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REINFORCED CONCRETE
BOX CULVERT AND WINGWALL
DESIGN AND ANALYSIS
COMPUTER PROGRAM USER S MANUAL
Version 2.3
Structures Design Office
Florida Department of Transportation
February, 1993
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TABLE OF CONTENTS
DISCLAIMER
vi
ABSTRACT
PREFACE
METHODOF SOLUTION
1
DIRECT ELEMENT METHOD OF BOX CULVERT ANALYSIS
2
THE MEMBER FLEXIBILITY MATRIX [ASAT]-l
5
DEAD LOAD EARTH PRESSURE AND WATER PRESSURE
6
SERVICE LOAD DESIGN
7
LOAD FACTORDESIGN
10
FATIGUE STRESS LIMITS
14
WINGWALLDESIGN CRITERIA
16
17
IE-IN LENGTHOF SKEWEDWINGWALL
19
SERINSTRUCTIONS
INPUT DATA TABLE
20
OUTPUT DATA
31
BAR SCHEDULE
35
EXAMPLES
37
STANDARD INPUT AND OUTPUT
38
SPECIAL AND DETAILED INPUT AND OUTPUT
43
54
PPENDIX A PROGRAM FLOW CHART.
56
PPENDIX B VARIABLE LISTING.
APPENDIX C
64
APPENDIX D
66
72
PPENDIX E BLANK INPUT CODINGFORMS.
..
75
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LIST OF FIGURES
FIGURE
1
Boundary Conditions
1
2
The P,X Diagram
3
The F,e Diagram
2
4
Member Statics Matrix
3
5
Member SAt Matrix
3
6
Member External Stiffness Matrix.
4
Stress Block
7
8
10
Strain Diagram. ...
9
P,M Diagram
12
10 16
ingwall Length Criteria.
11
Tie-in Length of Skewed Wingwall (0°-15°, 180°-165°)
17
12
Tie-in Length of Skewed Wingwall (15°-45°)
18
13
Bar Type Diagram.
34
14
Member Reference Diagram.
36
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LIS~~ OF TABLES
TABLE
1
20
nput Data Description
2
56
ariable Listing
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DISCLAIMER
Neither the programmer nor the Department take any responsibility for
the results this program may produce or
for the principles used and
procedures developed within the program and its documentation.
It is
required that a competent user will reasonably check all results to assure
validity and be himself fully responsible for the resulting plans he may
develop while using this program as part of the preparation process.
Paul T. C. Lee P.E
North Carolina Department of Transportation
No warranty expressed or implied is made by the Florida Department
of Transportation as to the accuracy and functioning of the added program
text or the results it produces nor shall the fact of distribution
constitute any such warranty and no responsibility is assumed by the
Florida Department of Transportation in any connection there with.
The
Engineer
of
Record
the
entire
risk
ssumes
the
quality
and
s
to
performance of this program for his particular application.
Liang Y. Hsia P.E.
Florida Department of Transportation
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ABSTRACT
The Reinforced Concrete Box Culvert and Wingwall Design and Analysis
Computer Program is the result of the joint efforts by North Carolina and
Florida Departments of Transportation.
The user may analyze or design a one two three or four barrel
reinforced concrete box culvert. Either service load or load factor
design method may be selected. Each of the barrels may have any clear
span from a minimum of two feet and a clear height from two feet to
fourteen feet. All barrels in one culvert are assumed to be identical in
size and shape. The culvert in this program may be a detached unit an
extended unit or a linked unit.
Individually the wingwalls extended from each corner of box culvert
may be placed on different angles the wingwall tops may be level or
sloped and the wingwall lengths may be designed or specified to meet job
site requirements.
Environment conditions ranging from slightly aggressive to extremely
aggressive must be selected to determine the required concrete type andcover.
By selecting the minimum output option of this program the output
may be processed into the construction plans in conjunction with the
Florida Department of Transportation Roadway and Traffic Design Standards.
This program may also be applied as a tool for special design and
analysis.
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PREFACE
he original Reinforced Concrete Box Culvert Computer Program was
developed Py Paul T. C. Lee of North Carolina Department ofTrans
This program was later modified py Arthur J. Haywood
Larry M. Sessions Liang Y. Hsia and Elsie R. Clary of Florida Department
of Transportation to add a wingwall design feature and to comply with the
Florida DOT Roadway and Traffic Standards. The updated Version 2.3 was
prepared to comply with the Florida DOT Special Provision 346 Portland
Cememt Concrete and AASHTO load factor.
The addition of skewed wingwall environment options culvert
extension and unit conversion were managed py Robert C. Burnett Jr. P.E.
in 1985 and coordinated by Liang Y. Hsia in 1991 and 1992.
The documentation was prepared by Paul T. C. Lee and Liang Y. Hsia.
The Florida version was typed by Charlene A. Williams proofread by
Charlie B. Harvey P.E. Chris Wild and Connie Adams and reviewed by RobertE.
Nichols P.E. All d:i agrams and coding forms were prepared by WilliamE.
Howell and Structures CADD engineers. The screen data entry panels were
developed by Kenneth B. Graham P.E. This documentation is available on
either double sided high density diskette or printed copy.
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METHODOF SOLUTION
The method of analysis is the displacement or stiffness method. In
this method, a matrix using the member s stiffness is formed to represent
the structure. Member stiffness is derived for three possible movements
which are rotational, vertical and horizontal movements at the ends of
members. Then the following boundary conditions are applied to the matrix:
No vertical displacement at the outside ends of bottom slab.
No lateral displacement at right end of bottom slab.
Boundary Conditions1
Through matrix maneuver, the displacements at the ends of each member
are computed for each given loading condition. Then the exact moments and
forces are determined by using the computed displacements. These moments
and forces are used to develop stresses, design reinforcements or adjust
member depth. If the member depth is increased, its impact is reevaluated
as above.
