GTU Paper Analysis Chapter 1 Introduction · 17. Explain the Belleville spring and its...

GTU Paper Analysis

Design of Machine Elements (2151907) Department of Mechanical Engineering Darshan Institute of Engineering & Technology

Chapter 1 – Introduction

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Theory

1. State and illustrate various principal design rules as per Casting design with

sketches.

07 05 07 07

2. State and illustrate various principle design rules used in design for forging. 07

3. Explain the designing for wear. 03

4. Design for creep. 03

5. Discuss the importance of selection of materials in machine design. 04 07 03

6. The series factor or geometric progression ratio for R10 series is (a) 1.26 (b) 1.12 (c) 1.58 (d) 1

01

7. Name the various alloying elements in ‘alloy’ steels. 03

8. What are the principles of design for manufacture and assemblies (DFMA)? 07 07 04

9. In which type of material Guest’s theory of failure is applicable? 01

10. What are the effects of following alloying elements on the properties of the materials? (i) Chromium, (ii) Molybdenum, (ii) Manganese

03

11. What are preferred numbers? 03 03

12. What are the principles for design of welded assemblies? Explain with neat sketch.

07

13. Why metals in their pure form are unsuitable for industrial purpose? 03

14. Explain principles of Design for Aesthetic and Ergonomics. 07

Examples

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1. What are preferred numbers? The maximum & minimum load carrying capacities of dumpers in a manufacturing unit are 630 KN and 40 KN respectively. The company is interested in developing seven models in this range. Specify their load carrying capacities.

05

2. Find out the number of R5 basic series from 1 to 10. 03

3. It is required to standardize 11 shafts from 100 to 1000 mm diameter. Specify their diameters.

03

GTU Paper Analysis


Chapter 2 – Design Against Fluctuating Loads

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Theory

1. Derive Soderberg’s equation and state its application to different types of

loadings.

07 07

2. What is endurance strength? Discuss the factors affecting endurance strength of the materials.

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3. Stress concentration factor is defined as ratio of (a) maximum stress to the endurance limit (b) nominal stress to the endurance limit (c) maximum stress to the nominal stress (d) nominal stress to the maximum stress

01

4. The endurance or fatigue limit is defined as the maximum value of the stress which a polished standard specimen can withstand without failure, for infinite number of cycles, when subjected to (a) static load (b) dynamic load

(c) static as well as dynamic load (d) completely reversed load

01

5. What are the Goodman and the Soderberg line? 03

6. What is stress concentration? State the methods of reducing stress concentration.

04 03 04

7. Define Stress Concentration Factor. 01

8. What do you mean by Factor of Safety for Fatigue Loading? 01

9. Write Goodman formula for fluctuating stresses. 01

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10. What is cumulative damage in fatigue? Explain in brief. 03

11. Compare among Gerber curve, Soderberg and Goodman lines for fluctuating stresses in machine component.

03

12. Explain Miner’s rules for Cumulative fatigue Damage. 04

13. Explain Goodman line design criteria for fluctuating stresses. 07

14. Explain fluctuating stress in detail 04

15. Explain S-N diagram for steels with neat sketch. 07

16. Explain cyclic stress characterization with mathematical formulations and graphs. 04

Examples

1. The following data refers to a transmission shaft: Torsional moment that varies from = - 100 Nm to + 600 Nm. The Ultimate tensile strength = 630 MPa, Yield strength = 360 MPa, Stress load correction factor = 0.6, Size correction factor = 0.85, Surface finish factor = 0.8, Reliability factor = 0.897, Factor of safety = 2, Calculate the shaft diameter using distortion energy theory of failure.

07

2. A machine component is subjected to fluctuating stress that varies from 40 to 100 MPa. The corrected endurance limit stress for the machine component is 270 MPa. The ultimate tensile strength and yield strength of material are 600 and 450 MPa respectively. Calculate the factor of safety using 1. Gerber theory, 2. Soderberg line and 3. Goodman line.

