PROJECT : PAGE :

CLIENT : DESIGN BY :
JOB NO. : DATE : REVIEW BY :
Bridge Design for Prestressed Concrete Box Section Based on AASHTO 17th Edition & ACI 318-19

INPUT DATA & DESIGN SUMMARY

BRIDGE SPAN L= 120 ft
SECTION DIMENSIONS SECTION PROPERTIES
T= 280 in, within [B , 300"] , (7112 mm) A= 15529.0 in2
B= 240 in, within [200", 280"] , (6096 mm) yt = 41.82 in
C= 110 in, within [80",180"] , (2794 mm) yb = 54.18 in
D= 96 in, within [L/15 , L/25] , (2438 mm) I= 19766329 in4
Tt = 12 in, within [8",18"] & >T/30 , (305 mm) St = 472656 in3
Tb = 24 in, within [8", 24"] & >B/30 , (610 mm) Sb = 364825 in3
W= 24 in, within [8", 24"] & >D/15 , (610 mm)
Tc = 24 in, within [14", 24"] & >C/12 , (610 mm)
Te = 6 in, (152 mm)
CONCRETE STRENGTH f 'c = 8 ksi, (55 MPa)
REBAR STRENGTH f y* = f y = 80 ksi, (552 MPa)
TENDON TENSILE STRENGTH fsu* = fpu = 270 ksi, (1862 MPa)
TENDON YIELD STRENGTH fpy = 243 ksi, (1675 MPa)
DISTANCE TO CENTROID OF COMPRESSION d' = 6 in, (152 mm)
DIST. TO CENTROID OF BOT. PRESTRESSED dp,b = 84 in, (2134 mm)
DIST. TO CENTROID OF WEB. PRESTRESSED dp,w = 76 in, (1930 mm)
DISTANCE TO CENTROID OF TENSION d= 80 in, (2032 mm)
TOP COMPRESSION REINF. 2 # 8 @ 12 in o.c., (305 mm)
BOTTOM TENSION REINF. 2 # 8 @ 12 in o.c., (305 mm)
WEB HORIZONTAL REINF. 2 # 8 @ 12 in o.c., (305 mm)
SHEAR STIRRUP REINF. 2 legs, # 10 @ 8 in o.c., (203 mm)
BOTTOM PRESTRESSING TENDONS
15 x 36 strands (each 0.5 in diameter & 0.153 in2 area )
EACH WEB PRESTRESSING TENDONS (13 mm) ( 99 mm2)
4 x 36 strands (each 0.5 in diameter & 0.153 in2 area )
TOTAL TENDON FORCE IMMEDIATELY AFTER PRESTRESS TRANSFER 0.75 fpy, (ACI 318-19 20.3) Pi = 23088.2 kips

TOTAL TENDON FORCE AT SERVICE LOAD AFTER ALLOWANCE LOSSES 0.6 fpy, (ACI 318-19 20.3) Pe = 18470.5 kips

MOMENT DUE TO SELF-WEIGHT MG = 22420.061131 ft-kips, (30398 kN-m) VERTICAL SHEAR FORCE Vu = 6886.735 kips, (30632.2 kN)
MOMENT DUE TO DEAD LOAD MD = 33750 ft-kips, (45759 kN-m) TORSIONAL MOMENT Tu = 35868.412 ft-kips, (48631 kN-m)
MOMENT DUE TO LIVE LOAD ML = 31500 ft-kips, (42708 kN-m) LATERAL BENDING MOMENT Mu,y = 41320.41 ft-kips, (56023 kN-m)
SECTION LOCATION ( 0, 1 or 2 ) 0 at midspan (Seismic/Wind Horizontal Bending Load)
PRESTRESSING METHOD ( 0, 1 or 2 ) 2 post-tensioned & bonded
EXPOSURE ( 0 OR 1 ) 0 mild exposure THE DESIGN IS ADEQUATE.

