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# Shear Friction Concrete Excel Calculations - Excel

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Shear Friction Concrete Excel Calculations document sample

• pg 1
```									                                                                                                                                             Designer or Checker:
_________________
8/22/2011

Load and Resistance Factor Design of Pre-stressed, Pre-cast
I-Girder and Bulb-Tee Bridges
Version x.x by S. Hida, Dec. 2000
Disclaimer: This spreadsheet workbook was created for engineers at
Caltrans as an educational tool, and to use on trial LRFD calculations.
The originator and the Caltrans Engineering Service Center bear no
responsibility for any situation that results from use of this Microsoft
Excel workbook. However, users are encouraged to call or email Sue
Hida with any questions or comments, 227-8738.

Instructions: Fill in yellow cells, only.
Fill in your bridge information here:

Swillup Creek Bridge, Br. No. 02-0040, District/Co./Rte. 02-Sis-96
1           2            3            4         5
Overall Deck Width (ft)34.35                      Span Lengths (ft)             83.6
Number of girders        6
Girder Area (in.^2)      516                      Girder                              5
Conc strength--f'c (ksi)=            Deck                               5
Conc strength--f'c (ksi)=
Girder Spacing (ft)      5.91                                 beta1=                  0.85                    beta1=                  0.85
Girder Width, Height (ft)1.75        4                        unit weight (kcf)       0.15                    unit weight (kcf)       0.15
Girder Haunch (avg--in)  1                                    Ec (bm)= 4286.826 (ksi)                         Ec (deck)= 4286.826 (ksi)
Deck Thickness (in.) 7.25                                                             .6fci before losses (C, ksi)                             3.00   (5.9.4.1.1)
Barrier (ft^2)           2.61                                                         .45fc after losses (DL only, C; ksi)                     2.25   (5.9.4.2.1)
AC overlay (ksf)         0.035                                                        .60fc after losses (DL+LL; ksi)                          3.00   (5.9.4.2.1)
Girder inertia (in^4)    137300                                                       .40fc after losses 0.5(DL+ADL+PS)+LL C                   2.00   (5.9.4.2.1)
Girder yb, yt (in.)      22.8        25.2                                             .0948fci before losses, 0.2ksi min (T, ksi)            -0.21   (5.9.4.1.2)
Girder tw (in.)          7.125                                                        .190fc after losses (bonded tendons,T; ksi)            -0.42   (5.9.4.2.2)
Girder tendon; 'e' (in.)                     22.8 (max)                               0 (DL only) after losses (T, ksi)                        0.00   (Caltrans)
Barrier wd (ft)          1.75                                                         Cracked concrete 0.24f'c, ksi                           0.54
Mild reinf. fy (ksi)            60   Es (ksi)=         29000
PS steel fpu (ksi)             270   Eps (ksi)=        28500 Lo-lax?      y                        old s-over          0.54   old IM           1.24

by S.Hida, v.0.0                                                               LRFD                                                                          1 of 41
Bridge Name, no.:                                                                                                                                                           Designer or Checker:
District, Co., PM:                                                                                                                                                          _________________
EA:                                                                                                                                                                                    8/22/2011

Span #      1               (Interior Girder)                      Section Property Calculator

)

2
^2

)^
cg
)

)
(ft

(ft

cg
/ft

p.
(k
k.

-y
yb

om
ea

yb
ic

y

g
t.
width (ft)                                                                                                                                                   Eff. Fl. Wd (ft)          width (

yb

A*

A(
ar

y-
th

Ic
w

C
Deck                5.91            0.60          3.57                           4.39       15.66                       -1.23              5.37         0.11            0.25Leff       19.4
Haunch              1.75            0.08          0.15                           4.04        0.59                       -0.88              0.11         0.00                   S       5.91
Girder                              4.00          3.58               0.54        1.90        6.81                        1.26              5.68         6.62   12ts+max(tw,0.5tf)    8.125
7.30               1.09                   23.06         3.16           1.53
I_total (ft^4)=        17.89        Controls (ft):    5.91
Sc_bot (in^3)           9790
Sc_top (in^3)           6716

)
)

er
^2
)

ird
)
(ft

(ft

/ft

/g
(k
h

ea
t

/ft
id

t.
ar

(k
w

w

Barrier                             5.22      0.783  0.1305
Overlay             30.85                    1.0798 0.17996
Utilities                                                 0
1.8628 0.31046

Section Property Calculator, cont.

by S.Hida, v.0.0                                                                                PC Girders                                                                               2 of 41
Bridge Name, no.:                                                                                                                                            Designer or Checker:
District, Co., PM:                                                                                                                                           _________________
EA:                                                                                                                                                                     8/22/2011

Span #     1               (Exterior Girder)              Section Property Calculator, cont.

)

2
^2

)^
cg
)

)
(ft

(ft

cg
/ft

p.
(k
k.

-y
yb

om
ea

yb
ic

y

g
t.
width (ft)                                                                                                                                        Eff. Fl. Wd (ft)

yb

A*

A(
ar

y-
th

Ic
w

C
Deck                5.36           0.60           3.24                          4.39 14.19                   -1.29           5.35        0.10               0.125Leff          9.7
Haunch              1.75           0.08           0.15                          4.04 0.59                    -0.94           0.13        0.00               Overhang           2.4
Girder                             4.00           3.58              0.54        1.90 6.81                     1.20           5.16        6.62   .5*(12ts+max(tw,0.5tf))    4.0625
6.96              1.04             21.59         3.10       1.59
I_total (ft^4)= 17.35              Controls (ft):        2.4
Sc_bot (in^3) 9676
Sc_top (in^3) 6513

by S.Hida, v.0.0                                                                       PC Girders                                                                          3 of 41
Bridge Name, No.:                                                                                                                                                            Designer or Checker:
District, Co., PM:                                                                                                                                                           _________________
EA:                                                                                                                                                                                     8/22/2011

Girder Distribution Factor (gdf)
k)

4)
ec

)
t^

^4
)
/d

^2
,f

)

)
(ft
(ft

(ft
)
)
m

)
bm

(ft
(ft

(ft

(ft
b

Kg
M-int.                                                                                                                  Dist.Factor (# of traffic lanes)

eg

de
E(

I(

ts
A

S

L
+Span1            1.00          6.62        2.40       3.58        27.30       5.91       83.60        0.60        0.23    0.54                                                          0.1
æ Kg ö
0.6   0.2
æ S ö æSö
0.075 + ç     ÷ ç ÷
è 9.5 ø è L ø
ç
ç 12 .0 Lt 3 ÷
÷
è          s ø

(T4.6.2.2.2b-1)
M-ext.
+Span1                                                                                                             0.23     0.40      æ       d ö
ç 0.77 + e ÷Mint
è       9.1ø
(T4.6.2.2.2d-1)
V-int.                                                                         5.91                                         0.66                      S         æ  S        ö
2

0 .2      +              -   ç           ÷
12         è 35        ø
(T4.6.2.2.3a-1)
V-ext.                                                                                                             0.23     0.38   æ                   d        ö
ç 0 . 6       +          e
÷ V   int
è                   10       ø
(T4.6.2.2.3b-1)
M-total                                                                                                                     3.21
(Total is interior gdf multiplied
by the total number of girders--
V-total                                                                                                                     3.98      for information only!)

by S.Hida, v.0.0                                                                          PC Girders                                                                                            4 of 41
Bridge Name, No.:                                                                                                                                               Designer or Checker:
District, Co., PM:                                                                                                                                              _________________
EA:                                                                                                                                                                        8/22/2011

Pre-stressing Force: Pjack_final                                                                                  Pjack           _   final    =
1
f - ft
e * yb
+
w/o LL      Service III                                                                                           A      I girder
ft_allowed (ksi)       0.00      0.190(fc')^0.5
Interior Girder
Stresses on Composite Section
Simple_Span (0.5l)                                 Stresses (My/I ksi)
M_DL     M_ADL M_HL93                            f_DL     f_ADL f_HL93                              w/o LL     Service III                    Pjack_final (k)
Span 1                 957    271      1182                            1.91     0.33        1.45                            2.24       3.19                        556.62

Exterior Girder
Stresses on Composite Section
Simple_Span (0.5l)                                 Stresses (My/I ksi)
M_DL     M_ADL M_HL93                            f_DL     f_ADL f_HL93                              w/o LL     Service III                    Pjack_final (k)
Span 1                 913    271       881                            1.82     0.34        1.09                            2.16       2.82                        492.19

Pre-stressing Force: Pjack_initial
Pjack_initial = Pjack_final + Aps*(f_losses)             Note: Aps and f_losses determined on next sheet, 'Losses'.

Interior Girder                                                                     Exterior Girder
)

)
(k

(k
)

)
si

si
al

al
(k

(k
2)

2)
in

in
.^

.^
s

s
_f

_f
se

se
(in

(in
ck

ck
os

os
s

s
a

a
Ap

Ap

Pjack_initial (k)    BDP 3.2 (LFD)                                                Pjack_initial (k)       BDP 3.2 (LFD)
l

l
Pj

Pj
f_

f_
Span 1                   556.62      3.52        52.91 742.83                 577     492.19                   3.52          52.91         678.40                     577

by S.Hida, v0.0                                                                   PC Girders                                                                                      5 of 41
Bridge Name, No.:                                                                                                                                                Designer or Checker:
District, Co., PM:                                                                                                                                               _________________
EA:                                                                                                                                                                         8/22/2011

Losses
# of strands                       23
area/strand (in.^2)             0.153
Elastic Shortening

Ep                                                           M ge    æ P  Pe2 ö                                                          æ 1    e2 ö
Df pES =         f cgp            where
f cgp = f g + f ps =          -ç i + i ÷ =       =
286 ftk * 12 in. / ft * (16 .5in)
- NAps f pi ç    +      ÷=
Eci                                                          I cg    çA    I cg ÷                   95,000 in.4                          çA     I cg ÷
è g        ø                                                        è  g        ø
f_cgp is the concrete stress at the center of gravity of PS tendons, that results from the PS force and DL
Interior Girder                                                                 Exterior Girder

M_girder         f_g            f_ps          f_cgp       Df_pES              M_girder        f_g            f_ps           f_cgp          Df_pES

Span 1                   469.57           0.94          3.81       -2.87        -19.09                469.57           0.94           3.81          -2.87        -19.09

Time-dependent Losses (Shrinkage, Creep, Relaxation)
é           f ' - 6.0 ù
Df LT = 33.0ê1.0 - 0.15 c         ú + 6.0 PPR      where PPR=1.0
ë              6.0 û                   (T5.9.5.3-1)
Subtract additional 6 ksi if low-lax.
