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Shear modulus Formula
When a force is applied on a body which results in its lateral deformation, the elastic coefficient is called the shear modulus. It is the ratio of shear stress to shear strain in a body. Is written as:
Shear modulus = (shear stress)/(strain) = (Force * no-stress length) / (Area of a section * change in the lateral length)
The equation is
G= = σ /ϵ = (F L) / (A Δx)

We have:
G: Shear modulus
σ : shear stress
ϵ : strain
F: Force applied
L: lateral length of the material without force applied
A: area of a section of the material
Δx: Change in the lateral length of the material after a force is applied
Shear modulus equation Questions:
1) Calculate the shear modulus of a body that experienced a stress of 5*104 N/m2 and a strain 4*10(-2).
Answer: The shear modulus is calculated using the formula,
G= σ / ϵ
G = (5*104 N/m2)/(4*10(-2)) = 1.25 *106 N/m2
G = 1.25 *106 N/m2
2) A cylindrical bar of width 10 mm is stretched from its original length to 10 mm using a force of 100 N. What is the Shear modulus of the system?
Answer: The shear modulus is found from the equation:
G= (F L) / (A Δx)
The area is calculated using A=π (d/2)2, where d is 10 mm, then A is
A= π (5 mm)2 = π (0.005 m)2 = 2.5*10(-5) m2
substituting the value of area, the force and the final lateral length,
G= (100 N 0.1 m) / (2.5*10(-5) m2 * (0.01 m))
G= 10 N*m/0.025*10(-5) m3 = 40000000 N/m2 = ????? KN/m2
Question:
G= ????? KPa