CHECK TRANSFER LOAD CONDITION (AASHTO 9.15.1 & 9.15.2.1)

ENTIRE SECTION PRESTRESSED ECCENTRICITY
e= 38.05 in
MIN. TOP FIBER STRESS
- Fti = -0.671 ksi
MAX. BOT. FIBER STRESS
Fbi = 4.400 ksi
MAX. ALLOWABLE STRESS
Fsi = 189.000 ksi

fsi = 182.250 ksi

< Fsi
[Satisfactory]

1 e  M 0.197 ksi > - Fti

f ti  P i     G 
 A St  St [Satisfactory]
(As')reqd = 0.000 in2 < (As')provd

 1 e  MG 3.157 ksi < Fbi (ACI 318-19 24.4 & 24.5) [Satisfactory]
f bi  P i     [Satisfactory]
 A Sb  Sb

CHECK SERVICEABILITY LOAD CONDITION (AASHTO 9.15.1 & 9.15.2.2)

CONCRETE DECK THICKNESS
t= 4 in
(0 for non-composite)
COMPOSITE SECTION PROPERTIES
b= 500 in
Ac = 17529.0 in2
yct = 40.82 in
ycb = 59.18 in
Ic = 23171159 in4
Sct = 567642 in3
Scb = 391537 in3
 (Cont'd)
MIN. TOP FIBER STRESS MAX. BOT. FIBER STRESS
Fte = 0.6fc' = 4.800 ksi, for total loads -Fbe = -(0, 3, or 6)(fc')0.5 = -0.537 ksi
Fte, G+D = 0.4fc' = 3.200 ksi, for sustained loads only MAX. ALLOWABLE STRESS
Fte, 0.5(G+D)+L = 0.4fc' = 3.200 ksi, for live + 50% sustained loads Fse = 0.8fy = 194.400 ksi, after all losses
fse = 145.800 ksi < Fse
[Satisfactory]

 1 e  M MDML 1.556 ksi < Fte [Satisfactory]

f te  P e     G 
 A St  S ct
 1 e  M MD 0.890 ksi < Fte, G+D [Satisfactory]
f te,G  D  P e     G 
 A St  S ct

 1 e  0.5( M G  M D)  M L 1.111 kis < Fte, 0.5(G+D)+L

f te,0.5(G  D) L  0.5P e      [Satisfactory]
 A St  S ct

 1 e  M MDML 0.429 ksi > -Fbe [Satisfactory]

f be  P e     G 
 A Sb  S cb
CHECK ULTIMATE LOAD CONDITION (AASHTO 9.15.1 & 9.17 ACI 318-19 20.3)
FACTORED ULTIMATE MOMENT
Mu,x = g ( bD MD + bL ML ) = 1.3 [ 1.0 ( MG + MD) + 1.67 ML]
(AASHTO Eq. 3-10) c = 0.003 0.85 f c'
= 141407.579 ft-k
A s' f s'
Mu,y = 41320.410 ft-k

Fc
Mu = (Mu,x2 + Mu,y2)0.5
= 147321.009 ft-k 
Parabolic
q= 16.3 deg Mu
A ps f ps
COMPRESSION ZONE FACTOR
b1 = 0.65 , (ACI 318-19 22.2.2)
TENDON TYPE FACTOR Asfy
0.280 gp = , (ACI 318-19 20.3.2.3.1)       2

RATIO OF TENSION REINF. r= 0.001 , (ACI 318-19 Chapter 2) 
 e f
'
C
2  c    c   , for 0   c   o  s E s , for  s   ty

RATIO OF COMPR. REINF. r' = 0.002 , (ACI 318-19 Chapter 2) f     o    o   , fS 
 f y , for  s   ty
C
 
RATIO OF PRESTR. REINF. rp = 0.006 , (ACI 318-19 Chapter 2)  e f

'
C
, for  c   o
INDEX OF TENSION REINF. w= 0.013 , (ACI 318-19 20.3.2.3.1) 
2  e f C'  f y 
 ty , for compression controlled
INDEX OF COMPR. REINF. w' = 0.016 , (ACI 318-19 20.3.2.3.1) o  ,  ty  , t  
Ec Es  ty  0.003 , for tension controlled

