!lb r'qr')cs -sA-T

rlr,,i+ -J

1L,tDfiru:u*1L 1he WOI;r'm ^L yq e -1he.

hrn "*ta-on,in piVuxe. up ori| lmA me+5 Wln)

Flor'. St:BgECrt,D't'O r)N11' LOAc,

@2to --

alVL

t-

tit^,

.

I

t.

r[' * B"rEa"k-

LMA= o , VTNVS

Raxb =45xgx+RZ =z+otil

o

Lv = oi Wet

Kn = +5\e - 24o = l2o tJN

**t Io '8e*en .','z

"rl;vn a.h' e tFiEtbI

25a

6rt,

rsolfno^l:

NhBn

ra"Kin'n

twrvun\

(rtrtioutg

,*;i "lDca J8

d9aa-

,i)

T\8,='2* ='''*KA = a,?;33 Kr{ +

6omtu\,

porhora

rrnmli,t a* Va{rlive avwl -}*mi"t

4^zr-$ tr9ffvt"w, e'tfrel'?tt*tt , rtDmlrt

"1.,

hDlgEl 'ff a 4a'bl-e-

F)K'xoNF".F

o-z.L

-+x+5x

-*

To

zaq.- z.z,*lC-a.3zzx))7 7 .

E,-o ' :)?-')'\- )\4'\

+ |

c'"ztz-21 c*">ax

!,oi+2.t.*7an , 7 a-f

- I zz'sx-r[x'Efo to J

f-ry'+ dl'+_t-_ l7:."t1-L B 1 I eaot + I-)6 -L )DrDl*?rt-u z.tEx6V I zz,vxz+ll3'\ + +" tL_l

6

r cr

Jo

L

fI:Jo

)*ETD

t

Efb

A.=

=

=

= -.85EIa

= lZf tUr-proaxc\;Ero

. 4-= 136 , unungrAETo

)

!,z'ffis"* +t,z a$ocfh

",,,a :r-+Arr" ot 4hL k*efite cat*lar@" k; -d,,tuyt 5 piTne-, v9z u.fiL "ILAJJ-.&'wetn E=exb5Nl,"*

"*a T = rlxt* nm*.

w

?$tsr't.

ptti^ *"-

BA

ts

t.a,

3,

d,oonW'^

l.rn^i,U

M

rnr

ftr,r

L,

c

O'-z

-ro-{---:x

-laa

. 6-2_

- lzatz+*) f%{_ ct.t2)

-l

.r%_==__l n .Jg To.*.-_-4---*

ttsN

E;elrn tfi.m ur,i+\,et&o! (o"Aat" .

lBxmWarn uj+tt ui+ m.,*,otnb ab c

Ue-rait rrnmrnt exPw'v"&t

M *e", Wb, JrcdAA

-,"W "tik ver'dco\ J,aA^e"

..

,, [* ufir mCIrmu"t a't -W varftuag

neu"w ld'nn i' -rat.,lo

?oKlor,.t

Mw dxEA

(-%et)Ux) dx + tEro )

\r\* -..' -4'-""'

Lf c"-") -^{lc--D"r" .

Ecn-L-.(J_b

(4oq++o) C)l-+L)Ax.

2EIc

LA=

Jo2

=fl

I ry *'f+ j- \ry'*l€Er.."l'rrrt ?'L ro oL

EZZ|Z * zryg3ZZ

frc EAo

= sl1E3o

.;v*o7",

L2Oc = [ lt1r3 = i+Ea r,

= f* *'1'F;)-

2

+JD

D

2-- | ^*'- doJo ETo

za- '1

l:g4 + eox Ie J.

.'. A

Cc-bx)'Axr_To

2-

+ ( (g+<e2taxIJ Ezaeo

+ ,lEoz?To.

-4aEAo

6" = lzoeTo

@

/,,F

t:

iL

,2. Ary:c+t"" ^:

ri,W r-d,,"h rhr.6.@W;,dgau Assrr+,re W"M -frtax"sral n;n;X&:| 50 llt t

-. I o t+rr lrr, @rlt"

{''=".

3

a-o,s

tk+'

o-l,2,

- L,O

'(..)

*1e(

[.5 rr.

