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 !'