Question

Two cylindrical rods (1) and (2) are welded together and loaded as shown. Rod (1) has cross-sectional area A 263 mm² and rod (2) has cross-sectional area A2 188 mm².

Determine the normal stresses ởi in rod (1) and σ2 in rod (2) if P₁ = 61 kN and P₂ = 106 kN L2

Answer 1

To determine the normal stresses in the two cylindrical rods, divide the forces applied to each rod by their respective cross-sectional areas after converting all units to the International System of Units (SI).

Step-by-step explanation:

The normal stress in a rod is calculated by dividing the force applied to the rod by the cross-sectional area of the rod. In the context of the question related to two cylindrical rods welded together, normal stresses σ₁ and σ₂ for rods (1) and (2) are found using the formulas:

σ₁ = P₁ / A₁

σ₂ = P₂ / A₂

where σ₁ and σ₂ are the normal stresses in rods (1) and (2), P₁ and P₂ are the forces applied to rods (1) and (2), and A₁ and A₂ are the cross-sectional areas of the rods. First, we need to convert all knowns to SI units.

Converting area from mm² to m²:

• A₁ = 263 mm² = 263 x 10⁻⁶ m²
• A₂ = 188 mm² = 188 x 10⁻⁶ m²

Converting forces from kN to N:

• P₁ = 61 kN = 61,000 N
• P₂ = 106 kN = 106,000 N

Now, we can calculate the stresses:

• σ₁ = 61,000 N / (263 x 10⁻⁶ m²)
• σ₂ = 106,000 N / (188 x 10⁻⁶ m²)

Performing the calculations gives us the values for σ₁ and σ₂ in Pascals (Pa).