Answer :
The value of Young's modulus is approximately 133.33 GPa, the value of Poisson's ratio is approximately -0.01375 and the thickness under a force of 800 kN is approximately 0.800 mm.
To calculate the values of Young's modulus (E) and Poisson's ratio (ν), we can use the formulas:
E = (F * L) / (A * ΔL)
ν = -ΔW / ΔL
where:
F is the axial force (1MN = 1,000 kN = 1,000,000 N)
L is the original length (1.5m = 1,500mm)
A is the original cross-sectional area (A = width * thickness)
ΔL is the change in length (2mm)
ΔW is the change in width (0.0275mm)
Let's calculate these values:
Calculate the original cross-sectional area (A):
A = width * thickness
A = 75mm * 50mm
A = 3750 mm²
Calculate Young's modulus (E):
E = (F * L) / (A * ΔL)
E = (1,000,000 N * 1,500 mm) / (3750 mm² * 2 mm)
E = 1,000,000,000 N mm / (7,500,000 mm³)
E = 133.33 GPa
Therefore, the value of Young's modulus is approximately 133.33 GPa.
Calculate Poisson's ratio (ν):
ν = -ΔW / ΔL
ν = -0.0275 mm / 2 mm
ν = -0.01375
Therefore, the value of Poisson's ratio is approximately -0.01375.
To find the thickness under a force of 800 kN, we can use the formula:
thickness = (F * L) / (A * E)
Let's calculate the thickness:
Convert the force to Newtons:
800 kN = 800,000 N
Calculate the new thickness:
thickness = (800,000 N * 1,500 mm) / (3750 mm² * 133.33 GPa)
thickness ≈ 0.800 mm
Therefore, the thickness under a force of 800 kN is approximately 0.800 mm.
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