Df_LT (ksi)      33.825

Stress after losses
0.75f_pu- Dfp_ES - Df_LT (ksi)

Interior Girder (ksi) (k) CHECK Aps                           Exterior Girder (ksi) (k) CHECK Aps
0.75f_pu                        losses     override f (final)     ASSUMPTION                  losses     override f (final)     ASSUMPTION
Span 1              202.50                           -52.91           0    149.59 526.3911 ok                      -52.91          0     149.59 526.3911

by S.Hida, v.0.0                                                                          PC Girders                                                                             6 of 41
Bridge Name, No.:                   Designer or Checker:
District, Co., PM:                  _________________
EA:                                            8/22/2011

force and DL

(k) CHECK Aps
ASSUMPTION
ok

by S.Hida, v.0.0       PC Girders                7 of 41
Bridge Name, No.:                                                                                                                  Designer or Checker:
District, Co., PM:                                                                                                                 _________________
EA:                                                                                                                                           8/22/2011

V--simple-span shear, k
M--simple-span moments, ft=k                                    wx
=
M _ girder      (l - x) M_gdr slab wx(l - x)
+     =
2                      2
V-DL (k)                                                                 eccentricity, e (in.)
interior  exterior     interior    exterior     interior   exterior     interior   exterior
girder     girder      girder      girder       girder     girder       girder      girder
Span       Point   x           V_gdr,slab=w(l/2-x)
1       0          0           46         44          0            0           0           0        0.00        0.00
1     0.1       8.36           37         35        169          169         344         329        6.00        6.00
1     0.2       16.7           27         26        301          301         612         584       12.00       12.00
1     0.3       25.1           18         17        394          394         804         767       18.00       18.00
1     0.4       33.4             9         9        451          451         918         876       18.00       18.00
1     0.5       41.8             0         0        470          470         957         913       18.00       18.00
1     0.6       50.2            -9        -9        451          451         918         876       18.00       18.00
1     0.7       58.5          -18        -17        394          394         804         767       18.00       18.00
1     0.8       66.9          -27        -26        301          301         612         584       12.00       12.00
1     0.9       75.2          -37        -35        169          169         344         329        6.00        6.00
1       1       83.6          -46        -44          0            0           0           0        0.00        0.00

Note: If stress checks are desired at harping points or point-of-stress
transfer, locations should be added above. Insert rows and copy
commands from another line, typical most sheets.

by S.Hida, V.0.0                                                                   PC Girders                                                   8 of 41
Bridge Name, No.:                                                                                       Designer or Checker:
District, Co., PM:                                                                                      _________________
EA:                                                                                                                8/22/2011

Barrier (ft^2)                      2.61
AC overlay (ksf)                    0.035
Utilities (k/ft/gdr)                0
Total, w (k/ft/gdr)                 0.310458
interior     exterior             interior  exterior
Span       Point   x                 girder       girder               girder   girder
1       0          0              13           13 .5wl               0         0         0
1     0.1       8.36              10           10                   98       98
1     0.2       16.7               8            8                 174       174
1     0.3       25.1               5            5                 228       228
1     0.4       33.4               3            3                 260       260
1     0.5       41.8               0            0        0        271       271 .125wl^2
1     0.6       50.2              -3           -3                 260       260
1     0.7       58.5              -5           -5                 228       228
1     0.8       66.9              -8           -8                 174       174
1     0.9       75.2             -10          -10                   98       98
1       1       83.6             -13          -13 .5wl               0         0         0

Note: If stress checks are desired at harping points or point-of-stress
transfer, locations should be added above. Insert rows and copy
commands from another line, typical most sheets.

by S.Hida, v0.0                                                                  PC Girders                          9 of 41
Bridge Name, No.:                                                                                                      Designer or Checker:
District, Co., PM:                                                                                                     _________________
EA:                                                                                                                               8/22/2011

Results from a corresponding QCONBRIDGE or CTBRIDGE(coming soon) run may be used for shear and moment
force effects. Verify that the dynamic load allowance, IM=1.33 per AASHTO LRFD, is toggled and included below.
Note: M- and V- riders have changed in LRFD. Do NOT attempt to tweek BDS for the HL93 negative M-demand!

V_LL (k)                      M_LL (ft-k)         (interior)       (exterior)
one lane times gdf times gdf one lane one lane times gdf          times gdf
Span Point      max(abs) (interior) (exterior) max--ss min--cont max--ss min--cont max--ss min--cont
1      0          113        75        43         0       0           0      0         0      0
1   0.1            98        65        38         1       0           0      0         0      0
1   0.2            84        56        32     1474        0        789       0      588       0
1   0.3            70        46        27     1901        0       1018       0      759       0
1   0.4            57        38        22     2150        0       1151       0      858       0
1   0.5            44        29        17     2208        0       1182       0      881       0
1   0.6           -57       -38       -22     2150        0       1151       0      858       0
1   0.7           -70       -46       -27     1901        0       1018       0      759       0
1   0.8           -84       -56       -32     1474        0        789       0      588       0
1   0.9           -98       -65       -38    0.841        0           0      0         0      0
1      1         -113       -75       -43         0       0           0      0         0      0

Note: If stress checks are desired at harping points or point-of-stress
transfer, locations should be added above. Insert rows and copy
commands from another line, typical most sheets.

by S.Hida, v.0.0                                                                       PC Girders                                  10 of 41
Birdge Name, No.:                                                                                                                       Designer or Checker:
District, Co., PM:                                                                                                                      _________________
EA:                                                                                                                                                8/22/2011

Results from a corresponding BDS run may be used for shear and moment force effects if IM is factored out. Dynamic load allo wances per
AASHTO LRFD, IM=1.33, must be factored in, below. CTBridge will soon be another option. Note that Caltrans will be modifyin g the p13
in AASHTO LRFD.

V_LL (k)                              M_LL (ft-k)                            (interior)         (exterior)
*1.33*gdf_LRFD/gdf_LFD/IM_LFD   BDS                  one lane one lane *1.33*gdf_LRFD/gdf_LFD/IM_LFD
Span Point      BDS             (interior) (exterior) max      min         max-cont min-cont max-cont min-cont max-cont min-cont
1     0         93                  123         71        0         0                                0     0          0     0
1   0.1         77                  102         59      664         0                            710       0       529      0
1   0.2         62                   82         47     1072         0                           1146       0       854      0
1   0.3         50                   66         38     1452         0                           1553       0      1157      0
1   0.4         38                   50         29     1608         0                           1719       0      1281      0
1   0.5          0                     0         0     1715         0                           1834       0      1367      0
1   0.6        -38                  -50        -29     1608         0                           1719       0      1281      0
1   0.7        -50                  -66        -38     1452         0                           1553       0      1157      0
1   0.8        -62                  -82        -47     1072         0                           1146       0       854      0
1   0.9        -77                 -102        -59      664         0                            710       0       529      0
1     1        -93                 -123        -71        0         0                                0     0          0     0

Note: If stress checks are desired at harping points or point-of-stress
transfer, locations should be added above. Insert rows and copy
commands from another line, typical most sheets.

by S.Hida, v.0.0                                                                        PC Girders                                                  11 of 41
Bridge Name, No.:                                                                                                                                                                                                                        Designer or Checker:
District, Co., PM:                                                                                                                                                                                                                       _________________
EA:                                                                                                                                                                                                                                                8/22/2011

Note: If stress checks are
Stresses at release: check compression                                                                                  Stresses at release: check                                                      desired at harping points or
point-of-stress transfer,
in bottom of girder                                                                                                     tension in top of girder                                                        locations should be added
above. Insert rows and copy
Before losses, girder only                                               Before losses, girder only                                                      commands from another line,
Compression check, bottom of girder--Service I                           Tension check, top of girder--Service III                                       typical most sheets.
æ 1 ey ö (g DL_ g MDL_ g )yb                                                                          æ 1  ey ö ( DL_ g MDL_ g )yt
g
ç
Pjack initial + b ÷ -
_                                   £ 0.6 f ' ci?                                                    _       ç
Pjack initial
çA
- t ÷+                   £ 0.0948 f ' ci?
çA     ÷                                                                                              è g  Ig ÷
ø         Ig
è g Ig ø          Ig
Ok w/mild As?
