Ramp 4 R1 1#6 Dist Change at Coupler Location

8/16/2019 Ramp 4 R1 1#6 Dist Change at Coupler Location

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CALCULATION OF LOSSES FOR POST-AASHTO LRFD SPECI

LOSS DUE TO FRICTION BETWEEN INTERNAL PRESTRESSING TENDO

WHERE,

N=NO. OF IDENTICAL PRESTRESSING TENDONSNO OF WEBS =

TOTAL JACKING FORCE for 1 WEB Pj =AREA OF ,0.6" DIA WIRE STRAND

K=WOBBLE FRICTION COFFICIENT=COEFFICIENT OF FRICTION

!=BASE OF NAPIERIAN LOGARITH SL=LENGTH OF GIRDERR=RADI#S OF C#R$E%= To&'( %!)&* of + r%!r

T!-%o- $!r& '( % /&'- ! fro o&&o '& !-%1 2 3 4

234 534 1234

1 2 3 440 720 1110

8f )F =f )j 9:1;! ;:K9L< 9 >>

P j=FORCE IN PRESTRESSING STEEL AT JACKING FOR ONE TENDON

f )j =STRESS IN PRESTRESSING STEEL

TOTAL JACKING FORCE P j =

A)/ =TOTAL AREA OF PRESTRESSING STEEL

T!-%o- $!r& '( % /&'- ! fro o&&o '&-?! & o- )o -&



LOSS CALCULATIONS FOR SINGLE WEB

CABLE L @L DIP *: > : > : > :r'%> :r'%>

7. 4 7. 4 0.400 0.1036 0.0 027. 4 17.40 0.400 0.1036 0.0 024.34 3 . 4 0.3 0 0.071 0.02 74.34 20.00 0.3 0 0.071 0.02 7

11. 0 1. 0 0.400 0.05 0.053212.24 4 . 4 0.0 4 0.0113 0.0762

7. 4 7. 4 0.400 0.1036 0.0 027. 4 17.40 0.400 0.1036 0.0 024.34 3 . 4 0.3 0 0.071 0.02 74.34 20.00 0.3 0 0.071 0.02 7

11. 0 1. 0 0.400 0.05 0.053212.24 4 . 4 0.274 0.0473 0.0762

7. 4 7. 4 0.400 0.1036 0.0 027. 4 17.40 0.400 0.1036 0.0 024.34 3 . 4 0.3 0 0.071 0.02 74.34 20.00 0.3 0 0.071 0.02 7

11. 0 1. 0 0.400 0.05 0.053212.24 4 . 4 0. 14 0.10 1 0.0762

REF 12.24 12.24 0.000 0.0000 0.000011. 0 3 . 4 0.000 0.0000 0.00004.34 20.00 0.000 0.0000 0.00004.34 24.34 0.000 0.0000 0.00007. 4 4.00 0.000 0.0000 0.00007. 4 4 . 4 0.000 0.0000 0.00004.34 60.00 0.000 0.0000 0.00004.34 64.34 0.000 0.0000 0.0000

11. 0 6.64 0.000 0.0000 0.000012.24 70.00 0.000 0.0000 0.0000

FRICTION LOSSES FOR SINGLE TENDON



@L: >7. 4

17.403 . 4

20.001. 04 . 4

LOSS DUE TO ELASTIC SHORTENING IN POST-TENSIONED MEMBER

WHERE,ANOTHER ALTERNATE FOR #LA,

%=TOTAL DEPTH OF GIRDER=

315. K/ 1420.7 )'

6000 )/ 1.2 )'35000000 )/ 176000 )'

674753.22 )/ 1.5 63 4 )'

4.7634 2 262

L: > : > : > :KN; > )'

7. 4 20 62 6744 1 .043 . 4 50 102 102 0 6.52

1. 20 62 11 37 13.224 . 4 50 102 0 .

8f )ES =::N;1> 39N>9E ) E 9f +)

f +) =P j A 39N>9::A )/ 9f ) &9:I+<! 39A+>;! 9 +9A+> :A)/ 9:I+<! 39A+><

A+=GROSS AREA OF SECTION

&=DEPTH OF NA FRO TOP =DEPTH OF NA FRO BOTTOS&=SECTION OD#L#S AT TOPSB=SECTION OD#L#S AT BOTTOI+= O ENT OF INERTIA OF GROSS ;SECTIONf ) =TENSILE STRENGTH OF PRESTRESSING STEEL

f ) &=STRESS IN PRESTRESSING STEEL I EDIATEL PRIOR TO TRAf ) &= 0.79:0.7f ) >

! =A$ERAGE ECCENTRICIT AT O ENT LOCATION #NDER CONS! P=CENTROID OF PRESTRESSING STEEL FRO TOP OR BOTTO

+= A O ENT D#E TO SELF WEIGHT OF GIRDER AT POINT #N

f =E) =E =229 2 39/ r&:f >

OD#LAR RATIO=-=E ) E

! ) ! + f +)

LOSS DUE TO ANCHORAGE SET

WHERE,=DISTANCE FRO END OF GIRDER TO POINT WHERE LOSSES AR

8L=ANCHOR SET THICKNESS 7.4341 43 1 .42

SO, LOSSES ARE BEING CO P#TED #PTO 1 .44 AND BE OND T= 34 .02 )'

