Test 19 - Thin Cylinders and Pressure Vessels

Question 1 ప్రశ్న 1

Which statement best describes the thin-wall idealization used for a cylindrical pressure vessel?

A The wall thickness is small compared with the vessel diameter, so membrane stresses may be treated as approximately uniform through the thickness and radial stress is small compared with the principal membrane stresses. B The wall thickness must be greater than the internal radius so that radial stress is uniform. C Hoop stress must be zero through most of the wall thickness. D The theory is valid only when the vessel material has Poisson's ratio equal to zero.

Question 2 ప్రశ్న 2

For a thin cylindrical vessel of mean diameter d and wall thickness t subjected to internal pressure p, which expression gives the circumferential or hoop stress?

A σh = pd/(2t) B σh = pd/(4t) C σh = 2pt/d D σh = 4pt/d

Question 3 ప్రశ్న 3

For a thin closed-end cylindrical vessel subjected only to internal pressure p, which expression gives the longitudinal membrane stress using mean diameter d and wall thickness t?

A σl = pd/(2t) B σl = pd/(4t) C σl = pt/(2d) D σl = 4pt/d

Question 4 ప్రశ్న 4

For a thin closed-end cylindrical pressure vessel subjected only to internal pressure, what is the relationship between hoop stress σh and longitudinal stress σl?

A σh = σl/2 B σh = σl C σh = 2σl D σh = 4σl

Question 5 ప్రశ్న 5

A thin cylindrical tube is open at both ends and is pressurized internally without any end caps or externally applied axial load. Ignoring local end effects, which membrane stresses are produced by the pressure?

A Hoop stress pd/(2t) and longitudinal stress pd/(4t) B Hoop stress pd/(2t) but no longitudinal pressure stress C Longitudinal stress pd/(4t) but no hoop stress D Neither hoop nor longitudinal stress

Question 6 ప్రశ్న 6

A thin closed-end cylinder has mean diameter 1000 mm, wall thickness 10 mm and internal pressure 2 MPa. What are the hoop and longitudinal stresses?

A σh = 50 MPa and σl = 25 MPa B σh = 100 MPa and σl = 50 MPa C σh = 100 MPa and σl = 100 MPa D σh = 200 MPa and σl = 100 MPa

Question 7 ప్రశ్న 7

A thin cylindrical pressure vessel has mean diameter 1200 mm and is subjected to an internal pressure of 2 MPa. If the allowable hoop stress is 120 MPa, what minimum wall thickness is required based only on hoop stress?

A 5 mm B 8 mm C 10 mm D 20 mm

Question 8 ప్రశ్న 8

A thin cylinder has mean diameter 1000 mm and wall thickness 8 mm. If the allowable hoop stress is 150 MPa, what internal pressure is permissible based only on the hoop-stress criterion?

A 1.2 MPa B 2.0 MPa C 2.4 MPa D 4.8 MPa

Question 9 ప్రశ్న 9

For a thin closed-end cylinder made of an isotropic linear-elastic material, radial stress being neglected, which expressions correctly give circumferential strain εh and longitudinal strain εl?

A εh = (σh - νσl)/E and εl = (σl - νσh)/E B εh = (σh + νσl)/E and εl = (σl + νσh)/E C εh = σh/E and εl = σl/E for every Poisson's ratio D εh = (σl - νσh)/E and εl = (σh - νσl)/E

Question 10 ప్రశ్న 10

A thin closed-end cylinder has d = 1000 mm, t = 10 mm, p = 2 MPa, E = 200 GPa and Poisson's ratio ν = 0.30. What are the circumferential and longitudinal strains?

A εh = 250 microstrain and εl = 500 microstrain B εh = 425 microstrain and εl = 100 microstrain C εh = 500 microstrain and εl = 250 microstrain D εh = 575 microstrain and εl = 350 microstrain

Question 11 ప్రశ్న 11

For the cylinder in the previous question, if its original length is 2000 mm, what are the approximate increases in diameter and length?

A Δd = 0.100 mm and ΔL = 0.425 mm B Δd = 0.200 mm and ΔL = 0.850 mm C Δd = 0.425 mm and ΔL = 0.200 mm D Δd = 0.850 mm and ΔL = 0.425 mm

Question 12 ప్రశ్న 12

For a thin closed-end cylindrical vessel undergoing small elastic deformation, which expression gives the approximate volumetric strain of the enclosed cylindrical volume in terms of circumferential strain εh and longitudinal strain εl?

A εv = εh + εl B εv = 2εh + εl C εv = εh + 2εl D εv = 2εh + 2εl

Question 13 ప్రశ్న 13

A thin closed-end cylinder has mean diameter d = 1000 mm, length L = 2000 mm, t = 10 mm, p = 2 MPa, E = 200 GPa and ν = 0.30. Using the elementary thin-wall approximation V ≈ πd²L/4 based on the given mean diameter, what are the approximate volumetric strain and increase in enclosed volume?

A εv = 0.000525 and ΔV ≈ 0.825 L B εv = 0.000950 and ΔV ≈ 1.49 L C εv = 0.001275 and ΔV ≈ 2.00 L D εv = 0.001900 and ΔV ≈ 2.98 L

Question 14 ప్రశ్న 14

A thin closed cylinder has d = 1000 mm, t = 10 mm and p = 2 MPa, giving σh = 100 MPa and σl = 50 MPa. If E = 200 GPa and the measured increase in diameter is 0.425 mm, what value of Poisson's ratio is implied?

