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A C.I. flat, 300 mm long and of 30 mm × 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 thickness (tensile). Determine the change in volume of the flat. Take E = 140 GN/m2 , and Poisson’s ratio = 0.25?
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A C.I. flat, 300 mm long and of 30 mm × 50 mm uniform section, is acte...
**Solution:**
Given data:
Length of C.I. flat, l = 300 mm = 0.3 m
Cross-sectional dimensions, b = 50 mm = 0.05 m, h = 30 mm = 0.03 m
Forces acting on the flat:
Tensile force in the direction of length, P1 = 25 kN
Compressive force in the direction of width, P2 = 350 kN
Tensile force in the direction of thickness, P3 = 200 kN
Elastic modulus of C.I., E = 140 GN/m2
Poisson’s ratio, ν = 0.25
We need to determine the change in volume of the flat.
**Formula:**
The change in volume of a body can be determined using the following formula:
ΔV/V = 3αΔT – βΔP
Where,
ΔV is the change in volume
V is the original volume
α is the coefficient of linear expansion
ΔT is the change in temperature
β is the bulk modulus of elasticity
ΔP is the change in pressure
**Calculation:**
1. Calculation of original volume:
The original volume of the flat can be determined as follows:
V = lbh
V = 0.3 × 0.05 × 0.03
V = 0.000045 m3
2. Calculation of change in length:
The change in length of the flat can be determined using the following formula:
ΔL/L = P1/E
Where,
ΔL is the change in length
L is the original length
P1 is the tensile force in the direction of length
E is the elastic modulus of C.I.
ΔL/L = 25 × 103/(140 × 109)
ΔL/L = 1.786 × 10-4
The change in length of the flat is 1.786 × 10-4 m.
3. Calculation of change in width:
The change in width of the flat can be determined using the following formula:
ΔW/W = -ν(P1/E) + (P2/E)
Where,
ΔW is the change in width
W is the original width
ν is Poisson’s ratio
P1 is the tensile force in the direction of length
P2 is the compressive force in the direction of width
E is the elastic modulus of C.I.
ΔW/W = -0.25(25 × 103)/(140 × 109) + (350 × 103)/(140 × 109)
ΔW/W = 2.321 × 10-4
The change in width of the flat is 2.321 × 10-4 m.
4. Calculation of change in thickness:
The change in thickness of the flat can be determined using the following formula:
Δh/h = P3/(E/2(1 + ν))
Where,
Δh is the change in thickness
h is the original thickness
P3 is the tensile force in the direction of thickness
E is the elastic modulus of C.I.
ν is Poisson’s ratio
Δh/h = 200 × 103/(140 × 109/2(1 + 0.25))
Δh/h = 2
Given data:
Length of C.I. flat, l = 300 mm = 0.3 m
Cross-sectional dimensions, b = 50 mm = 0.05 m, h = 30 mm = 0.03 m
Forces acting on the flat:
Tensile force in the direction of length, P1 = 25 kN
Compressive force in the direction of width, P2 = 350 kN
Tensile force in the direction of thickness, P3 = 200 kN
Elastic modulus of C.I., E = 140 GN/m2
Poisson’s ratio, ν = 0.25
We need to determine the change in volume of the flat.
**Formula:**
The change in volume of a body can be determined using the following formula:
ΔV/V = 3αΔT – βΔP
Where,
ΔV is the change in volume
V is the original volume
α is the coefficient of linear expansion
ΔT is the change in temperature
β is the bulk modulus of elasticity
ΔP is the change in pressure
**Calculation:**
1. Calculation of original volume:
The original volume of the flat can be determined as follows:
V = lbh
V = 0.3 × 0.05 × 0.03
V = 0.000045 m3
2. Calculation of change in length:
The change in length of the flat can be determined using the following formula:
ΔL/L = P1/E
Where,
ΔL is the change in length
L is the original length
P1 is the tensile force in the direction of length
E is the elastic modulus of C.I.
ΔL/L = 25 × 103/(140 × 109)
ΔL/L = 1.786 × 10-4
The change in length of the flat is 1.786 × 10-4 m.
3. Calculation of change in width:
The change in width of the flat can be determined using the following formula:
ΔW/W = -ν(P1/E) + (P2/E)
Where,
ΔW is the change in width
W is the original width
ν is Poisson’s ratio
P1 is the tensile force in the direction of length
P2 is the compressive force in the direction of width
E is the elastic modulus of C.I.
ΔW/W = -0.25(25 × 103)/(140 × 109) + (350 × 103)/(140 × 109)
ΔW/W = 2.321 × 10-4
The change in width of the flat is 2.321 × 10-4 m.
4. Calculation of change in thickness:
The change in thickness of the flat can be determined using the following formula:
Δh/h = P3/(E/2(1 + ν))
Where,
Δh is the change in thickness
h is the original thickness
P3 is the tensile force in the direction of thickness
E is the elastic modulus of C.I.
ν is Poisson’s ratio
Δh/h = 200 × 103/(140 × 109/2(1 + 0.25))
Δh/h = 2
Community Answer
A C.I. flat, 300 mm long and of 30 mm × 50 mm uniform section, is acte...
A C.I. flat, 300 mm long and of 30 mm × 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 thickness
(tensile). Determine the change in volume of the flat. Take E = 140 GN/m2
, and Poisson’s ratio = 0.25
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 thickness
(tensile). Determine the change in volume of the flat. Take E = 140 GN/m2
, and Poisson’s ratio = 0.25
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A C.I. flat, 300 mm long and of 30 mm × 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 thickness (tensile). Determine the change in volume of the flat. Take E = 140 GN/m2 , and Poisson’s ratio = 0.25?
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A C.I. flat, 300 mm long and of 30 mm × 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 thickness (tensile). 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 C.I. flat, 300 mm long and of 30 mm × 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 thickness (tensile). 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 C.I. flat, 300 mm long and of 30 mm × 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 thickness (tensile). Determine the change in volume of the flat. Take E = 140 GN/m2 , and Poisson’s ratio = 0.25?.
A C.I. flat, 300 mm long and of 30 mm × 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 thickness (tensile). 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 C.I. flat, 300 mm long and of 30 mm × 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 thickness (tensile). 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 C.I. flat, 300 mm long and of 30 mm × 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 thickness (tensile). Determine the change in volume of the flat. Take E = 140 GN/m2 , and Poisson’s ratio = 0.25?.
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