Young's modulus and Poisson's ratio are among the most important quantities in the area of stress and strain engineering. s V p 2 [ V DOI:,, Problems in Exploration Seismology & their Solutions, the Creative Commons Attribution-ShareAlike 3.0 Unported License (CC-BY-SA). ν = – ε trans / ε longitudinal. ρ 2 p An elastic parameter: the ratio of transverse contractional strain to longitudinal extensional strain. You may need to download version 2.0 now from the Chrome Web Store. p 2 2 The lower the number, the less amenable to "stretching" forces the material in question tends to be. σ Performance & security by Cloudflare, Please complete the security check to access. 1 0.5 The formula of Poisson’s Ratio is. V In addition, it is usually represented by the lower case Greek letter nu, ν. = –6%. − − Poisson's ratio can be expressed as. 2 = p s p 0.5 σ {\displaystyle 2\sigma ={\frac {[{\frac {V_{p}^{2}-V_{s}^{2}}{V_{p}^{2}-V_{s}^{2}}}]}{[{\frac {V_{s}^{2}}{V_{p}^{2}-V_{s}^{2}}}]}}}, 2 s σ = ½ ( VP2 − 2 VS2) / ( VP2 − VS2 ) Note that if VS = 0, then Poisson's ratio equals 0.5, indicating either a fluid, because shear waves do not pass through fluids, or a material that maintains constant volume regardless of stress, also known as an ideal incompressible material. V In proportion to the stress, the cross section contracts and the length elongates by ΔL from the length L the material had before receiving the tensile force (See the upper illustration in Fig. μ ( p p ) s {\displaystyle {\frac {[{\frac {V_{s}^{2}}{V_{p}^{2}-V_{s}^{2}}}]}{2}}=0.5-\sigma }, V − − − = {\displaystyle \mu } p − V {\displaystyle {\frac {V_{s}^{2}}{V_{p}^{2}-V_{s}^{2}}}=1-2\sigma }, [ Poisson's ratio is. 2 σ V σ V p − and V p s 2 2 s 2 2 V You can disable cookies at any time. − 13. s V ( {\displaystyle \rho } 2 V Young's modulus and Poisson's ratio are among the most important quantities in the area of stress and strain engineering. 1 2 V 2 V V V − Copyright 2020 Leaf Group Ltd. / Leaf Group Media, All Rights Reserved. and s, and s in terms of μ = Poisson's ratio. s V s 2 {\displaystyle V_{s}} {\displaystyle {\frac {V_{s}}{V_{p}}}=[{\frac {0.5-\sigma }{1-\sigma }}]^{1/2}}, This website uses cookies. = p p V − Following the bridge example, if a steel beam supporting the bridge is approximately 100 meters tall, and the change in length is 0.01 meters, then the longitudinal strain is εl = –0.01/100 = –0.0001. v’ – v / v × 100 = –0.01 (1 + v’) / v × 100. V This quantity can be calculated using a simple formula. s This physical phenomenon is known as strain and is defined as the change in length divided by the total length. ] Rubber is close to the high end; lead and clay are both over 0.40. V (1) This ratio is dimensionless and unitless as well. = {\displaystyle V_{s}} 2 s ] = − V V ν V V Longitudinal Strain = (102-100) / 100 = 0.02. ] ratio greater than 1.42. Longitudinal strain = Δl/l; Lateral strain = – ΔR/R ∴ Poisson’s ratio (v) = \(\frac{\text { Lateral strain }}{\text { Longitudinal strain }}=\frac{-\Delta R / … − 2 If you are on a personal connection, like at home, you can run an anti-virus scan on your device to make sure it is not infected with malware. s 1 − V p = For incompressible material, ν is approximately 0.5. σ σ 1 Figure E-5. Steel tends to be closer to 0.30 and iron derivatives lower still, in the 0.20 to 0.30 range. {\displaystyle V_{s}} If you are at an office or shared network, you can ask the network administrator to run a scan across the network looking for misconfigured or infected devices. = = This is close to the tabulated value of 0.265 for cast steel. {\displaystyle 2\sigma +{\frac {V_{s}^{2}}{V_{p}^{2}-V_{s}^{2}}}=1}, V − {\displaystyle V_{s}} V ε = ΔL/L. 0.5 The Poisson effect is the phenomenon wherein material tends to expand in the direction perpendicular to the compression. V p Learn more. p {\displaystyle [{\frac {0.5-\sigma }{1-\sigma }}]^{1/2}*V_{p}=V_{s}}, V in terms of p − {\displaystyle 1-\sigma ={\frac {V_{p}^{2}}{2(V_{p}^{2}-V_{s}^{2})}}}, 0.5 Your IP: 2 2 p V 0.5 2 2 Poisson’s Ratio Symbol: v is commonly used as the symbol for the Poisson’s ratio. If you continue without changing your browser settings, you consent to our use of cookies in accordance with our cookie policy. Derivation of Poisson's ratio. {\displaystyle V_{p}} σ {\displaystyle {\frac {V_{s}^{2}}{V_{p}^{2}}}={\frac {0.5-\sigma }{1-\sigma }}}, V = V 2 V s V p V ) 2 2 V {\displaystyle V_{p}} Cork has a value of about 0, meaning that it does not expand radially as it is compressed. V 2 = {\displaystyle V_{s}} − it will have a σ V {\displaystyle V_{p}} σ {\displaystyle [{\frac {0.5-\sigma }{1-\sigma }}]^{1/2}={\frac {V_{s}}{V_{p}}}}, [ 2 2 Write down the formula for Poisson's ratio: μ = –εt / εl. [ V L ) / ( D. ΔL) ……………. Note that a minus sign is used in this length change, as the beam is getting shorter by 0.01 meters. s − {\displaystyle 2\sigma ={\frac {V_{p}^{2}-2V_{s}^{2}}{V_{p}^{2}-V_{s}^{2}}}}, 2 − This page was last edited on 14 March 2015, at 20:10. Samuel Markings has been writing for scientific publications for more than 10 years, and has published articles in journals such as "Nature."

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