leaf springs leaf spring projects

7/25/2019 Leaf Springs Leaf spring projects

http://slidepdf.com/reader/full/leaf-springs-leaf-spring-projects 1/167

STATIC ANALYSIS ANDMODAL ANALYSIS OF

COMPOSITE MONO LEAF SPRING BY USING ANSYS

R. Ramanjaneyulu 1, M.Peeraiah2, K. Hemalatha3,A.Venugopal4

1Department of Mehanial !ngineering, ". V. #ni$er%ity, Pro&&atur, 'n&ia,rrramanjaneyulu(gmail.om2,Department of Mehanial !ngineering, ).V. *ollege of !ngineering, +irupati, 'n&ia,%hreepeeru(gmail.om

3Department of Mehanial !ngineering, ).V. *ollege of !ngineering, +irupati, 'n&ia,(gmail.om4Department of Mehanial !ngineering, ).V. *ollege of !ngineering, +irupati, 'n&ia,aluri$enu(gmail.om

BSTRACT

A %pring i% &efine& a% an ela%ti o&y, -ho%e funtion i% to &i%tort -hen loa&e& an&to reo$er it% original %hape -hen the loa& remo$e&. +hough there are many type% of

%pring%, yet the follo-ing, aor&ing to their %hape, are important i% gi$en y Helial

%pring%, *onial an& Volute %pring% , +en%ional %pring%, /aminate& 0or /eaf %pring%,Di%0or elle$ille %pring%. /eaf %pring% 0al%o no-n a% flat %pring% are ma&e out of flat

plate%. +he a&$antage of leaf %pring o$er helial %pring i% that the en&% of the %pring may e

gui&e& along a &efinite path a% it &eflet% to at a% a %trutural in a&&ition to energya%oring &e$ie. enerally leaf %pring% are -i&ely u%e& in automoile%. Mainly t-o type%

of leaf %pring% are pre%ent, they are Mono leaf %pring% an& Multi leaf %pring%. A ompo%ite i%

u%ually ma&e up of at lea%t t-o material% out of -hih one i% the in&ing material, al%o alle&

matri5 an& the other i% the reinforement material. +he a&$antage of ompo%ite material%o$er on$entional material% %tem largely from their higher %peifi %trength, %tiffne%% an&

fatigue harateri%ti%, -hih enale% %trutural &e%ign to e more $er%atile. A6)") i%

general7purpo%e finite element analy%i% 08!A %oft-are paage. 8inite !lement Analy%i% i%a numerial metho& of &eon%truting a omple5 %y%tem into $ery %mall piee% 0of u%er7

&e%ignate& %i9e alle& element%. +he aim of our projet i% to analy9e the mono leaf %pring

for $ariou% loa&% ma&e up of &ifferent ro%%7%etion% -ith three &ifferent material% i.e., %teel,

!7 gia%% fier an& aron fier. *ompari%on i% &one for three material% of &ifferent ro%%7%etion% of mono leaf %pring%.

1. INTRODUCTION

1.

A %

p

rin

g

f u

n

tio

n

i

%

t

o&

i

%t

ort-

h

e

nl

o



a

&

e&

a

n&

t

or

e

o$

e

r

it%

ori

g

in

a

l

%h

a

pe

-

he

n

t

he

l

oa

&

i%

r

e

m

o

$

e&

.

Me

ha

n

i

a

l

%

pri

ng

%

ar

e

u

%e

&

in

m

a

h

i

ne

%

an

&

ot

h

e

r



a

p

pli

ati

o

n%

m

a

in

l

y

to

e5

e

rtf

o

r

e

,

to

p

r o

$

i

&e

fl

e5

i

il

it

y

,

t

o

%t

o

r e

o

r a

%

or

e

ne

r g

y

.2. +ype% of %pring%

3. 1. Helial %pring%: Helial

%pring% are ma&e of -ire oile& in

the form of heli5 an& are primarily inten&e& for

ompre%%i$e or ten%ile loa&%. +he

ro%%7%etion of -ire from -hihthe %pring i% ma&e maye irular,

%;uare or retangular. +he t-o

form% of helial %pring% areompre%%ion helial %pring an&

ten%ion helial %pring Helial

%pring% are %ai& to e lo%ely

oile&, -hen the heli5 angleHelial %pring% are %ai& to e

lo%ely oile&, -hen the heli5

angle i% $ery %mall0<1=o, -here

a% in open oil helial %pring the

heli5 angle i% large.

4. A&

$

a

n



t

a

ge

:

+h

e

%e

%

p

rin

g

%

ar

ee

a

%y

t

o

ma

n

uf

a

t

u

r

e.

+

he

y

ar

e

a

$

a

il

a

l

ei

n

-i

&

e

r a

n

g

e.

+h

e

ya

r

e

hi

g

hl

y

r e

li

a

l

e

.+

h

ey

h

a

$



e

on

%

ta

n

t%

p

ri

ng

r

a

te

%.+

h

eir

p

e

r f

o

r m

a

n

e

an

e p

r

e&

i

t

e

&

mo

r

ea

u

r

a

te

l

y

.H

er

e

h

a

r

a

t

eri

%

ti

%

an

e$

a

rie

&

y



h

an

g

in

g

&i

m

e

n%

i

o

n%.

2. *onial an& Volute %pring%:

>. +he onial an& $olute%pring are %peial appliation%

-here the %pring rate inrea%e% in

inrea%e in loa& .Another feature

of the%e type% of %pring% i% the&erea%ing numer of oil% re%ult%

in an inrea%ing %pring rate. +hi%

harateri%ti i% %ometime%utili9e& in $iration% prolem%

-here %pring% are u%e& to %upport

to o&y that ha$e $arying ma%%.?. 3

.

+

or

%

i

on

% p

ri

ng

%

:

+

he

%

e%

p

rin

g

%

ma

y

eo

f h

e

li

a

l

or

%

pir

a

lt

y

p

e.

H

eli

al

t

y

p



e

%

of

%

pri

n

g%

a

r

eu

%

e

&-

he

r

et

h

e

lo

a

&t

e

n&

%

t

o-

i

n&

u

pt

h

e

%

p

ri

ng

%

an

&

ar

e

u

%e

&

i

ne

le

tr i

a

lm

e

h

a

ni

%

m

%.

)

pir

a

lt

y

p

e



i

%

u%

e

&-

h

er

e

t

he

l

o

a&

%t

e

n&

%

t

oi

n

r

e

a%

e

t

he

n

um

er

o

f

o

il

%a

n

&a

r

eu

%

e

&i

n

-

at

h

e

%a

n

&

l

o

%.

7. 4

.

/

a

m

i

n

at

e

&

o

r

/

e



a

f

%

p

ri

ng

%

:

8. +

h

el

a

mi

na

te

&

or

l

ea

f

% pri

n

g0

a

l%

o

no

-

na

%

fla

t

%

pri

n

g

on

%

i

%t

%

o

f a

nu

m

e

r

o

f fl

a

t p

l

at

e

%

0

n

o-

n

a%

l

e

a



$

e

%

o

f $

a

r y

i

n

gl

e

n

gt

h%

h

el

&

t

og

e

th

e

r

y

m

ea

n

%o

f

l

a

m

p

%

a

n&

olt

%.

+h

e

%

et

y

p

e%

of

%

pri

n

g

%a

r

em

o

%t

u

%

e&

i

na

u

to

m

o



il

e

%.@. >. Di% )pring%:

10. +he%e %pring% on%i%t% of

a numer of onial &i% %hiel&together y a entral olt or tue

+he%e %pring% are u%e& in

appliation% -here high %pringrate% an& ompat %pring unit% are

re;uire&.

11. 1.

1

./

e

af

%

pri

n

g

%:

/

ea

f

% p

ri

n

g%

a

l

%o

n

o

-

na

%

fl

at

%

pri

n

go

r

art

%

p

rin

g,

m

a&

e

u

po

f

fla

t

pl

a

t

e%.

+o

&

ay

l

e

a



f

%

pri

n

g%

a

r e

%

ti

llu

%

e

&i

n

o

mm

e

r

i

a

l$

e

hi

l

e%

%

u

h

a%

a

r

%,

$

an

%

an

&

tr u

%,a

n

&

r a

il-

a

y

a

r

ria

g

e%.

8

or

h

e

a$

y

$e

h

i

l

e

%,

http://en.wikipedia.org/wiki/Van




http://en.wikipedia.org/wiki/Truck





http://en.wikipedia.org/wiki/Railway_carriage

























t

h

ey

h

a$

e

th

e

a

&$

a

n

ta

ge

o

f %

p

r

ea

&

in

g

th

e

l

oa

&

mo

r

e-

i

&

e

l

y

o$

e

r t

h

e$

e

h

i

l

e

%

ha

%

%i

%.

