step by step design of psc girder by working stress method
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DESIGN OF PSC GIRDER
WORKING STRESS METHOD
1.0 SALIENT FEATURES AND DESIGN DATA1 c/c of pier to face of irt!a"" #
$ a%&"e of '(e! #
) Spa% * c/c of +eari%&', #
- "e%&t of preca't &irer #
Spa% * c/c of teporar '2pport' , for preca't &irer #
3 No of &irer' #
4 c"c i'ta%ce of te &irer' #
5 c"ear carria&e !a #
6 !it of footpat 7 A89 #
10 !it of eia% #11 O:era"" !it of te ec( #
1$ !it of ec( '"a+ +eo% ce%tre "i%e of o2ter &irer #
1) tic(%e'' of ec( '"a+ #
1- tic(%e'' of e% iapra& #
1 Grae of co%crete for ;S8 &irer M
for R88 ec( '"a+ M
T
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# ).000
"* PROPER+IES OF CO'POSI+E SEC+ION
A # 1.),1 #
# 0.-8- #
# 1.(1- #
$.$ SE8TION AT SU;;ORT *1=$,
'ae a' a+o:e for iffere%t 'ectio%'
).0 8AL8ULATION OF 9ENDING MOMENTS AND SHEAR
FOR8ES AT @ARIOUS SE8TIONS
).1 9M SF DUE TO SELF WEIGHT OF GIRDER
).$ 9M SF DUE TO DIA;HRAGMS
).) 9M SF DUE TO INSITU DE8K SLA9
).- 9M SF DUE TO SU;ERIM;OSED DEAD LOAD
). 9M SF DUE TO @EHI8ULAR LI@E LOAD
).3 9M SF DUE TO FOOT;ATH LI@E LOAD
).4 SUMMAR< OF 9ENDING MOMENTS AND SHEAR FOR8ES AT
@ARIOUS SE8TIONS
-.0
(.1 * CA/E POSI+IONS A+ 'IDSPAN AND ANCORAGES
c!"e o 1
Tpe of ca+"e # 5 T 1)
Area of ca+"e 65.4- # 456.6$
UTS # 156.4$0-45
a' of pre'tre'' $1
Tota" "e%&t of &irer # $-.300
Di'ta%ce of A%cora&e fro Mi 'pa% # 12.200
DIS+ANCES OF ARIO3S SEC+IONS FRO' S3PPOR+ AND 'IDSPAN
C!"e fo&ce
8a+"e' are 'tre''e fro +ot te e%.
8a"c2"atio% of force' i% te ca+"e' +efore a% after '"ip *'"ip # 3
$ Ic# $
t%
t
$" %"
8A9LE ;ROFILE OF O3+ER GIRDER 4G15G-*
$.
(&/$.
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Sectio% "e%&t of ( # 0.00$ A%&"e 2 # 0.14
'ectio% teta ca"c2"ate
" i% *, (B" µ∗θ for eac
Fo&ce Di!#&!
8a"c2"atio% of '"ip
SUMMAR< OF 8A9LE FOR8E AFTER SLI;C
HORIONTAL 8A9LE FOR8E 8OM;ONENTS *F # ;8OS*,,
@ERTI8AL 8A9LE FOR8E 8OM;ONENTS *F # ;SIN*,,
*CA/E E/ONGA+ION
E"o%&atio% # f > L !ere= A > E f # A:era&e ca+"e force at refere%ce 'ectio%
L # Le%&t of ca+"e *i% ,
A #
E #
4.0 EFFE8T OF FIRST STAGE ;RESTRESS
4.1 STRESSES IMMEDIATEL< AFTER I't STAGE ;RESTRESS
4.$ 8AL8ULATION OF LOSSES DUE TO I't STAGE ;RESTRESS
1 * /osses d7e to c&ee i coc&ete
* c".11.$ of IR8C15 $000 ,
8reep 'trai% i% perio +et!ee% ) a' (2
10 a' ,,
6.$$E0- .-0E0- # ).5$E0- per 100 (&/c$ 'tre'' i% c
ce%troi of pre'tre''i%& 'te
# ).5$E00- >
# $.05E0-
# creep 'trai% > o2"2' of e
# $.05E0- >
# (0-.))
2 * /osses d7e to sh&i:!#e of coc&ete
* c".11.) of IR8C15 $000 ,
Sri%(a&e of co%crete i% te perio of - ) a' a% 10
>#(∗"7µ∗θ e>
θ i% ra
Area of ca+"e *i% $,
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# 0.000-) 0.000) # 1.)0E0-
# 1.)0E0- >
# 2-).-0
) * /oss d7e to E!stic sho&tei# * c".11.1 of IR8C15 $000 ,
# 1.6E703
# -000 Fc
# 000 $0
# $$)30.3465
# $$)303.465
Mo2"ar ratio # 1.6E703 # 5.4$
$$)303.465
Lo'' D2e to E"a'tic Sorte%i%& # -.-1 >
$# 2),.26
( * /oss d7e to &e!