The length of each member for analysis purposes is measured from
center line to center line of the supporting members. It is assumed that
loading applied at top slab will be uniformly distributed over the entire
bottom slab. This assumption is based upon the premise that the bottom
slab is cast upon a mat of granular material. A more refined assumption
seems impractical due to the lack of precise soil information at each
site.
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DIRECT ELEMENT METHOD OF BOX CULVERT ANAL,YSIS
The direct element method is a procedure in which the external
stiffness matrix ASAT is built directly from geometric and elastic
properties of the elements, such as the top slab of a culvert, taken one
member at a time.
The required input data includes the degree of freedom; the number
of members and, for each member, the global degrees of freedom NP1, NP2,
NP3, NP4, NPS and NP6 at the initial and terminal points; the coordinates
of the terminal points referenced to the initial point as origin; the
modulus of elasticity and the cross-sectional area, A.
The procedure involves computing the local ASAT matrix of each member
in succession and assembling the elements of the local ASAT matrix into the
global ASAT matrix.
~.x.,
P6 ~
Initial
PoInt
2
The P,X Diagram
3
The F,e Diagram
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I 2;
-'
I
0
I 0
5 In oc
L
.2 I -coB c<
.3'
Slnoc I Cosoc
l~~
L L
fA] =
I
0
0
oc
I L
-SIn oc
L
CosO(
61-SfnO(I~I~
4
Member Statics Matrix
-5 K,
-C K,
5 K,
a
C K,
2K
Kf
SAT] =
C
-£ T K~
1-6
r K.e
K2
K2
The Member [SAT] Matrix
5
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62K2L 6£K2
L
5
-6 r K2
C
-6 Y Kt.
K2.
2K2
6~
L
12.~-
L' foe
ctK,-I2(f/~
6...k
L
~SK+f2~-
L~'~
Ct
SlKt+12(r) fe
-CSK 12~-
LI. ~
-srAi-/2('-fK£
6~Kp'
L
S
-6 r K2
6rK2
ASAT] =
2
4Kt.
S
-6 L K2.
6 ..s.
L
CS
CSKI-12~
ctKI+I2(t/~
l:
6.Q.
L
CSK 12. .§.x-
r Lz- E
-6~K2.
L
t
Fig
6
The Member External Stiffness Matrix
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THE MEMBER FLEXIBILITY MATRIX [ASAT]-l
[AST7] -1=
1
[AST T]
In the displacement method of culvert analysis, the joint
displacements matrix [X] is first computed from Eq. 6), then the internal
end forces matrix [F] from Eq. 4).
[P] = [A] x [F] 1
[e] = [B] x [X] = [A T] x [X] 2)
[F] = [8] x [e] 3)
3)
ubstituting Eq.
2) in Eq.
[F]=[SA7]x[X] 4)
1)ubstituting Eq.
4
in Eq.
[P]=[AST7]x[X] 5)
from which
[X]=[ASTT]-lX[P] 6)
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DEAD LOAD EARTH PRESSURE
AND WATER PRESSURE
The dead loads on the top slab include soil weight and concrete slabweigh
The soil weight will default at 120 PCF. The concrete weight is
set at 150 PCF. The equivalent fluid weight for wall earth pressure will
default to 30 PCF..
The program also investigates the condition of submergecl soil acting
on the walls. The submerged soil pressure is taken as one half of the
earth pressure acting on outside walls. Other dead loads in this case are
taken as full earth pressure. Live load surcharge will defaul.t to 2 feet.
Water pressure inside culvert barrels must be checkeci since this
pressure may reverse the wall moments and add to the sJ.ab positivemoments
The program will use the water pressure from the culvert flowing
full and empty as two loading cases.
LIVE LOAD
Influence lines are derived from applying a unit load moving from
left to right along the top slab at twentieth points of each span. Based
on these results the maximum moment and shear at tenth poi.nts of each
member are calculated.
Live load will default to the standard AASHTO HS20 load or military
load whichever controls. The user may specify the axle weight for a
special overload truck. The user may also specify a single axle load with
a specified design fill as an alternate to the regular live load. This is
usually used for heavy construction vehicles where the axle:; are spaced
far apart so that only one axle is on the culvert at a time. Impact will
apply to the top and bottom slabs and the exterior and interior walls of
the box culvert.
hen the culvert is subjected to traffic operating directly on the
top slab or when fill on the culvert is less than 2 feet deep the wheel
loads are distributed as are those on bridges. When fill is more than 2
feet deep the wheel loads are distributed over squares with sides equal
to 1.75 times the depth of fill. When these squares overlap the total of
the wheel loads is uniformly distributed over the combined reduced grossarea.
Live load may be neglected when the depth of fill is greater than 8
feet exceeds the span length of a single culvert or exceeds the total
width of a multiple barrel culvert.
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SERVICE LOAD DESIGN
The following procedure is used to compute the required area of steel
at three critical sections of each member; i.e., left end, midpoint and
right end. The steel stress is given from input or defaulted as fs and
then the stress block is determined through the iteration process. No
compression steel is considered and all tension steel is assumed to be
placed in one row.
Stress Block
7
Internal moment equals external moment: Mi = Me
MA = 0 i
.
Linear stress distribution:
.
Combine Eq. 1 and 2 to eliminate fIco
x(fs) xE
(d-.. E.) = M+P (d-. '
)x (d-x) 2 3 2
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he equation f(x) is solved by Newton's iteration process for
polynomial equations. The value of X is computed approximately to an
accuracy of 0.01 inch.
-f (x)
-x
X(n+l) -n f/(x)
If there is no tension stress because of large P and small M, then
= : E+~
I A
l
c
and the minimum amount of reinforcing steel would be used. If there are
tension stresses, the concrete stress f'c = fsX/n(d-X) and the area of
steel As = [~(f'c) (X) (b) -P] Ifs.
