REINFORCED CONCRETE BOX CULVERT AND WINGWALL DESIGN · PDF filei i reinforced concrete box...

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IREINFORCED CONCRETE

BOX CULVERT AND WINGWALLDESIGN AND ANALYSIS

COMPUTER PROGRAM USER'S MANUAL

IVersion 2.3

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Structures Design OfficeFlorida Department of Transportation

February, 1993

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I TABLE OF CONTENTS

I DISCLAIMER viABSTRACT

I PREFACE

METHOD OF SOLUTION 1

I DIRECT ELEMENT METHOD OF BOX CULVERT ANALYSIS 2

THE MEMBER FLEXIBILITY MATRIX [ASAT]-l 5

I DEAD LOAD, EARTH PRESSURE AND WATER PRESSURE 6

SERVICE LOAD DESIGN 7

I LOAD FACTOR DESIGN 10

FATIGUE STRESS LIMITS 14

WINGWALL DESIGN CRITERIA 16

17TIE-IN LENGTH OF SKEWED WINGWALL

I19USERINSTRUCTIONS

I INPUT DATA TABLE 20

OUTPUT DATA 31

I BAR SCHEDULE 35

EXAMPLES 37

I STANDARD INPUT AND OUTPUT 38

SPECIAL AND DETAILED INPUT AND OUTPUT 43

I 54APPENDIX A PROGRAM FLOW CHART.

56APPENDIX B VARIABLE LISTING.

I APPENDIX C 64

APPENDIX D 66

I 72APPENDIX E BLANK INPUT CODING FORMS.

INDEX.

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LIST OF FIGURESFIGURE

1 Boundary Conditions 12 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

Stress,

Strain Diagram. ...

9 P,M Diagram 1210 16Wingwall 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. 3414 Member Reference Diagram. 36

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I LIS~~ OF TABLES

TABLE

I 1 20Input Data Description.

2 56Variable 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 riskassumes the quality andas to

performance of this program for his particular application.

Liang Y. Hsia, P.E.

Florida Department of Transportation

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ABSTRACT

I The Reinforced Concrete Box Culvert and Wingwall Design and AnalysisComputer Program is the result of the joint efforts by North Carolina andFlorida Departments of Transportation.I

IThe user may analyze or design a one, two, three or four barrel

reinforced concrete box culvert. Either service load or load factordesign method may be selected. Each of the barrels may have any clearspan from a minimum of two feet and a clear height from two feet tofourteen feet. All barrels in one culvert are assumed to be identical insize and shape. The culvert in this program may be a detached unit, anextended unit or a linked unit.I

Individually, the wingwalls extended from each corner of box culvertmay be placed on different angles, the wingwall tops may be level orsloped and the wingwall lengths may be designed or specified to meet jobsite requirements.

Environment conditions ranging from slightly aggressive to extremelyaggressive must be selected to determine the required concrete type andcover.

By selecting the minimum output option of this program, the outputmay be processed into the construction plans in conjunction with theFlorida Department of Transportation Roadway and Traffic Design Standards.This program may also be applied as a tool for special design andanalysis.I

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PREFACE

IThe original Reinforced Concrete Box Culvert Computer Program wasdeveloped Py Paul T. C. Lee of North Carolina Department ofTransportation.

This program was later modified py Arthur J. Haywood,Larry M. Sessions, Liang Y. Hsia and Elsie R. Clary of Florida Departmentof Transportation to add a wingwall design feature and to comply with theFlorida DOT Roadway and Traffic Standards. The updated Version 2.3 wasprepared to comply with the Florida DOT Special Provision 346 PortlandCememt Concrete and AASHTO load factor.

The addition of skewed wingwall, environment options, culvertextension and unit conversion were managed py Robert C. Burnett Jr., P.E.in 1985 and coordinated by Liang Y. Hsia in 1991 and 1992. I

The documentation was prepared by Paul T. C. Lee and Liang Y. Hsia.The Florida version was typed by Charlene A. Williams, proofread byCharlie 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 oneither double sided, high density diskette or printed copy.

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I METHOD OF SOLUTION

The method of analysis is the displacement or stiffness method. Inthis method, a matrix using the member's stiffness is formed to representthe structure. Member stiffness is derived for three possible movementswhich are rotational, vertical and horizontal movements at the ends ofmembers. Then the following boundary conditions are applied to the matrix:

a.

