DESIGN OF REACTANGULAR OVER HEAD WA WATER TANK TANK Name of work :1 Tank size
pkn L=
6.00
x
2 !
Heig Height ht of towe towerr fro from m GL GL = "at# "at#ra rate te$ $ soi% soi% #nit #nit wt
6.00
&
' in$ press#re
=
m kNm! "#$m2
*
"ize of )o%#mns
= 0 0 !0
+
Permissible stress:-
7
,o , onrete
/ 4
"tee%
17.00 1.00 x
B=
0.30 m
4.00
x
H=
3.00
m
Foundation from G.L. Nm!
1.00
m
4.00
No
!00
m
Nom(er of )o%#ms Height of Braces
20
σ)) σ)()
5
Nmm2
m
13.33
7
2
.
0.66
0.03
f
415
σs)
10
Nomina% ,o5er
10 'a%% 'a%% Thi) Thi)kn knes ess s 11 Rein!r"ement #A$ F!r W%t W%ter er T%n& T%n& L!n' (%ll 6n si$e near )orner )orner Horizon Horizon in si$e mi$$%e horizonta% 9#t si$e mi$$%e horizonta% S)!rt (%ll 6n si$e near )orner )orner Horizon Horizon 9#t si$e mi$$%e horizonta% istri(#tion Sl%b "hort span Long span #* $ F! F!rr Rin' Rin' *e%m *e%m Bottom main 1st tier Bottom main 2n$ tier Top main $istri(#tion 2 %$ge strirr#ps #C$$ F! #C F!rr "!l+mn "!l+mns s ain 5erti)a% Letera% $istri(#tion #D $ F!r *r%"es ain ain istri(#tion #E$ F!r *!t !ttt!m *e% *e%m ain istri(#tion #F$$ F! #F F!rr R% R%tt !+ !+n, n,%t %ti! i!n n ain istri(#tion
)on)rete #nit wt Nmm
Nmm2
30
mm
220
mm
2&
kNm!
σs)
150
Nmm2
'ater #nit wt
.!0
kNm!
300
mm
,o%#mns3
Bottom "%a( thi)kness
72000
24000
20
mm Φ (ars
150
20 20
mm Φ (ars mm Φ (ars
150 300
mm )) 100 m height a(o5e the (ase8 near )orners mm )) #pto top mm )) #pto top
20 20 10
mm Φ (ars mm Φ (ars mm Φ (ars
150 300 230
mm )) mm ))8 mm ))
mm Φ (ars mm Φ (ars
mm )) mm ))8
mm Φ (ars mm Φ (ars mm Φ (ars mm Φ (ars mm Φ (ars
Nos Nos Nos mm )) mm ))
mm Φ (ars
mm ))
mm Φ (ars mm Φ (ars
mm )) )) mm ))
#pto top #pto top 5erti)a%
Both oth top top an$ (otto ottom m
wat wate e
0!0
12 *%se
!
mm φ (ars
%&'F(
mm )) in (oth $ire)tion
, 20
mm φ
20 mm φ
1*0
mm ))
1*0 mm ))
&00
220 20 mm φ
!00
mm ))
mm 20 mm φ
;
20 mm φ
20 mm φ
1*0 mm ))
20 mm φ
!00 mm ))
20 mm φ
!00 mm )
10 mm φ
2!0 mm )) (oth si$e
10 mm φ
20 mm φ
10 mm φ
mm ) $
1*0 mm))
!00 mm))
1*0 mm))
20 mm φ
mm))
20 mm φ
1*0
10 mm φ
!00 mm))
!00 mm))
2!0 2!0 mm) mm)) ) $3
B Bars)3 !00 "e)tion p%an at $epth of H& or 1 mt
"e)tion on ,
+00
220 mm
Bara3
20 20
mm φ
!00 mm ))
20 mm φ
+00 mm ))
10 mm φ
2!0 mm ))
Bar(3
20 20
mm φ
!00 mm ))
10 mm φ
2!0 mm ))
Bar)3
20 20
mm φ
!00 mm ))
20 mm φ
!00 mm )) Bar$3
20 20
mm φ
!00 mm ))
Bare3
10 10
mm φ
2!0 mm mm ))
!00
/ mm φ
mm )) (oth wa
!00
Ba r > "e)tion on ;B
pk?nan$wana@ahoo)oin
6tr
Nm!
tank3
m
)'*+G# ,F &'-/-#GL-& ,'& H'-) -/'& /-# 1 2 3 4 5 6
#ame of or" "n /an" si8e Height of toer from G.L. "at#rete$ soi% #nit wt 'in$ press#re "ize of )o%#mns Permissible stress:- oncrete 9 cc cDc *tee< =H>*)?
6.00 x 4.00 6.00 m 1700 kNm! 100 0!0 x 0!0
Nmm2
7
f@ sc
415 10 !0
=
" =
150
= 4/0 Nmm! 4/00 : wt of )on)rete = 2&000 Nmm2
20
10
m = 13.3 σst = Nmm2
7 Nmm2
σst
Nmm2
>or T
unit t. of ater
,o)rete =
=
; : 0++4 A : 040! sc : 1*0 Nmm2
Nmm2 Nmm2 ,o%#mns3 mm
1 Desi'n C!nst%nts:- >or HA" Bars
σ)()
72000
nit t of cocnrete : Nm! m : 1!!!
20 5
#omina< coer
σst
x 3.00 m 7200 )#m Foundation from G.L. 100 m ! 17000 Nm No#m(er of )o%#mns = &00 height of (ra)es = !00 m
=
230 Nmm2
0!/&
k =
0!24
k =
02/4
C =
0/72
=
0/40
=
040&
& =
1171
C =
102+
C =
041!
2 Desi'n ! erti"%l (%ll =-? Determin%ti!n ! *./. !r )!ri0!nt%l ben,in' :-- +00 &00 = 1*0 D 2 LB = Hen)e Both %ong an$ short wa%%s wi%% (en$ horizonta%% for #pper portion8 #pto poin 8 where horizonta% press#re is p=wH-h3
h : 1.00 m ∴ Here h = H& or 1 m whi)h e5er is greater Th#s top 200 m height of wa%%s wi%% (e (en$ horizonta%% whi%e the (ottom 100 m wi%% (e 5erti)a% )anti%e5er The (en$ing moments for horizonta% (en$ing ma (e $etermine$ ( moment $istri(#tion ( )onsi$ering tank as )ontin#os frame of #nit height at %e5e% of 1600 4/00 !00 100 3= 'ater press#re p at point is gi5en ( =p= w H - h 3 = The >ixe$ en$ moments for %ong wa%%
=
EL2
=
E
x
+00
2
F=
!00 E N-m 12 12 EB2 E x &00 2F= >ixe$ en$ moments for short wa%% = = 1!! E N-m 12 12 Cefer fig 1 ,onsi$er #arter frame FAE with oint ; rigi$ Taking )%o)k wise moment as positi5e an$ anti)%o wise moment as negati5e8 the fixe$ en$ moment ;> for %ong wa%% wi%% (e < !00 E whi%e the fixe$ en$ moments M AF for short wa%% wi%% (e
1!! E ,onsi$reing ;rea A an$ moment of inertia l f (oth the wa%%s to (e the same8 the stiffness of wa%%s wi%% (e in5erse% proportiona% to these %ength Th#s we ha5e fo%%owing ta(%e Ce%ati5e stiffness "#m istri(#tion fa)tor em(er "tiffness 2 1 1 AE x +00 = 2 = 0& * ! ! * ! 1 1 x +00 = ! = 0+ AF * 2 2 The moment $istri(#tion is )arrie$ o#t in the fo%%owing ta(%e ; Joint AE Member 0& Distribution facvtor
AF 0+
-
1
Balancing moments
-
0++7
p
-
Final moments
<
2!!
p
-
p
2!! p
2!! x 14+00 = &*7!! N-mm This s#pport moment wi%% )a#se tension at the water for)e
Hen)e moment at s#pports8 f=
p L2 x +00 2 f = &*7!! / / This (en$ing moment )a#se tension at o#ter fa)e p B2 x &00 2 B at the )enter short span = f = &*7!! / / B at the )enter %ong span =
This wi%% )a#se tension at the water fa)e =B? Desi'n ! se"ti!n :-
&2&+7
=
-+*!!
