ANALYSIS_AND_DESIGN_OF_T-BEAM_BRIDGE_SUP.docx

• • •

BY: BY: ABHISEK PANDA

3.6 3.6

SUPE SU PER R STRU STRUCT CTUR URE E DESI DESIGN GN::

3.6.1 AVAILABLE AVAILABLE DAT DATA: • Efective span o T-beam bride: !"#$$m  Tota% %ent& o bride: ''m •  Tota% • (%ear )idt& o carriae )a* +#'m ,I( ': !.." / I( 0: 12!34 • Kerb )idt&: 022mm ,bot& side5 pedestrians are a%%o)ed4 • Parapet: !222 mm × !'2 mm × !'2 mm 6 !#'m c7c )it& $-cast iron • • • • • • • • • • • • • • • • • • • • •

pipes as rai%in (amber: ! in !22 ,$+#' mm at center %inear%* var*in to 8ero at 9erbs4 earin coat: "2mm Kerb &ei&t above pavement: 122mm ,ins;rmo;ntab%e t*pe4 Kerb t*pe: ;%% saet* ens;red  Tota%  Tota% 9erb &ei&t above dec9 s%ab: 1"2 mm (%ear dept& o rade o concrete: ?$' Desin strent&:  cd cd @ 2#0+  c9 c97γ m?Pa ,Anne  A1 o I( !!1: 12!!4 >rade o stee% : Ce3!' ,IS !+"0 : 12224 Desin strent& o stee% :  *7!#!' @ 2#"+ * ?Pa ,c%a;se-!'#1#$#$ o I( !!1:12!!4 Poissons ratio: µ @ 2#1 ,Anne-B= B-$-! o I( !!1:12!! 4 Ana%*sis o dec9 s%ab: Piea;ds c;rve

3.6.2 DESIGN OF INTERIOR SLAB PANEL: PANEL:

 T&e s%ab is s;pported on o;r sides b* %onit;dina% and cross irders )&ic& c7c spacin is as s&o)n in t&e ;re above# T&e s%ab t&ic9ness is 1'2 mm and breadt& and %ent& respective%* are 1#'m and 3#'2+' m# t&e efective span span )i%% )i%% be ta9 ta9en as t&e t&e c%ea c%earr span span o t&e t&e s%ab s%abs s sinc since e t&es t&ese e are are t&e t&e contin;o;s s%abs# So efective )idt& B ef  @   @ 1#!m and efective %ent&
• • •

BY: BY: ABHISEK PANDA

B

u

v

L

4.5075m

One-wheel loaded area of  vehicle

2.5 m

Fig-7 (Int!i"! S#$% P$n# &it' "n &'# " T!$)*+ V'i)#, 3.6.2.1 L"$+:

Bn+ing "  "nt " t' S#$% P$n# +/ t" D D $+

ei&t o s%ab @ 2#1' × !× !× 1' @ 0#1' 9N7m1 ei&t o )earin coat @ 2#2"2 × 11 ×! ×! @ !#+0 9N7m1 ei&t o camber @ 2#3' 9N7m1  Tota%  Tota% dead )ei&t @ "#30 9N7m1 As Pie;ads c;rve is ;sed in desin5 &ence K @ B7< @ 1#'73#'2+' @ 2#'' A%so dead %oad moment is to be comp;ted and &ence ;7B @ !#2 and v7< @ !#2 Fsin Pie;ads c;rve or K@2#'5 ;7B @ !#2 and v7<@!#25 m!@2#23+ and m1@2#223 A%so or K@2#05 ;7B @ !#2 and v7< @ !#25 m!@2#23+ and m1 @ 2#2!0 Ater Ater interpo%ation5 )e nd t&at m!@2#23+ and m1@2#2!3'  Tota%  Tota% dead %oad on t&e s%ab is iven b* @ "#30 ×1#'×3#'2+' @ .'#$$  S&ort span moment is ?B @ .'#$$ ,2#23+G2#12×2#2!3'4 @ 3#+0 9N-m

• • •

BY: BY: ABHISEK PANDA


Bn+ing "nt +/ t" Li0 L"$+:

$. IRC I RC )#$ AA t!$)*+ V'i V'i)#: )#:

 T&e )&ee% is p%aced at t&e center o t&e s%ab as s&o)n in t&e ;re prev previo io;s ;s%* %*## Cor mai maim; m;m m bend bendin in  mome moment nt to be occ; occ;rrred5 ed5 t&e t&e %oad %oad dispersion is ta9en to be occ;rrin t&ro;& )earin coat on%*# T&e %oad is disperses at 3'2 t&ro;& t&e )earin coat as per Anne-B o I( I( !!1:12!!# Hence /  .452 .4  1.1 and 0  3.6  2 .4  3.76 Hence ;7B @ 2#323 5 v7< @ 2#"$31 and K @ B7< @ 1#'73#'2+' @ 2#''# eerrin to Pie;ads c;rve5 Cor K @ 2#'5 and or above ;7B and v7< va%;es5 m! @ 2#2"3 5 m1 @ 2#22. Simi%ar%* or K @ 2#05 )e et m! @ 2#2.' and m1 @ 2#2$ Ater Ater interpo%atin5 )e et m! @ 2#2". and m1 @ 2#2!. S&ort span bendin moment is iven b*5 ,ta9in contin;it* into acco;nt4 ?B @ 2#"×$'2×,2#2".G2#1×2#2!.4 @ 1'#."3 9N-m ?< @ 2#" ×$'2×,2#2!.G2#1×2#2".4 @ !2#$23 9N-m As per I( 0:12!25 c%a;se  12"#$5 or trac9ed ve&ic%es5 t&e impact actor is !2 or spans ;p to 32m# So ?B @ 1"#'" 9N-m and ?< @ !!#$$3 9N-m %. IRC )#$-AA )#$ -AA &'#+ 0'i)#: 0'i)# :

Co%%o)in diferent reerences and ;ides on bride enineerin5 its c%ear%* ;nderstood t&at t&o;& trac9ed ve&ic%e ives t&e severest efect a%on s&ort span7d span7dir irecti ection on b;t a%on a%on %on %on span5 span5 t&e )&ee%ed )&ee%ed ve&ic% ve&ic%e e ives ives severe severest st efect# B* oin t&ro;& Essentia%s o Bride Enineerin: D#J ictorL and #(#( desin: B#(# P;nmia5 A#K Jain and A#K JainL )e nd t&e o%%o)in %oad positionin ives t&e severest efect amon ot&er combinations#

BY: ABHISEK PANDA

• • •

1250 mm

1250 mm

W 1 = 37.5 kw

  m   m    5    7  .    3    5    2    2

W 2 = W3= 2.5 kw

1 15 0

2

W1

W2

300 m   m   m    5    7  .    3    5    2    2

3 W3 1000 mm

00 mm 4 W1

5 W2

 W3

Fig-4 (L"$+ing " &'#+ 0'i)# "! 0!t )t,

A%so as per I( 0:12!3 specications5 no ot&er ve&ic%es can come on to t&e pane% d;rin t&e above arranement# Bn+ing "nt )$#)/#$ti"n +/ t" 8'# L"$+ -2:

 T*re contact dimension : $22 mm × !'2 mm So ; @ 2#$G1×2#2"2 @ 2#302 m and v @ 2#!'G1×2#2"2 @ 2#$!2 m  T&e va%;e o ;7B @ 2#!"3 5 v7< @ 2#20. and B7< @ 2#'' Fsin Pie;ads c;rve5 m! @ 2#11 and m1 @ 2#12 Hence ?B! @ 01#' ,2#11G2#1×2#14 @ !0#1' 9N-m and 01#',2#1G2#11×2#14 @ !'#1' 9N-m

?
@

Bendin ?oment d;e to &ee%
• • •

BY: ABHISEK PANDA 370 mm W1

0.31 m

450 mm 00 mm

W1

450 mm 00 mm

Fig-9 (Bn+ing "nt )$#)/#$ti"n +/ t" 8'# L"$+-1,

So ; @ 1,;! G 4 @ 1,2#30G2#$+4 @ !#00m and v @ 2#$!m
No) ; @ 1 @ 1×2#$+ @ 2#+3 and v @ 2#$! K @ 2#''5 ;7B @ 2#1.0 and v7< @ 2#20. Crom Pie;ads c;rve5 m! @ 2#!"3 and m1 @ 2#!". ?B @ !$#$" 9N-m and ?< @ !$#011 9N-m

Hence tota% moment is iven b*5 ?B1 @ ,12#2$  !$#$"4 ×2#' 9N-m @ $#$1' 9N-m ?<1 @ ,11#!.$  !$#0114 ×2#' 9N-m @ 3#1"' 9N-m Bn+ing "nt +/ t" 8'# L"$+-3:

No) in t&is case ; @ 1,2#30G2#++4 @ 1#30m 5 v @ 2#$! m
?B$ @ $0#!2 - $1#2!O ×2#' @ 1#23' 9N-m ?<$ @ $0#!2 - $3#'1O ×2#' @ 2#+. 9N-m

• • •

BY: ABHISEK PANDA

Bn+ing "nt +/ t" 8'# L"$+ $t - 5:

 ; @2#30m5 v @ 1,v!G4 @ 1,2#$! G !#23'4 @ 1#+!m
Bn+ing "nt +/ t" &'# L"$+ $t  ;:

 ; @ 1,;!G4 @ 1,2#30G2#$+4 @ !#00m and v @ 1,v!G*4 @ 1,2#$!G!#23'4 @ 1#+!m K @ 2#''5 ;7B @ 2#003 and v7< @ 2#02! (oecient m! @ 2#2.12' and m1 @ 2#21+ Ater m;%tip%*in )it& ,; !G4,v!G*4 )it& bot& coecients5 m! @ 2#!2!' and m1 @ 2#2$23 ∗  ; @ 1 @ 1×2#$+ @ 2#+3m5 v @ 1* @ 1×!#23' @ 1#2.m K @ 2#'""5 ;7B @ 2#1.0 and v7< @ 2#303 So m! @ 2#!$3 and m1 @ 2#232' ?;%tip%*in )it& *5 )e et m!@2#2'1 and m1 @ 2#2!0 ∗  ; @ 2#+3m5 v @ 1#+!m K @ 2#''5 ;7B @ 2#1.0 and v7< @ 2#02! m! @ 2#!1 and m1 @ 2#2$ and m;%tip%*in )it& ,v!G*4 @ 2#'2!$5 m! @ 2#202 and m1@2#2!' ∗  ; @!#00 m and v @ 1#2.m K @ 2#''5 ;7B @ 2#003 and v7< @ 2#303 m! @ 2#2.' and m1 @ 2#2$" ?;%tip%*in )it& *,;!G4 @ 2#"+5 m!@2#2"$ and m1 @2#2$$ ∗

So m! @ ,2#!2!'G2#2'14-,2#202G2#2"$4O @ 2#2!2' m1 @ ,2#2$23G2#2!04-,2#2!'G2#2$$4O ≈ 2 37.5

?B3 @

0.460.31

2#2!2'G2#1×2O @ 1#+0! 9N-m

• • •

BY: ABHISEK PANDA 37.5

?<3 @

0.460.31

2#1×2#2!2'G2O @ 2#''1 9N-m

Bn+ing "nt +/ t" 8'# L"$+ $t -6:

! ; @ 1;!GO @ 12#30G2#++O @ 1#30 m and v @ 1v!GO @ 12#$!G!#23'O @ 1#+! m K @ 2#''5 ;7B @ 2#."3 and v7< @ 2#02! m! @ 2#20"5 m1 @ 2#21 ;!GOv!G*O @ !#1$×!#$'' @ !#0+ m!@2#!!$ and m1 @ 2#2$$3 ∗ 1 ; @ 1 @!#'3m and v @ 1* @ 1#2.m K@2#''5 ;7B @ 2#0!0 and v7< @ 2#303 m! @ 2#2.+5 m1 @ 2#2$" * @ 2#"23 Hence m! @ 2#2+" and m1 @ 2#2$2' ∗ $ ; @ 1;!GO @ 1#30m and v @ 1* @1#2.m K @ 2#''5 ;7B @ 2."3 and v7< @ 2#303 m! @2#2+3 and m1 @ 2#2$ *,;!G4 @ !#1"' m! @ 2#2.' and m1@2#2$" ∗ 3 ; @ 1 @ !#'3m and v @ 1,v!G*4 @ 1#+!m K @ 2#''5 ;7B @ 2#0!0 and v7< @ 2#02!1 m! @ 2#2.1 and m1 @ 2#21' ?;%tip%*in ,v!G*4 @ !#23$ )it& above coecients5 m! @ 2#2.0 and m1 @ 2#210 So na% coecients are5 m! @ ,2#!!$G2#2+"4-,2#2.'G2#2.04O @ 2 m1 @ ,2#2$$3G2#2$2'4-,2#2$"G2#2104O ≈2  T&e res;%tin moment is iven b*5 ?B0 @ ?<0 @ 2 9N-m ∗