No vertical displacement at the outside ends of bottom slab.

b.

No lateral displacement at right end of bottom slab.

Boundary Conditions

Fig.

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Through matrix maneuver, the displacements at the ends of each memberare computed for each given loading condition. Then the exact moments andforces are determined by using the computed displacements. These momentsand forces are used to develop stresses, design reinforcements or adjustmember depth. If the member depth is increased, its impact is reevaluatedas above.

I The length of each member for analysis purposes is measured fromcenter line to center line of the supporting members. It is assumed thatloading applied at top slab will be uniformly distributed over the entirebottom slab. This assumption is based upon the premise that the bottomslab is cast upon a mat of granular material. A more refined assumptionseems impractical due to the lack of precise soil information at eachsite.

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DIRECT ELEMENT METHOD OF BOX CULVERT ANAL,YSIS

The direct element method is a procedure in which the externalstiffness matrix ASAT is built directly from geometric and elasticproperties of the elements, such as the top slab of a culvert, taken onemember at a time.

The required input data includes the degree of freedom; the numberof members and, for each member, the global degrees of freedom NP1, NP2,NP3, NP4, NPS and NP6 at the initial and terminal points; the coordinatesof the terminal points referenced to the initial point as origin; themodulus of elasticity and the cross-sectional area, A.

The procedure involves computing the local ASAT matrix of each memberin succession and assembling the elements of the local ASAT matrix into theglobal ASAT matrix.

~.x.,

P6'~

IInitialPoInt I

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Fig.

2 The P,X Diagram

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Fig.

3 The F,e Diagram

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III I 2; -'

I 0 I 0

5 In ocL

I~

.2 I -coB c<

.3' Slnoc I Cosoc l~~L LfA] =

I4 0 0

I-SIn

ocI L

-SIn ocL5 CosO(

I61-SfnO(I~I~

Fig.

4 Member Statics Matrix

-5 K,0 -C K, 5 K, a C K,

2K!4Kf[SAT] =

C-£ T K~S1-6 r K.e4K22K2

The Member [SAT] Matrix

Fig.

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3

62K2L 6£K2

L

5-6 r K2 C-6 Y Kt.4K2. 2K2

6~L

CS~

12.~-r L'" foe-ctK,-I2(f/~

6...kL~SK+f2~-I L~'~

CtSlKt+12(r) fe -CSK 12~-r LI. ,~ -srAi-/2('-fK£L

6~Kp'LS-6 r K2c

6rK2[ASAT] = 2 4Kt.

S-6 L K2.-6 ..s.L

CSCSKI-12~

~K,-I2(f~

ctKI+I2(t/~

-CS~/P.~

l:

I-6.Q.LCSK 12. £.§.x-r Lz- "E -6~K2.L

-~Kt-I2(f~-CSKt+12~

t

seK,+I2{f)l.~

Fig 6 The Member External Stiffness Matrix

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I THE MEMBER FLEXIBILITY MATRIX [ASAT]-l

[AST7] -1= 1

[AST T]

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IIn the displacement method of culvert analysis, the joint

displacements matrix [X] is first computed from Eq. (6), then the internalend forces matrix [F] from Eq. (4).I

[P] = [A] x [F] (1

[e] = [B] x [X] = [A T] x [X] (2)

[F] = [8] x [e] (3)

(3)Substituting Eq. (2) in Eq.

[F]=[SA7]x[X] (4)

(1)Substituting Eq. (4 in Eq.

[P]=[AST7]x[X] (5)

from which

[X]=[ASTT]-lX[P] (6)

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DEAD LOAD, EARTH PRESSUREAND WATER PRESSURE

The dead loads on the top slab include soil weight and concrete slabweight. The soil weight will default at 120 PCF. The concrete weight is

set at 150 PCF. The equivalent fluid weight for wall earth pressure willdefault to 30 PCF..

The program also investigates the condition of submergecl soil actingon the walls. The submerged soil pressure is taken as one half of theearth pressure acting on outside walls. Other dead loads in this case aretaken as full earth pressure. Live load surcharge will defaul.t to 2 feet.

Water pressure inside culvert barrels must be checkeci since thispressure may reverse the wall moments and add to the sJ.ab positivemoments.

The program will use the water pressure from the culvert flowingfull and empty as two loading cases.

