UNIT-IV

D6ion.f RC.Ele erts iworiaRKs

yow.|.$it y 6tuhn a3 .h.rt otumn(x.y/Ju..2oo7) lS 4s6 clartfies €ctangutarotumns Es shorr.otumn when the Eflo of efre.tve b.gtn 0eff) to the te*t tateGt drmenston ts tss then 12, rne ratio is @[ed stendedes 6tro ol @lumn. rt t E @tumn ts of dtmenston bxD, srendemess 0 about najor axrs -tevD slenderness 6Uo nhout najor ai's rteylD Il any of these two 6tlo ts eqlat to or moe than 12,tt l, @lled a stende.6trnn. rr both stdes6E tsthan 12,.tttsa short cotimn: l.How ao

6

2.wrlt..hort not . on 6r...d cotumn (ir.y/Jun.2ooe) h hll burldhos, tareEt supports lke shefual 6n be p@tded $

loads aE taken by them. su.h

@lumnsaecled hE@d @tumn.

rhat the tateEt

3.D€nn6 snt-5xirr D6,dt,s(NoviD;2biei C.lumn such as the externatcotumn offEmed bu dtnqs orcotuBns crrytno crane load thbush cbels of a @tomn aE nor onty to d,re.r l@d (p),bu! atso the homenis du€ to th€ e(enhJclty ln.pplictlon of the toad. rn the above corumns the eeenrrrcrty is wtrh respect to one axisonly and these otrmns are said to be under unldxlalbendtng. 4.uniaxlal bending :nd bhn.t lrending( .y/rum)

uniaxl3l bEndinq:rn above rhe.6rumna the eccentndtv is wi$ respect to on_. axis onry and the @tumns are said to be under untaxtat bendtns

s,Olffer€ntlat between short

6thn

blaxial bendinq:a corner stumn ofa buildrng is subje.ted to eccehtrtc toad alons b.th thex and yaxtssuch @iuinns a.e said !6 be underbtaxlat

.nd tory .otunr(l{.yrune2oo7)

Shortcolunnr The perhi$tbte t@d for coluhns wrrh heliGtd Etnfomment.ha[ b. 1.o5tim*the permtsstbte toad for stmitar member with tateratdimenston. The ratlo of volume ol heti@t EtnfoEemeniofthe wtume of the core shal nor b€ tes than

0,16(49/.(

.r

)

(ck/ry)

msibtesxesi

in a Ernrorced o.rcrete @tumn

orpan

::",':,i:fl li"";iiTSnTJ::fl '#t""Tl,T"i::il:::,,",::,,T"":;,i*l:"""1,-*l s."r'ut I"

[btls< roD -ru-nr d membd @rrvhg

a{aload IrveriGtand havhg an . ,When dceeding tnree n6 rhe h4t tateEt d mens,on E @Ied as cotumneffe.trve t6nsrh ,.daseiy rn€ catuhB ba*d on type of to.ding and tranw.E€ reintor .em. ? @umn cn be ddjfied rnro rh€eryps b:sed on toadtng . wtth axta|loadind ,. @rumn r) rcruonwrtx unr.yrar e(;ntri. r.:dh" rrr) 6rufi n wtth btarrat e@nHc t@dtno rhe6rmm a@rdrns ro r.lsv;ce *,".*.""r."

_,"r""..

ii)sptEtorhelet a.wh.t l. utatty toad.d @tlmtr? (or) wr[..tort rt . or .d.r,lo.d.d 6tunr. An axt.t toaded erumn rrdremiLs rhe complBtve foae wtlhour an explardes,gn Equrrement to crry taE6t,oaas or e.a mo-..r (or) when the Jrne .ctEn of toad

,. .

pas*

tFrouqh trom cenrE of 96vrty ot catumn

g.sh.t t. e.nrtaly toad.d @trmn? /orwrtt .hort not , columr.