07

3. A hot rolled steel shaft is subjected to a torsional moment that varies from 330 Nm to –110 Nm and an applied bending moment at a critical section varies from 440 Nm to –220 Nm. The shaft is of uniform cross-section and no keyway is present at the critical section. Determine the required shaft diameter. The material has an ultimate strength of 550 MPa and yield strength of 410 MPa. Take the endurance limit as half the ultimate strength, factor of safety of 2, size factor of 0.85 and a surface finish factor of 0.62.

07 07

4. A cantilever beam made of carbon steel of circular cross-section as shown in figure, is subjected to a load which varies from –F to 3F. Determine the maximum load that the beam can sustain for an indefinite life. Factor of safety = 2, Stress

07 07

GTU Paper Analysis


concentration factor =1.42, Notch sensitivity = 0.9 Ultimate stress = 550 MPa, Yield stress = 470 MPa, Endurance limit = 275 MPa, Size factor = 0.85, Surface finish factor = 0.89.

5. A simply supported beam has a concentrated load at the centre which fluctuates from a value of ‘P’ to ‘4P’. The span of the beam is 500 mm and its cross-section is circular with a diameter of 60 mm. Taking for the beam material an ultimate stress of 700 MPa, a yield stress of 500 MPa, endurance limit of 330 MPa for reversed bending, and a factor of safety of 1.3, Calculate value of load ‘P’ based on Goodman’s formula. Take a size factor of 0.85 and a surface finish factor of 0.9.

07

6. A bar of steel having corrected endurance strength of 275 MPa, tensile yield strength of 415 MPa and ultimate tensile strength of 550 MPa. If it is subjected to an alternating torsional stress of ± 250 MPa, find the factor of safety against fatigue failure and the expected life of the component.

04

7. A transmission shaft carries a pulley midway between the two bearings. The bending moment at the pulley varies from 200 N-m to 600 N-m, as the torsional moment in the shaft varies from 70 N-m to 200 N-m. The frequencies of variation of bending and torsional moments are equal to the shaft speed. The shaft is made of steel FeE 400 having Ultimate tensile stress 540 N/mm2 and yield stress 400

07

GTU Paper Analysis


N/mm2. The corrected endurance limit of the shaft is 200 N/mm2. Determine the diameter of the shaft using a factor of safety of 2.

8. A solid circular shaft, 15 mm in diameter, is subjected to torsional shear stress, which varies from 0 to 35 N/mm2 and at the same time, is subjected to an axial stress that varies from –15 to +30 N/mm2. The frequency of variation of these stresses is equal to the shaft speed. The shaft is made of steel FeE 400 (Sut = 540 N/mm2 and Syt = 400 N/mm2) and the corrected endurance limit of the shaft is 200 N/mm2. Determine the factor of safety

07

9. A machine component is subjected to a flexural stress which fluctuates between +300 MN/m2 and –150 MN/m2. Determine the value of minimum ultimate strength according to 1. Gerber relation; 2. Modified Goodman relation; and 3. Soderberg relation. Take yield strength = 0.55 x Ultimate strength; Endurance strength = 0.5 x Ultimate strength; and factor of safety = 2. Compare the results on plot.

07

10. A 25 mm diameter shaft is made of forged steel 30C8 with Sut = 600 N/mm2. There is a step in the shaft the theoretical stress concentration factor at the step is 2.1. The notch sensitivity is 0.84. Determine the endurance limit of the shaft if it is subjected to a reversible bending moment

07

GTU Paper Analysis


Chapter 3 – Design of Springs

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Theory

1. Explain buckling of spring in detail. 04

2. What is nipping in a leaf spring? Discuss its role. 04 04 04 04

3. Explain surge phenomenon in spring. 04 03 01 03

4. When a helical compression spring is subjected to an axial compressive load, the stress induced in the wire is (a) tensile stress (b) compressive stress (c) torsional shear stress (d) bending stress

01 01

5. In leaf springs, the longest leaf is known as (a) lower leaf (b) master leaf (c) upper leaf (d) none of these

01

6. What is shot peening? 03

7. Define Spring Rate. 01

8. Which type of spring is mostly used in Gramophone? 01

9. What is the function of a spring? In which type of springs the behavior is non-linear?

03

10. Explain the following terms of the spring: (1) Free Length (2) Spring Rate (3) Spring Index (4) Solid Height.

04

11. The extension springs are in considerably less use than the compression springs, why?

03

12. What is helical torsion spring? How does it differ from helical compression spring?

07

GTU Paper Analysis


13. Classify and explain springs according to their shapes with neat sketches. 03

14. Prove that equal strength nested springs having the same solid length and deflection would have the same spring index.