LIVE LOAD

Influence lines are derived from applying a unit load moving fromleft to right along the top slab at twentieth points of each span. Basedon these results the maximum moment and shear at tenth poi.nts of eachmember are calculated.

Live load will default to the standard AASHTO HS20 load or militaryload, whichever controls. The user may specify the axle weight for aspecial overload truck. The user may also specify a single axle load witha specified design fill as an alternate to the regular live load. This isusually used for heavy construction vehicles where the axle:; are spacedfar apart so that only one axle is on the culvert at a time. Impact willapply to the top and bottom slabs and the exterior and interior walls ofthe box culvert.

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IIWhen 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 wheelloads are distributed as are those on bridges. When fill is more than 2feet deep, the wheel loads are distributed over squares with sides equalto 1.75 times the depth of fill. When these squares overlap, the total ofthe wheel loads is uniformly distributed over the combined, reduced grossarea.

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Live load may be neglected when the depth of fill is greater than 8feet, exceeds the span length of a single culvert or exceeds the totalwidth of a multiple barrel culvert.

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SERVICE LOAD DESIGN

I The following procedure is used to compute the required area of steelat three critical sections of each member; i.e., left end, midpoint andright end. The steel stress is given from input or defaulted as fs andthen the stress block is determined through the iteration process. Nocompression steel is considered and all tension steel is assumed to beplaced in one row.

Stress Block

Fig.

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Internal moment equals external moment: Mi = Me

1.

MA = 0 i.

Linear stress distribution:2.

Combine Eq. 1 and 2 to eliminate fIco

x(fs) xE (d-..!E.) = M+P (d-.!')nx (d-x) 2 3 2

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IThe equation f(x) is solved by Newton's iteration process forpolynomial equations. The value of X is computed approximately to anaccuracy of 0.01 inch.

-f (x)-xX(n+l) -n f/(x)

If there is no tension stress because of large P and small M, then

=!:!E+~I A

fl c

and the minimum amount of reinforcing steel would be used. If there aretension stresses, the concrete stress f'c = fsX/n(d-X) and the area ofsteel As = [~(f'c) (X) (b) -P] Ifs. I

The shear stress <fv) is computed as follows: Iv'fv = "Ed

where b = 12.0 inches

I*At the left or the right end of a member where sections are locatedless than a distance d from the face of the support, they will be designedfor the same shear, V, as that computed at a distance d.

The allowable concrete stress in compression is assumed to be O.4f'c'The allowable concrete shear stress is computed as follows:

For fills less than 2 feet:

Vc=O,9SVF:

IOR

I(Vc shall not exceed 1.6 ~whichever is greater.

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For fills greater than or equal to 2 feet:

Vc = 0.95 yI7r;

IOR

(Vc shall not exceed 1.8 ~whichever is greater.

p = reinforced ratio = As/bd

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ILOAD FACTOR DESIGN

The following procedure is used to check the critical sections ofeach member.

1.

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 uniformlydistributed over equivalent compression zone bounded by the edges of across section and a straight line located parallel to the neutral axis ata distance a = B1C from the fiber of maximum compression strain.

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b Ec .85f'0

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OAs£s

S~t!on Strain Equrvalent Stress

Fig.

8 Stress, Strain Diagram IP1 = 0.85 when f~ s 4000 psi

OR

I3. No compression steel is considered and all tension steel assumed

to be in one layer.

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4. Assume As Set

MRu = O.9bd2

p = O. 85f' c

fy

2RuI 1 -O.85fcl1 -

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O,85(31f'o 87000Pb = fy x 87000 + fy

Ip ~ O.5Pb. ; p ~ 0.002

.5Pb instead of O.75Pb*Best economy is achieved where p =

As = pbd

5. Compute Mu (Pure flexure)

a = ASfyO.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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I7. Compute Mb, Pb (Balanced Condition)

Ph = cI> [O.S5f'c X 12 X Bh -Asfy]

Mb = Pbeb = 4> O.8Sf'c x 12ab x

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= 0.85= 0.8= 0.7

For slabsFor Ext. WallFor Int. Wall

8. Assume straight line relation between pure compression andbalanced conditions, balanced conditions and pure flexure.

p

-Ala=

AII~bI8 I1K)ment of:::,::--~~=I.o 0' 8«1tl'Oft under G'xlal

0---::::~~=.9 ,oroe l-u"" "", ':::~ (J=.7

," ,,'"

Po

.7PoQ...~~! I

ebPb , ,':t~Po

AIMU

Moment. Ai

P,M Diagram

Fig.