=
42467
,onsi$ring (en$ing effe)t a%one8
Ce#ire$ $epth Ero5i$e tota% $epth T=
ax $esign B
∴
=
=
140
<
&2&+7 x 1171 x !0 =
1000 = 1000 220 mm
140
mm
10 mm
so that a5ai%a(%e $ =
=? Determin%ti!n 1+ll :- ire)t tension on Long wa%% = E L = E x B2 =
14+00
x
&00
2
=
3200
ire)t tension on short wa%% = E L = E x B2 =
14+00
x
+00
2
=
5!!00
=)? C%ntileer /!ment :-
,anti%e5er moment at( the (ase8 per #nit %ength
h2 4/00 x &00 x 100 2 = 6533 N-m + + This wi%% )a#se tension at water fa)e ='? Rein!r"ement %t "!rners ! l!n' (%lls.:- The #pper portion of %ong wa%%s is s#(e)te$ to (oth (en$i horizonta% $ire)tion as we%% as p#%% The reinfor)ement for (oth wi%% (e in horizonta% $ire)tion Hen)e reinfor)ement has to (e pro5i$e$ for a net moment > - Ex 38 where f is the moment at en$s )a#sin wH x
=
tension on water fa)e3 "imi%ar% 5erti)a% se)tion of #nit height 1 m3 of %ong wa%%8 at its en$8 at the %e5e% 100 m a(o5e the (ase 8 where reinfor)ement is pro5i$e$ at the water fa)e T 220 x= $= 140 = /0 mm 2 2 f - E% x &*7!! x 1000 3 x /0 ;st for B = = = 171& mm2 st$ 1*0 x 0/72 x 140 σ ;st for p#%%
=
Tota% ;st
=
#sing 20
mm (ars
EL
=
σs
171& < ;
!4200 1*0 2+1
= =
!1&x$ia 2 & x100 x !1&
=
"pa)ing of Bars = 1000 mm Φ (ar8 @ 20 Hen)e Ero5i$e$
150
mm2
2+1
175
mm2 =
147* =
per meter height
!1& x 20 & x 1*4 sa
x 20 = 314 100 = 1*0 mm
mm )) The a(o5e reinfor)ement is to (e pro5i$e
inner fa)e8 near the )orners8 an$ at a height 1.00 m a(o5e the (ase >or other height the a(o5e spa ma (e 5arie$8 sin)e (en$ing moment wi%% re$#)e =F? Rein!"ement %t t)e mi,,le ! l!n' (%ll. :- Tension o))#rs at o#ter fa)e Howe5er8 sin)e $istan)e of )orner of stee% fro water fa)e wi%% (e %ess than 225 mm8 permissi(%e stress wi%% (e 150 Nmm2 on% esign )onsta wi%% (e esign B
"= =
0.3!4 &2&+7
C:
0.!72
N-m per meter height
&: ;%so EL
=
1.171 !4200
N
&2&+7 x 1000 3 x /0 = 1*/2 mm2 1*0 x 0/72 x 140 σst$ EL !4200 ;st for p#%% = = = 2+1 mm2 s 1*0 Tota% ;st = 1*/2 < 2+1 = 1!43 mm2 per meter height !1&x$ia 2 !1& x 20 x 20 #sing 20 mm (ars ; = = = 314 & x100 & x 100 "pa)ing of Bars = 1000 x !1& 1/&! = 170 sa = 170 mm This is 5er near to the reinfor)ement pro5i$e$ at en$sHen)e pro5i$e$ 20 mm φ (ars 150
;st for B
- E% x
=
=
1.50 m form en$s )) Ben$ ha%f the (ars pro5i$e$ at en$s8 o#twar$sat $istan)e L& = mm φ (ars pro5i$e$ @ 300 This reinfor)ement is to (e pro5i$e$ at o#ter fa)e The a$$itiona% 20 are )ontin#e$ #pto the en$ =G? Rein!r"ement !r s)!rts (%lls.:- B at en$s=f = ;st for B
- EB x
=
σst$
=
;st for p#%%
=
Tota% ;st
=
#sing 20
mm (ars
&*7!!
ire)t p#%% p# =
N-m
&*7!! x 1000 3 1*0 x 0/72 x EL *//00 = = σs 1*0 1+*1 < ;
"pa)ing of Bars = 1000
!42
=
!1&x$ia 2 & x100 x !1&
x 140
/0
!42
mm2
2043
=
mm2 =
20&! =
N
*//00 =
mm2
1+*1
per meter height
!1& x 20 & x 1*& sa
x 20 = 314 100 = 1*0 mm
Hen)e pro5i$e mm f (ars @ 20 150 mm )) at inner fa)e near the en$s of short span The B at the )enter of short wa%%s )a#se tension at water fa)e #n%ikethat in the )enter of %ong wa%%s whe tension is pro$#)e$ at o#ter fa)e 3sin)e this B is sma%%8 on% nomina% reinfor)ement is re#ire$ "imi%ar%% we ha5e to pro5i$e nomina% reinfor)ement at o#ter fa)e8 Hen)e (en$ ha%f (ars o#twar$ at $istan)e B&= m from ea)h en$8 an$ )ontin#e remaning ha%f tro#ght Th#s at the )enter of span8 the reinfor)ement on ea fa)e wi%% )onsist of 20 mm φ (ars @ 300 mm )) =H? Rein!r"ement !r "%ntileer m!ment %n, ,istrib+ti!n rein!r"ement.:- max )anti%e5er moment= N-m 6533 +*!! x 1000 ;st = = 2+! mm2 1*0 x 0/72 x 140 0! B#t minim#m reinfor)ementin 5erti)a% $ire)tion = x 220 x 1000 3= ++0 mm2 100 "in)e ha%f of this area of stee% )an reist )anti%e5er momnt8 we wi%% pro5i$e = !!0 mm2 stee% area 5e on the inner fa)e an$ remaining area ie= !!0 mm2 5erti)a%% at o#ter fa)e to ser5e as $istri(#tion reinfor)ment !!0 m2 ∴ ;rea of stee% on ea)h fa)e = 2 !1&x$ia !1& x 10 x 10 #sing 10 mm (ars ; = = = 7!.5 & x100 & x 100 "pa)ing of Bars = 1000 x 7/* !!0 = 2!/ sa = 2!0 mm mm Φ (ar8 @ 10 Hen)e Ero5i$e$ 230 mm )) on o#t si$e fa)e8 at (ottom of %ong wa%% 2 Desi'n ! H!ri0!nt%l sl%be :- =-? L!%,in' %n, *./. :- Catio of %(
=
+00
&00 =
1*0 D
Let the thi)kness of s%a( for p#rpose of )a%)#%ating the se%f weight3
Loa$ $#e to se%f weight of "%a( :
1
x
100
x
0!0
2
/o a@ s
7200 Nm x 4/00 = 2400 Nm x
=
Loa$ $#e to water : 1 x 100 x !00 "#per impose$ %i5e %oa$ : 1 x 1 x 2000 = 2000 Nm ∴ Tota% %oa$ per meter r#n = !/+00 Nm Taking effe)ti5e $epth : !00 !0 = 270 mm we ha5e
L@ :
+00
This is )ase 2 9 2 : αxw%x 2 9@ : αw%x =B? Desi'n ! se"ti!n !r s)!rt s1%n :-
< ∴ 4
0!0 = r
:
6.30 m an$ %x = ly / lx = +!0
of ta(%e 10+8 from whi)h a x
=
&00 <
0!0 =
&!0 =
1&7 an$ α =
0.0!
4.30
m
0.056 =see ta
=
00/4
x !/+00 x
&!0 2=
+!*21
=
+!*21000
=
00+
x !/+00 x
&!0 2=
!44+/
=
!44+/000
+!*21 10 m wi$th for )a%)#%ation p#rposean B = ;ss#ming (earing = !00 mm +!*21000 ΒΜ Iffe)ti5e $epth re#ire$ = = = 270 041! x 1000 Cx( From oint of stiffness =def
= 0& J Howe5er #sing #n$er reinfor)ement se)tion8 an$ taking p 'e ha5e from mo$ifi)ation fa)tore = 1& for HA" (ars span &!00 span = 20 x 1& hen)e8 $ = = 2/ = 2/ $epth Hence roided tota< thic"ness : 300 mm #sing ! mm Φ (ars an$ a nomona% )o5er -ai
=
!00 -
!0
-
&
=
1*&
=
< -
ass#mming (en$ing of the (ars at &* $gree the %ength is
mm
J
mm !0
266 25!