on

e.ntrtca

I

ts

y to.ded

An lo.ded etumn rEsn,re rhe comprestle rorce w,tl an qptEt dBtgn -requ,remeirro crry tateE toads orend moments (o.) when rhe lne ofacl,on 6r toad oas<6atrav tEr renrre of oEvrty or @tumni tr ts . @lled as e.(enrrt@[y toaded

lo.wh.t lr unbraed cotunn? (or) wrtt.shorrnotes o. unbrac.d 6tumn

r
A cotumn ts

subjeded

be under untaxial bending

tosentllc load a ong oneaxis ontysu.h a @tumn issaid to

Tne momen! due to t@d

nandered nlm one direcUon ofcotumn is caled as untaxtat wrire sftort noles otr btaxiat b€rdang A lolumn rs {oiFcred ro (cenrric oad atong oorh x aia.;:::i lurh c EotJmn ts

bending

l2.whatIsbi.xht berdlng ? (or)

sard to be under bjaxtatbendnq {o.) fte homenr due ro todd narle

of

6l!mn

is

alled.s

ls,under whl.h condttion a.otumn tsd.etgned wttn axrat Acoluqn wrtl6xta oad cnd orartatbend,ng [email protected] 6olnd tn srruduee

oecu*

2/

or two malor reasons

btaxiat

'

i)

arallold

may hav€ naturdt

e.entdcltes breuqh salt ryith Ep€rt

ro

lorh rhe

rD@mer @luhns of a botldtng may be subleded to b.nding m@nts In bour the dlre.tlon along wrth aral load 14..t t6 th. @d.l l.@'m.ndrlld tor .tsndm llmttt ,.. otu n.? l)The u@rpdted lenoth b€tv*n tiE end E tr.tnts shal not rced 60 um6 t E least late6l dlnensron ola @lumn, ll) yln any d* one end of. @lumn rs lnEstEtned tt lGupported tengt. shoutd rct deed roo brd wh4 b and d .e wtdh .nd deput or clw *dton m..$Ed tn ,tae

$..r.t tfi. mlnl ur .@ndctty r4rnrmum

WheE,

to s.td.r.d nor @r!mn d..lgn? e@ntndry Gml.) ={ totsoo + d/30) but tes tnrn 20nfr

t!)un$pported tength ln b.ndtnl

drlat El dln6!i.n

3

i i

,tu ttDrr+F,*ed 4ehddl at

ced

oterc b ard
,b_.

&1

.

16,

.b

zoMEi&e{

*,

tlifrn\i!!^

O:zedt

icrhf bntl, . J=.

n

l_ a,t

talp.rqo qirne,lzion &1 ?A9T-B

t. 14

dLo,t qa. .rC,

.

._-

W,,**,""4""XXffi;u

|trffiffiwwm# "",t-ii* 5rJ1Gi;: ;:r .**"sn

ulr\rE/.,I

- \,

96 tn . .

tr'Y.}=* bbokL

u$Q-

!-bL u.rk

--

45oft tu\ x

* u, ,o" 1i*.0.@iaalL "^a *r.Jii

)/

4,"o,y^av1

'r? EIr.rD:-

\,;n ,,,,,*" ai)

t50'

i

+!. 3o

2*

$,L

X,e-r,4

4

1N,.

= ,;l5o

soo -=t

:5.5o-ll5

(i) aoan* eh; . 0.05h

=

ero,so,ria^

o.oS x 4so

sonnnY. "ak . -- @ < D,osh

*

.l

tg,-

&l.a-_

..-*t bqr{a .f e,o.n^6 uAc A,,,

"l' ;;":0,.t

E?=

o*"oro

A+

2,o.sDb+n61

_=L=

=

,

=

2159.n|!Yno_

oi .ra"+trtl _- a.,e ,llozsoo = 6i,vv.'-

bc

e.
=

_

2Jaa

: ttqqEa %lhz

"J*;^"Ia

k"l iL g.;,

P*. r.+u J"q a" 1o.6X,

,r.

Ar:

o 40x

?,o

ytqliqrg

+ a.6+ x r,Eo

I

a,s

li,

:l5qq1D4 r.+&o160 = e!.&o 66+

^t

P,- = ro,,c,65414,rg HEsul"r

tk

---

ultiw+Iz /.od,

qg1 1N*
PrL-. ,',ol!jo.L6+7,N.

o )<\. T0 Fr 1i

= o'aoo(han = r,o N ^.tn

l^n/ynr,,l

!

_- z.o N l,n\ahl

--

1rr^J-

+9,,.

q.r."*

4 h!W,",^r4n

hryrr,,tL.

sDLll-rIoN..-

u

+flr ar,r- .4 dbat-bL n!. ,4uo, .s, .o,..ft.L .."_, _..,, -_ 4$x4oo _ne

,^

* u'* '''*oooo-^u)-,^,

+&" "r..&.tar, dh'^!t \1D,",

'

'eW

/abt

-.L

] -+5o

tso

W4$";;ff.htu_L I 50;

*:y o'n u *'i,^tZ**, #=*

-o'ob3----),2^^", 6 '4 4!t

tu.rl&, D

zto, 20 C tSooDn

,+ao

r,r"- *^." -45?oh

! $

s-ri"'hi

-o

'}
.