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...12

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The shear stress (fv) is computed as follows:The allowable concrete shear stress is computed as follows:

I For fills less than 2 feet:

Vu.fv = M' b = 12.0 inches

I Vc = 2 ~

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OR

I(Vc shall not exceed 3.5 ~whichever is greater.

p = reinforcement ratio = As / bd

~M

s 1.0

For fills equal to or greater than 2 feet:

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Vc = 2 v'f1;

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(Vc shall not exceed 4. 0 ~whichever is greater. )

v ud ~ 1. 0~

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IFATIGUE STRESS LIMITS

The tensile reinforcement in box culvert elements subjected torepeated variations of reversals of stress shall be designed so that theactual range of stress does not exceed the allowable fatigue stress. Thedepth of fill also has a substantial effect on this fatigue range.

Such range between maximum and minimum stresses in tensilereinforcement caused by live load plus impact at service load shall notexceed:

f f = 21 -O. 33 fmin + 2. 4 AASHTO (8 -6 0)

ff = stress range, ksifmin = algebraic minimum stress level (tension-positive;

compression-negative), ksi

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At section where stress is not reversed.

fs = ~; where,

M = Live load moment rangejd = d -kd / 3 where kd is the distance from extreme compression

fiber to neutral axis.

2. At section where stress is reversed.

+M

fs=~ I(Tensile part of stress range)

rk -d'

d,1

-k

--M

-A:7'dfl a (Compzessive pazt of stzess zange); wheze,

Id' = distance from extreme compression fiber to centroid

compression reinforcement.d = distance from extreme compression fiber to centroid of tension

reinforcement

of

Total stress range = fs + f's

ICRACK CONTROL

The program checks maximum service load stresses in the reinforcingsteel for crack control as per AASHTO Article 17.6.4.7 I

98 ksi

fs=~AASHTO (17 -19)

Iis : Maximum service load stress

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IMINIMUM ECCENTRICITY

Minimum eccentricity will be checked for all members.

e =,!:!. M = P x ep'

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

Ir=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)

ECIgEI = 2.5(1 + ~d) AASHTO (8-44)

Ec = 57000 ~ AASHTO (8.7.1)

...

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I ~ Dead Load Momen td= Maximum To tal Momen t

Mc = 6 bX~b AASHTO (8-40)

Cm ~ 16b = Pu

1--cl>P c

AASHTO (8 -41 )

Cm = 1Mc = Magnified Moment c!I = 0.7

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IWINGWALL DESIGN CRITERIA

The following criteria of calculating wingwall height and length weredeveloped by FDOT Drainage Section.

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W t'nql4lall height H = Clear height of barrel

+ Top slob thickness

+ 1'-0" headwall

H -(H -/.5) 0< -45Transition WalIHt. =90 -45

W;ngwall standard length

1.5 H -Wall thickness + 3'-0-1 =

(For tS-<oc < 4S-J

(For 3/SO<oc < 34SOJ345 -Q(or 1, = 1 + (3 H -1) 345 -3/5

12 = 3 H

Fig.

10 Wingwall Length Criteria

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ITIE-IN LENGTH OF SKEWED WINGWALL

Tie-in length of straight wingwall is specified on Sheet 3 of 4 inFDOT Roadway and Traffic Design Standards. Figures 11 and 12 illustratesthe tie-in length of skewed wingwall in different ranges of skew angles.

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Angle of Skew

Sf

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~ Culvert

D = 1'-0"

Average Cl.Jt of top slab and side wallof exlstfng culvert when new culvertto 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

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Tie-in Length of Skewed Wingwa11 (0°-15°, 1BOO-165°)

Fig.

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~ of 8I1rra'

--,---

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;(,1'/,'Of _-A I

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D = /'-0'

Av". aJt of ~ 8iab 0tx1' sId, wolfof exIstIng all/eft wh8'? hM OIJIvert D + 2. '2. ~to be BXttrKJed from exlsfl~ cr.weft = 2. /' COB.d

= 32. CoB.4 ft.

LAY(JJT OF SKEW CULVERTWHEN ..d VARIES FROM '~TO 4SO

Fig.