* c".11.- of IR8C15 $000 ,
U"tiate te%'i"e 'tre%&t of !ire' # 18.,))
U"tiate te%'i"e 'tre%&t of 19 + 1) te%o% # 16
# ).6)
Area of eac 'tra% # 0.98,(
No. of ca+"e' # $.00 * $.00 of 16 T 1)E2i:a"e%t N 16 T 1) ca+"e' # $ > 15.4303
15.4303
# $.00
Referri%& c". of De'i&%
A:era&e force i% ca+"e'
# 299.)) = )01.,9 = )0-.), =
6
# )03.)$ t.
# )03.)$ UTS
).6) > $
# 0.-)0 UTS
A:era&e 'tre'' i% ca+"e' # )03.)$ > 1.00E70)
$.00 > 15.43
Lo'' 2e to re"a>atio% of H # 513).6) > )
# >21).)(
:#;c2.
Mo2"2' of E"a'ticit of Stee"= E' (&/c$.
Mo2"2' of E"a'ticit of 8o%crete= Ec
(&/c$.
:#;c2.
...
:#;c2.
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Tota" "o'' # -0.)) 7 $). 7
# 682.,-
a&e "o'' # 35$.4 > 100 #
513).6) a&e "o'' 2e to e"a'tic 'orte%i%& # $)4.$3 > 100
513).6)
i.e Ist!t!eo7s oss # 2.91
9a"a%ce "o'' # 5.)3 $.61
.-3
$0 i&er "o'' # 6.--
5.0 EFFE8T OF SE8OND STAGE ;RESTRESS
5.1 STRESSES IMMEDIATEL< AFTER II% STAGE ;RESTRESS
5.$ 8AL8ULATION OF LOSSES DUE TO II% STAGE ;RESTRESS
'ae a' i% 1't 'ta&e
5.) ADDITIONAL LOSS IN I't STAGE DUE TO II% STAGE ;RESTRESS
1 * Aitio%a" 'tre'' c.& of 8a+"e' # ErrC1$ -.-1
# E&&?-12
2 * /oss d7e to C&ee i coc&ete
8reep 'trai% i% co%crete # .-0E0- > ErrC1$
100 100
# ErrC1$
Lo'' 2e to 8reep i% co%crete # ErrC1$ > 1.6E703
# E&&?-12
) * /oss d7e to Sh&i:!#e i coc&ete
Sri%(a&e 'trai% at $% 'ta&e # ).00E0-
Lo'' 2e to 'ri%(a&e i% co%crete # ).00E0- > 1.6E703
# -8-.00
( * /oss D7e to E!stic Sho&tei# # ErrC1$ > 3.3)
$
# E&&?-12
# ErrC1$ 7 ErrC1$
# E&&?-12
Lo'' # ErrC1$ > 100
513).6)
ErrC1$
$0 i&er "o'' # E&&?-12
...
:#;c2.
...
...
:#;c2.
...
:#;c2.
...
:#;c2.
:#;c2.
... +ot! /oss
:#;c2.
