Question

A metallic cube whose each is 10 cm is subjected to a shearing force of 100kgf. The top face is displaced through 0.25 cm with respect to bottom. Calculate the shearing stress, strain and shear modulus.

Answer 1

Answer:

Shearing stress = 98000 N/$m^{2}$

Strain = 0.025

Shear modulus = 3920000 N/$m^{2}$

Explanation:

Shearing stress = $\frac{Force}{Area}$ = $\frac{100\times9.8}{0.1\times0.1}$ = 98000 N/$m^{2}$

Strain = $\frac{\Delta x}{h}$ = $\frac{0.25}{10}$ = 0.025

Shear modulus = $\frac{Stress}{Strain}$= $\frac{98000}{0.025}$ = 3920000 N/$m^{2}$

Answer 2

(a). The shearing stress is $9.8\times10^{4}\ N/m^2$

(b). The shearing strain is 0.025

(c). The shear modulus is $3.92\times10^{6}\ N/m^2$

Explanation:

Given that,

Force = 100 kgf

Displacement = 0.25 cm

Length = 10 cm

We need to calculate the shearing stress

Using formula of shearing stress

$\text{shearing stress}=\dfrac{F}{l}$

Put the value into the formula

$\text{shearing stress}=\dfrac{100\times9.8}{(10\times10^{-2})^2}$

$\text{shearing stress}=98000\ N/m^2$

$\text{shearing stress}=9.8\times10^{4}\ N/m^2$

We need to calculate the shearing strain

Using formula of shearing strain

$\text{shearing strain}=\dfrac{\Delta l}{l}$

$\text{shearing strain}=\dfrac{0.25\times10^{-2}}{10\times10^{-2}}$

$\text{shearing strain}=0.025$

We need to calculate the shear modulus

Using formula of shear modulus

$\text{shear modulus}=\dfrac{shearing stress}{shearing strain}$

$\text{shear modulus}=\dfrac{9.8\times10^{4}}{0.025}$

$\text{shear modulus}=3920000$

$\text{shear modulus}=3.92\times10^{6}\ N/m^2$

Hence, (a). The shearing stress is $9.8\times10^{4}\ N/m^2$

(b). The shearing strain is 0.025

(c). The shear modulus is $3.92\times10^{6}\ N/m^2$

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Topic : shear stress

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