A specimen of aluminum having a rectangular cross section 9.6 mm × 12.4 mm (0.3780 in. × 0.4882 in.) is pulled in tension with 35000 N (7868 lbf) force, producing only elastic deformation. The elastic modulus for aluminum is 69 GPa (or 10 × 106 psi). Calculate the resulting strain.

To calculate the strain, we first need to determine the stress that is applied to the specimen. Stress (σ) is defined as force (F) divided by the area (A) over which the force is distributed.

Given values: - Force, F = 35000 N - Width of the specimen, w = 9.6 mm = 0.0096 m - Height of the specimen, h = 12.4 mm = 0.0124 m - Elastic modulus of aluminum, E = 69 GPa = 69 x 10^9 Pa

First, we calculate the cross-sectional area of the specimen: A = w × h A = 0.0096 m × 0.0124 m A = 0.0001184 m²

Next, we calculate the stress using the force and the area: σ = F / A σ = 35000 N / 0.0001184 m² σ = 295635135.135 N/m² (or Pascals)

Strain (ε) is defined as the deformation (change in length) per unit length, but in cases where only the elastic modulus (E) and stress (σ) are known, we can use Hooke's Law which relates stress to strain in the linear elastic region: σ = E × ε

Rearranging to solve for strain, we get: ε = σ / E ε = 295635135.135 Pa / 69 x 10^9 Pa ε = 0.0042846 (dimensionless, as strain is a ratio)

Therefore, the calculated strain in the aluminum specimen is approximately 0.0043 (or 0.43%).

Extra: Strain is a measure of deformation representing the displacement between particles in the material body. It is a dimensionless quantity as it is a ratio of lengths. The concept of strain is fundamental in the study of materials science and engineering, particularly when looking at the behavior of materials under load.

Elastic deformation is the non-permanent change in shape of a material when stress is applied and removed. This type of deformation occurs below the elastic limit, which means the material returns to its original shape when the stress is released.

The elastic modulus, also known as Young's modulus, is a measure of the stiffness of a material. It is defined as the ratio of stress (force per unit area) to strain (relative change in shape) in the linear (elastic) region of the stress-strain curve. It has units of pressure, which are Pascals (Pa) in the International System of Units (SI).

Hooke's Law is a principle of physics that states that the force needed to extend or compress a spring by some distance is proportional to that distance. In materials science, it extends to say that the stress applied to a material is directly proportional to the strain, provided the material has not exceeded its elastic limit.

When you calculate stress, you are essentially determining how much force is acting over a particular area. High stress can cause a material to deform and possibly fail. By knowing the strain, engineers can predict how materials will behave under certain loads and ensure that structures and components are safe and effective for their intended purposes.