1 ,51.'u

lsr,6nsc

=

3doXio3

9:L:?!?g+ont12.

6"i- l r{i! o

"iai* ./a

plo"fu t-qt

gbqr*

r.4l +.,n -

:^^ ci) t4,

q*

*" aa "l a o,r*y &b$rlb ahlX

d;dmuttL

2t_

a|t t!5 +L,1.

1 tbzl]rn;.el

Lata

ri ) s",,". .

RESULT

=Voyn =

sa,tn

).

. .;) Atao,

4 """b"_"r,,t *Ari"_1

',rlffffii::,'ldu,,,,.g ,to".* *rjui

6,!d

Lzstz Ytln[\ t

z

zs

u":ffi:#:_*

Fe4,s a&d2

e"h{ ,_j'""V

+n

4

NrDo e,a..(!/.zL

-

u'rrvEM

9nrflt-

kaX.fi Aa.;rI I

LL) = z.tsan hod -thoo t1N

ULL Mz.o aoh! it - onA" Fe +ts .to F,no i

ahrl

tl.* 4*ln*,^ SOLUTIoa,,.-

ffi"*ruruxXX Abf"""fL h"A-

1a,,"*i",X zt-a+*l,

p

ptL

*

q1

o.

'-

: o.
.!cs 4. * 0.6*

__

o. oaAZ

Rc:

o.rrt

+o t to-Xo.

&,.rbyto3

9a A

I

I

o.

ba

a e+a?t s. strrtt *4oonos

tz.lotv: p, box@3 97'tt9oi1.11 *u-'

Fs*

^ 1,{r,a\L A!.t b^ A;AL 4 t4* dfl,o% =b=g+ror-i;

gu

t4B

*

x

o,

6h '?

!.

I -l^notlr4t +^s/rtwrx +254\4^

rqinhvw,** Li) z,o,^,1^

.i,)

L $- g.dL- .t

.

!* L ba' *o .

$! a ,+zs 5oo -a;

<.h)a! . 9,0.n.rt

o.DSb

= o,os,

+rs

. pt, ,wurltt ernri. z- o.os! r. {^,'615 qrua, e,, ,e*r*"

4

\=

AkL&+,

4xx+'>s

\ tsob2s,q.nL Aaaa, fl atul . cz. ,$'!- oy rzhlt "ti " tu*. Crr o zs - Asc),yyryrq B

t445t

F*

=o

to3 -

I

46,1"* fiL.ro,L+l3asL :r4ooxos

h scl +, I

E,

os

Asc .-

A4

ooxt oa

zao.o5n6c:gS5xloa Aec

t ba'6 4

= 16g5.4^n*rz Ls,n,rn Jid/yrula^ @qzsd;1;t

ti') r+t i,a.,whJ.

.1l*u,L

s

4nm

4 1"ry;ua";S- Lu =,r**"u I L;L

ffi:3 la.hi"t 1.*.*4

t;) Llq,tt 'n

t,r" aa""*^

c,;,i)

a8x d.iarw!,ar1

a,wt,r-.d..

iffi,j,@

-fv.o\\1iL

srn^t,. y lrtt

--- 4'15 uLo

r-,j*"1

- 4,o,to -

= asx.

cD=ooolan -zs+'r.

=n*,*n

-

@ loo,v,rh

t-

' T'l"ie

0ltel oern.-

/z;l-

,rod, = rsoohir. L,l-)

u&

ltao

:

&.so,m-

Ja|(nrir

arnd,

pe+rs

d&/.

9ou.trroN:-

l,t

tfu- .d;w"4r'r, a+ t'," {aL,4, ,/" t

*T y

-t\A^;A;y

"./,

A:,:

.,

.

i'- 44. \ral4n?L:6ai-,,D! +

&tr,l,

=o. 02 At

fu*u 4 db\\rrl- , A" =ni_o.oze7

",,;_h r..d,;..1:3",.",

ffii***#,y w+\,d,,,v^,, Pa

:

o'a(.k Bcio.6?&

I, og

(o,?-tEk tuc i o.6l ds nso

fu",

z:so rro3 l. 05

.".-\

o.4x yo.gan?ro.6+y4ls to,oas?: 2.sLEo>r to3 ' l.ds

15,-4ol n9 :: 2r5€rtlO3

,,os

e?. tsqtor.,+a4n'r2

l:

tsqqoa,?,

=

O = ,+5 t .a,r6an

c,, &ir.r,ctri. e& 4so*,,n qdL

m

t^*y" t,

ffi"ffi 6 -.

rLir

.

e

ri 4 xlad

+l- t^t *}.dt^^qd^

c.a(llr'{ t&r& rz,.

q.d,,,,,,nL

!i) 2o,y\dr

rii)€ * o qo5 3.- * ::i = *oanan

e*i o- 05o

e*.,i,

=zcnnvn

!

o,

:

q,t,.5,yn7yt

..- o

,

ost oso

45O .