The shear stress
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For fills greater than or equal to 2 feet:
Vc = 0.95 yI7r;
OR
Vc shall not exceed 1.8 ~
hichever is greater.
p = reinforced ratio = As/bd
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LOAD FACTORDESIGN
The following procedure is used to check the critical sections of
each member.
Loading = 1.3 (D + 1.667(L+I)n + PE E. + W.P.
PE = 1.0 for rigid culverts, including reinforced concrete boxes;
E = Earth pressure;
W.P.
= Water pressure, refer to page 6 about two loading cases.
2. A concrete stress of 0.85 flc will be assumed uniformly
distributed over equivalent compression zone bounded by the edges of a
cross section and a straight line located parallel to the neutral axis at
a distance a = B1C from the fiber of maximum compression strain.
b
Ec
.85f'0
OAs
£s
S~t on
Strain
EqurvalentStress
8
Stress, Strain Diagram
P1 = 0.85
when f~ s 4000 psi
OR
3. No compression steel is considered and all tension steel assumed
to be in one layer.
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4. Assume As Set
M
Ru = O.9bd2
p = O. 85f'
c
fy
2Ru
I-O.85fcl
-
O,85(31f'o 87000
b = fy x 87000 + fy
p ~ O.5Pb. ;
p ~ 0.002
.5Pb instead of O.75Pb
Best economy is achieved where p =
As = pbd
5.
Compute Mu (Pure flexure)
a = ASfy
O.8Sf'cb
cI> = 0.9
6.
Compute Po (Pure Compression)
Po = 4>[0. 85ft (Ag-Ast) + Astfy]
cI> = 0.7
Ast = As + As(min)
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7.
Compute Mb, Pb (Balanced Condition)
Ph = cI> [O.S5f'c X 12 X Bh -Asfy]
Mb = Pbeb = 4>
O.8Sf'c x 12ab x
= 0.85
= 0.8
= 0.7
For slabs
For Ext. Wall
For Int. Wall
8.
Assume straight line relation between pure compression and
balanced conditions, balanced conditions and pure flexure.
p
AII~bI8 I1K)ment of
:::,::--~~=I.o 0' 8«1tl'Oftunder G'xlal
0-
--::::~~=.9 ,oroe l-u
"" ""
, ':::~ (J=.7
,
"
,,'
"
Po
.7Po
Q..
.
~
~
eb
Pb
, ,
':t~
Po
AI
MU
Moment. Ai
P,M Diagram
9
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The shear stress (fv) is computed as follows:
The allowable concrete shear stress is computed as follows:
For fills less than 2 feet:
Vu.
v = M
b = 12.0 inches
Vc = 2 ~
OR
(Vc shall not exceed 3.5 ~
hichever is greater.
p = reinforcement ratio = As / bd
~
M
s 1.0
For fills equal to or greater than 2 feet:
Vc = 2 v f1;
OR
(Vc shall not exceed 4. 0 ~
hichever is greater.
)
v ud ~ 1. 0
~
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ATIGUE STRESS LIMITS
The tensile reinforcement in box culvert elements subjected to
repeated variations of reversals of stress shall be designed so that the
actual range of stress does not exceed the allowable fatigue stress. The
depth of fill also has a substantial effect on this fatigue range.
Such range between maximum and minimum stresses in tensile
reinforcement caused by live load plus impact at service load shall not
exceed:
f f = 21 -O. 33 fmin + 2. 4
AASHTO (8 -6 0)
ff = stress range, ksi
fmin = algebraic minimum stress level (tension-positive;
compression-negative), ksi
At section where stress is not reversed.
fs = ~; where,
M = Live load moment range
jd = d -kd / 3 where kd is the distance from extreme compression
fiber to neutral axis.
2. At section where stress is reversed.
+M
fs=~
Tensile part of stress range)
r
k -d
d,1
-k
--M
-A:7 d
fl
a
(Compzessive pazt of stzess zange); wheze,
d = distance from extreme compression fiber to centroid
compression reinforcement.
d = distance from extreme compression fiber to centroid of tension
reinforcement
Total stress range = fs + f s
RACKCONTROL
The program checks maximum service load stresses in the reinforcing
steel for crack control as per AASHTO Article 17.6.4.7
98 ksi
fs=~
AASHTO (17 -19)
s : Maximum service load stress
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MINIMUM ECCENTRICITY
Minimum eccentricity will be checked for all members.
e =, : . M = P x e
p'
If e < 1", then e = 1"
If e < 0.1 x T, then e = 0.1 x T
SLENDERNESS
Slenderness will be checked for walls only
r=o.3x~
T
T = wall thickness
r = {f radius of gyration
Slenderness will be neglected if Kl/r < 22. Where k = 2.0,Height.
1 = Clear
Pc = 1t2~
I v7 , 2
AASHTO (8-42)
ECIg
I = 2.5(1 + ~d)
AASHTO (8-44)
Ec = 57000 ~
AASHTO (8.7.1)
I -
T
3
g -
~ Dead Load Momen
d= Maximum To tal Momen
Mc = 6 bX~b
AASHTO (8-40)
Cm ~ 1
b = Pu
1--
cl>P
AASHTO (8 -41 )
Cm = 1
Mc = Magnified Moment
c I = 0.7
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INGWALL DESIGN CRITERIA
The following criteria of calculating wingwall height and length were
developed by FDOT Drainage Section.
W 'nql4lall height
H = Clear height of barrel
+ Top slob thickness
+ 1'-0 headwall
H -(H -/.5) 0< -45
Transition WalIHt.
=
90 -45
W;ngwall tandard length
1.5 H -Wall thickness + 3'-0-
1 =
(For tS-
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TIE-IN LENGTH OF SKEWED WINGWALL
Tie-in length of straight wingwall is specified on Sheet 3 of 4 in
FDOT Roadway and Traffic Design Standards. Figures 11 and 12 illustrates
the tie-in length of skewed wingwall in different ranges of skew angles.
