DARSHAN INSTITUTE OF ENGG. & TECH. · PDF fileDesign of Shaft, Keys and Couplings 7. Design of...

DARSHAN INSTITUTE OF ENGG. & TECH.

Department of Mechanical Engineering

B.E. Semester – IV

Machine Design & Industrial Drafting (2141907)

Batch: ____________ Roll No.: ___________

List of Assignments

Sr.

No. Title Start Date End Date Sign Remark

1. Design Against Static Load

2. Design of Cotter and Knuckle Joints

3. Design and Analysis of Levers

4. Design of Beams

5. Design of Columns

6. Design of Shaft, Keys and Couplings

7. Design of Threaded Joints

8. Design of Welded Joints

9. Design of Riveted Joints

10. Introduction of Limits, Fits and

Tolerances

Machine Design and Industrial Drafting (2141907)

B.E. Semester IV Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 1

ASSIGNMENT – 1 DESIGN AGAINST STATIC LOAD

Theory

1. What is stress concentration? Explain methods to relieve stress concentration? Explain

any two stresses with simple sketches.

2. Define factor of safety and state the important factors affecting the factor of safety.

3. Define following:(1) Proof Resilience (2)Preferred number (3)Principle stress

4. Explain Mohr’s circle diagram for principal stresses.

5. Explain the following principle theories of elastic failure:

[1] Max. Principle stress theory (Rankine theory)

[2] Max. shear stress theory (Coulomb theory or Tresca and Guest theory)

[3] Distortion energy theory (Von Mises and Hencky theory)

[4] Selection and use of failure theories

6. Distinguish clearly between bending and bearing stress.

7. Explain the following terms with neat sketches:(1)Tensile stress(2) Compressive

stress(3)Principle Stress (4) Bearing pressure

8. Classify the different types of load & explain each In brief.

9. Differentiate between (with neat sketch): (1) crushing and compressive stresses (2)

torsional and transverse shear stress.

10. Describe Hertz contact stress theory giving suitable example.

Examples

1. Determine the minimum size of a circular hole that can be punched in a M.S. plate, 5 mm

thick and having ultimate shear strength of 300 MPa. Take compressive strength of

punch as 360 MPa.

2. A mild steel link is as shown in Fig. 1, which is subjected to a tensile load of 80 kN. Find

the b. The permissible tensile stress is 70 MPa.



Fig. 1

3. An offset link subjected to a force of 25 kN is shown is shown in Fig.2, It is made of

grey cast iron FG300 and the factory of safety is 3. Determine the dimensions of the

cross section of the link.

Fig. 2

Fig. 3



4. A wall bracket with rectangular cross section is shown in following Fig. 3. The depth

of the cross-section is twice of the width. The force P acting on the bracket at 300 to

the horizontal is 5 KN. The bracket is made gray cast iron FG 200 (Sut = 200 N/mm2)

and factor of safety = 3.5 Determine the dimensions of the cross section of the

bracket.

5. The dimensions of an overhang crank are shown in Fig.4. The force P acting at

crankpin is 1 kN. The crank is made of steel 30C8 with allowable shear stress 100

MPa. Using maximum shear stress theory of failure, determine the diameter at

section XX.

Fig. 4

6. The load on a bolt consists of an axial pull of 10 KN together with a transverse shear

force of 5 KN. Find the diameter of bolt required according to (i) maximum principal

stress theory, (ii) maximum principal shear stress theory,

(iii)maximum distortion energy theory. Take permissible tensile stress at elastic limit

as 100 MPa and poison’s ratio as 0.3.



ASSIGNMENT – 2 DESIGN OF COTTER AND KNUCKLE JOINT

Theory

1. Explain the design process for spigot and socket cotter joint with neat sketch.

2. What are the uses of cotter joint? Why is taper provided on the cotter? What is the

purpose of clearance in Cotter Joints?

3. Write the advantages of cotter joint. State the different applications of the cotter joint.

4. Explain the design process for knuckle joint with neat sketch.

5. Write the advantages of knuckle joint. State the different applications of the knuckle

joint.

Examples

1. Design a socket and spigot joint to resist a tensile load of 28 KN. All the parts of the joint

are made from same material with following allowable stresses: σt=50 N/mm²,

σc=60N/mm², τ=35 N/mm², σb =50 N/mm².

