Under what axial tensile load, the diameter of a steel bar will be reduced from 8 cm to 7.995 cm? Take E as 2.0 ( 103 t/cm2 and Poisson’s ratio as 0.3.

To find the axial tensile load required to reduce the diameter of a steel bar from 8 cm to 7.995 cm, we can use the formula:

Δd = (4 * ν * E * L) / (π * d^2)

where:
Δd = change in diameter
ν = Poisson's ratio
E = Young's modulus
L = length of the bar
d = initial diameter

Given values:
Δd = 8 cm - 7.995 cm = 0.005 cm
ν = 0.3
E = 2.0 * 10^3 t/cm^2
d = 8 cm

Substituting these values into the formula, we can solve for L:

0.005 cm = (4 * 0.3 * 2.0 * 10^3 t/cm^2 * L) / (π * (8 cm)^2)

Simplifying:

0.005 cm = (2.4 * 10^3 t/cm^2 * L) / (64π cm^2)

To solve for L:

L = (0.005 cm * 64π cm^2) / (2.4 * 10^3 t/cm^2)

L ≈ 0.334 cm^3 / t

Therefore, the axial tensile load required to reduce the diameter of the steel bar from 8 cm to 7.995 cm is approximately 0.334 t.

To determine the axial tensile load under which the diameter of a steel bar will be reduced from 8 cm to 7.995 cm, you can use the concept of axial strain and Hooke's law.

Hooke's law states that the strain (ε) in a material is directly proportional to the stress (σ) applied to it, given by the equation ε = σ / E, where E is the Young's modulus of the material.

The axial strain can be related to the change in diameter using the equation ε = ΔL / L, where ΔL is the change in length and L is the original length.

Considering that the original diameter (D1) is 8 cm and the final diameter (D2) is 7.995 cm, the change in diameter (ΔD) can be calculated as ΔD = D1 - D2.

The change in length (ΔL) can be related to the change in diameter using the equation ΔL = (π * ΔD) / 4.

Finally, substituting these values into the equation ε = ΔL / L, we can solve for the axial strain ε.

Now we have the axial strain ε and the Young's modulus E, and we can calculate the stress (σ) using the equation σ = ε * E.

Since stress is force per unit area, the axial tensile load (F) can be calculated by multiplying the stress (σ) by the cross-sectional area (A) of the steel bar, given by A = (π * D1^2) / 4.

Let's calculate the axial tensile load:

1. Calculate ΔD:
ΔD = D1 - D2
= 8 cm - 7.995 cm
= 0.005 cm

2. Calculate ΔL:
ΔL = (π * ΔD) / 4

3. Calculate ε:
ε = ΔL / L

4. Calculate σ:
σ = ε * E

5. Calculate A:
A = (π * D1^2) / 4

6. Calculate F:
F = σ * A

Substituting the given values, including E = 2.0 * 10^3 t/cm^2 and Poisson's ratio = 0.3, into the above equations will give you the answer.