trnil -5MoMegr DrsTRt Bu..roN

ii'

.t,F '@

F5\,tr.r{

fu4:rrD bg MorrrDt d:lgc.siUttb>eend-iqg morr;o-rrt d.logroro

(t) Ft;d uae Ft?(ool eod nnorrrr:t:

ls

Relativa "3lifgoeas aryl dlciETl

Mraa = - \N!n .='- 3ox:q = -eol({u.m 1-17 - t2MFee =+ \N Lq

= + 9x* = {- 4 oKN.rD '

ls. -l

MFAa = -t{qb' = 4olt^olt}a---qe,glI K.u'rr)Lo b4

MFcts = +ltal a'b- = 1.4oX2avg =+lq.ek.\'rr)L<L ----E=--

fqctoa I

ar>algsi-t **. cor>xl.:ltousM ott^rod avxl a{Ta\^l tt @

soLu.rroN:

(a)

xo0NT] mrtoBeR QFLA'TTYE

j}"rrFFNEj6Lr).39|.^

Dre't'eIB(,DEI{FA TOP

a

BA"

ilc 31n.,'1n = u2r,

31 +el4 'lor;trltlSl

l,o

BAteo

H/T#J=3\ r\E = tsl.

9-t aga 'tt

iltffi)=z,

{orNf A a t-

C)AA

rs,'5/rr 9/r,f).tr+qo -s8'8 9.e-F.E'M -Qo .i.

Ralonao aatdclc-lt tqo +45 -q.b lq'o-

tni tto-I, M orrrntl c l,q r; -Be'4 o

fularro, B -+A'q - 6e.1

Firrel Morooot o qr'r -q t., oI

MAg =OuBA=+qlt(lt''rr'

' MBo =-41 K nlrr' ' '

MCg:oo)F)a-r1.Iit\ MomoDt d-r-'g3roro :

@ artaf,$is tbo acr:drrrcrrs bearo ldQatAatJ.roal of ltl.oroer:c dlstniburtoo orrl

Ft - oor)stADt

SOLUTTON i

(t) -to FTrj.{ eixd e.r:c'l I'AorOo-oL:

a-a thoucrlct"catr)'wre'

3d(N

in fibbrno

MpeA = -So-b%-'):MFSA = vla*b

Lr-

.= -4Ot>x*-.2D

= ^or(aqxo----e--

=-?8,8kru'm

,=, l4'2kN'fn

MFBc = =-lDtr = -lox(qS) z-ls.3gprD.rrrt.}- 12

MPce = uJ Lq =)P tE =+ la'g3Kr0 m12- lo

L"' 4Mrr>c =.FNfb - BoxlS'l xej- - +lo'D6[<n''m'-F- --'-T--

o4'66f.to ro

6 aiaL"c ibn"tt oo Factryr :

IAEMBC.EREIA.IIVFAIIFFNE53

.roTAl3fJFFNE55

(DtsTPT€}OTION

FACTOE,

aBA

Bc

Ys

Y+

t/s +a/4 =

q7.//2o Ya =4oho q

l/4 -sd-t lib - q

a

c.8

ED

y+

q^"V+='Xa

}hts\b =n146 Tl+nrlcerllbrr/t6

+.,

=9't

C1) Morr)oDt DtSt-ritxrttoD:

5orN1 A a c. gDOMornh@t AB gA Bo oB OD

DlscributtoD Fcortyr 4lq slq 4lt sl,l+to.5Ei

-to.55o

r l*.od oftl $/\orrlcrtsP()(cLge arA Oe\\govon la a-

qB.e +11.2 -13.35 +tB.38 _tn.5-g

-b.|)8

Inlt-r\al- Mornoff 4 -98.8 + tq,9- -la.3s +l3.aB -qo,66

F4ldelaq -q.6r -e'16 6-1'D +,o8

o&TY!, 9va2t *t'3r ,-ns -t.6eBcrlar:oirro -l'21 -l'E.l o.qe o"ro

CcrYTLt cn,ori : -U'Ol o 14.7 -{'T6

- O.2i) f- 1t1 o-33

Co,Yrll ovol -o.li O -22 -o,igPtlonnirn - 0.t0 :.O.t9. o.oT o.o6

o

Coxru orrol -o.0s o,04 -o. o6

Eolaocirn -o.o9- -0.o2 o.eg o.o3

Fir:a-}. Moroont-,s -so.38 15.05 -t5.05 t.r.66 -rY'66

3

,'4oKN

.FKI

11. 6b{- q@ -t>'o5 -Ra r CA)=oL

R@r: qo65KN

RBz= lor( +-.qo'tg,' RBf tq'g5KN

6pan e$

MeD =lr, bbFNro

f .5fo

Morogx,t, @'boctt' oz

o taoCls) - l't'66-Ro&) = o

Ro--5'B+nuRea = Bo $'84

R c, : qg' t6 k t'l

s )MBA = 15' ob*{Dn>

o.5m

at, To Dfa$l

(^use, so.s>i

qt')

PB

SpoD go,

MBc >15 o5 krom

.tqKtDt M.crrrot*- .b*t ^ , '::,"=lJoc')

-so'.6 -Ps' Ca):o

P.F = Ao-FBrh = aq't'fKN

-t* *t + .4.ox2' -ZoSq+ l@'

-{sqe = n'66nrm)uaB.

MD, -- O

\r,lr0-!'t

RQz

'fqk(t

tl

n bout B-

I

q$. I Ktl

strrrply

a Par,

.4Dan

gvu'

UqPdtng Mo.-rr:e9u : - " "

f:

AA

BC

aD

r M=W+-+91+9 ='4IK.oto !

rdl* - l n4: = eo<rorr>-B aNob - g,9x \b \pG

-_ e B, l2, kro'rf)-L ----- +

BMS:

I M=

.'M=

Mw<g =q8'13 - r!# ^r.E = n'OqK.9m

d

:;r.ju i] j&;'

#fll.

AUalvsr'e tre AtftroqI)e hoadod a3 tD &g. bgw, i4orlforJodlatriuurrcn Mo-$:e| cira 6**ar'traa uoo*lrg tAor*orrL

Cr) Freod o"dl MomaDta:M f.R A = :_ l^,Lab* ,. oo.-

: --aoxeJ aa. : -38.4k Jrr:Mree = NLlob*F = goxtxz

=+Dr,.6kNmMFac = _weba Ba-

;- = . 5oxttg' = -c.6.6,rr*,,,

MFaE :.yr1aab _ L^-..o.-

SDLUT 16N

MFBD: o -

BtL

MFp6 = o

='6extL =*1,"'33K'rlr?

DI3TI3IBDTToN

atls:0.3q+

= o.{o5

cD Df<9b"ri bflfi,oo krctor:

sYao

a\/w .

t/e

.:r r/3o = O'21o

t) MorDe-nt sDBtribuftoo i

wt@:Tc jrfz[tr) 6FD:

M$g = ag'411 6tOn,

I't\oa"y, (-ta,5De) . MDB= -6.a1nku,rD

,)

EB

BoKN

cPn

Taklrg MorDooL awut APoca l+ Ma a - leil(a2 -vtBt =oREf15 ) + 43.,+lt * 3o \g - 4n' UlqPAt=48'44+t..leR =TotaL tr,c.d -h

=go - 49.6e4eff'=Al 16btsN

IQs P4n go,

brKN

R{

$

5OT N'I A c-

MerDb@l AE 8A 8D Do eB

D lSt r ibudoD F4ctctt o. ao+ o.406 o.1'*loflqga{ Aot:d.l'Aofi-ppts. a a.lo.ocim

-?8,4 + 5.1,b

-to.oql

o

-te,56a

_26,q + ta.3a

-8.gbt

aa.st Lt at ol -o.0| -4:l'16

Flrul, Monrcrnf -As4ll A1.DH ^ta.D6.8 _a5ozl +q.{6+ I

-Rsx5 + t (3)'- HAg +MsA =-.o'