2. Design and draw a neat sketch of spigot rod for the cotter joint using the following data.

Axial load 30 KN, tensile stress 50 N/mm2, crushing stress 90 N/mm2 and shear stress

35 N/mm2

3. It is required to design a cotter joint to connect two steel rods of equal diameter. The

permissible stresses for the rods, spigot end and socket end are σt=96 N/mm²,

σc=134N/mm², τ=45 N/mm².For cotter, σt=80 N/mm², τ=40 N/mm². Each rod is

subjected to an axial tensile force of 80 KN.

Calculate the following dimensions:

(1.) Diameter of spigot

(2.) Width & thickness of cotter

(3.) Thickness of socket collar

4. Calculate the dimension of the socket end of a cotter joint used to connect two rods,

made of plain carbon steel 40C8 having yield point strength 380 N/mm2. The diameter

of each rod is 50mm and the cotter is made from a steel plate of 15mm thickness.

Assume (i) the yield strength in compression is twice of the tensile yield strength, (ii)

the yield strength in shear is 50% of the tensile yield strength, (iii) the factor of safety is

6.

5. Two rods of 50mm diameter are to be joined by a cotter joint, with thickness of cotter

as 12.5mm. If the joint is withstand an axial pull of 6000KN find the various dimensions

required. The permissible stresses are 300N/mm2 in tension, 200N/mm2in shear and

450N/mm2 crushing.



6. Design a knuckle joint to connect two rods subjected to tensile force of 50 KN. The rods

and pin are made of plain carbon steel 30C8. The permissible stresses are σt = σc = 80

MPa and τ = 40 MPa.

7. Design a knuckle joint to transmit 75 KN. The design stresses may be taken as 75 MPa

in tension, 60 MPa in shear and 150 MPa in compression.

8. It is required to design knuckle joint to connect two mild steel roads of equal diameter.

Each rod is subjected to an axil tensile load 50 KN. The permissible stresses are 80 MPa

in tension and crushing and 40 MPa in shear for all parts.

9. Design a knuckle joint to connect two mild steel bars under a tensile load of 25 kN. The

allowable stresses are 65 MPa in tension, 50 MPa in shear and 83 MPa in crushing.

Standard diameter of solid bars are 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40 mm. Check

failure of knuckle pin in shear, failure of rod end & forked end in tension, shearing and

crushing.

10. Design a knuckle joint for a tie rod of a circular section to sustain a max. pull of 70kN.

The ultimate strength of the material of the rod against tearing is 420N/mm2. The

ultimate tensile and shearing strength of the pin material are 510N/mm2 and

396N/mm2 respectively. Determine the tie rod section and pin section. Take F.S. = 6.



ASSIGNMENT – 3 DESIGN OF LEVER

Theory

1. Explain the basic types of levers with the help of neat sketches & examples.

2. Define following : (1)Arm of lever,(2) Leverage, (3)Displacement ratio (4) mechanical

advantage

3. Differentiate between simple and compound lever. Why a boss is generally needed at

the fulcrum of the levers?

4. State the application of hand and foot levers.

5. State and explain the different functions of levers. Why the levers are generally made

tapers?

6. What is lever? Explain the principle on which it works.

7. Briefly explain general procedure for lever design.

Examples

1. Design a bell crank lever to apply a load of 5 kN (vertical) at the end A of an horizontal

arm of length 400 mm. The end of the vertical arm C and the fulcrum B are to be fixed

with the help of pins inside forked shaped supports. The end A is itself forked.

Determine the cross-section of the arms and the dimensions of the pins. The lever is to

have mechanical advantage of 4 with a shorter vertical arm BC. The ultimate stresses in

shear and tension for the lever and pins are 400 MPa and 500 MPa respectively. The

allowable bearing pressure for the pins is 12 N/mm2. Assume a factor of safety as 4 and

the cross-section of the lever as rectangular with depth (b) as three times the thickness

(t).

2. A bell crank lever is to be designed to raise a load of 15 KN at the short arm end. The

arm lengths are 150 mm and 500 mm. The permissible stresses for lever and pin

materials in shear and tension are 60 MPa and 90 MPa respectively. The bearing

pressure on the pin is to be limited to 12 MPa. Assume the lever cross section as t x 4t

and fulcrum pin length as 1.25 times pin diameter.

3. Design a right angled bell crank lever having one arm 500 mm & the other 150 mm

long. The load of 5 kN is to be raised acting on a pin at the end of 500 mm arm & the



effort is applied at the end of 150 mm arm. The lever consists of steel forgings, turning

on a point at the fulcrum. The permissible stresses for the pin & lever are 84 MPa in

tension & compression & 70 MPa in shear, the bearing pressure on the pin is not to

exceed 10 N/mm2.