 Tota% bendin moment is iven b*5 ?B@ !0#1'G$#$1'G1#23'G$#0$'G1#+0! @ 1"#2!0 9N-m ?< @ !'#1'G3#1"'G2#+.G2#2'G2#''1 @ 12#.$ 9N-m App%*in contin;it* and impact5 B  24.16 .4 1.14  26.;5 *N- L  2.93 .4 1.14  19.76 *N-

• • •

BY: ABHISEK PANDA

 T&e impact actor is ta9en as !" as per c%a;se-12"#3 o I( 0: 12!3# It can be seen t&at t&e moment a%on s&ort span or trac9ed %oad is reater )&i%e t&e )&ee% %oad bendin moment a%on t&e %oner span is severer# Hence t&e moment or trac9ed %oad )i%% be ta9en a%on s&orter direction and moment a%on %oner direction )i%% be considered rom )&ee% %oad in t&e desin o  dec9 s%ab# 3.6.3 8IND LOAD ANAL
Since t&e str;ct;re is open in %onit;dina% cross section and it &as a%% possibi%ities t&at it )i%% be dro)ned inside )ater ;p to HC< %eve% d;rin storm= as t&e storm occ;rs in t&e tropica% reion especia%%* in India d;rin rain* season most o t&e times# Hence t&ere is no need to consider t&e %atera% )ind orce# B;t sti%% considerin )orst condition5 %ets ca%c;%ate t&e ;p%it orce# IS "+' ,part-III4 : !."+ )i%% be ;sed or t&is p;rpose# As per c%a;se-'#$5 IS "+' ,part - III4:!."+ sa*s t&at desin )ind speed is iven b* 5 V=  V% * 1 * 2 * 3 b @ '2 m7sec ,Appendi -A4 @ !"2 9mp& ,or B&;banes)ar 8one4 As per c%a;se  '#$5 t&e )ind speed is considered constant ;p to t&e &ei&t o  !2m o an* str;ct;re# * 1  1.4 ,Tab%e-!45 * 2  1. ,Tab%e-15 (ateor* -15 c%ass - A4 and * 3  1 ,Q @ 225 c%a;se  '#$#$#!4 Hence 8 @ !"2 × !#2" × !#22 × !#22 @ !.3#32 9mp& ≈ 1229mp& @ ''#'0 m7sec Fsin c%a;se- '#35 p8 @ 2#081 @ 2#0 × ,''#'041 @ !"'1#!' N7m1 @ !#"' 9N7m1  T&e so%idit* ratio is eM;a% to 22 in o;r case# Hence R @ 22 Crom tab%e-+ ,pae -!.45 ta9in  @ 22andR @ 22 5 (! @ ,-4!#3 @ !#3 ,s;ction4 As per c%a;se  0#1#1#+ ,pae - 1+4 or over&ans s%opin ;p)ard5 (1 @ 2#+' and t&e positive sin indicates t&at t&is )i%% be actin do)n)ard# Hence tota% press;re orce per ;nit r;n on t&e s%ab )i%% be ca%c;%ated separate%* or t&e canti%ever and intermediate road )a* section#

• • •

BY: ABHISEK PANDA

1.!0 m

Wind "re##ure force

2.1 m

2.1 m

1.!0 m

400 mm

Fig-1 (8in+ #"$+ "n S/>! St!/)t/!,

 T&e press;re distrib;tion is as s&o)n in t&e ;re# C;p%it7 m r ; n @ (!p8A @ !#3 ×  #"' ×  3#1 × !"#$$7!"#$$ @ !2#"+" 9N7m Cdo)n)ard 7m r;n @ (1p8A @ 2#+' ×  !#"'×  $#0 × !"#$$7!"#$$ @ 3#..' 9N7m ≈ '9N7m Hence it can be seen t&at t&e canti%ever section )i%% not be eperiencin an* ;p%it orce and t&e )ind press;re )i%% be in t&e same direction as t&at o t&e %ive %oad# A%so it can be noted t&at as per c%a;se  1!1#' o I( 0: 12!35 no %ive %oad )i%% be considered on t&e dec9 )&en )ind speed eceeds !$2 9mp&# No) t&e %onit;dina% irders can be seen as %oaded as be%o) ;re or intermediate spans#

4207.50 mm 10.!7! kw$m

Fig-11 (8in+ #"$+ $)ting L"ngit/+in$##? "n S/>! St!/)t/!,

 Tota% ;p)ard orce actin on one s%ab pane% is iven b*5 !2#"+" × 3#12+' @ 3'#++ 9N  .'#$$ ×2#" @ +0#103 9N ,dead %oad o s%ab

• • •

BY: ABHISEK PANDA

pane%4# Hence it can be conc%;ded t&at since ;p%it press;re is %esser t&an t&e dead )ei&t o s%ab pane% itse%5 no daner o neative s;ction and &ence )ind press;re need not be considered# A%so as t&e e%evated area o t&e s%ab pane% is M;ite %ess5 t&ere is no daner o %atera% press;re# Hence t&is can be omitted# 3.6.; S@EAR FORCE CALCULATION FOR INTERIOR SLAB PANEL: 3.6.;.1

8'# L"$+ S'$!:

Co%%o)in I(-!!1:12!! ,B-$#$5 Anne- B-$45 t&e dispersion o %oad t&ro;& )earin coat / s%ab )i%% be at 3'U# Hence dispersion o %oad is iven b* 2#"'G1,2#2"G2#1'4 @!#'!m# Cor maim;m s&ear to occ;r 5 t&e %oad dispersion s&o;%d be )it&in ace o  irder# So )&ee% %oad )i%% be 9ept at %east !#'!71@2#+''m rom t&e %onit;dina% irder ace= as s&o)n in t&e ;re#

Fig-12 (L"$+ +i>!i"n t'!"/g' +)* #$%,

eerrin I(-!!1:12!!5c%a;se-B $#1,pae-1+"45

−a /¿ %24Gb!

1

be @a,

4.2075

b7%2 @

2.1

@ 1#22$ V 1#22

  @1#0 %2@1#! a@2#+''m b!@$#0G1

×

be@1#0 × 2#+'',   @'#2!+m

2#2"@$#+0m

−0.755 /2.1 4G$#+0

1

• • •

BY: ABHISEK PANDA


@

5.017

 @ 0.#+0$

(

− 0.755)

69.763 × 2.1

?aim;m s&ear orce @

2.1

@33#0"! 9N7m S&ear orce )it& impact d;e to trac9ed ve&ic%e @ 3.#!' 9N7m 3.6.;.2 D$+ #"$+ '$!:  Tota% dead )ei&t@ "#30 KN7m1 8.46 × 2.1

 Tota% dead %oad s&ear@

2

@ "#""$ 9N7m

3.6.5 DESIGN BENDING OENT AND S@EAR FORCE:

 Toa% ?B @ $#"!G1"#'"@$1#$. KN-m ?% @ !#"13G!.#+0@1!#'"3 KN-m  Tota% s&ear orce@,"#""$G3.#!'4 KN7m @'"#2$ KN7m Since )e &ave considered %imit state met&od t&e above %oad va%;es )i%% be !#' times t&at o ca%c;%ated as per Ane A1 o I(: !!1-12!! So ?B @ 3"#'"'

'2 9N-m

?% @ $1#$+0

$$ 9N-m

; @ "+#23' 9N7m ?inim;m efective dept& as per maim;m bendin moment is iven b* d @

√(

6

50 × 10 0.36 × 35 × 0.48 × 10

3

× ( 1−0.416 × 0.48 ))

@ !2!#0$' mm As per tab%e  !3#15 c%a;se !3#$#1#! ,pae !314 o I(!!1: 12!!5 (%ear cover @32G"@3" mm So5 d @ 1'2 −¿ 3" @121 mm V !2!#0$ mm ,o94 Fsin !0 mm- ∅  bars5cover or s&ort span @ 1!2 −¿ " @121mm and cover or %on span @121 −¿ !0@!"0 mm# 3.6.6 REINFORCEENT DETAILS FOR INTEROIR SLAB PANEL: (i,A!$ " t# $#"ng '"!t +i!)ti"n

• • •

BY: ABHISEK PANDA

,Ast4B @

0.5 × 35 415

× ⌊ 1−

√

6

−

4.6 × 50 × 10

1

35 × 10

3

3

2

× 202

 ⌋ × 10 × 202

As per c%a;se -!0#0#!#! o I(:!!1-12!! f ctm × × bd ,Ast4min @ 2#10 t f  yk 

Crom tab%e -0#' ,Pae-$"4o I( :!!1-12!! Cctm@1#" N7mm1 C*9@ 3!' N7mm1 Bt@!222 mm D @ 121 mm ,Ast4min@$'3#$'! mm1 A%so same c%a;se specied ,Ast4min@2#22!$btd @ 101#0mm1 ,Ast4ma@2#21'Ac @2#21' × 250 × 1000 =6250 mm1

Spacin o bars as per c%a;se-!0#0#!#!,34 o I(-12!! is5 sma 1& @ 1 × 1'2 @ '22 mm In o;r case5spacin o !0 mm S ¿

/

1000 × π  4 × 16

∅

 bars is

2

716.008

@1"2#"!!mmV 1'2 mm A%so as per c%a;se-!'#1#! ,14 o I(:!!1-12!!5  T&e c%ear distance bet)een t&e para%%e% main reinorcin bars s&o;%d not be %ess t&an dG!2@12G!2@$2 mm and 12 mm 5 )&ic&ever is reater D@ areate si8e @ ass;med 12mm or s%abs5 providin !0 mm- ∅   bars 6 11'mm c7c ,,Ast4B4provided  @

/

1000 × π  4 × 16

2

225

@".$#0! mm1 A%so as per c%a;se -!1#1#15 pae  !12 o I(:!!1-12!!5 ;nder rare combination o %oads5t&e maim;m tensi%e stress %imits to 2#"  * is to avoid ine%astic strain5 ;ndesirab%e crac9in7deormation o str;ct;re and a%so to acco;nt or %on term creep#

• • •

BY: ABHISEK PANDA

e &ave ca%c;%ated t&e stee% area ta9in  *d@2#"+ *9 , as per c%-!'#1#$#$ I(:!!1-12!!4 (onsiderin t&e )orst case i#e rare combination o %oads5 additiona% stee%

−0.8

area reM;ired @!

