Machine Design i Ch5

8/11/2019 Machine Design i Ch5

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Machine Design I (254325)Chapter 5

Screws, Fasteners, and the

Design of Nonpermanent

Joints


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Introduction

Archimedes screw


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Introduction

Boeings 747

2.5


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Thread Standards and Definitions


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The Mechanics of Power Screws


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==

=+=

=+=

==

0cossin

0cossin

loadtheloweringfor

0cossin

0cossinloadtheraisingfor

NfNFF

fNNPF

NfNFF

fNNPF

V

LH

V

RH


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( )

( )

[ ]

[ ]

2

and2

2/

)/(1

)/(

and)/(1

)/(

/tan

sincos

sincos

andsincos

cossin

+

=

+

=

=

+=

+=

=+

=

+=

fld

lfdFdT

fld

fdlFd

T

PdT

dfl

dlfFP

dfl

fdlFP

dl

f

fFP

f

fFP

m

mmL

m

mm

R

m

m

mL

m

mR

m

L

R

RR

m

L

TFlTTe

FlT

ff

lfd

T

2//

2/

0iftan

0locking,-self

0

0

==

=

=

>

>

>


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CEk

lSS

A

F

d

F

A

F

d

T

dFfT

f

fld

fdlFdT

y

y

crit

r

r

ccc

c

m

mmR

1

2

buckling)JohnsonB.(J.columnshort

4

stressaxial

16

stressshearnominalmaximum

2

frictioncollaroftcoefficientheis

sec

sec

2

adsother threorAcmefor

2

2

3

=

==

=

=

+=


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( )( )

pnd

F

pnd

F

A

V

pnd

F

pnd

Fp

cI

M

FpM

pndpndCI

n

pndF

pndF

trtr

trtr

trtr

t

tmtm

3

2/2

3

2

3

stressshearetransversthe

624

4/

4/

2462/

rootat thestressbendingthe

threadsengagedofnumbertheis

22/

stressbearingthestresses,threadnominal

2b

2

2

b

B

B

===

===

=

==

==


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04

160

06

roottheoftopat thestressMisesvon

2z

3y

x

==

==

==

zx

r

r

yz

xy

tr

dF

d

T

pndF

power screw

compression tension

10.38 20.25 30.18 7 F0.38F, nt= 1

stress


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14/59


8-1


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Threaded Fasteners

(Hexagon-head bolt)

>+

+=

in6L2

1

2

in6L4

12

boltsseriesinch-

lengththreadthe

ind

ind

L

L

T

T

27ATablesee*

200L252

200L125122

48d125L62

boltsmetric-

>+


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Threaded Fasteners

(cap-screw heads)


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Threaded Fasteners

(machine screws, nut)


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Threaded Fasteners


Inch-series machine screws are generally available

in sizes from No. 0 to about 3/8 in.


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Threaded Fasteners


Hexagonal nut dimensions are given in Table A31.

During tightening, the first thread of the nut tends to take the

entire load; but yielding occurs, with some strengthening dueto the cold work that takes place, and the load is eventuallydivided over about three nut threads. For this reason youshould never reuse nuts; in fact, it can be dangerous to do so.


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JointsFastener Stiffness

Bolt

preload compression


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At = tensile-stress area (Tables 81,82)

lt = length of threaded portion of grip Ad= major-diameter area of fastener ld= length of unthreaded portion in

grip kb = estimated effective stiffness

dttd

tdb

d

dd

t

tt

lAlAEAAk

l

EAk

l

EAk

kk

kkk

kkk

+=

==

+=+=

or111

21

21

21


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See Table 8-7


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JointsMember Stiffness

30hardened steel,cast iron or aluminum members

EA

Pdxd =


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( )

( )[ ] ( )[ ]

))(tan2(

))(tan2(ln

tan

))(tan2(

))(tan2(ln

tan

2/tan2/tan

2tan

2tan

22tan

0

22

22

dDdDt

dDdDtEdPk

dDdDt

dDdDt

Ed

P

dDxdDxdx

EP

dDx

dDx

dDxrrA

EA

Pdxd

t

io

++

++==

++

++=

+++=

+

++=

+==

=


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8-8Tableindefinedand

)/exp(

5.25774.0

5.05774.05ln2

5774.0

5.1,2,2/

))(155.1(

))(155.1(ln

5774.030

))(tan2(

))(tan2(ln

tan

BA

lBdAEd

k

dl

dl

Edk

dDdtlkk

dDdDt

dDdDt

Edk

dDdDt

dDdDt

EdPk

m

m

wm

=

+

+=

====

++

++==

++

++==


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8-8Tableindefinedand

)/exp(

BA

lBdAEd

km =


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8-2


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Bolt Strength


29/59

Bolt Strength


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Bolt Strength


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Bolt Strength


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Tension Joints-The External Load