= 2++ / = for
N-mm
mm mm 7/7*
201 17*
01* x &!0 = 0+&* or +&0 mm 1*0 = 740 mm from the e$ge of the s%a = &+0 mm from the )enter of s#pp !0 than 01x%x = 01 x &!00 = &!0 K 1*0 = +10 mm e$ge strip %ength 7// 012 100 x 1000 x !00 = !+0 !1& x / x / = = 50 & x 100 *0 !+0 = 1!4+ sa = 1!0
Hen)e %ength of top (ars from e$ge of s%a( &+0 < The reinfor)ement of e$ge strip is gi5en ;st @12J = !1&x$ia 2 #sing / mm (ars ; = & x100 Eit)h s = = 1000 x ;s ; = 1000 x Hence roided ! mm Φ (ar8 130 mm )) =?
;ss#ming Beam wi$th = !00 mm !44+/000 B ;st3x = = = 7&* mm2 2!0 x 040 x 2*/ σst x x !1&x$ia 2 !1& x 12 x 12 #sing 12 mm (ars ; = = = 113 & x100 & x 100 Eit)h s = = 1000 x ;s ; = 1000 x 11! 7&* = sa = 1*2 1*2 Hence roided 12 mm Φ (ar8 150 mm )) for mi$$i%e strips of wi$th !2! m
4.30 ! for the e$ge strip of wi$tg (ent ha%f (ars at $istan)e = 01* l 4&0 from the )enter of s#pport8 or at a $istan)e of 1*0 ;5ai%a(%e %ength of (ars at the top 4&0 -
= =
< -
ass#mming (en$ing of the (ars at &* $gree the %ength is
Hen)e %ength of top (ars from e$ge of s%a(
7+0
<
0*!/ 01* 1*0 !0 K 1*0
m pro5i$e mm φ (ars @ !00 x +!0 = 04&* or 4&0 mm = 1040 mm from the e$ge of the s%a = 7+0 mm from the )enter of s#pp than 01x%x = 01 x +!00 = +!0 = 410 mm e$ge of s%a(
=)? C)e"& !r s)e%r %n, ,eel!1ment len't) in s)!rt s1%n "> at %ong e$ge = w%x r2
1&7 1000 x
200 <
1&7 3= 70!1& 2++ 3= 02+& Nmm
;t the %ong e$ges8 the $iameter of (ars sho#%$ (e so restri)te$ that the fo%%owing re#irement is satisfie$ 1! x1 1000 x 11! L0 < K L$ ;st at s#pports = = /70 M 1!0 Let #s )he)k $e5e%opment %ength at the en$s of s#pports 1 = σst ;st ) $ where B = /+4*!/ x 2!0 x 040& x 2++ = &/0/0*!1 5 = 70!1& Lx !00 Lo = -x = !0 3= 120 mm 2 2 1! x1 &/0/0*!1 L0 < = 1! x < 120 = 1004 mm M 70!1& φ σ st 12 x /70 e5%opment %ength L $ = = = 20!/ mm & τ($ & x 1+ x 0/ 3 ;%ternati5e%8 L$
= 58.3Φ
=
*/
x
12
=
700 mm
1
L0 L$ < K M = 1004 K 700 Hence ode reuirement are satisfied Note The )o$e re#ires that the positi5e reinfor)ement sho#%$ extention to s#pport at %east ( L$! L$!
=
1!x
='? C)e"& !r s)e%r %n, ,eel!1ment len't) in l!n' s1%n "> at %ong e$ge = 1!w%x = 0!! x ∴ nomina% shear stress at %ong e$ges 55327 =
x
&!0 = 1000 x
**!27 2*/ 3= 021& Nmm
;t the %ong e$ges8 the $iameter of (ars sho#%$ (e so restri)te$ that the fo%%owing re#irement is satisfie$ 1! x1 1000 x 11! L0 < K L$ ;st at s#pports = = /70 M 1!0 Let #s )he)k $e5e%opment %ength at the en$s of s#pports 1 = σst ;st ) $ where B = /+4*!/ x 2!0 x 040& x 2*/ = &++!&*00 5 = **!27 Lx !00 Lo = -x = !0 3= 120 mm 2 2 1! x1 &++!&*00 L0 < = 1! x < 120 = 121+ mm M **!27 φ σ st 12 x /70 e5%opment %ength L $ = = = 20!/ mm & τ($ & x 1+ x 0/ 3 ;%ternati5e%8 L$ Th#s
= 58.3Φ =
1!x
=
121+
= 1 M K
*/
x
12
=
<
L0
K
L$
700
700 mm
Hence ode reuirement are satisfied
=F? T!rsi!n%l rein!r"ement %t "!rners "ize of torsiona% mesh =%x * = &!0 ;rea of torsiona% reinfor)ement =!& ;st3x =
* = 0/+ < 01* = 101 m from s%a( ! mm2 & x 11&4 = /+2 !1&x$ia 2 !1& x 10 x 10 #sing 10 mm (ars ; = = = 7!.5 & x100 & x 100 Eit)h s = = 1000 x ;s ; = 1000 x 74 /+2 = 411 sa = 42 0 mm )) Hence roided 10 mm Φ (ar8 Howe5er it is prfera(%e to #se the same spa)ing as pro5i$e$ for main reinfr)ement in the short span8 main reinfor)ement in the mi$$%e strip has (een pro5i$e$ @ 170 mm )) whi%e for e$ge strip it is pro5i$e$ @
130 mm ))
mm f (ars @ Hen)e pro5i$e 10 170 mm )) in the short span $ire)tion 6n %ong span8 main reinfor)ement is @ 1*0 mm )) mm f (ars @ Hen)e pro5i$e 10 1*0 mm )) in the %ong span $ire)tion
F!r L!n' s1%n 3 Desi'n ! rin' *e%m :- =-? *en,in' m!ment %n, s)e%r !r"e:- Iffe)ti5e span of (eam
+00
;ss#me Tota% $epth of Beam
:
Let wi$th of Beam
:
0.60 m for )omp#tation of $ea$ weight 0.30 m
se%f Loa$ of Beam per meter r#n : 0+0 x %oa$ from water tank : !/+00 /ota< = = 2 2
0!0 =
6.30 m
:
0!0 Nm
x
1
x
=
6n)rease $epth o
4320 Nm
= 4220 Nm +!0 x +!0 = 21!000 N-m / 10 ! N-m or 21! x 10 + N-mm +00 = 12/7+0 N
=B? /!ment ! resist%n"e / 3%n, rein!r"ement A st3 Let #s ass#me that )enter of tensi%e reinfor)emet wi%% (e at = !0 < +00 *0 = **0 mm $ = ∴ n) = k)$ = 02/4 x **0 = 1*4 mm >or sing% reinfor)ement (a%an)e se)tion8 1 = C)($2 = 041! x !00 x /2/*0&20 ;rea of tensi%e reinfo)ement is gi5en ( ;st1 = = 2!0 x 040& x **0
20
=
**0
2
=
725
*0
mm a
/2/*0&20 mm2
= ? /!ment ! resist%n"e / 4 %n, rein!r"ement A st4 21!000000 /2/*0&20 = 2=-1 = 1!01&4*/0 Nmm This remaining B gas to (e resiste$ ( a )o#p%e pro5i$e$( tensi%e an$ )opressi5e rinfor)ements !0 < 20 = Let the )enter of )ompressi5e reinfor)ement (e p%a)e$ at *0 mm 1!01&4*/0 ;rea of tensi%e reinfo)ement is gi5en ( ;st2 = = 1132 mm2 2!0 x **0 *0 /ota< -st
=
=)? C!m1ressie rein!r"ement ∴ ;s)
=
=
<
11!2
= 1!56 mm2
;s)
m $ - n)3 ;st2 m)-13n)-$)3 1!! 1*
72*
x x
where n)
**0 1!!! -
1
= 02/4 x 3x
1*4 1*4
3 -
**0
*0
=
1*4
x
11!2 =
234
mm2
='? Rein!r"in' b%rs 1/*+ mm2 #sing 1+ = !1&x$ia 2 ; = & x100 Nom(er of Bars = ;st; = 1/*+ 201 = 16 mm Φ (ar8 p%a)e$ at (ottom an$ Hen)e Ero5i$e$ 7 (ars of ;st = mm (ars
!1& x & 42& !