INDEX OF PRESTR. REINF. wp = 0.173 , (ACI 318-19 20.3.2.3.1)
f C , E s  29000ksi ,  e  0.85 ,  cu  0.003
'
E c  57
STRESS IN BONDED TENDONS :
10

  8
f Pn

   
(k)

 f d  ' 248.462 ksi

f ps  f pu
1   p   MIN   p pu  , 0.17   
  1   '
fc dp  6
  
4
STRESS IN UNBOUNDED TENDONS :
2
Not applicable
0
 f 'c  0 2 4 6 8 10 12 14 16 18
f  MIN  f se  10  , f , f  60  
ps  100  p y se  -2
 
f -4
Mn (ft-k) Solid Black Line - Tension Controlled
 fc
'
 Not applicable Solid Red Line - Transition
f ps  MIN  f se  10  , f y, f se  30   Dash Line - Compression Controlled
 300  
 p  f Mn = 161491 ft-kips @ Pu = 0 kips
> Mu [Satisfactory]
  1 f Mn
e  '   S cb  136507 ft-k < [Satisfactory]
1.2M cr  1.2S b  P e     7.5 f c   M G   1  (AASHTO 9.18.2 & ACI 318-19 18.8.2, but ACI 318-19 waived)
  A c S b    Sb 
CHECK SHEAR CAPACITY (AASHTO 9.20, ACI 318-19 9 & 22)

84.00 in 89.44 psi

d  MAX  0.8h , d p   
f 'c  MIN 100 ,

 f 'c  

provd 

   
 '  V ud p   '  '  7266.41 kips
 MAX  MIN  0.6 f c  700MIN 1 ,   b wd , 5b wd f c  , 2b wd f c  , for f se  0.4 f
   M u  
pu
Vc   
 
 '
2b wd
 f c , for f se  0.4 f pu

  d 
  A ps f puS 
4267.20 kips  MAX  50b wS , bw  , for f  0.4 f 1.400 in2
 Av f yd    fy 80 df y  se pu

V s  MIN  , 8b wd f 'c   Av(min)     

 S    
 50b wS
 , for f se  0.4 f pu
 f y

24.00 in
 MIN  0.75d , 24  , for V  4b d f '
 s w c
S max   

 MIN  0.375d , 12  , for Vs  4bw d f '
c
  MIN  0.75d , 24  , for V  4b d f '
 s w c
S max   

 MIN  0.375d , 12  , for V s  4b wd f '
c
  MIN  0.75d , 24  , for V  4b d f '
 s w c
S max   

 MIN  0.375d , 12  , for V s  4b wd f '
c
(Cont'd)

 V c
 no shear re inf . requd , for case 1: V u  2
 1.400 in2 [Satisfactory], Case 3 applicable
 V c
, for case 2 :  V u  V c
Av,requd   Av (min) 2 

 MAX  Av,cal Av (min) 
, , for case 3 :  
Vc Vu    
VS Vc 

unsatisfactory , for case 4 :   V S  V c   V u
CHECK TORSIONAL CAPACITY (AASHTO 9.21, ACI 318-19 22.7)

Acp = 26880 in2

Pcp = 752 in Tu > 6093.124 ft-kips
'  Acp 
2 f pc
 fc 1 
 P cp 
fpc = 0.687 ksi
  4 f 'c
Aoh = 25293 in2 Thus, Torsional Reinf. Reqd.
Ph = 735 in

0.020 in2/in 85.96 in2

 
At  Tu  At   f yv  2 5 Acp f 'c  f yv   25b w  
 A L  MAX   P h   cot  37.5  ,  Ph   max  At ,  
S 1.7 Aoh f yv cos  37.5   S   f yL   f yL  
 f yL 

S

f yv  
 

0.215 in2/in < 0.635 in2/in

 At   A  2 At 50b w   At 
S   MAX  v ,   S  
 Total  S f yv    Pr ovD
Re qD  [Satisfactory]