Total Stress             f'c needed                                                                       Total Stress      allowable exceeded? (see Mild As sht)
Interior   Exterior    Interior   Exterior   Interior Exterior      Interior Exterior             Interior   Exterior         Interior     Exterior   Interior     Exterior Interior Exterior Interior Exterior
Span       Point           Girder     Girder      Girder     Girder     Girder    Girder       Girder     Girder             Girder     Girder           Girder       Girder     Girder        Girder    Girder Girder Girder       Girder
1             0       1.44       1.31        0.00       0.00       1.44       1.31                                      1.44       1.31             0.00         0.00       1.44          1.31
1           0.1       2.18       1.99        0.34       0.34       1.84       1.65                                      0.62       0.57             0.37         0.37       0.99          0.94
1           0.2       2.92       2.67        0.60       0.60       2.32       2.07                                     -0.20      -0.18             0.66         0.66       0.47          0.48
1           0.3       3.66       3.34        0.79       0.79       2.87       2.56                                     -1.01      -0.93             0.87         0.87      -0.15         -0.06
1           0.4       3.66       3.34        0.90       0.90       2.76       2.44                                     -1.01      -0.93             0.99         0.99      -0.02          0.07
1           0.5       3.66       3.34        0.94       0.94       2.72       2.41                                     -1.01      -0.93             1.03         1.03       0.02          0.11
1           0.6       3.66       3.34        0.90       0.90       2.76       2.44                                     -1.01      -0.93             0.99         0.99      -0.02          0.07
1           0.7       3.66       3.34        0.79       0.79       2.87       2.56                                     -1.01      -0.93             0.87         0.87      -0.15         -0.06
1           0.8       2.92       2.67        0.60       0.60       2.32       2.07                                     -0.20      -0.18             0.66         0.66       0.47          0.48
1           0.9       2.18       1.99        0.34       0.34       1.84       1.65                                      0.62       0.57             0.37         0.37       0.99          0.94
1             1       1.44       1.31        0.00       0.00       1.44       1.31     4.7899     4.26082               1.44       1.31             0.00         0.00       1.44          1.31 ok       not ok ok         ok

Note: Pjack_initial is higher because losses are                                           Allowable:           3 ksi                                                                               Allowable: -0.212 ksi
higher. Thus, a higher strength concrete than                                                                            Note: Must add mild reinforcement to top of girder for
before (4.2 ksi min) is required. If less Pjack is                                         T>0.0948(f'ci)^0.5            initial stressing. This is due to such a high
used with 4 ksi concrete, the allowable stress for                                                                       Pjack_initial being required, which is due to such high
DL-girder only
tension in the bottom of the girder will be                                                                              long-term losses!
C<0.60f'ci
exceeded.

by S.Hida, v.0.0                                                                                                                PC Girders                                                                                                               12 of 41
Bridge Name, No.:                                                                                                                                                                                                                          Designer or Checker:
District, Co., PM:                                                                                                                                                                                                                         _________________
EA:                                                                                                                                                                                                                                                  8/22/2011

Note: If stress checks are desired at harping points or point -of-stress transfer, locations
Stresses in Service--bottom of girder                                                                      should be added above. Insert rows and copy commands from another line, typical most
sheets.

Compression check, bottom-of-girder                                                    Tension check, bottom-of-girder
æ 1 ey ö (g DL_ g, slabMDL_ g, slab)yb (g ADLMADL)ycb                                                             (g              M DL_ g, slab )yb       (g ADLM ADL + g LLMLL )ycb
ç   + b÷-                                                                                                 ....-                                       -                                   ³ 0.190 f ' c ?
DL_ g , slab
_
Pjack final                                     -               £ 0.45f ' c ?
çA   Ig ÷              Ig                    Ic                                                                                       Ig                               Ic
è g     ø
Total Stress         f'c needed                                                                       Total Stress           f'c needed
Interior     Exterior      Interior   Exterior   Interior   Exterior Interior Exterior                                   Interior       Exterior       Interior   Exterior   Interior   Exterior
Span       Point          Girder       Girder        Girder      Girder    Girder     Girder   Girder     Girder                                   Girder         Girder         Girder      Girder    Girder     Girder
1             0      1.08         0.95              0          0      1.08       0.95                                                         0.00           0.00           1.08        0.95
1           0.1      1.63         1.44     0.80368      0.77581       0.83       0.67                                                         0.80           0.78           0.83        0.67
1           0.2      2.19         1.93    1.428765      1.37921       0.76       0.56                                                         2.19           1.96           0.00       -0.03
1           0.3      2.74         2.43    1.875254      1.81022       0.87       0.61                                                         2.85           2.56          -0.11       -0.14
1           0.4      2.74         2.43    2.143147      2.06882       0.60       0.36                                                         3.25           2.92          -0.51       -0.50
1           0.5      2.74         2.43    2.232445      2.15502       0.51       0.27                                                         3.37           3.03          -0.63       -0.60
1           0.6      2.74         2.43    2.143147      2.06882       0.60       0.36                                                         3.25           2.92          -0.51       -0.50
1           0.7      2.74         2.43    1.875254      1.81022       0.87       0.61                                                         2.85           2.56          -0.11       -0.14
1           0.8      2.19         1.93    1.428765      1.37921       0.76       0.56                                                         2.19           1.96           0.00       -0.03
1           0.9      1.63         1.44     0.80368      0.77581       0.83       0.67                                                         0.80           0.78           0.83        0.67
1             1      1.08         0.95              0          0      1.08       0.95 2.39715 2.11968                                         0.00           0.00           1.08        0.95 10.91608 10.11565

Allowable:    2.250 ksi                                                                                Allowable:      -0.425 ksi

T>0
C<0.45fc'
T<0.190(fc')^0.5

by S.Hida, v.0.0                                                                                                                                              PC Girders                                                                               13 of 41
Bridge Name, No.:                                                                                                                                                                                                                                                                                                                             Designer or Checker:
District, Co., PM:                                                                                                                                                                                                                                                                                                                            _________________
EA:                                                                                                                                                                                                                                                                                                                                                     8/22/2011

Stresses in Service--top of girder
After losses--Service I, DL+ADL+LL                                                                                           After losses--Service I, .5(DL+ADL)+LL                                       Tension check, top-of-girder at supports
Compression check, top-of-girder                                                                                             Compression check, top-of-girder                                             Service I, Compression check at midspan

Pjack_ final
ö (
ç 1 - eyt ÷ + DL_ g, slab DL_ g, slab t + (g ADLMADL + g LLMLL )yc £ 0.60 f ' c ?
æ            g           M           )y                                                                                    +
[0.5(g DL M DL )]yt     +
[0.5(g ADL M ADL ) + g LL M LL ]yct     £ 0.40 f ' c ?
.... +
(g   DL _ g , slab   M    DL _ g , slab   )y   t
+
çA    Ig ÷               Ig                          Ic                                                                                Ig                                   I cg
è g       ø                                                                                                                                                                                                                                        Ig                                       Ic
Total Stress         f'c needed                                                    Total Stress           f'c needed                                                    Total Stress       allowable exceeded?
Interior   Exterior                     Interior        Exterior        Interior Exterior Interior Exterior                    Interior       Exterior   Interior Exterior    Interior Exterior            Interior        Exterior          Interior   Exterior     Interior    Exterior
Span       Point            Girder     Girder                       Girder          Girder          Girder Girder Girder Girder                            Girder         Girder     Girder Girder        Girder Girder                Girder          Girder            Girder      Girder      Girder      Girder
1             0        1.08       0.95                         0.00            0.00            1.08     0.95                                          0.00           0.00       1.08     0.95                                     0.00            0.00              1.08        0.95
1           0.1        0.47       0.41                         0.79            0.76            1.26     1.17                                          0.40           0.38       0.86     0.79                                     0.79            0.76              1.26        1.17
1           0.2       -0.15      -0.13                         1.68            1.56            1.54     1.43                                          0.98           0.89       0.83     0.76                                     1.41            1.35              1.26        1.22
1           0.3       -0.76      -0.67                         2.21            2.04            1.44     1.37                                          1.28           1.16       0.52     0.49                                     1.85            1.77              1.09        1.10
1           0.4       -0.76      -0.67                         2.52            2.33            1.76     1.66                                          1.46           1.32       0.70     0.65                                     2.11            2.02              1.35        1.35
1           0.5       -0.76      -0.67                         2.61            2.43            1.85     1.75                                          1.51           1.37       0.75     0.70                                     2.20            2.11              1.44        1.44 ok           ok          (compression)
1           0.6       -0.76      -0.67                         2.52            2.33            1.76     1.66                                          1.46           1.32       0.70     0.65                                     2.11            2.02              1.35        1.35
1           0.7       -0.76      -0.67                         2.21            2.04            1.44     1.37                                          1.28           1.16       0.52     0.49                                     1.85            1.77              1.09        1.10
1           0.8       -0.15      -0.13                         1.68            1.56            1.54     1.43                                          0.98           0.89       0.83     0.76                                     1.41            1.35              1.26        1.22
1           0.9        0.47       0.41                         0.79            0.76            1.26     1.17                                          0.40           0.38       0.86     0.79                                     0.79            0.76              1.26        1.17
1             1        1.08       0.95                         0.00            0.00            1.08     0.95 3.0912 2.922                             0.00           0.00       1.08     0.95     2.6968    2.3846                0.00            0.00              1.08        0.95 ok           ok          (tension)

Allowable:3.000 ksi                                                                 Allowable: 2.000 ksi

C<0.4f'c
C<0.45fc'
T<0.190(fc')^0.5

C       T                         C

At center-span:                                                                                                                                                                    C
+             +               =        C                 +     =      C                                   +      =

T
P/A           Pe/Sb          M_dl/Sb         ?                     M_adl/Sb                                         M_LL/Sb

C T                                        T                                                T                    T
At bent:
+             +               =        C                 +     =      C                                   +      =

C                                                    C                  C
P/A

by S.Hida, v.0.0                                                                                                                                                                      PC Girders                                                                                                                                                          14 of 41
Bridge Name, No.:                                                                                                                Designer or Checker:
District, Co., PM:                                                                                                               _________________
EA:                                                                                                                                         8/22/2011

Strength Limit States: factored moment demand, Mu (ft-k)
Interior Girder                                        Strength I              Strength II         Where is
1.75*HL93          1.35*P13      Total Mu                Total Mu            tension?
Span Point 1.25*DL 1.5*ADL          max--ss min--cont max--ss min--cont max--ss      min--cont max--cont min--cont    (t or b)
1    0       0       0                 0        0        0        0            0          0             0     0       b
1  0.1     430     146                 1        0     959         0         578        577         1535    577        b
1  0.2     765     260             1381         0    1548         0        2407       1026         2573   1026        b
1  0.3    1004     342             1782         0    2096         0        3128       1346         3442   1346        b
1  0.4    1148     391             2015         0    2321         0        3553       1538         3860   1538        b
1  0.5    1196     407             2069         0    2476         0        3672       1603         4078   1603        b
1  0.6    1148     391             2015         0    2321         0        3553       1538         3860   1538        b
1  0.7    1004     342             1782         0    2096         0        3128       1346         3442   1346        b
1  0.8     765     260             1381         0    1548         0        2407       1026         2573   1026        b
1  0.9     430     146                 1        0     959         0         578        577         1535    577        b
1    1       0       0                 0        0        0        0            0          0             0     0       b

Note: If stress checks are desired at harping points or point-of-stress
transfer, locations should be added above. Insert rows and copy
commands from another line, typical most sheets.