1+ x sa
x 1+ 100
= 201
=
No
10
nos rest (ar p%a)e$ at top ti !0 keeping a )%ear $istan)e of 2* mm (etween the two tier 8 keep a nomina% )o5er 8 se 2*mm φ spa)er (ars at 1 m ))
24!& mm2 #sing 20 = !1&x$ia 2 ; = & x100 Nom(er of Bars = ;st; = 24!& !1& = 20 mm Φ (ar8 at top 8 in one tier8 Hen)e Ero5i$e$ 10 (ars of ;st = mm (ars
!1& x & 4!&
20 x sa
x 20 100
= 314
=
No
10
keep a nomina% )o5er 8
!0
pk?nan$wana@ahoo)oin
=F? C+rt%ilement ! rein!r"ement The (en$ing at an point $istan)e x meters from the )enter of the span is gi5en ( where the moment 1 wL2 wx2 wx2 x1000 = 1 x 1000 / 2 2 an$ are in N-mm #nit ;t the point where )ompressi5e reinfro)ement is not re#ire$8 the (en$ing moment sho#%$ (e e#a% to 1 1 =
∴
1
=
∴
x
=
21 -3 1000w
Hen)e at x =
2.50
-
wx2 2
x
1000
22 2 x 1!01&4*/0 = = 2*0 m 1000w 1000 x &2420 m from the )enter8 )opmressi5e reinfor)ement is no %onger re#ire$ an$ =
it ma8 there fore 8 )#rtai%e$ Howe5er8 )#rtai% on% 5 (ars an$ )ontin#e 5 (ars #pto s#pports ;t this se)tion (en$ing moment 1 on Hen)e tensi%e reinfor)ement re#ire$ =; st1 = 72* mm2 whi)h wi%% nee$ on%
7
(ars
Hen)e )#rtai%e$
3
(ars of 2n$ tier at this point an$ )ontin#e rest of the
(ars at s#pports =G? S)e%r rein!r"ement Near the s#pport8 where the "> is maxim#m8 the se)tion is sing% reinfo)e$ sin)e the two )ompressi5e reinfor)ing (ars ser5e as ho%$ing (ars of the strirr#ps3 !0 ;5ai%a(%e effe)ti5e $epth = +00 / = *+2 mm 12/7+0 M τ5 = = = 07+ N mm2 !00 x *+2 ($ 7 x 201 = 1!&0 mm2 100;st 100 = x 1!&0 = 074 J ∴ ($ !00 x *+2 Hen)e from Ta(%e permissi(%e shear t )3= 074 J stee% = D 07+ Nmm 0!* Nmm2 whi)h is D than the nomina% shear stress hen)e shear reinfor)ement is &euired V ) = T)($ = 0!* x !00 x *+2 = %%% N
;5ai%a(%e ;st
=
V s #sing ∴
"5
=
V Vc =
10
mm 2 %eg strirr#p ;s5
=
σs5 x ;s5 x $ Vs
12/7+0
-
=
!1&x$ia 2 !1& x = 2 x & x100 & 2!0 x *+20 x 1*70 = = +47*0
=
%%% 10 x 241
N x
10 100 sa
= 1*70 240
pk?nan$wana@ahoo)oin
Howe5er8 minim#m shear reinfor)ement is go5erne$ ( expression 217* x ;s5 x f = 217* x 1*70 x &1* = &72 mm "5 = ( !00 07* x *+2 = &21* K !00 "#(e)t to maxim#m of 07*$ or ( whi)h e5er is %ess=
Hence roide the 10 mm
min
strirrus I 20 mm c$c
=H? C)e"& !r ,el!1ment len't) :- The )o$e stip#%ates that at the simp%e s#pports8 where reinfor)ement is )onfine$ 1!x1 ( a )ompressi5e rea)tion8 the $iameter of the reinfor)ement (e s#)h that < L0 K L$ M
= moment of resistan)e of se)tion8 ass#ming a%% reinfor)ement stress to σst 2!0 x 1!&0 x 040& x *+2 = = 1*+* x 10 + N-mm 1000000 = 12/7+0 N an$ L0 = "#m of an)hore 5a%#e of hooks
1
M
Let #s pro5i$e a s#pport e#a% to wi$th of wa%% - )o5er8 ie 300 !0 = 270 m 0 Let the )%ear si$e )o5er xF = !0 mm >or a ang%e 40 (en$ ha5ing an)horege 5a%#e of / Φ8 %s 270 we ha5e8 L0 = xF 3 = !0 3 = 10* mm 2 2 1! x1 M
<
L0
e5%opment %ength
= =
;%ternati5e%8 L$ Th#s
1! φ σ st
& τ($ = &* Φ
=
1!x
=
1+/*
x = = 1 M K
1*+* x 10 + 12/7+0 1+
<
x
10* 2!00
&
x
1+
x
&*
x
1+
=
<
L0
K
L$
720
= 1+/* mm
0/
= 714
3
mm
720 mm
Hen)e ,o$e re#irement are satisfie$
4 Desi'n ! Rin' be%m F!r s)!rt s1%n =-? *en,in' m!ment %n, s)e%r !r"e:- Iffe)ti5e span of (eam
&00
;ss#me Tota% $epth of Beam
:
Let wi$th of Beam
:
0.60 m for )omp#tation of $ea$ weight 0.30 m
se%f Loa$ of Beam per meter r#n : 0+0 x %oa$ from water tank : !/+00 /ota< = = 2 2
0!0 =
4.30 m
:
0!0 Nm
x
=
1
&!0 x &!0 = / 10 ! N-m or &00 =
;rea of tensi%e reinfo)ement is gi5en ( ;st1
=
2!0
041! x /2/*0&20 x 040& x
4320 Nm
=
4220 Nm
=B? /!ment ! resist%n"e / 3%n, rein!r"ement A st3 Let #s ass#me that )enter of tensi%e reinfor)emet wi%% (e at = !0 +00 *0 = **0 mm $ = ∴ n) = k)$ = 02/4 x **0 = 1*4 mm >or sing% reinfor)ement (a%an)e se)tion8 1 = C)($2 =
x
9O
!00 **0
44200 100
N-m
x 10 + N-mm
/*/&0
<
20
=
x
**0
2
725
=
=
N
*0
mm a
/2/*0&20 mm2
= ? /!ment ! resist%n"e / 4 %n, rein!r"ement A st4 44200000 /2/*0&20 = 2=-1 = 1+!&4*/0 Nmm This remaining B gas to (e resiste$ ( a )o#p%e pro5i$e$( tensi%e an$ )opressi5e rinfor)ements !0 < 20 = Let the )enter of )ompressi5e reinfor)ement (e p%a)e$ at *0 mm 1+!&4*/0 ;rea of tensi%e reinfo)ement is gi5en ( ;st2 = = mm2 142 2!0 x **0 *0 =
/ota< -st
72*
<
1&2
=
!67 mm2
pk?nan$wana@ahoo)oin
=)? C!m1ressie rein!r"ement ∴ ;st
=
;s)
m $ - n)3 ;st2 m)-13n)-$)3
where n)
= 02/4 x
**0
=
1*4
=
1!! 1*
x x
**0 1!!! -
1
x
1*4 1*4
3 -
*0
x
36
mm2
1&2
=
1+ x
x 1+ 100
= 201
=
No
='? Rein!r"in' b%rs #sing 1+
;st = mm (ars
/+7 ;
mm2 = !1&x$ia 2 & x100
=
Nom(er of Bars = ;st; = /+7 201 = 16 mm Φ (ar8 p%a)e$ at (ottom an$ Hen)e Ero5i$e$ 3 (ars of
!1& x & &!1
sa
*
nos rest (ar p%a)e$ at top ti mm f (ars keeping a )%ear $istan)e of 2* mm (etween the two tier 8 keep a nomina% )o5er 8 se 2*mm φ spa)er (ars at 1 m ))
#sing 20
;st = mm (ars
!+4 ;
mm2 = !1&x$ia 2 & x100
=