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 designor the long coding form for special analysis and design. These codingforms are provided in Appendix E. Each input field and the default valueis described in the following Input Data Table. The output is explainedin the following sections of Output Data, Bar Schedule and Examples.I

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IINPUT DATA TABLE

Input Requirements for Reinforced Concrete Box Culvertsand Wingwall Computer Program

Header Card and Card One

CARDNUMBER

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CARD

COLUMN!VARIABLE

NAMEFORMAT DESCRIPTION

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DEFAULT

VALUE

* 1 KAST Al HEADER CARD NA

* 2- 3 COMM(I) I2 NARUN NUMBERIdentification only

I* 4-22 COMM(I) A19 NAME NA

* 23-28 COMM(I) A6 NA

IP HONE NUMBERExtension phone number

* 29-80 COMM(I) A52 NA

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HEADINGHeading, project no., date

1 1 KaNE II

!

CARD HEAD NO.

Valid code: 1NA

I1 2 LVLD II LIVE LOADValid code1 : HS203 : HS155 : HSIO7 : Blank9 : None

1

2 : H2O4 : HIS6 : HIO8 : Special

1 3 LVOMT II 2OMIT LIVE LOADValid code1 : Live load to be neglected2 : Live load to be used.regardless of fill height

Live load may be neglected forsingle box cul,vert if depth offill is more than 8 ft. andexceeds span length;for multiple box culvert it maybe neglected if depth of fillexceeds the distance betweenfaces of end supports.

I1 4 IZOF II 2ZERO FILL STRESS CHECKValid code1 : Stress check at zero fill2 : No stress check at zero

fill I1 5-9 OVERLD F5.0 0OVERLOAD STANDARD TRUCK AXLE

WEIGHTValid code: Blank-xxxxx LB

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Card One <Continued)

CARDNUMBER

i CARD IVARIABLE I FORMAT

COLUMN NAMEDESCRIPTION

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DEFAULTVALUE

I 1 10 IDSN 11 2IDESIGN METHODValid code1 : Service Load Design2 : Load Factor Design

I 1 PRINT M, V, P @ 1/10 POINTSValid code1

1 : PrintElse: Not print

11 MTEN 11 2

1 12 IINFN Il 2PRINTING LIVE LOAD INFLTJENCELINEValid code:1 : PrintElse: Not print

1.01 13-15

IDNEG

I F3.2 DESIGN NEGATIVE MOMENT POSITIONValid code: 0.0 -1.0Defined by a ratio from 0.0 to1.0 where 0.0 represent:3 thejoint centerline and 1.0represents the face of ",all orslab. AASHTO (8.8.2)

I 1

116-18

EWGT F3.0 120PCF

WEIGHT OF SOILI Valid code: ODD-xxx PC]~

1 19-23 FYST F5.0 60,000PSI

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YIELD' STRENGTH OF REINFORCEMENTFyValid code; Blank-xxxx:< PSI

24,000PSI

1 124-28 FSTL F5.0 ALLOWABLE STEEL STRESSFsValid code : Blank-xx~{ PSI

3,400PSI

1 29-32 I FCONC F4.0 COMPRESSIVE CONCRETE DESIGNSTRESS FcValid code: Blank-xxxx PSI

.

F3.0 ALLOWABLE CONCRETE SHEAR STRESSValid code: Blank-xxx J?SIBlank means by AASHTOspecifications

1 33-35 FSHRPSI

36-38

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FSTIR F3.01PSI

ALLOWABLE CONCRETE SHEAl~ STRESSWITH STIRRUPSValid code: Blank-xxx PSIBlank means no stirrups desired

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Card One (Continued)

CARDNUMBER

CARDCOLUMN

VARIABLE! FORMAT

NAME

DESCRIPTION DEFAULTVALUE

1 39-41 ADDS F3.2 THICKNESS INCREMENT OF :~LABSValid code: Blank-x.xx INCH

0.5 IN

1 42-44 ADDW F3.2 THICKNESS INCREMENT OF \'lALLSValid code: Blank-x.xx INCH

0.5 IN

1 45-47 covs F3.2

..

