Final answer:
To calculate the normal stress on a cylindrical steel rod, we find the weight of the rod section above the point of interest, then we divide this force by the cross-sectional area. By knowing the density and dimensions of the rod as well as utilizing Young's modulus for steel, we can determine both the stress and strain at specific locations along the rod.
Step-by-step explanation:
To determine the normal stress in a cylindrical steel rod, we must first understand that the stress is a result of the rod's own weight. The rod has a density (P) of 7.8 g/cm³, a length of 2.0 m, and a diameter of 5.0 cm. Since stress is defined as force per unit area (Equation 12.34), and the force in this case is due to the weight of the rod above the point of interest, we calculate this force for the segments above 1.0 m and 1.5 m from the lower end of the rod.
For case (a), to find the normal stress at 1.0 m from the lower end, we calculate the weight of the top 1.0 m of the rod. For case (b), we calculate the weight of the top 0.5 m of the rod. The weight (W) can be calculated using the density, the gravitational acceleration (g = 9.81 m/s²), and the volume of the respective rod segment.
The cross-sectional area (A) of the rod is found using the diameter. The normal stress (σ) is then W/A. Using Young's modulus (Y) for steel, which can be typically found in reference tables, we can relate stress to strain (Equation 12.36) and thereby calculate the compressive strain the rod experiences.