4. A right angle bell crank lever is shown in Fig-1. The load W = 4.5KN. The lever consists

of forged steel material and a pin at the fulcrum. Take the following permissible stress

for the pin and lever material. Safe stress in tension = 75MPa, Safe stress in shear =

60MPa, Safe bearing pressure on pin = 10N/mm2. The length of fulcrum pin is 1.25

times the diameter of fulcrum pin. Calculate the following:

(1.) Reaction at fulcrum pin (2). Fulcrum pin dimensions (3). Lever dimensions

Fig. 1

5. Design a lever of a lever loaded safety valve based on following data:

Steam pressure acting on the valve = 1.2 MPa

Valve diameter = 60 mm.

Width to thickness ratio for lever = 3:1

Length to diameter ratio for pins = 1.25:1

The material used is forged steel with t

s =80MPa, t =50 Mpa,

s =100 Mpa, Pb = 20 Mpa

The lever has a rectangular cross section. The distance between the fulcrums and the

dead weights on lever is 800 mm and distance between the fulcrum and the pin

connecting the spindle of the valve to the lever is 100 mm. Calculate: (i) the length and

the diameter of the pin connecting the valve spindle to the lever (ii) the lever cross

sectional dimension



6. The lever of a lever loaded safety valve shown in Fig. 2. The valve is 80 mm and valve

has to blow off at a pressure of 1.25 MPa. The permissible stress in tension, shear and

crushing are 70 MPa, 20 MPa and 50 MPa respectively. The permissible bearing

pressure for the pin may be taken as 20 MPa. Design the pins and the lever; assume

rectangular cross section of the lever with height equal to three times the thickness.

Fig. 2

7. A lever loaded safety valve is 70mm in diameter and is to be designed for a boiler to

blow off at pressure of 1N/mm2 gauge. Design a suitable mild steel lever of rectangular

cross section. For mild steel: Permissible tensile stress =70MPa, Shear stress = 50MPa,

Bearing pressure intensity = 25N/mm2. The pin is also made of mild steel. The distance

from the fulcrum to the weight of the lever is 880mm and the distance between the

fulcrum and pin connecting the valve spindle links to the lever is 80mm.

8. Design a rocker arm lever having equal arms of 160 mm length inclined at 135 for an

exhaust valve of a gas engine subjected to a maximum force 2500 N at roller end.

Consider – I cross section 6t x 2.5t x t size (where t = thickness of web and flange) for

lever. The permissible stresses for the lever material are 80MPa in tension and design

bearing pressure is pin 6 MPa for pin.


B. E. Semester – IV Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 1

ASSIGNMENT – 4 DESIGN OF BEAMS

Theory

1. Distinguish between beams, columns and strut giving suitable examples.

2. Explain types of beams with neat sketch.

3. Explain types of supports (or end conditions) of beam with neat sketch.

4. Explain types of loads on beam with neat sketch.

5. Define following with reference to beam with neat sketch: (i) Deflection, (ii) Slope

and (iii) Flexural rigidity.

6. List the equations for slope and deflection for following types of beams with

different loading conditions:

(i) Cantilever beam with point load at free end

(ii) Cantilever beam with UDL on the entire span

(iii) Cantilever beam with point load at free end and UDL on the entire span

(iv) Simply supported beam with central load

(v) Simply supported beam with UDL on the entire span

(vi) Simply supported beam with central load and UDL on the entire span

Examples

1. A 2 metres long cantilever beam is having 100 mm width and 200 mm depth,

carrying point load at free end. If deflection at free end is 6 mm, calculate point load

at free end. Take E = 2 x 105 N/mm2.

2. A cantilever beam of span 1.5 metres carries a point load of 20 kN at its free end.

Find maximum slope of beam. Flexural rigidity (EI) = 2 x 104 kN.m2.

3. A hollow rectangular section 200 mm x 450 mm external and 15 mm thickness is

used for 2.7 metres cantilever beam, subjected to UDL of 64 kN/m and point load of

60 kN at free end, both downward. Find maximum slope and deflection. Take E =

200 GPa.

4. A simply supported beam 3 metres in span is subjected to UDL of 10 kN/m over

entire span with central point load 5 kN. The cross section of beam is 150 mm wide x

300 mm depth. Calculate the maximum slope & deflection for the beam.

5. A cantilever beam 120 mm x 200 mm is 2.5 metres long. What UDL should the beam

carry to produce a deflection of 5 mm at free end? Take E = 2 x 105 N/mm2.