!

ff6 = 23'15tio{

;sourflo^l: FYDrn fu lnaA /1frPj^z = 50X l'.5 + lo x I',5 x3'9'g

Bw = 4l'25 HN

R, A =

ED + 1,5 x(-o -41'25 = z+15l'jN'

i/rr* ?stsN '

Wam u;+A u;+ vept{i cd -looe

ruxitmanrurE

rcRrtoil

Otlff*

,L;n;k

M

fn

Fbx*.r*

"4a;\

Q.

+v2s** 9(g:+t)

veet{i 6tr Jlnod ab cs pcd-live cn{ J^ffi\$"Ut"u"i*6'Jo.btc

.-ri P're1:'uccct

kc

4

- (r+,x)**q

Gn

g.,"qsd5 nno rns,f "" fodlrLc rcqo#'ve ' )W

A

o-1.5-

zbn5*

-{x

-9

o-l.

23'15t-7+-t,6

*'! co+,'r;

ET

A. )i ,,yl^ tp ax* | i*a'rscx+'s;-mrlFt4J-ET'e-t"ELo'2r

e,5+

\'D+,'r,d-6c2*'fl' f ' -4a"*!# dx.

DDr,E | ,, .---

= { 7"V1r^i1 Ax-Ll l:u,#-3'rrr*53'q3eJ L-T 6)""-{)€

* j'f ^^

ri ;=i'-r {

n4"= | "sT* 1'"" + !pf+ rru ̂ f -t t' o'*{"

+[-rf + ,r.orr^t *z,qn€+*4o''o lyt"-L; -+rb'T r '"'a * c2"'11 ta; -r-) o ' F ),

-- -22,885

.'. A.-= 22'886 ,u4"^yt,d.eT

@

'4' De*rM;nL tln-o vet*i^a!- arA iruof )hL tu, a,,A * +ra @'1k

. )A-; zonir^I ArSlrrtt ".xh.ar:n .t*, F;ff; AsSL/ye-

y*u iwr.63 +,4,@u4^&b @,rya

totst

orB"?'

l-urvrr,E

l,-1

mt

n2

P{o'r:rr.o,,o,[,

E

g- r'5

G

,x

O

rJ

.D

o *1,5

*2a'x

.-Ct,u)q)

a

\:rl

E:E.

ca-z

E5

r'l-t_ -t-

Exrye"rfu,{b .ft",r-r"Yt * * y*t-P*, !:,**rri-:** *or-,;r* \rwLb)^l." -eecl

^* ^W #, ai"d

B

-3a *Lox

*5

- ("c+L)

L]:

ruto- vwbld J'x'lar.- 'Ln,% +a ,fuAp-

-BA

T l.5rn C1-. t.5rn *j2r-o

a) hl$a. "nU ,';+uoc'h'cdiba/af e

b) F ro$^a- toi+4u*i+ ye<izon+"l"Nnad of E

Itt

u = J l4rn,cit

i,5 .z 2-- o+

[ :ox(r,s #)*'t

1Jo**{ ceo.

l.Eonb,. o

-f n -= I t*+fficle+[9oc]2.*( (qo+aox))))o-oa

= I 4* *7':'+ [<o

a] : o

Lo'" *

L*o_)-- &.zF+l@ +24D

-- +1$'26-

-- +i&tser

= [urn,cldJ

Z9-

- o rc * | zox clx* [ 6eo+tox ) Cx*z)dxJ,J2D

= [r s#l "+ [ ( r,ox\ sox #6 o) "lq .

L- ..r.O I-b

=- 6a + f ry'+ *tnooil'L" c- -{

t+rlld

Aq. ,

'z--r=LMI-),

EAr

Ary

EIAEH

:306'6'l

= g06.6-l

EX

Arn.

f

zlwr,n

Ia) fue"iru un+u uri+ledical

)@A a*A

9rKnoN

llI BAt

o",iA.*

Mt',,etc

M

lnl

m2

flzx-uralPic, ),*ti

ba,- z4o

2o

w

C

o-b+o -i?Dx.

c-r-L-.),

A

++-

I

I

I

I

'it',i. bl,A;rq mDNwrt e*blut*hs *cc u Atur- *a a";'na 'la^'d,

ry\t),u.e,+D ";;* vqh)al "L*S ot A"ard nr' Arc-h t'J/i+vd*;cnt

m".a 0t c ctgts- 4"b,rJ.fud, $r"<U'6rloA; rnmolrJ: cn''f'XA\-b'vWtiv

a,,A on dnweA ilAL iL Ma,h Pcsi+ive')

A

a*2Llna

Lo

b)gyslyp r;gfyiDm-ar babD

Er

EAn

"n,ry'f:--,99f] *wo1*y*-sry

= 2LO

Nar/ E = 2-4.o}tPa = z1+r.Yqf Nlr,*.