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6.0 STRESS DUE TO DIFFERENTIAL SHRINKAGE
For A&e of ;reca't U%it 2pto 90 a'
Differe%tia" 'ri%(a&e 'trai # 2.00E>0(
re2ctio% factor for creep effect M -
o2"2' of e"a'ticit of co%crete # 000.00 >J Fc# 000.00 >J -
Differe%tia" ' # 5.30E0 > ).)E70
Area of effecti:e ec( '"a+ # )00.000 > $.0
Te%'i"e force i% te '"a+ 2e to iffere%tia" 'ri%(a&e
Moe%t i% te &irer 2e to iffere%tia" 'ri%(a&e
10.0 RE8A;ITULATION OF STRESSES U;TO SER@I8E
10.1 8HE8K FOR STRESSES AT @ARIOUS STAGES OF LOADING
I * CEC@ FOR 'AI'3' CO'PRESSIE S+RESSES
A' per c".4.1 of IR8C15 $000
Te 8opre''i:e 'tre'' i% te e>tree fi+re of co%crete ieiate" after pre'tre''i%& or afte
te tra%'fer of pre'tre'' +efore a""o!i%& for f2rter "o''e' 2e to 'ri%(a&e creep 'a"" %ot
e>ceeC
i , 0.(- > c2+e 'tre%&t at te tie of tra%'fer
A' per c".4.$ of IR8C15 $000
Te copre''i:e 'tre'' i% te e>tree fi+re of co%crete after a""o!i%& for a"" "o''e' eiter 2ef2"" D.L or f2"" D.L L.L 'a"" +e 0.)) fc(C # 0.)) >
# 1(8.-0
1 * S+RESS CEC@ I''EDIA+E/$ AF+ER 1st S+AGE PRES+RESSING
Referri%& c". of De'i&%
Ma>. 8opre''i:e Stre'' # ,0.(8 * At Sectio%
Te 1't Sta&e ;re'tre''i%& i' o%e after ) a' of ca'ti%& of &irer or
te co%crete a' attai%e a c2+e 'tre%&t of 200
Te a>. peri''i+"e cop. 'tre''C
i , 0. > $00 # 100
+he !
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Te $% Sta&e ;re'tre''i%& i' o%e after 10 a' of ca'ti%& of &irer or
te co%crete a' attai%e a c2+e 'tre%&t of )(6.-
Te a>. peri''i+"e cop. 'tre''C
i , 0. > )-3. # 14).$
+he !
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11.0 ULTIMATE STRENGTH 8HE8K
( Vide cl.12 of IRC:18 - 2000 )
REF * F!i7&e " $ied of Stee
Mult = 0.9 x db x As x fp
!e"eAs = A"e# of !i$! te%sile steel
fp = t!e ultite te%sile st"e%$t! of steel
db = t!e dept! of t!e be#& f"o& t!e i&u& co&p"essioc$ of steel te%do%s
REF * F!i7&e " c&7shi# of coc&ete i co&essio oe
Mult =
!e"e
b = idt! of eb= t!e idt! of '#%$e
t = t!ic%ess of '#%$e
1$.0 SHEAR FOR8E 8AL8ULATION
1$.1 8AL8ULATION OF SHEAR REINFOR8EMENT AT @ARIOUS SE8TIONS
1$.$ MA SHEAR AND 8ORRES;ONDING 9ENDING MOMENT
@2 # 1.$ * S.F1 7 S.F$, 7 $ * SF), 7 $.*S.F-,
M2 # 1.$ * M1 7 M$, 7 $ *M), 7 $.*M- ,
( t - & )
c* she!& &eifo&ceet
1$.) 8HE8K FOR MAIMUM SHEAR
M#xi&u& s!e#" fo"ce = bd x 0.0- ( t )
0.1*+ bd+$f
c( $,
) 0.8(
f -b)(d
+-t,2) x t f
c(
f
!* 3ti!te she!& &esist!ce of sectio 7c&!c:ed i fe
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1$.- ;RO@ISION FOR HORIONTAL SHEAR
o"i3o%t#l s!e#" st"ess =
1$. DESIGN OF TRANS@ERSE REINFOR8EMENT
("efe" cl +11.4 IRC:22-198+)
5!e lo%$itudi%#l s!e#" fo"ce V6 pe" u%it le%$t! s!#ll %ot exceed
(i) 0.76s fc 6s = le%$t! of s!e#" pl#%e(ii)
As = u& of c,s #"e# of ste
As V6 - 0.086s fc
1).0 DEFLE8TION 8AL8ULATIONS
M#x. de'ectio% u%de" # 6 c#usi%$ # . &o&e%t of ; M ; :
= - x
(8 < I
!e"e >6 =
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0.7 0.2
= 0.2170
= M#x. p"est"essi%$ fo"ce #t #%c!o"#$e e%d
= t.
= 0.217
0
= 0.217 x 0
= 0.00 t.
e"&issible st"ess fo" e - 714 st = 0.8* x 7140
= /+10.4
A"e# of steel "eDui"ed = 0.00 = 0.00
/+10.4
P&ovided SPIRA/
20 5 8 &o7ds 1 o
A"e# of ste = /.172 x 8 x 1
= 2-.1)
B 0.00 SAFE
16.0 +ee&!t7&e #&!diet?