Nom(er of Bars = ;st; = !+4 !1& = 20 mm Φ (ar8 at top 8 in one tier8 Hen)e Ero5i$e$ 2 (ars of
2
!1& x & 11/
20 x sa
x 20 100
= 314
=
No
2
keep a nomina% )o5er 8
!0
#F$ C+rt%ilement ! rein!r"ement The (en$ing at an point $istan)e x meters from the )enter of the span is gi5en ( where the moment 1 wL2 wx2 wx2 x1000 = 1 x 1000 / 2 2 an$ are in N-mm #nit ;t the point where )ompressi5e reinfro)ement is not re#ire$8 the (en$ing moment sho#%$ (e e#a% to 1 1 =
∴
1
=
∴
x
=
21 -3 1000w
Hen)e at x =
0.0
-
wx2 2
x
1000
22 2 x 1+!&4*/0 = = 040 m 1000w 1000 x &2420 m from the )enter8 )opmressi5e reinfor)ement is no %onger re#ire$ an$ =
it ma8 there fore 8 )#rtai%e$ Howe5er8 )#rtai% on% 1 (ars an$ )ontin#e 1 (ars #pto s#pports ;t this se)tion (en$ing moment 1 on Hen)e tensi%e reinfor)ement re#ire$ =; st1 = 72* mm2 whi)h wi%% nee$ on%
3
(ars
Hen)e )#rtai%e$
2
(ars of 2n$ tier at this point an$ )ontin#e rest of the
(ars at s#pports =G? S)e%r rein!r"ement Near the s#pport8 where the "> is maxim#m8 the se)tion is sing% reinfo)e$ sin)e the two )ompressi5e reinfor)ing (ars ser5e as ho%$ing (ars of the strirr#ps3 !0 ;5ai%a(%e effe)ti5e $epth = +00 / = *+2 mm /*/&0 M τ5 = = = 0*1 N mm2 !00 x *+2 ($ ! x 201 = +70 mm2 100;st 100 = x +70 = 0&0 J ∴ ($ !00 x *+2 Hen)e from Ta(%e permissi(%e shear t )3= 0&0 J stee% = D 0*1 Nmm 02+ Nmm2 whi)h is D than the nomina% shear stress hen)e shear reinfor)ement is &euired V ) = T)($ = 02+ x !00 x *+2 = %%% N V s /*/&0 = V Vc = = %%% N 2 !1&x$ia !1& x / x / mm 2 %eg strirr#p ;s5 #sing / = = 2 x = 100* & x100 & x 100 2!0 x *+20 x 100* σs5 x ;s5 x $ = = = !04 sa !00 ∴ "5 Vs &200&
;5ai%a(%e ;st
=
pk?nan$wana@ahoo)oin
Howe5er8 minim#m shear reinfor)ement is go5erne$ ( expression 217* x ;s5 x f = 217* x 100* x &1* = !02 mm "5 = ( !00 07* x *+2 = &21* K !00 "#(e)t to maxim#m of 07*$ or ( whi)h e5er is %ess=
Hence roide the ! mm
min
strirrus I 300 mm c$c
=H? C)e"& !r ,el!1ment len't) :- The )o$e stip#%ates that at the simp%e s#pports8 where reinfor)ement is )onfine$ 1!x1 ( a )ompressi5e rea)tion8 the $iameter of the reinfor)ement (e s#)h that < L0 K L$ M = momen o res s an)e o se) on8 ass#m ng a re n or)emen s ress o st 1 2!0 x +70 x 040& x *+2 = = 7/2+ x 10 + N-mm 1000000 M = /*/&0 N an$ L0 = "#m of an)hore 5a%#e of hooks Let #s pro5i$e a s#pport e#a% to wi$th of wa%% - )o5er8 ie 300 !0 = 270 m 0 Let the )%ear si$e )o5er xF = !0 mm >or a ang%e 40 (en$ ha5ing an)horege 5a%#e of / Φ8 %s 270 we ha5e8 L0 = xF 3 = !0 3 = 10* mm 2 2 1! x1 7/2+ x 10 + L0 < = 1! x < 10* = 1240 mm M /*/&0 φ σ st 1+ x 2!00 e5%opment %ength = = = 714 mm & τ($ & x 1+ x 0/ 3 ;%ternati5e%8 L$ Th#s
= &* Φ
= 1
&*
x
1+
=
<
L0
K
L$
720 mm
=
1!x
=
1240
M K
+00
Cefer to fig1 x !00 x 1.00
= 1/00 kN
= = x x
0!0 0!0 +00 &00
m x x x
0!0 !00 !00
m x x
0! 0!
x x x x
4/0 0!0 0!0 0!0
x x x
0!0 0!0 0!0
x x x
+00 +00 +00
ea$ %oa$ per )o%#mn = 12&! & "hear for)e in ea)h )o%#mn $#e to win$ = 1/00 & Ben$ing moment in )o%#mn = &* x 1* 6f 5 = $ire)t %ao$ $#e to win$8 taking moment a(o#t B8 we ha5e 2 5 x +00 < +7* x &00 ∴ 5 = 1!* 27 3 12 = ? Desi'n ! "!l+mn se"ti!n "ize of )o%#mn 300 x 300 ;xia% %oa$ = p = !11 400
= = =
3 Desi'n ! t!(er:- =-? L!%,in' %n, m!ments:- 'in$ %oa$ on tank
=B? L!%, !n "!l!+mns:- ;s#mption Tank wa%% Thi)kness "ize of )o%#mn ea$ weight of tank 2 2 'eight of water "e%f weight of )o%#mns "e%f weight of Bra)esP
7200 & 2 2
720
Hen)e ,o$e re#irement are satisfie$
= =
x 2& x 2& "#( Tota%
= 2+0 = 17! = &!! = 70*+ x 2& = *2 x 2& = 2+ x 2& = 2+ Tota% $ea$ %oa$= 12&!
!11 kN &* kN +7* kNm 1/00 x 7* 400 kN
mm = !20
kN
Ben$ing moment = = I))entri)it e =
roide ;) %e
+7* kN-m +7* x 1000 x 1000 = 22 mm !20 x 1000 The %oa$ an$ e))entri)it is sma%% tr 0/ J stee% of )on)rete se)tion 0/ ;st = x !00 x !00 = 720 mm2 100 mm φ (ars Nos of (ars = 720 201 = 16 4 Nos ;t)#a% ;st pro5i$e$ = /0& mm2 mm2 = 1* x 13.33 x /0& 3F= !00 x !00 3< =
= =)? Stress in "!n"rete
!00
x 12
/!*7*4/00
!00 mm&
)ompressi5e stress
!
<
1* x
or
/!*/ x
=
∴
σF)) σ))
<
σF)( σ)(
D
10F/
!20 x 1000 10+07*4/ +7* x
Ben$ing stress =
13.33 x
1
:
/0& x
mm& =
*
<
2
sing )o5er *0 mm !02
121
h =
Nmm2
1000 x 1000 x /!*7*4/00 !02
100
1*0
=
= 0777 D
121 1
Nmm2
,..
7
='? L%ter%l rein!r"ement:- iameter of tie
= 1+ $ & = mm & Φ mm (ars for tie se = * Ei)th sha%% (e at %east of a3 Least %atera% $iamention of )o%#mns (3 1+ time of %ongit#$ina% (ars 1+ x 1+ Q &/ time of %atera% reinfor)ement &/ x * sing * mm tie @ 2&0 mm )) =F? Desi'n ! br%"es oment in (ra)e = 2 x 4.5 x 1* oment in (ra)e 1!* "hear for)e in (ra)e = = ha%f %ength of (ra)e 2 "ize of (ra)es as#me F= !00 x !00 mm )o5er 1!*0 x 1000 x 1000 ;st = σst$ = 140 x 0.03 x 270 B#t minim#m area of stee% is gi5en ( 0/* ($ 0/* x 300 x 270 ;st = = f 415 mm φ (ars Nos of (ars = 241 roide 11! = 12 3
roide
& s)!(n in ,r%(in'.
