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E )(amp le .1 CL· 50lt.N ~A {.c B *, ..It' bWl ~ 6»1. ,11 ;Y D.e.t,om)ol -the rzacti6Vl of -Jht rol/.er- 8~yt B tff -+hi bitffYl . El L6l1~fetni. d= r- n- C ::: 4-3 -z: ,e where, r ~ ~ac bilJYl.. n :. eJt~d1WvitlfY) 'e.rn. chDose au.rr«T f, i Bj as l'lolQl1tiani . 5l>k.N ?I PYi.ma~ 8'1vw ctwr2 I Nl 0 .. Wlt1Vlrb8Z 9ccTi(5tJ M M, Bc 0$ xsb 0 x. CA '.5: X ~ 12- -50 (x-6)= -50Jl+3O'D ")(

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I· E )(amp le .1 CL·

50lt.N

~A{.c B*,

..It' bWl~

6»1.,11 ;Y

D.e.t,om)ol -the rzacti6Vl of -Jht rol/.er-8~yt B tff -+hi bitffYl . El L6l1~fetni.

d= r- n - C ::: 4-3 -z: ,e

where, r ~ ~ac·bilJYl..n :. eJt~d1WvitlfY) 'e.rn .

chDose au.rr«T f, i· Bj as l'lolQl1tiani .

5l>k.N ?I

PYi.ma~ 8'1vw ctwr2 I Nl 0

..Wlt1Vlrb8Z 9ccTi(5tJ M M,

Bc 0$ x s b 0 x.

CA '.5: X ~ 12- -50 (x-6)= -50Jl+3O'D ")(

Refu +0 V<RrI1pl~ 14. > l' in ~ddf/i1JYl --h> --!he ~fd l6'!d ~

8"YF J f3 -9ettk.9 so fIllll . (;lIVen t:1 ~SOtJO/) k IJ fYl, z , p,-..lIII B/lAD .

(o€8cdJ"'e bt~~I·t.e In eVrtC17l (JY1-to ~~).- D· 6!"' .: - er (f{)() S7/;

SD j)7J1) + S6l)OO R I

V Cu-N

38-1.<. Ii-' -~

, ~ bP?Ill+,UP:Al,t

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I' 67.69

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E~Wlple 2 .•

Ddtvmine -tht aacfitmQ od-th~ 8t.tfp-trvts -fov -th{ heaM ..£1 con ~~t'lt '

J)t1AVV Sfi' s. BMD.

et:: r-rt-C = 4-3 ::.,0cno1:>:!e AJJ tll& red{J1t')z;1tfnt·

rvltw)Yb8'( 8fCTi6N Mo rnlAB O~x~3'6 - 2X2./2 ;: _ x!l. :x,.BD 3,6 ~x~ 5·/ -1 (3.,')(x -I.g) + i2.·71(il-3,') z - 2,2 ( X - 3, 1:,)

-7.2)(. + il fjb + 12·T7x -it~ I- ;;: -1,2')( +- 7.j2-.:.

" z: .1S"1 X -33·D ID-G I:"",'

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.:lOW 5kN!tYtI lE

~4~18

i c t>'11/

I-( 3m IF "">rYl If ,SlY! A' 4flII 7t# "c = ;).00 q-Nfo,<-lAB: (, )(ID -..t m4

18G .::.5)( ID -r fYJ4

I Ct>: 4-.x 10-r 1Y')4 .

De1omit')t -ihl moment at A ttnd 1't1.e ~Uff()rirltict10ns -rv 1n.( bLam .fU>d aJso -ihe. rt*t1fo1}S t:tt B £, c .

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c hoos€ J'UffOyf B 2 C ~ Yl4uncftmt .

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PVlIYltll1j Slvuthlr£@- ~c.lY) tttt ((f1id·

- Ro.1r1ove '~o(l1ndant.

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t<a\lIntltJInr I@- ttrf~ ~Vlt f ~/taJ

- ~oV'R. r~ lo-ztd.

=

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'fJ ~ tvllF 0

2 fI.3(3r€)- 2&J:) ..f 2.r(I,S) .- 3ctJ =0ctJ= 64t;::.N

,12.\5r

+

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-

MtMr!>£f{ <Sf:CiiON M MI Wlz.. -~(,*)l)(:t)(~x) = -o..2o~3x';\ 1X: O~X64- 0 0

CE 4-f: ~ ~ sS -1(S)(4)(~~t)C4)= :16.b67 -10 'l- 0X-4-

E6 S,} ~ x ~7 :26."q-IO'){. -,U)(~_).r):;.136.661 -30x 0 X-er

I3A "1 ~ 'X ~/O 13~.6(61-JOXI (x-7) Z-4

6f)"m'E.I A»:= ;;.00 K 10 ~ X 6 )C I 0 -r z: 11/000

t I60 : .J.O0X ID ~)( s:« to -r:>- 10) 0 00

tlcD = dOO>(lOb X 4XIO-J = g}OOQ

&1 = J MI~dx s: J IO(~-'flcl;( = 0.00075E1 7 12,000

012 z: 8" ~Jft'1:' dx < J;o (,£-1-)(;( -4) ti;>( ~ ~IO 1(,'-1/ x -I- 28dl( ; 0.001U{r12,ODO 12,{515tJ·

8zz = J 1- (~":4-)2.d~ -t-S'o (~-4).2..dx. .: '1XIO-lE- + S.?{XIO-3 z: 6.oo6fr1- 10)000 7 12-,(5{5V

t-leKibllitJ tYlt@1X = [6J1 812. ] ::. r a.ooo7S- o,oof'l7r J/\" 82.f 6'2-2. L0 .ODla?r D·(J()6fS

I,

l

.. + :,::~:;s :~::~ [::j 0 [ :Jo·oDo7S14 -I-o.tJVlf7~K2 = e.ot --0D·D/J/~7.J 1<, -t o.@6/~ ~2- .: O,/J'{4-<B

-0.05""

(

t----J nHk>Jm

~e;g ~~v.

Mt'M6~~ 8fCf/orL Mv

m YYL

DC D5x,~4- Nil· 0 0

Ct::" 4~x~.~ 26.667-/O'Jt.. +-Z3,52(X.-4-) = 13S2?(- 'lI.J-t 0 -I

(8 r,~::;x~ 7 13,rz7( -bTlfJ -}()( z -rs).:= 42Sj -'.4~~ D ~J~

6A 7~K~/O 42.s1"~·Lf-~x + 7.~(x-7) = ,·38;( -12.lr3 -I -/