Question

A cylindrical bar of steel 10.2 mm (0.4016 in.) in diameter is to be deformed elastically by application of a force along the bar axis. Determine the force that will produce an elastic reduction of 3.4 ×10-3 mm (1.339 ×10-4 in.) in the diameter. For steel, values for the elastic modulus (E) and Poisson's ratio (ν) are, respectivley, 207 GPa and 0.30.

Answer 1

To determine the force that will produce an elastic reduction in the diameter of the cylindrical steel bar, we can use the formula for strain. Using the values for the elastic modulus, diameter, and elastic reduction in diameter, we can calculate the force.

Step-by-step explanation:

To determine the force that will produce an elastic reduction in the diameter of the cylindrical steel bar, we can use the formula for strain. Strain is defined as the change in length divided by the original length. In this case, the change in length is the elastic reduction in diameter, and the original length is the diameter of the bar.

Using the formula: Strain = (change in length) / (original length), we can rearrange the formula to solve for the force: Force = (Elastic modulus) * (Area) * (strain), where Area is π * (radius)².

Substituting the given values for the elastic modulus, diameter, and elastic reduction in diameter into the formula, we can calculate the force.