5 .43 )'6.04

LONG TERM PRESTRESS LOSS DUE TO CREEP OF CONCRETE, SHRIN

FOR BO GIRDER TI E DEPENDENT LOSSES= 33

LOSS 16.02

IMMEDIATE LOSSES

TOTAL I EDIATE LOSSES=FRICTION<ELASTIC SHORTENING<AN

AT 7. 4 = 5. 2

AT 3 . 4 = 16.53

AT 1. = 36.61

AT 4 . 4 = 21.05

TIME DEPENDENT LOSSES

TOTAL TI E DEPENDENT LOSSES=CREEP<SHRINKAGE<RELA ATI

AT 7. 4 = 16.02

AT 3 . 4 = 16.02

AT 1. = 16.02

AT 4 . 4 = 16.02TOTAL LOSSES

8f )A =8f 1; L)A

L)A =::SQRT:E ) :8L>L)F > 8f )F >

L)A =

8f=398f )f 9L)A L)F

8f )A = 8f )A: > =

TOTAL LOSSES=I EDIATE<TI E DEPENDENT LOSSES

AT 7. 4 = 3 . 6

AT 3 . 4 = 23.54

AT 1. = 3.6

AT 4 . 4 = .11

STRESSES AT EXApplied Moments and Shears

Station/ :T; >

AT S&'r& Co )(!rAT 7. 4 07 2 25AT 3 . 4 104 1 3 112 ;23AT 1. 1164 75 53 7AT E-% 0 0 0 0

AT 9.7 ! "M#$ %&'( S)*+STAGE 1 AT INITIAL STAGE BEFORE LOSSES

242 7.324 :KN>

ALLOWABLE TENSIONALLOWABLE COMPRESSION

STAGE 3 AT SER$ICE STAGE AFTER ALL LOSSES

37127.744 :KN>D#E TO PER ANENT LOAD<PRESTRESS


D#E TO LI$E LOAD<1 3:D#E TO PER ANENT LOAD<PRESTRESS L


D#E TO S# OF EFFECTI$E PRESTRESS<PER ANENT LOAD<LI$E

% 1 % 3 % &

P =

f &= ;P A+ S&

f = ;P A+; P 9! S < : % 1< % 3> S

P! =

f &= ;P ! A+ S&

f = ;P ! A+ ; P ! 9! S < : % 1< % 3< % > S

f &= 1 39:; P ! A+ ; P ! 9! S& < : % 1< % 3 < % > S&> < LL S&

f = 1 39:; P ! A+ S> ; LL S

ALLOWABLE TENSION

ALLOWABLE COMPRESSION

AT 24.7 ! "F#&'( I+( &#/& S0))/&(STAGE 1 AT INITIAL STAGE BEFORE LOSSES

2331 .30 :KN>



3600 .73 :KN>D#E TO PER ANENT LOAD<PRESTRESS




f &= ;P ! A+ S&

f = ; P ! A+ ; P ! 9! S < : % 1< % 3< % < LL> S

P =

f &= ;P A+; P 9! S& < : % 1< % 3> S&

f = ;P A+ S

P! =

f &= ;P ! A+; P ! 9! S& < : % 1< % 3< % > S&

f = ;P ! A+ S

f &= ;P ! A+ ; P ! 9! S& < : % 1< % 3< % < LL> S&

f = ; P ! A+ S

AT 41.4! "M#$ / T #&$ S)*+STAGE 1 AT INITIAL STAGE BEFORE LOSSES

35 3 .245 :KN>



33314.05 :KN>D#E TO PER ANENT LOAD<PRESTRESS


D#E TO LI$E LOAD<1 3:D#E TO PER ANENT LOAD<PRESTRESS L




AT 4.7 ! "E+$ S0))/&(STAGE 1 AT INITIAL STAGE BEFORE LOSSES

P =

f &= ;P A+ S&

f = ;P A+ ; P 9! S < : % 1< % 3> S

P! =

f &= ;P ! A+ S&

f = ;P ! A+ ; P ! 9! S < : % 1< % 3< % > S

f &= 1 39:; P ! A+ S&> ; LL S&

f = 1 39:; P ! A+ ; P ! 9! S < : % 1< % 3< % > S> < LL S

f &= ;P ! A+ S&

f = ; P ! A+ ; P ! 9! S < : % 1< % 3< % < LL> S

3667 .1 10 :KN>



30 5 .5610 :KN>D#E TO PER ANENT LOAD<PRESTRESS




P =

f &= ;P A+ S&

f = ;P A+ ; P 9! S < : % 1< % 3> S

P! =

f &= ;P ! A+; P ! 9! S& < : % 1< % 3< % > S&

f = ;P ! A+ S

f &= ;P ! A+ ; P ! 9! S& < : % 1< % 3< % < LL> S&

f = ; P ! A+ S

ENSION PRESTRESS BOX GIRDERFICATIONS

AND DUCT

:4.7.4.3.3 ;1>

645.00 To- 6 4 .75 KN6.003.00

127 .15 )'

27 5.00 To-/ 25 37.55 KN17 .00 To-/ 240.676 K )/

630.003 30.002.20E;06 :)!r of &!-%o->

0.34

20.00 40000125.60

1.64 1640

1 2 3 4340 20 610

1 2 3 4770 11 0 1240660 50 200

3

3

T!-%o- $!r& '( % /&'- ! fro o&&o '& ' < ! o !-&(o '& o-

T!-%o- $!r& '( % /&'- ! fro o&&o '& ' ; ! o !-&(o '& o-

STRESSING FROM 1 END

@ K98L< 98:r'%> :r'%> : )'>

0.13 0.13 0.0622 0.725 54.660.13 0.3 5 0.1364 0.5511 166.060.0770 0.2 0.1656 0.5 5 316. 50.0770 0. 6 0.310 0.5100 364. 00.1303 0.4667 0.3 52 0. 4 0 227.0.07 0 0.6627 0.2 66 0. 0 1 07.20

0.13 0.13 0.0622 0.725 54.660.13 0.3 5 0.1364 0.5511 166.060.0770 0.2 0.1656 0.5 5 316. 50.0770 0. 6 0.310 0.5100 364. 00.1303 0.4667 0.3 52 0. 4 0 227.0.1120 0.6500 0.240 0. 0 3 12.36

0.13 0.13 0.0622 0.725 54.660.13 0.3 5 0.1364 0.5511 166.060.0770 0.2 0.1656 0.5 5 316. 50.0770 0. 6 0.310 0.5100 364. 00.1303 0.4667 0.3 52 0. 4 0 227.0.1 1 0. 110 0.245 0.6755 30.56

0.0000 0.0000 0.0 1 0.7467 60.330.0000 0.0000 0.051 0.7316 107.450.0000 0.0000 0.0770 0.704 121.670.0000 0.0000 0.1162 0.5703 142. 20.0000 0.0000 0.1 54 0.5630 173.510.0000 0.0000 0.150 0.52 320.70.0000 0.0000 0.1750 0.530 340.750.0000 0.0000 0.3142 0.5062 3 0.660.0000 0.0000 0.3437 0. 64 213.360.0000 0.0000 0.37 0 0. 20 247.01

for 2 &!-%o-/ )!r ! o-/ %!r &* / &' (!

!;:K9 ΣL< 98 >

8f )F



: )'> :KN>54.66 274. 6.12

166.06 6 .33 11.57316. 5 1001.43 14.43

364. 0 1336.1 17.00227. 1465.24 3 .201 . 171 .56 37.66

8f )F 8F )F 8f )F

:4.7.4.3.2 ;1>

:C4.7.4.3.2 ;1>4.26 4260000 Fro A &oC'%1.64 16400.45 4521.0 1063.5 352.4E<1.44 14 .7E<

1.642 164.2E<10 Fro A &oC'%3 0 K/ 1570 )'

TABLE 4.7.2;1

)' )'