 @ 2#2"2 @ " o reM;ired stee% area#

0.87

8

So " o ,Ast4reM;ired @

100

×

+!0#22' @ '+#1" mm1

Ast to be provided@+!0#22'G'+#1"@++$#1" mm1 ".$#0! mm1  (At,B>!"0. 493.61 2 (ii, A!$ " t# $#"ng #"ng +i!)ti"n

Providin !1mm- ∅  bars5

,Ast4< @

0.5 × 35 415

,Ast4min@2#10

×

×

[ √ −

1

f ctm f  yk 

6

−

1

4.6 × 33 × 10 3

35 × 10

2

× 190

×b f  ×d

]

3

× 10 × 190

@ 3"2#'$ mm1

, c%-!0#0#!5I(:!!1-12!!4

Cctm@ 1#" N7m1 ,tab%e-0#' o I(:!!1-12!!4 ,Ast4min @2#10

×

2.8 415

× 1000 × 190

 @$$$#$2! mm1

A%so as per same c%a;se 5 ,Ast4min @2#22!$btd@13+ mm1 ,Ast4ma@ 2#21'Ac@2#21' × 250 × 1000

@01'2 mm1

Spacin o bars as per c%a;se-!0#0#!#!,3 o I(:!!1-12!! is5 Sma ¿  1&@1 × 250=¿  '22 mm or 1'2mm , sma%%er va%;e is ta9en4

,o94

• • •

BY: ABHISEK PANDA

S@

/

1000 × π  4 × 12

2

  @1$'#$0mm

480.53

Hence providin spacin o bars 6!+' mm c7c / ;sin !1mm

,,Ast4%4provided  @

∅  bars

2

/

1000 × π  4 × 12 175

@030#$2 mm1

A%so as per c%a;se-!'#1#!,14 o I(:!!1-12!!5 t&e c%ear distance bet)een t&e para%%e% main reinorcin bars s&o;%d not be %ess t&an d G!2@12G!2@$2 mm or 12 mm ,%arer va%;e is ta9en4# A%so asper c%a;se-!1#1#15P-!12 o %oads 5t&e ma tensi%e stress in stee% is %imited to 2#" *9 to avoid ine%astic stain 5;ndesirab%e crac9in7deormation o  str;ct;re / a%so to acco;nt or %on term creep#

−0.8 Hence more area reM;ired is @ ,!

0.87

4,Ast4reM;ired

@2#2" × 3"2#'$@$"#33 mm1

 

,Ast%4reM;ired or creep crac9in  @3"2#'$ +¿ $"#33 @'!"#.+ mm1 030#$2 mm1 ,Ast4<#prov@030#$2 mm1 ∗

Cor detai%ed reinorcement provision5 p%ease reer to Appendi B attac&ed )it& t&is t&esis#

3.6.7 S@EAR C@EC IN INTERIOR DEC SLAB PANEL:

;"+#23' KN7m @ Ed# rdc @

[ 0.12 k (80 ρ f  1

dc @,minG2#!'

K@!G

√

) + 0.15 σ cp ] b)d

σ cp

200

d

0.33

 ck 

@ !G

4b)d

√

,c%a;se- !2#$#15 I(:!!1-12!!4

,minim;m4

200 250

@!#".3  1#2 ,o94

• • •

BY: ABHISEK PANDA $71

!71 c9

min@ 2#2$!K     ρ1=

A st  bw d

 ≤

@2#2$! × 1.995

3 /2

0.5

× 35

@2#3+" and

σ cp =0

2#21 @".$#0!71@330#"2 mm1

As% @, Ast4B 71

b) @!2225 d @ 121  ρ1

−3

@ 1#1! × 10

@2#2211!  2#21

,o94

[ 0.12 × 1.894 × (80 × 0.00221 × 35 ) ] × 1000 × 250 0.33

dc@

@!2$#0"3 KN7m

,dc4min@!!.#'2 KN7m So minim;m s&ear resistance isdc@ !!.#' KN7m No s&ear reinorcement is necessar* in s%abs# 3.6.4 DESIGN OF CANTILEVER SLAB:

≫

 Ed @ "+#23' KN7m

• • •

BY: ABHISEK PANDA

Fig-13 (C$nti#0! >"!ti"n " S#$%, 3.6.4.1

D$+ #"$+ "nt:

Hand rai% ,%;mp s;m4@1 KN
@$#3' 9N-m

#(#( post @ 2#!' × 0.15 × 1 × 25

@2#'01 9N


@'#1' 9N


Li0 #"$+ "n !%:

<#< @322 97m1@3 KN7m1
• • •

BY: ABHISEK PANDA

<#<@3 × 2#0@1#3 KN7m
,c%- 12. o I(:0-12224

"nt +/ t" &'# #"$+:

As per I(-0:12!25 on%* I(-c%ass A / I(-c%ass-B e&ic%es can come to t&e canti%ever portion5since it can &ave a minim;m distance !'2 mm rom 9erb #

57 kw 150 mm

500 mm

0.5 m

Fig-1; (8'# #"$+ "n )$nti#0! #$%,

Fsin I(-!!1:12!!5 Anne;re:B-$,145Pae-1+.5 efective dept& ,Be 4@ !#1aGb! a@2#0' m b!@   0.25 + 2 × 0.080

@2#3! m

• • •

BY: ABHISEK PANDA

Be @!#1 × 0.65 + 0.41  @!#!. m
√

dreM;ired @

6

119 × 10 3

0.36 × 35 × 0.48 × 10

×( 1−0.416 × 0.48 )

@!'0#"2 mm ∅  bars5

Providin 32 mm c%ear cover /!0 mm Efective dept& provided is

dprovided @322-,32G"4@$'1 mm ≫ !'0#"2

,o94

3.6.9 REINFORCEENT IN CANTILEVER SLAB:

?ain reinorcement is iven b* 0.5 × 35

,Ast4main @

415

[ √ 1

−

6

1

−

4.6 × 119 × 10 35 × 10

3

2

× 352

]

3

× 10 × 352

@.0"#32'0 mm1 Spacin o !0 mm- ∅  bars is iven b*

S

@!222

 π  2 × × 16 4

@12+#0 mm

Providin !0 mm- ∅  bars 6 !.2 mm c7c5 ,Ast4main @ !2'"#11 mm1

• • •

BY: ABHISEK PANDA

Distrib;tion moment is iven b* ?dc @ !#' × [ 0.3 × 56.043 + 0.2 × 25.02 ] @$!#.3! 9N-m Distrib;tion reinorcement is ,Ast4dc @ $3.#1 mm1= Providin !1mm- ∅ bars 6 !+' mm c7c ,Ast4dcOprovided @030#1+ mm1 ¿  $3.#1 mm1 

,o94

Detai%in o reinorcement is done in Appendi-B

∗

3.6.1

C@EC FOR S@EAR IN CANTILEVER PORTION:

 Tota% s&ear@dead %oad s&ear G %ive%oad s&ear 5.7

@ 1$#!01 +¿ !#' × 1.19 + 2.4 = 97.411 ,)&ere !#!.@ be ,Anne-B$5I(:!!1-12!!44 Desin s&ear @ !#' × 97.41 @ !30#!!' 9N@Ed As per c%a;se-!2#$#1,14 o I(:!!1-12!!5 S&ear resistance o a str;ct;re is iven b* / dc @2#!19 (80 ρ1 f ck ) +(0.15 σ cp )¿ b w d 1 3

S;bWect to min dc@,minG2#!'

K@!G

√

200

d

@!G

√

200 400

σ cp

4b)d

@ !#+ ¿

min@2#2$!9$71 c9!71  

/

/

3 2 1 2 @2#2$! × 1.71 × 35  

@2#3!

1#2

,o94

BY: ABHISEK PANDA

• • •

 ρ

 A sl ! @ bw d

1058.22

@

1000 × 400

−3  @ 1#03' × 10

−3

dc@2#!1 × 1.71 × ( 80 × 2.645 × 10 × 35 ) ,dc4min@2#3! × 1000 × 400

1 /3

3 O × 10 × 400

@!03 9N

¿ Ed @!30#!' 9N

Xdc @!03 9N

@!'"#.$ 9N

,o94

A%so I(:!!1-12!!5c%-!2#$#1,'4 specied t&e o%%o)in criteria# ed ≤ 2#'b)dv cd

@2#0!

− f ck  310

O

−35   @2#0!

310

O@2#'$1

So 2#'b)dv cd@ 2#' × 1000 × 400× 0.532 × 0.36 × 35 @!$32#03 KN ¿  Ed 

,o94

 T&e %ive %oad app%ied is 2#0' m rom t&e ede o s;pport# T&e same c%a;se species t&at is t&e app%ied %oad is at av i#e 2#'d to 1d ,122mm to "22mm 45t&en t&ere )i%% be red;ction actor m;%tip%ied to  ed#So in o;r case t&e dead %oad s&ear )i%% be as its i#e 1$#!01 KN B;t %ive %oad s&ear )i%% be ,!#'  β  @ red;ction actor@a 71d v

av@ 0'2 mm  β  @

650 2 × 400

@2#"!1'

×

57 1.19

4

×β

• • •

BY: ABHISEK PANDA

%s@!#'  

57

×

1.19

× 0.8125

@'"#$++KN

 Tota% s&ear@"3 9N ed@!10 KN

¿ !10 9N

dc@!03 KN ∗

,o94

It ma* be noted t&at t&e do)n)ard )ind orce )i%% be on%* ' × !#"@. KN aainst %ive %oad "0#11 KN# Hence5 t&ere is no need o combination o %oads ta9in )ind efect in to acco;nt#

3.6.11 DEFLECTION C@EC FOR CANTILEVER SLAB:  T&e deection )i%% be c&ec9ed as per is 3'0:1222#since )e &ave diferent %oadin at diferent positions5)e &ave to consider t&em separate 3.6.11.1

Fi!t T!$i# (Ann-) " i ;56:2,:

S'"!t t! +)ti"n

,Ir4end@

b× d 12

3

3

=

1000 × 200

8

=6.67 × 10 mm

12

4

8 4 8 4 ,Ir4mid @   22.5 × 10 mm , ( I gr ) at 0.65 m= 29.35 × 10 m m

Ccr @

0.7 √ f  ck 

2

=4.141 N / m m 8

,?r4end@ ,?r4mid @

4.141 × 6.67 × 10

=27.6 kN −m

100 4.141 × 22.5 × 10

8

150

=62.115 kN −m

,?r42#0'm@+3#!'" 9N-m Ec @   5000 √ f ck =2.958 × 10  N / m m 4

5

Es @

2 × 10

2

N 

 E s  , m= =6.76  E c mm 2

 Transormed area o compression stee% @,m-!4ZAsc @$31+#.$mm1

• • •

BY: ABHISEK PANDA

 Transormed area o tension stee%@mZAst @  

7152.08 mm

2


1000 × x ×

2

[r

500 x

 x 2

+ 3427.93 × ( x −46 )=7152.08 × (152 − x )

+ 10580.01 x −1459363.34 = 0

[r @33#3+mm 2

500 x

At mid5

+ 10580.01 x −1960008.94 = 0

\@'1#.1mm 2

At 2#0'm5

500 x

+ 10580.01 x −2158693.7 =0

\@''#.+mm 2

2

%#& = 105!mm

105! mm

200 mm

30 0 mm

2

%#c = 5'5mm

1000 mm (end)

1000 mm (mid)

2

5'5 mm

2

105! mm

327.7! mm

1000 mm (a& 0.5m)

2

5'5 mm

Fig-15 (A!$ " Rin"!)nt in +i!nt )ti"n " )$nti#0! #$%, 1

,Ir4end@ @ 

3

1.117 × 10

,Ir4mid @  

3

2

× 1000 × ( 44.47 ) + 3427.93 × ( 44.47 −46 ) + 7152.08 × ( 152−44.47 ) 8

mm

4

8

3.1264 × 10

,Ir4at 2#0'm @  

2

mm 8

5.58 × 10

4

mm

4

8@ %ever arm iend@2#.d@!$0mm58mid@110mm58at 2#0'm@1'!mm ,?4end@9erbGport/rai%inG%#d;e pedestrian@+#3"G$#3'G2#.+G3#$'G$#13@!.#3.9n-m ,?mid4@)#cG#( s%ab@!$#!19n-m

to

BY: ABHISEK PANDA

• • •

?2#0'm@)&ee% %aod@30#+29n-m i m

(

)

(¿¿ r )end  z end  x end b w × × 1− ( ) 1.2− ( m)end d end d end b ,Ief 4end@ @ (¿¿ r )end ¿ ¿ 8

3.67 × 10

8

1.117 × 10 1.2

−

  27.6 19.49

4

mm

 I   I   I  (¿¿ gr )end ( k ) (¿¿ eff )end <¿ (¿¿ r )end <¿

¿

 I 

−¿ ¿  I  (¿¿ r )mid (¿¿ eff )mid =¿

¿

 I   I  8

So

(¿¿ r )mid=3.1264 × 10 m m (¿ ¿ eff )mid=¿ ¿

4

8 4 ,Ief 4at 2#' m@   88.84 × 10 m m >¿ ,Ir4at 2#0'm

So ,Ief 4at 2#0' m@  

8

29.35 × 10

mm

4

3   10212 × ( 1800 ) wl ! 1 = =1.83 mm , 4end@ 3 E c I r 3 × ( 2.958 × 104 ) × ( 3.67 × 10 8) 3