by S.Hida                                                                     PC Girders                                                     15 of 41
Bridge Name, No.:                                                                                                             Designer or Checker:
District, Co., PM:                                                                                                            _________________
EA:                                                                                                                                      8/22/2011

Strength Limit States: factored moment demand, Mu (ft-k)
Exterior Girder                                          Strength I       Strength II         Where is
1.75*HL93           1.35*P13       Total Mu         Total Mu            tension?
Span Point 1.25*DL 1.5*ADL         max--ss min--cont max--cont min--cont max--ss min--cont max--cont min--cont (t or b)
1    0        0       0               0         0        0          0          0     0          0        0     b
1  0.1      411     146               1         0      714          0        558   557       1272      557     b
1  0.2      730     260           1029          0    1153           0       2020   990       2144      990     b
1  0.3      958     342           1328          0    1562           0       2628  1300       2862     1300     b
1  0.4     1095     391           1502          0    1730           0       2987  1486       3216     1486     b
1  0.5     1141     407           1542          0    1845           0       3090  1548       3393     1548     b
1  0.6     1095     391           1502          0    1730           0       2987  1486       3216     1486     b
1  0.7      958     342           1328          0    1562           0       2628  1300       2862     1300     b
1  0.8      730     260           1029          0    1153           0       2020   990       2144      990     b
1  0.9      411     146               1         0      714          0        558   557       1272      557     b
1    1        0       0               0         0        0          0          0     0          0        0     b

by S.Hida                                                           PC Girders                                                            16 of 41
Bridge Name, No.:                                                                                                                                               Designer or Checker:
District, Co., PM:                                                                                                                                              _________________
EA:                                                                                                                                                                       8/22/2011

Mild Steel Calculations for Top As
Note: As and ds must be non-zero                                      (depth to ctd of mild C-steel)
Trial-and-error until fMn is acceptable.      ds (in.)             53 ds' (in.)          2 top (in.^2) Where is tension?              dp (in.)
As (in.^2)              As' (in.^2)           (depth to centroid of mild steel)                 Aps
interior    exterior    interior exterior     interior    exterior    interior exterior            exteriorInterior Exterior interior exterior
interior
Span       Point   girder      girder      girder     girder     girder      girder      girder    girder      girdergirder Girder      Girder girder    girder
1       0          0.01        0.01       0.01     0.01            53          53         2          2      0     0 b          b            25.20    25.20
1     0.1          0.01        0.01       0.01     0.01            53          53         2          2      0     0 b          b            31.20    31.20
1     0.2          0.01        0.01       0.01     0.01            53          53         2          2      0     0 b          b            37.20    37.20
1     0.3          0.01        0.01       0.01     0.01            53          53         2          2      0     0 b          b            43.20    43.20
1     0.4          0.01        0.01       0.01     0.01            53          53         2          2      0     0 b          b            43.20    43.20
1     0.5          0.01        0.01       0.01     0.01            53          53         2          2      0     0 b          b            43.20    43.20
1     0.6          0.01        0.01       0.01     0.01            53          53         2          2      0     0 b          b            43.20    43.20
1     0.7          0.01        0.01       0.01     0.01            53          53         2          2      0     0 b          b            43.20    43.20
1     0.8          0.01        0.01       0.01     0.01            53          53         2          2      0     0 b          b            37.20    37.20
1     0.9          0.01        0.01       0.01     0.01            53          53         2          2      0     0 b          b            31.20    31.20
1       1          0.01        0.01       0.01     0.01            53          53         2          2      0     0 b          b            25.20    25.20

Note: If stress checks are desired at harping points or point-of-stress
transfer, locations should be added above. Insert rows and copy
commands from another line, typical most sheets.

by S.Hida, v.0.0                                                                       PC Girders                                                                           17 of 41
Bridge Name, No.:                                                                                                                                                         Designer or Checker:
District, Co., PM:                                                                                                                                                        _________________
EA:                                                                                                                                                                                 8/22/2011

A ps f pu + As f y - As fy '-0.85b1 f c' (b - bw ) h f
'
Mild Steel Calculations for Top As, cont.
c=
f pu                     A ps f pu + As f y - As ' f y '                                         fps (Eqn. 5.7.3.1.1-1)
0.85 f c' b1bw + kA ps                      c =
dp                                               f pu
0.85 f c ' b 1b + kA ps                                                                       c
dp                                               f ps = f pu (1 - k      )
c (in.)        a (in.; a=b1*c)                         dp
f py
k = 2(1.04 -         )     c_T-beam (in.)            c_Rect (in.)
k f pu                                                         T-beam if c is > hf; otherwise rect.
k        interior    exterior    interior    exterior          interior exterior interior     exterior    interior exterior interior exterior
Span Point       2.08 girder            girder      girder      girder            girder girder      girder      girder      girder girder girder       girder
1    0           2.08           0.00        0.00        2.84        5.21       Rect     Rect             2.84        5.21     2.41     4.43 206.72        153.95
1 0.1            2.08           0.00        0.00        2.97        5.68       Rect     Rect             2.97        5.68     2.53     4.82 216.48        167.82
1 0.2            2.08           0.00        0.00        3.07        6.05       Rect     Rect             3.07        6.05     2.61     5.14 223.63        178.73
1 0.3            2.08           0.00        0.00        3.15        6.34       Rect     Rect             3.15        6.34     2.67     5.39 229.09        187.54
1 0.4            2.08           0.00        0.00        3.15        6.34       Rect     Rect             3.15        6.34     2.67     5.39 229.09        187.54
1 0.5            2.08           0.00        0.00        3.15        6.34       Rect     Rect             3.15        6.34     2.67     5.39 229.09        187.54
1 0.6            2.08           0.00        0.00        3.15        6.34       Rect     Rect             3.15        6.34     2.67     5.39 229.09        187.54
1 0.7            2.08           0.00        0.00        3.15        6.34       Rect     Rect             3.15        6.34     2.67     5.39 229.09        187.54
1 0.8            2.08           0.00        0.00        3.07        6.05       Rect     Rect             3.07        6.05     2.61     5.14 223.63        178.73
1 0.9            2.08           0.00        0.00        2.97        5.68       Rect     Rect             2.97        5.68     2.53     4.82 216.48        167.82
1    1           2.08           0.00        0.00        2.84        5.21       Rect     Rect             2.84        5.21     2.41     4.43 206.72        153.95

by S.Hida, v.0.0                                                                              PC Girders                                                                              18 of 41
Bridge Name, No.:                                                                                                                                                                       Designer or Checker:
District, Co., PM:                                                                                                                                                                      _________________
EA:                                                                                                                                                                                               8/22/2011

Mild Steel Calculations for                                      a               a                    a
M n = A ps f ps (d p - ) + As f y (d s - ) - As' f y' (d s' - )
Top As, cont.                                                    2               2                    2
Aps f ps d p + As f y d s                                                                          a hf                               æ aö        æ    aö           æ ' aö
de =                                                                          + 0.85 f c (b - bw ) b1h f ( -
'
Mn = Aps f psçdp - ÷ + As f y çds - ÷ - As f y' çds - ÷
'
Aps f ps + As f y                (max. As check per 5.7.3.3.1)                                   2  2
)
è 2ø        è    2ø           è    2ø
de              (Eqn. 5.7.3.3.1-2) c/de    c/de<0.42?            -Mn-Tbeam                      -Mn-Rect.                                      controlling Mn (ft-k)
(ft-k; Eqn. 5.7.3.2.2-1)       (ft-k; 5.7.3.2.3, b=bw)
interior exterior interior exterior             interior   exterior   interior      exterior         interior               exterior               interior   exterior
Span Point girder    girder    girder girder               girder     girder     girder        girder           girder                 girder                 girder     girder
1    0      25.20     25.20     0.11   0.21             YES        YES                 -261          -21                          3                    3         1454       1038
1 0.1       31.20     31.20     0.10   0.18             YES        YES                 -255          -18                          3                    3         1900       1417
1 0.2       37.20     37.20     0.08   0.16             YES        YES                 -250          -15                          3                    3         2354       1815
1 0.3       43.20     43.20     0.07   0.15             YES        YES                 -247          -13                          3                    3         2812       2228
1 0.4       43.20     43.20     0.07   0.15             YES        YES                 -247          -13                          3                    3         2812       2228
1 0.5       43.20     43.20     0.07   0.15             YES        YES                 -247          -13                          3                    3         2812       2228
1 0.6       43.20     43.20     0.07   0.15             YES        YES                 -247          -13                          3                    3         2812       2228
1 0.7       43.20     43.20     0.07   0.15             YES        YES                 -247          -13                          3                    3         2812       2228
1 0.8       37.20     37.20     0.08   0.16             YES        YES                 -250          -15                          3                    3         2354       1815
1 0.9       31.20     31.20     0.10   0.18             YES        YES                 -255          -18                          3                    3         1900       1417
1    1      25.20     25.20     0.11   0.21             YES        YES                 -261          -21                          3                    3         1454       1038

by S.Hida, v.0.0                                                                             PC Girders                                                                                             19 of 41
Bridge Name, No.:                                                                                                                                          Designer or Checker:
District, Co., PM:                                                                                                                                         _________________
EA:                                                                                                                                                                  8/22/2011

Aps f py
j = 0.90 + 0.10 ( PPR )   PPR =
Aps f py + As f y
Mild Steel Calculations for Top As, cont.                                                      *No Aps for continuity. Thus, f,
Mcr (ft-k)
min. Mu (ft-k)          fcr*Ic/yct (ft-k)     fps*Ic/yct (ft-k)      (=fcr*St+fps*St)           f Mn (ft-k)            1.2Mcr (ft-k)

interior   exterior interior    exterior   interior   exterior   interior    exterior    interior       exterior    interior   exterior
Span Point girder     girder    girder     girder     girder     girder     girder      girder      girder         girder      girder     girder
1    0           0         0     870.76     844.52 1750.30 1501.06              2621        2346                             -3145.27 -2814.69
1 0.1          577      557      870.76     844.52     755.71     648.10        1626        1493                             -1951.77 -1791.14
1 0.2         1026      990      870.76     844.52    -238.88    -204.86         632         640                             -758.263 -767.592
1 0.3         1346     1300      870.76     844.52 -1233.46 -1057.82            -363        -213                                     0          0
1 0.4         1538     1486      870.76     844.52 -1233.46 -1057.82            -363        -213                                     0          0
1 0.5         1603     1548      870.76     844.52 -1233.46 -1057.82            -363        -213                                     0          0
1 0.6         1538     1486      870.76     844.52 -1233.46 -1057.82            -363        -213                                     0          0
1 0.7         1346     1300      870.76     844.52 -1233.46 -1057.82            -363        -213                                     0          0
1 0.8         1026      990      870.76     844.52    -238.88    -204.86         632         640                             -758.263 -767.592
1 0.9          577      557      870.76     844.52     755.71     648.10        1626        1493                             -1951.77 -1791.14
1    1           0         0     870.76     844.52 1750.30 1501.06              2621        2346                             -3145.27 -2814.69

by S.Hida, v.0.0                                                               PC Girders                                                                              20 of 41
Bridge Name, No.:                                                                                                                                                                    Designer or Checker:
District, Co., PM:                                                                                                                                                                   _________________
EA:                                                                                                                                                                                            8/22/2011
As f y                       æ    a ö
a =                             = As fyçds - ÷
Mild Steel Calculations for Top As, cont. gdr
As--top of
0 . 85 f c '1 b
M

Mn (in.-k)
n
è    2ø
f_t=Mn/(Ig/yt) (ksi)
If |fMn|<min(1.2|Mcr| and 1.33|Mu|), need to increase As                      interior exterior interior exterior  interior   exterior   interior    exterior
girder girder girder girder          girder     girder     girder      girder
1.33Mu (ft-k)   Is As (see pg 1 of this sheet) ok?                        0.93    0.93       7.50       7.50 2357.48      2357.48        0.43        0.43

interior exterior interior   exterior BDS for
Span Point girder girder girder         girder comparison
1    0         0        0 n.a.       n.a.
