Test 20 - Thick Cylinders

Question 1 ప్రశ్న 1

Which feature most clearly distinguishes thick-cylinder stress analysis from the elementary thin-cylinder approximation?

A Radial stress and circumferential stress can vary significantly through the wall thickness and must be determined as functions of radius. B Hoop stress is assumed uniform and radial stress is identically zero throughout the wall. C Only longitudinal stress is considered because hoop stress vanishes. D The cylinder must always be subjected to external pressure rather than internal pressure.

Question 2 ప్రశ్న 2

Using tensile normal stress as positive, which pair represents Lamé's equations for radial and circumferential stresses in a thick cylinder under axisymmetric pressure loading?

A σr = A - B/r² and σθ = A + B/r² B σr = A + Br² and σθ = A - Br² C σr = A/r - Br and σθ = A/r + Br D σr = A + B/r² and σθ = A - B/r²

Question 3 ప్రశ్న 3

A thick cylinder has inner radius a, outer radius b, internal pressure pi and external pressure po. With tensile stress taken as positive, which radial-stress boundary conditions are correct?

A σr(a) = +pi and σr(b) = +po B σr(a) = -pi and σr(b) = -po C σr(a) = -po and σr(b) = -pi D σr(a) = 0 and σr(b) = 0 for every pressure loading

Question 4 ప్రశ్న 4

For a thick cylinder with inner radius a, outer radius b, internal pressure pi and external pressure po, which expressions correctly determine the Lamé constants A and B?

A A = (pi a² - po b²)/(b² - a²), B = (pi - po)a²b²/(b² - a²) B A = (pi b² - po a²)/(b² - a²), B = (pi + po)a²b²/(b² - a²) C A = (pi + po)/2, B = (pi - po)(b² - a²) D A = pi a²/(a² + b²), B = po b²/(a² + b²)

Question 5 ప్రశ్న 5

A thick cylinder is subjected to internal pressure only, with zero external pressure. Where does the maximum tensile circumferential stress occur?

A At the outer surface B At the arithmetic mean radius C At the inner surface D At the radius where radial stress is zero

Question 6 ప్రశ్న 6

A thick cylinder has inner radius 100 mm, outer radius 150 mm and internal pressure 12 MPa, with zero external pressure. What are the radial and circumferential stresses at the inner surface?

A σr = -12 MPa and σθ = 31.2 MPa B σr = 0 and σθ = 19.2 MPa C σr = -12 MPa and σθ = 19.2 MPa D σr = +12 MPa and σθ = 31.2 MPa

Question 7 ప్రశ్న 7

For the same cylinder with a = 100 mm, b = 150 mm and pi = 12 MPa, what are the radial and circumferential stresses at the outer surface?

A σr = -12 MPa and σθ = 31.2 MPa B σr = 0 and σθ = 19.2 MPa C σr = -4.8 MPa and σθ = 24.0 MPa D σr = 0 and σθ = 9.6 MPa

Question 8 ప్రశ్న 8

For the thick cylinder with a = 100 mm, b = 150 mm and pi = 12 MPa, what are the stresses at radius r = 125 mm approximately?

A σr = -4.224 MPa and σθ = 23.424 MPa B σr = -6.000 MPa and σθ = 25.200 MPa C σr = +4.224 MPa and σθ = 23.424 MPa D σr = -4.224 MPa and σθ = 13.824 MPa

Question 9 ప్రశ్న 9

For a thick cylinder with a = 100 mm, b = 150 mm and internal pressure 12 MPa only, what are the Lamé constants A and B?

A A = 9.6 MPa and B = 216000 MPa·mm² B A = 12 MPa and B = 120000 MPa·mm² C A = 21.6 MPa and B = 96000 MPa·mm² D A = -9.6 MPa and B = 216000 MPa·mm²

Question 10 ప్రశ్న 10

A thick cylinder has inner radius 100 mm, outer radius 150 mm, internal pressure 20 MPa and external pressure 5 MPa. What are the circumferential stresses at the inner and outer surfaces?

A 34 MPa at the inner surface and 19 MPa at the outer surface B 20 MPa at the inner surface and 5 MPa at the outer surface C 27 MPa at the inner surface and 12 MPa at the outer surface D 40 MPa at the inner surface and 10 MPa at the outer surface

Question 11 ప్రశ్న 11

For the cylinder with a = 100 mm, b = 150 mm, pi = 20 MPa and po = 5 MPa, what are the radial and circumferential stresses at r = 125 mm?

A σr = -10.28 MPa and σθ = 24.28 MPa B σr = -5 MPa and σθ = 19 MPa C σr = -12 MPa and σθ = 26 MPa D σr = +10.28 MPa and σθ = 24.28 MPa

Question 12 ప్రశ్న 12

A thick cylinder has inner radius 80 mm and outer radius 120 mm and is subjected only to an external pressure of 10 MPa. Which set of surface stresses is correct?

