Prestressed Concrete Girder Design For Bridge Structure Based On AASHTO 17th Edition & ACI 318-14

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Prestressed Concrete Girder Design for Bridge Structure Based on AASHTO 17th Edition & ACI 318-14 INPUT DATA & DESIGN SUMMARY f 'c =

6

ksi, (41 MPa)

fy* = fy =

60

ksi, (414 MPa)

T=

42

in, (1067 mm)

fsu* = fpu =

270

ksi, (1862 MPa)

B=

28

in, (711 mm)

fpy = 12 8

243 # #

ksi, (1675 MPa) 8 8

6

@

C= D= E= F= G= W=

8 72 10 7 5 8

in, (203 mm) in, (1829 mm) in, (254 mm) in, (178 mm) in, (127 mm) in, (203 mm)

CONCRETE STRENGTH REBAR STRENGTH TENDON TENSILE STRENGTH TENDON YIELD STRENGTH COMPRESSION REINF. TENSION REINF. SHEAR STIRRUP REINF. 2 legs, # PRESTRESSING TENDONS 36 strands (each

0.5 in diameter & (13 mm) DISTANCE TO CENTROID OF COMPRESSION d' = DISTANCE TO CENTROID OF PRESTRESSED dp =

(

12 (305 mm) 0.153 99 4.5

SECTION SECTION DIMENSIONS

in o. c. in2 area ) mm2) in, (114 mm)

SECTION PROPERTIES A= 1125 in2 yt = 34.65 in

64

in, (1626 mm)

DISTANCE TO CENTROID OF TENSION GIRDER SPAN LENGTH

d= L=

68 80

in, (1727 mm) ft, (24.38 m)

GIRDER SPACING

S=

8

ft, o.c., (2.44 m)

I= St =

CONCRETE DECK THICKNESS

t=

8

in, (203 mm)

Sb =

yb =

37.35 in 762125 in4 21995

in3

20405

in3

TENDON FORCE IMMEDIATELY AFTER PRESTRESS TRANSFER fpy, (ACI 318-14 20.3) Pi = 1070.8 0.8 TENDON FORCE AT SERVICE LOAD AFTER ALLOWANCE LOSSES 0.64

fpy, (ACI 318-14 20.3)

CHECK TRANSFER LOAD CONDITION (AASHTO 9.15.1 & 9.15.2.1) PRESTRESSED ECCENTRICITY

e= - Fti =

29.35

in

MIN. TOP FIBER STRESS

-0.581

ksi

MAX. BOT. FIBER STRESS

Fbi =

3.300

ksi

MAX. ALLOWABLE STRESS

Fsi =

fsi

=

194.400 ksi

189.000 ksi >

Fsi

[Unsatisfactory]

1 e  M f ti  P i     G   A St  St 1 e  M f bi  P i     G   A Sb  Sb

0.091

ksi

- Fti > [Satisfactory]

1.879

ksi

Fbi < [Satisfactory]

(As')reqd

= 0.000 in2 (ACI 318-14 24.4 & 24.5)

(As')provd < [Satisfactory]

CHECK SERVICEABILITY LOAD CONDITION (AASHTO 9.15.1 & 9.15.2.2) MIN. TOP FIBER STRESS Fte = 0.6fc' = 3.600 Fte, G+D = 0.4fc' = 2.400

ksi, for total loads ksi, for sustained loads only

Fte, 0.5(G+D)+L = 0.4fc' =

2.400 ksi, for live + 50% sustained loads MAX. BOT. FIBER STRESS -Fbe = -(0, 3, or 6)(fc')0.5 = -0.465 ksi MAX. ALLOWABLE STRESS Fse = 0.8fy = 194.400 ksi, after all losses

fse

=

155.520 ksi

Fse < [Satisfactory]

856.6

kips

MOMENT DUE TO SELF-WEIGHT MOMENT DUE TO DEAD LOAD MOMENT DUE TO LIVE LOAD

MG = MD = ML =

1042 1000 1354

ft-kips, (1413 kN-m) ft-kips, (1356 kN-m) ft-kips, (1836 kN-m)

FACTORED SHEAR FORCE

Vu =

250

kips, (1112.0 kN)

FACTORED TORSIONAL MOMENT

Tu =

52

ft-kips, (71 kN-m)

SECTION LOCATION ( 0, 1 or 2 ) PRESTRESSING METHOD ( 0, 1 or 2 ) EXPOSURE ( 0 OR 1 ) THE DESIGN IS INADEQUATE, SEE ANALYSIS

Pe =

kips

0 2 0

at midspan post-tensioned & bonded mild exposure

Additional 4 #8 Longitudinal Reinforcement Required for Torsion

(Cont'd)

 1 e  M MDML  f te  P e     G S ct  A St 

0.377 ksi

 1 e  M MD  f te,G  D  P e     G S ct  A St 

0.075 ksi

 1 e  0.5( M G  M D)  M L  f te,0.5(G  D)  L  0.5 P e     S ct  A St 

Fte

<

Fte, G+D

<

0.340

kis

<

COMPRESSION ZONE FACTOR

b1 =

0.75

, (ACI 318-14 22.2.2)

TENDON TYPE FACTOR RATIO OF TENSION REINF. RATIO OF COMPR. REINF.

gp =

0.280 0.002 0.003

, (ACI 318-14 20.3.2.3.1) , (ACI 318-14 Chapter 2) , (ACI 318-14 Chapter 2)

0.002 0.022 0.033

, (ACI 318-14 Chapter 2) , (ACI 318-14 20.3.2.3.1) , (ACI 318-14 20.3.2.3.1)

0.086

, (ACI 318-14 20.3.2.3.1)

RATIO OF PRESTR. REINF. INDEX OF TENSION REINF. INDEX OF COMPR. REINF.

w= w' = wp =

INDEX OF PRESTR. REINF.