,

! 1

(

15350 × 1800

4mid @

(

4

8 × 2.958 × 10

3

)

) × (3.1264 × 10 ) 8

=1.21 mm

×

 136 152

( 1−

44.47 152

) @

• • •

,

BY: BY: ABHISEK PANDA ! 1

1

4At 2#0'm @  E c I r

[

1.15 × w × l 2

2

+

 ] =

wl 3

3

0.64 mm

 Tota%  Tota% deection d;e to s&ort tern %oadin @$#0"mm D)ti"n +/ t" '!in*$g acs@9$Ψcs%1 9$@2#',or canti%ever4 pt@2#+ 5pc@2#3  pt − pc

93@2#+1

 pt  √  p

=0.26 <1.0

2#1'≤ pt − p c =0.3 < 1.0 ( k ) ,Ψcs 4end@

−7 3.9 × 10

acs@2#0$mm Note-:&ere at ot&er points5t&e ]Ψcs )i%% ive m;c& %esser va%;e re%atin re%atin %east s&rin9ae deection# Deection d;e to creep Ece @

 Ec 1

+"

" @!#0,or 1"-da*s strent&4

Ece @  

4

1.1377 × 10

 N / m m

2

m @Es7Ec @ !+#'"  Transormed  Transormed area or compression stee% ,m-!4Asc @ ."03#+ mm1  Transormed  Transormed area or tension stee% mAst @ !"'."#.$ mm1
!222××

2

 G ."03#+×,-304 @ !"'."#.$×,!'1-4

[r '221G1"30$#0$  $1"2"!$#'0 @ 2 [r  @ '+#32 mm At mid: '221 G 1"30$#0$  '!32+20#'0 @ 2 [r  @ +0#"'$mm At 2#0' m: '221 G 1"30$#0$  '0'+$"3#"$' @ 2 [r  @ "!#0' mm

• • •

BY: BY: ABHISEK PANDA

Same %ever arm as ;sed beore )i%% be ;sed# 1  I r .end  = × 1000 × (57.4)3 + '!4.70(57.4 − 4)2 + 1!5'!.'3(152 − 57.4)2 3

So Simi%ar%* Ir#mid @ +#$×!2" mm3 and Ir at 2#0'm @ .#11×!2" mm3

= ( I r .eff ) end  end 

 I r .end   M  b z x 1.2 − ( r  )end × ( )end × (1 − ) end ×  w  M d d b

@ 1#$2×!2" mm3

= 5.5' × 10! mm4

So Ir#end Ief#end Ir#end ,[K4 8 4 Simi%ar%* ,Ief 4mid@ −4.17 × 10 m m < ¿ ,Ir4mid 8

,Ief 4mid @

7.3 × 10

,Ief 4at 2#0'm @  

mm

4

8

29.35 × 10

mm

4

B;t in t&is case 5or ca%c;%atin perm# (reep ;sin above eM;ations / E ce5on%* permanent %oad )i%% be ta9en care o #no %ive %oad )i%% be t&ere So ,4end@9erb G#( po%/rai%in@'#1'G1#'01@+#"!1 9N7m ,4mid @#(G#(  @#(G#( s%ab@!#"'G!$#'@!'#$' 9n7m ,ai#cc4perm@

( # end end ) × l

3

3 E ce × I eff 

3

+

(# mid )× l

8 E ce × I eff 

@,1#$.G!#$'4mm@$#+3mm S&ort term deection d;e to permanent %oad 7 $ 812 × 10

3

3

3

3

15 $ 35 × 10 × 1800 × 1800 + 4 8 @ 3 × 2 $ 958 × 10 × 3 $ 67 × 10 8 × 2 $ 958 × 104 × 3 $ 1264 × 108

ai#perm

@!#3G!#1!@1#0!mm So deection d;e to creep is iven b* $#+3-1#0!@!#!$mm  Tota%  Tota% deection is @$#0"G2#0$G!#!$ @'#33mm Ho)e Ho )eve verr t&is t&is dee deect ctio ion n )i%% )i%% be %ess %esser er in prac practi tica ca%% as mor more acc; acc;ra rate te ca%c;%ations )i%% revea% t&e res;%t As per c%a;se !1#3#! o I(:!!1-12!!5t&e deection s&o;%d be %imited to @ cantile%er cantile%er span 375

• • •

BY: BY: ABHISEK PANDA 1800

@

375

= 4.8 mm < 5.44 mm

N"& #t )')* it $ >! )#-23.2 " i:;56-2  s@112#1+5 pt@2#+ ?odication actor@!#1,-35p-$"4 pc@2#3 ?odication actor@!#!1 span =7 (fr cantile%er ) dept&

Basic

span dept& @+×!#!1×!#1@.#32"

?odied [;r

span dept& @ 0.#32",o94

B;t revisin t&e section as providin !0 R bars 11'mm c7c / !1mm R bars611'mm bars611'mm a%ternative a%ternative%*/r %*/rec&ec9 ec&ec9in5t in5t&e &e deection deection criteria criteria is satised# satised# 1 Hence tota% reinorcement provided is iven b* !$.0 mm # 3.6.11 3.6.11.2 .2 S)"n+ S)"n+ T!$i T!$i##- R)')* R)')*ing ing " +)t +)ti"n i"n "! C$nti#0 C$nti#0! ! S#$%(Ann ) " IS-;56:2,: S'"!t t! +)ti"n ,Ir4end@

b× d

3

12

3

=

1000 × 200 12

8

=6.67 × 10 m m

4

8 4 8 4  I gr ) .65 m= 29.35 × 10 m m ,Ir4mid @   22.5 × 10 m m , ( I

Ccr @

0.7 √ f  f  ck   ck 

=4.141 n / m m

2

8

,?r4end@ ,?r4mid @

4.141 × 6.67 × 10

=27.6 kN −m

100 4.141 × 22.5 × 10

8

150

=62.115 kN −m

,?r42#0'm@+3#!'" 9n-m f ck =2.958 × 10  N / m m Ec @   5000 √ f  4

5

Es @

2 × 10

n

 E s  , m= =6.76  E c mm 2

2

• • •

BY: ABHISEK PANDA

 Transormed area o compression stee% @,m-!4ZAsc @$+12#.0mm1  Transormed area o tension stee%@mZAst @  

2

9436.96 m m


  1000 ×

500 x

2

x×

 x 2

+ 3720.96 × ( x −46 )=9436.96 × (152− x )

+ 13157.92 x −1605582.08 =0

@@3'#21mm At mid @

500 x

2

+ 13157.92 x −2549278.08 =0

\@'.#3'mm At 2#0'm @

500 x

2

+ 13157.92 x −2811436.83= 0

\@01#.+mm 1

,Ir4end@

3

× 1000 × ( 45.02 ) + 3720.96 × ( 45.02− 46 ) + 9436.96 × ( 152 −45.02 ) 3

2

2

8 4 @   1.38 × 10 mm

,Ir4mid @

4.2 × 10

,Ir4at 2#0'm @  

8

mm

4

8

5.27 × 10

4

mm

8@ %ever arm# 8end@2#.d@!$0mm58mid@110mm58at 2#0'm@1'!mm ,?4end@9erbGport/rai%inG%#d;e pedestrian@+#3"G$#3'G2#.+G3#$'G$#13@!.#3.KN-m ,?mid4@)#cG#( s%ab@!$#!1KN-m ?2#0'm@)&ee% %aod@30#+2KN-m i m (¿¿ r )end  z end × × 1.2− ( m ) d ,Ief 4end@ end end (¿¿ r )end

(

¿ ¿

−

1

 xend d end

)

@

4.5 × 10

8

mm

4

to

• • •

BY: ABHISEK PANDA  I   I   I  (¿¿ gr )end ( k ) (¿¿ eff )end <¿ (¿¿ r )end <¿

¿

 I 

−¿ ¿  I  8

(¿¿ r )mid= 4.2 × 10 m m (¿ ¿ eff )mid =¿ ¿ ,Ief 4at 2#0' m@  

4

8

54.44 × 10

4

m m <¿ ,Ir4at 2#0'm@

8

  29.35 × 10

mm

4

3

wl ! 1 , 4end@ 3 E c I r =1.5 mm , , ! 1 4mid 1

 E c I r

[

1.15 × w × l 2

2

+

 ] =

wl 3

@

0.9 mm

5

3

0.64 mm

 Tota% deection d;e to s&ort tern %oadin @$#23mm D)ti"n +/ t" '!in*$g acs@9$Ψcs%1 9$@2#',or canti%ever4 pt@2#.1 5pc@2#31' 93 ¿ 0.37 < 1.0 2#1'≤ pt − p c =0.495 < 1.0 ( k ) ,Ψcs 4end@  

−7 5.55 × 10

acs@2#.mm Deection d;e to creep-: Ece @

 Ec 1

+"

" @!#0,or 1"-da*s strent&4

, ! 1 4At

2#0'm

@

• • •

BY: ABHISEK PANDA

Ece @

 Es

N 

4

  1.1377 × 10

mm

 5m@  E ce =17.58

2

 Transormed area o compression stee% @,m-!4ZAsc @!2+!2#0"mm1  Transormed area o tension stee%@mZAst @  

24541.68 mm

Dept& o ne;tra% ais at diferent section At end at mid \@0$#1mm @"'#'00mm 8

,Ir4end@   2.80 × 10 mm

4

5

8

,Ir42#0'm@   2.80 × 10 mm

,Ir4mid@  

8

9.03 × 10

2

at 2#0'm @.!#2"mm

mm

4

4

8 4 ,Ief 4mid@ −5.63 × 10 m m <¿ ,Ir4mid 8

6.08 × 10

,Ief 4end @  

,Ief 4at 2#0'm @  

mm

4

47.80 × 10

8

 ,4end@+#"!1 9N7m5 ,ai#cc4perm@

( # end ) ×l

3

3 E ce × I eff 

mm

4

= )&ic& s&o;%d not be reater t&an Ir at 2#0'm

,4mid @!'#$' 9N7m 3

+

(# mid )× l

8 E ce × I eff 

@,1#1G!#!4mm@$#$mm S&ort term deection d;e to permanent %oad 3

7.812 × 10

3

3

3

  15.35 × 10 × 1800 × 1800 + 4 8 @ 3 × 2.958 × 10 × 3.67 × 10 8 × 2.958 × 10 4 × 3.1264 × 10 8

ai#perm

@!#3G!#1!@1#0!mm Deection d;e to creep @ 2#0.mm ≈ 2#+2mm Hence tota% deection @ $#23 G 2#.G2#+ @ 3#03 mm  3#" mm ,o94 3.6.12

ANC@ORAGE LENGT@ OF BARS:

3.6.12.1

Int!+i$t D)* S#$% P$n#:

(i,

In '"!t +i!)ti"n:

main bars @ !0 mm ∅ 6 11' mm c7c

,%b#net4B@

' a lb ×

 A st re(  A st pr%ided

,pae no-!'15 c%-!'#1#3#$5 o I(:!!1-12!!4

• • •

BY: ABHISEK PANDA  A st re(

716.005

 A st pr%ided  @ ' a

 @2#"0'

893.61

@! ,or strai&t bars4

%b @9 ∅ ∅ × 0.87 f  y

@

4 f bd

16 × 0.87 × 415

@

,  bd@$#2 N7mm1 tab%e-!'#$ o pae

4 × 30

-!'25I(:!!1-12!!4 @3"!#3 mm A%so 9@$2

 or ?$' concrete o tab%e-!'#3 o I(:!!1-12!!O

%b @ $2 × 16  @ 3"2 mm %ets ta9e %b@3"2mm ,%b#net4B @! × 480 × 0.865 @3!'#2 mm )  312 mm %b#min @2#$%b @!33 mm

,or tension anc&orae4

%b#min @2#0%b@1"" mm

, or compression anc&orae4

%b#min@!2 ∅ @!02 mm or !22 mm %b#net ¿ %b#min (ii,

,o94

In #"ng +i!)ti"n:

 A st$ re(  A st $ pr%ided  @

480.53 646.30

@2#+3$

2#+'

• • •

BY: ABHISEK PANDA ' a

@!