+!l

W:t7* : o'rrau .{r{a

M

t"qa 4,,-e-

r.os C6.+fck Ac+ o.Ally tu.).

4 +l_ "A,"^^

+,t",t.^".

A* 4'o*"t p(:

,aa**;

=r.,:

rs9r4a. ra-tsc

t,osao.+xr-6arEqo-r.-

- '" rFq+b'Lrt+tso,J

2,4\o : A,zaa,sor t; = r,os(o.4!t,Asr043.r3_rs.) ' "'"o+ LfiA'r\g Ase: =ael.J,.ayz

;T;.f:;:Y,.',=iza2hah, ' Di,r..rl*

FM

,o I '

*-%"hfu;NT ^,

"t"d

.

r Na '9 ,e"r, "{ & ,-". . = --u-\2x4o) -

-:-- -L o.'aoorh_n

".^,._

^.r .!

r385/h4nh

. -'"h".'r

+ Lzxr)

.

i'rL.ffII;:::!?"* o * s3s6 -B

s Pa*&.rLqr

@ .&

-

io p &;l k^a;" 4""'t'utuL ,/orl*l4 . Tl,{ 6 Uo., (r*"1w, a".l

,:b"l fli.a+

8,b" 4 tl,ta^tv2ft- ai,L "r.d"r"n . Meb

4,,otr rn y ADo4ntrl

ffif;,ffiA".,-!*.,,.,-t.o,",h*r F*b\nJ {e-i,,*

=

ffiffi,il: tif^r1

& ;; ti^,

rsarnr,fl

dk ud!\)u,,\an a.;,,,*.

-o'r3

"<)^^r,L

b, # =''''

Jq( bo

Mr lcr<

[ Do

= o.69s 2Eox /+oo x4@2

o,l l+

, 6,{,.".^j ro J.".,a,, *s &l<

Rsc

=3- x 45orooo

Asc = +i.ooqaq,AL

1;".#.* *1""!-^ t a-i,*4,,,^

ffitpq

9Y "*

nd*.,ry

r.t,n*ttz &," "p ""Lr,,,,* rntutltL .tu^L e{riorlr-.|

ll"d

fo{t 1jd Mel'1lrd

e!) Hdrp

urd,tD2

w Z.ffy

goLU.lto^J.-

"^rr" "y

6Lt=

,tid*"rk, h,,L ,* ,-J^n

qo +tz.s =

sL-s'n+n

d' ^ or.s a 4Bo

{* 4 =o.," 4;1L AL u^')o-) ratrav.ru

..J1"

*a

n;aa.,"^_,t

lct or =o.31

.

t4'.

i*l D:

ru$Ut a J""r, _e_

n

,^^+",f ,& &,n

,

P:o'oqv2o P :r'6 7.

i

4".

=Ii " n, asno 4 : AA6-eftdz

-fr!4.\r;Jo 6!qeA

4 ,t-.-

.d.*nnj^

L2q4]5.,,nt)

Mc l. as

a'*'"j a j

W*W

,1"^rrt , -_

q

o.oss.

r,,;;t*,,,

fuc =2ro zltn., -frh64J^dr 6 bo* .l ur** ,4
,.,1

?

,,

;;f

"r=,o

tr!#il:'---* ^;W,^ :4r,o_2L40-8)

&

+soo = rr tt 3a6 !

:t.3Ej_

'

=t

H- l

. \r61!i4a.4

:0'36 cr.ss? -o

+

)"Lst Y+ x

-4(5 = c'oo6a

.,., _, =

=s6"p

7u 34t;.lr

.

o.or&

aL

at:v*it ,*,aut . a,ot Ah -: -< D.,1A I rb. ,.l Ics

_

0'or nu

-'

La; !i;

s o.006r_ P_
;;;a2

:

Ffu 4..

.