+

he

i

m p

o

rta

n

eo

f

le

a

f %

p

ri

n



g

i

%t

o

a

r

r y

u

m p

l

o

a&

%0i

.

e&

u

e

to

r

oa

&

ir r

e

g

ul

a

riti

e

%,

%

u

p

p

o

rt%

t

he

ha

%

%

i%

-

e

ig

ht,

on

tr

o

l%

a

5l

e

&a

m

p

in

g

,

o

ntr

o

l

%



r

a

i

ng

f

or

e

%,a

n

&

to

pr

o

$i

&

e

e

tt

er

%

u%

p

e

n%

i

on

.

/e

a

f

%

p

ri

ng

%

ar

e

&e

%

i

gn

e

&

in

t-

o

-a

y

%

:1

.

Mu

lt

il

e

a

f %

p

rin

g

%2

.

M

o



n

o

le

a

f %

p

rin

g

%.

12. 2

.

C

o

n

s

t

r

u

c

ti

o

n

o

f

le

a

f

s

p

r

i

n

g

:

13.

)e

m

ie

ll

i

p

ti

a

ll

e

af

%

p

rin

g

%

ar

ea

l

mo

%

t

un

i

$e

r

%a

ll

y

u%

e

&f

o

r %

u

%

p



e

n

%i

o

ni

n

lig

h

t

an

&

h

ea

$y

om

m

e

r

i

al

$

eh

i

le

.

8o

r

a

r

%

a

l

%

o,t

h

e%

e

ar

e

-

i&

e

l

yu

%e

&

f o

r

r

ea

r

%u

%

pe

n

%

io

n

.

14. )

em

i

e

lli



p

ti

a

l

le

a

f %

p

ri

ng

%

on

%i

%

t%

o

f

an

u

m

e

r o

f

l

ea

$

e%

all

e

&

l

a

&e

%.

th

e

%e

l

a&

e

%

$a

r y

i

nl

e

n

gt

h

.+

h

e

o

m

po

%

ite

%

pri

n

g

i



%

a%

e

&o

n

th

e

t

he

o

r

yo

f a

ea

m o

f

un

if

or

m

%tr

e

n

gt

h

.

1. 2

.3

A

n

a

l

y%

i

%o

f

le

a

f

% p

ri

n

g

ha

r

a

t

e

ri%

ti

%

:

1?. +

h

e

f u

n

tio

no

f

a

le



a

f

% p

ri

ng

m

ay

e

an

a

l

y9

e&

ym

e

a

n%

o

f %

o

me

%

i

m p

l

et

y

pe

%

o

f

e

am

%

an

&

th

e

ir

h

a

r

a

te

ri

%ti

%.

*o

n

%i

&

er

a

an

ti

le

$

er

e

a



m o

f

r

e

ta

n

gu

l

a

r

r

o%

%

%e

ti

on

,

-h

o

%e

-

i&

t

h

i%

B

C

t

hi

n

e

%%

B

hC

a

n&

l

e

ng

t

h

B/

C,i

%

%u

j

e

t

e&

t

oa

l

o

a&

B

8C

a

tit

%

f

r



e

e

en

&

.D

u

et

o

t

hi

%

l

oa

&t

h

e

e

a

m t

ri

e%

t

o

e

n

&a

n

&t

h

em

a

5

i

m

u

m

en

&i

n

gm

o

m

en

t

at

t

he

fi

5

e&

e

n&

i

%

1. E

m

a5

F

)

F

M

Z = M

1G. E

m



a5

F6 F

b

1!. Ma5

i

m

um &

e

fl

e

tio

n

,

o

t

ai

ne&

a

tt

h

e

f r

e

ee

n

&i

%

g

i

$

e

n

y

,

2=.

m

a5

F

F l3

3 EI =

)

l2

Eh

21.

m

a5

F2

3

)

l2

Eh

22. I

h

er

e

,

!'

%t

h

e

!l



a

%

ti

m

o&

u

lu

%

o

f t

h

e

% p

rin

g

ma

t

e

ria

l.

)i

n

e

t

h

el

e

af

%

pri

n

g

i

%

%

im

il

la

r

to

%

i

m p

l

y

%u

po

rt

e

e

am

.l

et

u

%

o

n

%i

&

er

a

%i

m

p

l



y

%

u p

o

rte

&

e

a

m

o

f l

e

ng

t

ho

f

l

en

g

th

/

02

l

an

&

a

e

n

tr a

l

lo

a

&

o

f

I0

2

8.

+

he

-

i

&t

h

a

n&

th

i

n

e

%%

o

f p

l

at

e

%

0o

r

e

a

m

m

a

y



e

B

C

an

&

Bh

C

r

e%

p

e

ti

$e

l

y.

8

o

r t

h

i%

a%

e

,

ma

5

im

u

m

e

n

&

i

n

g%

tr

e%

%

in

&

u

e

&

a

tt

he

en

t

e

r '

%

23. E

m

a5

F

MY

I =

24. E

m

a5

F6 Fl

bh2



)

i

mil

a

rly

,

ma

5

i

mu

m

&

efi

l

ati

o

n

at

t

he

en

t

er

i

%

m

a5

F

W

48

2. 8

r

om

t

he

a

o

$

e

t-

o

a

na

ly

%

i%

-

e

a

n

o

m

et

o

on

lu

%

io

n

t

h



a

t

th

e

%i

m

pl

y

)

u p

p

o

rte

&

e

am

of

l

en

g

th

/

02

l

%

u

j

e

t

e&

t

o

a

l

oa

&

I0

2

8

m

a

y

e

tr

ea

te

&

a%

D

o

u

l

e

a

nti

l

e

$e

r

e

a

m f

it

t

e



&

%

i&

e

y

%

i&

e

a

n&

l

o

a&

e&

a

tit

%

e

n&

%.

2?. 2

.

4D

!

)

'

6

J8/

!

A8

)

P

R

'

6

:

2. )

i

n

e

t

he

l

ea

f

% p

ri

ng

i

%

o

n

%tr

u

t

e

&

y

e

rta

in

n

u

m



e

r

of

f

ull

l

en

g

t

h/

e

a

$e

%a

n

&o

t

h

er

yg

r

a&

u

a

te

&

le

n

gt

h

l

e

a

$

e%,

it

i%

&

e%

i

g

no

n

t

he

a

%

i%

o

f

o

m

i

n

e&

%

tr

en

g

th

a

n&

&

e

fl



e

tio

n

h

a

r a

t

eri

%

ti

%

of

ot

h

f

ull

l

en

g

th

a

n

&g

r

a&

u

at

e

&

l

e

a

$e

%.

8F

/

oa

&

a

p p

li

e

&a

tt

h

ee

n

&

of

t

he

%

pri

n

g

.8

f

Fl

o

a&

%

h

a



r

e

&

y

f u

ll

le

n

g

th

l

e

a$

e%.

8

g

F

l

o

a&

%

ha

r

e&

y

th

e

gr

a

&u

a

t

e

&

l

ea

$

e%

a

lo

n

g

-it

h

m

a%

te

r

le

a

f

6

Ft

o

ta

l

nu

m

er

o

f l

e

a$

e

%.



6

f

Fn

u

m

e

r e

5

tr

af

u

ll

le

ng

t

hl

e

a

$e

%

6

g

F

nu

m

er

o

f g

r

a&

u

a

t

e

&

le

a

$e

%

in

l

u&

i

n

gm

a%

t

er

l

e

af

F-

i

&t

h

o

f e

a

h

l

ea

f

t

F



t

h

i

ne

%

%o

f

e

a

h

l

ea

f l

F

ha

lf

7

le

n

gt

h

of

l

e

af

%

pri

n

go

r

l

e

n

g

th

o

f

a

nti

l

e

$e

r

I

Ft

ot

a

ll

o

a

&tr

a

n%

m

itt

e

&

to

t

he

a

5l

e

o

f



$

e

hi

le

A

l%

o

,

IF

2

8

8

F8

f

L8

g

6

F 6

f

L 6

g

8ir

%

t

o

n

%i

&

er

t

h

e

h

a

lf p

o

rti

o

no

f

t

he

fi

r

%t

gr

o

u p

o

f

th

e

le

a

f %

p

ri

ng

-

hi

hl

o

o



%

li

e

a

a

n

til

e

$

er

e

am

on

t

a

in

i

ng

6

g

n

u

m

e

r

of

g

r a

&

ua

t

e

&

l

ea

$

e%

i

n

l

u

&i

n

g

ma

%t

e

r l

e

a

f.%

i

n

e

th

e

l

oa

&

i%

a

p p

li

e

&



a

t

th

e

f r

e

ee

n

&

of

t

h

em

a%

t

er

l

e

af,

i

no

r

&e

r

t

ofi

n

&o

u

tt

h

e

i

n

&

u

e

&%

tr

e%

%

a

n&

&

e

fle

ti

o

n,t

h

e

le

a

$e

%

ar

e

a

%%

u

me

&

to

e

a



r

r

an

g

e&

i

n%

u

h-

a

y

th

at

t

he

y

an

etr

e

at

e

&

a%

a

tr i

a

ng

u

l

a

r

p

la

t

e.