A= @xw* nm4 =t*,xo4xtftAm+. '

Lf=rPXto-Ern4

= O,122Ntrrs=1Q2x ro-4*.

tgoec) G7-)d't

.,.Lt )dx

31

IItJO

*3,-* A15 X m ry) '

r A ZLO --1 '" AA= fr;G;,*e- ''-

-'. au = o'122'mfir

E:EAc- = lMm,-*xJ

s

--o *o+ [C ao - l3oe(

JoBf.L

= | (-+o*ttbxtdJD

r a- zt3-- | -nx * I3o*- II 5t.LJO

.'.A- . 99 o _e'- aL- z4oxuixl6DxLo -

.'.Ag = 'Q'75mrn'i(fi

.6. Fiv*+ra,p*icat ery*ry 4 y fu z*.**\A).aaleA as xharrn ",;" dV, -rta c/f qtaa * +t w:W,xi,.arnm afig- .$!lwn aa bnclTo& V = Z.og^lnr7.

j

SO LITflD

P

l20 Kr.I

E

tzakN

E

BfutQ8 drra tD

Murphy-pc

Stamp

r

-:

ltt -6;ivrrt,o,

Ooo, * =Ps>-6o,9'l

P-9h -- 6o"UZ lsN Cr)

ppe '=?pq x* *P",c = 6o#45: loa-t5l'l 6a1nz

K-b* -\rro-tD u* ,la"a akp:fru$F"i"g fu tr'"6' fi".r, ff* qlrtUbitunscayudB.

?e.g =?cp=PaA.=Pur=o .

',on f;ii* o,{.e6 -:1lT Ya cr)

4 c,oe=PrA";=l h.lCc-)

Fus€lrwr, cahilah;Y'\ o'3*- cat*;aA N* 'tu tnAa'

MEMBEK lE^JOrrH AReAIN

ttMM n

?-6BcE,N

!r MMa' "

h- mrcs,^l

l{^lruLAE

Ats

bcCD

9r

B

AD

4ooo

{orc3ooo

4aoa

4coo

fooo

looo

lDeo

tfra

looo

15oo

4515

-+5* t.oF

-6c

-'6oi z

o

o

o

*l

a

4v

o

O

o

i os-oiioIi.1

Ij

! 4st'sT!IIItt.I

:

l!

:i

ItlIil

i{IIIffii

7

tn

+'ruY =1zz'ff,'- A

]:QWI+<;' at D= 2W.A-.,: )-1gx.c*- 2 <_-T

I x13r55Ao:-'cab

.'. A, - v'bL1 rlrtfi'

I

1

i

uodat{2

6

4 +u,,b r'&'.+lzrnilrL -$,a veutqfi aa-}[r-c+rrs^

4^ r.:,n i" frq.-no Qs a:tta* + mpnbel<z ArDE at@ t ar,mr&, grjrt)" -tfa* $ +ha. o4hst hrrnb,gttt;oni.TdW E=ttt.l5s1f6$. U*P

l,rz h"*, ;" u,/,atrrF.

fu* *A rrn a.s ,rfr; b"P-Forcex:

nt , niwv

Pn,{DI8.A

From *ha %;t;frutn * 4^* e,.pa6Vg,g -* (o cr

?.9 xo,6 = ?6p ay

B

6oPrt | '

t 4a*,tYft KN ax ufi+J;,rKt, ryac(jr&gwJ/fu.

?oL = 1515N C'r)

Pco= 4{1N Cc1

=?o*X o, B= J 5 X6,8 = 6o 15 N C c_)

=?c6XO,{, = y'rTlSN C-rJ.

$1t"JUAJ lT /.'^ ^

,/--).