.d I
~
I
I
I
Angle of Skew
Sf
, Ct>t
I
I
I
I
I
~ Roadway ~I
I
I
I
I
~ Culvert
D = 1'-0
Average Cl.Jtof top slab and side wall
of exlstfng culvert when new culvert
to be extended from existing c'Ulvert =
(20 + 20) /
z. / Cos~
z. ft.
COB .d
LAYOUT OF SKEW CULVERT WING
WHEN L1 VARIES FROM OOTO 150
& FROM IBOOTO 1650
Tie-in Length of Skewed Wingwa11 (0°-15°, 1BOO-165°)
11
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~ of8I1rra'
--,---
;
(,1'
/
,
'Of _-A I
~I
D = /'-0'
Av . aJtof ~ 8iab tx1'Id, wolf
of exIstIng all/eft wh8'?hM OIJIvert D + 2. '2. ~
to be BXttrKJedrom exlsfl~ cr.weft = 2. /' COB.d
= 3
2. CoB.4 ft.
LAY(JJTOF SKEWCULVERT
WHEN.d VARIES FROM ~TO 4SO
12
Tie-in Length of Skewed Wingwall (15°-45°)
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USER INSTRUCTIONS
The user may select either the short coding form for routine design
or the long coding form for special analysis and design. These coding
forms are provided in Appendix E. Each input field and the default value
is described in the following Input Data Table. The output is explained
in the following sections of Output Data Bar Schedule and Examples.
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INPUT DATA TABLE
Input Requirements for Reinforced Concrete Box Culverts
and Wingwall Computer Program
Header Card and Card One
CARD
NUMBER
CARD
COLUMN
VARIABLE
NAME
FORMAT
DESCRIPTION
DEFAULT
VALUE
*
1
KAST
Al
HEADER CARD
NA
*
2- 3
COMM(I)
I2
NA
UN NUMBER
Identification only
4-22
COMM(I)
A19 NAME
NA
*
23-28
COMM(I)
A6
NA
HONE NUMBER
Extension phone number
*
29-80
COMM(I)
A52
NA
EADING
Heading, project no., date
1
1
KaNE
II
CARD HEAD NO.
Valid code: 1
NA
2 LVLD
II
LIVE LOAD
Valid code
1 : HS20
3 : HS15
5 : HSIO
7 : Blank
9 : None
1
2 : H2O
4 : HIS
6 : HIO
8 : Special
1
3
LVOMT II
2
MIT LIVE LOAD
Valid code
1 : Live load to be neglected
2 : Live load to be used
.regardless of fill height
Live load may be neglected for
single box cul,vert if depth of
fill is more than 8 ft. and
exceeds span length;
for multiple box culvert it may
be neglected if depth of fill
exceeds the distance between
faces of end supports.
4
IZOF II
2
ERO FILL STRESS CHECK
Valid code
1 : Stress check at zero fill
2 : No stress check at zero
fill
1
5-9 OVERLD
F5.0
0
VERLOAD STANDARD TRUCK AXLE
WEIGHT
Valid code: Blank-xxxxx LB
0
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Card One
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Card One (Continued)
CARD
NUMBER
CARD
COLUMN
VARIABLE
FORMAT
NAME
DESCRIPTION
DEFAULT
VALUE
1
39-41
ADDS
F3.2
THICKNESS INCREMENT OF :~LABS
Valid code: Blank-x.xx INCH 0.5 IN
1
42-44
ADDW
F3.2
THICKNESS INCREMENT OF \'lALLS
Valid code: Blank-x.xx INCH
0.5 IN
1
45-47
covs
F3.2
2.5 IN
3.5 IN
TOP SLAB CONCRETE COVER
Measured from center of bar to
face of concrete
Slightly aggressive env:Lronment
Moderately/Extremely ag~Jressive
environment
Valid code: Blank-x.xx INCH
1
48-50 'COVB
F3.2
2.5 IN
3.5 IN
BOTTOM SLAB CONCRETE CO"ER
Measured from center of bar to
face of concrete
Slightly aggressive env:.ronment i
Moderately /Extremely ag~Jressi ve
environment
Valid code: Blank-x.xx INCH
1
51-53
covw
F3.2
2.5 IN
3.5 IN
EXTERIOR WALL CONCRETE COVER
Measured from center of bar to
face of concrete
Slightly aggressive envj.ronment
Moderately/Extremely ag~rressive
environment
Valid code: Blank-x.xx INCH
1
54-56
COVIN
F3.2
2.5 IN
3.5 IN
INTERIOR WALL CONCRETE COVER
Measured from center of bar to
face of concrete
Slightly aggressive envj.ronment
Moderately/Extremely ag~rressive
environment
Valid code: Blank-x.xx INCH
57 ISAMS
11
2
SAME TOP & BOTrOM SLAB DESIGN
Valid code
1 : Same thickness and
same steel
ELSE: Set thickness of each
slab.
1
58
11
SAMW
2
AME EXTERIOR & INTERIOFt WALL
THICKNESS
Valid code
1 : Same thickness
ELSE: Set thickness of each
wall.
