Help Poisson's Ratio Calculation Problem

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In summary, the conversation discusses the calculation of the modulus of elasticity and determination of Poisson's Ratio for a bar under an axial load. After calculating the stress and strain values, the modulus of elasticity is found to be 2.06 GPa. The conversation also mentions a possible typo in the question regarding the width contraction, leading to a more reasonable Poisson's Ratio of 0.453 instead of 4.53.
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lizr1
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Hi. I can't seem to see where I am going wrong or if i have gone wrong as the answer I got for Poissons Ratio looks incorrect. Can anyone help or point me in the right direction? Thanks.

An axial load of 28.5kN is applied to a bar of length280mm, width 38mm and thickness 21mm. After the load is applied, the bar elongatesby 4.85mm and the width contracts by 2.98mm. At he prescribed load, note thatthe stress in the bar is less than its proportional limit.



1) Calculate the modulus of elasticity
2) Determine Poisson’s Ratio


1) Calculate the modulus of elasticity

Cross Sectional Area = 38 *21 = 798mm2

Stress(σ) = (F)/(A) = 28.5 / 798 = 35.71 MPa

Strain(ε) = (e)/(L) = 4.85 / 280 = 0.01732 mm/mm

Modulus of elasticity: σ = Eε

35.71 = (E)(0.01732) = 2.06 GPa

2) DeterminePoisson’s Ratio

εlat = Δwidth/width = -2.98 / 38 = -0.0784

v = -εlat / εlong = -(-0.0784 / 0.01732) = 4.53
 
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  • #2
Maybe the 2.98 is a typo. Maybe it should be 0.298. That would make the poisson ratio 0.453 which seems much more reasonable. 4.53, as you noted, is way out of the ballpark.

Chet
 
  • #3
Thanks you were right there was a typo in the question!
 

1. What is Poisson's Ratio?

Poisson's Ratio is a measure of the ratio of lateral strain to axial strain for a given material. It is denoted by the Greek letter nu (ν) and is typically used to describe the behavior of materials under stress or strain.

2. How do you calculate Poisson's Ratio?

To calculate Poisson's Ratio, you need to know the longitudinal strain (εL) and the transverse strain (εT) of a material. Poisson's Ratio is then calculated as the negative ratio of transverse strain to longitudinal strain (ν = -εTL).

3. What is a common problem encountered when calculating Poisson's Ratio?

A common problem encountered when calculating Poisson's Ratio is obtaining inaccurate or inconsistent values due to experimental errors or uncertainties in measurements. This can be minimized by using precise measuring instruments and performing multiple trials to obtain an average value.

4. What is the significance of Poisson's Ratio in material science?

Poisson's Ratio is an important parameter in material science as it provides information about the stiffness and flexibility of a material. It also helps in predicting the behavior of materials under different types of stress and strain, which is crucial in engineering and design applications.

5. Can Poisson's Ratio be negative?

Yes, Poisson's Ratio can be negative for certain materials, such as auxetic materials, which exhibit a negative Poisson's Ratio. This means that when these materials are stretched in one direction, they become thicker in the perpendicular direction, unlike most materials that become thinner. Negative Poisson's Ratio materials have unique properties that make them useful in specific applications.

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