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Unformatted text preview: EME 236 Properties and Mechanics of Materials Spring 2008 Lecture 05: Poisson's Ration and Modulus of Rigidity Today: Homework questions: New Topics: Poisson's Ratio Modulus of Rigidity Shear Stress Testing Homework: Read Section 3.6 to 3.8 Work Problems from Chap 3: 31, 35, 41 Following today's class you should be able to: explain what Poisson's ratio, ν, represents write the equation that relates E, G, and ν  know how to read the modulus of rigidity off of a shear stressstrain diagram be able calculate axial and lateral strain to solve problems that involve E, G, and ν Poisson's Ratio: When a deformable is subjected to axial stress, the body's length changes. At the same time there is also a small change in the body's shape along a direction lateral to the axial force. Essentially, as a body elongates, it also get narrower. If a force acts to compress the body and shorten its length, the body gets fatter. The ratio that comes the relative change deformation of the lateral deformation to the axial deformation is called Poisson's ratio. Deformed Length: ' long L L δ = + Deformed width: ' lateral r r δ = Lateral Strain: long lateral r δ ε = Axial (Longitudinal) Strain: long longitudinal L δ ε = Poisson's Ratio (ratio of lateral to longitudinal strain): lateral longitudinal ε ν ε = The negative sign indicates that as the length increases the lateral dimension decreases. Values for Poisson's ratio generally fall between 1/4 and 1/2. r L P δ lateral L P δ long Example 1: A rod of steel is 10 in long and has a 0.50 in diameter. A 20 kip load pulls on each end of the bar. Given a modulus of elasticity of 30 x 10 6 psi and Poisson's ratio of 0.30 a) what is the elongation of the bar, δ x ? b) what is the strain along the bar, ε x ? c) what is the strain along the lateral direction, ε dia ? d) what is change of diameter experienced by the bar, δ dia ? Example 1: 20 kip 20 kip L = 10 in D = 0.50 in A rod of steel is 10 in long and has a 0.50 in diameter. A 20 kip load pulls on each end of the bar. Given a modulus of elasticity of 30 x 10 6 psi and Poisson's ratio of 0.30 a) what is the elongation of the bar, δ x ? b) what is the strain along the bar, ε x ?...
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 Spring '11
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