04

15. Why is factor of safety in spring preferred near to unity? 03

16. Explain the stresses induced in compression and tension spring. 04

17. Explain the Belleville spring and its applications. 03

18. Explain the design steps of semi elliptical laminated multi leaf spring. 04

19. Explain leaf spring with neat sketch. 03

20. Explain springs in series and parallel connections with sketch. 04

21. Explain the merits and demerits of Non-circular cross section wire used in spring 04

22. Explain concentric spring and its applications. 03

Examples

1. Design a helical compression spring from the following data: Minimum load = 100 N, Maximum load = 225.6 N, Compression of spring = 10 mm, Permissible shear stress for spring material = 440 MPa, Spring end – square and ground ends, Modulus of rigidity for spring material = 0.80 x 105 MPa.

07

2. A semi-elliptic leaf spring consists of two extra full length leaves and eight graduated length leaves, including the master leaf. The center to center distance between the two eyes of the spring is 1 m. The maximum force acting on the spring is 10 kN and the width of the leaf is 50 mm. The spring is initially preloaded in such a way that when the load is maximum, the stresses induced in all the leaves are equal to 350 N/mm2. The modulus of elasticity of the leaf material is 2.07 x 105 N/mm2. Determine: (i) The thickness of leaves. (ii) The deflection of the spring at maximum load.

07

3. A helical compression spring made of oil tempered carbon steel is subjected to 07

GTU Paper Analysis


a fluctuating load from 400 N to 1000 N. The spring index is 6 and the design factor of safety is 1.25. If the yield stress in shear is 770 MPa and endurance stress in shear is 350 MPa, Find: 1. Size of the spring wire, 2. Diameters of the spring, 3. Number of turns of the spring, and 4. Free length of the spring. The compression of the spring at the maximum load is 30 mm. For spring material, the modulus of rigidity is 80 KN/mm2. Spring ends are square and ground.

4. A semi-elliptical laminated vehicle spring to carry a load of 6000 N is to consist of seven leaves 65 mm wide, two of the leaves extending the full length of the spring. The spring is to be 1.1 m in length and attached to the axle by two U-bolts 80 mm apart. The bolts hold the central portion of the spring so rigidly that they may be considered equivalent to a band having a width equal to the distance between the bolts. Assume a design stress for spring material as 350 N/mm2. Determine: 1. Thickness of leaves 2. Deflection of spring 3. Diameter of eye 4. Length of leaves. Take E = 210 KN/mm2, Bearing pressure = 8 N/mm2.

07

5. The valve of an aircraft engine is operated by a cluster of two concentric springs made of same material. The maximum load on the spring is 6500 N. The permissible shear stress for the spring material is 625 N/mm2. Assuming spring index for both springs as 6 and the deflection under the load should not exceed 30 mm. Calculate the main dimensions of the springs. G = 8 ×104 N/mm2. Use standard coil clearance.

07

6. A semi-elliptical spring has ten leaves in all, with the two full length leaves extending 625 mm. It is 62.5 mm wide and is made of strips 6 mm thick. The leaves are pre-stressed so as to equalize stresses in all leaves.

07 07

7. Design a helical compression spring for a maximum load of 1000 N for a deflection of 25 mm using the value of spring index as 5. The maximum permissible stress for spring wire is 420 N/mm2, and modulus of rigidity is 84 KN/ mm2.

07

8. Design a leaf spring for following specification: Total load = 14 tonnes, Numbers of springs supporting the load = 4, Maximum number of leaves = 10, Span of the spring = 1000 mm, Permissible deflection = 80 mm, Take Young Modulus = 0.2 x 106 N/mm2, Allowable stress in spring material = 600 N/mm2

07

GTU Paper Analysis


9. Design a close coiled helical compression spring for a service load ranging from 2250 N to 2750 N. The axial deflection of the spring for the load range is 6 mm. Assume a spring index of 5. The permissible shear stress intensity is 420 N/mm2 and modulus of rigidity, G = 84 kN/mm2.