,or strai&t bars4

%b @9 ∅ @$2 × 12 @$02mm 12 × 0.87 × 415

or %b@

 @ $0!#2' mm

4×

So %b @ $02 mm %b#net @! × 360 × 0.75  @ 1+2 mm %b#min @2#$%b@!2" mm

,tension anc&or4

@2#0 %b@1!0 mm

,compression anc&or4

%b#min @!2 ∅  @!12 mm or !22 mm %b#net ¿ %b#min 3.6.12.2

C$nti#0! #$%:

 A st$ re(

872.56

 A st $ pr%ided  @ ' a

1058.22

@2#"13

,c%-!'#1#3#$ o I(:!!1-12!!4

 @!

%b@9 ∅  @$2 × !1@$02 mm %b#net @2#"13 × [email protected]#03 3.6.13

$22 mm

CANTILEVER SLAB STIFFENING:

As per c%a;se -!0#0#!#3-,!4,a4/,b4 o I(:!!1-12!!5t&e ;ns;pported ede o a s%ab para%%e% to trac /be*ond t&e c%ear road )idt& /&avin var*in dept& s&a%% be stifened at an* partic;%ar point to t&e resistin moment o '22mm adWacent strip at t&at partic;%ar point# 93.61

,Ast B42#'m stripOin main s%ab bet)een irder @

2

= 446.805 mm

2

• • •

BY: ABHISEK PANDA 1396.26

,Ast B42#'m stripOin canti%ever section @

2

2

646.27

,Ast %42#'m stripOin main s%ab bet)een irder @

2

=323.135 mm

646.27

,Ast <42#'m stripOcanti%ever s%ab bet)een irder @ 3.6.1;

2

= 698.132 m m > 446.805 m m ( k )

2

2

=323.135 mm

2

DESIGN OF LONGITUDINAL GIRDER:

Efective span@!"#$$ m rid )idt&@322mm s%ab t&ic9ness@1'2 mm ?ain beam spacin@1#' m Dept& o rib @ !322 mm  Tota% dept& @!322G1'2G!'2@!"22mm@D ($,

REACTION FACTOR:

(o;rbons met&od can be app%ied to o;r desin since span to dept& ratio is reater t&an 1# Arranement o c%ass-AA trac9ed %oad or maim;m eccentricit* is as iven be%o)#

* = 0.075 m

2.0 5m

% e = 1.1m

+ B

7.5 m

Fig-16 (A!!$ngnt ))nt!i)it?,

As per (o;rbons orm;%a 5

"

)#$-AA

t!$)*+

#"$+

"!

$i/

BY: ABHISEK PANDA

• • •

∑w

@

+ ∑ I 

∑d

!

n

deO

2

 x

@eaction actor It ma* be noted t&at  A@c since t&e same %oadin can be reversed in t)o cases# 2 # 1

A@

3

3 I 

!G

2 × 2.5

2

× I 

× 2.5 × 1.1

O

n@ no o irders @$ d@spacin o irders@1#' m !@$'2 KN ⇒

❑ A@c@

3 × 1.1

w 3

!G

2 × 2.5

O

, @+22 9N @ tota% a%e

%oad 4 B @ 1!7$!G2O @ 1!7$ @2#$$ (%,

DEAD LOAD:

F!" )$nti#0! #$%:

ei&t o parapet rai%in@1 9N7m earin coat@2#2"2 × !#2' ×  11@!#"3" 9N7m (anti%ever s%ab@2#$ × !#" × 1' @ !$#' 9N7m Kerb@2#1" × 0.75 × 25  @ '#1' 9N7m Parapet @ 2#32 9N7m  Tota% dead %oad rom canti%ever s%ab @1$9N7m XTota% dec9 s%ab %oad @1 × 1$G"#30 × '#3 @.!#0"3 9N7m

• • •

BY: ABHISEK PANDA


2#3 × 1.4 × 25  @ !'#'2 9N7m  Tota% )ei&t per irder @ ,$$#1$G!'#'4@3"#+" ≈

49

9N7m

C!" gi!+!:

Dead )ei&t o one cross irder is@2#$ × !#3 × 25 @!2#'2 9N7m  T&is %oad epands ;p to 1#' m bot& sides on intermediate irder Hence reaction rom cross irder @ !2#'2 × 1#'@10#1' 9N  T&e end cross beams )i%% not be considered since t&eir %oads )i%% be direct%* transerred to s;pport t&ro;& piers# Hence end reactions need not be considered#  T&e presentation is as o%%o)s

2.25 k

2.25 k

4.5075 m

4 ,$m 2.25k

4.5075 m

2.25 k

4.5075 m

2.25 k

4.5075 m

• • •

BY: ABHISEK PANDA 2.25 k

2.25k

2.25 k

4' k$m

Fig-17 (R$)ti"n !" C!" Gi!+! "n L"ngit/+in$# Gi!+!,

?aim;m dead %oad bendin moment at center o span is5 ,?ma4dead %oad @

49 × 18.33

2

8

+

26.25 × 18.33 4

+

26.25 × 18.33 4

@1$22 9N-m

 Tota% dead %oad s&ear at s;pport is 49 × 18.33

,dead4s@ (),

2

+

26.25 × 2 2

+

26.25 2

@3""#30

3".9N

LIVE LOAD BENDING OENT IN GIRDER:

Span @!"#$$ m5 Impact @!2= or maim;m bendin moment to occ;r5 t&e %ive %oad is p%aced centra%%* on t&e span as s&o)n be%o)# 3. m

700 k

a = '.15 m

  = '.1 5 m

3.!2

3.!2 a = 4.5!25 e

Fig-14 (P"iti"n " C#$-AA t!$)*+ L"$+ "! $i/ %n+ing "nt,

BY: ABHISEK PANDA

• • •

1


2

,

  3.6825

+ 4.5825 4^  × 700 =2892.75 *N 

−m

  2893 kN 

Bendin

moment )it& impact / reaction actor @2#''$ × 1.10 × 2893 =1759.812 *N − m 1760 kN −m

is

iven

b*

,?%4o;ter irder

,?%4inner irder@2#$$$ × 1.10 × 2893 =1059.711060 kN −m

(+,

LIVE LOAD S@EAR:

Cor s&ear orce to be maim;m5t&e %oadin s&o;%d be arraned as s&o)n lon/i&udinal /irder  +

W 1= 350 k B

3. m W2= 350 k

2.05 m 2.5 m 0.45 m

% 4.5075 m

4.5075 m

4.5075 m

4.5075 m cro## /irder 

1.53 m

be%o)# 1 0.!03 %

B

1 3. m

Fig-19 (Li0 #"$+ $!!$ngnt "! $i/ '$! "!) ,

&ee% %oad p%aced at startin )i%% be ivin maim;m s&ear i#e# startin point o eit&er end= eit&er ]A or ]B # Aain one )&ee% &as to be p%aced on one irder to ive severe efect as t&e distrib;tion %oad )i%% occ;r on%* or one )&ee% %oad# eaction o ])1 on irder-B is iven b* $'2

×

 0.45 2.5

@0$ 9N

• • •

BY: ABHISEK PANDA

eaction o ]1 on irder-A is iven b* $'2

×

 2.05 2.50

 @1"+ 9N

 Tota% %oad on irder B @$'2G0$ @ 3!$ KN 413 × 16.53

?aim;m reaction on s;pport o irder ]B is @

 @ $+1#33 9N

18.33

?aim;m %ive %oad s&ear inc%;din impact @!#! × 372.44 =409.68 410 kN 

TABLE-;(Dign Bn+ing "nt $n+ S'$! "!) "n Gi!+! 4

Bn+ing "ntGi! +!

D.L Bn+ing "nt

L.L Bn+ing "nt

T"t$# Bn+ing "nt

Unit

[;ter >irder

1$22

!+02

3202

9N-m

Inner >irder

1$22

!202

$$02

9N-m

S'$! F"!)Gi!+ !

D.L S'$!

L.L S'$!

T"t$# S'$!

Unit

[;ter >irder

3".

3!2

"..

9N

Inner >irder

3".

3!2

"..

9N

CALCULATION ET@OD:

OF

nE I r 12

A @, π 

4

2

 4

 EI  3 4  + ¿ &

()

π  -  & C @ 2 n 4 ,  + 4,  E I r 4

¿

BENDING

OENT

USING

(, @ENDR<-AEGAR

• • •

BY: ABHISEK PANDA  E I 1

c @  E I 2  @! <@ span o bride dec9 @ !"#$$ m & @ spacin o %onit;dina% irders @ 1#' m n @ n;mber o cross irders @ ' EI @ e;ra% riidit* o %onit;dina% irder (J @ torsiona% riidit* o %onit;dina% irder E E

I 1 I r

/E

I 2

@ e;ra% riidities o t&e o;ter / inner %onit;dina% irders

 @ e;ra% riidit* o one cross beam #  eff = 2.5 m

250 mm

1.!0 m 400 mm

Fig-2 (Si>#i+ T-%$ L"ngit/+in$#gi!+! )ti"n,

As per c%a;se  +#0#!#1 o I( :!!1-12!! 5 t&e efective ane )idt& )i%% be ca%c;%ated# Bef# ! @ 2#1  

×b 1+ 0.1 l 0

@2#1 × 1.05 + 0.1 × 18.33 =2.043 m

2#1%2@$#00m V 1#23$ m B)@2#3 m Bef @1 × 1#23$G2#3

,o94

• • •

BY: ABHISEK PANDA @3#3"0 m

B@ 1#' m 3#3"" m X bef @1#'m 1= m

250 mm

1.!00 mm 300 mm

Fig-21 (Si>#i+ T-%$ C!" gi!+! )ti"n,

bef#!@2#1b!G2#!%2 @2#1 × 2.1037 + 0.1 × 0.7 × 2.5

 

2#1%2 @2#1 × 0.7 × 2.5=0.35 > 0.596 m Xbef#!@2#$' m bef @1 × 0.35 + 0.3=1 m b @3#'2+' mV!m L"ngit/+in$# gi!+!:  A 1+¿ A

2

 A1 x 1 + A 2 x 2  x´ =

¿

+ 2.5 × 0.25 + 1.55 × 0.4

2.5 × 0.25 × 0.125 1.55 × 0.4 × 1.025

@ @2#'+ m

,o94

BY: ABHISEK PANDA

• • •

I<@

2.5 × 0.25

3

12

+ ( 2.5 × 0.25 ) × ( 0.448 ) + 2

0.4 × 1.55 12

3

+ ( 0.4 × 1.35 ) × 0.452 = 0.3795 m 2

4

C!" gi!+!:  A1 . 1+ A 2 . 2  x´ =  A 1+ A 2

¿

 I r =

1 × 0.25

3

12

¿ 0.2261 m

+ 0.3 × 1.55 × 1.025  @2#+!2 m 1 × 0.25+ 0.3 × 1.55

1 × 0.25 × 0.125

2

+ 1 × 0.25 × 0.585 +

0.3 × 1.55

3

12

+ 0.3 × 1.55 × 0.315

2

4

18.33 2.5

 A @

12 4

π 

׿

4

$

×

 5 × E × 0.2261

 E × 0.3795

=144.64

3  J @  a b

b 2500 = =10 a 250 ⇒

❑ / =0.312

, Tab%e-+#$ o N# Kris&na aW; 5Desin o 

Brides 4 b 1550 = = 3.875 a 400 ⇒

❑ / =0.2787 4 3 3  J @ a$ b @ 2#$!1 × 0.25 × 2.5 + 0.2787 × 0.4 × 1.55  @ 2#2$." m

BY: ABHISEK PANDA

• • •

2

C@

π  2.5  0.43 E × 0.0398 × × =0.0102 0 2 ×5 18.33  E × 0.2261

 T)o etreme va%;es o ]C can be ta9en into ana%*sis i#e# C @ 2 or C @ 0 $  1 

√

( 2 √  A ) ¿ 0 − 1  ) (¿  Ta9in C @ 2 or ana%*sis 5 (3 + 2 √  A )  1  2 = 1 3 +¿ 0