6. Cross section of wooden beam is 100 mm x 240 mm. It is simply supported with 4

metres span. Find out UDL that can be placed on its full span so that deflection at

centre is 6 mm. Take E = 0.11 x 105 N/mm2.

7. A steel tube of external diameter 60 mm and 8 mm thickness is used as simply

supported beam of span 4 metres. If it deflects 10 mm due to a central load, find

magnitude of the point load. Take E = 2 x 105 N/mm2.



ASSIGNMENT – 6 DESIGN OF SHAFTS, KEYS AND COUPLINGS

Theory

SHAFTS

1. Explain functions and classification of shaft.

2. Define – Shaft, Axle and Spindle. Also state the difference between shaft, axle and

spindle with examples.

3. Explain shaft design subjected to twisting moment only.

4. Explain shaft design subjected to bending moment only.

5. Explain shaft design subjected to combined twisting moment and bending moment.

6. Explain shaft design based on torsional rigidity and lateral rigidity.

7. Explain the ASME code for shaft design.

8. Explain critical speed of shaft in details.

KEYS

1. What are the basic functions of the key? Explain different types of keys with its

applications.

2. Derive strength equations of sunk key based on shear and crushing (or

compression) failures.

3. Show that square key is equally strong in shearing and crushing compare to

rectangular key.

4. What is splined shaft? State the applications of splined shaft. Explain the design of

splined shaft.

COUPLINGS

1. Explain the purpose, requirements and types of shaft couplings.

2. Differentiate between flexible coupling and rigid coupling.

3. How does the working of a clamp coupling differ from that of a muff coupling?

4. Draw a neat sketch of a protected type flanged coupling and write the design

procedure with the design equations for different failure criteria.



Examples SHAFTS

1. Compare the weight, strength and rigidity of a hollow shaft of same external

diameter as that of solid shafts, both the shafts are made of same material. Assume

that diameter ratio for the hollow shaft is di/do = 0.6.

(Refer R. S. Khurmi – Ex. 14.22)

2. A steel spindle transmits 4 KW at 800 r.p.m. The angular deflection should not

exceed 0.25⁰ per metre of the spindle. If the modulus of rigidity for the material of

the spindle is 84 x 103 N/mm2, find the diameter of the spindle and the shear stress

induced in the spindle. (R. S. Khurmi – Ex. 14.21)

3. Determine the diameter below which the angle of twist of a shaft is the controlling

factor in design of solid shaft in torsion. The allowable shear stress is 56 MPa and

the maximum allowable twist is ¼ degree per meter. Take G = 84 GPa.

4. Find the diameter of a solid shaft to transmit 30 kW at 230 rpm. The shear stress is

50 MPa. If a hollow shaft is to be used in place of solid shaft, find the inside and

outside diameters when the ratio of inside to outside diameter is 6:8.


5. A line shaft is driven by means of a motor placed vertically below it. The pulley on

the line shaft is 1.5 meter in diameter and has belt tensions 5.4 kN and 1.8 kN on the

tight side and slack side of the belt respectively. Both these tensions may be

assumed to be vertical. If the pulley be overhang from the shaft, the distance of the

centre line of the pulley from the centre line of the bearing being 400 mm, find the

diameter of the shaft. Assume maximum allowable shear stress of 42 MPa.

(R. S. Khurmi – Ex. 14.8)

6. A 600 mm diameter pulley transmits 16 kW power at a speed of 400 rpm. Pulley is

cantilever at a distance of 200 mm from the nearest bearing. The weight of the

pulley is 1500 N. It is driven by a horizontal belt drive. The co-efficient of friction

between belt and pulley is 0.3 and the angle of lap 180⁰. Take the fatigue and shock

factors as Kb = 2.0 and Ks = 1.5. Determine the shaft diameter. The allowable shear

stress in the shaft may be taken as 50 MPa.

7. Design a shaft to transmit power from an electric motor to a lathe head stock

through a pulley by means of a belt drive. The pulley weighs 200 N and is located at

300 mm from the centre of the bearing. The diameter of the pulley is 200 mm and

the maximum power transmitted is 1 KW at 120 RPM. The angle of lap of the belt is

180 degree and coefficient of friction between the belt and the pulley is 0.3. The

shock and fatigue factors for bending and twisting are 1.5 and 2.0 respectively. The

allowable shear stress in the shaft may be taken as 35 MPa.