2 .71 26.20 3.6016.7 15.1 1.2020.62 23.20 3.2115.4 17. 3 1. 1

3.60

+9I+ ->>

3 3

2 2

2 2

SFER

IDERATION T POINT #NDER CONSIDERATION

ER CONSIDERATION

8f )ES 8f )ES 8f )ES

8f )ES =



BEING CO P#TED

:C4.7.4.3.1>20.00

IS POINT LOSSES D#E TO ANCHORAGE SLIP ARE MERO

AGE OF CONCRETE AND RELAXATION OF STEEL

)' TABLE :4.7.4.2.1>

HORAGE SET

N OF STEEL



REME FIBER

F' &or!% $ S!r ! F' &or!%

:T> T; T;0 0 0

32 55 13 5 1541.0;37 4 437 1552 3667.0140 623 17 350 .5

0 0 2 4 0 0

350 .5

-12 .13 ;153.0 1301 )/ OK

-1 3 7.99 ;32 2.75073 )/ OK

4 . 45 . 7761 2 )/-245 4 ;247 .43344 )/

-1 23.1 ;324. 302 3 )/ OK

-1241 .79 ;1500. 6164 )/ OK

3214.51 66.36742 4 )/-15 3 ;3675.1 171 )/

OAD>

LOAD

.49 &+ LL

"KN6! 2

"KN6! 2

"KN6! 2

"KN6! 2

"KN6! 2

"KN6! 2

"KN6!2

"KN6! 2



-3311. ; 50.20 13 )/ OK

-932 . 4 ;1243.4 161 )/ OK

3214.51 66.36742 4 )/

-245 4. ;247 .43344 )/

-3 42.95 ; 1.2 52 6 )/ OK

-11442.1 ;1647.427 7 )/ OK

4 . 45 . 7761 2 )/-245 4. ;247 .43344 )/

-12 5. ;152.7053 5 )/ OK

-11412. 3 ;1644.1 513 )/ OK

3214.51 66.36742 4 )/-15 3. ;3675.1 171 )/

LOAD717.99 10 .124 2 2 )/ OK

-1 4 .7 ;3153.243 )/ OK

3214.51 66.36742 4 )/-245 4. ;247 .43344 )/

"KN6! 2

"KN6! 2

"KN6! 2

"KN6! 2

"KN6! 2

"KN6! 2

"KN6! 2

"KN6! 2

"KN6! 2

"KN6! 2

"KN6! 2

"KN6! 2

"KN6! 2

"KN6! 2

"KN6! 2

"KN6! 2



-325 .9 ; 6. 2 )/ OK

-5992.57 ;120 .21 )/ OK

4 . 45 .40 )/-245 4 ;247 .43 )/

-35 7.23 ;443.17 )/ OK

-47 2. ;670.65 )/ OK

3214.51 66.3 )/-15 3 ;3675.1 )/

OAD>-4 9 .25 ;472.3 60 )/ OK

1 2 .9753 324.102 47 )/ OK

3214.51 66.3 )/-1 3 ;3275.24 )/

LOAD- 993.9 ;567.2 )/ OK

-7 . 45 1 ;110.3 )/ OK

3214.51 66.3 )/-245 4 ;247 .43 )/

"KN6! 2

"KN6! 2

"KN6! 2

"KN6! 2

"KN6! 2

"KN6! 2

"KN6! 2

"KN6! 2

"KN6! 2

"KN6! 2

"KN6! 2

"KN6! 2

"KN6! 2

"KN6! 2

"KN6! 2

"KN6! 2



-4 1 . 2 ;451.65 )/ OK

- 7 . 3 ;7 7. )/ OK

4 . 45 .40 )/-245 4. ;247 .43 )/

-3 77. 4 ; 6.25 )/ OK

- 153.7 ; 41.5 )/ OK

3214.51 66.3 )/-15 3. ;3675.1 )/

LOAD-3 77. 4 ; 6.25 )/ OK

- 153.7 ; 41.5 )/ OK

3214.51 66.3 )/-245 4. ;247 .43 )/

"KN6! 2

"KN6! 2

"KN6! 2

"KN6! 2

"KN6! 2

"KN6! 2

"KN6! 2

"KN6! 2

"KN6! 2

"KN6! 2

"KN6! 2

"KN6! 2

CHECK FOR FLEXURE ST

FOR - MOMENT"AT SUPPORT 3 !

' F' &or!% o !-&, =

3667 To-.*=TOTAL DEPTH OF GIRDER

1.14.3

0.3342

0.3NO. OF WEBS= 3

0.51.6

1.434

NO. OF TENDONS= 6.00AREA OF 24,0.6" DIA WIRE STRAND

f = =

O ENT D#E TO SELF WEIGHT= % 1

O ENT D#E TO CO PONENTS AND ATACH ENTS= % 3

O ENT D#E TO WEARING S#RFACE AND #TILITIES= %

O ENT D#E TO $EHIC#LAR LI$E LOAD= LL

= 1.349 % 1<1.349 % 3<1.49 % <1. 49 LL

! ) =CENTROID OF PRESTRESSING STEEL FRO TOP%) =DISTANCE FRO E TRE E CO PRESSION FIBERS TO PRESTRE

%) = TOP FLANGE WIDTH :!U! & !>= f&

TOP FLANGE THICKNESS=& f&

BOTTO FLANGE WIDTH= f

BOTTO FLANGE THICKNESS=& f

WIDTH THICKNESS OF WEB= !

! ! ==

TOTAL AREA OF PRESTRESS STEEL= A )/

f ) =SPECIFIED TENSILE STRENGTH OF PRESTRESSING STEEL

f )V= IELD STRENTH OF PRESTRESSING STEEL

f V= IELD STRENTH OF NON;PRESTRESSING STEEL

f = SPECIFIED STRENGTH OF CONCRETEE) = OD#L#S OF ELASTICIT OF PRESTRESSING STEEL

WHERE, 0.35

0. 4

OTHERWISE, 0.54;::f ;35> >90.0. 4A// ! /! & o- / R! &'-+ ('r

FOR RECTANG#LAR SECTION,

= 33. 0 - 467

16.70 - 37

FOR T;SECTION

= 20. -32.00 - 45

NOW, 332.40 K/

2 5 02 K ). - 0152 5 02 K ). - 015

M#+#!0! R #+ /&8 ! +( R 0#& ! +(

.02 )'4.50 )'

2:S : 1fr < 3f )! > ; %- : S S- ; 1 >> 2 0

f )/ =f ) 1;X9: %) >X=3 1.0 ;:f )V f ) >

IF f = 0 )', Y 1=Y

1=

Y1=

=:A )/ 9f ) <A/9f/;A/ 9f/ > ::0.549f 9Y19 f ><:X9A)/ 9f ) %) >>

'=Y 19

=:A )/ 9f ) <A/9f/;A/ 9f/ ; 0.549f : f ; ! ! >9&f > ::0.549f 9Y19 ! ! >

'=Y 19

f )/ =

- =A )/ 9f )/ 9:%) ;' 3><A/9f/9:%/;' 3>;A/ 9f/ 9:%/ ;' 3> < ::0.549f 9: f ;

- =f - =

Z r

r / (!//!r of r

1.22

r = 2:S : 1 f r < 3 f )! > ; % - : S S- ; 1 > Z S f r>>f r =

f )! =

11642 0 To-;

r = 2 0 To-;2440 To-;

2440 To-;

AT 41.4! "M#$ / T #&$ S)*+

NO. OF WEBS= 30.4

10.734

*=TOTAL DEPTH OF GIRDER

WHERE, 0.35

' F' &or!% o !-&, =

350 . 4 To-.

A// ! /! & o- / R! &'-+ ('r

FOR RECTANG#LAR SECTION,=:A)/9f) <A/9f/;A/ 9f/ ; 0.549f : f ; ! ! >9&f > ::0.549f 9Y

= 12. 1 - 2 510.24 - 362

FOR T;SECTION

= 17.22 -1 .47 -

S f rr =

1.229 =

r=


! ! ==

! ) =CENTROID OF PRESTRESSING STEEL FRO TOP

f )/ =f ) 1;X9: %) >X=3 1.0 ;:f )V f ) >

%) =





= 1.349 % 1<1.349 % 3<1.49 % <1. 49 LL

'=Y 19

=:A )/ 9f ) <A/9f/;A/ 9f/ ; 0.549f : f&; ! ! >9&f&> ::0.549f 9Y19 ! ! >

'=Y 19

NOW, 3 2.27

5035 5.22 K ). - 7343.235035 5.22 K ). - 7343

M#+#!0! R #+ /&8 ! +( R 0#& ! +(

2:S : 1fr < 3f )! > ; %- : S S- ; 1 >>6.3 )'

12.35 )'2552 To-;2 2 To-;

2 2 To-;

CHECK FOR SHEAR STR

:'> C 8: C&#(#8*; S 8(#/+ /& S *&

Cr & '( D /&'- ! fro F' ! of S ))or& "% " / L'r+!/& o: > 5 .72

: > 1042.03: > 0. 3* 1155/o,

1155.00Cr & '( S! & o- / '& D /&'- ! % fro F' ! of S ))or& .! D /&'- !

= 1155.00

M ( /$ I 4.5.6.4$ = 415.7E< N

$- L!//!r of> $ < $/>

#$

f )/ =

- =A )/ 9f )/ 9:%) ;' 3><A/9f/9:%/;' 3>;A/ 9f/ 9:%/ ;' 3> < ::0.549f 9: f ;

- =

f - =

Z r

r / (!//!r of r

1.22

r =f r f

)! =

r =1.229 =

r =

%! ;' 30.7% !

% =

f 1 3 9 9%

$ < $ /

0.166 9 K 9 f 1 3 9 9 %

KK 3.26 [ 3.0K 3.00

$ 256. E< N

$/ =157.7E< N

$/ =/

#/! (!++!% -o.30 'rA = 11 3.00 3

/ = 202.45

$ : 9 % > [

3.56 [ 5.0

M ( /$ II 4.5.2. .2

$ = 415.7E< N

$- = $ < $/ < $) 4.5.2.2;1$) = 0 4.5.2. .2$ L!//!r of $ \ $

$ =$% = 3 6. E< N S*!'r for ! '& /! &$ = 3 3.2E< N C4.5.2. .2

' = 361 45.1E<4 N; ' f' &or!%

r! = S 9 : fr < f )! ; %- S- >fr = 2.2 )' 4. .3.6

f )! = 4.50 )'%- = 12736 .2E<4 N; To&'( -f' &or!% %

or -o- o )o/ &!r! = 11757 .2E<4N;

$ = 66 34.7E<1 N Z

$ = 66 34.7E<1 N

: 1 < : f) 0.166 f 1 3>>1 3 [ 3.0

$ ; $

A 9 fV 9 % / A 9 fV 9 % $/

1.34 9 f 1 3

0.0434 9 f 1 3 9 9% < $% < $ 9 r! ' Z 0.

