A brass alloy is known to have a yield strength of 240 MPa (35,000 psi), a tensile strength of 310 MPa (45,000 psi), and an elastic modulus of 110 GPa (16.0 * 106 psi). A cylindrical specimen of this alloy 15.2 mm (0.60 in.) in diameter and 380 mm (15.0 in.) long is stressed in tension and found to elongate 1.9 mm (0.075 in.). On the basis of the information given, is it possible to compute the magnitude of the load necessary to produce this change in length? If so, calculate the load; if not, explain why.

Based on the calculations, it is impossible to compute the magnitude of the load because the strain due to yielding is lesser than the strain due to elongation (testing).

Given the following data:

Yield strength = 240 MPa (35,000 psi).

Tensile strength = 310 MPa (45,000 psi).

Elastic modulus = 110 GPa (16.0 * 106 psi).

Diameter = 15.2 mm (0.60 in).

Length = 1.9 mm (0.075 in).

What is shear modulus?

Shear modulus can be defined as the ratio of shear stress to shear strain with respect to a physical object. Thus, shear modulus arises as a result of the application of a shear force on an object which eventually leads to its deformation or elongation.

Mathematically, the shear strain due to elongation is given by this formula;

[tex]\epsilon = \frac{\Delta L}{L} \\\\\epsilon = \frac{1.9}{380}\\\\\epsilon = 0.005[/tex]

Mathematically, the shear strain due to yielding is given by this formula;

[tex]\epsilon' = \frac{S}{E} \\\\\epsilon' = \frac{240}{110 \times 1000}\\\\\epsilon = 0.0021[/tex]

Based on the calculations, we can deduce that the strain due to yielding is lesser than the strain due to elongation (testing), which makes it impossible to compute the magnitude of the load.

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