€0.6

rtu dlg *,r.,a

.Co.htn_

,",:" r-- -

#*_!tr;tr@fi;ou*^ ffin4fi;;1-.*.,*-Frbtu4le4 o".r;;" A.tv*.t .r""-.^t n* =

..*I

I

@

srlultoN:,,otwwa q hv,E

H^I

o - -aE = o., 4,,,n^

l,

"t o

dqg

".ro


or

rn

rt:t

4

,

p

,qsF

"**;x u "t""*

,b fi. obr,r

P

,oo --_.t-4o3.+nrf

: n !9al{L r+ bo}G 4,r,,*_

dl_n

*o ukn^.,

l.n oo

I'o€i '

M|r

4zxrl!

:

o.o55

l,05 = a.os:,

.

,b &"

"g4ur- Je-e,.

,(h

4""

=l:1, o*+"o. roo

t1"

Ea. - 7Le.b.L.6h, :

.

p,6ur:tq e

b4

.

ol zonnq Jid,nul>, L2+rz.n *,

D6lon of R.C.Elefr€nts

twoitaRl(s ?' l.How do Yow .la$lfcy @ludn as shora .olrmn(Uav/'ln€zooD z.wlt 3hon notE otr b6edoludn ( nvlrun.2oog) ll 3.Deflr. qnl-5xlat b.ndlng( d/D@2o09) ?| 4.Differ.ntlat tEtwocn gnl.nal b.ndlry atd bl.xl.l l,'ndi8(MavlJqn') f' s.Drll.r.rd.t betw..n.ho.t @lrmtr and lons @lumn(M.vl1tn12oo7) ?t

6.wh.t i'.olumn? fr-r\E{r.rr f! 7,.la..llY th. @tumr3 based on tvp. or bidlng .nd tr:ndeB t'lnlo'en'l|t'l a.wh.t l. .xlrllY lcd.d 6lumn? (o.) w.it .hon nd€ or r:l.llv totd'd 6lunn' P ! g.wh.t [email protected] lo.d.d olim? ,'or srlt€ shon not" cn 4"ntrLtllv lo'd6d

to.wh.t ls !nbr..ed @l!mn? (or) wrlt€ shon hot u on untra.cd 6l!mn ?2 1l.what i. unlaxlal b.n.Ihg? (G) wrn .h6rt hot6 on rnlail.l b.trding wrtt.3hon not€. on bl.n.l b'hdlng l3.underwhich Gondltlor a 6lomr i. deslgn€d wlth tal lo'd ttrd blaxitl bending? h 14.5t.te thc .od.l r..omfrchdstion ror .l.nderne$ liriB lor GoluBns? P3 15.st.te th€ minifrum eccenkl.itv to .orcld€red ror .oludn d'sign? tJ

12.what

l. blsxlal

bGnding ? (or)

.@ !t'N,,''4.

1.

6lunn 4s0hmx450hn l elnlorced wlth 8 b.u 6f 20nm dianeter. The efieclrveleru ofthe col!6n is 2.75m\lind th. ultimate load for tho @lumn. use M20 A short R.cc

ut\x"r }..r - ?4

.on.r.r.andF.2to{..1.

). 3.

. .

relnfo@d Loncrete column h 450mmx4mmm and has tocr'ry a fadored loadof 18001(N. The unsqported lensth of th€ mlumn is 2h. Find the area of reinfo@ment requlred. Use M2o @ncrete and ter5o steel l$ lN.6 .r,t - PL A relnfored concr*e column ol2.75m efiective length cardes an lal load oa 160oxN.

A

Desrm the cotu

m

n usl na M2O @ncrete an d Fe41s

steel Nolk-

-B1+i

4. Dengn a dEul.r6lum; to.arry an aiialload of lsool(N. fte column has dn eff€
berow Na4r.

siz€ of the @lumn =

condde

mix

2e.t Fa

'lOOhmXrO06r

= Mzo

charactednrc nrenclh of reinforcenent = 415N/mm^2 FactoEdload = 2000m Factored momem = [oxNM Arangem€nt of relnforcement = on two sides

6,

Findthe reinforcement requiredfora clrcularcon.rete@lum. tothefollostna

&{ q 1,"1 },

paltr(ura,s Didmele' olrh.@lumn - 450itr

condetemlr ReinforFment tactored load

=

M20

-Fe41s = 1500KN

Fa.toieddoment =1100M 7, Findthereidfor.ementrequledforaci.cular.olumntothefollowincpariicula6 DEmete, o(lhe.olumn

Gradeofon.rete

Gradetosteel Iddoredload Pu

.45omm =M20 = Fe415

l200rN

Factor€dmomentMu =100KNM

lccl\1'1 t !'