07

10. A semi-elliptic leaf spring used for automobile suspension consists of three extra full-length leaves and 15 graduated-length leaves, including the master leaf. The centre-to-centre distance between two eyes of the spring is 1 m. The maximum force that can act on the spring is 75 kN. For each leaf, the ratio of width to thickness is 9:1. The modulus of elasticity of the leaf material is 207000 N/mm2. The leaves are pre-stressed in such a way that when the force is maximum, the stresses induced in all leaves are same and equal to 450 N/mm2. Determine (i) the width and thickness of the leaves; (ii) the initial nip.

07

11. A wagon weighing 1530 Kg mass and moving with a speed of 3 km/hr is to be brought to rest by means of a buffer made of two closed helical springs of circular section, on each end of wagon. The spring stiffness is 30 kN/mm and spring index is 6. Maximum permissible shear stress is not to exceed 600 N/mm2. Find the diameter of wire and number of coils in each spring. Take for spring material G = 8.4 x 104 N/mm2. Check the design for buckling.

07

12. A laminated spring of an automobile is to carry a load of 5 kN. The spring is made 1000 mm between the supports. Design the spring. Number of leaves to be taken as 8 with two of them of full length. Distance between U-bolts may be taken as 60 mm.

07

13. A spring having outer diameter of coil as 72 mm, deflects for 50 mm at the maximum load of 700 N. Calculate the wire diameter and number of turns for the spring if the shear stress is 300 MPa and modulus of rigidity 84 KN/mm2. Take spring index of 8.

07

14. Design a helical compression spring with plain ends made out of bronze for operating load range of 100 N to 150 N. The deflection of the spring is 6 mm and spring index = 9. The allowable shear stress for spring is 300 MPa and modulus of rigidity is 80 KN/mm2. Determine (1) Diameter of spring wire (2) Mean coil diameter (3) Total number of turns (4) Stiffness of spring

07

15. Calculate the dimensions of a helical spring for a spring loaded Ramsbottom safety valve from the following data: Valve diameter = 65 mm, Maximum

07

GTU Paper Analysis


pressure when the valve blows off freely = 0.73 N/mm2 Valve lift when pressure rise from 0.7 to 0.73 N/mm2 = 3.2 mm Maximum permissible stress = 500 N/mm2 Spring Index = 6 Modulus of rigidity = 0.85x105 N/mm2.

GTU Paper Analysis


Chapter 4 – Belt and Chain Drive

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Theory

1. Explain any two type of chain with neat sketches. 05

2. Explain the polygon action of chain. 02

3. Compare the belt and chain drives. 03

4. Explain tooth correction factor for roller chain. 03

5. Explain load and power transmitting capacity of chain drive. 04

6. Derive the expression of a ratio of driving tensions for the flat belt drive. Explain the effect of

centrifugal tension on ratio of driving tensions in brief. 07

07

7. Derive an expression for the ratio of driving tensions of a V-belt drive. 07 07

8. What is crowning of the pulley? State the objectives of providing crowning. 03 04

9. Explain the step by step procedure used for design of chain drive system. 07 03

10. Why is the cross-section of the pulley an elliptical arm? Why is major axis of the cross-section in the

plane of rotation?

03

11. State the advantage and disadvantage of the chain drive over belt and rope drive. 04

12. Sketch the cross section of a V-belt and label its important parts. 03

13. Explain the difference between belt slip and belt creep. 03

14. Explain the design of belt. 04

GTU Paper Analysis


15. State the advantages of chain drive over belt drive 04

16. Explain effect of slip and creep on belt drive 03

17. List advantages and disadvantages of chain drive 04

18. Explain effect of initial tension on belt drive 03

19. Explain working of (1) Compound belt drive (2) Fast and loose pulley belt drive with neat sketch 04

20. What is the purpose of providing steel or nylon cords in the inner case of V-belt? 03

21. What are the application of Flat, V, Round and Timing belt belts in engineering? 04

22. What is polygon effect in chain drive? How it is minimized? 03

23. Explain the procedure for selection of a standard V belt. 04

Examples

1.