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Card One (Continued)
CARD
NUMBER
CARD
COLUMN
VARIABLE
NAME
FORMAT
DESCRIPTION
DEFAULT
VALUE
1
59
IBSH
Il
1
AR SCHEDULE
Valid code
1 : Print bar schedule
2 : Not print bar sched1~le
1
60-62
SPACMAX
F3.1
18.0 IN
AX. BAR SPACING
DESIGN
Valid code: Blank-18.0 INCH
1
63-65
SPACMIN
F3.1
4.0 IN
BAR SPACING
DESIGN
Valid code: 04.0-18.0 :[NCH
1
66-67
MAXSIZ
12
11
AX. BAR SIZE
Valid code: 01-11
1
68-69
MINSIZ
12
4
BAR SIZE
Valid code: 04-11
1
70-72
CN
F3.1
9
ODULAR RATIO
Valid code: 1-9
1
73
ENVIR
11
1
NVIRONMENT CONDITION
Valid code: 0-3 See Not:e (1)I
: Slightly aggressive
1 : Slightly aggressive
2 : Moderately aggressi lTe
3 : Extremely aggressivE~
NOTE:
(1)
The environment condition is required to determine t:he default minimum
concrete cover of reforcing steel and concrete clas~;:
Under a slightly aggressive environment condition, concrete cover is 2
inches and Class II concrete is selected.
Under a moderately or extremely aggressive environment condition,
concrete cover is 3 inches and Class IV concrete is selected.
Leave this field blank for a slightly aggressive environmentcondition.
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Card Two and Card P
CARD
NUMBER
CARD
COLUMN
VARIABLE
NAME
FORMAT
DESCRIPTION
DEFAULT
; VALUE
2
1
KTWO
II
2
ARD NO.2
Valid code: 2
2
2-5
EDLU
F4.3
0
XTRA UNIFORM DEAD LOAD
Valid code: Blank-x.xxx K/FT
2
6-10
EDLCI
F5.3
EXTRA CONCENTRATED DEAD LOAD
Valid code: Blank-xx.xxx KIPS
0
2
11-13 EDLXl
F3.2
POSITION OF CONCENTRATEDOAD
Measured from centerline of the
leftmost wall of the culvert
Valid code: Blank-x.xx FT.
0.00
2
14-18
EDLC2
F5.3 EXTRA CONCENTRATED DEAD LOAD-2
Valid code: Blank-xx.xxx KIPS
0
2
19-21
EDLX2
F3.2
POSITION OF CONCENTRATEDLOAD-2
Measured from centerline of the
leftmost wall of the culvert
Valid code: Blank-x.xx FT.
00.0
22-26
IEDLC3
F5.3 EXTRA CONCENTRATED DEAD LOAD-3
Valid code: Blank-xx.xxx KIPS
0
2
27-29
EDLX3
F3.2
00.0
OSITION OF CONCENTRATEDLOAD-
Measured from centerline of
the leftmost wall of the
culvert
Valid code: Blank-x.xx FT.
2
30-34 WHEER F5.3
SPECIAL WHEELLIVE LOAD
Enter weight of one wheel
Valid code: Blank-xx.xxx KIPS
0
2
35-38 FILLR
F4.2
00.00
ARTH FILL
Measured to top of slab
Valid code: Blank-xx.xx FT.
2
39-42 OFACT
F4.2
OVERSTRESS FACTOR
Valid code: 1.00-xx.xx
1.00
p
1
KPAS Al
i REINFORCEMENT RATIO CARD
iFor Load Factor design only
Ip = As / bd
Optional card always follow
Card 1 or Card 2
Valid code: P
2-4
PAS
F3.3
REINFORCEMENT RATIO
Valid code: .xxx
.012
Leave Card 2 or Card P out if default value is selected.
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Card Three Continued)
CARD
NUMBER
CARD
COLUMN,
VARIABLE
NAME
FORMAT
DESCRIPTION
DEFAULT
VALUE
3
29
KBASE
Al
BLANK
LOOR SUPPORT JOINT CONDITION
Valid code
X : No floor with fixed end
support
IH
: No floor with hinged
support
: Full floor
3
30-33 TSLAB
F4.2
9 IN
OP SLAB THICKNESS
Leave this field blank to use
default seeded minimum value
to design optimized thickness
Valid code: Blank-xx.xx IN.
3
34
KFXTS Al
BLANK
IXED TOP SLAB THICKNESS
Valid code
F : Fixed thickness
3
135-38
I BSLAB
F4.2
9 IN
BOTTOM SLAB THICKNESS
Leave this field blank to use
default seeded minimum value
to design optimized thickness
Valid code: Blank-xx.xx IN.
3
39
KFXBS
Al
BLANK
IXED BOTTOM SLAB THICKNESS
Valid code
F : Fixed thickness
3
40-43 WALLR
F4.2 9 IN
XTERIOR WALL THICKNESS
Leave this field blank to use
default seeded minimum value
to design optimized thickness
Valid code: Blank-xx.xx IN.
3 44
KFXW
Al
BLANK
IXED EXTERIOR WALL THICKNESS
Valid code
F : Fixed thickness
3
45-48
F4.2
WALLR
9 IN
NTERIOR WALL THICKNESS
Leave this field blank to use
default seeded minimum value
to design optimized thickness
Valid code: Blank-xx.xx IN.
3
49
KFXTS Al
BLANK
IXED INTERIOR WALL THICKNESS
Valid code
F : Fixed thickness
NOTE:
Use fixed slab or wall thickness to override the calculated thicknesses
or to match the existing box culvert structure for a culvert extension project
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Card Three (Continued)
CARD
NUMBER
CARD i
COLUMN
VARIABLE
FORMAT
NAME
DESCRIPTION
DEFAULT
VALUE
3
50-52
SURCH
F3.1
2.0 FT
IVE LOAD SURCHARGE
Valid code: Blank-xx.x FT.
3
53-54
PRESS
F2.0
30 PCF
AXIMUM SOIL EQUIVALENT FLUID
PRESSURE
For lateral earth pressure
Valid code: Blank-xx PCF
3
55-56 PMIN
F2.0
15 PCF
MINIMUM SOIL EQUIVALENT FLUID
PRESSURE
For checking positive moment
Valid code: Blank-xx PCF
3
57-59 PWAT
F3.1
WATERWEIGHT
'Valid
code
: 62.4 PCF
-1 : No water pressure
62.4
3
60-62
TFILT
F3.1
2.0 IN
TOP HAUNCH
Valid code Blank-xx.x IN.