-e*r.s- +9a -43t Atr +4q .5+q

=O

2 Mea = c1't 14

"t-4'etqq l.rl.orl]eDL a'bo'Lt - g,

?c(3)+ Mga-l.rlrs -WQJ =D

e4@> + 95' o Ll - q. lD4 - boQ9 =o

Pa : tl. B'I6liN

?ga=bo -\ 31 I

PBc- ' + 6'6aexN

1'

f.(99 : 12'556(.u02

l,re, '

,ir

MpB--6.arq Krprn

qbar-L A,

e

tsrB

ftrlrtn6

FBDC+)-MBD-Mog =oPDr}L4) - \ 2. 5 5i8 _6. q'lq

=oFeo--+.n***

. F DB :4.Toq kN

Btroptr6 Su?pof1tra4 b@-rCtng Morsrtit,6pan n, = \Na-b, = 8orgx2 =q6KDm''x'F''x'5e€aJD Bc = 51-1! = 6ixlll =_4oKilm

lr\t el2'-T-

6.i.rqK*lt)

.5FO;

c9t'lg6<tt

tt.3'IB gn

.'$'/ln"tgoic wwrtel. .flrrrr,e loodc.d as stwuso fi. ag vp-'.*' aoro,n)L of j{.gg.ibehoD rnb]rcod a.r{Sirrl@t) rrto 6fp9 drd,srp

(t) rlzed oDd MorDoDt-J iMrAA

= Mp.Eo'\=M FBc =MFDa:O

Retrr-thp .*iffi:egl and Morcorre aisriuurtor>

DT'T'EIBUTTC)N FACTER'

r/ser./b

--%

tla - +,,- > /n:91 /s'

=ah

o\do t;uxl.g.

Ye. =

MCD

,(erJ!\

aEtd-7M -BC = QrrJoD

A )bclrc,aMcD=-tokNft>

"o

NBA --qxlo--AERNfir.

1 *r, vatuz' q$u,tp\ r..*o', e-,

\ t,noo =tran a tr-rrzs

t

'kr?s= "7s

,+*1/g=sh

+3Zo=1,2,llg a-t".fr/eo

At/2o

torrt :A a c o

9c CA c.DA6 BF ,DO

o.E't s,4unrrgortlCo o'5 o'5

-(oFEilIs

nrfdPag

- 9.o -qo

5.nt +t9,8.lo to

5;, ertTtr Or@ 5 i,gs

-r.hc s.B5 -: ?, \-'E"tnt+4 -r-h^9-l'+ryE -o.1lt

-o.t(2b:'tl9. o'405 o.egg

st-L,, .5 v'

a.^lnt)CO o 119-

D.qg2 o'asbcnNrq otl@ o,gs,6

0.lol -o.ro2 -o. l,{q^ ^n .t Y1r1O

-o.lot

-o.lol -oo5I--9:L:..===-

^ ^v'.r\ln ?\ \la)l 0.o54(r lyt ea, v .

BalaD& 10@ o'o5'o' o.o2€ o.oql

'196a1 \(unoct -tf.4o6 -'lc2b+

s1{)05 Fc}f@r

$Rtflo=o\1. tl - rr)Ag + ct)fl L1--'-_l-

: \O'3t15'4r-r-5

= 5.84kH

H$*-t c-ot MOc---l--_,t.66+,o.1

5-- ts.o,LEN

Hs =5-8ltl'53 2 6'nt K{'l

qctuol SD*d fttoo- =@K\l

L.

Potto = FP ="t' 3B kN*- - T-11 [o

D

o

0

5i6'53a_

ll t -Y eat--?t-rt f*r"g +^"l"yu -f

UNIT.VMOMENT DISTRIBUTION METHOD

1. What is the difference between absolute and relative stiffness?Absolute stiftress is represented in terms of E, I and I such as 4EI / /.Reldive stiffiress is represented in terms of I and I omitting the constant E. Relativestiftess is tre ratio of stiffiress to two or more members at a joint.