A flat belt drive transmits 50 kW at 25 m/s. The mass of the belt is 1.75 kg per metre of belt length and

width the belt is 180 mm. The belt drive is cross belt drive having driver pulley of 350 mm and driven

pulley of 1050 mm. The centre distance between two pulleys is 5 m. Calculate the length of belt; angle

of contact; belt tensions and thickness of belt. Take mass density of belt = 1000 kg/m3 and coefficient

of friction between belt and pulley surface =0.35.

07

2.

Two V Belts of section B are transmitting power on grooved pulleys. Angle of Groove is 350. Belt angle

is 400. The driver pulley of 300 mm runs at 1500 rpm and driven pulley is 600 mm diameter. The

coefficient of friction between belt and pulley is 0.3. If the power transmitted is 150 kW, determine (i)

Centrifugal tension (ii) maximum tension, (iii) length of the belt for open drive. (iv) designation of the

belt, (v) the speed at which maximum power can be transmitted The mass of the belt is 0.193 kg per m

length For Section B Belt. Assume centre distance between pulleys is 900 mm.

07

3.

Design a 10 mm thick rubber belt to drive a dynamo generating 20 KW at 2250 R.P.M. and fitted with a

pulley 200 mm diameter. The dynamo efficiency to be 85%. Allowable stress for belt = 2.1 MPa,

Density of rubber = 1000 kg/m3, Angle of contact for dynamo pulley = 1650, μ = 0.3. 07

4. A compressor, requiring 90 KW, is to run at about 250 R.P.M. The drive is by V-belts from an electric 07

GTU Paper Analysis


motor running at 750 R.P.M. The diameter of pulley on compressor shaft must not be greater than 1

metre while the centre distance between the pulleys is limited to 1.75 metre. The belt speed should not

exceed 1600 meters/min. Determine the number of V-belts required to transmit the power if each belt

has a cross-sectional area of 375 mm2, density 1000 kg/m3 and an allowable tensile stress of 2.5 MPa.

The groove angle of the pulleys is 350. The coefficient of friction between the belt and the pulley is 0.25.

Calculate also the length required of each belt.

5.

A fan is driven by open belt from a motor runs at 880 rpm. A leather belt 8 mm thick and 250 mm wide

is used. The diameter of motor pulley and driven pulley are 350 mm and 1370 mm respectively. The

centre distance is 1370 mm and both pulleys are made of cast iron. The coefficient of friction of leather

on cast iron is 0.35. The allowable stress for the belt is 2.5 MPa, which allows for factor of safety. The

belt mass is 975 kg/m3. Determine the power capacity of belt drive.

07

6.

A cast iron pulley transmits 20 kW at 300 rpm. The diameter of pulley is 550 mm and has four straight

arms of elliptical cross-section in which the major axis is twice the minor axis. Find the dimensions of

the arm if the allowable bending stress is 15 MPa.

04

7.

A leather belt 9 mm x 250 mm is used to drive cast iron pulley 900 mm in diameter at 336 r.p.m. If the

active arc on smaller pulley is 1200 and the stress in the tight side is 2 N/mm2, find the power capacity

of the belt. The density of leather may be taken as 980 kg/m3, and μ = 0.35. 07

8.

Two parallel shafts whose center lines are 4.8 m apart, are connected by an open belt drive. The

diameter of the larger pulley 1.5 m and that of smaller pulley 1.05 m. The initial tension in the belt

when stationery is 3 KN. The mass of the belt is 1.5 kg/m length. The co-efficient of friction between

the belt and the pulley is 0.3 Taking centrifugal tension in to account, calculate the horse power

transmitted, when smaller pulley rotates at 400 r.p.m.

07

9.

