Final answer:
Stress in a material subjected to a load is calculated as the force per unit area. For a cylindrical steel rod, stress depends on the force exerted by the weight of the portion of the rod above the point of interest and the cross-sectional area of the rod. This calculation is vital for ensuring structural integrity in engineering applications.
Step-by-step explanation:
The student's question deals with stress in mechanical members subjected to various loads. Stress is the internal distribution of force per unit area within a body that balances and reacts to the external loads applied to it. To calculate stress, you use the formula σ = F / A, where σ represents stress, F is the force, and A is the cross-sectional area of the material.
Example Calculation:
(a) For a cylindrical steel rod of density ρ = 7.8 g/cm³, length 2.0 m, and a diameter of 5.0 cm, the weight of the rod causing stress is the volume times the density times gravitational acceleration (9.81 m/s²). At 1.0 m from the lower end, only half the rod contributes to the stress, so the force F is half the rod's weight. The area A is πr², where r is the radius of the rod. The normal stress is then σ = F / A.
(b) At 1.5 m from the lower end, the calculation is similar but only includes the weight of the bottom 0.5 m of the rod. Handling real-life engineering scenarios such as a cylindrical rod under a distributed load or a crane lifting a heavy weight involves understanding the fundamental stress-strain relationship and its applications.