2. Defrc: Continuous beam.A Continuous beam is one, which is supported on lnore than two supports. For usualtm$

9n the beam hogging ( - ive ) moments causing conve*ity upwards at iire supports andseirg ( + ve ) moments causing concavity upwards occui at mid span. -

3. *E ae tb advzntages of Continuous bearn over simply supporled beam?l- Ihe mximum bending moment in case of coniinuous beam is much less than in case- ' dilfy ryrU hezrr of same span carrying same loads.2 hre of-tinuous beam, the average bending moment is lesser and hence lighter

'n-Ed#in'tlx d,- a be rred to resist the beiding moment.

4. In a member A[ ifrr- 6'-f 0 K}{m is applied at A, what is the moment carried over to B?CUY otu nrnl'* :Etrof lb Alied m*e"t.'.Cary over mGb B : -lO5 : _5 KNm

5' What are the momenb induocd h e bca ne.nrs, fu one end is given a unit rotation, the otherend being fixed. What is tte mrneiftqd calkd?

Whm0: l,B Mae =4EI

IMsa=?El

IMAs is the stiftiess of AB at B.

6.r\ beanr is tixed at A and sinriri;. i,i:)Jorjj ai B end C. AB: BC : l'. ljlexural rigidities of AB andBC are 2EI and EI respectively. Find the distribution factors atjoint B if no morlent is to betransferred to support C

Joint B: Relative stiffness: L- : 2[ for BA.lt

l x lp =-31 1o. r"4t4t

Distribution factors:DF for BA: Koe _ :

Ks.1 * Kgc

DF for BC: Kec =Kgc * Keo

= 8/l :0.727

= 3/tt = o.2jj

Ksa:2

Ksc:%:0.75

22 + 0.75

0.is2 + 0.75

l2-

7. Defrne: Moment distribution method.( Hardy Cross mrthod).It is widely used for the analysis of indeterminate structures. In this method, all lhe

members of the structure are first assumed to be fixed in position and fixed end moments due to

external loads are obtained.

8. Define: Stiffness factor.It is the moment required to rotate the end while acting on it through a unit rotation,

without translation of the far end being(i) Simply supported is given by k : 3 EI / L(ii) Fixed is given bY k = 4 EI / L

where, E = Young's modulus of the beam material.

I : Moment of inertia of the beam

L = Beam's span length.

9. Define: Distribution factor.when several members meet at a joint and a moment is applied at the joint to produce

rotation without translation of the members]the moment is distributed among all the members

meeting at that joint proportionate to their stiftress.

Distribution factor = Relative stiftiess / sum of relative stiffness at the joint

If there is 3 members, Distribution factors : kr h k3

of the applied moment.Car" o'. er iactor ( C.O) :

end A, e motrtjili equal ro ilalic.o:0.5

k1 +k2+k3 kr +k2+k3 kr +kl+k3

10. Define: Carry over moment and Carry over factor'

carry over moment: it is aerrneo as the moment induced at the fxed end of the beam by the

actionofamomentappliedattheotherend,whichishinged.Carryovermomentisthesamenatue

,A. rnoinent applied at the hings'J crtd B " carries ovei'.to the hxed

iiLa AiiiJ.il:i oil:'.npi:..::i i'.j 'Lll:rl: ' 'l 'l tire sli'rc r 'i-riit'';r:l s:n-;:'

1l. Defne Flexurd Rigidity of Beams.

The product or youogi, modulus (E) and moment of inertia (D is called Flexural Rigdity

@t) of Beams. The unit is Nmm'.

12. Define: Constant strength beam.

If the flexural Rirrai v Grl is constant over the uniform section, it is called constant

stength beam.

13. What is the sum of distribution factors at ajoint?

Sum of distribtrtion factors at ajoint = l'

14' Define'the term 'sway" lrame due to the unslmmetry in

dimensions, loads, moments of inerti4 end conditions' etc'

L)--