1 0.1          0        0 n.a.       n.a.                                                    Ultimate Moment Check (interior girder)
1 0.2          0        0 n.a.       n.a.                                                     1-span PS I-girder Bridge, using AASHTO LRFD
1 0.3          0        0 n.a.       n.a.
1.33Mu--top
1 0.4          0        0 n.a.       n.a.
1 0.5          0        0 n.a.       n.a.                -4000                                                                                        1.2Mcr--top
1 0.6          0        0 n.a.       n.a.
1 0.7          0        0 n.a.       n.a.
phi*'Mn--top capacity

Moment (ft-k)
1 0.8          0        0 n.a.       n.a.                -3000
1 0.9          0        0 n.a.       n.a.              -3500
1    1         0        0 n.a.       n.a.                -2000
-3500                                                                                                  Note: AASHTO
LRFD 5.7.3.3.2
requires
fMn>min(1.33*
-1000                                                                                    Mu,1.2Mcr). Here,
the design is
0                                                                           1    acceptable.

0
Distance along span (10th points)

by S.Hida, v.0.0                                                                          PC Girders                                                                                             21 of 41
Mild Steel Calculations for Bottom As
Note: As and ds must be non-zero                                       (depth to ctd of mild C-steel)
Trial-and-error until fMn is acceptable.       ds (in.)             53 ds' (in.)           2 bot (in.^2)
As (in.^2)              As' (in.^2)            (depth to centroid of mild steel)                 Aps
interior    exterior    interior   exterior    interior    exterior    interior exterior            e
interior xterior
Span       Point   girder      girder      girder     girder      girder      girder      girder    girder      girdergirder
1       0          0.01        0.01       0.01      0.01            53          53         2           2 3.52 3.5
1     0.1          0.01        0.01       0.01      0.01            53          53         2           2 3.52 3.5
1     0.2          0.01        0.01       0.01      0.01            53          53         2           2 3.52 3.5
1     0.3          0.01        0.01       0.01      0.01            53          53         2           2 3.52 3.5
1     0.4          0.01        0.01       0.01      0.01            53          53         2           2 3.52 3.5
1     0.5          0.01        0.01       0.01      0.01            53          53         2           2 3.52 3.5
1     0.6          0.01        0.01       0.01      0.01            53          53         2           2 3.52 3.5
1     0.7          0.01        0.01       0.01      0.01            53          53         2           2 3.52 3.5
1     0.8          0.01        0.01       0.01      0.01            53          53         2           2 3.52 3.5
1     0.9          0.01        0.01       0.01      0.01            53          53         2           2 3.52 3.5
1       1          0.01        0.01       0.01      0.01            53          53         2           2 3.52 3.5

Note: If stress checks are desired at harping points or point-of-stress
transfer, locations should be added above. Insert rows and copy
commands from another line, typical most sheets.
A ps f pu + As f y - As fy '-0.85b1 f c' (b - bw ) h f
'

c=
f pu                       A ps f pu + As f y - As ' f y '
0.85 f c' b1bw + kA ps                      c =
dp                                                 f pu
0.85 f c ' b 1b + kA ps
dp
Where is tension?                 dp (in.)                      f py       c_T-beam (in.)            c_Rect (in.)
k = 2(1.04 -         )
k f pu
Interior     Exterior interior exterior                   k        interior    exterior    interior    exterior
Girder       Girder girder    girder    Span Point     2.08       girder      girder      girder      girder
b              b             25.20     25.20    1     0        2.08          -2.32        4.83        2.84        5.21
b              b             31.20     31.20    1 0.1          2.08          -2.57        5.36        2.97        5.68
b              b             37.20     37.20    1 0.2          2.08          -2.77        5.78        3.07        6.05
b              b             43.20     43.20    1 0.3          2.08          -2.94        6.13        3.15        6.34
b              b             43.20     43.20    1 0.4          2.08          -2.94        6.13        3.15        6.34
b              b             43.20     43.20    1 0.5          2.08          -2.94        6.13        3.15        6.34
b              b             43.20     43.20    1 0.6          2.08          -2.94        6.13        3.15        6.34
b              b             43.20     43.20    1 0.7          2.08          -2.94        6.13        3.15        6.34
b              b             37.20     37.20    1 0.8          2.08          -2.77        5.78        3.07        6.05
b              b             31.20     31.20    1 0.9          2.08          -2.57        5.36        2.97        5.68
b              b             25.20     25.20    1     1        2.08          -2.32        4.83        2.84        5.21
Mild Steel Calculations for Bot. As, cont.
A ps f pu + As f y - As ' f y '                                        fps (Eqn. 5.7.3.1.1-1)
f pu                                                                               Aps f ps d p + As f y d s
0.85 f c ' b 1b + kA ps                                                 f ps = f pu (1 - k
c      de =
dp            c (in.)        a (in.; a=b1*c)                         dp
)            Aps f ps + As f y
de
T-beam if c is > hf; otherwise rect.
interior exterior interior     exterior    interior exterior interior exterior                interior
girder girder      girder      girder      girder girder girder       girder       Span Point girder
Rect     Rect             2.84        5.21     2.41     4.43 206.72         153.95    1     0     25.20
Rect     Rect             2.97        5.68     2.53     4.82 216.48         167.82    1 0.1       31.20
Rect     Rect             3.07        6.05     2.61     5.14 223.63         178.73    1 0.2       37.20
Rect     Rect             3.15        6.34     2.67     5.39 229.09         187.54    1 0.3       43.20
Rect     Rect             3.15        6.34     2.67     5.39 229.09         187.54    1 0.4       43.20
Rect     Rect             3.15        6.34     2.67     5.39 229.09         187.54    1 0.5       43.20
Rect     Rect             3.15        6.34     2.67     5.39 229.09         187.54    1 0.6       43.20
Rect     Rect             3.15        6.34     2.67     5.39 229.09         187.54    1 0.7       43.20
Rect     Rect             3.07        6.05     2.61     5.14 223.63         178.73    1 0.8       37.20
Rect     Rect             2.97        5.68     2.53     4.82 216.48         167.82    1 0.9       31.20
Rect     Rect             2.84        5.21     2.41     4.43 206.72         153.95    1     1     25.20
Mild Steel Calculations for                                        a                   a                    a
M n = A ps f ps (d p -    ) + As f y (d s - ) - As' f y' (d s' - )
Bot. As, cont.                                                     2                   2                    2
Aps f ps d p + As f y d s                                                                             a hf                                  æ aö        æ    aö           æ ' aö
Aps f ps + As f y                                                      + 0.85 f c (b - bw ) b1h f ( -
'
)          Mn = Aps f psçdp - ÷ + As f y çds - ÷ - As f y' çds - ÷
'
(max. As check per 5.7.3.3.1)                                      2    2                                è 2ø        è    2ø           è    2ø
(Eqn. 5.7.3.3.1-2) c/de   c/de<0.42?               -Mn-Tbeam                       -Mn-Rect.