Iu*n6 6.dn1,vvbLLJ,.$ecc6g

fft !ot\w<, rw.t\il641s eart fu uri'flq^,

qyA +k ahe .hfulafuJd J* r"l"ta,.1V&tr , c*tc"&afi;^s ;t'rablz asa caerlizt, euLb VL verrtta-L We+6, *ze.

A -- LPKLAE

MEMEE6 lE^J&TH,N

"MM "

ARen,N

9-MM

?- rfffr=,N

HN

,<-tuBeE

Nfir..t

3e!AE

o

o

I4+*

o

4sB5n&g

135.-16&,

AB

tsc

.DE

EF

MDL

CF

4&ozlooo

40.aa

4@o

4€o0

44oO

4oo

4ooo-r[i

SDoO

hoo

.soo

ryoo

2N

boo

2&A

7*O2nO

oc

-O,5-o.5

-O.E

o

*a'5

A,S'[i

o.sVZ

6'.= /.f$ - 4rg's3o

[= 2rxu =l2rJP'AEE'A'= il22J9 = 2' D'It rnrn' zDo

.. A= a'Olts rnm'

i G)

SA - 1 UNIT -1 (16 marks)

Ueitg thc prlnciple of otri.ual worh, delcrmidc tl:c horizontal disptorrlateat ofruppt t D Slhc fiptne dlr,wt in Ftg, t 2t, Tho uolttet of I an indiatql olonetllc nefun" E = 200 x Iff kl{ I a2 atd. I = 8A0 x lf mt.

ItEI

dr,Sro Lnorttrgl ,

--n

L{,,I!

tFis' I'?4

EH=Ogires ' He= lkN(r-)(Sign for momenta : IaIt clockwis€ +ve ; Rigtrr antiloclwisc +ve)

mr - 1*t

xI,lIl!K- rrI

xt

1.,"

limits O to 2mz, . l.(2 +:1) lioits O to 2m

Roal momcntr, M. Due b lho givcn loading, the support reactione and rsal msmentsrre computrd ar uuder.

no ' l:unr=1x4

'. !H- 0rivesTsking morneut.r about A,

lirnits O to {mlimits O to 6m

. II^ = 60kN (+-)

r

iF

Vox5-6Or3-O. V5-E0r2l5.20tN(t)

f,tt/-09fuev^-20LN( t)Ut=5o xrt[lr- 60 x (2 +rr)-60 xz. - 100+ 50 i rr*[Q xr, o l(X) kN,[lt=0Mro20xrr

Virauat work oquraion :

l.(ail^=l#= lj <rr'r (1or"*' . I;

gr*#|00'd,,..[ g"#&+liseff*e

- f2 (50rrz) &r . f2 (200+ loor2)drz - ^ . fl {0radra-Jo ---ui---Jo EI *"-Jo --Ei-

= ti [" +l .['*o -'*4, | -[#l]

. $ trsrar*ooo*u*1. l?it'1233.s3

-too;toEx s,filo-T - 0.O2056 m= 20.56 mm

Hcrizontal displaccment oIsupport D, (Ar)* = 20.55 mm (-+).

t:\\

lhta lp ,urlrydotvtrtaar wrt, cterormtnettn rwrtawnt &sprwnwtr oiaXX:.,

,f * fmnu cl',wn i" rtr.. t.so. iiii E ;6;1ir irffi'fr' , idQta-")

;tI

llF.4m-+l

-. Vlrtuat rloEclrtr, r'r. nomoyr t&o clt.rrot trod -O apply uDlt hortzoaiol lo&rt at C,T&c *rrpporr roncioor nrd iatqrnol vlnuql-o-"nt" u, o*p-,if,i ;;ilr..

lt(N

J,rkN

)Jll : O givesToking rnonrenls obout C,

Hr = lkN (*-lYAx4+1x5=0

(r), rr)

tr1

o;{t'-

@

lO klUm

F-an--l

,(- - -'

y---lr *r,..,i

r.?5 kN

7

ReaI momeatr Duo to the given external loading, tha support roactions nnd roalnromeDts aro omputed as shown bclow.

fH lr 0 give* H^=30kN(t-)Trtlng momonlq abouL A, nc,.l: IO t.I r.lA-3Or*.5* 0

(5(Jlh){8"c80+?5a155

fi," e 38.?5 lil$B^ = Totel losd- Bo r !Q 1 4- 38.?i r 1.25 kt{It, = 30 x1ltil"= 0lh"-40&r-25)

(Jt varlca from o to ,.5)G, to be suboliluteil from 2.6 to 6 sl)

I

x!x--- x

39 I n"=m.rsu

,,t

T5m

o

x----flr=30lN

A4 m-,_-->.