$ =f) = .54 )'$ = 40077.7E<1 N

$ = 40077.7E<1 N

$/ = $- ; $ = $ ;$ = 136410.1E<1 N

/ =

1.56 [ 1.51.50

= 70 %!+

A = 11 3.00 3

/ = 530.14

M ( /$ III 4.5.2. .3

"* D ( &!#+ M0 *+$ <0 *( C&#(#8*; S 8(#/+361 45.1E<4 N.4157 7.0E<1 N

=2.150.05

"= D ( &!#+ T (*,B (* *+$ R 0#& $ S *& S)*8#+>&rV 15.1

;0.00061

17.342.47

$ =$ = 2 6605.3E<1 N

$/ =$/ = 320001.5E<1 N

: 0.16 9 f 1 3 < 0.2 9 f) >9 9% < $)

: A 9 fV 9 % 9: o&] < o& > 9 / - > $/

o&] =o&] =

=$ =

$ ^ %N 3

f =

]= o&]=_ = : : %> < 0.4 9 N < 0.4 : $ ; $ ) > o&] ; A)/ 9 f)o>

Fro T' (! 4.5.2. .3;1 R!) X '( !/ of ] '-% Y '+' -/& f '-% _ T* / / '- &!r'& ! )ro !//!/ & (( ] '-% Y ! o !/ o-/&'-&

] = o&]=Y=$ / = :$ ^>;$

0.052 Y :f >1 3 %

:$ ^>; $

11 3.00

1 .66

"$ D ( &!#+ M*?#!0! S)*8#+> R 0#& $

' S)' -+ "/ ' " / S '((!/& of Fo((o -+: >

: > 0.5 %: >/o,

/ ' =

200 [ / ' = 4 4 '& 200 C C

" C 8: A$ 0*8@ / L/+>#(0$#/+*; R #+ /&8 ! +(

365616

73 0257

" S#$ R #+ /&8 ! +( #+ ( W =

0. 1

11.44A// ! /)' -+ '& 300

53 0.12PRO$IDE

CUR<E TENDON EFFECT

"> I+-P;*+ F/&8 E 8(

A = 3

/ = A f V % o&] $/

/ =

A f V 0.052 :f >1 3

/ =

A)/ f)/ < A / f V ` :% ^ f > < 0.4 :N > < : $A)/ f )/ =

:% ^ f > < 0.4 :N > < : $ ^ ;$)> ; 0.4 $ / > o&]

A)/ f)/ < A / f V ` : $ ^ ;0.4 $/ ; $)> o&]

: $ ^ ;0.4 $/ ; $)> o&] =

A/XZ 0.001:% ! ; 60>3 of *! +*&

A/X[ A / <A PS 13003 of *! +*&

A/X= 3

^30a300

mailto:%C3%B820@200mm%20c/c



o/ ]= 0.727 01 1 1 ]=341 33

R'% / of C r '& r! of T!-%o-,R= 125600151.6226262626 N

W*!r!,251.73 N

" O0(-/ -P;*+ F/&8 E 8(

341 33R'% / ofT!-%o- $!r& '( C r != 4 .4R'% / of C r '& r! of T!-%o-,R= 4 400.00

127.264353 273 N

W*!r!,62.5 N

' S)' -+ of Co-b-! !-& R! -for ! !-& "/ ' " / S '((: > 2 & !/ % ' of % &

: >/o,/ ' =

PRO$IDE

F ; -=P 9 o/ ] R

F' &or!% &!-%o- For !,P =

F ; -=

S*!r! R!/ /&'- ! of Co- r!&! Co !r '+' -/& P ((;o & V D! '& o-

^$ - = 0.79:0.229% 9f 1 3>

F ;o &=P cRF' &or!% &!-%o- For !,P =

F ;o &=

S*!r! R!/ /&'- ! of Co- r!&! Co !r '+' -/& P ((;o & V D! '& o-

^$ - = 0.79:0.229% 9f 1 3>

^13a 40





RENGTH

3667 To-.104 To-.

1 3 To-.112 To-.4 To-.

354.160:STRENGTH;1>

1.64 6 .7625 - 1640

0. 5 15.57546 -

6.0643 - 11 030 . 2 -

5.545 -115.116 -

.5 -

21. 7 6 -63.7743 -60.0 32 -

630 33 30 3 3.7660547 -3

1570 )' 3 .21 K/S!!, T' (! C4. .2.1.1;1

1 01 )' 3 6.55 K/1 )' 60.07 K/

1.2 )' 6.00 K/17 000 )' 35473.16 K/

1.0 4.4. .3.10.7 4.4. .3.1

SING STEEL CENTROID



4. .2.1.1;14. .2.1.1;3

04 0.64

4. .2.1.1;

CALCULATE 8 FOR T SECTION

4. .2.1.1;2

1427.704 )'

4. .2.3.3;1 To-. To-. OK

4. .2.2.3

4. .2.2.3;1 1= 1.64. .3.6 3= 1.1

2= 1

To-;

Y1 = f' &or for o- r!&! /&r!-+&*

:X9A)/ 9f ) %) >>

! >9&f >9:' 3;&f 3>>

To-;

OK

17.656 -27.2 3 -

26. 171 -1.64 6 .7625 -0. 2 16.73776 -

1.33 5.0225 -

350 . 4 To-.1164 To-.

75 To-.53 To-.

623 To-.

:STRENGTH;1>

19 ! ! ><:X9A)/9f) %)>>

CALCULATE 8 FOR T SECTION

4. .2.1.1;2:X9A)/ 9f ) %) >>

K/ 16 6.770 )'

To-. To-. OK

OK

NGTH

4.5.3.7 %!= :A)/9f)/9%)<A/9fV9%/> :A)/9f)/%!= 11 0.034

f Fo((o -+

6. - B W C!-&!r( -! '-% Cr & '( S! & o-

0.0 0 L

4.5.6.4;14.5.6.4;3

4.5.6.4;

! >9&f >9:' 3;&f 3>>

4.5.6.2;2

4.5.6.4;2

OK

4.5.2. .2;1 C/!=#+ $ S *& *o- % ! &o -f' &or!% %!'% (o'%/ - ( % -+ DC \ DW

o !-& '& /! & o- % ! &o ! &!r-'((V '))( !% (o'%/

'% (o'% o !-& ' & -+ o- &*! o-o( &*! & o-

1.56E<06 N

6 9 f 1 3 9 9%

4.5.2. .2;2

4.5.2. .2;

2.0604.5.2. .3;1

3.56

4.5.2.2;2

39 : E / 9 A/ < E ) 9 A) >



476.30 4.5.3.4;1740. 4.5.3. ;1 \ 3

600 4.5.3. ;1 \ 3

476.30

OK

N213 257 N OK

N OK

4. .2. ;

4. .2. ;

;$ ) > ; 0.4 $ / > o&]

