Elasticity Problem Calculation

Study Notes

Elasticity - Problem Calculation

The problem deals with calculating the elasticity of a metal bar.
The metal bar is subjected to compression.
The bar undergoes contraction, which is a decrease in length.
The initial length is the original length before compression.
The change in length refers to the difference between the original length and the length after compression.
Strain is calculated by dividing the change in length by the original length.
Stress is the force applied per unit area.
The problem asks to find the values of Young's modulus and Bulk modulus.

Young's Modulus

Young's modulus is a measure of a material's stiffness.
It represents the ratio of stress to strain in a material under tensile or compressive stress.
Young's modulus can be calculated using the formula: Young's Modulus = Stress / Strain
The change in length is given as 0.33.
The initial length is not given, so we cannot calculate Young's Modulus.

Bulk Modulus

Bulk modulus is a measure of a material's resistance to compression.
It is defined as the ratio of pressure to volumetric strain.
In the problem, the Bulk modulus is given as 104.117.
The relationship between Young's Modulus (E), Bulk Modulus (K), and Poisson's ratio (ν) is: K = E / ( 3(1-2ν)).
Poisson's ratio is a measure of the material's tendency to change shape in response to stress.

Calculating Poisson's Ratio

Poisson's ratio can be calculated using the formula: ν = ( Lateral Strain / Axial Strain)
Lateral Strain is the change in width or thickness of the material divided by the original width or thickness
Axial Strain is the change in length divided by the original length.
In the problem, the Axial Strain is given as 0.33.
The Lateral Strain is not given, so we cannot calculate Poisson's ratio.

Relationship Between Elasticity and Modules

The relationship between Young's modulus, Bulk modulus, and Shear Modulus (G) is:
- E = 3K(1-2ν)
- G = E / ( 2(1+ ν))
Shear modulus (G) measures a material's resistance to shear stress or the deformation of the material under tangential forces.
Since we do not have the values of Young's modulus or Poisson's ratio, we cannot calculate Shear Modulus either.

Description

Test your understanding of elasticity through practical problem calculations. This quiz focuses on determining Young's modulus and Bulk modulus by analyzing stress and strain in a metal bar under compression. Calculate changes in length and apply formulas to understand material stiffness.