2.5 IN3.5 IN

TOP SLAB CONCRETE COVERMeasured from center of bar toface of concreteSlightly aggressive env:LronmentModerately/Extremely ag~JressiveenvironmentValid code: Blank-x.xx INCH

1 48-50 'COVB F3.2

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2.5 IN3.5 IN

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BOTTOM SLAB CONCRETE CO"ERMeasured from center of bar toface of concreteSlightly aggressive env:.ronment iModerately /Extremely ag~Jressi veenvironmentValid code: Blank-x.xx INCH

1 51-53 covw F3.2

.I2.5 IN3.5 IN

EXTERIOR WALL CONCRETE COVERMeasured from center of bar toface of concreteSlightly aggressive envj.ronmentModerately/Extremely ag~rressiveenvironmentValid code: Blank-x.xx INCH

1 54-56

:

COVIN F3.2

I2.5 IN3.5 IN I

INTERIOR WALL CONCRETE COVERMeasured from center of bar toface of concreteSlightly aggressive envj.ronmentModerately/Extremely ag~rressiveenvironmentValid code: Blank-x.xx INCH

I1 57 ISAMS 11 2

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SAME TOP & BOTrOM SLAB DESIGNValid code1 : Same thickness and

same steelELSE: Set thickness of each

slab.

1 58 11ISAMW 2SAME EXTERIOR & INTERIOFt WALLTHICKNESSValid code1 : Same thicknessELSE: Set thickness of each

wall. II

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Card One (Continued)

CARDNUMBER

CARDCOLUMN

VARIABLENAME

FORMAT DESCRIPTION DEFAULTVALUE

1 59 IBSH Il 1BAR SCHEDULEValid code1 : Print bar schedule2 : Not print bar sched1~le

1 60-62 SPACMAX F3.1 18.0 INMAX. BAR SPACINGDESIGNValid code: Blank-18.0 INCHI 1 63-65 SPACMIN F3.1 4.0 IN

MIN.

BAR SPACINGDESIGNValid code: 04.0-18.0 :[NCH

1 66-67 MAXSIZ 12 11MAX. BAR SIZEValid code: 01-11

1 68-69 MINSIZ 12 4

MIN.

BAR SIZEValid code: 04-11

I 1 70-72 CN F3.1 9MODULAR RATIOValid code: 1-9

1 73 ENVIR 11 1

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ENVIRONMENT CONDITIONValid code: 0-3 See Not:e (1)I

: Slightly aggressive1 : Slightly aggressive2 : Moderately aggressi'lTe3 : Extremely aggressivE~

NOTE:

(1) The environment condition is required to determine t:he default minimumconcrete cover of reforcing steel and concrete clas~;:

Under a slightly aggressive environment condition, concrete cover is 2inches 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

CARDNUMBER

CARDCOLUMN

VARIABLENAME

FORMAT DESCRIPTION

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DEFAULT; VALUE

2 1 KTWO II 2CARD NO.2Valid code: 2

2 2-5 EDLU F4.3 0EXTRA UNIFORM DEAD LOADValid code: Blank-x.xxx K/FT

2 6-10 EDLCI F5.3 EXTRA CONCENTRATED DEAD LOADValid code: Blank-xx.xxx KIPS

0

2 11-13 EDLXl F3.2 POSITION OF CONCENTRATED LOADMeasured from centerline of theleftmost wall of the culvertValid code: Blank-x.xx FT.

0.00

2 14-18 EDLC2 F5.3 EXTRA CONCENTRATED DEAD LOAD-2Valid code: Blank-xx.xxx KIPS

0

2 19-21 EDLX2 F3.2 POSITION OF CONCENTRATED LOAD-2Measured from centerline of theleftmost wall of the culvertValid code: Blank-x.xx FT.

00.0

I2 22-26 IEDLC3 F5.3

I

EXTRA CONCENTRATED DEAD LOAD-3Valid code: Blank-xx.xxx KIPS

0

2 27-29 EDLX3 F3.2 00.0POSITION OF CONCENTRATED LOAD-Measured from centerline ofthe leftmost wall of theculvertValid code: Blank-x.xx FT.

2 30-34 WHEER F5.3 SPECIAL WHEEL LIVE LOADEnter weight of one wheelValid code: Blank-xx.xxx KIPS

0

I2 35-38 FILLR F4.2 00.00 I

EARTH FILLMeasured to top of slabValid code: Blank-xx.xx FT.