= = =
!00 mm 2*+ mm 2&0 mm
=
1!* kN-m
= +7* kN =
!0
=
241
mm2
=
1++
mm2
Nos ;t)#a% ;st pro5i$e$ = !!4 mm2 Both at top an$ (ottom with )o5er mm J of stee% pro5i$e$ !!4 x 100 !00 x 270 = 0&2 J M 6.75 x 1000 Nomina% shear stress t5= = 00/! Nmm2 ($ 300 x 270 >rom ta(%e T) = 027 Nmm2 00/! D 027 #omina< shear reinforcement are roided #se + mm 2 %egge$ strirr#ps 8 the spa)ing is gi5en (8 2 x 2!.26 x &1* ;s5 x f s = = = 140 mm D 202* 0& x ( 0&0 x 300 mm Legge$ Φ (ars @ 2 10 mm )) 6
Ltr
nk3 Nm!
ater
$ as
N-m
k en$ r
N-mm
N-mm N-mm
N N
g in g of
mm2
at ing
ts
mm2 mm mm ))
mm2
e 8 100 )h
rti)a%%
mm2
D
N-mm N-mm
mm
mm
mm2
mm
( rt8 mm mm mm2 mm2
mm
mm2
mm mm ( rt8 mm
24!4
mm2
N
mm
mm2
N
$ge mm2
mm
(eam
o5e
Nmm
mm2
r8 mm
mm2
mm
mm2
mm
300
o5e
Nmm
mm2
r8 mm
mm2
mm
mm2
mm
300
kN kN kN kN kN kN kN kN
100
!0
-L'* ,F )'*+G# ,#*/-#/* Gra$e of )on)rete
-1*
-20
-2*
-!0
-!*
-&0
o$#%ar Catio
1/+7
1!!!
104/
4!!
/11
71/
σ)() Nmm2 m σ)()
*
7
/*
10
11*
1!
4!!!
4!!!
4!!!
4!!!
4!!!
4!!!
k)
0&
0&
0&
0&
0&
0&
)
0/+7
0/+7
0/+7
0/+7
0/+7
0/+7
C)
0/+7
121&
1&7&
17!&
144&
22*&
E) J3
071&
1
121&
1&24
1+&!
1/*7
Gra$e of )on)rete
k)
0!24
0!24
0!24
0!24
0!24
0!24
1*
)
0/4
0/4
0/4
0/4
0/4
0/4
20
C)
07!2
102*
12&&
1&+&
1+/&
140!
2*
E) J3
0&!!
0+0+
07!+
0/++
0447
1127
!0
k)
02/4
02/4
02/4
02/4
02/4
02/4
!*
)
040&
040&
040&
040&
040&
040&
&0
C)
0+*!
041&
111
1!0+
1*02
1+4/
&*
E) J3
0!1&
0&&
0*!&
0+2/
0722
0/1+
*0
k)
02*!
02*!
02*!
02*!
02*!
02*!
)
041+
041+
041+
041&
041+
041+
C)
0*74
0/11
04/*
11*4
1!!2
1*0+
E) J3
02!
0!22
0!41
0&+
0*!
0*44
a3 σst = 1&0 Nmm2 >e 2*03 (3 σst = 140 Nmm2 ) 3 σst = 2!0 Nmm2 >e &1*3 $3 σst = 27* Nmm2 >e *003
ermissiD
in concrete =+* 4562000?
Eermissi(%e shear stress in )on)rete t5 Nmm2
($
-1*
-20
-2*
-!0
-!*
-&0
D 01*
01/
01/
014
02
02
02
02* 0*0 07* 100 12* 1*0 17* 200 22* 2*0 27*
022 024 0!& 0!7 0&0 0&2 0&& 0&& 0&& 0&& 0&& 0&&
022 0!0 0!* 0!4 0&2 0&* 0&7 0&4 0*1 0*1 0*1 0*1
02! 0!1 0!+ 0&0 0&& 0&+ 0&4 0*1 0*! 0** 0*+ 0*7
02! 0!1 0!7 0&1 0&* 0&/ 0*0 0*! 0** 0*7 0*/ 0+
02! 0!1 0!7 0&2 0&* 0&4 0*2 0*& 0*+ 0*/ 0+0 0+2
02! 0!2 0!/ 0&2 0&+ 0&4 0*2 0** 0*7 0+0 0+2 0+!
!00 an$ a(o5e
Gra$e of )on)ret τ($ N mm23
Grade of concrete
10 1* 20 2* !0 !* &0 &* *0
9aximum shear stress τ)max in concrete =+* 4562000? Gra$e of )on)rete
τ)max
"hear stress t)
-1* 1+
-20 1/
Ceifor)ement J
-2* 14
-!0 22
-!* 2!
-&0 2*
Gra$e of )o
σ)tmax
100-s b, 01* 01+ 017 01/ 014 02 021 022 02! 02& 02* 02+ 027 02/ 024 0! 0!1 0!2 0!! 0!& 0!* 0!+ 0!7 0!/ 0!4 0& 0&1 0&2 0&! 0&& 0&* 0&+ 0&7 0&/ 0&4 0* 0*1 0*2 0*! 0*& 0** 0*+ 0*7 0*/ 0*4 0+ 0+1 0+2 0+! 0+& 0+* 0++
/-45
/-45
01/ 01/ 01/ 014 014 014 02 02 02 021 021 021 022 022 022 02! 02! 02& 02& 02& 02* 02* 02* 02+ 02+ 02+ 027 027 027 02/ 02/ 02/ 024 024 024 0!0 0!0 0!0 0!0 0!0 0!1 0!1 0!1 0!1 0!1 0!2 0!2 0!2 0!2 0!2 0!! 0!!
