Question

A tensile stress is applied along the long axis of a cylindrical steel rod with a diameter of 15 mm. If the deformation is entirely elastic, determine the magnitude of the load required to produce a 0.007 mm change in diameter. Assume the modulus of plasticity is 200 GPa and Poisson's Ratio is 0.27.

Answer 1

To find the load required to produce a change in diameter, use the stress and modulus of elasticity formula. Calculate the load by substituting the given values into the formula, resulting in an approximate value of 74.36 N.

Step-by-step explanation:

To determine the magnitude of the load required to produce a 0.007 mm change in diameter, we can use the formula for stress:

Stress = Load / Area

Since the deformation is entirely elastic, we can use the modulus of elasticity instead of the modulus of plasticity. The modulus of elasticity (or Young's modulus) is given by:

E = Stress / Strain

We can rearrange the formula to solve for Load:

Load = Stress * Area = E * Strain * Area

Using the given values, we can calculate the load:

Load = (200 * 10⁹ Pa) * (0.007 mm * 10⁻³ m) * (Pi * (15/2 * 10⁻³ m)²)

After evaluating the calculation, we find that the magnitude of the load required to produce a 0.007 mm change in diameter is approximately 74.36 N.