⇒

❑ 1  2   @  1 3=¿

3 4 1  =0.83 ( 2r 5ter girder , 2 =0 ) 3

¿

 1 ¿

 2#$0 ,Cor inner irder5 C @ 24

Dign "nt "! t!i"! gi!+! :

Dead %oad moment @ 1$22 9N-m
@ 1".$ × 1.1 × 0.83

 Tota% moment @ 3.3!#22 9N-m

@ 103!#$! 9N-m

¿ 4060 k  N-m as ca%c;%ated ;sin (o;rbons

met&od Int!i"! gi!+!:

Dead %oad moment @ 1$22 9N-m
@!!3'#0$ 9N-m

−m> 3360 kN − m as ca%c;%ated b*

3446 kN 

(o;rbon  s met&od (, ODIFIED COURBONS ET@OD:

e : Internationa% Jo;rna% o scientic / Enineerin researc& o%;me 3 5 Iss;e $ 5?arc&  12!$ ,ISSN 111. -''!"4

• • •

BY: ABHISEK PANDA

St;d* o Efectiveness o (o;rbon ] s T&eor* in t&e Ana%*sis o T  beam brides

6

B*: ?#># Ka%*an / &etti /# P# S&riram As per Wo;rna%5 t&e* &ave st;died t&e 3-%ane / 0-%ane bride o spans var*in !'m-$' or minim;m $-%onit;dina% irders var*in n;mber o irders# T&e* &ave combined (o;rbons met&od /ri%%ae met&od ,STAAD pro4 to et t&e res;%ts# As per Wo;rna%5  p n

1 +

Pi @

ned i

∑ d i 2



Z correction actor  R x

 ∑W  ∑ I × d x × e    1 +  ÷÷ × Correction Factor  2 n  d I  × ∑  x    

[r  @ e &ave ca%c;%ated a @ c@[;ter irder @2#''$) b@inner irder@2#$$$) (orrection actor is iven b*5  Y@ correction actor5@ span o bride \@!"#$$m  y = 0.000134 × (1!.33) 2 − 0.00'! ×1!.33 + 1.05 @ 2#.1!3 ,ro;nded ;p to 3 decima%4 A@(@ ,o;ter irder4 corrected@2#''$Z2#.1!3@2#'2.' B@, inner irder4 corrected@2#$$$Z2#.1!3@2#$20"  Tota% bendin moment [;ter irder@1$22G1".$Z!#!2Z2#'2.'@$.1!#32 KN-m Inner irder@1$22G1".$Z!#!2Z2#$20"@$1+0#$$ KN-m [;t o a%% $-ana%*sis5 Hendr*-Jaear met&od ives t&e &i&est moment Desin moment[;ter %onit;dina% irder@!#'Z3++!#$!@+3!!#'2@+3!1 KN-m Intermediate irder@!#'Z$1+0@'!0. 9N-m Desin s&ear S&ear orce @"+!Z!#'@!$3"#'2 9N (g,

DESIGN OF REINFORCEENT OF OUTER GIRDER:

• • •

BY: ABHISEK PANDA


?; @2#$0Z $'Z 1'22Z ,!02241Z   @!!+"!9N-m Imposed moment ca%c;%ated @+3!1 9N-m@?a ?; VV?a ,&ence ne;tra% ais %ies inside ane section4 0.5 × 35 415

× 1 − 1 −

4. × 7412 × 10 35 × 2500 × 1502

 × 2500 ×150

,Ast4reM;ired @ @!$+32#12 mm1 providin $2mm dia bars as main reinorcin bars5 13740.2 (π  $ 4) × 302

= 1'.43 = 20 no.

 Tota% bars reM;ired @
π 

4

× 30 2 = 14137.17 mm2

So ,Ast4provided@  T&e spacin bet)een %onit;dina% bars is As per IS 3'0:12225 c%a;se-10#$#15 t&e spacin s&o;%d be minim;m o  o%%o)in Diameter o bars @$2mm 'mm more t&an nomina% maim;m si8e o coarse areate @12G'@1'mm [;r spacin is $'#$$ is satisactor*# ∗ Cor detai%in o reinorcement5 p%ease reer to Appendi-Battac&ed )it& t&is t&esis#

• • •

BY: ABHISEK PANDA

(', DESIGN REINFORCEENT FOR INNER GIRDER: d @ !022 mm5 D  @ 1'2mm and b  @ 1#'m Ass;min ne;tra% ais to be )it&in t&e anes5 ?; @ !!+" 9N-m App%ied moment @ ?; app%ied @ '!0. 9N-m  ?; 0.5 × 35  4. × 51' × 10 1 − 1 − 415  35 × 2500 × 1502



 × 150 × 2500 

So Ast#reM @ @ .3'$#02 mm1 Providin !0- 1" mm R bars in 3- ro)s5 ,Ast4provided  @ ."'1#2$ mm1 ∗ Cor detai%in o reinorcement5 p%ease reer to Appendi-B attac&ed )it& t&is t&esis# (i, CALCULATION OF ANC@ORAGE LENGT@: (%a;se -!'#1#3#$ o I(:!!1-12!! O/t! gi!+! a a (¿¿ s ) pr%ided 7lbmin
¿

' a l b ¿


 A  A (¿¿ st ) pr%ided @! at a section (¿ ¿ st ) re(d

¿ ¿ ' a

So

()( ) ∅

%b@

×

4

30

@

@!

4

×

f  yd f bd

 0.87 × 415 3

@.21#01' ) 903 mm

[r %b@9_@[email protected] %b#net @%[email protected]$mm %b#min@2#$%b@1""#.mm or !22mm or !2_@$22mm Inn! gi!+! 28

%b@

4

×

 0.87 × 415 3

%b#net @"3$mm

=842.45 ) 843 mm

• • •

BY: ABHISEK PANDA 2


3

%b#net,!0#'#!#3# o I( :!!1-12!!4

@021mm,o;ter irder4 @'01mm,inner irder4 (H, BAR CURTAILENT:

As )e 9no) )&en t&e %oad is divided in t&e same ratio as t&e span is divided at a point )&ere B#?oment to be ca%c;%ated5 maim;m B#? is obtained# In I
(i, L"$+ $t /$!t! >$n $t ;.5425  !" n+ " gi!+! 0.'m

2.7m

700 k

2.74 2.74 4.5!25

13.7475 m 3.44

Fig-22.1 (B$! )/!t$i#nt-8'# #"$+ $t /$!t! >$n,  T&e %oad arranement is as s&o)n in t&e ;re ta9in I
@

2

[ 3.44 +2.764 ] × 700=2171.40 kN − m

Dead %oad moment: @ 

488.46 × 4.5825

2

− 49 × 4.5825 × 0.5 =1724 kN −m

As per H-J met&od5 )&ee% %oad B? inc%;din impact / coecient 2171.40 ×1.10 × 0.!3 = 1'!2.5 kN − m @

(

 Tota% desin moment on o;ter irder@

1.5 1982.5

 Tota% desin moment on inner irder@

1.5 1724

(

+ 1724 =5560 kN −m)

+ 1.1 × 2171.40 × 0.36 ) @$"+0 9N-

m (ii, L"$+ $t $ +it$n) 6.47; !" n+ " gi!+!

• • •

BY: ABHISEK PANDA 1.35m 2.25m

3.45

3.45

4. 3

.!74 m

11.45 m

Fig-22.2 (B$! )/!t$i#nt-8'# #"$+ $t 6.47; !" n+ " gi!+!,

&ee% %oad moment@

[

700 × 3.45

+ 4.3 ] × 0.5 = 2712.5 kN −m

2 Dead%oad moment@   488.46 × 6.874− [ 49 × 0.5 × 6.874 + 26.25 × 2.2165 ]

@1!319N-m  Tota% desin b#m on o;ter irder d;e to impact and H#J coecient @

+ 2142= 6928 kN −m 1.5 ¿

2712.5 × 1.1 × 0.83

 Tota% desin b#m on inner irders d;e to impact and H#J coecient@

+ 2142 =4825 kN −m 1.5 ¿

2712.5 × 1.1 × 0.36

(iii,L"$+ $t $ +it$n) 2.29125  !" n+ " gi!+!

Fig-22.3 (B$! )/!t$i#nt-8'# #"$+ $t 2.29125 !" gi!+! n+,

&ee% %oad moment@

[

+

700 × 1.6112 2.005

] × 0.5 @!1009N-m

Dead %oad moment@   488.46 × 2.29125−49 × 0.5 × ( 2.29125 )= 991 kN −m  Tota% desin moment on o;ter irder@

(

+

1.5 991 1.1 × 0.83 × 1266

)=3220.30 kN −m

BY: ABHISEK PANDA

• • •

 Tota% desin moment on inner irder@

(

+

1.5 991 1.1 × 0.36 × 1266

) =2238.50 kN − m

,94 REJUIRED STEEL AREA AS PER BAR CURTAILENT: (1,L"$+ $t /$!t! >$n $t ;.5425  !" n+ " gi!+! O/t!

(  A st.reqd  ) o.g  =

0.5 × 35 415

× 1 − 1 −

4. × 550 × 10 35 × 2500 × 150

2

gi!+!:

 × 2500 ×150 = 101'2.3mm2

1 ×

π 

4

× 302 = 1130'.73mm2

Providin !0-$2mm R bars 5,Ast#reMd4[#>@ Note-:3-bars are c;rtai%ed be*ond t&e section providin deve%opment %b#net etension i#e at $#0+.'m rom ends o irders# Inn! gi!+!:  A st$re(

¿ ¿ ¿

@

( A st . prov ) = 12 ×

π 

4

× 2!2 = 73!'.02mm2

Providin !1-1"mmdia bars 5 Note-:3-bars are c;rtai%ed be*ond t&e section providin deve%opment %b#net etension i#e at $#+$.'m rom ends o irders (2,L"$+ $t $ +it$n) 6.47; !" n+ " gi!+! O/t! gi!+! :

(  A . ) = 12!04.'5mm2  st req

 A st $ pr%

Providin !.-$2mm dia bars 5 @

¿ ¿ ¿

Note-:!-bars are c;rtai%ed at a distance o '#.+!m rom ends o s;pport Inn! gi!+!:  A st$ re(

¿ ¿ ¿

• • •

BY: ABHISEK PANDA  A st $ pr%

¿ ¿ ¿

Providin !'-1"mm dia bars@

Note-:!-bars are c;rtai%ed at a distance o 0#2$!m rom ends o s;pport (3, L"$+ $t $ +it$n) 2.29125  !" n+ " gi!+! O/t! gi!+!:  A st$ re(d

¿ ¿ ¿

 A st $ pr%

¿ ¿ ¿

Providin !2-$2mm dia bars5@

Note -:!2-$2mm dia bars are c;rtai%ed rom !#$""m rom ends o s;pport Inn! gi!+!:  A st$ re(

¿ ¿ ¿

 A st $ pr%

¿ ¿ ¿

Providin "mm R bars 5

Note -:"-1"mm R bars are c;rtai%ed rom !#33"1'm rom ends o irder (a& &hi# #ec&ion 12-30 φ ar# are ac&uall reuired a/ain#& 1-30φ ar# from fur&her calcula&ion)

'03 mm '03 mm

'.15m

'03mm = l .n e& .3!!m 10.'71 m 15.554 m

4.5!25 m

,[FTE >IDE4

'.1 5m

• • •

BY: ABHISEK PANDA (a& &hi# #ec&ion ac&uall 10-2!φ ar# will e reuired a/ain#& 12-2!φ ar# "rovided)

!4 3 mm

!43 mm

'.15m

!43 mm = l .n e&

'.15m

.2!m 10.!51 m 15.4335 m

,INNE >IDE4 Fig-23 (B$! )/!t$i#nt P!nt$ti"n "! L"ngit/+in$# Gi!+!, (#, CALCULATION OF INDUCED S@EAR AT DIFFERENT SECTIONS: (i, 8'# #"$+ $t t$!ting

