A plane element is subjected to a shear stress τ = 360MPa which results to a shear strain σ = 0.008rad.

a) determine the shear modulus G of the element
b)What is the horizontal displacement, d, of the element if te height of the element is equal to 50mm

I worked out part a to be 45GPa (360*10^6/0.008), but not entirely sure.

Thank you for your help
Sam

To determine the shear modulus, you can use the formula:

G = τ / σ

Given that the shear stress τ is 360 MPa and the shear strain σ is 0.008 rad, you can substitute these values into the formula to find G.

G = 360 MPa / 0.008 rad
= 45,000 MPa
= 45 GPa

So, your calculation for part a is correct. The shear modulus G of the element is indeed 45 GPa.

Moving on to part b, to calculate the horizontal displacement of the element (d), you need to use the equation:

d = γ * h

where d is the horizontal displacement, γ is the shear strain, and h is the height of the element.

Given that the shear strain γ is 0.008 rad and the height h is 50 mm, first, you need to convert the height to meters.

h = 50 mm = 50 / 1000 m
= 0.05 m

Now, you can substitute these values into the equation to calculate the horizontal displacement (d).

d = 0.008 rad * 0.05 m
= 0.0004 m

Therefore, the horizontal displacement (d) of the element is 0.0004 meters or 0.4 mm.

I hope this helps! Let me know if you have any further questions.

To determine the shear modulus of the element, we can use the formula:

G = τ / γ

where:
G is the shear modulus,
τ is the shear stress, and
γ is the shear strain.

By substituting the values given:
τ = 360 MPa,
γ = 0.008 rad,

we can calculate:

G = 360 MPa / 0.008 rad = 45 GPa.

Your calculation for part a is correct. The shear modulus of the element is indeed 45 GPa.

Moving on to part b, to calculate the horizontal displacement (d) of the element, we can use the formula:

d = γ * h

where:
d is the horizontal displacement,
γ is the shear strain, and
h is the height of the element.

By substituting the given values:
γ = 0.008 rad,
h = 50 mm = 0.05 m,

we can calculate:

d = 0.008 rad * 0.05 m = 0.0004 m = 0.4 mm.

Therefore, the horizontal displacement of the element is 0.4 mm.