5!e te&pe"#tu"e $"#die%t e?ect s!#ll be e@#lu#ted #s pe" IRC: + fo" "ise #%
5!e e?ect of te&pe"#tu"e di?e"e%ce it!i% t!e C $i"de" #%d dec sl#b s!
positi@e #%d "e@e"se te&pe"#tu"e di?e"e%ces #s s!o% i% E$ belo.
1*.8 10.+
!1=0./!F0.14& !1 7 0.*
!2=0./!F0.10& !2
0.8
!/=0./!F0.14& !/
2.1 +.+
+'t
(
(
+'t
... +'t
$,c&$.
...
c2.
c2. ...
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positi@e te&pe"#tu"e di? "e@e"s
5!e p"ocedu"e #dopted fo" lo%$itudi%#l #%#lsis fo" te&pe"#tu"e $"#die%t is
i% t!e text G"id$e ec e!#@iou"G b C. #&bl.
Assu&e t!#t t!e dec expe"ie%ces te&pe"#tu"e c!#%$e !ic! i%duces st"es
"i$idl "est"#i%ed t!"ou$!out #%d t!e% t!e e?ects of "ele#si%$ t!e t!eo"eticsupe"i&posed.
Sectio &oe&ties?
5!e t!e"l st"esses s!#ll be e@#lu#ted fo" e#c! of t!e lo%$itudi%#l &e&be
sep#"#tel fo" di?e"e%t dept! #%d fo" solid sl#b i% t!e c#%tile@e" po"tio% #%d
HR t!e te"i#l p"ope"ties s!#ll
#) CoeJcie%t of t!e"l exp#% = 0.0000114
fo" co%c"ete #%d steel
b) Modulus of el#sticit = 0.4 ti&es t!e s!o"t te"& &odulu
= 0.4 x /./4
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REF
REF
HR
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HR
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HR
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REF
1
e&
%o'
(0
(0
2>6
$
0.1990
0.22),
0.2)12
>
-
)
)
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0.--)
0.9(-
0.)90
-
,>1,
4
6
11
1$
1)
1
13
15
at ac( e%,
-
)
)
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*i% (N,
# 0 T 1) > 65.4-
#
# 1.6E70-
$6
)0
)1
at2rit a%
at2rit
%crete at te
e".
-.-1
100
"a'ticit of H.T 'tee"
1.6E703
a'
$.
N/$.
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1.6E703
* c".10.1.1 of IR8C15 165 ,
* c".10.$ of IR8C15 165 ,
'tre'' i% co%crete at te
tie of 'tre''i%&
5.4$
to%%e'
> 15.4))
to%%e'
7 0 of 16 T 1)7 0 > 15.4303
)08.)9 = )10.(9 = )12.-6
# 816).9)--
> 0.54
c$.
:#;c2.
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$1).)- 7 $)4.$3
5.)3
))
)-
)4
)5
7 5.00
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)6
# 0.-)0
# ))-10.$
# 28.8-
# 400
# $13))6.44 (&
# 216.)( t
-0
-)
o-0
- > - ,
after
SAFE
(&/c$.
:#;c2.
c$.
:#;c2.
...
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after
6 > 6 ,
*Sectio% 6 > 6 ,
* At Sectio% ( > ( ,
* At Sectio% 6 > 6 ,
* At Sectio% 6 > 6 ,
:#;c2.
...
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-
% ed$e to t!e
-4
-5
1
-
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3
el pe" u%it le%$t!
4
'ectio%.
6
1-1
x 0.04//
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f#ll i% te&pe"#tu"e
ll be de"i@ed f"o& t!e
0.24 !1=0.2! F 0.24&
0.24 !2=0.2! F 0.24&
0.2 !/=0.24! F 0.2&
0.2 !7=0.24! F 0.2&
c2.
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te&pe"#tu"e di?