8

or

t

h

i%

t

h

ei

n&

i

$i

&

u

al

l

ea

$

e%

a

r

e%

e

pa

r

at

e

&

a



n

&

th

e

ma

%

te

r

l

ea

f

i

% p

la

e&

a

t

th

e

e

n

te

r

.t

he

n

th

e

%e

o

n

&

l

ea

f

i%

ut

l

o

ng

it

u

&i

na

ll

yi

n

t

ot

-

oh

a

l$

e

%

,e

a

h

o

f -

i

&

t



h

0

2

a

n

& p

l

a

e

&

o

ne

a

h

%i

&

e

of

m

a%

t

er

l

e

af.

+

he

%

am

e

m

e

t

h

o&

i

%a

&

o p

t

e

&f

o

r

ot

he

r

al

%

o

.t

h

er

e

%u

lt

a

nt

i

%a

p

pr

o

5

i



m

a

te

l

ya

tr

ia

n

g

ul

a

r

pl

at

e

of

t

h

i

ne

%

%0t

a

n&

a

ma

5

im

u

m

-

i

&

th

a

tt

h

e%

u

p

po

rt

a

%0

6

g

N

t

h

em

a

5i

m

um

%

tr

e%

%

pr

o

&u

e

&



a

t

th

e

fi5

e

&e

n

&

i%

g

i

$e

n

y

2G. )

g

F

M

Z

2@. +

h

em

a

5

im

um

&e

fl

e

ti

o

n p

r

o&

u

e

&

a

tt

h

e

f r

ee

e

n&

o

f

tr i

a

ng

u

la

r

p

la

t

ei

%

gi

$

e

n



y

3=.

g

F

F g

2 E

)

g

l2

Et

31. )

i

mil

a

rly

,

t

he

%

e

o

n&

g

r

ou

p

o

f l

ea

$

e

%i.

e

.

th

e

e5

tr

af

u

ll

le

n

g

th

le

a

$e

%

an

etr

e

at

e

&

a%

r

e

t

an

g

u

l



a

r

pl

a

te

o

f t

h

i

n

e

%%

0t

a

n&

u

n

if o

r

m

-i

&

th

0 N f

.

th

e

ma

5

im

u

m

in

&

u

e

&

e

n

&i

n

g

%tr

e%

%

at

fi

5

e&

e

n&

,

32.

F

(¿¿ f . l)( t

2

1

12( N f b) t

σ f = M

I

33. +h

e

&e



fl

e

ti

o

na

t

th

e

f

r e

e

e

n&

0i.

e

.l

o

a

& p

o

in

t

i%

g

i

$e

n

y

34.

δ f = F f

3

3>. )

i

n

e

th

e

le

a

f

% p

ri

n

gi

%t

h

e

o

m

i

n

e&

f

or

m

o

f

f u

ll

le

n

gt

h

l



e

a

$e

%

an

&

gr

a

&

ua

t

e

&l

ea

$

e%,

t

h

e&

e

fle

tio

n

p

r o

&

u

e

&i

n

o

t

h

ty

p

e%

o

f l

e

a

$e

%

a

r e

%a

m

e.

3?. i.

e.

δ g=δ f

0o

r

2

3σ f l2

Et

3.

σ f =3

2σ g

3G. 8r

o

m t

h

ea



o

$e

e

;u

a

tio

n

-

e

a

n

un

&e

r

%t

a

n

&t

h

at

-

he

n

t

he

l

ea

f

% p

ri

n

g

i

%

&e

fl

e

t

e&

,

t

he

f

u

lll

en

g

th

l

e

a$

e

%a

r

em

o

r

e%

tr

e%

%

e&

t

h

a



n

g

r a

&

ua

t

e&

l

e

a$

e

%

y

>=

O

.&

u

e

to

t

hi

%

e5

tr

a

%tr

e

%%

t

he

li

f

e

o

f

f u

ll

le

n

gt

h

l

ea

$

e

%a

r e

r

e&

u

e&

om

p

ari

n

g

to

t

he

li

f e

o

f

g



r

a

&u

a

te

&

le

a

$

e%

-

h

i

hi

%

un

&

e

%ir

a

l

e

an

&

h

en

et

h

e%

tr

e

%

%

i

n&

u

e

&

in

o

th

t

y

pe

%o

f

% p

ri

n

g%

a

r e

m

a&

e

e

;u

a

l

y

pr

o

$

i



&

i

ng

a

% p

e

i

a

l

ar

r

a

ng

em

e

nt

i

n

th

e

% p

ri

ng

.

)

u p

p

o%

e

th

e

n

i

p

p

in

g

i%

n

ot

a

&

o p

t

e

&,

th

e

n%

tr

e

%%

e

%i

n

&u

e

&i

n

f u

ll

le

n

g

t



h

l

ea

$

e%

a

n&

g

r

a&

u

a

te

&l

e

a$

e

%

ar

e

&if

f

er

e

n

ta

n

&t

h

ey

m

a

y

e

a

l

u

l

at

e

&

a%

f

o

llo

-.

3@. 8o

r

%

u

h

a

%

e,

σ f =3

2σ

4=. i.

e

.6 F f l

N f b t 2

41. *

an



e

lli

n

g

o

mm

o

n

pa

r

a

me

te

r

%,-

e

g

et

42.

F f

N f =

3

2

43. i.e

. F −

44.

F =3 f

2

4>.

Jr

F g=[34?. 6

o

-

E

g

F

e

n&

i

ng

%

tr e

%

%i

n

g

r a

&

ua

t

e&

l

e

a$

e

%

4.

¿ 6 F gl

N g b t 2=



4G. A

n

&8

f

F

e

n&

i

n

g%

tr

e

%%

in

&

u

e

&

in

f

ull

l

en

g

t

hl

e

a$

e

%,

4@.

3

2σ g=

3

2 [b

>=. Defl

e

ti

o

n,

-

h

i

h

i%

om

m

on

to

f u

ll

le

n

gt

h

an

&

g

r a

&

u



a

t

e&

l

ea

$

e%

i

%

gi

$

e

n

y

>1.

δ =2σ g

3

>2.

¿2¿ l

2

3 Et

[>3.

¿ Eb t

3(

>4.I

e

h

a$

e

n

o

-n

t

h

at

t

he

r

ei

%

a

me

t

h

o&

to

e

;u

a

li

9e

t

he

%

tr e

%

%

in

a

llt

h

el

e

a

$



e

%

y

p

r o

$

i&

i

n

ga

g

a

p

all

e

&n

i

p

"in

et

-

ee

n

f

ull

l

en

g

th

a

n

&

g

r

a&

u

at

e

&l

e

a

$e

%,

ef

or

e

jo

i

n

in

g

tig

h

tly

y

th

e

li

p

pi

n

g



o

lt

%,a

n

&if

t

he

li

p

o

lt

%a

r e

ti

gh

t

e

ne

&

,t

h

ef

u

ll

le

n

gt

h

an

&

g

r

a

&

ua

t

e&

l

ea

$

e

%-

il

l

e

n&

i

no

p

p

o%

it

e&

ir

e

ti

o

n%

a

n&

t

he

i

n

it



i

a

l%

tr

e%

%

&u

e

t

ot

h

i

%

en

&

in

g

m

ay

er

e

lie

$

e

&o

r

in

r e

a

%

e

&

i

no

r

&e

r

to

e

;

ua

li

9

et

he

%

tr e

%

%

in

ot

h

ty

p

e

%o

f

le

a

$e

%.

+

h



e

$

al

$

eo

f

ni

p

0

*,

li

p p

in

g

lo

a

&

an

&

th

e

o

m

m

on

%

tr e

%

%i

n

a

ll

t

h

el

e

a$

e

%m

a

y

e

o

ta

in

e

&f

r

o

m t

h

ef

o

llo

-

i

ng

r

el

a

tio

n

%.



>>. I

e

n

o

- t

h

at

σ g

a

n

&

σ f

>?.'

n

th

i

%

a%

e%

i

n

eσ g

,

-e

ma

y

,

>.