(R. S. Khurmi –Ex. 14.13)



8. A belt driven C. I. pulley of 0.9 m diameter overhangs the bearing by 0.2 m as shown

in below figure. The pulley is driven from the bottom by a belt. The angles of lap and

tension on tight side are 180° and 2600 N respectively. The weight of pulley is 600

N. Assume co-efficient of friction between pulley and belt is 0.25. Shaft is made up of

30C8. σyt = 400 N/mm2, σut = 500 N/mm2. Determine the shaft diameter according to

ASME code. Take Ks=1.0, Kb=1.5.


9. The armature shaft of a 40 kW, 720 r.p.m. electric motor, mounted on two bearings

is as shown in below figure. The total magnetic pull on the armature is 7 kN and it is

assumed to be uniformly distributed over a length of 700 mm midway between the

bearings. The shaft is made-up of steel with an ultimate tensile strength of 770 MPa

and yield strength of 580 MPa. Determine the shaft diameter using ASME code if, Kb

= 1.5 and Kt = 1.0. Assume that the pulley is keyed to the shaft.

(V. B. Bhandari – Ex. 9.7)



COUPLINGS

1. Design a muff coupling which is used to connect two steel shafts transmitting 40 kW

at 350 r.p.m. The material for the shafts and key is plain carbon steel for which

allowable shear and crushing stresses may be taken as 40 MPa and 80 MPa

respectively. The material for the muff is cast iron for which the allowable shear

stress may be assumed as 15 MPa.


2. Design a clamp coupling to transmit 30 kW at 100 r.p.m. The allowable shear stress ,

for the shaft and key, is 40 MPa and the number of bolts connecting the two halves

are six. The permissible tensile stress for the bolts is 70 MPa. The coefficient of

friction between the muff and the shaft surface may be taken as 0.3. Take width of

key = Shaft diameter/4 and thickness of key = Shaft diameter/6. Assume number of

bolts = 4. (R. S. Khurmi –Ex. 13.5)

3. Design a cast iron split muff coupling to transmit a power of 10 kW at 250 rpm.

Consider an overload of 25%. The allowable shear stress in the shaft and key is 36

MPa and for the muff 16 MPa. Take the co-efficient of friction 0.3 and the tensile

strength of the high tensile bolts 150 MPa.

(Refer R. S. Khurmi –Ex. 13.5)

4. Design a cast iron protective type flange coupling to transmit 15 kW at 900 r.p.m.

from an electric motor to a compressor. The service factor may be assumed as 1.35.

The following permissible stresses may be used :

Shear stress for shaft, bolt and key material = 40 MPa

Crushing stress for bolt and key = 80 MPa

Shear stress for cast iron = 8 MPa

Standard shaft diameter: 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40 mm.

Take number of bolts are 3.


5. Design a protective type of cast iron flange coupling for a steel shaft transmitting 15

kW at 200 r.p.m. and having an allowable shear stress of 40 MPa. The working stress

in the bolts should not exceed 30 MPa. Assume that the same material is used for

shaft and key and that the crushing stress is twice the value of its shear stress. The

maximum torque is 25% greater than the full load torque. The shear stress for cast

iron is 14 MPa. (R. S. Khurmi –Ex. 13.7)

6. Design and draw a cast iron flange coupling for a mild steel shaft transmitting 90 kW

at 250 r.p.m. The allowable shear stress in the shaft is 40 MPa and the angle of twist

is not to exceed 1° in a length of 20 diameters. The allowable shear stress in the

coupling bolts is 30 MPa. Take width of key = shaft diameter/4 and thickness of key

= shaft diameter/6. Assume no. of bolts = 4. (R. S. Khurmi –Ex. 13.8)



7. The shaft and the flange of a marine engine are to be designed for flange coupling in

which the flange is forged on the end of the shaft. The following particulars are to be

considered in the design: Power of the engine = 3 MW, Speed of the engine = 100

r.p.m., Permissible shear stress in bolts and shaft = 60 MPa, Number of bolts used = 8

and Pitch circle diameter of bolts = 1.6 × Diameter of shaft.

Find: 1. diameter of shaft; 2. diameter of bolts; 3. thickness of flange; and 4. diameter

of flange.


8. A flexible coupling as shown in below figure is used to transmit 15 kW power at 100

rpm. There are six pins and their pitch circle diameter is 200 mm. The effective

length of the bush, the gap between the two flanges and the length of pin in contact

with the right hand flange are 35, 5 and 23 mm respectively. The permissible shear

and bending stress in the pin are 35 N/mm2 and 152 N/mm2 respectively. Calculate

pin diameter by shear & bending considerations.