2 39-42 OFACT F4.2 OVERSTRESS FACTORValid code: 1.00-xx.xx

1.00

p 1 KPAS Al i REINFORCEMENT RATIO CARDiFor Load Factor design onlyIp = As / bdOptional card always followCard '1' or Card '2'Valid code: P I

2-4p PAS F3.3 REINFORCEMENT RATIOValid code: .xxx

.012

NOTE:

Leave Card 2 or Card P out if default value is selected.

24

I

I Card Three

CARDNUMBER

I

CARD

COLUMN!VARIABLE

INAMEFORMAT DESCRIPTION DEFAULTI

VALUE

3 1 KTHR II 3ICARD NO.3Valid code: 3

3 2-3 ,NCARD I2 NACULVERT NUMBERValid code: 01-99Unique no. for identification

3 4 NBOX II NA[ NUMBER OF BOX CULVERTBARRELSValid code: 1-4

3 5-8 NSPAN F4.2 NACLEAR SPAN OF EACH BARRELMeasured from inside of leftbarrel wall to right ofbarrel wallValid code: 02.00-xx.xx FT.

3 9-12 NHITE F4.2 NAI CLEAR HEIGHTMeasured from top of bottomslab to bottom of top slabValid code: 02.00-16.00 FT.I

3 13-17 NFILL F5.2 NA

IDESIGN FILLMeasured from bottom of topslab to the average elevationof the roadway surface.Valid code: OOO.OO-xxx.xx FT.

3 18-22 LENG F5.2 NAILENGTH OF CULVERTMeasured from left to right!face

of culvert along centerline of culvertValid code: xxx.xx FT.

3 23-25

ILSKE

13 000LEFT HEADWALL SKEW ANGLEMeasured from lineperpendicular to center lineof culvert in clockwisedirection to headwall faceValid code: OOO-xxx DEGREE

3 26-28 RSKE I3 000

IRIGHT SKEW ANGLEMeasured from lineperpendicular to center lineof culvert in clockwisedirection to headwall faceValid code: OOO-xxx DEGREE

I

.25

..

Card Three (Continued)

CARDNUMBER

CARDCOLUMN,

VARIABLENAME

FORMAT DESCRIPTION DEFAULTVALUE I

3 29 KBASE Al BLANKFLOOR SUPPORT JOINT CONDITIONValid codeX : No floor with fixed end

supportIH : No floor with hinged

support: Full floor

3 30-33 TSLAB F4.2 9 INTOP SLAB THICKNESSLeave this field blank to usedefault seeded minimum valueto design optimized thicknessValid code: Blank-xx.xx IN.

3 34 KFXTS Al BLANKFIXED TOP SLAB THICKNESSValid codeF : Fixed thickness

3 135-38 I BSLAB F4.2 9 IN

I

BOTTOM SLAB THICKNESSLeave this field blank to usedefault seeded minimum valueto design optimized thicknessValid code: Blank-xx.xx IN.

3 39 KFXBS Al BLANKFIXED BOTTOM SLAB THICKNESSValid codeF : Fixed thickness

3 40-43 WALLR F4.2 9 INEXTERIOR WALL THICKNESSLeave this field blank to usedefault seeded minimum valueto design optimized thicknessValid code: Blank-xx.xx IN.

I3 44 KFXW Al BLANKFIXED EXTERIOR WALL THICKNESS

Valid codeF : Fixed thickness

3 45-48 F4.2IWALLR 9 ININTERIOR WALL THICKNESSLeave this field blank to usedefault seeded minimum valueto design optimized thicknessValid code: Blank-xx.xx IN.

3 49 KFXTS Al BLANKFIXED INTERIOR WALL THICKNESSValid codeF : Fixed thickness

NOTE: .,Use fixed slab or wall thickness to override the calculated thicknessesor to match the existing box culvert structure for a culvert extension project II

26

I

.

Card Three (Continued)

CARDNUMBER

CARD i

COLUMNVARIABLEIFORMAT

NAMEDESCRIPTION DEFAULT

VALUE3 50-52 SURCH F3.1 2.0 FTLIVE LOAD SURCHARGE

Valid code: Blank-xx.x FT.

