrated load at the centre? Explore: You rarely find a wooden spring or even think of wood as stretching like a metal. Yet wood is flexible. It bends and springs back to its original shape unless you bend it so much that you hear those very faint cracking sounds and realize that you have bent it too much. Wood is still used a great deal in the construction of buildings and some wonderful new architectural designs are made from wooden structures. Wood is not going to be replaced in the near future, so we do need to know about its elastic properties. We want a value that we can look up for a particular type of wood, so that when we have a beam that is of known length and width, we are able to work out how much it might bend when it supports a load. The constant which describes the elasticity of the wood (or spring or other stretchable material) is called Young s Modulus. Explain: When a rod flexes, it experiences a lengthening by its convex side and a concave contraction. The behavior of the rod is determined by the Young's modulus of the material it is made; so that the value of the modulus can be determined by experiments bending. We use a rod of rectangular cross section resting on thin supports at both ends. If we apply a vertical force F down, at the midpoint of the rod, the elastic deformation that this experience translates into a decline of that point, Page 2

4 called arrow of bending or just bending, S. According to Hooke's Law, force F is proportional to the deflection S, that is: Where k is the Stiffness Coefficient Elaborate: F ks In the book Mechanics of Materials, Stephen Timoshenko and James M. Gere, 1997, present the analysis of this phenomenon by resistance of materials for a rod of rectangular section. 4Yab L F S Where L1 is the distance between the two thin supports, a the width and b the rod thickness. If F is measured in Newtons and all lengths in meters, the Young's modulus Y will be expressed in N/m 2 or Pascal. What did you learn? For a well-run classroom experiment with multiple measurements of deflection at various loads and repeats, the accuracy should be on the order of 1% to 5% of the wood's modulus. If the meter stick is assumed to be red maple with the grain oriented in the direction of the length of the beam and the moisture content to be around 12%, the modulus should be 12.4 GPa. Evaluate: Invite students to attempt the following problem: Example 1: A steel bar of uniform thickness of 1 cm, width of 10 cm and length of 1m. Using a Young s Modulus of 2 x N/m 2, calculate the magnitude of force F to deflect a distance of 3 cm. Page 3

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