Question

Compute the elongation of the square bar AB in Figure P3–46 if it is 1.25 m long and made from aluminum 6061-T6.

a) Clearly describe the figure or diagram (Figure P3–46) and the relevant parameters or dimensions associated with the square bar AB.
b) Specify any given data related to the material properties of aluminum 6061-T6 that are necessary for the elongation calculation.
c) Provide a step-by-step process or formula for computing the elongation of the square bar AB, considering any relevant principles of material science or mechanics.

Ensure a thorough and detailed explanation of the calculation, including any assumptions made in the process.

Answer 1

a) The figure, P3–46, represents a square bar denoted as AB. The relevant parameter is the length of the bar, which is given as 1.25 m.

b) Given data includes the material specification, aluminum 6061-T6. The properties needed for the elongation calculation include the original length of the bar (L), the cross-sectional area (A), and the Young's modulus (E) for aluminum 6061-T6.

c) To compute the elongation (ΔL) of the square bar AB, one can use Hooke's Law:
`\( \Delta L = (P \cdot L)/(A \cdot E) \)`, where P is the applied force, L is the original length, A is the cross-sectional area, and E is the Young's modulus. If the force is not given, it is crucial to consider the loading conditions and any additional information to determine the applied force accurately.

Step-by-step explanation:

a) The figure P3–46 likely illustrates a square bar denoted as AB. For clarity, it's essential to describe any additional features or dimensions specified in the figure, even though they are not explicitly mentioned in the question. In this case, the key parameter is the length of the square bar, denoted as 'L,' which is given as 1.25 m.

b) The material properties of aluminum 6061-T6 are crucial for the elongation calculation. Relevant data includes the original length of the bar (L), the cross-sectional area (A), and the Young's modulus (E) for aluminum 6061-T6. These material properties are fundamental in understanding how the material responds to an applied force and undergoes deformation.

c) The elongation (ΔL) can be calculated using Hooke's Law, a fundamental principle in material science and mechanics. Hooke's Law is expressed as
`\( \Delta L = (P \cdot L)/(A \cdot E) \)`, where P is the applied force, L is the original length, A is the cross-sectional area, and E is the Young's modulus. It's important to note that if the applied force (P) is not given, the loading conditions and any additional information must be considered to determine the force accurately. This formula helps predict the deformation or elongation of a material under the influence of an applied force within the elastic limit.