A bar of steel 24 mm in diameter was subjected to a
tensile load of 60 kNs and measured extension on a 20-cm
gauge length was 0.009 cm and the change in diameter was
0.00375 cm. Calculate the Bulk modulus?
Answer / Rohit Kumar Singh
The bulk modulus (K) can be calculated using Hooke's Law for a cylinder under axial tension: F = (k * (A * d)) / ((L - ΔL/L) + (d * Δd/d)). Here, F is the applied force, A is the cross-sectional area, d is the initial diameter, L is the gauge length, and ΔL is the extension. We can rearrange this equation to solve for K: K = (F * (L + (ΔL/L))) / ((A * d) - (ΔL * d) - (Δd * A)). Substitute the given values: F = 60 kNs, L = 20 cm = 0.2 m, A = π * (24 mm)^2 / 4 = 301.5787 cc, d = 24 mm + 0.00375 cm = 24.00375 mm, ΔL = 0.009 cm = 0.009/100 m = 0.00009 m. After calculating K, convert it from Pascals (Pa) to GPa if necessary.
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