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(b) Derive the expression of longitudinal stress, o, for a closed thick cylinder which has inner...
Problem 1: (a)A thick-walled cylinder, made from a homogeneous and isotropic elastic material, has an inner...
Problem 1: (a)A thick-walled cylinder, made from a homogeneous and isotropic elastic material, has an inner radius a and outer radius b. The cylinder is subjected to an internal pressure pi, and is under plane stress conditions. In this case the displacement field is of interest is given by and the stress field of interest is given by C2 C2 where, with (E and v) denoting the Young's modulus and the Poisson's Ratio. EA EB Show that b2 b2 (b/a)2-1)...
UESTION # 2: (20 Marks) The thick cylinder shown in Fig. Q2(a) is made of high strength steel wit...
UESTION # 2: (20 Marks) The thick cylinder shown in Fig. Q2(a) is made of high strength steel with an internal diameter of 200 mm and an external diameter of 300 mm. It is subjected to an internal pressure P 60 MPa The cylinder is assumed to have closed ends, as depicted in Fig. Q2(b) (a) Determine the stress state acting on the element abcd located on the outer surface of the cylinder as a result of Pi; see Fig....
4. Consider the situation of radial flow between two concentric cylinders. The outer cylinder has a...
4. Consider the situation of radial flow between two concentric cylinders. The outer cylinder has a radius of R and the inner cylinder has a radius KR. Assume flow is only in the radial direction and assume v, = v(r). Use the continuity equation and the relevant momentum balance equations to derive an expression for the pressure difference Pi-Po between the outer and inner cylinders as a function of the volumetric flow rate with L being the length of the...
Question 1 Show that the ratio of the maximum tangential stress to the average tangential stress ( η ) in a thick-walled elastic cylinder, subjected only to internal pressure, is (1+22) / (1+), where...
Question 1 Show that the ratio of the maximum tangential stress to the average tangential stress ( η ) in a thick-walled elastic cylinder, subjected only to internal pressure, is (1+22) / (1+), where λ-RRi. Plot in a diagram the value of η as function of λ.
Question 1 Show that the ratio of the maximum tangential stress to the average tangential stress ( η ) in a thick-walled elastic cylinder, subjected only to internal pressure, is (1+22) / (1+),...
Problem 4 [40 marks] A brass cylinder (E = 75 GPa and v = 0.33) of...
Problem 4 [40 marks] A brass cylinder (E = 75 GPa and v = 0.33) of outer radius 150 mm and inner radius 100 mm is to be press-fit over a steel cylinder (E = 200 GPa and v = 0.28) of outer radius 100.02 mm and inner radius 50 mm. a) Find the interface pressure; [20 marks] Draw the radial and hoop stresses in both cylinders generated due to misfit; [20 marks] c) For Masters Students only: Draw radial...
A thick ring has inner radius 1/2R, outer radius R, and mass M. Find an expression...
A thick ring has inner radius 1/2R, outer radius R, and mass M. Find an expression for its rotational inertia. Express your answer in terms of the variables R and M.
Derive the capacitance per unit length (C/length) for two coaxial cylinders. The inner cylinder has radius...
Derive the capacitance per unit length (C/length) for two coaxial cylinders. The inner cylinder has radius a and the outer cylinder has radius b.
3.5 A compound thin cylinder has a common diameter of 100 mm and the inner cylinder has a thickness of 2,5 mm. The r...
3.5 A compound thin cylinder has a common diameter of 100 mm and the inner cylinder has a thickness of 2,5 mm. The radial pressure between the two cylinders is 200 kPa and the difference between the two common diameters before shrinkage was 4,305 x 10-3 mm. Determine the (a) thickness of the outer cylinder; (b) resultant hoop stresses in both cylinders if the compound cylinder is subjected to an internal pressure of 180 kPa (E 200 GPa). 2 mm]...