01/ 014 02 021 022 02! 02& 02* 02+ 027 02/ 024 0!0 0!1 0!2 0!! 0!& 0!* 0!+ 0!7 0!/ 0!4 0& 0&1 0&2 0&! 0&& 0&* 0&+ 0&+ 0&7 0&/ 0&4 0*0 0*1
100-s b, 01* 01/ 021 02& 027 0! 0!2 0!* 0!/ 0&1 0&& 0&7 0* 0** 0+ 0+* 07 07* 0/2 0// 04& 100 10/ 11+ 12* 1!! 1&1 1*0 1+! 1+& 17* 1// 200 21! 22*
egree 1 1* 2 2* ! !* & &* * ** + +* 7 7* / /* 4 4* 10 10* 11 11* 12 12* 1! 1!* 1& 1&* 1* 1** 1+ 1+* 17 17* 1/ 1/* 14 14* 20 20* 21 21* 22 22* 2! 2!* 2& 2&* 2* 2** 2+ 2+*
0+7 0+/ 0+4 07 071 072 07! 07& 07* 07+ 077 07/ 074 0/ 0/1 0/2 0/! 0/& 0/* 0/+ 0/7 0// 0/4 04 041 042 04! 04& 04* 04+ 047 04/ 044 100 101 102 10! 10& 10* 10+ 107 10/ 104 110 111 112 11! 11& 11* 11+ 117 11/ 114 120
0!! 0!! 0!! 0!& 0!& 0!& 0!& 0!& 0!* 0!* 0!* 0!* 0!* 0!* 0!* 0!+ 0!+ 0!+ 0!+ 0!+ 0!+ 0!7 0!7 0!7 0!7 0!7 0!7 0!/ 0!/ 0!/ 0!/ 0!/ 0!/ 0!4 0!4 0!4 0!4 0!4 0!4 0!4 0!4 0& 0& 0& 0& 0& 0& 0& 0& 0&1 0&1 0&1 0&1 0&1
27 27* 2/ 2/* 24 24* !0 !0* !1 !1* !2 !2* !! !!* !& !&* !* !** !+ !+* !7 !7* !/ !/* !4 !4* &0 &0* &1 &1* &2 &2* &! &!* && &&* &* &** &+ &+* &7 &7* &/ &/* &4 &4* *0 *0* *1 *1* *2 *2* *! *!*
121 122 12! 12& 12* 12+ 127 12/ 124 1!0 1!1 1!2 1!! 1!& 1!* 1!+ 1!7 1!/ 1!4 1&0 1&1 1&2 1&! 1&& 1&* 1&+ 1&7 1&/ 1&4 1*0 1*1 1*2 1*! 1*& 1** 1*+ 1*7 1*/ 1*4 1+0 1+1 1+2 1+! 1+& 1+* 1++ 1+7 1+/ 1+4 170 171 172 17! 17&
0&1 0&1 0&1 0&1 0&2 0&2 0&2 0&2 0&2 0&2 0&2 0&2 0&! 0&! 0&! 0&! 0&! 0&! 0&! 0&! 0&& 0&& 0&& 0&& 0&& 0&& 0&& 0&& 0&& 0&* 0&* 0&* 0&* 0&* 0&* 0&* 0&* 0&* 0&* 0&* 0&* 0&* 0&+ 0&+ 0&+ 0&+ 0&+ 0&+ 0&+ 0&+ 0&+ 0&+ 0&+ 0&+
*& *&* ** *** *+ *+* *7 *7* */ */* *4 *4* +0 +0* +1 +1* +2 +2* +! +!* +& +&* +* +** ++ ++* +7 +7* +/ +/* +4 +4* 70 70* 71 71* 72 72* 7! 7!* 7& 7&* 7* 7** 7+ 7+* 77 77* 7/ 7/* 74 74* /0 /0*
17* 17+ 177 17/ 174 1/0 1/1 1/2 1/! 1/& 1/* 1/+ 1/7 1// 1/4 140 141 142 14! 14& 14* 14+ 147 14/ 144 200 201 202 20! 20& 20* 20+ 207 20/ 204 210 211 212 21! 21& 21* 21+ 217 21/ 214 220 221 222 22! 22& 22* 22+ 227 22/
0&7 0&7 0&7 0&7 0&7 0&7 0&7 0&7 0&7 0&7 0&7 0&7 0&7 0&/ 0&/ 0&/ 0&/ 0&/ 0&/ 0&/ 0&/ 0&/ 0&/ 0&/ 0&/ 0&4 0&4 0&4 0&4 0&4 0&4 0&4 0&4 0&4 0&4 0&4 0&4 0&4 0*0 0*0 0*0 0*0 0*0 0*0 0*0 0*0 0*0 0*0 0*0 0*0 0*1 0*1 0*1 0*1
/1 /1* /2 /2* /! /!* /& /&* /* /** /+ /+* /7 /7* // //* /4 /4* 40
Ta(%e 10+ ending moment cofficientsfor rectangu
Tpe of pane%an$ moment
1
12
00!2 002&
0 0
00&! 00!+
00!7 002/
0 0
00&/ 00!+
00!7 002/
0 0
00*2 00!4
00&7 00!*
0 0
00+ 00&*
00&* 00!*
0 0
00*2 00&
00!*
0
00*1
00*7 00&!
0 0
0071 00*!
0
00*4
6nterior pane%s 1
!egative moment at continuous edge "ositive moment at mid span
9ne short e$ge $is)ontin#os 2
!
& *
+
7
!egative moment at continuous edge "ositive moment at mid span #ne long edge discontinuos !egative moment at continuous edge "ositive moment at mid span $%o ad&acent edge discontinuos !egative moment at continuous edge "ositive moment at mid span $%o s'ort edge discontinuos !egative moment at continuous edge "ositive moment at mid span $%o long edge discontinuos !egative moment at continuous edge "ositive moment at mid span $'ree edge discontiuos
one %ong e$ge )ontin#os
/
!egative moment at continuous edge "ositive moment at mid span $'ree edge discontiuos
one short e$ge )ontin#os !egative moment at continuous edge "ositive moment at mid span
00&!
224 2!0 2!1 2!2 2!! 2!& 2!* 2!+ 2!7 2!/ 2!4 2&0 2&1 2&2 2&! 2&& 2&* 2&+ 2&7 2&/ 2&4 2*0 2*1 2*2 2*! 2*& 2** 2*+ 2*7 2*/ 2*4 2+0 2+1 2+2 2+! 2+& 2+* 2++ 2+7 2+/ 2+4 270 271 272 27! 27& 27* 27+ 277 27/ 274 2/0 2/1 2/2
0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1
4
four edge discontinuos "ositive moment at mid span
fo#r e$ge $is)ontin#os % %x
positive Long span moment at )offi)iet a mid span for a%% 5a%#e
x
α
1 11 12 1! 1& 1* 17* 2
00*+ 00+& 0072 0074 00/* 00/4 01 0107
of %%x
00*+ 00*+ 00*+ 00*+ 00*+ 00*+ 00*+ 00*+
00*+
0
0072
o$ifi)ation J stee% 0 01 01* 02 02* 0! 0!* 0& 0&* 0* 0** 0+ 07 0/ 04 1 11 12 1! 1& 1* 1+ 17 1/ 14 2 21 22 2! 2& 2* 2+ 27 2/ 24 !
2/! 2/& 2/* 2/+ 2/7 2// 2/4 240 241 242 24! 24& 24* 24+ 247 24/ 244 !00 !01 !02 !0! !0& !0* !0+ !07 !0/ !04 !10 !11 !12 !1! !1& !1*
0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1 0*1
ermissiD
in concrete =+* 4562000?
Dd
-10
-1*
-20
-2*
-!0
-!*
-&0
-&*
-*0
--
0+
0/
04
1
11
12
1!
1&
)ee
HA" Bars
τ($ N mm23
k$ = L$ Φ
τ($ N mm23
k$ = L$ Φ
0+
*/
04+
+0
0/
&&
12/
&*
04
!4
1&&
&0
1
!*
1+
!+
11
!2
17+
!!
12
24
142
!0
1!
27
20/
2/
1&
2*
22&
2+
ermissiD
Ogm2 !00 *00 700 /*0 1000 11*0 1!00 1&*0 1+00
Nmm23 2* &0 *0 +0 /0 40 100 110 120
Ogm2 2*0 &00 *00 +00 /00 400 1000 1100 1200
in kgm2 -+0 /0 40 100 110 120 1!0 1&0
Nmm23 -0+ 0/ 04 10 11 12 1! 1&
ermissiD
)rete
-10 12
-1* 20
-20 2/
-2* !2
-!0 !+
-!* &0
-&0 &&
sin 0017 002+ 00!* 00&& 00*2 00+1 0070 007/ 00/7 004+ 010& 011! 0122 01!1 01!4 01&/ 01*+ 01+* 017& 01/2 0141 0144 020/ 0/14 022* 02!! 02&2 02*0 02*4 02*4 027+ 02/& 0242 0!01 0!04 0!17 0!2+ 0!!& 0!&2 0!*0 0!*/ 0!+7 0!7* 0!/! 0!41 0!44 0&07 0&1* 0&22 0&!1 0&!/ 0&&+