Bre 1'25 kN

{V*= -5V"r=-8{*-1.25 ic. Y**I.lIftN(JIV = 0 Ervc-r

r,l , = l.a, (r, varies from 0 to 2,5m),,r, = 1$3 (*{ varics from 2.5 ta 6.Cmlrn, = 1.2$q'r (x, variqs from 0 to {m}

it, = 39.75 xr, - ro-t,.f = BB.?EI, - tu lVlrtucl work oquatloa;

1.(Q)5=J 3.#

0ru varias fron 0 to 4m)

(90*:? - 80rr3 - ?Err) dr,EI

* f (48.44rsr -_q:r*rr).g

ff k'l

i-

- J:t (rrrttgl-rr)ar, -fl ry

7rr 80*,?4r. 3&orI --r-..r- a IJo EI 'Jrr

{6.)- . fi s*fl"r;: l$,&.[!trd;@e

T3rl1I

= #[+]. -trt+[,.*[o'*t-"u+l. $ [r*"t; - $a, - za\ *Its * *. - ff * +.

J

- $ nsc.rs -?oa.trs + roas.as? -ors1 =fi gau,urer

E oE x lffklUrnrI r t[ x IOf mm{ r:4 x ld x l(}ltlci x l{}4mr

; (i*,r-ffiffu=o.roem.(.6slr F t08 rinm.

Ilorizontal displaccmcn*of point C o 108 mm.

Dcurmina tt* octti+*l displc*r,'rrr;t* of ioild C of tha stee, Oz6* thown itflfj I.8. f,i3 crorr *ecfio nutr arc* af edrh mtrfibar h A * 4AA 7alra..t 6nfi, ft x 2 xIffNl,rl,tft'.

fc-.,"-+|<---., -+f- o * +l

Real mouents. Duo to the given exiornal loading, tho support reactions nnd rnglrnoments aro computcd as Bhown bclow.

IH;O givos H^ = S0 kN (r-)Tttlng mom(.nls about A, Rc r 4 : lO x 4 r .lO - 3O r *.f, r 0(.) (r) (+)

4Ere80+?5=155f,'" = 38'?5 lt\Be = Total lord - Bo r tQ 1 4- 38,?S : 1.25 kNlf, = 30 xr,tl= AIbr-30(rr-25)

x---30ld,l

kr varlcf, from o to 2.5)

Gt to bo substiluted frorn 2.5 to 6 m)

Tx

o

I

x!

I n"= sa.rs mr

,"

x----He= 30 kN

6

Rr= 1'25 *N

4V**-5Va=-6/{--1.25 is, Y^*X.lEtrrN{JIV = 0 trivc-rVc= 1'26kN(tt,rl r = I .:; I (r, varic.s from 0 to 2.5m )

,lr,r = l-t':t (i, t'ru'ies frrrm 2.5 to 5.0m)rrr, = 1.2\ lx, vnrics frorn O to 4ml

(g

J.ilIls

"Ex

)1 '

6sc'

etd6

"9

o.3EE

45'.n4i.*ffi

Yirtud lorccr L furovt dl tho(eil{mal}losds ondalglyaunitvcrticat foroonljoint;C of the tucg fuialysD tho hrar usiag tho aol[od ofjointe.

r O3Stll E

rBkt{ 1l

F-s61-+-srn-lk-sm-l

Taks uommtr aboutD,lI^ x I - I r I - 0V^x9*Ix9,V^= IfikN

To= Total lond -Yi = 1- Ui = et3kN.Ioiat A : Initially nsoumc all forrnr tl lc leruilc.

fY= 0giv*r**coe{6'+U8=0(?) (t)

rt pcos{5f =- l/B

t* =-';fo;=-0..r?1LN A

.h^,;* 0;{?t *Ntcomp.l

I3m

I

-,.*-....:

@

*ot - - *pc/cos {6'; - 0.66€/Aos,l5'; -0-${2.

