A structural steel rod has a radius of 10 mm and a length of 1m .A 100 KN force streches it along its length. Calculate stress strain and elongation where E= 2*10 power 11 N /m power -2

To solve this problem, we need to calculate stress, strain, and elongation for the given structural steel rod under a tensile force. Let’s break this down step by step, using the provided values: a radius of 10 mm, a length of 1 m, and a force of 100 kN. The Young's modulus (E) is given as 2 x 10¹¹ N/m².

Calculating Stress

Stress (σ) is defined as the force (F) applied per unit area (A) of the material. The formula to calculate stress is:

σ = F / A

First, we need to calculate the cross-sectional area (A) of the rod. The area for a circular cross-section is given by:

A = πr²

Given that the radius (r) is 10 mm, we must convert this to meters:

r = 10 mm = 0.01 m

Now we can calculate the area:

A = π(0.01 m)² = π(0.0001 m²) ≈ 3.14 x 10^-4 m²

Now we can calculate the stress:

σ = 100,000 N / (3.14 x 10^-4 m²) ≈ 318,310,000 N/m² or 318.31 MPa

Finding Strain

Strain (ε) is defined as the amount of deformation experienced by the material in the direction of the applied force divided by the original length. The formula is:

ε = σ / E

Now that we have the stress, we can calculate the strain:

ε = 318,310,000 N/m² / (2 x 10¹¹ N/m²) = 0.00159155

This means the rod experiences a strain of approximately 0.00159, indicating how much it stretches relative to its original length.

Calculating Elongation

Elongation (ΔL) can be calculated using the original length (L) and the strain:

ΔL = ε × L

Given the original length of the rod is 1 m:

ΔL = 0.00159155 × 1 m = 0.00159155 m

This translates to approximately 1.59 mm of elongation of the rod due to the applied force.

Summary of Results

• Stress (σ): 318.31 MPa
• Strain (ε): 0.00159
• Elongation (ΔL): 1.59 mm

In summary, applying a force of 100 kN to the steel rod results in a stress of about 318.31 MPa, a strain of 0.00159, and an elongation of approximately 1.59 mm. These calculations help to understand how materials respond to forces and are essential in fields like structural engineering and materials science.