: 2 IN.
-1.0 : Zero top haunch
3
63-65 BFILT
F3.1
2.0 IN
OTTOMHAUNCH
Valid code Blank-xx.x IN.
: 2 IN.
-1.0 : Zero top haunch
3
66
KRACH
Al
BLANK
AUNCH CONSIDERATION
Valid code
: Haunch not to be considerea
X : Haunch to be considered by
1983 AASHTO8.8
3
67
KHWAL
Al
BLANK
HEADWALL ELIMINATION BLANK
Valid code
: Eliminate no headwall
B : Eliminate both headwall
L : Eliminate left headwall
R : Eliminate right headwall
3
68-79
CaMS
A12
COMMENTS
Valid
code: Free comments
3
80
ITEST
11
SPECIAL PRINTOUT
Not normally used. strictly for
testing purpose
Valid code
1 : Print DL, SP, WP and LL
moments and shears
: No off
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Card Four
CARD
NUMBER
CARD
COLUMN
VARIABLE
FORMAT
NAME
DESCRIPTION
DEFAULT
VALUE
4
1
KFOR
II
4
ARD NO.4
Valid code: 4
4
2-3 NCARD
12
NA
ULVERT NUMBER
Identify each culvert with
a unique number
Valid code: 1-99
4
4
IMINKEY
II
BLANK
INIMUM OUTPUT KEY
: Minimum output
Leave it blank, 0 or 1
to turn off all output
except what is required
for Florida Roadway Design
Standards
1 : Minimum output
2 : Detailed output
4
5 WINGTY
II
BLANK
INGWALLTYPE
Valid code
: Straight wingwall which
aligns with the headwall
1 : Straight wingwall same as
BLANK
2 : Skewed wingwall which
points to different
azimuth angle from culvert
headwall skew angle
4
6-8
WLSKEF 13
LSKE
EFT FRONTWINGWALLSKEWANGLE
Measured from line
perpendicular to center line of
culvert in clockwise direction
to wingwall face
Valid code: 0-45 degree
225-360 degree
BLANK: Wingwall parallel
to the headwall
4
9-11 WLSKEB
13
LSKE
EFT BACK WINGWALLSKEWANGLE
Measured from line
perpendicular to center line of
culvert in clockwise direction
to wingwall face
Valid code: 135-315 degree
BLANK: Wingwall parallel
to the headwall
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Card Four (Continued)
CARD
NUMBER
CARD
COLUMN
VARIABLE
IFORMAT
NAME
DESCRIPTION
DEFAULT
VALUE
4
13
RSKE
IGHT FRONT WINGWALL SKEW ANGLE
Measured from line
perpendicular to center line of
culvert in clockwise direction
to wingwall face
Valid code: 0-135 degree
315-360 degree
BLANK: Wingwall parallel
to the headwall
4
I3
RSKE
IGHT BACK WINGWALL SKEW ANGLE
Measured from line
perpendicular to center line of
culvert in clockwise direction
to wingwall face
Valid code: 45-225 degree
BLANK: Wingwall parallel
to the headwall
4
F4.2
LEFT FRONT WINGWALL LENGTH
Overrides calculated wingwall
length, if length is specified,
the wingwall front tip length
will be identical to the height
at joint of wingwall & culvert
Valid code: 0.00-99.99 FT.
BLANK: Calculated length
4
F4.2 LEFT BACK WINGWALL LENGTH
Overrides calculated wingwall
length, if length is specified
the wingwall front tip length
will be identical to the height
at joint of wingwall & culvert
Valid code: 0.00-99.99 FT.
BLANK: Calculated length
26-29 F4.2
RIGHT FRONT WINGWALL LENGTH
Overrides calculated wingwall
length, if length is specified
the wingwall front tip length
will be identical to the height
at joint of wingwall & culvert
Valid code: 0.00-99.99 FT.I
BLANK: Calculated length
30-33
WSKRB
F4.2
RIGHT BACK WINGWALL LENGTH
Overrides calculated wingwall
length, if length is specified
the wingwall front tip length
will be identical to the height
at joint of wingwall & culvert
Valid code: 0.00-99.99 FT.
BLANK: Calculated length
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Card Four
(Continued)
CARD
NUMBER
CARD
COLUMN
VARIABLE
FORMAT
NAME
DESCRIPTION
DEFAULT
VALUE
4
34 CULEXT
II
BLANK
ULVERTEXTENSION
A calculated tie-in length
will be excluded from the new
culvert bottom slab at each
side which is connected to the
existing culvert
Valid code
: New culvert with (BOTH)
left and right
wingwalls
1 : New culvert with (BOTH)
left and right
wingwalls
2 : New culvert extends (LEFT)I
from left side of
existig culvert with
left wingwall only
3 : New culvert extends (RIGH)
from right side of
existig culvert with
right wingwall only
4 : New culvert connects (NONE)
existing culverts
with no wingwall
(BOTH)
(LEFT)
4
35 NOHEAD 11
BLANK
(BOTH)
(BOTH)
NUMBER OF HEADWALLiValid
code
: Left and right
headwalls
1 : Left and right
headwalls
2 : Left headwall only
3 : Right headwall only
4 : No headwall
(LEFT)
(RIGH)
(NONE)
4
36-37
F2.1wcovs
2.5 IN
3.5 IN
COVER FOR OUTSIDE FACE OF WALL
Slightly aggressive environment
Moderately/Extremely aggressive
environment
Valid code: Blank-x.xx INCH
38-39 F2.1
IALLCOV
2.5 IN
3.5 IN
ALL OTHER FACES CONCRETE COVER
Slightly aggressive environment
Moderately/Extremely aggressive
environment
Valid code: Blank-x.xx INCH
40-49
A1OPROJNO PROJECTNUMBER
Valid code: Free format
4
50-80
LOCSTA
A47
LOCATION IDENTIFICATION
Valid code: Free format
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OUTPUT DATA
Three categories of output are available from this program:
The first category is the Standard Box Culvert and Wingwall Design
Output which may be incorporated into the Florida Department of
Transportation Roadway and Traffic Design Standards Indexes 280 and 290 to
produce a complete design.