(ft-k; Eqn. 5.7.3.2.2-1)        (ft-k; 5.7.3.2.3, b=bw)
exterior interior exterior   interior   exterior   interior      exterior          interior               exterior
girder    girder girder      girder     girder     girder        girder            girder                 girder
25.20     0.11    0.21   YES        YES                1194         1016                         1457                 1040
31.20     0.10    0.18   YES        YES                1646         1399                         1903                 1419
37.20     0.08    0.16   YES        YES                2104         1800                         2356                 1818
43.20     0.07    0.15   YES        YES                2566         2214                         2815                 2230
43.20     0.07    0.15   YES        YES                2566         2214                         2815                 2230
43.20     0.07    0.15   YES        YES                2566         2214                         2815                 2230
43.20     0.07    0.15   YES        YES                2566         2214                         2815                 2230
43.20     0.07    0.15   YES        YES                2566         2214                         2815                 2230
37.20     0.08    0.16   YES        YES                2104         1800                         2356                 1818
31.20     0.10    0.18   YES        YES                1646         1399                         1903                 1419
25.20     0.11    0.21   YES        YES                1194         1016                         1457                 1040
aö         æ    aö    ' 'æ '    aö
Mild Steel Calculations for Bot. As, cont.
p - ÷ + A f y çds - ÷ - A f y çds - ÷
s               s
2ø         è    2ø         è    2ø
controlling Mn (ft-k)            min. Mu (ft-k)            fcr*Sb (ft-k)           fps*Sb (ft-k)

interior    exterior              interior    exterior interior      exterior   interior   exterior
girder      girder     Span Point girder      girder    girder       girder     girder     girder
1454       1038    1     0           0         0       269.31     269.31     541.33     478.67
1900       1417    1 0.1           577      557        269.31     269.31     819.64     724.77
2354       1815    1 0.2         1026       990        269.31     269.31 1097.95        970.86
2812       2228    1 0.3         1346      1300        269.31     269.31 1376.26 1216.96
2812       2228    1 0.4         1538      1486        269.31     269.31 1376.26 1216.96
2812       2228    1 0.5         1603      1548        269.31     269.31 1376.26 1216.96
2812       2228    1 0.6         1538      1486        269.31     269.31 1376.26 1216.96
2812       2228    1 0.7         1346      1300        269.31     269.31 1376.26 1216.96
2354       1815    1 0.8         1026       990        269.31     269.31 1097.95        970.86
1900       1417    1 0.9           577      557        269.31     269.31     819.64     724.77
1454       1038    1     1           0         0       269.31     269.31     541.33     478.67
Aps f py
j = 0.90 + 0.10 ( PPR )   PPR =
Aps f py + As f y   Mild Steel Calc
As, cont.                                                     *No Aps for continuity. Thus, f,                If |fMn|<min(1.2|Mcr| and
Mcr (ft-k)
Mdl(Sbc/Sb-1)                    (fcr+fps)Sb-               f Mn (ft-k)           1.2Mcr (ft-k)
Mdl(Sbc/Sb-1)
interior         exterior     interior      exterior    interior     exterior    interior  exterior
girder           girder       girder        girder      girder       girder      girder    girder   Span Point
0            0        810.64        747.98        1454         1038 972.768 897.5759      1      0
215          199        873.48        794.73        1900         1417 1048.18 953.6733      1 0.1
383          354        984.21        885.77        2354         1815 1181.05 1062.93       1 0.2
503          465      1142.81       1021.12         2812         2228 1371.37 1225.346      1 0.3
575          532      1070.99         954.67        2812         2228 1285.19 1145.607      1 0.4
599          554      1047.05         932.52        2812         2228 1256.46 1119.027      1 0.5
575          532      1070.99         954.67        2812         2228 1285.19 1145.607      1 0.6
503          465      1142.81       1021.12         2812         2228 1371.37 1225.346      1 0.7
383          354        984.21        885.77        2354         1815 1181.05 1062.93       1 0.8
215          199        873.48        794.73        1900         1417 1048.18 953.6733      1 0.9
0            0        810.64        747.98        1454         1038 972.768 897.5759      1      1
As f y                       æ    a ö
a =                             = As fyçds - ÷
Mild Steel Calculations for Bot. As, cont. gdr
As--top of
0 . 85 f c '1 b
M   n

Mn (in.-k)
è    2ø

If |fMn|<min(1.2|Mcr| and 1.33|Mu|), need to increase As                      interior exterior interior exterior   interior
girder girder girder girder           girder
1.33Mu (ft-k)       Is As (see pg 1 of this sheet) ok?                    0.93    0.93       7.50        7.50 2357.48

interior   exterior   interior   exterior BDS for
girder     girder     girder     girder comparison
0          0   YES        YES
767.31     741.01    YES        YES                                                  Ultimate Moment Check (interior girder)
1364.1     1317.4    YES        YES                                                   1-span PS I-girder Bridge, using AASHTO LRFD
1790.4        1729   YES        YES
2046.2        1976   YES        YES
2131.4     2058.4    YES        YES                      0
2046.2        1976   YES        YES
1790.4        1729   YES        YES                    0
1364.1     1317.4    YES        YES
Moment (ft-k)

767.31     741.01    YES        YES                 1000
-3500
0          0   YES        YES               -3500
2000

3000

4000
Distance along span (10th points)
æ    a ö
M   n   = As fyçds - ÷
è    2ø
f_t=Mn/(Ig/yt) (ksi)
exterior   interior    exterior
girder     girder      girder
2357.48        0.43        0.43

Check (interior girder)
dge, using AASHTO LRFD
1.33Mu--bot
1.2Mcr--bot
1
phi*'Mn--bot capacity

10th points)
Bridge Name, No.:                                                                                                                                                              Designer or Checker:
District, Co., PM:                                                                                                                                                             _________________
EA:                                                                                                                                                                                      8/22/2011

Shear--San Diego '99 ('00 Interim) Method
Vu, factored shear demand
Strength I           Strength II                          Tendon profile (degrees                                          de: distance from
1.25DL+1.5ADL+1.35P13                  from horizontal)             Vp              Where is tension? As to comp. face
max(Str I, II)
Interior  Exterior Interior Exterior Interior Exterior     Interior Exterior    Interior    Exterior       Interior       Exterior   Interior   Exterior
Span Point      (ft)       Girder     Girder Girder      Girder Girder Girder         Girder     Girder    Girder      Girder         Girder         Girder     Girder     Girder Span
1     0          0         208       150       243      170     243       170        0.00       0.00      0.00        0.00    b              b                 25.2       25.2    1
1 0.1         8.36         175       125       199      139     199       139        3.85       3.85     37.37       33.05    b              b                 31.2       31.2    1
1 0.2        16.72         144       101       157      109     157       109        3.85       3.85     37.37       33.05    b              b                 37.2       37.2    1
1 0.3            0         112         77      120        81    120         81       3.85       3.85     37.37       33.05    b              b                 43.2       43.2    1
1 0.4        33.44          82         53       83        54     83         54       0.00       0.00      0.00        0.00    b              b                 43.2       43.2    1
1 0.5         41.8          51         30        0         0     51         30       0.00       0.00      0.00        0.00    b              b                 43.2       43.2    1
1 0.6        50.16         -82        -53      -83       -54     83         54       0.00       0.00      0.00        0.00    b              b                 43.2       43.2    1
1 0.7        58.52        -112        -77     -120       -81    120         81       3.85       3.85     37.37       33.05    b              b                 43.2       43.2    1
1 0.8        66.88        -144      -101      -157     -109     157       109        3.85       3.85     37.37       33.05    b              b                 37.2       37.2    1
1 0.9        75.24        -175      -125      -199     -139     199       139        3.85       3.85     37.37       33.05    b              b                 31.2       31.2    1
1     1       83.6        -208      -150      -243     -170     243       170        0.00       0.00      0.00        0.00    b              b                 25.2       25.2    1

Note: If stress checks are desired at harping points or point-of-stress
transfer, locations should be added above. Insert rows and copy
commands from another line, typical most sheets.

by S.Hida, v.0.0                                                                            PC Girders                                                                                     30 of 41
Bridge Name, No.:                                                                                                                                                                      Designer or Checker:
District, Co., PM:                                                                                                                                                                     _________________
EA:                                                                                                                                                                                              8/22/2011

Vu / j - V p              Vu - jV p
bv ³                    ? v =                                                  Shear
Shear--cont.                                                                                         0.25 f 'c d v               j bv d v
dv=max[Mn/%, max(0.9de, 0.72h)]            Is bv adequete (Eqn. 5.8.3.3-2)?                Shear stress on the concrete
Asfy+Apsfps                       Mn                                                      bv (in.)                           (Eqn. 5.8.3.3-2)             v/f'c

Interior   Exterior Interior    Exterior        Interior       Exterior      Interior   Exterior    Interior   Exterior     Interior        Exterior   Interior   Exterior
Point       Girder      Girder Girder       Girder          Girder         Girder        Girder     Girder      Girder     Girder       Girder          Girder     Girder     Girder Span
0      728.05      542.36    1454        1038            34.56          34.56          6.25       4.38    ok          ok             1.097           0.768      0.219      0.154      1
0.1      762.39      591.17    1900        1417            34.56          34.56          4.26       2.81    ok          ok             0.747           0.492      0.149      0.098      1
0.2      787.55      629.56    2354        1815            35.87          34.60          3.06       2.02    ok          ok             0.536           0.355      0.107      0.071      1
0.3      806.78      660.55    2812        2228            41.83          40.47          1.84       1.13    ok          ok             0.323           0.199      0.065      0.040      1
0.4      806.78      660.55    2812        2228            41.83          40.47          1.77       1.19    ok          ok             0.311           0.208      0.062      0.042      1
0.5      806.78      660.55    2812        2228            41.83          40.47          1.09       0.65    ok          ok             0.191           0.114      0.038      0.023      1
0.6      806.78      660.55    2812        2228            41.83          40.47          1.77       1.19    ok          ok             0.311           0.208      0.062      0.042      1
0.7      806.78      660.55    2812        2228            41.83          40.47          1.84       1.13    ok          ok             0.323           0.199      0.065      0.040      1
0.8      787.55      629.56    2354        1815            35.87          34.60          3.06       2.02    ok          ok             0.536           0.355      0.107      0.071      1
0.9      762.39      591.17    1900        1417            34.56          34.56          4.26       2.81    ok          ok             0.747           0.492      0.149      0.098      1
1      728.05      542.36    1454        1038            34.56          34.56          6.25       4.38    ok          ok             1.097           0.768      0.219      0.154      1
Notes: 1) Effective shear depth, dv, is
least where M is close to 0. If "need         Note: bv=1.75ft=21in at supports with notched ends
flare" appears, web should be                 only; bv=7.125in web thickness, typ.
thickened or a larger girder selected.
2) f =0.9 for shear.