Ci-13#! ,S&ear orce ca%c;%ation-&ee% %oad at startin4 350 + 350 ×

0.45 2.5

= 413kN 

App%*in impact5 tota% s&ear @3'3#$9N

• • •

BY: ABHISEK PANDA 454.3 ×

1.53 1!.33

= 410kN 

Aain reaction at s;pport is @ 4' ×1!.33 2

+

2.25 2

+

2 × 2.25 2

= 4!'kN 

Dead %oad s&ear @  Tota% s&ear@"..9N ` .22 9N (ii, S'$! $t 9.165 !" n+ " gi!+! 0.303 0. 5

Ci-13#1 ,S&ear orce ca%c;%ation-&ee% %oad at midd%e4 1 2

0.5 + 0.303 × 413 × 1.1 = 1!2.54 kN 

 Trac9 s&ear orce at midd%e is @ 4!' − (4' × '.15 + 2.25) = 13.5 kN 

Dead %oad s&ear@  Tota% s&ear@!.0#12'`1229N (iii, S'$! $t ;.5425 !" n+ " gi!+! 0.553 0.75

4.5!25

Ci-13#$ ,S&ear orce ca%c;%ation-&ee% %oad at M;arter span4 1

 Trac9 s# at 3#'"1'm@ Dead %oad s&ear@

489

2

[ 0.75+ 0.5536 ] × 413 × 1.1 =296.113 kN 

−( 49 × 4.5825 )=264.46 kN 

 Tota% s&ear@'0!9N (i0, S'$! $t 1.95 !" n+ " gi!+! 0.!'4

1.'5m

0.'72

• • •

BY: ABHISEK PANDA

Ci-13#3 ,S&ear orce ca%c;%ation-&ee% %oad at !#.' m rom end4 <#< s&ear@$0!#33!9N 489

D#% s&ear @

−( 49 × 1.95 )=393.45 kN 

 Tota% s&ear@+''9N

(0,

S'$! $t 3. !" n+ " gi!+! 0.!33 0.4

3m

Ci-13#' ,S&ear orce ca%c;%ation-&ee% %oad at $#2 m rom end4 <#< s&ear@$$'#$39N D#< s&ear@3".-,3.Z$4@$319N  Tota% s&ear@0+"9N (0i, S'$! $t 6.47375 !" n+ " gi!+! 0.25 0.42!

Ci-13#0 ,S&ear orce ca%c;%ation-&ee% %oad at 0#"+$+'m rom end4 <#< s&ear@1$.#$1'9N D#< s&ear@

489

−( 49 × 6.87375 + 26.25 )=126 kN 

 Tota% s&ear@$00 9N (0ii, S'$! $t ;.3425  !" n+ " gi!+! 0.54 0.71

4.3!25m

Ci-13#+ ,S&ear orce ca%c;%ation-&ee% %oad at 3#$"1' m rom end4

BY: ABHISEK PANDA

• • •

 Trac9 s&ear at 3#$"1' m @ 2#' 2#+0!G2#'03O×!#!2×3!$ @ $2! 9N Dead %oad s&ear @ 3".  ,3.×3#$"1'4 @ 1+' 9N  Tota% s&ear orce @ '+0 9N ,viii4 Ass;min bearin @3'2mm / an %i9e compression e%d at an an%e 3'5tota% dept& ;p to )&ic& s&ear reinorcement is not necessar* is iven b*5 3'2G!'02@12!2@1#2!m Hence s&ear at 1#2!m rom end o irder is 0.!'03 0.'4

2.01m

Ci-13#" ,S&ear orce ca%c;%ation-&ee% %oad at 1#2!m rom end4

(

+

413 × 1.1 × 0.5 0.8903 0.694

<#% s&ear@ D#d s&ear@

489

)= 360 kN 

−( 49 × 2.01 ) =390.51 kN 

 Tota% s&ear@+'2#'!KN ) 751 kN  (, S@EAR RESISTANCE C@EC:
¿

@

0.6 × 1560 × 2

No)

=1.872> 0.645 (k )

 π  2 2  A sw =1 × × 30 =706 m m ( 5ter girder ) 4

/

1×

 π  4

2

2

× 28 =615 m m ( inner girder )

As per c%a;se !2#$#$#$ o I(:!!1-12!!5 No)

% rds =

s@2#03'm

asw   × z × f  ywd   ( ct" + ct' ) sin'  s

O

• • •

BY: ABHISEK PANDA

8@2#.d@2#.Z!'02@!332mm f  ywd

@2#"Z3!'@$$1 N / mm 706

(8  /ds )3 $9 @ 8  /d $ m ax

2

× 1404 × 332 × 2 ×

645

1

√ 2

=721.55 kN  2

@ ∝cw bw % 1 f cd z ( ct" + ct' )/( 1 + cot " )❑

@!Z322Z2#.Z!'02Z2#0Z2#$0Z$'Z171 @313'#0.0VV+1!#'' KN ,o94

( 8  /ds ) I $9 @

615 645

× 1404 × 332 × 2 ×

1

√ 2

@01"#'3$ 313'#0.0 9N ,o94 Desin s&ear resistance o member )it&o;t s&ear reinorcement is iven b* 0.33 dc @ [ 0.12 k ( 80 ρ1 f ck ) + 0.15 σ cp ] × b w d ( cl −10.3 .2 f I/ : 112−2011 )

σ cp

@2 3

1

2

vmin@   0.031 k  f ck 2 K@

1

+

√

200

d

=1 +

√

200 1560

=1.358 < 2 (k )

vmin@2#1.

( % min+ 0.15 σ cp ) bw d

,dc4min@

@2#1.Z322Z!'02@!"!#!2' 9N No)

 ρ1=

A st  bw d

Since &a% reinorcement is a%)a*s avai%ab%e t&ro;&o;t5 ,

ρ1

,

ρ1

0.5 × 14137.167

4[#>@

400 × 1560 0.5 × 9852.03

4I#> @

400 × 1560

=0.01133< 0.02

=7.89 × 10− < 0.02 3

[ 0.12 × 1.358 ( 80 × 0.01133 × 35) ] × 400 × 1560 0.33

,dc4[#> @

¿ 318 kN > % /dc$ min ( k )

BY: ABHISEK PANDA

• • •

[ 0.12 × 1.358 ( 80 × 7.89 × 10

−3

,dc4I#>@ @

0.33

× 35 )

] × 400 × 1560

> % /dc$ min (k )

282 kN 

(n, S@EAR GIRDER:

REINFORCEENT

DISTRIBUTION

ON

OUTER

 Tota% s&ear at ace o s;pport@ .229N Ho)ever as its simp%* s;pported / a bearin o 3'2mm is provided5a an %i9e compression ie%d )i%% eist &avin steepest an%e @3' ;p to )&ic& no s&ear reinorcement )i%% be necessar*# so t&e efective section or s&ear )i%% be at 2#3'G!#'02@1#2!m rom end o irder  Tota% s&ear at 1#2!m@+'!9N Desin s&ear@!#'Z+'!@!!10#'2 9N S&ear resisted b* irder )it&o;t s&ear reinorcement @ ,dc4[#>@$!" 9N Hence desin s&ear or )&ic& s&ear reinorcement )i%% be provided@Ed @,!!10#'2-$!"4KN@"2"#'2 9N  T&e s&ear resistin capacit* o avai%ab%e bent ;p bars at t&at section is +1!#'' 9N B;t as per c%a;se -!2#$#$#$,14/ c%a;se-!0#'#1,$4 o I( :!!1-12!!5on%* '2 o t&e s&ear )i%% be resisted b* t&e bent ;p bars Hence s&ear to be resisted b* %in9s7stirr;ps 808.50

B*

2

=404.25 kn

c&ec9:,as)#ma4bent 0.5 × 10 × 0.6 × 0.36 × 35 × 400 × 645 1

√ 2

@

;p

bars

=4154.21 mm > 706 mm ( k ) 2

2

× 0.8 × 415

V0!'mm1,o94
As) @

4×

4

2

2

× 8 = 201.062 m m =201 m m

2

Fsin c%a;se-!2#$#$#1 o I(:!!1-12!!5 rd#ma@

∝

cw bw % 1 f cd z

f cd

(ct" + tan" )

BY: ABHISEK PANDA

• • •

@

1 × 400 × 0.9 × 1560 × 0.6 ×

 0.36 × 35 2

@1!11#"3"9NVV323#1' 9N ,o94 As per same c%a;se 5spacin o vertica% stirr;ps iven b* asw × f  ywd × z× ct"

S@

% rds 201 × 0.9 × 1560 × 0.8 × 415 × 1

@

3

404.25 × 10

= 231.766 mm

 
0.072 × √ f ck 

f  yk 

)#min@

=

0.072 × √ 35 415

=1.026 × 10−

3

Provided s&ear reinorcement ratio is  A sw

, ρ

)4@ s × b × sin w

∝

=

201

=2.125 × 10− >¿ , ρ 200 × 400 3

4,o94

)#min

S&ear orce at 3#'"1'm rom ends o irder '0!9N# Here no bent ;p bars are avai%ab%e Desin s&ear@"3!#'9N  π 

,As%4o#@  ρ

¿

!

18 ×

4

2

2

× 30 =12723.45 m m

 4o#@2#212$. V 2#215

8620.53

 ρ

¿

(

!

 4i#@

)

0.33

,vrdc4o# @  

0.12 × 1.358 × 80 × 0.02 × 35

,vrdc4i# @  

0.12 × 1.358 × 80 × 0.0138 × 35

(

)

400 × 1560

× 400 × 1560=383.855 ) 383 kN 

0.33

× 400 × 1560 =339.615 ) 339 kN 

S&ear to be resisted b* stirr;ps is ,"3!#'-$"$4 9N @3'"#' 9N d#ma@1!11#"3"V3'"#'2 9N,o94 Spacin o stirr;ps is 201 × 0.9 × 1560 × 0.8 × 415 × 1

S@

3

458.50 × 10

=0.0138 ) 0.02

= 204.344 mm

BY: ABHISEK PANDA

• • •


s@

166 × 10

3

=564.408 mm

As per c%-!0#'#1,+4 o I(:!!1-12!!5 S%ma @2#+'d,!Gcot4@2#+'Z!'02Z!@!!+2mmV'03#32"mm,o94 B;t As per c%-!0#'#$,$534 o I(:!!1-12!!5 species or torsion criteria to be satised5t&e minim;m spacin s&o;%d be $'2mm or 1 8

1

o;ter perimeter o t&e memberO@

8

× 3200 =400 m }( lesser f tw )

So provide 3-%eed -"mm R vertica% stirr;ps 6$02mm c7c in t&e midd%e strip band o %ent& 3#'"1'm Aain it s&o;%d satis* , ρ , ρ , ρ

4

 @  

) min

1.026 × 10

−3

201

4

) prov

 @

4

) min

350 × 400

=1.436 × 10− >( ρw )min (k ) 3

(", S@EAR REINFORCEENT DISTRIBUTION ON INNER GIRDER: 2#3'G!#'0@1#2!m rom irder end  Tota% desin s&ear@!!10#'29N ,dc4I#>@1"1 9N Desin s&ear or )&ic& s&ear reinorcement )i%% be provided@"33#'29n Bent ;p bars s&ear resistance is ,ds4I#> @01"#'3$ 9N 844.50

B;t it )i%% be ta9in on%*

2

=422.25 kN 

est 311#1'9n )i%% be ta9en care o b* t&e vertica% stirr;ps# Providin "mm R -3 %eed stirr;ps5 2 As)@12! m m

(%-!2#$#$#1 o I(:!!1-12!! species rd#ma@1!11#"3"9N VV 311#1'9N,o94 Co%%o)in same c%a;se5 spacin o stirr;ps5

BY: ABHISEK PANDA

• • •

201 × 0.9 × 1560 × 0.8 × 415 × 1

S@

3

422.25 × 10

= 221.88 mm

Provide "mm-3%eed stirr;ps 6122mmc7c ;p to 3#$"1'm rom end o irder on bot& sides , ρ

 @  

4

) min

201

, ρ

4

) prov

 @

1.026 × 10

−3

=2.5125 × 10− >( ρw )min (k ) 3

200 × 400

S&ear at 3#$"1'm is iven b* '+0 9N# Desin s&ear@!#'Z'+0@"039N No bent ;p bars are avai%ab%e &ere# ,dc4I#>@$$. 9N S&ear to be resisted b* stirr;ps@'1'9N  d#ma@1!11#"39N VV'1'9N Spacin o stirr;ps is iven b* 201 × 0.9 × 1560 × 0.8 × 415 × 1

S@

302.50 × 10

3

=178.46 mm

Provide "mm-3%eed stirr;ps 6!02mmc7c ;p to 0#"+$+'m S&ear at 0#"+$+'m rom end o irder is= Desin s&ear@!#'Z$02@'3.9N  π 

16 ×

,Ast4avai%ab%e@

9852.035

 ρ

¿

4

!