(V. B. Bhandari Ex – 9.23)


B.E. Semester – IV Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 1

ASSIGNMENT – 7 Design of Threaded Joints Theory

1. Explain the different types of screw threads used in power screw stating their

applications.

2. Differentiate between power screw and threaded joint.

3. What do you understand by the single start and double start threads? Define

following terms: (a) Major diameter, (b) Minor diameter, (c) Pitch and (d) Lead.

4. Derive an equation for torque required to raise (lift) load by square threaded screw.

5. Derive an equation for torque required to lower load by square threaded screw.

6. Derive an equation for efficiency of square threaded screw and maximum efficiency

of a square threaded screw.

7. What is self-locking and over-hauling of power screw? What is significance of these

properties? Show that the efficiency of self-locking screws is less than 50%.

8. Discuss on bolts of uniform strength giving examples of practical applications of

such bolts.

9. Explain the purpose of a turn buckle (or Coupler) with neat sketch and describe its

design procedure.

Examples

1. The mean diameter of the square threaded screw having pitch of 10 mm is 50 mm. A

load of 20 KN is lifted through a distance of 170 mm. The external and internal

diameters of the bearing surface of the loose head are 60 mm and 10 mm

respectively. The coefficient of friction for the screw and the bearing surface may be

taken as 0.08.

Find the work done in lifting the load and the efficiency of the screw, when

a) The load rotates with the screw, and

b) The load rests on the loose head which does not rotate with the screw.

2. The lead screw of a lathe machine has single start trapezoidal threads of 52 mm

nominal diameter and 8 mm pitch. The screw is required to exert an axial force of 2

kN in order to drive the tool carriage, during turning operation. The thrust is carried

on a collar of 100 mm outer diameter and 60 mm inner diameter. The values of co-

efficient of friction at the screw threads and the collar are 0.15 and 0.12 respectively.

The lead screw rotates at 30 rpm. Calculate:

a) The power required to drive the lead screw, b) The efficiency of the screw.

3. A power screw having double start square threads of 25 mm nominal diameter and

5 mm pitch is acted upon by an axial load of 10 kN. The outer and inner diameters of

screw collar are 50 mm and 20 mm respectively. The coefficient of thread friction

and collar friction may be assumed as 0.2 and 0.15 respectively. The screw rotates at

12 r.p.m. Assuming uniform wear condition at the collar and allowable thread



bearing pressure of 5.8 N/mm2, find:

a) The torque required to rotate the screw; b) The stress in the screw; and

c) The number of threads of nut in engagement with screw.

4. A machine vice as shown in Fig.1 has single start square threads with 22 mm

nominal diameter and 5 mm pitch. The outer and inner diameters of the friction

collar are 55 mm and 45 mm respectively. The values of coefficient of friction for

threaded collar are 0.15 and 0.17 respectively. The machinist can comfortably exert

a force of 125 N on the handle at a mean radius of 150 mm. Assuming uniform wear

for the collar calculate:

a) Clamping force developed between the jaws

b) The overall efficiency of the clamp

Fig.1

5. A triple threaded power screw, used in a screw jack, has a nominal diameter of 50

mm and a pitch of 8 mm. The threads are square and the length of nut is 48 mm. The

screw jack is used to lift a load of 7.5 KN. The coefficient of friction at the threads is

0.12 and collar friction is negligible. Calculate: (i) the principal shear stress in the

screw body, (ii) the transverse shear stresses in the screw and the nut, (iii) the unit

bearing pressure. State whether the screw is self-locking or not.

6. The nominal diameter of a triple threaded square screw is 50 mm, while pitch is 8

mm. It is used with a collar having outer diameter of 100 mm and inner

diameter of 65 mm. The coefficient of friction at thread surface as well as at collar

surface can be taken as 0.15. The screw is used to raise a load of 15 kN. Using

uniform wear theory for collar friction, calculate: (i) Torque required to raise load,

(ii) Torque required to lower load and (iii) Force required to raise load, if applied

at a radius of 500 mm

7. The screw shown in Fig.2 is operated by a torsional moment applied at the lower

end. The nut is loaded and prevented from turning by guides. The outside diameter

of the screws is 50 mm, pitch of 8 mm and the thread is acme triple start. The



coefficient of friction of the threads is 0.15. Assume the friction in ball bearing as

negligible. If the torsional moment Mt is 45 Nm.

a) Determine the load which could be raised

b) Would the screw be overhauling?

c) Determine the average bearing pressure between the screw and nut thread

surfaces.

