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A CI flat 300 mm long and of 30 mm x 50 mm uniform section is acted upon by the following forces uniformly distributed over the respective cross-section, 25 kN in the direction of length (tensile), 350 kN in the direction of the width (compressive) and 200 kN in the direction of the thickness (tension). Determine the change in volume of the flat. Take E = 140 GN/m² and Poisson's ratio 0.25.?
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A CI flat 300 mm long and of 30 mm x 50 mm uniform section is acted up...
Given information:
Length of flat (L) = 300 mm = 0.3 m
Width of flat (b) = 30 mm = 0.03 m
Thickness of flat (h) = 50 mm = 0.05 m
Force in the direction of length (F1) = 25 kN = 25,000 N (tensile)
Force in the direction of width (F2) = 350 kN = 350,000 N (compressive)
Force in the direction of thickness (F3) = 200 kN = 200,000 N (tensile)
Young's modulus (E) = 140 GN/m² = 140 × 10^9 N/m²
Poisson's ratio (ν) = 0.25

Calculating strains:
Strain in the direction of length (ε1) = F1 / (A × E)
Where A is the cross-sectional area
A = b × h = 0.03 m × 0.05 m = 0.0015 m²
ε1 = 25000 / (0.0015 × 140 × 10^9) = 0.119

Strain in the direction of width (ε2) = F2 / (A × E)
ε2 = -350000 / (0.0015 × 140 × 10^9) = -0.238

Strain in the direction of thickness (ε3) = F3 / (A × E)
ε3 = 200000 / (0.0015 × 140 × 10^9) = 0.119

Calculating Poisson's ratio:
ν = -ε2 / ε1 = -(-0.238) / 0.119 = 2

Calculating change in volume:
Change in volume (ΔV) = V × (ε1 + ε2 + ε3)
Where V is the initial volume of the flat
V = L × b × h = 0.3 m × 0.03 m × 0.05 m = 0.00045 m³
ΔV = 0.00045 × (0.119 + (-0.238) + 0.119) = 0.000045 m³

Therefore, the change in volume of the flat is 0.000045 m³.

Explanation:
To determine the change in volume of the flat, we first calculate the strains in the three directions - length, width, and thickness. This is done using the formula strain = force / (cross-sectional area × Young's modulus). The cross-sectional area is calculated by multiplying the width and thickness of the flat.

Next, we calculate Poisson's ratio by dividing the strain in the width direction by the strain in the length direction. In this case, since the strain in the width direction is compressive, we take its negative value.

Finally, we calculate the change in volume using the formula change in volume = initial volume × (sum of strains in all directions). The initial volume is calculated by multiplying the length, width, and thickness of the flat.

In this case, the change in volume is found to be 0.000045 m³.
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A CI flat 300 mm long and of 30 mm x 50 mm uniform section is acted upon by the following forces uniformly distributed over the respective cross-section, 25 kN in the direction of length (tensile), 350 kN in the direction of the width (compressive) and 200 kN in the direction of the thickness (tension). Determine the change in volume of the flat. Take E = 140 GN/m² and Poisson's ratio 0.25.?
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A CI flat 300 mm long and of 30 mm x 50 mm uniform section is acted upon by the following forces uniformly distributed over the respective cross-section, 25 kN in the direction of length (tensile), 350 kN in the direction of the width (compressive) and 200 kN in the direction of the thickness (tension). Determine the change in volume of the flat. Take E = 140 GN/m² and Poisson's ratio 0.25.? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A CI flat 300 mm long and of 30 mm x 50 mm uniform section is acted upon by the following forces uniformly distributed over the respective cross-section, 25 kN in the direction of length (tensile), 350 kN in the direction of the width (compressive) and 200 kN in the direction of the thickness (tension). Determine the change in volume of the flat. Take E = 140 GN/m² and Poisson's ratio 0.25.? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A CI flat 300 mm long and of 30 mm x 50 mm uniform section is acted upon by the following forces uniformly distributed over the respective cross-section, 25 kN in the direction of length (tensile), 350 kN in the direction of the width (compressive) and 200 kN in the direction of the thickness (tension). Determine the change in volume of the flat. Take E = 140 GN/m² and Poisson's ratio 0.25.?.
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