a material has a youngs modulus of 1.25*105N/mm2 and a poissons ratio of 0.25.calculate the modulus of rigidity and the bulks modulus.
Given:
E=1.25*10^5 N/mm²
ν=0.25
G=E/[2(1+ν)]
K=E/[3(1-2ν)]
To calculate the modulus of rigidity (or shear modulus), we can use the relation:
Modulus of rigidity (G) = Young's modulus (E) / (2 * (1 + Poisson's ratio))
Given:
Young's modulus (E) = 1.25 * 10^5 N/mm^2
Poisson's ratio (ν) = 0.25
Plugging in the values into the formula, we get:
G = 1.25 * 10^5 N/mm^2 / (2 * (1 + 0.25))
G = 1.25 * 10^5 N/mm^2 / (2 * 1.25)
G ≈ 50,000 N/mm^2
Therefore, the modulus of rigidity for the given material is approximately 50,000 N/mm^2.
To calculate the bulk modulus (K), we can use the relation:
Bulk modulus (K) = Young's modulus (E) / (3 * (1 - 2 * Poisson's ratio))
Plugging in the values, we get:
K = 1.25 * 10^5 N/mm^2 / (3 * (1 - 2 * 0.25))
K = 1.25 * 10^5 N/mm^2 / (3 * (1 - 0.5))
K ≈ 83,333.3 N/mm^2
Therefore, the bulk modulus for the given material is approximately 83,333.3 N/mm^2.
To calculate the modulus of rigidity and the bulk modulus, we need to use the formulas that relate these properties to Young's modulus (E) and Poisson's ratio (ν).
The formulas are as follows:
Modulus of Rigidity (G) = E / (2 * (1 + ν))
Bulk Modulus (K) = E / (3 * (1 - 2 * ν))
Given values:
Young's modulus (E) = 1.25 * 10^5 N/mm^2
Poisson's ratio (ν) = 0.25
Let's substitute these values into the formulas:
Modulus of Rigidity (G) = (1.25 * 10^5 N/mm^2) / (2 * (1 + 0.25))
= 1.25 * 10^5 N/mm^2 / (2 * 1.25)
= 1.25 * 10^5 N/mm^2 / 2.5
= 5 * 10^4 N/mm^2
Therefore, the modulus of rigidity is 5 * 10^4 N/mm^2.
Bulk Modulus (K) = (1.25 * 10^5 N/mm^2) / (3 * (1 - 2 * 0.25))
= 1.25 * 10^5 N/mm^2 / (3 * (1 - 0.5))
= 1.25 * 10^5 N/mm^2 / (3 * 0.5)
= 1.25 * 10^5 N/mm^2 / 1.5
= 8.333 * 10^4 N/mm^2
Therefore, the bulk modulus is 8.333 * 10^4 N/mm^2.