A At r = 80 mm: σr = 0, σθ = -36 MPa; at r = 120 mm: σr = -10 MPa, σθ = -26 MPa B At r = 80 mm: σr = -10 MPa, σθ = +36 MPa; at r = 120 mm: σr = 0, σθ = +26 MPa C At both surfaces σr = σθ = -10 MPa D At r = 80 mm: σr = 0, σθ = +36 MPa; at r = 120 mm: σr = -10 MPa, σθ = +26 MPa

Question 13 ప్రశ్న 13

A thick cylinder has inner radius 100 mm and outer radius 150 mm and is subjected only to internal pressure. If the allowable maximum hoop stress at the bore is 100 MPa, what is the maximum permissible internal pressure according to Lamé's equation?

A 24.0 MPa B 30.77 MPa C 38.46 MPa D 50.0 MPa

Question 14 ప్రశ్న 14

A thick cylinder has a fixed inner radius of 100 mm and carries an internal pressure of 20 MPa with zero external pressure. If the maximum allowable hoop stress at the bore is 80 MPa, what minimum outer radius is required according to Lamé's equation?

A 115.5 mm B 125.0 mm C 129.1 mm D 150.0 mm

Question 15 ప్రశ్న 15

For fixed cylinder geometry and fixed internal pressure pi, the external pressure po is increased from zero while remaining less than pi. Which statement is correct according to Lamé's equations?

A The constant B decreases because it is proportional to pi - po, and the circumferential stresses at both the inner and outer surfaces decrease. B The constant B increases and the maximum tensile hoop stress necessarily increases. C The stresses are unchanged because external pressure does not appear in Lamé's solution. D Radial stress becomes zero at both surfaces.

Question 16 ప్రశ్న 16

A thick cylinder is subjected to equal internal and external pressures p. What stress state is predicted by Lamé's equations in the radial-circumferential plane?

A σr = σθ = -p throughout the wall B σr = -p and σθ = +p throughout the wall C σr = 0 and σθ = -p throughout the wall D σr varies from -p to 0 while σθ remains zero

Question 17 ప్రశ్న 17

According to Lamé's equations, which quantity is independent of radius throughout the wall of a thick cylinder?

A σθ - σr B σθ + σr C σθ/σr D σθσr

Question 18 ప్రశ్న 18

How does the difference between circumferential and radial stress vary with radius according to Lamé's equations?

A σθ - σr = 2B/r² B σθ - σr = 2Ar² C σθ - σr = A/B D σθ - σr is constant for all radii

Question 19 ప్రశ్న 19

A thick cylinder has a = 100 mm, b = 200 mm, internal pressure 10 MPa and external pressure 5 MPa. At what radius does the circumferential stress change from tensile to compressive?

A 115.5 mm B 141.4 mm C 173.2 mm D No sign change occurs within the wall

Question 20 ప్రశ్న 20

A closed-end thick cylinder with inner radius 100 mm and outer radius 150 mm is subjected only to an internal pressure of 12 MPa. Assuming the pressure acts on the closed bore area and is resisted uniformly by the annular metal area, what longitudinal stress is produced away from end disturbances?

A 4.8 MPa tension B 9.6 MPa tension C 12 MPa tension D 19.2 MPa tension

Question 21 ప్రశ్న 21

A thick cylinder has inner radius 50 mm, outer radius 100 mm and internal pressure 8 MPa, with zero external pressure. What are the radial and circumferential stresses at the inner surface?

A σr = -8 MPa and σθ = 13.33 MPa B σr = 0 and σθ = 5.33 MPa C σr = -8 MPa and σθ = 8 MPa D σr = -4 MPa and σθ = 16 MPa

Question 22 ప్రశ్న 22

For the cylinder in the previous question, considering only the radial and circumferential stresses at the inner surface, what is the maximum in-plane shear-stress magnitude there?

A 5.33 MPa B 8.00 MPa C 10.67 MPa D 13.33 MPa

Question 23 ప్రశ్న 23

Consider the following statements about Lamé stress distributions in a thick cylinder:
1. Radial stress at a pressure boundary equals the negative of the applied pressure when tensile stress is positive.
2. Under internal pressure only, tensile hoop stress is normally maximum at the inner surface.
3. The quantity σr + σθ is constant through the wall according to Lamé's equations.
4. Under internal pressure only with zero external pressure, radial stress is tensile at the bore.

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 thick-cylinder quantity with its correct Lamé relationship or boundary condition:
1. Radial stress
2. Circumferential stress
3. Inner radial boundary condition
4. Outer radial boundary condition

P. A + B/r²
Q. -po
R. A - B/r²
S. -pi

Which matching is correct?

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

Question 25 ప్రశ్న 25

A thick cylinder has inner radius 100 mm and outer radius 200 mm and is subjected only to internal pressure. If the measured circumferential stress at the outer surface is 8 MPa, what are the internal pressure and the circumferential stress at the bore?

A Internal pressure = 8 MPa and bore hoop stress = 13.33 MPa B Internal pressure = 12 MPa and bore hoop stress = 20 MPa C Internal pressure = 16 MPa and bore hoop stress = 24 MPa D Internal pressure = 20 MPa and bore hoop stress = 32 MPa

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