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A thin cylindrical pressure vessel of diameter 2.5m and thicknesses 18m is subjected to an internal pressure of 1.2 N per sq. mm . In addition , the vessel vid also subjected to an axial tensile load of 2800KN. Determine the normal and shear stress on a plane at an angle of 60degree to the axis of the vessel v. Find also the maximum shear stress?
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A thin cylindrical pressure vessel of diameter 2.5m and thicknesses 18...
**Problem Statement:**
A thin cylindrical pressure vessel of diameter 2.5m and thickness 18m is subjected to an internal pressure of 1.2 N per sq. mm. In addition, the vessel is also subjected to an axial tensile load of 2800KN. Determine the normal and shear stress on a plane at an angle of 60 degrees to the axis of the vessel. Find also the maximum shear stress.
**Solution:**
To determine the normal and shear stress on a plane at an angle of 60 degrees to the axis of the vessel, we need to consider the combined effect of internal pressure and axial tensile load on the vessel wall.
1. **Normal Stress:**
The normal stress on a plane at an angle of 60 degrees to the axis of the vessel can be calculated using the following formula:
σn = σx*cos^2(θ) + σy*sin^2(θ) + 2*τxy*sin(θ)*cos(θ)
where,
σn = normal stress
σx = stress in the axial direction (due to axial tensile load)
σy = stress in the circumferential direction (due to internal pressure)
τxy = shear stress
2. **Stress due to Internal Pressure:**
The stress in the circumferential direction (σy) due to internal pressure can be calculated using the formula:
σy = pd/2t
where,
p = internal pressure
d = diameter of the vessel
t = thickness of the vessel wall
Substituting the given values, we get:
σy = (1.2 N/mm^2)*(2500 mm)/(2*18 mm)
3. **Stress due to Axial Tensile Load:**
The stress in the axial direction (σx) due to axial tensile load can be calculated using the formula:
σx = P/A
where,
P = axial tensile load
A = cross-sectional area of the vessel wall
Substituting the given values, we get:
σx = 2800 kN/(π*(2500/2)^2 - π*(2500/2-18)^2)
4. **Shear Stress:**
The shear stress (τxy) can be calculated using the following formula:
τxy = (σx - σy)/2
5. **Maximum Shear Stress:**
The maximum shear stress occurs on a plane at 45 degrees to the axis of the vessel. Therefore, the maximum shear stress can be calculated using the formula:
τmax = (σx - σy)/2
By substituting the values, the normal stress, shear stress, and maximum shear stress can be determined.
A thin cylindrical pressure vessel of diameter 2.5m and thickness 18m is subjected to an internal pressure of 1.2 N per sq. mm. In addition, the vessel is also subjected to an axial tensile load of 2800KN. Determine the normal and shear stress on a plane at an angle of 60 degrees to the axis of the vessel. Find also the maximum shear stress.
**Solution:**
To determine the normal and shear stress on a plane at an angle of 60 degrees to the axis of the vessel, we need to consider the combined effect of internal pressure and axial tensile load on the vessel wall.
1. **Normal Stress:**
The normal stress on a plane at an angle of 60 degrees to the axis of the vessel can be calculated using the following formula:
σn = σx*cos^2(θ) + σy*sin^2(θ) + 2*τxy*sin(θ)*cos(θ)
where,
σn = normal stress
σx = stress in the axial direction (due to axial tensile load)
σy = stress in the circumferential direction (due to internal pressure)
τxy = shear stress
2. **Stress due to Internal Pressure:**
The stress in the circumferential direction (σy) due to internal pressure can be calculated using the formula:
σy = pd/2t
where,
p = internal pressure
d = diameter of the vessel
t = thickness of the vessel wall
Substituting the given values, we get:
σy = (1.2 N/mm^2)*(2500 mm)/(2*18 mm)
3. **Stress due to Axial Tensile Load:**
The stress in the axial direction (σx) due to axial tensile load can be calculated using the formula:
σx = P/A
where,
P = axial tensile load
A = cross-sectional area of the vessel wall
Substituting the given values, we get:
σx = 2800 kN/(π*(2500/2)^2 - π*(2500/2-18)^2)
4. **Shear Stress:**
The shear stress (τxy) can be calculated using the following formula:
τxy = (σx - σy)/2
5. **Maximum Shear Stress:**
The maximum shear stress occurs on a plane at 45 degrees to the axis of the vessel. Therefore, the maximum shear stress can be calculated using the formula:
τmax = (σx - σy)/2
By substituting the values, the normal stress, shear stress, and maximum shear stress can be determined.
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A thin cylindrical pressure vessel of diameter 2.5m and thicknesses 18m is subjected to an internal pressure of 1.2 N per sq. mm . In addition , the vessel vid also subjected to an axial tensile load of 2800KN. Determine the normal and shear stress on a plane at an angle of 60degree to the axis of the vessel v. Find also the maximum shear stress?
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A thin cylindrical pressure vessel of diameter 2.5m and thicknesses 18m is subjected to an internal pressure of 1.2 N per sq. mm . In addition , the vessel vid also subjected to an axial tensile load of 2800KN. Determine the normal and shear stress on a plane at an angle of 60degree to the axis of the vessel v. Find also the maximum shear stress? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A thin cylindrical pressure vessel of diameter 2.5m and thicknesses 18m is subjected to an internal pressure of 1.2 N per sq. mm . In addition , the vessel vid also subjected to an axial tensile load of 2800KN. Determine the normal and shear stress on a plane at an angle of 60degree to the axis of the vessel v. Find also the maximum shear stress? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A thin cylindrical pressure vessel of diameter 2.5m and thicknesses 18m is subjected to an internal pressure of 1.2 N per sq. mm . In addition , the vessel vid also subjected to an axial tensile load of 2800KN. Determine the normal and shear stress on a plane at an angle of 60degree to the axis of the vessel v. Find also the maximum shear stress?.
A thin cylindrical pressure vessel of diameter 2.5m and thicknesses 18m is subjected to an internal pressure of 1.2 N per sq. mm . In addition , the vessel vid also subjected to an axial tensile load of 2800KN. Determine the normal and shear stress on a plane at an angle of 60degree to the axis of the vessel v. Find also the maximum shear stress? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A thin cylindrical pressure vessel of diameter 2.5m and thicknesses 18m is subjected to an internal pressure of 1.2 N per sq. mm . In addition , the vessel vid also subjected to an axial tensile load of 2800KN. Determine the normal and shear stress on a plane at an angle of 60degree to the axis of the vessel v. Find also the maximum shear stress? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A thin cylindrical pressure vessel of diameter 2.5m and thicknesses 18m is subjected to an internal pressure of 1.2 N per sq. mm . In addition , the vessel vid also subjected to an axial tensile load of 2800KN. Determine the normal and shear stress on a plane at an angle of 60degree to the axis of the vessel v. Find also the maximum shear stress?.
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