6 F g .l

N g b t 2= 6

N

>G. I

he

r

e8

F

8

g

L

8

f

an

& 6

F

6

f

L

6

g

>@. i.

e. F f

N f = F

N

?=. H

en

e

t

he

%tr

e

%%

i



n

&

u

e

&i

n

all

l

e

a$

e

%,

?1.σ =

6 F

Nb

?2. Ih

e

n

th

e

le

a

f %

p

ri

ng

i

%m

a

5i

m

um

&

e

fl

e

t

e&

,

th

e

n

i p

,C =δ g−

?3. 0g

r

a&

u

at

e

&

le

a

$e

%

-il

l

&

efl

et

m

or

e

t



h

a

nt

h

ef

u

lll

e

n

gt

h

l

ea

$e

%

y

the

?4.

C = 6

N g

?>.

¿ 6 F l

3

NEb t

??. +

h

el

o

a&

t

o

e

a

p

p

li

e&

o

nt

h

e

li

p

o

lt

%

to

l

o

%e

t

h

eg

a

pi

%

&e

t

e

r m

i

ne

&

y

t

h

e



f

a

t

t

ha

t

th

e

g

a p

i

%

e;

ua

l

to

t

h

ei

n

iti

a

l&

e

fl

e

ti

on

o

f t

h

e

f

u

ll

le

n

gt

h

le

a

$

e%

a

n

&g

r a

&

ua

t

e

&l

e

a$

e

%.?.

n

o

- t

h

atC =δ fi+

?G. i.

e



.

2

NE

[email protected] F

N =

2

=.2 F

N =

1.

F b= N

2. y

e

;u

a

ti

ng

t

hi

%

li

p

pi

n

g

l

oa

&0

8

t

o

t

h

et

e

n%

il

er

e

%

i%

ti

n

g%

tr e

n

gt

h

o

f

o

lt,

i.

e.

( !

4 )d"

2

s

-h

e

r

e%t

i

%t

h



e

a

llo

-

a

l

et

e

n

%il

e

%

tr e

%%

f

or

t

h

e

o

ltm

a

te

ri

a

l,t

h

e&

i

am

e

t

e

r

o

f t

h

e

o

ltm

a

y

e$

a

l

ua

te

.

+h

e

r

el

a

tio

n

%h

i

p

e

t

-e

e

nt

h

e

r



a

&

iu

%

of

ur

$

a

tu

r

e

,

am

er

a

n

&%

p

an

i

%g

i

$

en

yt

h

ee

;

u

a

ti

o

na

%

2 #Y −I

h

er

e

R

Fr

a

&i

u

%

of

ur

$

at

u

r e

" F

*

am

er

/

1

F

h

a

lf



%

p

an

o

f %

p

rin

g

)

in

e

B"

Ci

%

$e

r

y

%m

a

ll

o

m p

a

r

e&

t

oB

R

C,t

h

e

$

a

l

$e

o

f "2

a

n

en

e

g

le

t

e

&a

n

&

he

n

e

#= l1

2

2Y

a

n&

am

er

i

%t

a



e

ne

;

ua

l

to

t

h

em

a

5

im

um &

e

fl

e

ti

on

o

f t

h

e%

p

ri

ng

.

/e

t

B 6

C

e

t

he

t

ot

a

ln

o

.

of

l

e

a$

e%

i

n

l

u

&i

n

gm

a

%t

e

r

le

a

f.+

h

en

o

.

o



f

l

ea

$

e%

n

ot

h

a

$i

n

g

ey

e%

i

%0

6

7

1

/

et

2

l1

F

%

p

an

l

en

g

th

o

f

%

p

ri

ng

.

aF

-

i&

t

h

of

a

n&

-h

i

h

i

%

no

t

ha

$

in

g

%

pri

n

ga

tio

n

a

n



&

h

en

e

n

o-

n

a

%i

n

e

ff e

ti

$

el

e

n

gt

h

+h

e

n2

l

F

!ff

e

ti

$

el

e

n

g

t

h

F2

l1

7a

8

or

a

l

ea

f

%

pri

ng

h

a$

i

n

go

n

ef

u

lll

e

n

gt

h

le

a

f e

5

l



u

&

in

g

th

e

ma

%

t

er

l

e

af,

th

e

le

n

g

th

o

f a

ll

le

a

$

e%

a

r e

al

u

l

a

t

e&

a

%f

o

llo

-

%

3. /e

n

g

th

of

%

ma

ll

e

%t

l

ea

f

F Effe"ti

N

in

e

ff

e

ti

$e

l

en



g

t

h4.

0i

.e

.

fir

%

t

le

a

f

¿ N

>.

/

en

g

th

o

f ne

5

tl

e

af

F2

N

/

en

g

t

h

o

f

th

ir

&l

e

af

F2 l

N −1∗

)

im

il

a

rly

?. /

en

g

th

o

f 0 6

7

1t

h

le

a

f

F2 l

N −1∗

. '

n

g

e



n

e

r a

l,

th

e

le

n

g

th

o

f

an

yl

e

af,

%

t

art

i

ng

f

r o

m

%

ma

ll

e%

t

le

a

f

i

%

o

t

a

in

e

&a

%2 l

N −1∗

,

-h

e

r

eB

r

C$

a

rie

%

f r o

m

1

to

0

67

1.

G. +h

e

le

n



g

t

ho

f

nth

l

ea

f

-

hi

h

i%

ma

%

te

r

l

ea

f

@.F

2

N

G=. F

2

l1

L

0

&L

t

2I

h

er

e

&

Fi

n

%i

&

e&

i

a

me

t

e

r o

f e

y

e

t

Ft

h

i

ne

%

%o

f

m

a%

t

er

l

ea

f.

)



i

m

ila

rl

y,

f

or

a

l

ea

f

%

pri

ng

h

a$

i

n

gt

-

of

u

lll

e

n

gt

h

le

a

$e

%

e

5

l

u&

i

ng

t

he

m

a

%t

e

r

le

af,

t

he

l

e

ng

t

ho

f

Br t

hC

l

ea

f

% p

ri

ng

f

r

o



m

%

ma

ll

e%

t

le

a

f

i%

g

i

$e

n

y

/e

n

g

th

o

f B

r thCl

e

a

f F

F2

N

I

he

r

eB

r

C

$a

ri

e%

f

r o

m

1

t

o0

6

72

.

th

e

0

67

2

t

h

,

0 6

7

1t

h

a

n&

6th

l

e

a$

e

%



a

r

eh

a

$i

n

ge

;

u

al

l

e

ng

th

%,

-it

h

a

ne

5

tr a

l

en

g

t

hf

o

r e

y

e%

o

f

m

a

%

te

r

le

a

f 0

6th

.

#1. 3

.

D

$S

I

%

N

I

N

%

&

R

O

C

$

D

U

R

$

'

O

R

($

A

'

S

&

R

I



N

%

:

G2. 1. 8rom the a$ailale &ata, note the

loa&% to e %upporte&, no. of %pring%re;uire&, %pae a$ailale an& other

-oring on&ition%.G3. 2. +hen hoo%e a %uitale material

for the leaf %pring an& a%%ume it% &e%ign

yiel& %tre%% in en&ing. #%ually the

material% u%e& for leaf %pring% are %ilion%teel an& hromium mangane%e %teel an&

the allo-ale %tre%% i% ranging from 4== to

?== nm2.G4. 3. a%e& on the re;uirement, a&opt

pre %tre%%ing metho& if re;uire&. #%ually

thi% pre %tre%%ing or nipping i% preferale%o a% to mae all the lea$e% to e e;ually

%tre%%e&. enerally among all the lea$e%,

a&opt at lea%t t-o lea$e% inlu&ing ma%ter

leaf a% full length lea$e% an& on%i&er other lea$e% a% gra&uate& lea$e%.

G>. 4.Determine the %tre%% in&ue& in

the orre%pon&ing lea$e% an& al%o fin& outthe &efletion pro&ue& u%ing proper

e;uation%. )imilarly, e$aluate the -i&th

an& thine%% of lea$e%. 8in& out thelength of lea$e%, amer, lipping loa&,

the ra&iu% of ur$ature et. u%ing proper

relation%. Dra- a neat %eth of leaf %pring.

G?.

#). 3.1 D'M!6)'J6) J8 +AK'6

/!A8 )PR'6):

GG.

G@. 8

o

r

e

a

t

in

go

n

%

p

ri

n

g

i%

:

2

=

==

n

!0. *

.

T

+

$

O

R

I

TA

(

C

A

(

C

U

(

A

T

IO

N

S

:

!1. 4.



1A

6

A/

"

)')

J

8

MJ

6

J

/!

A

8

)P

R

'

6

I

'

+H

R

!