A thick cylinder is 100 mm outer diameter and 50 mm inner diameter. It is pressurised to 112 MPa gauge on the inside. Take E = 205 GPa and ν = 0.27. Calculate the following:
A thick cylinder is 100 mm outer diameter and 50 mm inner diameter. It is pressurised to 112 MPa gauge on the inside. Take E = 205 GPa and ν = 0.27. Calculate the following: a). The circumferential stress on the outside layer b). The circumferential stress on the inside layer c). The longitudinal stress d). The circumferential strain in the outside layer e). The circumferential strain in the inside layer f). The change in the inner diameter g). The change...
Problem 1 [45 marks] A cylinder (= 230 MPa) which is initially free from residual stress...
Problem 1 [45 marks] A cylinder (= 230 MPa) which is initially free from residual stress has internal radius 0 = 20 mm and external radius a = 50 mm. Determine: a) The maximum internal pressure without yielding the cylinder. Give your answer in MPa. (5 marks] b) The fully plastic internal pressure. Give your answer in MPa. [5 marks] C) The radius to which the material yields, when the pressure is 150 MPa. Give your answer in mm. [10...
Problem 1: (a)A thick-walled cylinder, made from a homogeneous and isotropic elastic material, has an inner radius a and outer radius b. The cylinder is subjected to an internal pressure pi, and is under plane stress conditions. In this case the displacement field is of interest is given by and the stress field of interest is given by C2 C2 where, with (E and v) denoting the Young's modulus and the Poisson's Ratio. EA EB Show that b2 b2 (b/a)2-1)...
UESTION # 2: (20 Marks) The thick cylinder shown in Fig. Q2(a) is made of high strength steel with an internal diameter of 200 mm and an external diameter of 300 mm. It is subjected to an internal pressure P 60 MPa The cylinder is assumed to have closed ends, as depicted in Fig. Q2(b) (a) Determine the stress state acting on the element abcd located on the outer surface of the cylinder as a result of Pi; see Fig....
4. Consider the situation of radial flow between two concentric cylinders. The outer cylinder has a radius of R and the inner cylinder has a radius KR. Assume flow is only in the radial direction and assume v, = v(r). Use the continuity equation and the relevant momentum balance equations to derive an expression for the pressure difference Pi-Po between the outer and inner cylinders as a function of the volumetric flow rate with L being the length of the...
Question 1 Show that the ratio of the maximum tangential stress to the average tangential stress ( η ) in a thick-walled elastic cylinder, subjected only to internal pressure, is (1+22) / (1+), where λ-RRi. Plot in a diagram the value of η as function of λ.
Question 1 Show that the ratio of the maximum tangential stress to the average tangential stress ( η ) in a thick-walled elastic cylinder, subjected only to internal pressure, is (1+22) / (1+),...
Problem 4 [40 marks] A brass cylinder (E = 75 GPa and v = 0.33) of outer radius 150 mm and inner radius 100 mm is to be press-fit over a steel cylinder (E = 200 GPa and v = 0.28) of outer radius 100.02 mm and inner radius 50 mm. a) Find the interface pressure; [20 marks] Draw the radial and hoop stresses in both cylinders generated due to misfit; [20 marks] c) For Masters Students only: Draw radial...
3.5 A compound thin cylinder has a common diameter of 100 mm and the inner cylinder has a thickness of 2,5 mm. The radial pressure between the two cylinders is 200 kPa and the difference between the two common diameters before shrinkage was 4,305 x 10-3 mm. Determine the (a) thickness of the outer cylinder; (b) resultant hoop stresses in both cylinders if the compound cylinder is subjected to an internal pressure of 180 kPa (E 200 GPa). 2 mm]...
Problem 1 [45 marks] A cylinder (= 230 MPa) which is initially free from residual stress has internal radius 0 = 20 mm and external radius a = 50 mm. Determine: a) The maximum internal pressure without yielding the cylinder. Give your answer in MPa. (5 marks] b) The fully plastic internal pressure. Give your answer in MPa. [5 marks] C) The radius to which the material yields, when the pressure is 150 MPa. Give your answer in mm. [10...
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