Question

consider a cylindrical specimen of some alloy with a diameter of 0.39 inch. a tensile force of 340 lbf produces an elastic reduction in diameter of 2.64 x 10⁻⁵ inch. compute the modulus of elasticity for this alloy, given that poisson's ratio is 0.35.

Answer 1

Using the provided formula and inserting the known values, the modulus of elasticity for the alloy is calculated to be approximately 7.87 x 10⁶ lbf/in².

Step-by-step explanation:

To determine the modulus of elasticity for the alloy given the provided data, we will use the relationship between tensile stress, strain, and Poisson's ratio. We need to apply the formula E = (F * d) / (π * Δd * ν), where E is the modulus of elasticity, F is the tensile force, d is the original diameter of the specimen, Δd is the elastic reduction in diameter, and ν is Poisson's ratio.

By inserting the known values:

• Diameter of the cylindrical specimen (d) = 0.39 inch
• Tensile force (F) = 340 lbf
• Reduction in diameter (Δd) = 2.64 x 10⁻⁵ inch
• Poisson's ratio (ν) = 0.35

The calculation is performed as follows:

E = (340 lbf * 0.39 inch) / (π * 2.64 x 10⁻⁵ inch * 0.35)

After performing the calculation, we find that the modulus of elasticity for the alloy is approximately 7.87 x 10⁶ lbf/in².