The second category is the Special Output which tabulates shear and
moment generated by dead load live load soil and water at tenth point of
each member.
The third category is the Detailed Output which tabulates shear
stress at critical sections and reinforcing bar splice lengths.
Combinations of these three output categories may be generated by
triggering either one or both of the Special Print and Minimum keys.
The output data has the following reports:
Input Data Reflection
The first page of every output is an echo of input and default data.
The user can verify this page with his coded input form to detect and
correct any discrepancy. The concrete covers coded and echoed on this
page are the dimensions measured from the center of bar to the face ofconcr
2. Standard Output:
2.1 The first part of this output provides a detailed description of
material properties box culvert and wingwall geometry calculated design
dimensions and concrete quantities. The concrete covers on this page are
the dimensions measured from the face of reinforcing bars to the face of
concrete and have the following default values;
2 in.
3 in.
3 in.
Slightly aggressive environment:
Moderately aggressive environment:
Extremely aggressive environment:
The valid range of headwall and wingwall skew angles is detailed on
Sheet 1 of 5 of Index 290. Based on the wingwall skew angle and drainage
considerations the length height and front tip height of each wingwall
are calculated from the equation in Figure 10 on page 16. If all wingwall
lengths and front tip heights are identical a condensed output will
automatically be created. Two sample input coding forms and output reports
are shown on Pages 38 through 53.
The total wingwall length with barrel width tabulated on the output
is the sum of the front wingwall length barrel width and back wingwalllength.
The Pour 1 barrel concrete quantity is the sum of the bottom slab
the bottom haunch and the 2 in. height of exterior and interior walls cast
with the bottom slab.
2.2 The second part of this output tabulates the reinforcing bar
number set size spacing type length weight and total
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The mark and type of the reinforcing bars are directly cross-
referenced with Index 290.
The column heading of SET is derived from dividing the individual
total designed reinforcing bar length by the standard 40 ft. stock length.
In the case of a box culvert extension, the C3 bar will replace the
Cl bar in the bottom slab to accomodate the reduced length of the new box
culvert bottom slab which will be tied to the existing box culvert bottomslab.
3. Special OUtput:
The following are column headings and definitions of the SpecialOutput:
3.1 Service Load Design
3.1.1
Maximum design moment at the critical section, in kip-it
3.1.2
Axial Force: Axial design load corresponding with maximum moment
at the same section in kips.
3.1.3
Maximum design shear force at the critical section,
in kips.
.1.4
Concrete Stress: Concrete compressive stress due to design moment
and axial force, in psi.
3.1.5
Shear Stress: Shear stress at the section, in psi
Required area of steel reinforcement, in square inches.
3.1.7
Allowable shear stress, in psi.
3.1.8
Allowable concrete co~pressive stress, in psi.
3.2 Load Factor Design
3.2.1
Maximum load
section, in kip-ft.
design
actor
the
oment
at
critical
3.2.2
Axial Force: Axial design load corresponding with maximum .moment
at same section, in kips.
3.2.3
Maximum load factor design shear force at the critical
section, in kips.
3.2.4
Axial designcompression,
in kips
load
strength
of
the
section in
pure
3.2.5
Design moment strength of the section pure flexure),
in kip-ft.
3.2.6
Design moment strength of the section when assumed ultimate
strain of concrete and yielding of tension reinforcement occurs
simultaneously balance conditions), in kip-ft.
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3.2.7
PB: Axial design load strength of the section when assumed
ultimate strain of concrete and yielding of tension reinforcement
occurs simultaneously balance conditions), in kips.
3.2.8
As: Required area of tension reinforcement, in square inches
3.2.9 Shear Stress: Shear stress at the section, in ksi
3.2.10 MA: Allowable moment strength of a section under axial design
load condition, in kip-ft.
in psi
.2.11 VA: Allowable shear stress
4
Detailed Output:
In either the Service Load or the Load Factor design, the moments,
forces, stresses, etc. are given for each critical section of each member
as listed below:
M: Member identification number.
T: Thickness of that member, in inches.
Lt End: At bottom for wall, at the left end of the slab
Rt End: At top for wall, at the right end of the slab.
Mid Span: At 0.4, 0.5, 0.6 of the span, from left to right, whichever
is the greatest.
Bar Design
This part of output is used for the North Carolina Department of
Transportation Standard and is printed for output verification between the
North Carolina and Florida versions.
Corner Bar T): Corner at top slab, Al.
Corner Bar B): Corner at bottom slab, A2
TSLAB+: Top slab bottom bar, A1OO.
TOp slab top bar, A300
BSLAB+: Bottom slab top bar, A200
Bottom slab bottom bar, A300
Exterior wall inside bar, Bl
EXTOUT: Exterior wall outside bar, B2.
Interior wall bar, B3.
Longitudinal bar, Cl.
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Bar Schedule.
Moment, shear, axial force at tenth points.
(option)
Influence Line (option): This is an extensive printout, and should only
be requested when necessary.
Member reference
M:Member; Lt. End; R:Rt. End
13 Member Reference Diagram
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BAR SCHEDULE
Normally, the bar schedule is printed with the design option but may
be omitted with the analysis option. The user must refer to the Florida
DOT Roadway and Traffic Design Standards Index No. 290 to determine the
exact location of bars.
:
Top corner bars
A2 :
Bottom corner bars.