*+

A 6

#

/

AR

*

R

J)

)

)

*!

+

'

J 6

:

@2. )

+

!!

/

MA

+

!R

'

A

/:

R

!

A*

+'

J

6

8

JR

*

!)

A

+ 6

J

D!

1

0

61

:

@3. 8

Q

F=

8

"



F

2

==

=

@4. +

a

i

n

g

mo

m

en

t

%a

ou

t

n

o&

e

10

6

1:

@>. M

9

,

2

>

=

2=

=

=M

9

,

>

==

=

==

@?. Mo

m

e

nt

o

fi

n

ert

i

ao

f

a

r e

ta

n

gu

l

a

r

e

a

m:

@.

F

&3



1

2

F0

>

=

1

>3

1

2F

1

4

=?

2.

>

mm4

@G. De

fl

e

ti

on

o

f

th

e

an

til

e

$

er

e

am

-it

h p

o

in

t

l

oa

&

at

t

he

f

r

ee

e

n&

: ,

0

I

/3

0

3!

'

F

0

2=

=

=



2

>=3

0

3

2

1

=>

1

4=

?2

.

>

F

3

.

m

m

@@. )

tr e

%

%

:

,

0

?I/

0

&2

1==.

F

0

?

2

==

=

2

>

=

0

>

=

1

>2

1=1.

F2??.

?

?

6

mm2

102.

*.2

S

-

u

ar

e

c

r

o

s

s



s

e

c

ti

o

n:

1=3.R!A

*

+

'J

6

8

JR

*

!)

A

+

6J

D

!

10

61

:

1=4.

' F

=

'

/

F2=

=

=

1=>.

+ai

ng

m

om

e

nt

%

a

o

u

t

no

&e

1

0 6

1

:

1=?.

,

2>

=

2

=

=

=

,

>=

==

=

=



p

o

in

t

lo

a

&a

t

t

he

f

r

ee

en

&

:

,

0I

/3

0

3!

'

111.

F

02

===

2>

=3

0

3

2

1

=>

4

?

G3

3

.

=>

112.

F1.11

m

m

113.

)tre%

%:

,

0

?I

/

0

&2

114.

F0?

2

=



=

=

2

>

=

0

2

.

3

G

2

.3

G2

11>.

F

14

?

.

1>

6

m

m2

11.

*.3T

r

ap

e

i

u

4

c

r

o

s

s

se

c

ti

o

n

:

11.

R!A

*+

'

J 6 8

J

R

*!

)

A

+ 6

JD

!

10

6

1

:

11G.8 F

=

8

/

F

2

=



F

1

G.

>30

0

3

3

=

L

>

=

1

2F

?@

=

4

.2

@

mm4

123.

Defl

e

tio

no

f

th

e

a

nti

l

e$

e

r

e

a

m

-it

h

po

i

nt

l

o

a&

a

tt

h

ef

r

ee

e

n

&:

,

0

I/



3

03

!

'

124. F

0

2

==

=

2

>

=3

03

2

1

=>

?@

=

4

.2

@

12>.

F=.?

mm

12?.

)tre%

%:

,0

?I

/

h20

3

aL

12.

F0?

2

=

==

2

>=

1

G

.

>20

03

3=

L>

=



12G. F

?

=

.@

> 6

mm2

12!.

*.*

A

na

l

5

s

i

s

o

f

4

o

no

l

e

a

f

s

p

r

i

n

g6

it

7

e

8

g

l

a

s

s

fi

9

er

4

a

t

e

r

i

a

l:

130.

2..2

.1

R

!*

+

A

6

#

/A

R

*

R J

)

)

)*

!+'

J

6

:



131.

R!A

*+

'

J 6 8

J

R *

!

)

A+

6

JD

!

10

6

1

:

132.

8Q F

=8

"

F

2

==

=

133.+ai

ngm

o

me

n

t

%

a

o

u

tn

o

&e

1

0

61

:

134.

M ,

2>

=

2

=

=

=M

9

,>

=

==

=

=

13>.

Mo

m

en

to

f

in

e



rt

i

ao

f

ar

e

t

a

n

gu

l

a

r

ea

m

:

13?.

F

&3

12

F

0>

=

1>3

12

13. F

1

4

=

?

2.

>

mm4

13G.

Defl

e

ti

o

no

f

th

e

a

n

ti

le

$

er

ea

m

-

it

h p

oin

t

lo

a

&



a

t

th

e

f r

e

ee

n

&

:

,

0

I

/3

0

3

!'

F

02

=

==

2>

=3

0

3

G

=

1

=3

1

4

=?

2

.>

F@

.

2

>m

m

13@.

)tre%

%:

,

0

?

I/

0

&2

14=.

F0?

2

=

==

2>

=

0

>

=



1

>2

141.F2??

.

??

6

mm2

1*2.

*.S-

u

a

r

e

c

r

o

s

s

se

c

ti

o

n

:

143.

R!A

*

+'

J 6 8

J

R

*

!

)A

+

6J

D

!1

0

6

1:

144.

' F

=

'

/

F

2=

=

=

14>.

+ai

ng

m

om

e

n

t%

a

ou

tn

o

&e

1



n

o

ft

h

e

a

nti

l

e

$e

r

ea

m

-it

h

p

oi

n

tl

o

a&

a

tt

h

e

f r

e

ee

n

&:

,

0

I

/3

0

3!

'

F

0

2

==

=

2>

=3

03

G

=

1

=3

4?

G

3

3.

=

>

1>=.F2.

m

m



1>1.

)tre%

%

,

0?

I/

0

&2

F0

?

2

=

==

2>

=

02

.3

G

2

.3G2

1>2.

F

1

4

?

.1

>

6

m

m2

13.

*.C

i

r

c

u

l

a

r

c

r

o

s

s

s

e

c

tio

n

:

1>4.

R!A

*+

'

J

6 8

J

R *

!

)



A

+

6J

D

!1

0

61

:

1>>.8Q F

=

8

"

F

2=

=

=

1>?.

+ai

ng

m

om

e

nt

%

a

o

u

t

no

&e

1

0 6

1

:

1>.

M9 ,

2>

=

2

=

=

=M

9

,

>

=

==

=

=

1>G.

Mo

me

n

to

f

in

e

rt

ia

o

f

a*

'R

*

#/

A



R

e

a

m:

1>@.

F

U&4

?

4F

3

=

.@4

?

4F

4

4

?

2.

3

mm4

1?=.Defl

eti

o

no

f

t

h

e

a

n

til

e

$e

r

ea

m

-

ith

p

oi

n

t

lo

a

&a

t

th

e

f r

e

e

en

&

:

,

0

I/3



0

3

!'

1?1.

F

02

=

=

=

2

>=3

0

3

G

=

1=3

4

4

?

2

.

3

1?2.

F2.@m

m

1?3. S

t

r

e

s

s

:

,

3

2I

/

D3

1?4. F

0

32

2=

=

=

2

>

=

0

3

=.

@3

F1

2

.?

2 6

m

m2



1.

*.

T

r

a

pe

i

u

4

c

r

o

s

s

s

e

c

ti

o

n

:

1??.

R!A

*

+'

J 6 8

J

R *

!

)

A+

6

JD

!

10

6

1

:

1?.

8Q F=

8

"

F

2

=

==

1?G.+ai

ngm

o

me

n

t

%a

ou

t

no

&

e

10

6

1

:

[email protected] ,

2

>=



2

=

==

M

9 ,

>

==

=

=

=

1=.

Mom

e

nt

o

fi

n

e

rti

a

of

a

+R

A

P

!T

'

#

M

e

am

:

11.

F

h3

0

3a

L

1

2

F

1G

.

>30

03

3=

L

>=

12

F

?

@

=4.

2

@m

m4



12.

Defl

e

ti

on

o

ft

h

e

a

n

ti

le

$e

r

e

a

m

-

ith

p

oi

n

tl

o

a

&a

t

th

e

f r

e

e

e

n

&: ,

0I

/3

0

3

!'

F

02

==

=

2

>

=3

0

3

G

=

1

=3

?@

=

4

13.

F

1



.

?

@m

m

14.

)tre%

%

,

0?

I

/

h20

3a

L

1>.

F 0?

2==

=

2

>

=

1

G

.

>200

3

3

=

L>

=

1?.

F

?=

.

@

> 6

mm2

1)).

*.)A

n

a

l

5

s

is

o

f

4

o

n

o

l

e

a

fs

p

r

i

n

g

6



it

7

c

a

r

9o

n

fi

9

e

r

4

a

t

e

ri

a

l:

1)#.

R

e

t

a

ng

ul

a

r

r

o

%%

%e

ti

on

:

1@.