Ma%#e of ang%e egree )os 1 1000 1* 1000 2 0444 2* 0444 ! 0444 !* 044/ & 044/ &* 0447 * 044+ ** 044* + 044* +* 044& 7 044! 7* 0441 / 0440 /* 04/4 4 04// 4* 04/+ 10 04/* 10* 04/! 11 04/1 11* 04/0 12 047/ 12* 047+ 1! 047& 1!* 0472 1& 0470 1&* 04+/ 1* 04++ 1** 04+& 1+ 04+1 1+* 04*4 17 04*+ 17* 04*& 1/ 04*1 1/* 04&/ 14 04&+ 14* 04&! 20 04&0 20* 04!7 21 04!& 21* 04!0 22 0427 22* 042& 2! 0421 2!* 0417 2& 042& 2&* 0410 2* 040+ 2** 040* 2+ 0/4/ 2+* 0/4*
tan 0017 02+2 00!* 00&& 00*2 00+1 0070 0074 00/7 004+ 010* 011& 012! 01!2 01&0 01&4 01*/ 01+/ 017+ 01/* 014& 020! 021! 0/!4 02!1 02&0 02&4 02*4 02+/ 02+4 02/7 024+ 0!0+ 0!1* 0!2* 0!!* 0!&& 0!*& 0!+& 0!7& 0!/& 0!4& 0&0& 0&1& 0&2& 0&!* 0&&0 0&*+ 0&++ 0&7+ 0&// 0&44
)ot *724* *+!00 2/+&& 2241! 140/! 1+!+2 1&!11 12707 11&!7 10!/* 4*+! /777 /1&4 7*47 7114 ++41 +!1* *4+! *+7! *!4+ *1&2 &41* &70& 1142 &!!2 &1++ &011 !/+7 !7!2 !72! !&// !!7+ !272 !172 !07/ 24/4 240* 2/2& 27&7 2+7& 2+0* 2*!4 2&7* 2&1& 2!*+ 2!00 2271 214& 21&/ 210! 20&4 200+
0&*& 0&+2 0&+4 0&77 0&/* 0&42 0*00 0*0/ 0*1* 0*22 0*!0 0*!7 0*&* 0**2 0**4 0*++ 0*7! 0*/1 0*// 0*4* 0+02 0+04 0+1+ 0+2! 0+24 0+!+ 0+&! 0+&4 0+*+ 0++! 0++4 0+7+ 0+/2 0+// 0+4* 0701 0707 071! 0714 072* 07!1 07!7 07&2 07&4 07** 07+0 07++ 0772 0777 07/+ 07// 074! 0744 0/0&
27 27* 2/ 2/* 24 24* !0 !0* !1 !1* !2 !2* !! !!* !& !&* !* !** !+ !+* !7 !7* !/ !/* !4 !4* &0 &0* &1 &1* &2 &2* &! &!* && &&* &* &** &+ &+* &7 &7* &/ &/* &4 &4* *0 *0* *1 *1* *2 *2* *! *!*
0/41 0//7 0//! 0/74 0/7* 0/70 0/++ 0/+2 0/*7 0/*! 0/&/ 0/&! 0/!4 0/!& 0/24 0/!& 0/14 0/1& 0/04 0/0& 0744 074! 07// 07/! 0777 0772 07++ 07+0 07** 07&4 07&! 07!7 07!1 072* 0714 071! 0707 0701 0+4* 0+// 0+/2 0+7+ 0++4 0++! 0+*+ 0+&4 0+&! 0+!+ 0+24 0+2! 0+1+ 0+04 0+02 0*4*
0*10 0*21 0*!2 0*&! 0**& 0*++ 0*77 0*/4 0+01 0+1! 0+2* 0+!7 0+&4 0++2 0+7* 0+74 0700 071! 072+ 07&0 07*& 07+7 07/1 074* 0/10 0/2& 0/!4 0/*& 0/+4 0//* 0400 041+ 04!! 04&4 04++ 04/! 1000 101/ 10!+ 10*& 1072 1041 1104 11!0 11*0 1171 1142 121! 12!* 12+2 12/0 1!0! 1!27 1!*1
14+! 1421 1//1 1/&2 1/0& 17+7 17!2 1+4/ 1++& 1+!2 1+00 1*70 1*&0 1*11 1&/! 1&7! 1&24 1&02 1!77 1!*1 1!27 1!0! 12/0 12*7 12!* 121! 1141 1171 11*0 11!0 1111 1041 1072 10*& 10!+ 101/ 1000 04/! 04++ 04&4 04!! 041+ 0402 0//* 0/+4 0/*& 0/!4 0/2& 0/10 0742 07/1 07+7 07*& 07&0
0/04 0/1& 0/14 0/2& 0/24 0/!& 0/!4 0/&! 0/&/ 0/*! 0/*7 0/+2 0/++ 0/70 0/7* 0/74 0//! 0//7 0/41 0/4* 0/44 040! 040+ 0410 041& 0417 0421 042& 0427 04!0 04!& 04!7 04&0 04&! 04&+ 04&/ 04*1 04*& 04*+ 04*4 04+1 04+& 04++ 04+/ 0470 04/2 047& 047+ 047/ 04/0 04/2 04/! 04/* 04/+
*& *&* ** *** *+ *+* *7 *7* */ */* *4 *4* +0 +0* +1 +1* +2 +2* +! +!* +& +&* +* +** ++ ++* +7 +7* +/ +/* +4 +4* 70 70* 71 71* 72 72* 7! 7!* 7& 7&* 7* 7** 7+ 7+* 77 77* 7/ 7/* 74 74* /0 /0*
0*// 0*/1 0*7& 0*++ 0**4 0**2 0*&* 0*!7 0*!0 0*22 0*1* 0*0/ 0*00 0&42 0&/* 0&77 0&70 0&+2 0&*& 0&&+ 0&!/ 0&!1 0&2! 0&1* 0&07 0!44 0!41 0!/! 0!7* 0/14 0!*/ 0!*0 0!&2 0**+ 0!2+ 0!17 0!04 0!01 0242 02/& 027+ 02+7 02*4 02*0 02&2 02!! 022* 021+ 020/ 0144 0141 01/2 017& 01+*
1!7+ 1&02 1&2/ 1&** 1&/! 1*11 1*&0 1*70 1+00 1+!2 1++& 1+4/ 17!2 17+7 1/0& 1/&2 1//0 1421 14+! 200+ 20*1 2047 21&* 214* 22&+ 2!00 2!*+ 2&1& 2&7* 11!+ 2+0* 2+7& 27&7 1+4+ 240& 24/4 !07/ !172 !271 !!7+ !&// !+0+ !7!2 !/+/ &011 &204 &!!2 &*11 &70* &41* *1&* *!4+ *+7! *477
0727 071! 0700 0+/7 0+7* 0++2 0+&4 0+!7 0+2* 0+1! 0+01 0*/4 0*77 0*++ 0**& 0*&! 0*!2 0*21 0*10 0&4/ 0&// 0&77 0&++ 0&*+ 0&&* 0&!* 0&2& 0&1& 0&0& 0//0 0!/& 0!7& 0!+& 0*40 0!&& 0!!* 0!2* 0!1* 0!0+ 024+ 02/7 0277 02+/ 02*4 02&4 02!/ 02!1 0222 021! 020! 014& 01/* 017+ 01+7
04// 04/4 0444 0441 044! 044& 044* 044* 044+ 0447 044/ 044/ 0444 0444 0444 1000 0444/ 04444 1000
/1 /1* /2 /2* /! /!* /& /&* /* /** /+ /+* /7 /7* // //* /4 /4* 40
01*+ 01&/ 01!4 01!1 0122 011! 010* 004+ 00/7 007/ 0070 00+1 00*2 00&& 00!* 002+ 0017 0004 0000
+!1* ++41 717/ 7*47 /1&* /777 4*17 10!/4 11&!1 1271+ 1&!02 1+!+2 140/! 2241! 2/+!7 !/244 *724* 11&4!1 1000
01*/ 01&4 01!4 01!2 012! 011& 010* 004+ 00/7 0074 0070 00+1 00*2 00&& 00!* 002+ 0017 0004 0000
on four side ith roision for torsion at corners =+*456 2000? an )offi)ient axfor 5a%#e of LLx
Long span )offi)iet a for a%% 5a%#e of %%x
1!
1&
1*
17*
2
00&7 00!4
00*1 00!4
00*! 00&1
00+ 00&*
00+* 00&4
00!2 002&
00*1 00!4
00** 00&1
00*7 00&&
00+& 00&/
00+/ 00*2
00!7 002/
00*7 00&&
00+! 00&7
00+7 00*1
0077 00*4
00/* 00+*
00!7 002/
00+* 00&4
0071 00*!
007* 00*+
00/& 00+!
0041 00+4
00&7 00!*
00*+ 00&!
00*4 00&&
00+ 00&*
00+* 00&4
00+4 00*2
00!*
00*7
00+!
00+/
00/
00//
00&* 00!*
007+ 00*7
00/ 00+
00/& 00+&
0041 00+4
0047 007!
00&!
00+*
0071
007+
00/7
004+
00*7 00&!
0074
fa)tore >=&1* fe= 2&0 2 14 1/ 17 1+ 1* 1& 1!* 1! 12* 12 11* 112 11 1 04* 04! 041 04 04 0/4 0/4 0// 0// 0/+ 0/+ 0/* 0/* 0/& 0/& 0/! 0/! 0/2 0/2 0/1
00/*
00/4
01
0107
00*+
