To determine the elongation and change in diameter of a steel specimen, you can use the formulas for tensile strain and Poisson's ratio.
The elongation can be calculated using the force applied and the Young's modulus for the steel. The change in diameter can be calculated using the axial strain and Poisson's ratio.
To determine the elongation of the steel specimen in the direction of the applied stress, we can use the formula for tensile strain.
Tensile strain (ε) is defined as the change in length (ΔL) divided by the original length (L).
The formula for tensile strain is: ε = ΔL/L. In this case, the force applied is 48900 N, the original length is 250 mm, and the Young's modulus for steel is needed (provided in Table 9.10) to calculate the change in length.
To calculate the change in diameter of the specimen, we can use the formula for Poisson's ratio. Poisson's ratio (ν) is defined as the negative ratio of lateral strain (ΔD/D) to the axial strain (ΔL/L).
The formula for Poisson's ratio is: ν = -ΔD/D / ΔL/L. Given the change in length (ΔL) from the previous calculation, we can calculate the change in diameter.
Since the diameter change is related to the axial strain, we need to determine whether the diameter will increase or decrease. If the axial strain is positive, meaning the material is elongating, then the diameter change (ΔD) will be negative, meaning the diameter will decrease.
If the axial strain is negative, meaning the material is contracting, then the diameter change (ΔD) will be positive, meaning the diameter will increase.