Determine the modulus of elasticity, Poisson's ratio and the shear modulus.

In summary, the given rod experiences an axial deformation of 0.150 in when subjected to an axial force of 52.0 kip, causing its diameter to decrease by 0.0007 in. Using the equations E = PL/Aδ, √=-ΔDL/DΔL, and G=E/2(1+√), we can determine the modulus of elasticity, Poisson's ratio, and shear modulus for the rod's material, which are approximately 30 Msi, 0.3, and 10000 ksi, respectively.
  • #1
texasfight
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Homework Statement


A rod with a diameter of 1.00 in and length of 6.0 ft undergoes an axial deformation of 0.150 in when subjected to an axial force of 52.0 kip. The diameter of the rod decreases by 0.0007 in at this load. Determine the modulus of elasticity, Poisson's ratio and the shear modulus for the rod's material.


Homework Equations


E = PL/Aδ
√=-ΔDL/DΔL
G=E/2(1+√)

The Attempt at a Solution


E = (52.0 kip)(72.0 in)/(((∏(1.0in)2)/4) = 31800Ksi
√ = (-(-0.0007 in)(2.00 in))/((1.00 in)(0.150in)) = 0.009
G = 31800 ksi/(2(1+0.0009)) = 15900 Ksi

Somehow the correct answer for the modulus of elasticity is about 30 Ksi, the Poisson's ratio is 0.3 and the shear modulus is about 10000 ksi
 
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  • #2
texasfight said:

Homework Statement


A rod with a diameter of 1.00 in and length of 6.0 ft undergoes an axial deformation of 0.150 in when subjected to an axial force of 52.0 kip. The diameter of the rod decreases by 0.0007 in at this load. Determine the modulus of elasticity, Poisson's ratio and the shear modulus for the rod's material.


Homework Equations


E = PL/Aδ
√=-ΔDL/DΔL
G=E/2(1+√)

The Attempt at a Solution


E = (52.0 kip)(72.0 in)/(((∏(1.0in)2)/4) = 31800Ksi
√ = (-(-0.0007 in)(2.00 in))/((1.00 in)(0.150in)) = 0.009
G = 31800 ksi/(2(1+0.0009)) = 15900 Ksi

Somehow the correct answer for the modulus of elasticity is about 30 Ksi, the Poisson's ratio is 0.3 and the shear modulus is about 10000 ksi

In your calculation for E, you forgot to divide by the [itex]\Delta[/itex]L. Also, the correct answer for E is not 30 Ksi, it is 30 Msi. The elastic properties in this problem are those for steel.
 

What is the modulus of elasticity?

The modulus of elasticity, also known as Young's modulus, is a measure of a material's ability to deform elastically (i.e. return to its original shape) when a force is applied to it. It is represented by the symbol E and is measured in units of force per unit area, such as pounds per square inch (psi) or newtons per square meter (N/m^2).

How is the modulus of elasticity determined?

The modulus of elasticity is determined by measuring the stress and strain of a material under tension or compression. Stress is defined as the force applied per unit area, while strain is a measure of the change in length of a material relative to its original length. By plotting stress versus strain on a graph, the slope of the resulting curve will give the modulus of elasticity.

What is Poisson's ratio?

Poisson's ratio is a measure of the ratio of lateral strain to axial strain when a material is stretched or compressed. It is represented by the symbol ν (nu) and has a value between -1 and 0.5. A material with a high Poisson's ratio will tend to become thinner when stretched, while a material with a low Poisson's ratio will tend to become thicker.

How is Poisson's ratio determined?

Poisson's ratio is typically determined experimentally by measuring the change in lateral and axial strain of a material when it is subjected to stress. It can also be calculated using other material properties, such as the modulus of elasticity and shear modulus.

What is the shear modulus?

The shear modulus, also known as the modulus of rigidity, is a measure of a material's resistance to shear deformation. It is represented by the symbol G and is measured in units of force per unit area, such as pounds per square inch (psi) or newtons per square meter (N/m^2). The shear modulus is related to the modulus of elasticity and Poisson's ratio through mathematical equations.

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