lmih rrccdculatrd uring ttre urcthod ofjoiltr.f5Q

50

6*

l,ol.'oi.so* Sllld,l 50ldl 50161 so

T3m

,lRA

EB -Ogivesf.* * F^. r:or ,15' = 0t-r) (-f)

F^B +{- 70.?1, cq$ {0'i* 0

By sJmnrtrf,

Jolnt Ar

rlolnt E':

Fa cor {5'+ F"* = 0(-r) (*i

f-0.-+f- ro--+f--inj

n^-no=ff eEoLl{

8[ = 0 gives

Fleee {5' + 50 r O

(t) (t)F"u. --SlYcs 45'. - ?0'71tI*P*r'*?0.?l tlt (tqupJ

IN

F* * ?0JIL coa {E+Frs ' 60 kN (futrile)EV* {} givcr

f?icos.15' - Fr2'r S(T) (+ )- Fra '- ?Prcoa '16'' Fra = ?0'?l mr 45o

. Frs * $0 kN(TenailclEH - 0 glves

fioe =0.9{2L!I(ouPJEorl torcar, F. Ihc rssl &rotrin ttro noolerr dos tp tte Eiws rystoro 0f ertasaal

50 *N

,@

III = Q giresl^r, . col 45' + l^" c 0(q) {-*l

{- O.{?t } cos 15. + la"r 0

tlolnt F :

iloint C :

Jolnt D, :

lrr = 0.8it8 LN Osrrflo){lI o 0 giveo

ln cas .t6' r.lrB = O('rl

lr" r O.$38 LIiI {conp)EI/ = 0 giyrec

&r cc {5'-{, r 0(T) ( l)' lp^ cos rl5'.: lr"

0.,6? I coe ,[5. . .trs"' frt = oSsl tN (fonrllrl

dolEt S !

(-rllrc - - &rr ot ,15. r - 0.{ZI : cog CE r - 0.&}ll lN

!V * 0 6veg166 coo 116' + f,o . O(?) (tt

tr, . .x$,-- ffi *. o.czr

*u" - 0.rl?1 t$ (rourp-)

EI * 0 gives*uC - tar + it3ecos,ts' r0(-rl {*-)

lqr r 0,339

(+). lnc*ls.r-f,srcos46.

e0,888- (-Od?l ) ros,tS.I.. " 0,S$6 tN (Iouoiln)f,V rr O givcg

itqg- l - 0(T)(l)

lce = I kN (Fenoile)

Ifl = 0 rivesl.r-&o:o(-r) (e)

t"o-E.r-9.6165*co = 0.666 kN (Tonstls)ItI r 0 giler

Ips +rls 45' + *Dc - g((*) {r-)

LE

6F = BE's DE "JmT = d.Zd8 m

Lll{ r tac),"8SArrange tlre dat* in the tabGJffi forta.

t*FL= 923-682 x (I0{0)zNrnm

(ad,*xffi =ffi#=11.5{rnm.'. ?ertical displ aenrent ofjoint C = lI. G4 rnm (downsard),

tlsing lfu printiplt of uinual worh, dttermtwthe uertical r:nil horizontal de.fi eclian componthts oliot nt9 of rf,etress in Flg. 1.6. g

= ZA0 x ltrtl\r/mt oftdcross.scfloaal drea af cach kr _ 160x lai mz. (""* U*3 "f",9

,50 kN

&l{a lf,lmf,cr k F0.Nl

LtEl

&FLfilln)

I AT - 0.{?l - ?0.?l 1.218 lt1,3ll? rE - 0.s33 - t0.00 !t.(b 49.980

3 ED - 0.9.t? - ?0.? l 4,A3 ?et.08l1 DC 0.666 60.00 3.00 99.000

6 CB 0.866 60.00 to0 99.000

G BA 0.939 S0;00 4.00 49.950

, ['B 03:E 50.00 3.00 {9.060

I BE -AA7l, 0 LAS o

I EC Lqx) 50.00 3.m 150.00

' TFL E 92?-aaz

@

r

I

L

We knowtfiatI.A.X*

rrr

He=1

Vlr{ual foroeg k1 : {for horieontal dlsplaoement at C)Remove the real (extarnal) loail and apply a onit hori?ontsl forre ai C ofthe tn:es.