Fig.2

8. The pull in the tie rod of an iron roof truss is 50 kN. Design a suitable adjustable

Screwed joint (turnbuckle). The permissible stresses are 75 MPa in tension, 37.5

MPa in shear and 90 MPa in crushing.

9. A double threaded power screw with ISO metric trapezoidal threads with 15°semi-

angle of thread is used to raise a load of 300 kN. The nominal diameter is 100 mm

and pitch is 12 mm. the coefficient of friction at screw threads is 0.15. Neglecting

collar friction, calculate; (i) torque required to raise the load, (ii) torque required

to lower the load and (iii) efficiency of the screw.

10. Design a turnbuckle for a capacity of 40 kN, which is used for adjusting

tension in a v-belt drive of a machine tool. The permissible stresses for rods and nut

are 80 MPa in tension, 50 MPa in shear and 80 MPa in crushing.



ASSIGNMENT – 8 Design of Welded Joints Theory

1. What do you understand by the term welded joint? Explain advantages and

disadvantages of welded joints over riveted joints.

2. Classify and explain the types of welded joints with neat sketches and weld symbols.

3. Discuss the standard location of elements of a welding symbol.

4. Derive equations of strength for transverse and parallel fillet welded joints with neat

sketches.

5. Deduce the design equation for circular fillet weld subjected to torsion.

6. What do you mean by eccentric loaded welded joint? Write the detail design

procedure for designing such a joint.

Examples

1. A plate 60 mm wide and 80 mm thick. It is welded with another plate by means of single transverse and double parallel fillet welds. Find the length of each parallel fillet if allowable tensile and shear stresses in the weld material are 80 and 60 MPa respectively.

2. Two steel plates, 120 mm wide and 12.5 mm thick, are joined together by means of double transverse fillet welds. The maximum tensile stress for plates and welding materials should not exceed 110 N/mm2. Find required length of weld, if strength of weld is equal to strength of plates

3. A circular shaft, 75 mm in diameter, is welded to the support by means of a circumferential fillet weld. It is subjected to a torsional moment of 3000 N-m. Determine the size of weld, if the maximum shear stress in the weld is not to exceed 70 N/mm2.

4. A solid rectangular bar of 100mm width and 150mm depth is welded to vertical column by means of fillet weld all around. The joint is subjected to 25 KN at distance of 500 mm from the plane of weld. Determine throat thickness using allowable stress of weld is 75 N/mm2.

5. A welded joint as shown in Fig.1, is subjected to an eccentric load of 2 KN. Find the size of weld, if the maximum shear stress in the weld is 25 N/mm².

Fig.1



6. A shaft of rectangular cross-section is welded to a support by means of fillet welds, as shown in Fig.2 Determine the size of the welds, if the permissible shear stress in the weld is limited to 75 N/mm2.

Fig.2

7. A bracket is fillet welded to a structure as shown in Fig.3, which is subjected to a

load of 50 kN. Find the size of weld required if allowable shear stress is not to exceed

75 MPa. Take polar moment of inertia J =𝑡 (b+𝑙)3

6

Fig.3

8. A welded joint has to support a load of 80 kN. Suggest a suitable size of fillet weld if the safe shear stress for the weld material is 80 MPa. Refer the given Fig.4.

Fig.4



9. A bracket carrying a load of 15 KN is to be fillet welded as shown in Fig.5. Find the size of weld required if the allowable shear stress is not to exceed 80 MPa.

Take polar moment of inertia J = t 𝑙 (3b2+𝑙2)

6

Fig.5

10. Fig.6 shows 12 mm thick plates loaded by the forces of 100 KN applied eccentrically. Determine the required lengths L1 & L2 of the fillet welds so that they will be equally stressed in shear. Take working stress in shear for side fillets to be equal to 80 N/mm2.

Fig.6

11. A bracket is welded to the side of a column and carries a vertical load P, as shown in Fig.7. Evaluate P so that the maximum shear stress in the 10 mm fillet welds is 80 MPa.

Fig.7



ASSIGNMENT – 8 Design of Riveted Joints Theory

1. Define riveted joints. Classify and explain the different types of riveted joints with

neat sketches.

2. Explain the following terms related to riveted joints:

a) Pitch, b) Margin, c) Diagonal pitch and d) Transverse pitch.

3. Explain caulking & fullering in terms of riveted joint.

4. Discuss the different types of failures in riveted joint (or the various ways in which

a riveted joint may fail).