AIOO :
TOp slab positive (main bars)
AIOl to AlSO :
TOp slab positive, left side cut bars
* A151 to A199
bars
Op slab positive, right side cut
A200 :
Bottom slab positive,
(main bar
A201 to A250 :
Bottom slab positive, left side cut bars
* A251 to A299 :
Bottom slab positive, right side cut bars.
A300 :
Top slab negative (main bars).
A301 to A350 :
Top slab negative, left side cut bars
A351 to A399 :
TOp slab negative, right side cut bars.
A400 :
Bottom slab negative (main bars)
A401 to A450 :
Bottom slab negative, left side cut bars.
A451 to A499 :
Bottom slab negative, right side cut bars.
BI : Exterior wall inside bars
Exterior wall outside bars, from construction joint to
construction joint.
Interior wall bars
Cl : Longitudinal bars (Florida Standard)
C2 : Top slab bars
C3 : Longitudinal bars replace Cl at bottom of slab when a new culvert
is extended from an existing culvert.
Left side head wall bars, (Florida Standard)
* G2 : Right side head wall bars,
C. Standard).
Left side end bars,
(N. ~. Standard)
* S3 : Right side end bars,
(N. C. Standard).
* If Left and Right skew angles are the same,
combine left and right bars.
the computer output will
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Bar sizes range from #4 to #11 and spacings from 4 to 18 . Bars A1,
A2, A300, A400 and B2 have the same spacing and the requirement for Class
C tension lap splices applies.
For a single box with a span less than 5 feet, the corner bar will
be a U-Shaped bar.
Bar Types
STRAIGHT -BAR
I, 8 -I
lYPE I BAR
TYPE II BAR
I~ B _1
(.,)
TYPE 10 BAR
14
Bar Type Diagram
B: Horizontal dimension (slab)C:
Vertical dimension (wall)
D: Vertical dimension (wall)
There are no 'B2' bars if the clear height is less than 6 feet as the
corner bars will overlap.
Refer to the Florida Department of Transportation Roadway and Traffic
Design Standards Index No. 290, Sheet 1 of 5 for bar splice details.
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EXAMPLES
Depending upon the desired output, input data can be divided into two
categories. The first category is the mandatory input data to develop the
output for the design of standard highway box culverts and wingwalls. The
second category is the input data required for a special design or
structural analysis. The data in the second category can all be changed
from preselected defualt values to special values required by user to
perform detailed special design or analysis.
The first category of mandatory input is described on Page 38; i.e.,
the Short Coding Form. The complete input data which includes the
mandatory and special input data is described on Page 43; i.e., the Long
Coding Form.
The input requirements of both coding forms are defined in Table-l.
Cards 1 and 2 should be omitted if default values are selected.
Example Problems:
A new reinforced concrete box culvert is required at station 220 +
36 of US 90 to satisfy the following requirements:
Environment condition Slightly aggressive
Number of -barrels 1
Clear span 8 ft.
Clear height 6 ft.
Design fill distance from finish grade at roadway
centerline to bottom of top slab) 4 ft.
Length of box culvert along the centerline) 200 ft.
Skew angle of left headwall 15 degree
Skew angle of right headwall 20 degree
Skewed wingwall angle
Left front ~ 350 degree
Left back 200 degree
Right front 60 degree
Right back 80 degree
Project number 55030-3418
Location Leon county, US 90, Station 220 + 36
Based on this data, a standard coding form is prepared and shown on
Page 38.
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PROGRAM FLOW CHART
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APPENDIX B
VARIABLE LISTING
'P'1'
'2'
'3'
'4'
AAREA
AB
ABAR
ADATE
ADDS
ADDW
ADI(I)
AFLOOR
AHITE
ALIVE
ALLCOV
ANDWIL
ANDWIR
AR
AR(L)
AREA(J)
IARR(I)
ARR(2)
ARR(3)
ASAT
ASB
ASP
ASPB
ASPM
ATYPE
Al
I A2
A3
A4
BARD
BB
BBARH
BD
BFILT
BNDWIL
BNDWIR
BSLAB
BTYPE
BI
CE
CHCU
CN
COMM(17)
CaMS
COMS(3)
COVB
COVIN
COVS
COVW
CULEXT
A1
11
11
11
11
REINFORCEMENT RATIO CARD
CARD NO.1 -MATERIALS
CARD NO.2 -LOADINGS
CARD NO.3 -BOX CULVERT
CARD NO.4 -WINGWALL
AREA OF REBAR
DEPTH OF EQUIV. RECT. STRESS BLOCK AT BALANCED CONDITION
AREA OF REINFORCING BARS IN ARRAY #4-#11
I
DATE
SLAB THICKNESS INCREMENT
WALL THICKNESS INCREMENT
F3.2
F3.2
w.w.
HS20, H2O, HSI5, H15, HSIO, HIO LIVE LOADS
WINGWALL CONCRETE COVER EXCEPT FRONT FACE
LEFT STRAIGHT WINGWALL LENGTH IN INTEGER
RIGHT STRbIGHT WINGWALL LENGTH IN INTEGER
AREA OF REBAR REQUIRED AT CONTROLLING PT.
2.1
w.
w.
w.
w.
w.
EXTERNAL STIFFNESS MATRIX
AREA OF REBARREQUIREDAT CRITICAL SECTION
TENSION REINFORCEMENT ATIO ASP=AS/bd
REINFORCEMENT RATIO IN BALANCED CONDITIONS
TRIAL REINFORCEMENT ATIO ASPM=O.5xASPB
TYPE OF BARREL; SINGLE, DOUBLE, TRIPLE, QDRPLE
AREA OF TOP SLAB SECTION I
AREA OF EXTERIOR WALL SECTION
AREA OF INTERIOR WALL SECTION
AREA OF BOTTOM SLAB SECTION
--I.-