Fi = preload P = external tensile load Pb = portion of P taken by

bolt Pm = portion of P taken by

members

Fb= Pb+ Fi = resultant boltload Fm= Pm Fi = resultant load

on members C= fraction of external load

P carried by bolt 1 C= fraction of external

load P carried by members


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34/59


80 %


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Relating Bolt Torque to Bolt Tension

15.0for0.2

625.0sectan1

sectan

2

2625.0

sectan1

sectan

2

25.12/)5.1(

2sectan1

sectan

2

/tan

2sec

sec

2

6)-(8and5)-(8form

===

=

+

+

=

+

+

+

=

=+=

+

+=

=

+

+=

c

i

cm

cciic

m

c

ccimi

m

cci

m

mmi

ffK

dKFT

ff

f

d

dK

Ktcoefficientorque

dfFdFf

f

f

d

dT

dddd

dfF

f

fdFT

dl

dfF

fld

fdldFT

&


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37/59


8-3


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Statically Loaded Tension Joint with

Preload

n = load factor 1bolt stress proofstrength


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Preload Fm = 0 (8-25)


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Preload

Bowman preload = 75% proof load

Proof strength Sp = 0.85 Sy


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Preload 8-4


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Gasketed Joints

boltofnumbertheis

circlebolttheofdiametertheis

63

pressureofuniformityadequatemaintainto

/)]1([

)1(

/

N

D

Nd

D

ANCnPFp

FnPCF

NA

Fp

b

b

gi

im

g

m

=

=

=


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Fatigue Loading of Tension Joints

Peterson bolt 15 percent under the head

20 percent at the end of the thread

65 percent in the thread at the nut face

Kf


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i di f T i i


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F i L di f T i J i


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iam

t

i

t

m

tt

ii

t

iba

iba

ib

A

F

A

CPA

CP

A

FFCP

A

FF

FFFFF

FFFF

+=

+=

=+

==

==

==

2

22

)(

2

2/)(2/)(

and

minmax

minmax

F i L di f T i J i


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F i L di f T i J i


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( )( )

( )

( )

am

p

p

tuti

ff

eut

tute

f

i

eut

itutef

tii

aaf

Sn

ASCF

nn

SSP

ASS

n

FC

SSCP

FASSn

AF

Sn

+=

+=

==

+

=

=

=

strengthprooftheusingyielding,ofypossibilitcheck the

1

1/GoodmanFor

2

0,1preload,noFor

2

/Goodman,For

/

saftyofFactor

0

0

F i L di f T i J i


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8-5

B lt d d Ri t d J i t L d d i


50/59

Bolted and Riveted Joints Loaded in

Shear

B lt d d Ri t d J i t L d d i


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Shear

tdA

AF

AF

cIM

FtM

=

=

=

=

=

/

/

/

2/



52/59


ShearThe usual analysis involves

Bearing in the bolt (all bolts participate) Bearing in members (all holes participate)

Shear of bolt (all bolts participate eventually)

Distinguishing between thread and shank shear Edge shearing and tearing of member (edge bolts

participate)

Tensile yielding of member across bolt holes Checking member capacity



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Shear 8-6



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Shear



55/59


Shear Shear Joints with Eccentric Loading

Direct load or primary shear F = V1/n

n number of bolt

Moment load or secondary shear M1



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Shear



57/59


Shear

L

L

+++=

=

==

+++=

222

1

2

1

/4

CBA

nn

C

C

B

B

A

A

CCBBAA

rrr

rMF

dF

r

F

r

F

r

F

rFrFrFM



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Shear 8-7

Reference


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Reference

Budynas, R.G. and Nisbett, J.K., Shigleys

Mechanical Engineering Design, 8th

ed.,McGraw Hill, 2008.

Machine Design i Ch5

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