=

-3



4.10. .2.1;130 %!+r!!/ 0.2 70 01 r'% '-/

N

13. K f&

OK, Pro %! - R! -for ! !-&

4.10. .2.1;1N

7.44 K f&

OK, Pro %! - R! -for ! !-&

/& of Fo((o -+40.00 4.10. .2

600

40.00

of !/,$ r= ^$ -

of !/,$ r= ^$ -



EFFECTI$E FLANGE WIDTH

%o= 1.64/)'-=(= 20

E-% /)'- for o-& - o / + r%!r( = 0.59( 7 .735

-&!r or /)'- for o-& o / + r+!r( = 0.69( 05.676

= PH SICAL WIDTH 1, 3, 2

!1, !3, !2 = !U! & ! %&*=!U! & ! ?'-+! %&* for -&!r or )or& o- of ' /)'-

/=!U! & ! ?'-+! %&* '& -&!r or / ))or& or for '-& (! !r'=&r'-/ & o- - !U! & ! ?'-+! %&* &'X!- '/ (!//!r of

1> )*V/ '( ?'-+! %&* '& !' * / %! of !3> /)'-

( =/)'- (!-+&* &'X!- for %!&!r - -+ of !U! & ! ?'-+! %&*

o- &o) ?'-+!for '-& (! !r )or& o- 1

!1=.79 1

for --!r of ! / 3!3=0.7"9 3

for o&&o ?'-+! 2!2=.79 2

+$ ')*+ =6;# = 6=

1 ( 0.14 0.44 0.523 ( 0.020 4 1 12 ( 0.0444522 0.7 0.75

fro /r ! :!-%

Por& o->fro r !: %%(! Por& o->



F -% / '-% fro r ! LRFD FIG. .6.3.6.3;3+$ ')*+ =

E-% Por& o-

= 1 1.75 3.755= 2 0. 25 0. 25= 3 1.3006 1.20 23

W! W %&* '& S ))or& 0.5W! W %&* '& % 0.4

To) EU! & ! F('-+! W %&* '& E-% S)'- = E-% Por& o-.026

To) EU! & ! F('-+! W %&* '& I-&!r or S)'- = E-% Por& o-4.313

Bo&&o EU! & ! F('-+! W %&* '& E-% S)'- = E-% Por& o-.0013

Bo&&o EU! & ! F('-+! W %&* '& I-&!r or S)'- = E-% Por& o-2.12

N/+-P& '(& '' $ R #+ /&8 ! +(A/ 6.4 0.01F/= 30 )' 61.0 K/%/= 1463.4 61.4 -3A/ = 6.4 0.01F/ = 30 )' 61.0 K/%/ = 5 .4 2. -3

%%(!Por& o-

3 -3

3 -3



A/fV>



o- !r/& o- f' &or T; &o N;750 2 6.2

$ M/! +(



LRFD .6.3.6.3

6 .7625 -1151.16 -

- 0.19( 7 . 735 - 0.29%o

- 0.19( 0.5676 -

2.6 1 1. 273 - E&& 4

13 .46435 -

0. 25 37.0464 - OK 36.140553 -

1.22 43.43334 - OK .3 00323 -

#+( &#/& ')*+ =6;# = 6=

1 ( 0.3 0.25 0. 33 ( 0.0 1 1 12 ( 0.0 111 0.5 0.7

fro /r !

:!-%Por& o->

fro r !

: %%(!Por& o->



#+( &#/& ')*+ =

= 1 1.265 3.473= 2 0. 25 0. 25= 3 1.06 3 1.37275

7.043

.66

.31 6

2.45 76

o !r= 4% ' of 'r= 0. 7

% ' of 'r= 34

E-%Por& o-

%%(!Por& o-

%%(!Por& o-

%%(!Por& o-

%%(!Por& o-

%%(!Por& o-

TORSIONINPUTS)'- = 20W %&* = 7.5f = 6f = 6fV = 60E = 676E)/ = 35000E (% /&!!( = 37000D!)&* of G r%!r = 1.64No . Of W! / = 3S! & o-'( Ar!' A = 4.260

o !-& Of I-!r& ' I = 1.642C!-&ro % of G r%!r fro o&&o = 1.06C!-&ro % of G r%!r fro &o) = 0.452S! & o-'( o% ( / Bo&&o S = 1.44S! & o-'( o% ( / To) S& = 3.5

To&'( Ar!' of Pr!/&r!// -+ S&!!( = 0.03 3W! W %&* = 0.50W! W %&* for S*!'r= 0.50! '(!-& %&*= ! = 1.60

= 1.434! '(!-& %&* S*!'r= ! = 1.434No . Of W! / = 3

To) ?'-+! &* X-!// 334Bo&&o ?'-+! &* X-!// 300

f) = 3 X/f) = 304. X/P = A)/.f) = 55 0. 033077

INPUT FROM MODEL

T = 4124.0

$ :F(! r!>= 116 .0

= 17200

N :F' &or!% ' '( for ! &!-/ (! < ! o )r!// ! ; !> = 0

PROPERTIES OF GIRDER "OUTSIDE

d= R!/ /&'- ! f' &or:&or/ o->= 0.70 T r= 0.134ef A )3 P e:1<f) .134ef >

0.34dT r= T =$ ! =$ :?! r!><T %/ :3Ao>

=ABS:$ ;d$)> :d % > =f =

STEP -CALCULATE 06 8 *+$ #+$ ? *+$

? ABS"M06$ . N0 . "<0 -<) 8/( -A)' )/6

A)/= 31. 52f)o= 173.0

E)= 35000]= 33.75A/= 0.01

o&] 3.247

? 0.00011 73

? ABS"M06$ . N0 . "<0 -<) 8/( -A)' )/6

0.000022

#/! &* / '( ! of &o f -% ] '-%YFro LRFD TABLE 4.5.2. .3.1

For ?1Y=]=

STEP -DETERMINE RE UIRED SPACING OF STIRRUPS

F/&S *&

$ = 0.0216Yef667.23

$/=:$ d>;$ ;$) =$/= S*!'r for & 'rr !% V &r'-/ !r/! r! -for ! !-&$/= A fV% : o&]> /Ar!' of /*!'r r! -for ! !-& )ro %!% (!+ =

$ d = $-=$ <$/<$)

No. of /*!'r r! -for ! !-& (!+/ )ro %!% =g/ = A .fV.% .: o&]> $/ =A /= $/ :fV9% 9 o&]>A /= 0.07 112302

F/& T/&'#/+

T- =3AoA&fV o&] /Ar!' of /*!'r r! -for ! !-& )ro %!% (!+ =No. of /*!'r r! -for ! !-& (!+/ )ro %!% =

T- = T d 65 66.1 4623 K ).I- *

g/ = 3AoA&fV o&] T-39A& /= T- :Ao9fV9 o&]>39A& /= 0.07 3776103

F/& C/!=#+ $ S *& J T/&'#/+

A /<3A& /= 0.17A <& /= A /<3A& /=/= A <& :A /<3A& />/= 27. 5

S( ) N/.7C 8: ( L/+>#(0$+*; R #+ /&8 ! +( $0 (/ T/&'#/+ *+$

A(=T-.)* :3AofV> 26.0 -315.0 -3

P* = 21 .2 I- *A(.fV=T-.)* :3Ao> 316 .45 K )/

A(.fV=T-.)* :3Ao> 1052. 7 K )/2622.43 K )/

E 0*(#/+ 1 262 K )/

503.037 7 K )/H +8 1 2 A)' /:

:% . ^ f > < 0.4 :N

:A/)9f)/><:A/9fV>=

'= AS D#E TO OTHER LOADS=

= AS D#E TO TENDON FORCE EFFECTS ON WEB=

= '<:.49 > 3. 1 - *3

%= :.4'>< 1.25 - *3

!= . 9:'< > 1. - *3

Ar!' of /&!!(= 3. 1 - *3

')*8#+> 2 .2 #+8



DESIGN

256 - *X/X/X/X/ LRFD E .4. .3.X/ LRFD E .4. . .3X/ LRFD E .4. .2.3

64.0 :I- *>

: 3> 5207: > 27 313: > 3.0 :I- *>: > 32.0 :I- *>: 2> 7 443: 2> 1 20 5

2

K )/

X ).f&

K )