R!A

*+

'

J 6 8

J

R *

!

)

A+

6

JD

!

10

6

1

:

1G=.

8Q F

=8

"

F

2

==

=

1G1.+ai

ngm

o

me

n

t



%

a

o

u

tn

o

&e

1

0

61

:

1G2.

M9 ,

2>

=

2

=

=

=M

9

,>

=

==

=

=

1G3.

Mo

m

en

to

f

in

e

rt

i

ao

f

ar

e

t

a

n

gu

l

a

r

ea

m

:

1G4.

F

&3

12

F

0>

=

1>3

12

F1

4

=

?2



.

>

mm4

1G>.

Defl

e

ti

o

no

f

th

e

a

n

til

e

$

er

ea

m

-

ith

p

o

in

tlo

a

&a

t

t

h

e

f r

e

ee

n

&:

1G?.

,

0

I

/3

03

!

'

F

02

===

2>

=3

0

3

1

>

=

1

=3



1

4=

?

2.

>

F

4.

@

m

m

1G.

)tre%%

,

0

?I

/

0

&2

1GG.

F 0?

2

=

=

=

2>

=

0

>

=

1>2

F2

?

?.

?

?

6

m

m2

1#!.

2.).3

.

2

S

U

A

R

$

C

R

O

S

S

S

$

C

T

I

ON

:

1@=.R!A

*

+



'

J

6

8

JR

*!

)

A+

6

J

D!

1

0 6

1

:

1@1.

8Q F

=8

"

F

2=

==

1@2.+ai

n

g

mo

men

t

%a

o

u

t

no

&

e1

0

61

:

[email protected] ,

2

>=

2=

=

=M

9

,

>=

=

==

=

1@4.

Mo

m

en

t

o

fi

ne

rt

ia

o



f

a

)S

#

AR

!

e

a

m

F

&3

12

F

02

.

3G

2

.

3G3

1

2

1@>.F4?G

33.

=

>m

m4

1@?.

Defl

e

ti

on

o

ft

h

e

a

n

ti

le

$e

r

e

a

m

-

ith

p

oi

n

tl

o

a

&a

t

th

e

f r

e

e



e

n

&:

,0

I/3

0

3

!

'

1@.

F

02

=

==

2>

=3

0

3

1>

=

1

=3

4

?G

3

3.

=

1@G.

F1.4

G

mm

1@@.

)tre%%

:

,

0

?

I



/

0

&2

2==.

F 0?

2

=

==

2>

=

0

2

.

3

G

2

.3

G2

2=1.

F

1

4?

.1>

6

m

m2

202.

*.#

c

i

r

cu

l

a

r

c

r

o

s

s

s

ec

ti

o

n

:

2=3.

R!A

*+

'

J 6 8

J

R *

!

)

A+

6JD

!

10

6



1

:

2=4.

8Q F

=8

"

F2

=

=

=

2=>.

+ain

gmo

m

en

t

%

a

o

ut

n

o&

e

1

0 6

1

:

2=?.

M9 ,

2

>

=

2

=

=

=M

9

,>

=

==

=

=

2=.

Mo

me

n

to

f

in

e

rt

ia

o

fa

+

R A

P

!

T'

#

M

e

a

m:



2=G.

F

U&4

?4

F

3

=

.@4

?

4F

44

?2

.

3

mm4

2=@.

Defl

e

ti

o

no

f

t

he

a

n

ti

le

$

e

r

e

am -

it

h p

o

i

nt

l

oa

&

at

t

h

ef

r

ee

e

n&

:

,

0

I

/3

03

!

'



21=.

F

02

=

==

2>

=3

0

3

1>

=

1

=3

4

4

?

2.

211.F1.>

>

m

m

212. )

tr

e%

%

:

,

3

2

I

/

D3

213.

F0

3

2

2

=

==

2>

=

0

3=

.

@3

214. F1

2

.?

2

6

m

m2

21.

*.#T

r



a

p

e

i

u4

c

r

o

s

s

s

e

c

ti

o

n

:

21?.

R!A

*

+'

J

6

8J

R

*!

)

A+

6

J

D!

1

0 6

1

:

21.

8Q F

=8

"

F2

=

==

21G.

+ain

g

mo

m

en

t

%a

o

ut

n

o&

e

10

6

1

:

21@.

M9 ,

2>

=

2

==

=



M

9

,

>

=

==

=

=

22=.

Mo

me

n

to

f

in

e

rti

a

o

fa

+

R A

P

!T

'

#

M

e

am:

221. F

h3

0

3

aL

1

2

F1

G

.

>30

0

3

3=

L>

=

12

222.F?@

=

4.

2

@

mm4

223.Defl

e

ti

on

o



f

t

he

an

ti

le

$

e

r

e

a

m -

it

h p

o

i

nt

l

oa

&

at

t

he

f

r

ee

e

n&

: ,

0

I

/

3

03

!

'

F

02

=

=

=

2

>

=3

0

3

1

>

=

1

=>

?@

=

4

.2

@

224.

F=.=@

m

m



22>.

)tre%

%:

,

0?

I

/

h20

3a

L

22?.F

0

?

2

=

==

2>

=

1

G

.

>20

0

3

3=

L

>

=

22. F

?

=.

@

> 6

m

m2

22G..

%

e

n

e

r

i

c

s

t

ep

s

t

o

s

o

l

;

i

n

ga

n

5

&

r

o

9



l

e

4

i

nA

N

S

/

S

22!.

/

i

e%

ol

$

in

g

a

ny

pr o

le

m

a

n

a

ly

ti

a

lly

,

y

o

un

e

e&

t

o&

e

fi

ne

0

1

y

ou

r

%o

l

u

tio

n

&o

m

ai

n

,

02

th

e

ph

y

%

i



a

lm

o

&e

l,

03

ou

n

&

ar

y

o

n&

it

i

on

%

an

&

04

t

he

p

hy

%

i

a

l

p

r

o

pe

rt

ie

%.

"o

u

t

he

n

%

ol

$e

t

he

p

r

o

l

em a

n

& p

r

e

%e

n

tt

h

er

e

%



u

lt

%.'

n

nu

m

eri

a

lm

e

t

ho

&%,

t

he

m

a

in

&

if f

e

r e

n

ei

%

an

e

5tr

a

%

t

e

p

a

ll

e&

m

e%

h

g

en

e

r

ati

on

.

+h

i

%

i%

t

he

%

te

p

t

ha

t

&i

$

i&

e

%

t



h

e

o

m

pl

e

5m

o

&

el

i

n

to

%m

a

lle

l

e

me

n

t%

t

ha

t

e

o

me

%

ol

$

a

l

e

in

a

no

t

he

r

-

i%

e

t

oo

o

m

pl

e

5

%it

u

ati

o

n.

e

lo

-

&

e%

ri

e

%



t

h

e p

r

o

e

%%

e

%

in

t

e

r m

in

o

lo

g

y

%li

g

htl

y

mo

r

e

att

u

ne

t

ot

h

e

%

o

ft

-a

r

e.

uil

&

eo

m

e

tr y

:*

o

n%

tr

u

t

a

t-

o

or

t

h

r e

e

&i

m

en

%

i

o



n

a

lr

e

pr

e

%e

n

t

ati

o

n

of

th

e

o

j

e

t

t

o

e

mo

&

e

le

&

an

&

te

%

t

e

&

u

%i

n

gt

h

e-

o

r

p

l

a

ne

o

o

r &

i

n

at

e

%y

%

te

m

-

it

hi

n

A 6

)

")

.

D



e

fi

ne

M

at

e

ria

l

P

r o

p

e

rti

e%

:

6o

-

t

ha

t

th

e

pa

rt

e

5i

%

t%,

&

efi

n

e

a

li

r a

r

yo

f

th

e

n

e

e

%

%a

r y

m

at

e

ri

al

%

th

a

t

o

m

po

%

et

h

eo

j

e



t

0o

r

pr

o

je

t

e

i

n

gm

o&

e

le

&

.

+h

i

%i

n

l

u

&

e%

t

he

r

ma

l

a

n

&

m

e

h

an

i

a

l

p

r o

p

e

rti

e%.

en

e

r

at

e

Me

%

h:

A

t

th

i

% p

o

in

t

A

6



)

"

)u

n

&e

r

%t

a

n

&%

t

h

em

a

e

u p

o

f

th

e

pa

rt

. 6

o

-

&

efi

n

eh

o

- t

h

e

m

o

&e

l

e&

%

y%

t

e

m %

h

o

ul

&

e

r

o

en

&

o-

n

in

t

o

fin

it

e p

i

e

e

%.