#s $e%e"#ll discussed
ses !ile t!e dec is
l "est"#i%ts #"e
s of t!e $"id
s!#ll be #s s!o% belo.
e
s
2
/7.88
*.87
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7.12
c& f"o& c$
c& f"o& c$
c& f"o& c$
c& f"o& c$
$c&
t&
HR
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HVA6
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12.9/
c& f"o& c$
c& f"o& c$
c& f"o& c$c& f"o& c$
c& f"o& c$
$c&
HR
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REF * CA/C3/A+ION OF ENDING 'O'EN+ AND SEAR FORCES A+ ARIO3S
SEC+IONS
Fo""o!i%& 'ectio%' are co%'iere for te e'i&% of ;S8 &irer
Sectio% 00 '2pport
Sectio% 11 e% of tic(%i%& of !e+
Sectio% $$ i of tic(%i%& of !e+
Sectio% )) 'tart of tic(%i%& of !e+
Sectio% -- 0.)L
Sectio% 0.-L
Sectio% 33 0.L i 'pa%
REF I ENDING 'O'EN+ D3E +O SE/F EIG+ OF GIRDER 4'1*Wei&t of i'pa% 'ectio% # REF >
Wei&t of '2pport 'ectio% # REF >
Wei&t of e% tic(%i%& #
9.M S.F. at :ario2' SE8TION
'ectio%' 2e to 11 $$
SELF WEIGHT
M 1 0.00 )4.00
S.F. 1 0.00 0.33
REF ENDING 'O'EN+ D3E +O INSI+3 DIAPRAG' = DEC@ S/A 4'2*
8a"c2"atio% of !ei&t of ec( '"a+
!it of ec( '"a+ o% &irer #
tic(%e'' of ec( '"a+ #
!ei&t of ec( '"a+ #
Diapra& # REF > REF >
9.M S.F. at :ario2' SE8TION
'ectio%' 2e to 11 $$
iapra&
M $ 0.00 $3.00
S.F. $ 0.00 0.-4
).) ENDING 'O'EN+ D3E S3PERI'POSED DEAD /OAD 4')*
9e%i%& oe%t 2e to '2peripo'e ea "oa i' ta(e% fro o2tp2t of Gri a%
S2peripo'e ea "oa
UDL o% o2ter e+er
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Reactio% 2e to cra'+arrier
o% &irer G1 a% G)
*a, cra' +arrier # 0.))) >
*+, !eari%& coat f"oor "oa # 0.03 >
*c, rai"i%& # 0.$ >
9.M S.F. at :ario2'
'ectio%' 2e to 11 $$
SIDL
M ) 3-.00 6.$0
S.F. ) 0.00 4-.)
).( ENDING 'O'EN+ AND SF D3E +O EIC3/AR /IE /OAD 4'(*
C!ss ,0R wheeed c&itic!
IM;A8T FA8TOR # 1 7
9.M S.F. at :ario2'
'ectio%' 2e to 11 $$
LL c"a'' 40R
M - 101.00 51.13
S.F. - 0.00 -.63
LL i%c" ipact
M - 0.00 0.00
S.F. - 0.00 0.00
C!ss A 2 !es
IM;A8T FA8TOR # 1 7
*Refer cop2ter o2tp2t pa&e' i%c"2i%& re2ctio% factor of 0.6,
9.M S.F. at :ario2'
'ectio%' 2e to 11 $$
LL 8"a'' a $"a%e'
M - 0.00 0.00
S.F. - 0.00 0.00
'ectio%' i%c" ipact
M - 0.00 0.00
S.F. - 0.00 0.00
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C!ss A 1 !es
for a> oe%t
REF REF REF
IM;A8T FA8TOR # 1 7
*Refer cop2ter o2tp2t pa&e' i%c"2i%& re2ctio% factor of 0.6,
9.M S.F. at :ario2'
'ectio%' 2e to 11 $$
LL 8"a'' a $"a%e'
M -
S.F. -
'ectio%' i%c" ipactM - 0.00 0.00
S.F. - 0.00 0.00
Foot!th /ive /o!d
effecti:e 'pa% L # REF c/c +eari%&
9a'ic i%te%'it ;? # 00
I%te%'it of "oa ; # ;? *
# 00 *
# REF
!it of footpat # 1.
"oa o% (er+ # )3.0 >
9.M S.F. at :ario2'
'ectio%' 2e to 11 $$
FOOT;ATH LL
M - 0.00 0.00
S.F. - 0.00 0.00
).- ENDING 'O'EN+ AND SF D3E +O /A3NCING 4'-*
9.M S.F. at :ario2'
'ectio%' 2e to 11 $$
LL c"a'' 40R
M 0.00 0.00
S.F. 0.00 0.00
(&/$.
(&/$.
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