A steel bar 10m long and 10cm ×2.5cm in section .It is subjected to an axial pull of 250KN. Determine the intensities of normal and tangential stresses on a plane.
To determine the normal and tangential stresses on a plane of the steel bar, we need to calculate the cross-sectional area and apply the formulas for normal and tangential stresses.
1. Calculate the cross-sectional area:
Given that the steel bar has a length of 10m and a cross-section of 10cm × 2.5cm, we need to convert the dimensions to meters:
- Width: 10cm = 10/100 = 0.1m
- Height: 2.5cm = 2.5/100 = 0.025m
Now, we can calculate the cross-sectional area (A) by multiplying the width and height:
A = Width × Height = 0.1m × 0.025m = 0.0025m²
2. Calculate the normal stress (σ):
The normal stress on a plane is calculated by dividing the applied force by the cross-sectional area.
σ = Force / Area
Given that the axial pull on the steel bar is 250 kN (kilonewtons), we need to convert it to newtons:
Force = 250 kN = 250 × 1000N = 250,000N
Now, we can calculate the normal stress:
σ = 250,000N / 0.0025m² = 100,000,000N/m² = 100 MPa (megapascals)
3. Calculate the tangential stress (τ):
The tangential stress on a plane is zero because there is no shear force or torsion acting on the steel bar. Therefore, τ = 0.
Therefore, the intensities of the normal and tangential stresses on the plane are:
Normal stress (σ) = 100 MPa (megapascals)
Tangential stress (τ) = 0 MPa (megapascals)