A



p

p

ly

/

oa

&

%:

J

n

e

t

h

e%

y%

t

em

i

%

f u

ll

y&

e

%i

g

n

e&

,

th

e

la

%

t

t

a

%

i

%

to

ur

&

e

nt

h

e

%y

%t

e

m

-

ith

on

%

tr a

i

nt

%,

%

u

h

a%

p

hy

%

i



a

ll

o

a&

i

ng

%

o

r

o

u

n&

ar

y

o

n

&

iti

o

n%.

J

t

a

i

n)

o

lu

ti

on

:

+

h

i

%

i%

a

t

u

all

y

a

%t

e

p

,

e

a

u%

e

A

6)

"

)n

e

e&

%

t

ou

n

&e

r

%t

a

n

&



-

it

hi

n

-h

a

t%

t

a

te

0

%

te

a&

y

%t

a

t

e,

tr

an

%

ie

n

t

et

.t

h

e p

r

o

l

em

mu

%t

e%

o

l

$e

&

.

23=. Pre%ent the Re%ult%: After the

%olution ha% een otaine&, there are many-ay% to pre%ent A6)")C re%ult%, hoo%e

from many option% %uh a% tale%, graph%,

an& ontour plot%.

231.

.

OD

A

(

A

N

D

S

T

A

TI

C

A

N

A

(



/

S

I

S

232.

?.1 M

J

DA

/

A

6A

/

"

)'

)233. Mo&al analy%i% i%

u%e& to &etermine the $iration

harateri%ti% 0natural fre;uenie%an& mo&e %hape% of a %truture or a

mahine omponent -hile it i%

eing &e%igne&. 't an al%o %er$e a% a

%tarting point for another, more&etaile&, &ynami analy%i%, %uh a% a

tran%ient &ynami analy%i%, a

harmoni re%pon%e analy%i%, or a%petrum analy%i%. Mo&al analy%i% i%

u%e& to &etermine the natural

fre;uenie% an& mo&e %hape% of a%truture. +he natural fre;uenie%

an& mo&e %hape% are important

parameter% in the &e%ign of a

%truture for &ynami loa&ingon&ition%. +he general proe%% for a

mo&al analy%i% on%i%t% of the%e

primary %tep%: 1.uil& themo&el.2.Apply loa&% an& otain the

%olution.3.!5pan& the

mo&e%.4.Re$ie- the re%ult%.

23*.

23>.8ig

?

.1

:

m

on

ole

a

f %

p

rin

g

o

f R

e

t

a

ng

l

e

a

r e

ao

f

r

o



%

%

%e

tio

n

23?.

?.3

)

+A

+

'*

A

6

A/

"

)

')

J

6

/!

A

8)

R

' 6

)

:?

.

3.

1

8o

r

R

e

t

an

g

ul

a

r

ar

e

a

of

r

o

%%

%

e

ti

o

n:

?

.3

.

2

8o

r

%t

e

el

m

a

t



e

ri

al:

23.

8

i

g

.

?.

2:

V

on

7

Mi%

e

%)tr

e

%%

P

lo

t

o

f )

t

ee

l

Mo

n

o

/e

a

f )

p

rin

g

23G.?.3.4

8

or

!

7

l

a%

%

fi

e

r

ma

t

eri

a

l:

23!.

24=.8ig.

?



.

3

:V

o

n7

M

i%e

%

)

tr e

%

%

Pl

ot

o

f !

7

g

la

%

%fi

er

M

o

no

/

ea

f

) p

ri

n

g

241.

?.3.>

8o

r

*a

r

o

n

fi

e

r

m

at

eri

a

l:

2*2.

243.

8ig.?

.

4:

V

on

7M

i%e

%

)tr

e



%

%

Pl

o

to

f

*a

r

on

fi

er

Mo

n

o/

e

a

f )

p

rin

g

2**.

.3.

'

o

r

S

-

ua

r

e

a

r

e

a

o

f

c

r

o

ss

s

e

c

ti

o

n

:

'

o

rs

t

e

e

l

4

a

t

e

r

i

a

l:

2*.

24?.

8ig.

?.

>

:V



o

n

7M

i%

e%

)

tr e

%

%

Pl

o

t

of

)t

e

el

M

o

no

/

ea

f

) p

ri

n

g

2*).

24G.

8ig.

?.

?

:D

e

fle

ti

on

P

l

ot

of

)

te

e

l

Mo

n

o/

e

af

)

p

rin

g

2*!..3.)

'

o

r

$

8

%



l

a

s

s

fi

9e

r

4

a

t

e

r

i

a

l:

20.

2>1.

8ig.

?

.

:V

o

n

7M

i%

e%

)tr e

%

%

Pl

o

t

o

f !

7

gl

a

%%

fi

er

/

e

af

) p

ri

ng

22.

'or

C

a

r9

o

n

fi

9

e

r

4

a

t

er

i

a

l:



23.

2>4.8ig.

?

.

G:

D

ef

o

r m

e

&a

n

&

#n

&

ef

o

r m

e

&

Pl

o

t

of

*a

r

on

fi

er

M

on

o

/e

a

f

) p

ri

n

g

2>>.

2>?.

8ig.?.

@

:V

o

n7

M

i%

e%

)

tr e

%

%P



l

o

to

f

*a

r

o

n

fi

e

r

M

on

o/

e

af

)

p

rin

g

2).

.3.#

'

o

r

C

i

r

c

u

la

r

a

r

e

a

o

f

c

r

o

s

ss

e

c

ti

o

n

:

2#.

'or

s

t

e

e

l

4

a

t

e

r

i

a

l:

2!.

2?=.

8ig.?.

1

=:

D

e



f

o

r m

e

&a

n

&#

n

&

ef

o

r

me

&P

l

ot

o

f

)t

e

el

M

on

o

/

ea

f

) p

ri

ng

21.

2?2.8ig.

?

.

11

:

Vo

n7M

i%

e

%)

tr

e%

%

Pl

o

t

of

)

te

e

l

Mo

no

/

e

af



)

p

rin

g

23.

2?4.

8ig.?

.1

2

:D

e

fle

tio

no

f)

t

ee

l

Mo

n

o/

e

a

f)

p

ri

n

g

2.

.3.!

'

o

r

$

8

%

l

a

s

s

fi

9

e

r

4

a

t

e

r

i

a

l:

2.

2?.

8ig.

?.

1

3:

D

ef



o

r

me

&

an

&

#n

&

e

f o

r

m

e&

Pl

o

to

f

!

7g

l

a%

%

fi

e

r

Mo

n

o/

e

af

)

p

ri

n

g

2#.

[email protected].

?

.1

4:V

o

n

7M

i%

e%

)

tr e

%

%

Pl

o

to

f

!

7g

la

%

%

fi



e

r

/e

a

f )

p

rin

g

2=.

'or

C

a

r

9

o

n

fi

9

e

r

4

a

t

e

ri

a

l:

2)1.

22.8ig.

?

.1

>

:

D

ef

o

r m

e

&a

n

&

#n

&

e

f o

r m

e

&P

l

o

to

f

*a

r

o

n

fi

e

r

Mo

n

o/

e

a

f



)

p

rin

g

2)3.

24.

8ig.?

.

1

?:

V

on

7

Mi%

e

%)

tr

e

%%

P

lo

t

o

f *

a

r

o

nfi

e

r /

e

af

)

pri

n

g

2).

.3.!

'

o

r

T

r

e

p

i

o

i

<

a

la

r

e

a

o

f

c

r

o

s

ss

e

c

ti

o

n

:



2).

'or

S

t

e

el

a

t

e

r

i

a

l:

2)).

2G.

8ig.

?.

1

:D

e

f o

r

me

&

an

&

#

n&

e

f

o

r

me

&

Pl

o

to

f

)

te

e

l

Mo

no

/

ea

f

)

pri

n

g

2)!.

2G=.

8ig.?

.

1G

:

Vo



n

7

Mi%

e

%)

tr

e%

%

P

lo

t

o

f )

te

e

lm

o

n

o/

e

af

)

pri

n

g

2#1.

).

OD

A

(

A

N

A

(

/

S

I

S

O

N

(

$

A

'

S

R

I

N

%

S

:

2#2.

).1

'

o

r

R

e

c

t

an

g

u

l

a

r

C

r

o

s

ss

e

c

ti

o

n

:



2#3.

S

t

e

el

a

t

e

r

i

a

l:

2#*.

2G>.8ig

?

.1

@

:8

ir

%t

M

o

&e

o

f V

i

r

e

a

ti

o

n

2#.

2G.8ig

?

.2

=:

%e

on

&

Mo

&

eo

f

V

i

r

ati

o

n



2##.

2G@.

8ig?

.