A centrifugal blower driven by horizontal belt drive running at 600 r.p.m. by a 15 kW, 1750 r.p.m.

electric motor. The center distance is twice the diameter of the larger pulley. The density of the belt

material = 1500 kg/m3; maximum allowable stress = 4 MPa; Coefficient of friction at motor pulley and

blower pulley is 0.5 and 0.4 respectively; peripheral velocity of the belt = 20 m/s. Determine the

following: 1. Pulley diameters; 2. belt length; 3. cross-sectional area of the belt; 4. minimum initial

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GTU Paper Analysis


tension for operation without slip.

10.

A 15 KW power transmitting leather belt drive running at 1440 rpm to 480 rpm. The center distance

between the pulleys is twice the diameter of the bigger pulley. The belt should operate at 20 m/s

approximately. Calculate the diameters pulleys and the length of the belt for open belt drive.

04

11.

Two shafts 1.2 m apart connected by pulley having multiple V-grooves. The system is required to

transmit 84 kW power. The driving pulley is running at 900 rpm and has an effective diameter of 240

mm while the driven pulley diameter is 640 mm. groove angle of the pulley is 450. The belt used can

safely withstand a pull of 1890 N and each has cross section area of 395 mm2. Density of the belt

material is 1200 kg / m3. Coefficient of friction is 0.23. Calculate the number of belts required to

accomplish the job.

07

12. Design a chain drive to actuate a compressor from 15 kW electric motor at running 970 rpm and

compressor running at 330 rpm. Minimum center distance should be 550 mm. The chain tension may

be adjusted by shifting the motor rails. The compressor is to work 16 hr/day.

07

13.

The centre distance between two shafts is 4 m for a flat belt drive. The thickness of the belt is 10 mm. The driving pulley having 350 mm diameter is rotating with 1800 RPM. Driven pulley is rotating with 600 RPM. Considering slip of 5% determine outer diameter of driven pulley and belt length for (1) open belt drive (2) crossed belt drive

07

14. Design a V-belt drive from the given data. Motor power = 3.75 KW, Belt Width = 17 mm, Speed of motor = 1440 RPM, Belt thickness = 11 mm, Speed reduction = 4, Belt area = 140 mm2, Density of belt= 1.5 x 10(-5) N/mm3, Endurance limit for belt is 10N/mm2

07

15.

A Leather belt, 160 mm wide and 7 mm thick is used to transmit 3kW under light shock load conditions for which service factor is 1.2.the driving pulley is of 160 mm diameter and operates at 1440 rpm. The driven pulley is 480 mm in diameter and centers of pulley are 2.4 m apart. Considering open belt drive, w=11,200 N/mm3 for belt, μ = 0.4 between pulley and belt, and allowable tension per mm width at 3m/s is equal to 7.2 n/mm. Determine Centrifugal tensions, Tensions on tight and slacks sight, Factor of safety and Design power.

07

16. A simple chain no.06 B is used to transmit power from a transmission shaft running at 1000 rpm to another shaft running at 500 rpm. There are 21 teeth on driving sprocket wheel and operation is

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GTU Paper Analysis


smooth without any shock. Calculate: 1. power transmission capacity of the chain 2. chain velocity 3. chain tension 4. factor of safety based on breaking load 5. Length of chain if centre distance is 50p

GTU Paper Analysis


Chapter 5 – Pressure Vessels

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Theory

1. Explain Clavarino’s and Birnie’s equation in detail. 07

2. Explain autofrettage for cylinders (or What is pre-stressing the cylinder? What are the various methods used for it?).

03 03 04

3. Explain Area compensations for nozzles. 04

4. State the different equations used for the design of thick cylinder subjected to internal pressure based on materials and end conditions.

07

5. Explain various types of ends used for pressure vessels giving practical applications of each. 07 04

6. What are the types of end closures used for cylindrical pressure vessels? Explain any one with neat sketch. 04

7. In case of pressure vessels having open ends, the fluid pressure indices (a) longitudinal stress (b) circumferential stress(c) shear stress (d) none of these

01

8. In a thick cylinder shell subjected to internal pressure ‘p’, the maximum radial stress at the outer surface of the shell is (a) zero (b) p (c) -p (d) 2p

01

9. Lame’ s equation is derived based on (a) maximum principal stress theory(b) maximum strain theory (c) maximum shear stress theory(d) maximum distortion energy theory

01

10. Birnie’s equation is applicable to (a) open cylinders made of ductile material(b) closed cylinders made of ductile material (c) cylinders made of brittle material(d) open cylinders made of brittle material

01

GTU Paper Analysis


11. Drive the Lame’s equation for thick cylinders. 04

12. When pressure vessel is said to be a thin cylindrical shell? 01

13. Define Longitudinal Stress. 01

14. On which type of stress the design of pressure vessel is based on? 01

15. What are the important points to be considered while designing the pressure vessels? 03

16. Distinguish between circumferential stress and longitudinal stress in a cylindrical shell, when subjected to internal pressure.