X ).f&

K )/

:I- * 3> :I- * >

:I- * 2> :I- * 2>

3 :I- * 3>



100.0 5 I- *1 0. 5 I- *

6 .76062 I- *46.47 7 I- *

533.1372 0. 5 I- *

6.0637711 .62 5 I- *60.37435 I- *

762.6 5

21 .3712 I- *

60.0 I- * %!=%!)&*;1106. I- * 0.79%!

60.0 I- *

for !(( ('r /&r & r!/164022476023 OK LRFD E .4.5.3.1;4

:O-! + r%!r>0 X )/

116 X )/

313 X )/0.7 LRFD E .4.5.2.2;3

2 71 X )/ /:

LRFD E .4.5.3.1;2 (o//! 21.050.210 61

3

I- *3

3 I- * 3



1 6576 K ); -1 1 K );f&

221 K );f& T/&'#/+ !0'( = 8/+'#$ & $4124.0 K );f&

1414 X )/ LRFD E .4.5.3.1;

0.600.100 f

0.0750.10.1

"E'A' E)A)'diff

-3 2 TENDONS PER WEBX/ for 1

X/%!+r!! #/! $ '-% $) of &o&'( + r%!rI- *3

for 1

OK,+ >; 0.11 715

"E'A' E)A)' E8A8

0.023771

*+$ 06 8 .12.05

33.75

Fro LRFD TABLE 4.5.2.2;3K )/

63 .01 X )/

0.

Co ) &! '( ! of Y orr!/)o-% -+ &o &*! '( !/ of 06 8 J

-3



13 No/.46.1 I- *

Fro LRFD TABLE 4.5.2.6.30.

No/.

26.3 I- *

13 0.A/& rr )= 4.35 -3

3.37674 -3 f&

?0&

Fro LRFD TABLE 4.5.6. ;2

1 O-! !3 O-! !

Fro LRFD TABLE 4.5.2.4;1

-3

f r!/ (&/ 'r! &'X!- for *o(!r %+! /! & o- &*!- -o of ! /



3.20 INCH3

0.32 INCH3



S&r' - S&r' -0 0.032991 0.125 0 0.032991 0.125

f21.8 24.3 0.075 3.75 3.24

0.122.5 24.9 0.1 3.14 2.91

0.7 0.6 diff 0.61 0.33

28 1 for 1 24.4 13.2

0.7 0.025 0.61 0.3322.5 24.325 3.14 2.91

14.6 for 1 1.84

0.4816686 0.06070344

theta= 22.9816686 eta= 3.07929656

'!*?A/& rr ) :A />?! r!<:A />&or/ o-

.95 I+8

TORSIONINPUTS)'- = 20W %&* = 7.5f = 6f = 6fV = 60E = 676E)/ = 35000E (% /&!!( = 37000D!)&* of G r%!r = 1.64No . Of W! / = 3S! & o-'( Ar!' A = 4.260

o !-& Of I-!r& ' I = 1.642C!-&ro % of G r%!r fro o&&o = 1.06C!-&ro % of G r%!r fro &o) = 0.452S! & o-'( o% ( / Bo&&o S = 1.44S! & o-'( o% ( / To) S& = 3.5

To&'( Ar!' of Pr!/&r!// -+ S&!!( = 0.03 3W! W %&* = 0.40W! W %&* for S*!'r= 0.40! '(!-& %&*= ! = 1.00

= 0.734! '(!-& %&* S*!'r= ! = 0.734No . Of W! / = 3

To) ?'-+! &* X-!// 334Bo&&o ?'-+! &* X-!// 300

f) = 3 X/f) = 304. X/P = A)/.f) = 55 0. 033077

INPUT FROM MODEL

T = 4124.0

$ :F(! r!>= 76.0

= 12254

N :F' &or!% ' '( for ! &!-/ (! < ! o )r!// ! ; !> = 0

PROPERTIES OF GIRDER "OUTSIDE

To) ?'-+! %&* = 34 3.00Bo&&o ?'-+! %&* = 24 4.00

To&'( %!)&* of + r%!r = 1640.00%/ = 1 2 .40

40 64347 1

PROPERTIES OF GIRDER "CENTERLINE

To) ?'-+! %&* = 1723Bo&&o ?'-+! %&* = 3755

To&'( %!)&* of + r%!r = 1423

2 6 70

752

= 734.00% = EU! & ! /*!'r %!)&* 1155.00

= 734.00

STEP 2- DETERMINE THE CROSS SECTION PARAMETERS

= 3Ao =

STEP 3-CHECK THE WEB WIDTH

!r fV &*'& !U! & ! ! %&* / '%! '&! &o )r! !-& &*! r /* -+$)= =$ = =$ =d$- =$- 0.34f % <$) =d= R!/ /&'- ! f' &or= =d$- =

STEP 4-CALCULATE SHEAR STRESS

C*! X f &or/ o- /& ! o-/ %!r!% T `0.34dT rf) = 2. X/

A )= To&'( 'r!' !- (o/!% V &*! o &/ %!

)!r !&!r of o- r!&! ro// /! & o-Po=L!-+&* of &*! o &/ %! )!r !&!rof &*! ro// /! & o-

Ao= Ar!' !- (o/!% V &*! /*!'r ?o )'&*)!r !&!r of o- r!&! ro// /! & o-Po=L!-+&* of &*! C!-&!r( -! )!r !&!r

of &*! ro// /! & o-

= EU! & ! ! %&*for /*!'r

= EU! & ! ! %&*for &or/ o-

A8) 2 6P8 2A/=A ) 3 P

d= R!/ /&'- ! f' &or:&or/ o->= 0.70 T r= 0.134ef A )3 P e:1<f) .134ef >

0.34dT r= T =$ ! =$ :?! r!><T %/ :3Ao>

=ABS:$ ;d$)> :d % > =f =

STEP -CALCULATE 06 8 *+$ #+$ ? *+$

? ABS"M06$ . N0 . "<0 -<) 8/( -A)' )/6

A)/= 31. 52f)o= 173.0

E)= 35000]= 33.2A/= 0.01

o&] 3. 24

? ;0.0011 277

? ABS"M06$ . N0 . "<0 -<) 8/( -A)' )/6

0.00000

#/! &* / '( ! of &o f -% ] '-%YFro LRFD TABLE 4.5.2. .3.1

For ?1Y=]=

STEP -DETERMINE RE UIRED SPACING OF STIRRUPS

F/&S *&

$ = 0.0216Yef25.2

$/=:$ d>;$ ;$) =$/= S*!'r for & 'rr !% V &r'-/ !r/! r! -for ! !-&$/= A fV% : o&]> /Ar!' of /*!'r r! -for ! !-& )ro %!% (!+ =

$ d = $-=$ <$/<$)

No. of /*!'r r! -for ! !-& (!+/ )ro %!% =g/ = A .fV.% .: o&]> $/ =A /= $/ :fV9% 9 o&]>A /= 0.016 0 02

F/& T/&'#/+

T- =3AoA&fV o&] /Ar!' of /*!'r r! -for ! !-& )ro %!% (!+ =No. of /*!'r r! -for ! !-& (!+/ )ro %!% =

T- = T d 65 66.666666666 K ).I- *

g/ = 3AoA&fV o&] T-39A& /= T- :Ao9fV9 o&]>39A& /= 0.07 35715

F/& C/!=#+ $ S *& J T/&'#/+

A /<3A& /= 0.11A <& /= A /<3A& /=/= A <& :A /<3A& />/= 1 .59

S( ) N/.7C 8: ( L/+>#(0$+*; R #+ /&8 ! +( $0 (/ T/&'#/+ *+$

A(=T-.)* :3AofV> 26.0 -315.0 -3

P* = 21 .2 I- *A(.fV=T-.)* :3Ao> 316 .47 K )/

A(.fV=T-.)* :3Ao> 1052.50 K )/3217.2 K )/

E 0*(#/+ 1 3217 K )/

503.037 7 K )/H +8 1 2 A)' /:

:% . ^ f > < 0.4 :N

:A/)9f)/><:A/9fV>=

'= AS D#E TO OTHER LOADS=

= AS D#E TO TENDON FORCE EFFECTS ON WEB=

= '<:.49 > 1. - *3

%= :.4'>< 0.70 - *3

!= . 9:'< > 1.07 - *3

Ar!' of /&!!(= 1. - *3

')*8#+> 14. 2 #+8



DESIGN

256 - *X/X/X/X/ LRFD E .4. .3.X/ LRFD E .4. . .3X/ LRFD E .4. .2.3

64.0 :I- *>

: 3> 5207: > 27 313: > 3.0 :I- *>: > 32.0 :I- *>: 2> 7 443: 2> 1 20 5

2

K )/

X ).f&

K )

X ).f&

K )/

:I- * 3> :I- * >

:I- * 2> :I- * 2>

3 :I- * 3>



100.0 5 I- *1 0. 5 I- *

6 .76062 I- *46.47 7 I- *

533.1372 0. 5 I- *

6.0637711 .62 5 I- *60.37435 I- *

762.6 5

21 .3712 I- *

26. I- * %!=%!)&*;1106. I- * 0.79%!

26. I- *

for !(( ('r /&r & r!/164022261435 OK LRFD E .4.5.3.1;4

:O-! + r%!r>0 X )/

76X )/

3444 X )/0.7 LRFD E .4.5.2.2;3

3377 X )/ /:

LRFD E .4.5.3.1;2 (o//! 21.050.210 61

3

I- *3

3 I- * 3



1 6576 K ); -1 1 K );f&

221 K );f& T/&'#/+ !0'( = 8/+'#$ & $4124.0 K );f&

5 X )/ LRFD E .4.5.3.1;

0.440.073 f

0.0750.092

0.1"E'A' E)A)'

diff -3 2 TENDONS PER WEB

X/ for 1

X/%!+r!! #/! $ '-% $) of &o&'( + r%!rI- *3

for 1

OK,+ >; ;1.1 2774

"E'A' E)A)' E8A8

0.00 37

*+$ 06 8 . 92.23

33.2

Fro LRFD TABLE 4.5.2.2;3K )/

113. X )/

0.

Co ) &! '( ! of Y orr!/)o-% -+ &o &*! '( !/ of 06 8 J

-3



No/.106.5 I- *

Fro LRFD TABLE 4.5.2.6.30.

No/.

2 .2 I- *

0.A/& rr )= 1. 6 -3

1.237174 -3 f&

?0&

Fro LRFD TABLE 4.5.6. ;2

1 O-! !3 O-! !

Fro LRFD TABLE 4.5.2.4;1

-3

f r!/ (&/ 'r! &'X!- for *o(!r %+! /! & o- &*!- -o of ! /



S&r' - S&r' -0 0.003997 0.125 0 0.003997 0.125

f21.8 24.3 0.075 3.75 3.24

0.09222.5 24.9 0.1 3.14 2.91

0.7 0.6 diff 0.61 0.33

28 1 for 1 24.4 13.2

0.476 0.017 0.4148 0.224422.276 24.317 3.3352 3.0156

16.328 for 1 2.5568

0.065263016 0.01021953

theta= 22.34126302 eta= 3.32498047

'!*?A/& rr ) :A />?! r!<:A />&or/ o-

27. I+8

S *& R '#'(*+8 (/ P0;; O0(

O-! *'(f of &*! !U! & ! (!-+&* of &*! f' ( r! )('-! - /*!'r \ &!-/% = 1 0 Co !r o- % & 6.5 -

160 O &/ %! % ' of % & 6. -

150 .3 -30 0.5 -

400 30 -310 5. -

30 16.5 -330 5.5 -

S& rr ) / -+= 0.000653 3 0. -3

310 5. -f = 2 . 4 )' 4 K/$- = 3.51 K ) -$r = 3.274 K ) - OK $ = 1.02 K ) -

C&*8:#+> / C/ & C/+8& ( LRFD 4.10. .2.1 ;1L/8*; S;*= A8(#/+

430 1. 22222 f&% = 6.5F ; -= 13. K f&F ;o &= 7.44 K f&

!-% = . 7 X );f& f&

% = 3.34 X );f& f&f = 6 X/fr= 0.400 X/ 400 )/

B*h2 13 *=% = 6.5 - B=

21 . 23

V= 2. -f/ = 9V If/ = 0.45 X/ S! & o- / Cr' X!%

To&'( o !-& = . 7i = 0.0014 161A/ = 0.134 7444

/)' -+ for S& rr )/ = 1.7 -

$-= .149% !U 9:f >h1 3%!U =

%% &=

% &/)' -+/ % &=&=%!U = % <%% & =%!U = & ;%% & 3 =%!U = % <%% & </ % & 3 =

%!U =

* %/=

I (o '( =

I (o '( = -



- for r !% !(! !-&

13 -

TIME DEPENDANT LOSS CALCULATIONS

kf PLT= 109:f ) 9A)/ A+>9 *9 /&<139 *9 /&<kf )R



.9. .3-1

CHECK FOR FLEXURE

FOR - MOMENT"AT SUPPORT !

1 33 .34 To-.*=TOTAL DEPTH OF GIRDER

1.1216.64

0.345.6

0.334NO. OF WEBS=

0.7

2.62. 4

NO. OF TENDONS= REFAREA OF 22,0.6" DIA WIRE STRAND

f = =

WHERE, 0.35





= 1.349 % 1<1.349 % 3<1.49 % <1. 49 LL

! ) =CENTROID OF PRESTRESSING STEEL FRO TOP

%) =DISTANCE FRO E TRE E CO PRESSION FIBERS TO PRES%) =

TOP FLANGE WIDTH= f&

TOP FLANGE THICKNESS=& f&

BOTTO FLANGE WIDTH= f

BOTTO FLANGE THICKNESS=& f


! !==

TOTAL AREA OF PRESTRESS STEEL= A )/

f ) =SPECIFIED TENSILE STRENGTH OF PRESTRESSING STEEL

f )V= IELD STRENTH OF PRESTRESSING STEELf V= IELD STRENTH OF NON;PRESTRESSING STEEL

f = SPECIFIED STRENGTH OF CONCRETEE) = OD#L#S OF ELASTICIT OF PRESTRESSING STEEL

f )/ =f ) 1;X9: %) >X=3 1.0 ;:f )V f ) >

0.54OTHERWISE, 0.54;::f ;35> >90.

0. 6A// ! /! & o- / R! &'-+ ('r


= REF - REFREF -

FOR T;SECTION

= REF - REFREF -

NOW, REF K/

REF K ). - REFREF K ). -

M#+#!0! R #+ /&8 ! +( R 0#& ! +(

6.12 )'REF )'

S : fr < f )! > ; %- : S S- ; 1 > REF

REFREF To-;REF To-;

15733 To-;

REF To-;

FOR MOMENT"AT MID SPAN 22.2 !

IF f =35 )', Y 1=Y1=Y1=

=:A )/ 9f ) > ::0.549f 9Y19 f ><:X9A)/ 9f ) %) >>

'=Y 19

=:A )/ 9f ) ; 0.549f : f ; ! ! >9&f > ::0.549f 9Y19 ! ! ><:X9A)/ 9f )

'=Y 19

f )/ =

- =A )/ 9f )/ 9:%) ;' 3> < ::0.549f 9: f ; ! >9&f >9:' 3;&f 3>>

- =f - =

Z r

r / (!//!r of 1.3 r

1.22

r = S : f r < f )! > ; % - : S S- ; 1 > Z S f rf r =

f )! =

S f rr =

1.39 r =1.229 =

r =

112 7.634 To-.