EII = 0 giyes Hr a fkN (r-)

,'rrl!!- * 611 69.xCCI * r tan 50' * (3 -*l tan rl0'

x - (8 - *) ton {0'/ lun 6O': = (3 -*) x 0J04r a 2.112-0,?€4r

r+0,?0rlr=2,112

x-2.11211.704-. 1.939 m{3 -* ) - 3,0 - 1.239 r l.?61 a

n CCI * 1.239 x tan 50'r 1,4?? nt

AC =J(UBg)i +(La??)2 = 1.928 nn

BC.J(L?6U2 +(LC??)2 = n.298 rnT-nking mornenis about A,Vn x $- 1 r 1,47? * 0

VB=0.rt92kN(?)Ve = 0,49? l$l t J. )!V

'o 0 gives

&^" . cos 40'- 0.492 r 0

rloint A:

(t) (.1)

t.239md<- 1.761m

V'A- 0.587

JolntA: lV = O glves' &^gcotd0'+O.587-O' h/uo-0'687lcos{0'

= - 0.?66 kt{l^c;0.?66 lO{(comp.}XH = 0 givea

[^" . coa 60' + lt^" = 0(-r) ('+)&eg o - tec' cos 500

' = -GO.?SB)cos 60.A,lr= 0.692 (Tensile)

IVc O givee0.766 cos 40'- 1-8"". cos 60" = 0(t). (,t.)(J)

0.687 - 1= t*. coa 50'0.643 nt"o

l's = 0.6{3 kr\ (comp.)The values arc ahown ln cotumn 4 of the tabfc.

' 1r(N

I.f2#"i\

{rfib

V'B = O.{l3t<N

rfolntC:

r.

JolotC:

*ro .0.{9?col {f r 0.{l{3 LN O+mllt)lH li0 givcs

0(x)"

lo.u6{f +*6-1r0(.+) (-+)(e)

O.6I2ca58+k r- 1- 0iorO.68?kNOearitQ

fY- 0 Erver

te' - lcrt cta {0'/coe f0'

i

o.19

ica cot {0' +*ss cor5fl = 0(I) (J)

*' - O'642 x l'192* * 0.?6i ht{

tor 0.?65 kN(comp.)?ho i v*luea aro tabqlstod ai bslsw (ro1. $)

Ylrtuol forco& \ : (fot verfiqrl digplpqtont tt Cl&rmuvc tlrc ex(*rnrl toud anil apply a unit vcrtical forcc at C,

Taking moments about B, Y^ x I -l x 1.?6L = 0

Y^= 1,?6l.lx = 0.S8? kNlP, = 1 -i 0.68? = 0.413 kN

S.tlo, Irlcmbcr (k)r, filv f( trrr)

L(rt)

rrh.L ftf.L

I .il) 0.68? 0.r02 ?c.8 s.0 . tr9,D6! r08.849

2 AC 0.6{2 - 0,160 - 11{.} 1.928 -1.2.2i 169.693

3 CB - 0,?65 - o.s{g -96.45 2,298 r69.556 r{2,616

E r5?.298 r2l. i

L

f,oal Forcer, F : Tho reol forcct in the mcmbera due to the givon altcmal load urocald atcd as bolow.

fhe only givea force la of magnitude 150 hN and applied at C verticalty. Therefore thehcces in the membera will bc 150 tirnca the l, valuea.

F,rs = 0.1192 x 160 = ?3.8 kN Oensile)Frc- 0.?66 x 160 - llltS $'f (Comp.)

Fca = 0.&lS x 160 - SC.a6 H'I loottrr.,theee yalue! aro shomn in cotuen 6 ofthe table.

f irtsdrdiqrdin:lA=tEEorirchf drllcctim of potutC : Ua,ch. Dr. *

-157198r(2tE x t0! x 150 x 1S{} - O.OO52A m - 6.24 mm (-r)

Verticd .rcf,iectioa ol point C I 1(6"\ = "U, ft.421.1E8[2(X] x lOt x 160 r 106)

=O.01,1 m- f{rrun(i }.: Ilorizontal defleqtion of point C = 5,24 mm (-rl

Vetical deJlec-tion of goint C = 14 mrn ( I ).

r $,1