Examples

1. Find the efficiency of the double riveted lap joints with zig-zag riveting is to be designed for 13 mm thick plates. Assume 80 MPa, 60 MPa and 120 MPa in tension, Shear and crushing respectively. Also calculate pitch of rivets.

2. Design a double riveted, double strap, chain type butt joint for plates having 10 mm thickness. Also find efficiency of the joint. Take σt = 95 N/mm², σc =155 N/mm² and τ =80 N/mm².

3. A double riveted double cover butt joint in plates 20 mm thick is made with 25 mm diameter. Rivets at 100 mm pitch. The permissible stress are σt =120 N/mm2, Shear stress= 100 N/mm2, σc= 150 N/mm2. Find the Efficiency of joint, taking the strength of the rivets in double shear as twice than that of single shear.

4. Design a double riveted butt joint with two cover plates for the longitudinal seam of a boiler shell 1.5 m in diameter subjected to a steam pressure of 0.95 N/mm2. Assume joint efficiency as 75%, allowable tensile stress in the plate 90 MPa, Compressive stress 140 MPa & shear stress in the rivet 56 MPa. A bracket is supported by means of four rivets of same size as shown in Fig.1. Determine the diameter of rivet if the maximum shear stress is 140 MPa.

Fig.1

5. A bracket is to be attached to a wall with the help of six rivets. The different arrangements in which the bracket can be attached to the wall with these rivets are shown in Fig.2. The maximum allowable stress in shear is 60 N/mm2. Determine the



way in which the rivets should be arranged so that the design is economical. The bracket is required to support a load of 90 KN with an eccentricity of 200 mm. Also determine the diameter of rivet for the selected arrangement.

Fig.2

6. An eccentrically loaded lap riveted joint is to be designed for a steel bracket as shown in Fig.3. The bracket plate is 25 mm thick. All rivets are to be of same size, load on the bracket P = 50 KN, rivet spacing c =100 mm, load arm e = 400 mm, permissible shear stress is 64 MPa, and crushing stress is 120 MPa. Determine the size of the rivets to be used for the joint.

Fig.3

7. A bracket is subjected to a load of 32 KN which is joined to a structure by means of 8 numbers of rivets as shown in Fig.4 Find the size of the rivets if the permissible shear stress is 80 MPa.

Fig.4



8. Find the value of P for joint shown in Fig.5, based on a working shear stress of 100 MPa for rivets. Each of four rivets is of 20 mm diameter.

Fig.5


B. E. Semester IV Department of Mechanical Engineering Darshan Institute of Engineering and Technology, Rajkot 1

ASSIGNMENT 10 – INTRODUCTION TO LIMITS FITS AND

TOLERANCES

Theory

1. Define and explain following terminology used in relation with the tolerances with

the help of neat sketch:

(a) Limit (b) Basic size (c) Tolerance (d) Allowance

(e) Deviation (f) Clearance (g) Fit

2. Explain types of tolerances with neat sketch and explain applications for it.

3. Explain types of deviations with neat sketch and explain applications for it.

4. Explain types of clearances with neat sketch and explain applications for it.

5. Explain types of fits with neat sketch and explain applications for it.

6. What is surface roughness? Explain the parameters (or characteristics) used for

surface roughness measurement with sketch.

7. Explain the machining symbols with all parameters.

8. Explain hole-based and shaft based limit system with neat sketch. Give appropriate

examples also.

9. Give symbols for following various geometrical tolerances and explain meaning of it:

Straightness, Flatness, Circularity, Parallelism, Perpendicularity, Cylindricity,

Symmetry, Angularity and Concentricity

10. Explain maximum metal condition (MMC) and least metal condition (LMC).

Examples

1. In bush and pin assembly, pin of 30 mm diameter rotates in a bush. The tolerance for

pin is 0.025 mm while for bush is 0.04 mm. If allowance is 0.1 mm, determine

dimensions of pin and bush considering hole-basis system.

2. A journal of nominal diameter 79 mm rotates in a bearing. The upper and lower

deviations in hole diameter are respectively +0.05 mm and 0.00 mm, while those for

shaft are respectively -0.03 mm and -0.07 mm.

Calculate: (i) Extreme diameters for hole and shaft, (ii) Tolerances for hole and shaft

and (iii) maximum and minimum clearance.

3. Find the tolerances, maximum interference and type of fit for the data for the

following given data:

Hole ϕ50+0.25-0.10 and Shaft ϕ50+0.20-0.20.

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