A// ! /! & o- / R! &'-+ ('r


= REF - REFREF -

REF K ). - REFREF K ). -

CHECK FOR SHEAR S

:'> C 8: C&#(#8*; S 8(#/+ /& S *&

Cr & '( D /&'- ! fro F' ! of S ))or& "% " / L'r+: > $AL#E

: > 101: > 0. 3* 1050/o,

$AL#ECr & '( S! & o- / '& D /&'- ! % fro F' ! of S ))or& .! D /&

= $AL#E

M ( /$ I 4.5.6.4$ = 160.0E<4 N

$- L!//!r of> $ < $/>

#$





= 1.349 % 1<1.349 % 3<1.49 % <1. 49 LL

=:A )/ 9f ) > ::0.549f 9Y19 f&><:X9A)/ 9f ) %) >>

'=Y 19

- =A )/ 9f )/ 9:%) ;' 3><::0.549f 9 f&9&f&>9:%) ;&f& 3>>

- =

f - =

%! ;' 30.7% !

%=

f 1 3 9 9%

$ < $ /

0.166 9 K 9 f 1 3 9 9 %

KK REF [ 3.0K REF

$ REF N

$/ =REF N

$/ =/

#/! 16 (!++!% -o. 30 'rA = 215 .00 3

/ = $AL#E

$ : 9 % > [

$AL#E [ .71

M ( /$ II 4.5.2. .2

$ = 160.0E<4 N

$- = $ < $/ < $) 4.5.2.2;1$) = 0 4.5.2. .2$ L!//!r of $ \ $

$ =$% = 706.0E< N S*!'r for ! '& /!$ = 67 .0E< N C4.5.2. .2

' = 101600.0E<6 N; ' f' &or!%

r! = S 9 : fr < f )! ; %- S- >fr = 2.37 )' 4. .3.6

f )! = REF )'%- = 600600.0E<4 N; To&'( -f' &or!% %

or -o- o )o/ &!r! = REF N;

$ = $AL#E N Z

$ = $AL#E N

: 1 < : f) 0.166 f 1 3>>1 3 [ 3.0

$ ; $

A 9 fV 9 % / A 9 fV 9 % $/

1.34 9 f 1 3

0.0434 9 f 1 3 9 9% < $% < $ 9 r! '

$ =f) = REF )'$ = REF N

$ = $AL#E N

$/ = $- ; $ = $ ;$ = $AL#E N

/ =

$AL#E [ 1.5$AL#E

= 70 %!+

#/! 16 (!++!% -o. 30 'rA = 215 .00 3

/ = $AL#E

M ( /$ III 4.5.2. .3

"* D ( &!#+ M0 *+$ <0 *( C&#(#8*; S 8(#/+101600.0E<6 N.160000.0E<3 N

=$AL#E$AL#E

"= D ( &!#+ T (*,B (* *+$ R 0#& $ S *& S)*8#+>&rV 15.1

$AL#E

17.342.47

$ =$ = $AL#E N

$/ =$/ = $AL#E N

: 0.16 9 f 1 3 < 0.2 9 f) >9 9% < $)

: A 9 fV 9 % 9: o&] < o& > 9 / - > $/

o&] =o&] =

=$ =

$ ^ %N 3

f =

]= o&]=_ = : : %> < 0.4 9 N < 0.4 : $ ; $ ) > o&] ; A)/ 9 f

Fro T' (! 4.5.2. .3;1 R!) X '( !/ of ] '-% Y '+' -/& f ' T* / / '- &!r'& ! )ro !//!/ & (( ] '-% Y ! o !/ o-/&'-&

] = o&]=Y=$ / = :$ ^>;$

0.052 Y :f >1 3 %

:$ ^>; $

#/! 16 (!++!% -o. 30 'r215 .00

$AL#E

"$ D ( &!#+ M*?#!0! S)*8#+> R 0#& $

' S)' -+ "/ ' " / S '((!/& of Fo((o -+: >

: > $AL#E: >/o,

/ ' =

$AL#E [ $AL#E$AL#E

" C 8: A$ 0*8@ / L/+>#(0$#/+*; R #+ /&8 ! +(

REF

$AL#E

" S#$ R #+ /&8 ! +( #+ ( W =

0.2

REFA// ! /)' -+ '& 300

REF REFPRO$IDE

CUR<E TENDON EFFE

"> I+-P;*+ F/&8 E 8(

A = 3

/ = A f V % o&] $/

/ =

A f V 0.052 :f >1 3

/ =

A)/ f)/ < A / f V ` :% ^ f > < 0.4 :N > < :A)/ f )/ =

:% ^ f > < 0.4 :N > < : $ ^ ;$)> ; 0.4 $ / > o&]

A)/ f)/ < A / f V ` : $ ^ ;0.4 $/ ; $)> o&]

: $ ^ ;0.4 $/ ; $)> o&] =

A/XZ 0.001:% ! ; 60>3 of *! +*&

A/X[ A / <A PS 13003 of *! +*&

A/X= 3

^30a300



REFR'% / of C r '& r! of T!-%o-,R= 1400000

REF N

W*!r!,33.6 N

" O0(-/ -P;*+ F/&8 E 8(

REFR'% / of C r '& r! of T!-%o-,R= 1400000

REF N

W*!r!,5 4.35 N

' S)' -+ of Co-b-! !-& R! -for ! !-& "/ ' " / S: > 2 & !/ % ' of % &

: >/o,

/ ' =PRO$IDE

F ; -=P RF' &or!% &!-%o- For !,P =

F ; -=

S*!r! R!/ /&'- ! of Co- r!&! Co !r '+' -/& P ((;o & V D! '&

^$ - = 0.79:0.229% 9f 1 3>

F ;o &=P cRF' &or!% &!-%o- For !,P =

F ;o &=

S*!r! R!/ /&'- ! of Co- r!&! Co !r '+' -/& P ((;o & V D! '&

^$ - = 0.79:0.229% 9f 1 3>

^13a 40





STRENGTH

434.4 To-.423 To-.

To-.1 05.4 To-.

354.160:STRENGTH;1>

1.4 47.045 -0.2 1 .46 6 -

. 7026 -644.4 25 -

7.5 2 -225.4773 -

5.545 -

24. 2 5 -

1 1. 273 -124.522 -

REF 3REF 3 REF -3

1570 )' 3 .21 K/S!!, T' (! C4. .2.1.1;1

1 01 )' 3 6.55 K/30 )' 60.76 K/

0 )' 4.51 K/17 000 )' 35473.16 K/

1.0 4.4. .3.10.7 4.4. .3.1

4. .2.1.1;14. .2.1.1;3

TRESSING STEEL CENTROID



04 0.64

4. .2.1.1;

REF

4. .2.1.1;2

REF )'

4. .2.3.3;1 To-. To-. OK

4. .2.2.3

4. .2.2.3;14. .3.6

To-;

To-;

REF

Y1 = f' &or for o- r!&! /&r!-+&*

%) >>



407 To-.241 To-.42 To-.

3142.4 To-.

:STRENGTH;1>

REF

To-. To-. OK

RENGTH

4.5.3.7

/& of Fo((o -+

$AL#E -- ! B W C!-&!r( -! '-% Cr & '( S! & o-

$AL#E L

4.5.6.4;14.5.6.4;3

4.5.6.4;



25. 1 4.5.3.4;1$AL#E 4.5.3. ;1 \ 3$AL#E 4.5.3. ;1 \ 3

$AL#E

$AL#E

N$AL#E N REF

N REF

4. .2. ;

4. .2. ;

CT

$ ^ ;$ ) > ; 0.4 $ / > o&]

=

-3



4.10. .2.1;1N

REF

4.10. .2.1;1N

REF

'((!/& of Fo((o -+40.00 4.10. .2

600

40.00

o- Fof !/,$r= ^$

-

o- Fof !/,$ r= ^$ -

Ramp 4 R1 1#6 Dist Change at Coupler Location

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