04

17. Compare the stress distribution in thin and thick walled pressure vessels. 03

18. What are the objectives of providing openings in pressure vessels? 03

19. Explain different types of supports used for pressure vessels. 04

20. What are the design criteria and failure modes in pressure vessels? 03

21. Explain the design procedure with mathematical formulations for pressure vessels. 04

22. Explain pre-stressing of cylinders and its importance in pressure vessels design. 03

23. Explain the area compensations method to determine the area of reinforcement fora nozzle opening with neat sketch.

04

24. What is pre-stressing? Why is it required in pressure vessels 03

25. Derive the equation of hoop stress and longitudinal stress for thin cylinder. 07

26. Explain any two types of end covers used in pressure vessels. 03

27. Which theory of failure is used while designing a pressure vessel? Why? 03

28. Derive the relation to determine the cylinder thickness based on maximum shear stress theory and maximum distortion energy theory.

04

29. Derive the expression of resultant load in terms of stiffness on the bolted assembly of Cylinder –Head-Gasket joints.

03

30. Explain the area compensations method to determine the area of reinforcement for a nozzle opening with neat sketch.

04

Examples

GTU Paper Analysis


1. A cast iron pipe of internal diameter 200 mm and thickness of 50mm carrieswater under a pressure of 5 N/mm2. Calculate the tangential and radial stressesat Radiuses (r)=100 mm; 110 mm; 130 mm; 140 mm and 150 mm. Sketch thestress distribution curves.

07

2.

The piston rod of a hydraulic cylinder exerts pressure of 10 MPa. The internaldiameter of the cylinder is 350 mm. The C.I. cover plate of thickness 15 mm isfixed to the cylinder by means of 8 bolts with a nominal diameter of 16 mm andzinc gasket of 5 mm thickness. The bolts are made of steelFeE350(σy = 350 N/mm2).The flange thickness is 15 mm. Each bolt is initiallytightened with a pre-load of 18 kN. Determine factor of safety of the boltsconsidering the effect of the gasket. Assume E for steel= 207 GPa; E for castiron =100 GPa; E for Zinc=90 GPa.

07

3. A cylinder of 50 mm inner radius is subjected to an internal pressure Pi. What is thethickness, if the maximum hoop stress calculated by thick cylinder formula is10% greater than value obtained assuming uniform hoop stress across the wholesection? By how much does the minimum hoop stress differ?

07

4.

A high pressure cylinder consists of steel tube with 20 mm and 40 mm as inner and outer diameter respectively. It is jacketed by outer steel tube with 60 mm outer diameter. The tubes are assembled by shrinking process in such a way that the maximum principal tensile stress in any tube is restricted to 100 N/mm2. Find the shrinkage pressure and original dimension of the tube. Take E = 207 KN/mm2.

07 07

5.

A high pressure cylinder consists of an inner cylinder of inner and outer diametersof 200and 300 mm respectively. It is jacketed by an outer cylinder with an outsidediameter of 400 mm. The difference between the outer diameter of the inner cylinderand the inner diameter of the jacket before assembly is 0.25 mm (E = 207 kN/mm2).Calculate the shrinkage pressure and the maximum tensile stress induced in any ofthe cylinders.

07

6. The piston rod of a hydraulic cylinder exerts an operating force of 10 KN. The friction due to piston packing and stuffing box is 10 % of operating force. The pressure in the cylinder is 10 N/mm2. The cylinder is made of cast iron FG200 and factor of safety is 5. Determine diameter and thickness of the cylinder.

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7.