by S.Hida, v.0.0                                                                               PC Girders                                                                                          31 of 41
Bridge Name, No.:                                                                                                                                                                                            Designer or Checker:
District, Co., PM:                                                                                                                                                                                           _________________
EA:                                                                                                                                                                                                                    8/22/2011

Assume e is positive; use Eqn. 5.8.3.4.2-1 ('00).                      If e is negative, use Eqn 5.8.3.4.2-3 ('00)
Shear--cont.                                                                               é Mu                                           ù               é Mu                                           ù
assumed stress angle q, (nonzero for columns)                               ê d + 0.5 N u + 0.5(Vu - V p ) cotq - Aps f po ú               ê d + 0.5 N u + 0.5(Vu - V p ) cotq - Aps f po ú
ex = ê v                                            ú £ 0.002 e x = ê v                                            ú £ 0.002
per T5.8.3.4.2-1 ('00)   Nu (tensile is positive)       max Mu              ê            2( Es As + E p Aps )              ú               ê       2( Ec Ac + Es As + E p Aps )           ú
ê
ë
ú
û
ê
ë                                              ú
û
Interior       Exterior    Interior   Exterior   Interior      Exterior         Interior       Exterior          fpo=0.7fpu                                       Interior           Exterior
Point         Girder         Girder      Girder     Girder     Girder        Girder           Girder          Girder                 189 Span                Point              Girder              Girder Span
0           27             25            0          0          0             0       -0.00181        -0.00205                                      1           0       -0.00009            -0.00010       1
0.1           28             22            0          0     1535          1272          0.00009        -0.00039                                      1         0.1        0.00009            -0.00002       1
0.2           40             34            0          0     2573          2144          0.00113         0.00057                                      1         0.2        0.00113             0.00057       1
0.3           40             36            0          0     3442          2862          0.00158         0.00092                                      1         0.3        0.00158             0.00092       1
0.4           40             40            0          0     3860          3216          0.00209         0.00136                                      1         0.4        0.00209             0.00136       1
0.5           40             40            0          0     4078          3393          0.00227         0.00152                                      1         0.5        0.00227             0.00152       1
0.6           40             40            0          0     3860          3216          0.00209         0.00136                                      1         0.6        0.00209             0.00136       1
0.7           40             36            0          0     3442          2862          0.00158         0.00092                                      1         0.7        0.00158             0.00092       1
0.8           40             34            0          0     2573          2144          0.00113         0.00057                                      1         0.8        0.00113             0.00057       1
0.9           27             22            0          0     1535          1272          0.00011        -0.00039                                      1         0.9        0.00011            -0.00002       1
1           26             25            0          0          0             0       -0.00177        -0.00205                                      1           1       -0.00009            -0.00010       1

Notes: 1) A "look
and returns a value of
theta must be changed until th
C and T centroids due to appli
q                                                                                                                                                                                       Hence Vc is small at 0.8l1 and

by S.Hida, v.0.0                                                                            PC Girders                                                                                                                     32 of 41
Bridge Name, No.:                                                                                                                                                                          Designer or Checker:
District, Co., PM:                                                                                                                                                                         _________________
EA:                                                                                                                                                                                                  8/22/2011

Eqn. 5.8.3.3-4
Spacing reqd. (5.8.2.7) (in.)
Shear--cont.                                                                                            Av
³
Vu - j (V p + Vc )                          If Vu<0.125f'cbvdv, then s=0.8
Vc = 0.0316b f 'c bv d v a, angle of inclination of       s jf y d v (cotq + cota ) sin a                      If Vu>0.125f'cbvdv, then s=0.4
Does theta match estimate within 2 degrees?                     b           Vc, Eqn. 5.8.3.3-3 stirrups to longitudinal                               Av for two legs (in.^2)

Interior   Exterior        Interior                        E
Exterior Interior xterior     Interior Exterior      Interior    Exterior Interior      Exterior    Interior      Exterior
Point            Girder     Girder          Girder          Girder Girder Girder          Girder Girder          Girder      Girder Girder         Girder      Girder        Girder      Span
0           27.9       24.7    ok              ok                2.4     2.7        42.11    46.28            90          90           0.79        0.39          0.62        0.62     1
0.1           26.9       22.5    ok              ok                2.6     3.1        45.24    54.63            90          90           0.66        0.16          0.62        0.62     1
0.2           41.0       33.7    ok              ok                1.9     2.4        34.31    41.46            90          90           0.79        0.18          0.62        0.62     1
0.3           40.8       36.4    ok              ok                2.0     2.2        41.07    45.43            90          90           0.51        0.04          0.62        0.62     1
0.4           40.8       40.8    ok              ok                2.0     2.0        41.07    39.73            90          90           0.36        0.08          0.62        0.62     1
0.5           40.8       40.8    ok              ok                2.0     2.0        41.07    39.73            90          90           0.01        0.00          0.62        0.62     1
0.6           40.8       40.8    ok              ok                2.0     2.0        41.07    39.73            90          90           0.36        0.08          0.62        0.62     1
0.7           40.8       36.4    ok              ok                2.0     2.2        41.07    45.43            90          90           0.51        0.04          0.62        0.62     1
0.8           41.0       33.7    ok              ok                1.9     2.4        34.31    41.46            90          90           0.79        0.18          0.62        0.62     1
0.9           26.9       22.5    ok              ok                2.6     3.1        45.24    54.63            90          90           0.63        0.16          0.62        0.62     1
1           27.9       24.7    ok              ok                2.4     2.7        42.11    46.28            90          90           0.75        0.39          0.62        0.62     1
Note: If Av/s is a                                  face-of-
Notes: 1) A "look-up" function uses the v/fc and strain values calculated (based on an assumed q),                                           negative value, Av/s is
and returns a value of q from the 'v/fc vs theta' chart on the 'theta_beta' worksheet. The assumed
theta must be changed until there is a match, i.e. use 'trial-and-error'. 2) The distance between the
C and T centroids due to applied loads is small near the point of inflection where Mu is small.
Hence Vc is small at 0.8l1 and0.2l2.

Distance from face of support
controlling value for shear, wh
max(dv, 0.5dvcot
only controls when stress crac
less than 26.5 degrees.

by S.Hida, v.0.0                                                                                        PC Girders                                                                                         33 of 41
Bridge Name, No.:                                                                                                                                                            Designer or Checker:
District, Co., PM:                                                                                                                                                           _________________
EA:                                                                                                                                                                                    8/22/2011

Spacing reqd. (5.8.2.7) (in.)                              Critical section is max(dv, 0.5dvcotq), where dv and q are
If Vu<0.125f'cbvdv, then s=0.8dv; 24.0 in. max.            taken at location of maximum shear: Span 1 rt end;                Shear--final
If Vu>0.125f'cbvdv, then s=0.4dv; 12.0 in. max.            dv=41.4in., q=22. Hence, critical section is 51.23 in. from             Mu        N    æV                ö
face of support.                                                  T=         + 0.5 u + ç u - 0.5Vs - V p ÷ cotq
çf                ÷
Spacing, s (in.)            Reqd. s                                                                                       d vf      f è                    ø
fSVp             (Results compiled here for plotting--interior gdr only.
Interior Exterior Interior Exterior     Vc               LFD calculated on separate sheet.)                                                    T (Eqn. 5.8.3.5-1)
Point     Girder Girder Girder Girder Vs          Vs       fVn     Vs (LFD)|Vu|    f(0.25f'cbvdv +Vp) f(Vc+Vp+Vs)                  LFD Vu LFD fVn (k)        Asfy+Apsfps OK?
0            9       19        9     12   267    278     277       420     243            277     277        416         277       226      339       -409.957 728 ok
0.1           11       48      11      24   214    267     267       161     199            277     311        219         219       185      252       257.5109 762 ok
0.2            9       41        9     24   168    216     216       106     157            287     321        160         160       146      183       726.8597 788 ok
0.3           15     175       15      24   127    185     185       124     120            335     369        182         182       111      154       752.8799 807 ok
0.4           21       88      21      24    89    117     117       124      83            335     335        148         148        77      130       877.5351 807 revise
0.5        1414     7440       24      24    77    107     107       124      51            335     335        148         148        28      112       905.7185 807 revise
0.6           21       88      21      24    89    117     117       124      83            335     335        148         148        77      130       877.5351 807 revise
0.7           15     175       15      24   127    185     185       124     120            335     369        182         182       111      154       752.8799 807 ok
0.8            9       41        9     24   168    216     216       106     157            287     321        160         160       146      183       726.8597 788 ok
0.9           12       48      12      24   214    267     267       168     199            277     311        226         226       185      252       250.5997 762 ok
1             10       19      10      12   267    278     277       439     243            277     277        433         277       226      339       -427.696 728 ok

face-of-bent                                                                              Note: LRFD capacity, Vn,           Must check that mild steel is extended
0.5dvcotq
is lesser of                       beyond where it is no longer needed. Note
dv=Eqn C5.8.2.9-1                                                         0.25fc'bvdv+Vp, and                that at the inflection point, Aps is near the
45 degrees                                                        Vc+Vs+Vp (Eqns 5.8.3.3-            center of the member. Much As would be
1, 2). Must increase               needed to satisfy this equation.
dv=0.9de                                                      girder dimensions if
capacity is less than
dv=0.72h

Distance from face of support equals
controlling value for shear, which is the
max(dv, 0.5dvcotq). Note that 0.5dvcotq
only controls when stress crack angle, q, is
less than 26.5 degrees.

by S.Hida, v.0.0                                                                             PC Girders                                                                                  34 of 41
Bridge Name, No.:                                                                                                                                                               Designer or Checker:
District, Co., PM:                                                                                                                                                              _________________
EA:                                                                                                                                                                                       8/22/2011

AASHTO LRFD
Shear Capacity, fVn (interior girder)
Comparison of AASHTO
Vc
600
fVn=f*min[(Vs+Vc+Vp), (0.25f'cbd+Vp)]
Vs
Pretensioned, Preca
500
Vp                                                                    Shear Demand vs. S
Shear (k)

400
phi*(Vs+Vc+Vp)
300
200                                                                                              phi*(0.25f'cbvdv+Vp)

100                                                                                              phi*Vn_controlling                             400
0                                                               Note: LRFD capacity, Vn = 0.25fc'bvdv+Vp (Eqn 5.8.3.3-1) only
controls over Vs+Vc+Vp at approx. 2.3 ft from bents 2 and 3,
0                                                       1   which is within the cap area. This new eqn provides a check that
Vc contributes amply to Vn.