 4I#>@

2

× 28 =9852.035 mm

400 × 1560

2

=0.016 < 0.02

,dc4I#>@$'0#023 9N S&ear to b resisted b* %in9s and7stirr;ps ,'3.-$'0#02349n@!.1#$.09n ) 193 kN  Providin minim;m s&ear reinorcement spacin o $'2mm c7c5 201 × 0.9 × 1560 × 0.8 × 415 × 1

ds@

350

= 267.691 kN > 193 kn ( k )

So Provide "mm-3%eed stirr;ps 6$'2mmc7c in midd%e strip-band o %ent& 3#'"1'm , ρ

  )4min @

1.026 × 10

−3

• • •

BY: ABHISEK PANDA 201

, ρ

4

) prov

(>,

 @

350 × 400 × 1

=1.436 × 10− >( ρw ) min (k ) 3

SURFACE REINFORCEENT:

Fig-25 (S/!$) Rin"!)nt >!"0ii"n, S;race reinorcement )i%% be provided ta9in a s;race area o t&e cover portion o;tside o t&e stirr;ps# S;race area on one ace o irder@"+Z!322@!1!"22mm1 2#2! Act#et @!1!"mm1 e &ave side ace reinorcement o approimate%* '-!1mm dia bars )&ic& provide '0'#'mm1 Providin !2mm R bars 6!'2mmc7c5tota% stee% area provided per ;nit r;n is π 

× 52 × 1355 ×

1000 150

÷ 1000 = 70'.47 mm2

@  Tota% reinorcement@!1+3#.+0V!1!"mm1,[K4 S;race area on %o)er end i#e at oot o [email protected]@$0"22 @2#2! Act#et@$0"mm1 Provision o 3-!0mm R bars )i%% be ivin 4×

π 

4

× 12 = !04.25mm2

@ A%so stirr;ps )i%% be ivin π 

@

× 52 × 3302 ×

1000 150

÷ 1000 = 172.7' mm2

BY: ABHISEK PANDA

• • •

 Tota% area provided@.+0#1'mm1V$0"mm1,o94 ∗ A%% t&e s;race reinorcement bars are perect%* anc&ored/&ence )i%% be servin as s&ear reinorcement a%so appear same c%a;se,'4 a%so ∗ A%so side ace %onit;dina% bars )i%% be servin as side ace reinorcement or stabi%it* as per c%a;se-10#'#!#$ o IS-3'0:1222 (, C@EC FOR BAR CURTAILENT ADEJUAC< AS PER CURTAILENT OF GIRDER BARS:  T&e c&ec9 )i%% be done as per c%a;se !0#'#!#$ of I(:-!!1-12!!,pae -!+04/ c%a;se-!0#'#!#3 of I(:!!1-12!!,pae -!++4 Beore c&ec9in5it ma* be noted t&at t&e %onit;dina% bar c;rtai%ment r;%e as per ;re-!0#1 o I(:!!1-12!!,pae -!++4 )i%% be ta9en care o or end sections on%* since at end o irders5t&ere is maim;m s&ear /minim;m reinorcement is actin ;pon a%% ot&er sections )i%% be o;nd saer i  a;tomatica%%* i end section are o;nd saer Crs@tensi%e capacit* o reinorcement

= 0.!7  f y ast = n × 0.!7 f y × π  × d 2 4

n@n;mbers o bars at ends5 d@diameter o bars ( F rs ) o. g   = 10 ×

π 

× 30 2 × 0.!7 × 415

4

@1''1#!!19N 8×

,Crs4I#>@

π  4

2

× 28 × 0.87 × 415 =2778.54 kN 

∆ F td 

 T&e above Crs s&o;%d be reater t&at CsG  F s = Ed ×

a1 d 

+ N Ed 

 N  Ed  = 0 a1 = z (

co& θ  2

) (co& θ  = 1)

0.'d  2  F s = Ed ×

0.' d  2 d 

= 0.45 Ed 

Efective s&ear )i%% occ;r at 1#2!m rom end /its va%;e is !!10#'29N

BY: ABHISEK PANDA

• • •

Cs@2#3'Z!!10#'2 ` '2+9N )0 ⇒

At ends ?ed ∆

 Ctd@2#' Ed,

 1 ed  z

=0

  ct" − ct' 

4

@2#'Z!!10#'2Z!@'0$#1'9N A%so anot&er va%;e o Cs appear -!0#1,A4 is  1  Ed  z

+ N  Ed =0

∆

CsG  Ctd @'0$#1'G'2+@!2+2#1'9n1''1#!!1 9n@,Cs4o# At midd%e5  1 ed  z

, ,

 1 ed  z  1 ed  z

@

 1 edmax  z 6

4[#>@ 4I#>@

7412 × 10

0.9 × 1560 5169 × 10

=5280 kN 

6

0.9 × 1560

=3682 kN 

,Cs4[#>@'1"29n5,Cs4i#@$0"19N ,∴ Ed@2/ a%so

∆

 1  Edmax

 Ctd

 z

4

,CS4[#>@1''1#!!1×1@'!23#1139N ,CS4I#>@!++"#'3×1@$''+#2"9N As per c%a;se -!0#'#3,'4 o irc:!!1-12!!53-!0mmR bars )&ic& are provided as side ace reinorcement )i%% be servin as resistin bars or bendin o  irder section# So tensi%e capacit* o tota% 3-!0mm R bars is iven b*5 4×

π 

4

× 12 × 0.!7 × 415

So ,CS4[#>@'!23#113G1.2#$+3@0$.3#02 9N V,o94 ,CS4I#>@$"3+#3'39N V$0"19N ,o94 3.6.15 DESIGN OF CROSS GIRDER: Se%-)ei&t@2#$Z!#3Z1'@!2#' 9N7m S%ab %oad )i%% be distrib;ted as s&o)n be%o)

• • •

BY: ABHISEK PANDA

45

45

1.25m

2.5 m

Fig-26 (D$+ #"$+ +it!i%/ti"n !" #$% "nC!" Gi!+!, Dead %oad rom s%ab @1Z2#'Z1#'Z!#1'Z"#30@10#3$+' 26.4375

So ;d% %oad @

2.5

=10.575 kN / m

 Tota% %oad ,dead )ei&t4 @1!#2+'9N7m Ass;min riid cross irder5 21.075 × 5

eaction on %onit;dina% irder is @

3

=35.125 kN 

Cor ma# Bendin moment5 t&e %oads s&o;%d be 9ept at eM;a% distance rom intermediate %onit;dina% irder o bot& sides o cross irder#

• • •

BY: ABHISEK PANDA

4.5075 m

1.! m 1.! m 2.05m

4.5075 m

2.5 m

2.5 m

4.5075 m

0.' 0.'

Fig-27 (8'# #"$+ $!!$ngnt "! $i/ %n+ing "nt "n C!" Gi!+!, No) or ca%c;%atin %oad5 o%%o)in diaram ma* be provided at benecia%
@

2×

 350 2

×

( 4.5075−0.9 ) 4.5078

=280.12 kN 

eaction on eac& %onit;dina% irder 280.12 × 2

@

3

=186.75 kN 

?a# Bendin moment on cross irder ;nder %oad @!"0#+'Z!#3+'@1+'#3'0 9N-m In c&ec9in impact5 ?c @$2$9N-m Dead %oad moment ;nder )&ee% %oad 5

• • •

BY: ABHISEK PANDA 2

@   35.125 × 1.475−21.075 ×

( 1.475) 2

=28.884 kN −m

 Tota% desin moment@$$19N-m F%timate moment @ ?; @3."9N-m Since t&e cross irder ed at intermediate irder5,-4ve moment )i%% eist# As per D#J victor5 Essentia% Brides Enineerin5 reerrin to ?orrice-
498 × 10

,Ast 4Gve@

( − 0.416 ×

0.87 × 415 × 1660 × 1

250 1600

=886.45 mm

2

)

Providin 3-12mm R bars ,Ast 4provided @!1'0#03mm1 Provision o 3-!0-mm R bars at top )i%% ive ,Ast 4-ve@"23#1'mm1V,Ast 4reM;ired @!$'#!'1mm1 Provide 3-!1mm R bars eac& ace ;niorm%* as side reinorcement# 3.6.15.1

S@EAR C@EC FOR CROSS GIRDERS:

(%-!2#$#1 o I(:!!1-12!! K@!#$$ vmin@2#1"! cp@2  ρ1

@1#0!"Z!2-$

dc@2#!1Z!#$$Z,"2Z1#0!"Z!2-$Z$'42#$$Z$22Z!022@!3+#"$! 9N dc#min@2#1"!Z$22Z!022@!$3#""2 9N Desin s&ear Ed @!#'!"0#+'G$'#!1'O@$$1#"!1' 9N Etra s&ear to be resisted b* stirr;ps is @!"3#." ) 185 kN  Providin "mm dia -3 %eed stirr;ps As) @12!mm1 Spacin,s4@ '!.#3$mm5"mm R 3-%eed 6$22mm c7c Aain s&ear reinorcement ratio

BY: ABHISEK PANDA

• • •

s ×b w × sin '   ρw

@

¿

,c%-!0#'#1 o I( !!1:12224

 A

¿

@!#1"..Z!2-$  ρ (¿¿ w ) @

0.072 × √ 35 415

¿

=1.026 × 10−

3

 ρ

Ass;mim

¿ ¿ 4min 5 ¿

201

s@

−3 300 × 1 × 1.026 × 10

=653.021 mm> 300 mm ( k )

4 -1  m mφ  an #

4-1 mmφ 12mm φ #ide face reinforcemen& 4-20 mmφ

! mm φ 4 -le // ed #&irru"#  300 mm +$+

4 -2 0m mφ  ar#

4 lo//ed !mm φ  300 mm +$+

Fig-24 (Rin"!)nt +t$i#ing " C!" Gi!+!,

(%a;se -!0#'#1 o I(:!!1-12!!,05 +5 "5.54 species t&at smin@dG!2@$2mm 32mm 1_s@1Z"@!0mm Sma@2#+'d,!Gcot4@2#+'Z,!G24@!13'mm As per t&e (%a;se -!0#'#$ o I(:!!1-12!!5  T&e %in9s )i%% not to be o reater spacin o o%%o)in !7" ,perimeter o member4@3"+#'mm or $'2mm [;r provision o $22m ,o9a*4

• • •

BY: ABHISEK PANDA

3.6.16 ODIFIED ANC@ORAGE FOR BARS AT T@E ENDS OF GIRDERS: At t&e ends o irders5bearin avai%ab%e is on%* 3'2mm#&ence standard .2 bend as per  !'#1 o irc:!!1-12!! )i%% be provided# So modied %b#net )i%% be %b#net @2#+Z%bZ!@2#+%b %b @.2$mm,or $2mm R bars4 %b @"3$mm,or 1"mm R bars4 ,%b#net4[#> @0$1mm ,%b#net4I#> @'.2mm

REFERENCES:

!# I(:!!1-12!!= ([DE [C PA(TI(E C[ ([N(ETE [AD BID>ES5 INDIAN [AD ([N>ESS 1# I(:0-12!3= STANDAD SPE(ICI(ATI[NS AND ([DE [C PA(TI(E C[ [AD BID>ES= SE(TI[N : II <[ADS AND STESSES $# I(:0-12!2= STANDAD SPE(ICI(ATI[NS AND ([DE [C PA(TI(E C[ [AD BID>ES= SE(TI[N : II <[ADS AND STESSES