A steel tube 30 mm outside diameter and 25 mm internal diameter and length 500 mm is subjected to a tensile load of 37 KN, determine the change in length in mm to 3 decimal places when the load was applied. For the material E = 210 GPa.
Stress=σ=Force/Area
Strain=ε=σ/E
Change in length = ε*Length.
Useful conversion factors
1 GPa = 10^9 Pa
1 kN = 10^3 N
1 m = 1000 mm
Try to do calculations in standard units, namely kg, m, s.
To determine the change in length of the steel tube, we can use the formula for axial deformation:
ΔL = (F * L) / (A * E)
Where:
ΔL is the change in length
F is the tensile load
L is the original length
A is the cross-sectional area of the tube
E is the Young's modulus of the material
First, let's calculate the cross-sectional area of the tube:
Outside radius = outside diameter / 2 = 30 mm / 2 = 15 mm
Inside radius = inside diameter / 2 = 25 mm / 2 = 12.5 mm
The cross-sectional area can be calculated by subtracting the area of the inner circle from the area of the outer circle:
A = π * (R_outer^2 - R_inner^2)
Where R_outer is the outside radius and R_inner is the inside radius.
A = π * (15^2 - 12.5^2)
Next, let's calculate the change in length:
ΔL = (37,000 N * 500 mm) / (A * 210 * 10^9 N/mm^2)
Since E is given in GPa, we need to convert it to N/mm^2 by multiplying by 10^9.
Finally, we can calculate the change in length by substituting the values:
ΔL = (37,000 N * 500 mm) / (A * 210 * 10^9 N/mm^2)
Calculate the value of A and substitute it into the formula.
Evaluate the formula to get the change in length in mm to 3 decimal places.