A 0.20 B 0.25 C 0.30 D 0.40

Question 15 ప్రశ్న 15

A closed thin cylinder has mean diameter 1000 mm, thickness 10 mm, E = 200 GPa and ν = 0.30. If its measured circumferential strain due solely to internal pressure is 425 microstrain, what is the internal pressure?

A 1.0 MPa B 1.5 MPa C 2.0 MPa D 2.5 MPa

Question 16 ప్రశ్న 16

For a thin spherical pressure vessel of mean diameter d, wall thickness t and internal pressure p, what is the membrane tensile stress in the shell?

A σ = pd/(2t) B σ = pd/(4t) C σ = pt/(2d) D σ = 4pt/d

Question 17 ప్రశ్న 17

A thin spherical vessel has mean diameter 1000 mm, thickness 10 mm and internal pressure 2 MPa. What tangential membrane stress is developed?

A 25 MPa B 50 MPa C 100 MPa D 200 MPa

Question 18 ప్రశ్న 18

The spherical vessel in the previous question is made of a material with E = 200 GPa and ν = 0.30. What are the tangential strain and approximate increase in diameter?

A ε = 0.000125 and Δd = 0.125 mm B ε = 0.000175 and Δd = 0.175 mm C ε = 0.000250 and Δd = 0.250 mm D ε = 0.000350 and Δd = 0.350 mm

Question 19 ప్రశ్న 19

A thin cylindrical vessel and a thin spherical vessel have the same mean diameter, wall thickness and internal pressure. How does the cylinder hoop stress compare with the spherical membrane stress?

A The cylinder hoop stress is one-half of the spherical stress. B They are equal. C The cylinder hoop stress is twice the spherical stress. D The cylinder hoop stress is four times the spherical stress.

Question 20 ప్రశ్న 20

A thin cylinder and a thin sphere have the same diameter and are designed for the same internal pressure and allowable membrane stress. Based only on the elementary pressure-stress criterion, how do their required wall thicknesses compare?

A The cylinder requires half the spherical thickness. B The cylinder and sphere require equal thickness. C The cylinder requires twice the spherical thickness. D The cylinder requires four times the spherical thickness.

Question 21 ప్రశ్న 21

A thin closed-end cylindrical vessel has d = 1000 mm and t = 10 mm. If the allowable hoop stress is 120 MPa and the allowable longitudinal stress is 80 MPa, what maximum internal pressure satisfies both limits?

A 1.6 MPa B 2.0 MPa C 2.4 MPa D 3.2 MPa

Question 22 ప్రశ్న 22

Which statement best explains why radial stress is usually neglected in elementary thin-cylinder membrane analysis?

A Radial stress is exactly zero everywhere through the wall. B Radial stress is compressive at the inner surface and changes through the thickness, but for a sufficiently thin wall its magnitude is small compared with the much larger hoop and longitudinal membrane stresses. C Radial stress equals hoop stress at every point in a thin wall. D Radial stress can be neglected only when Poisson's ratio is zero.

Question 23 ప్రశ్న 23

Consider the following statements about thin pressure vessels:
1. In a closed thin cylinder under internal pressure alone, hoop stress is twice longitudinal stress.
2. For an ideal open-ended thin tube with no axial end load, internal pressure produces hoop stress but no longitudinal pressure stress.
3. A thin spherical shell develops equal tangential membrane stresses in mutually perpendicular surface directions.
4. The radial stress is assumed to be larger than the hoop stress in the thin-wall approximation.

Which statements are correct?

A 1 and 4 only B 1, 2 and 3 only C 2, 3 and 4 only D 1, 2, 3 and 4

Question 24 ప్రశ్న 24

Match each thin-pressure-vessel quantity with its uniquely described elementary relationship, using mean diameter d:
1. Closed-cylinder hoop stress
2. Closed-cylinder longitudinal pressure stress
3. Thin-sphere tangential membrane stress
4. Small volumetric strain of the cylindrical enclosed volume

P. pd/(2t), acting circumferentially in the cylinder
Q. pd/(4t) = σh/2, acting axially in a closed cylinder
R. pd/(4t), acting equally in mutually perpendicular tangential directions of a sphere
S. 2εh + εl

Which matching is correct?

A 1-P, 2-Q, 3-R, 4-S B 1-Q, 2-P, 3-S, 4-R C 1-R, 2-S, 3-P, 4-Q D 1-S, 2-R, 3-Q, 4-P

Question 25 ప్రశ్న 25

A thin closed-end cylinder has mean diameter 800 mm, wall thickness 8 mm, length 3000 mm and internal pressure 1.5 MPa. If E = 200 GPa and ν = 0.30, which set of values is correct?

A σh = 37.5 MPa, σl = 18.75 MPa, Δd ≈ 0.128 mm and ΔL ≈ 0.113 mm B σh = 75 MPa, σl = 37.5 MPa, Δd ≈ 0.255 mm and ΔL ≈ 0.225 mm C σh = 75 MPa, σl = 75 MPa, Δd ≈ 0.210 mm and ΔL ≈ 0.315 mm D σh = 150 MPa, σl = 75 MPa, Δd ≈ 0.510 mm and ΔL ≈ 0.450 mm

Answer Key || సమాధానాల పట్టిక

Related Quizzes || సంబంధిత క్విజ్‌లు

Civil HMWSSB, Unit 2 - Strength of Materials and Theory of Structures Quiz

TGPSC HMWSSB Quiz

Answer Key సమాధానాల పట్టిక

Related Quizzes సంబంధిత క్విజ్‌లు