A steel tank for shipping gas is to have an inside diameter of 200 mm and a length of 1000 mm. The gas pressure is 10.5 N/mm2. The permissible stress is to be 56 MPa. (a) Determine the required wall thickness, using the thin cylinder equation. (b) Determine the thickness using Clavarino’s equation.

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8. A thick cylinder having 120 mm external diameter and 60 mm internal diameter is subjected to an internal fluid pressure of 15 MPa and external fluid pressure of 6 MPa. Determine the resultant hoop and radial stresses at inner and outer surface of cylinder. Also sketch curves showing the stresses distribution.

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GTU Paper Analysis


9.

An accumulator is required to store 150 liters of water at a pressure 20 MPa. Assuming the length of stroke to be 3 meter, determine: (a) The diameter of the ram. (b) The internal diameter of the cylinder, assuming a clearance of 40 mm. (c) The thickness of the cylinder, if the permissible stress of the cylinder (made of CI) is 60 N/mm2.

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10.

A shrink fit assembly formed by shrinking one tube over another, is subjected to an internal pressure of 60 N/mm2. Before the fluid is admitted, the internal and the external diameters of the assembly are 120 mm and 200 mm and the diameter of the junction is 160 mm. If after shrinking on, the contact pressure at the junction is 8 N/mm2, Determine using Lame’s equations, stresses at the inner, mating and outer surfaces of the assembly after the fluid has been admitted.

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11.

A closed vessel is to be designed to withstand an internal pressure of 5 MPa having inside diameter of 450 mm. The properties of the vessel material are yield strength is 300 MPa, ultimate tensile strength is 500 MPa, Poisson’s ratio = 0.3. Determine the required wall thickness of the vessel using a factor of safety of 1.5 based on yield strength on the basis of i) maximum principal stress theory, ii) maximum shear stress theory.

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12.

The cover of a cylindrical pressure vessel made of cast iron. The inner diameter of the cylinder is 500 mm and the internal pressure is limited to 2 MPa. The cover is fixed to the cylinder by means of 16 bolts with a nominal diameter of 20 mm. Each bolt is initially tightened with a preload of 20 kN. The bolts are made of steel FeE 250 having yield stress = 250 N/mm2. The Youngs module of elasticity for steel, cast iron and zinc is 207 kN/mm2, 100 kN/mm2and kN/mm2 respectively. Determine the factor of safety for bolts considering the effect of the gasket. Assume thickness of cylinder cover, cylinder flange and zinc gasket is 25 mm, 25 mm and 5 mm respectively.

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13.

A pressure vessel consists of a cylindrical shell with an inside diameter of 1650 mm, which is closed by torispherical heads with a crown radius of 1300 mm. The operating pressure inside the vessel is 1.5 MPa. The yield strength of the material used for the shell and head is 255 N/mm2 and the weld joint efficiency may be assumed to be 0.8. The corrosion allowance is 2 mm. Determine the thickness of the cylindrical shell and the torispherical head.

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14. A thin spherical shell with a storage capacity of 5000 litres is subjected to internal pressure of 1.5 N/mm2 . Determine the thickness of the shell. Take allowable stress for shell material = 75N/mm2 consider joint efficiency 75%.

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15. An accumulator is required to store 175 litres of water at a pressure of 25 N/mm2 . Assume the length of the stroke to be 3 meter. Determine (1) The diameter of the Ram (2) The internal diameter of the cylinder (3) The thickness of the cylinder if the allowable stress of the cylinder made of cast iron is 60 N/mm2.

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16. A hydraulic cylinder with closed ends is subjected to an internal pressure of 15 MPa. The inner and outer 07

GTU Paper Analysis


diameters of the cylinder are 200 mm and 240 mm respectively. The cylinder material is cast iron FG300. Determine the factor of safety used in design. If the cylinder pressure is further increased by 50%, what will be the factor of safety?

17. A thick cylinder 120 mm inner diameter and 180 mm outer diameter carries fluid under a pressure of 9 MPa. Find the tangential and radial stresses across the wall and sketch the stress distribution.

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GTU Paper Analysis Chapter 1 Introduction · 17. Explain the Belleville spring and its...

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