Distance along span (10th points)                                                                                               300

Shear (k)
200

100

0
0
Distance along span (10th

by S.Hida, v.0.0                                                                               PC Girders                                                                                   35 of 41
Bridge Name, No.:                                         Designer or Checker:
District, Co., PM:                                        _________________
EA:                                                                 8/22/2011

Comparison of AASHTO LRFD '00, vs. LFD
retensioned, Precast I-girder Bridge
Shear Demand vs. Shear Capacity

Vu (LRFD)

Vu (LFD)

phi*Vn (LRFD)

phi*Vn (LFD)

phi*Vn (LRFD using
A/s from LFD)

1
Distance along span (10th points)

by S.Hida, v.0.0                             PC Girders               36 of 41
Designer or Checker
_________________
8/22/2011

AASHTO LRFD Table 5.8.3.4.2-1, '00 Interims
A "lookup" function called on the previous sheet, returns values for theta and beta

e <=                -0.1   -0.0002   -0.0001   -0.00005       0 0.000125        0.00025   0.0005   0.00075   0.001    0.1
index num.             2         3         4          5       6        7              8        9        10      11     12

theta         e*10^-3 <=
v/f'c <=            -0.2     -0.1      -0.05          0   0.125       0.25          0.5     0.75         1     1.5      2
0         22.3     20.4         21       21.8    24.3       26.6         30.5     33.7      36.4    40.8   43.9
0.075          18.1     20.4       21.4       22.5    24.9       27.1         30.8       34      36.7    40.8   43.1
0.1         19.9     21.9       22.8       23.7    25.9       27.9         31.4     34.4        37      41   43.2
0.125          21.6     23.3       24.2         25    26.9       28.8         32.1     34.9      37.3    40.5   42.8
0.15          23.2     24.7       25.5       26.2      28       29.7         32.7     35.2      36.8    39.7   42.2
0.175          24.7     26.1       26.7       27.4      29       30.6         32.8     34.5      36.1    39.2   41.7
0.2         26.1     27.3       27.9       28.5      30       30.8         32.3       34      35.7    38.8   41.4
0.225          27.5     28.6       29.1       29.7    30.6       31.3         32.8     34.3      35.8    38.6   41.2

beta          e*10^-3 <=
v/f'c <=            -0.2     -0.1      -0.05          0   0.125       0.25          0.5     0.75         1     1.5      2
0         6.32     4.75        4.1       3.75    3.24       2.94         2.59     2.38      2.23    1.95   1.67
0.075          3.79     3.38       3.24       3.14    2.91       2.75          2.5     2.32      2.18    1.93   1.69
0.1         3.18     2.99       2.94       2.87    2.74       2.62         2.42     2.26      2.13     1.9   1.67
0.125          2.88     2.79       2.78       2.72      2.6      2.52         2.36     2.21      2.08    1.82   1.61
0.15          2.73     2.66       2.65        2.6    2.52       2.44         2.28     2.14      1.96    1.71   1.54
0.175          2.63     2.59       2.52       2.51    2.43       2.37         2.14     1.94      1.79    1.61   1.47
0.2         2.53     2.45       2.42        2.4    2.34       2.14         1.86     1.73      1.64    1.51   1.39
0.225          2.39     2.39       2.33       2.33    2.12       1.93          1.7     1.58       1.5    1.38   1.29

by S.Hida, v.0.0                                                   PC Girders                                                   37 of 41
Bridge Name, No.:                                                                                                     Designer or Checker:
District, Co., PM:                                                                                                    _________________
EA:                                                                                                                             8/22/2011

LFD Shear Capacity
1 lane, where gdf=s/11;
IM=1+50/(L+125)

(Av/s)*fy*de

.)
in
2/

b
)
(k

S
.^

k)
l)/
(i n
Vu

ft-
fd
Sb

L
)
an

t

(
(k

_D
e-
in

/s
D

cr
r*
Span Point
Sp

Po

LF

Av

Vs

(f p

M

M
fc
1          0   226.2498    0.1033             274          438          880         1318          0
1        0.1     185.19    0.0413             110          438          677         1115        344
1        0.2   145.7418    0.0413             110          438          619         1057        612
1        0.3   111.1284    0.0413             110          438          708         1145        804
1        0.4   76.51503    0.0413             110          438          489          927        918
1        0.5         28    0.0413             110          438          416          854        957
1        0.6    -76.515    0.0413             110          438          489          927        918
1        0.7   -111.128    0.0413             110          438          708         1145        804
1        0.8   -145.742    0.0413             110          438          619         1057        612
1        0.9    -185.19    0.0413             110          438          677         1115        344
1    1          -226.25    0.1033             274          438          880         1318          0

Note: If stress checks are desired at harping points or point-of-stress
transfer, locations should be added above. Insert rows and copy
commands from another line, typical most sheets.

by S.Hida, v.0.0                                                     PC Girders                                                  38 of 41
Bridge Name, No.:                                                                                                      Designer or Checker:
District, Co., PM:                                                                                                     _________________
EA:                                                                                                                              8/22/2011

VassocMcr
Vci = 0.019* f 'c bgwde +VDL +         .

LFD Shear                                                                                      Mmax

(                     )
V = 0.111 f 'c +0.3fpe bgwde +Vp
cw

S)
BD
0.9*[Vs+min(Vci,Vcw)]
m

S)
f ro

BD
/I M

om
w

(f r

ax
4
L_

m
oc

s
ne

/M
(L

ss

la

cr
L

a
L
L
_D

Ll
D
_L

M
fVn (k)

df
Span Point                                                                                               Vci (k)     Vcw (k)
V_

V_

V*
*g
M

M

1      0                 0                           46            0                   604491         604547         103           339
1    0.1               664                           37           77                      126             172        170           252
1    0.2              1072                           27           62                       56              94        200           183
1    0.3              1452                           18           47                       33              62        230           154
1    0.4              1608                            9           32                       15              34        192           130
1    0.5              1715                            0           16                        5              15        192           112
1    0.6              1608                            9           32                       15              34        192           130
1    0.7              1452                           18           47                       33              62        230           154
1    0.8              1072                           27           62                       56              94        200           183
1    0.9               664                           37           77                      126             172        170           252
1   1                    0                           46            0                   604491         604547         103           339

AASHTO LFD
Shear Capacity, fVn (interior girder)
Vcw
400
350
Vci
300
Shear (k)

250
200                                                                                              Vs
150
100                                                                                              phi*(Vs+min(Vci, Vcw)
50
0

by S.Hida, v.0.0                                                      PC Girders                                                  39 of 41
Interface Shear Transfer - Shear Friction (5.8.4)
Vn = cA + m[ Avf f y + P ] (Equation 5.8.4.1-1)
cv               c
Is Avf provided> Avf
Vu max(Str I, II) (k) V_uh=Vu/d_vh (k/ft)   Vn=V_uh/0.9 (k/ft) solve for Avf (in.^2/ft): Avf provided (in.^2/ft)            reqd?
Interior   Exterior    Interior Exterior    Interior Exterior    Interior    Exterior      Interior   Exterior        Interior   Exterior
Span Point     Girder       Girder    Girder   Girder      Girder    Girder     Girder       Girder       Girder      Girder         Girder     Girder
1     0        243          170      58.8     41.2        65.3      45.7       0.77         0.45         0.79        0.62         ok         ok
1 0.1          199          139      48.2     33.6        53.5      37.3       0.58         0.31         0.66        0.31         ok         ok
1 0.2          157          109      38.0     26.2        42.2      29.2       0.39         0.17         0.79        0.31         ok         ok
1 0.3          120            81     29.1     19.7        32.3      21.8       0.22         0.05         0.51        0.31         ok         ok
1 0.4           83            54     20.2     13.1        22.4      14.5       0.06        -0.07         0.36        0.31         ok         ok
1 0.5           51            30     12.4       7.1       13.7        7.9     -0.09        -0.18         0.31        0.31         ok         ok
1 0.6           83            54     20.2     13.1        22.4      14.5       0.06        -0.07         0.36        0.31         ok         ok
1 0.7          120            81     29.1     19.7        32.3      21.8       0.22         0.05         0.51        0.31         ok         ok
1 0.8          157          109      38.0     26.2        42.2      29.2       0.39         0.17         0.79        0.31         ok         ok
1 0.9          199          139      48.2     33.6        53.5      37.3       0.58         0.31         0.63        0.31         ok         ok
1     1        243          170      58.8     41.2        65.3      45.7       0.77         0.45         0.75        0.62       not ok       ok

Horz. shear depth d_vh (ft):        4.1
cohesion, c (ksi)   0.075
friction, mu       0.6
Acv (in.^2/ft)     252
Avf>0.05bv/fy?        Vn<0.2fcAcv             Vn<0.8Acv
(Eqn. 5.8.4.1-4)      (Eqn. 5.8.4.1-2)       (Eqn. 5.8.4.1-3)
.05bv/fy=     0.0175 0.2fcAcv=          252   0.8Acv=        201.6
Interior   Exterior   Interior   Exterior    Interior   Exterior
Span Point      Girder      Girder    Girder      Girder     Girder      Girder
1     0      ok          ok        ok          ok         ok          ok
1 0.1        ok          ok        ok          ok         ok          ok
1 0.2        ok          ok        ok          ok         ok          ok
1 0.3        ok          ok        ok          ok         ok          ok
1 0.4        ok          ok        ok          ok         ok          ok
1 0.5        ok          ok        ok          ok         ok          ok
1 0.6        ok          ok        ok          ok         ok          ok
1 0.7        ok          ok        ok          ok         ok          ok
1 0.8        ok          ok        ok          ok         ok          ok
1 0.9        ok          ok        ok          ok         ok          ok
1     1      ok          ok        ok          ok         ok          ok

```
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