How Do You Calculate Shear Modulus from Poisson's Ratio and Young's Modulus?

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SUMMARY

The discussion focuses on calculating the shear modulus (G) of titanium using its Young's modulus (E) and Poisson's ratio (V). The Young's modulus of titanium is given as 110 GPa, and Poisson's ratio is specified as 0.33. The formula used for this calculation is E = 2G(1 + V), which leads to a shear modulus of 41.35 GPa after rearranging the equation to solve for G. Participants emphasize the importance of understanding the relationships between stress, strain, and elastic modulus in this context.

PREREQUISITES
  • Understanding of Young's modulus and its significance in material science.
  • Familiarity with Poisson's ratio and its application in elasticity.
  • Basic knowledge of shear stress and shear strain concepts.
  • Ability to manipulate algebraic equations to isolate variables.
NEXT STEPS
  • Learn about the derivation and application of the formula E = 2G(1 + V).
  • Research the properties of titanium and its mechanical behavior under stress.
  • Explore shear modulus calculators and their underlying principles.
  • Study the relationship between tensile stress, tensile strain, and elastic modulus in materials.
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Students and professionals in materials science, mechanical engineering, and anyone involved in the analysis of material properties and elastic behavior.

haamed
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hi there, I am completely stuck on this question and was wondering if anyone could help me out here;

''a metal wire has a diameter of 1mm. when subjected to a tensile load of 200N the diameter is 0.99925. if the youngs modulus of the titanium is 110GPa, determine the shear modulus of the metal.''

the forumula for shear modulus is 'shear stress/shear strain'

but finding shear strain applies to displacement of solids.

using poisson's ratio means i need to find the length but there isn't one specified,

i am stuck
 
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Try this out.

First calculate the tensile stress produced from the loading. Then look at the relations between stress, strain, and the elastic modulus.

EDIT: Sorry I missed that you already have the elastic modulus. Disregard the above.

Thanks
Matt
 
lol, i read the question carefully and realized titanium pops up, so the formula

E=2G (1+V) might do

V= 0.33
E=110GPa
i found a shear modulus calculator anf found the answer is 41.35GPa

but to work it out i have to rearrange the equation to make G the subject?
 
Last edited:

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