21

:

+hir

&

mo

&

eo

f

$

i

r

ati

o

n

2!0.

).2'

o

rS

-

u

a

r

e

C

r

o

s

s

s

ec

ti

o

n

:

2!1.

'or

S

t

e

e

l

a

t

e

r

i

a

l:

2!2.

2@3.

8ig?

.22

:

8ir

%

t



M

o

&e

o

f V

i

r

a

ti

on

2!*.

2@>.

8ig

?.

23:

%

e

o

n

&M

o

&e

o

f

Vi

r

a

ti

on

2!.

).2

'

o

r

$

8

%

l

a

s

s

fi

9

e

r

a

t

e

r

i

a

l:

2!).

2@G.

8ig?.

2

48

ir

%



t

M

o&

e

of

V

i

r

e

ati

o

n

2!!.

3==.8ig

?

.2>

:

%e

on

&

M

o&

e

of

V

i

r

a

tio

n

301.

).3

'

o

r

C

a

r

9

o

n

'

i

9

e

r

4

a

t

e

r

i

al:

302.

3=3.

8ig?

.

2?

:

8

ir



%

t

Mo

&

eo

f

Vi

r

ati

o

n

30*.

).*

'

o

r

C

i

r

c

u

l

ar

C

r

o

s

s

s

e

c

ti

on

:

'

o

r

S

t

e

e

l

4

a

te

r

i

a

l:

30.

30.

30). ).

'

o

r

T

r

e

p

i

oi

<

a

l

C

r

o

s

s

s

ec

ti

o

n

:

'



o

r

30#.

#.

R

$

S

U

(

T

S

A

N

D

C

ON

C

(

U

S

I

O

N

S

3=@.

R

$

S

U

(

T

S

:

A

% p

e

rt

h

em

a

n

ua

l

a

l

u

l

a

tio

n

%

an

&a

n

al

y

%

i%

i

ma

g

e%

310.

'OR

S

T

A

TI

C

A

N

A

(



/

S

I

S

:

'o

r

r

e

c

t

a

n

g

u

la

r

4

o

n

o

l

e

a

f

s

p

r

i

n

g

311. 'o

r steel312.

313.

314.

31>.

31?.

31.

32). 'o

r e8

glass

fi9er32G.

32@.

33=.

331.

332.

333.

3*3. 'or

steel

344.

34>.

34?.

34.

34G.

34@.

3!. 'or

car9on

fi9er

3?=.

3?1.

3?2.

3?3.

3?4.

3?>.

3>.

'OR N

O

D

A

(

A

N

A

(

/

S/

S

:

R e

ta

n

g

ul

a

r

r

o%



%

%

e

ti

on

:

f o

r

%

te

e

l

e7

gl

a

%%

fi

er:

3?. 8JR

*

AR

J 6

8

'

!R

:)

S#

A

R !

*

R J

)

)

1. '

o

r

s

t

e

e

l2.

3.

4.

5.

?.

7.

17.'

o

r

e

8

g

l

a

s

s

f

i

9

e

r

1G.

19.

2=.

21.

22.

23.

33.'

o

r

c

a

r

9

on

f

i

9

e

r34.

35.

3?.

37.

3G.

39.



)!

*

+'

J 6

:8JR

)

+!

!

/:

3. 8J

R

!7

/

A

))

8

'

!

R :

3G.

3@. N

3G=.

3G1.

3G2.

3G3.

3G4.

3G>.

3G?.

3G. 8J

R

*A

R

J 68

'

!

R

:

3GG.

*#R

*

#

/

AR

*

R

J

)

)

)!

*

+

'

J 6

:

8

J

R

)

+

!

!

/

:

3G@.

3@=.

NN

3@1.

3@2.

4@.>=.



)!+

3@3.

3@4.

3@>.

3@?.

3@.

8JR

!7

/A

)

)

8'

!R

:

[email protected]@@. N

'6D!

Q J8

DA+A

)!+)

J6

R!)#

/+)

8'/!

N

4==.

4=1. )!+

+'M!

8R!S

/JAD

)+!P

)#)

+!P

*#M#

/A+'V

!

4=2. 1

12.1=?

1

1

1

4=3. 2

4.GG?

1

2

2

4=4. 31>.44

1

3

3

4=>.

4=?.

8JR

*A

R

J 6

8

'

!

R

:

4=.

N

4=G.

4=@.

41=.

1

411.

2

412.

3

413.

414.

8JR

+

R !



P

'

TJ

'

DA

/

*R

J

)

))

!

*

+'

J 6

:

8J

R )

+

!!

/

:

41>. NN

'6D!

Q J8

DA+A

)!+)

J6

R!)#

/+)

8'/!

NN41?.

41. )!+

+'M!

8R!

S

/JA

D

)+!P

)#)

+!P

*#M

#/A+

'V!

41G. 1

.@

2

1

11

41@. 2

1?.@G

3

1

2

2

*20.

3

4G.?

>

1

3

3*21.

422.

.3

C

O

N

C

(

U

S

IO

N

S

:

'

n

ou

r

pr

o

je

t-

e



h

a

$e

a

na

l

y9

e

&

am

o

n

ol

ea

f

% p

ri

n

gu

%

in

g

th

r

e

e&

if

f e

r

en

t

m

a

t

e

ria

l

%a

%

%t

e

e

l,e

7

g

la

%%

fi

r

e

,

a

r

o

n

fi

e

r

an

&

th

r

ee

&

if

f



e

r

en

t

r

o

%%

%

e

ti

o

n

%r

e

t

an

g

u

la

r,

%;

u

ar

e

,t

r a

p

e9

i

um

.

I

e

h

a

$e

a

na

l

y9

e

&

am

o

n

ol

ea

f

% p

ri

n

gu

%

in

g

A 6

)

"

)%

o

ft-

a

r e

.

'

n



A

6

)"

)

-e

h

a&

&

o

ne

%

t

ati

a

n

al

y

%

i%

o

nm

o

no

l

e

af

%

pri

n

gt

o

$

a

li

&

at

e

th

e

%tr

e

%

%o

n

&

if f

er

e

nt

m

a

te

ri

al

%

ha

$

i

ng

&

if f

e

r e

n

t



r

o

%%

%

e

ti

on

%.

y

o

m

pa

rin

g

th

e

%

tr e

%

%a

n

&&

e

fl

e

ti

on

$

al

u

e

%,

t

h

e%

u

ita

le

m

a

te

ri

a

lf

or

m

on

o

l

ea

f

% p

ri

ng

i

%

a

r

o

n

fi

e

r

h



a

$

in

g

tr a

p

e9

i

u

m

r

o

%%

%

e

ti

o

n.

I

eh

a

$e

a

l%

o

&

on

e

mo

&

al

a

n

a

l

y%

i

%o

n

mo

n

o

le

a

f

% p

rin

g

to

$

a

li&

a

te

t

he

f

r

e;

u

en

y$

a

l

u



e

%

on

&

if f

e

r e

n

t

ma

t

e

ria

l%

h

a$

i

n

g&

if

f e

r

en

t

r o

%

%%

e

ti

o

n

%.

y

o

%

er

$

in

g

t

he

r

e

%u

lt%

%

te

e

l

ma

t

eri

a

lh

a

$

in

g

le

%

%m

o

&

e



$

a

lu

e

%i

n

&if

f

e

r e

n

t

r

o%

%

%e

ti

on

%.

)o

-

e

o

n

l

u

&e

t

ha

t

y

t

a

i

n

g%

tr

e%

%

$

al

u

e

%i

nt

o

o

n

%

i&

e

r a

ti

on

i

n

&e

%

ig

n

of

m

o

n



o

l

ea

f

% p

ri

ng

,

ar

o

nfi

e

r

ha

$

i

ng

tr

a p

e

9i

u

m

r o

%

%%

e

ti

o

n

g

i

$e

%

go

o

&r

e

%

ult

.

yt

a

i

ng

m

o

&e

$

al

u

e%

i

n

to

on

%

i&

e

r

a



ti

o

n,

t

he

e%

t

m

at

e

ri

al

i%

%

te

e

l

f o

r

mo

n

ol

e

a

f %

p

rin

g

.

*23.

BIB

(

I

O

%

R

A

&

+/

1. +heory ofMahine%7 Khurmi

*2*.

2

.

A

+

e5

t

o

o

o

f

Ma

hi

n

eD

e

%i

g

n

8

42>.

).M&

.

Wa



l

a

lu

&

ee

n

3. *ompo%ite Material% 7 V.

42?. Ragha$an

*. Material )iene An&Metallurgy8J.P Khanna

5. A6)")711.= for engineer%

an& &e%igner% 7Prof. )ham +ioo

leaf springs leaf spring projects

Documents