COMPOSITE SECTION PROPERTIES b= 96 in, (ACI 318-14 6.3.2) Ac = 1893 in2

[Satisfactory]

FACTORED ULTIMATE MOMENT Mu = g ( bD MD + bL ML ) = 1.3 [ 1.0 ( MG + MD) + 1.67 ML] = 5594.134 ft-k

yct =

26.97

in

ycb =

53.03

in

Fte, 0.5(G+D)+L

Ic =

[Satisfactory]

-Fbe  1 e  MGMDML 0.501 ksi >  f be  P e    S cb  A Sb  CHECK ULTIMATE LOAD CONDITION (AASHTO 9.15.1 & 9.17 ACI 318-14 20.3)

r= r' = rp =

[Satisfactory]

1448000 in4

Sct =

53691

in3

Scb =

27305

in3

[Satisfactory]

c = 0.003

0.85 f c' A s' f s' Fc Parabolic

, (AASHTO Eq. 3-10)

A ps f ps Asfy

STRESS IN BONDED TENDONS :



    f pu d    ' p f ps  f pu 1     MIN   p '     1  fc dp  

STRESS IN UNBOUNDED TENDONS :

f

ps

f

ps



 , 0.17     

  f 'c  MIN  f se  10  , f y , f se  60     100  p  

Not applicable

'   fc  MIN  f se 10  , f y , f se  30     300  p  

Not applicable

 M n    A ps f

ps

o 

252.864 ksi

7964

 d p  d c   A s f y  d  d c   A's f y  d c  d '  

>

ft-k Mu



2 0.85 f C'



Ec

, E c  57 f 'C , E s  29000ksi

     2 0.85 f 'C  2   c     c   , for 0   c   o fC    o    o    ' 0.85 f C , for  c   o  s E s , for  s   t fS  f y , for  s   t e s,max = 0.0021 , (ACI 318-14 7.3.3 or R21.2.2) c= 18.4 in, by pure math method Fc = 1612.817 kips dc = 4.971 in As 'fs' = 159.158 kips As fy = 379.200 kips Aps fps = 1392.775 kips

[Satisfactory]

f Mn 4901 ft-k < [Satisfactory] (AASHTO 9.18.2 & ACI 318-11 18.8.2, but ACI 318-14 waived)

  1  S  e  1.2 M cr  1.2S b  P e     7.5 f 'c   M G  cb  1   Sb    Ac S b  

CHECK SHEAR CAPACITY (AASHTO 9.20, ACI 318-14 9 & 22)

d  MAX  0.8h , d p  

  MAX   Vc     2b wd

64.00

in

 f 'c  MIN 100 , 

   V ud p    '  MIN  0.6 f c  700MIN 1 ,   b wd , 5b wd M u        f 'c , for f se  0.4 f

  f 'c  , for 

provd

77.46

  

f se  0.4 f

pu

psi

116.39

kips



pu

 Av f yd  , 8b wd f 'c   V s  MIN  S  

281.60

kips

'  MIN  0.75d , 24  , for V s  4b wd f c   S max   '   MIN  0.375d , 12  , for V s  4b wd f c

Av ,requd

 f 'c  , 2b wd 

 f 'c 

  d  A ps f puS  bw  MAX  50b wS ,  fy 80df y   Av(min)      50b wS , for f se  0.4 f pu   f y 12.00

   , for f  0.4 f se   

pu



0.164

in2

in

V c  no shear re inf . requd , for case1: V u  2  V c    Av (min) , for case 2 : 2  V u  V c    MAX  Av,cal , Av (min)  , for case 3 : V c  V u    V S  V c    unsatisfactory , for case 4 :   V S  V c   V u

0.523

in2

[Satisfactory], Case 3 applicable

 Av ,requd   2   MAX  Av,cal , Av (min)  , for case 3 : V c  V u    V S  V c    unsatisfactory , for case 4 :   V S  V c   V u

(Cont'd)

CHECK TORSIONAL CAPACITY (AASHTO 9.21, ACI 318-14 22.7) Acp

=

576

in2

Pcp

=

160

in

fpc

=

1.487

ksi

Aoh

=

290

in2

Ph

=

145

in

At Tu   S 1.7 Aoh f yv cos  37.5 

 At  S   Total

Tu

>



2  f pc  Acp  f 'c   1  4 f 'c  P cp 

11.405

ft-kips

Thus, Torsional Reinf. Reqd.

0.013

 A  2 At 50b w   MAX  v ,   S f yv  Re qD 

in2/in

0.069

3.19 in2    f yv  A 5 Acp f 'c 25b w    At   f yv  2  Ph  cot  37.5  ,  max  t ,   A L  MAX   P h   f yL  S  S   f yL  f yL f yv        for Torsion Additional 4 #8 Longitudinal Reinforcement Required

in2/in

<

 At    S    Pr ovD

[Satisfactory]

0.073

in2/in