Question

Two solid cylindrical rods AB and BC are welded together at B and loaded as shown. Take d1 = 30 mm, d2 = 50 mm, and P = 85 kN. Find the average normal stress at the midsection of rod BC. (Input the answer with the appropriate sign.) The average normal stress at the midsection of rod BC is MPa.

Answer 1

The average normal stress at the midsection of rod BC is calculated to be 43.3 MPa, using the cross-sectional area and the given force applied to the rod.

Step-by-step explanation:

The average normal stress at the midsection of rod BC can be found by first calculating the cross-sectional area of the rod and then using the formula for stress, which is σ = P / A, where σ is stress, P is the applied force, and A is the area. Given that d2 = 50 mm for rod BC, convert this to meters (0.05 m) for consistency in units. The area, A, for a cylinder is π(d/2)^2. Therefore, A = π(0.05/2)^2 square meters. With P = 85 kN (which is 85000 N), we can calculate:

Area A = π(0.025)^2 ≈ 1.9635e-3 m²Stress σ = P / A = 85000 N / 1.9635e-3 m² ≈ 4.33e7 Pa

Converting to megapascals (MPa), the stress is 43.3 MPa. This is the average normal stress at the midsection of rod BC under the given load.

Answer 2

Main Answer:

The average normal stress at the midsection of rod BC is -128.57 MPa.

Step-by-step explanation:

The negative sign indicates that the stress is compressive. The average normal stress at the midsection of rod BC is calculated using the formula σ = P/A, where P is the applied load and A is the cross-sectional area. In this case, the cross-sectional area is
`π/4 * (d2^2 - d1^2)` for rod BC. Substituting the given values, we find the stress to be -128.57 MPa.

This compressive stress arises because the larger diameter (d2) is subjected to a greater load, causing the material to experience compression at the midsection. The negative sign is conventionally used to denote compressive stresses. The formula captures the fundamental concept that stress is the force applied per unit area. In this scenario, the force P is spread over the cross-sectional area of rod BC, resulting in compressive stress.

Understanding the stress distribution in welded structures is crucial for designing and ensuring the structural integrity of components. In this case, the compression at the midsection of rod BC may influence material selection and welding techniques to withstand the applied load effectively.