The following data was obtained from a tensile test of steel. The test specimen was 15mm in diameter and 50 mm in length.
Load(kN)/elongation mm)
5 /0.005
10 /0.015
30 /0.048
50 /0.084
60 /0.102
64.5 /0.109
67 /0.119
68 /0.137
69 /0.16
70 /0.229
72 /0.3
76 /0.424
84 /0.668
92 /0.965
100 /1.288
112 /2.814
127 /fracture
Given that at fracture, the minimum diameter was 9.6mm. calculate the reduction in cross-sectional area. Expressing the answer as a percentage of the original cross-sectional area.
This is a duplicate post that has already been answered.
To calculate the reduction in cross-sectional area, we need to compare the original cross-sectional area with the minimum cross-sectional area at fracture.
First, let's calculate the original cross-sectional area A_original using the diameter of the test specimen before the test. The formula for the cross-sectional area of a circle is A = π * (diameter/2)^2.
A_original = π * (15mm/2)^2
A_original = π * (7.5mm)^2
A_original = 56.25π mm^2
Next, we need to calculate the cross-sectional area A_fracture at the minimum diameter of 9.6mm. Again, using the formula for the cross-sectional area of a circle:
A_fracture = π * (diameter/2)^2
A_fracture = π * (9.6mm/2)^2
A_fracture = π * (4.8mm)^2
A_fracture = 23.04π mm^2
Now, we can calculate the reduction in cross-sectional area as a percentage.
Reduction in cross-sectional area = ((A_original - A_fracture) / A_original) * 100
Reduction in cross-sectional area = ((56.25π - 23.04π) / 56.25π) * 100
Reduction in cross-sectional area = (33.21π / 56.25π) * 100
Reduction in cross-sectional area = 0.59 * 100
Reduction in cross-sectional area = 59%
Therefore, the reduction in cross-sectional area is 59% of the original cross-sectional area.