3 53-54

I

PRESS F2.0 30 PCFMAXIMUM SOIL EQUIVALENT FLUIDPRESSUREFor lateral earth pressureValid code: Blank-xx PCF

3 55-56 PMIN F2.0 15 PCF

I

MINIMUM SOIL EQUIVALENT FLUIDPRESSUREFor checking positive momentValid code: Blank-xx PCF

3 57-59 PWAT F3.1 WATER WEIGHT'Valid code

: 62.4 PCF-1 : No water pressure

62.4

3 60-62 TFILT F3.1 2.0 IN

ITOP HAUNCHValid code Blank-xx.x IN.

: 2 IN.-1.0 : Zero top haunch

3 63-65 BFILT F3.1 2.0 IN

I

BOTTOM HAUNCHValid code Blank-xx.x IN.

: 2 IN.-1.0 : Zero top haunch

3 66 KRACH Al BLANKHAUNCH CONSIDERATIONValid code

: Haunch not to be considereaX : Haunch to be considered by

1983 AASHTO 8.8

3 67 KHWAL Al BLANK

I

HEADWALL ELIMINATION BLANKValid code

: Eliminate no headwallB : Eliminate both headwallL : Eliminate left headwallR : Eliminate right headwall

3 68-79 CaMS A12

I

COMMENTS!Valid code: Free comments

3 80 ITEST 11 SPECIAL PRINTOUTNot normally used. strictly fortesting purposeValid code1 : Print DL, SP, WP and LL

moments and shears: No off

27

ICard Four

CARDNUMBER

CARDCOLUMN

VARIABLE! FORMAT

NAME

DESCRIPTION

I

DEFAULTVALUE

4 1 KFOR II 4CARD NO.4Valid code: 4

4 2-3 NCARD 12 NACULVERT NUMBERIdentify each culvert witha unique numberValid code: 1-99 I

4 4 IMINKEY II BLANKMINIMUM OUTPUT KEY: Minimum output

Leave it blank, 0 or 1to turn off all outputexcept what is requiredfor Florida Roadway DesignStandards

1 : Minimum output2 : Detailed output

.

4 5 WINGTY II BLANKWINGWALL TYPEValid code

: Straight wingwall whichaligns with the headwall

1 : Straight wingwall same asBLANK

2 : Skewed wingwall whichpoints to differentazimuth angle from culvertheadwall skew angle

4 6-8 WLSKEF 13 LSKELEFT FRONT WINGWALL SKEW ANGLEMeasured from lineperpendicular to center line ofculvert in clockwise directionto wingwall faceValid code: 0-45 degree

225-360 degreeBLANK: Wingwall parallel

to the headwall

4 9-11 WLSKEB 13 LSKELEFT BACK WINGWALL SKEW ANGLEMeasured from lineperpendicular to center line ofculvert in clockwise directionto wingwall faceValid code: 135-315 degree

BLANK: Wingwall parallelto the headwall

28

ICard Four (Continued)

CARDNUMBER

CARDCOLUMN

VARIABLEIFORMATNAME

DESCRIPTION

I

DEFAULT

VALUEI4

112-14iWRSKEF

13 RSKERIGHT FRONT WINGWALL SKEW ANGLEMeasured from lineperpendicular to center line ofculvert in clockwise directionto wingwall faceValid code: 0-135 degree

315-360 degreeBLANK: Wingwall parallel

to the headwall

4

!15-17IWRSKEB

I3 RSKERIGHT BACK WINGWALL SKEW ANGLEMeasured from lineperpendicular to center line ofculvert in clockwise directionto wingwall faceValid code: 45-225 degree

BLANK: Wingwall parallelto the headwall

4

[18-21IWSKLF

F4.2 LEFT FRONT WINGWALL LENGTHOverrides calculated wingwalllength, if length is specified,the wingwall front tip lengthwill be identical to the heightat joint of wingwall & culvertValid code: 0.00-99.99 FT.

BLANK: Calculated length

4

122-25

F4.2

IWSKLB

LEFT BACK WINGWALL LENGTHOverrides calculated wingwalllength, if length is specifiedthe wingwall front tip lengthwill be identical to the heightat joint of wingwall & culvertValid code: 0.00-99.99 FT.


26-29 F4.24

IWSKRFI

RIGHT FRONT WINGWALL LENGTHOverrides calculated wingwalllength, if length is specifiedthe wingwall front tip lengthwill be identical to the heightat joint of wingwall & culvertValid code: 0.00-99.99 FT.I


30-33 WSKRB F4.24 RIGHT BACK WINGWALL LENGTHOverrides calculated wingwalllength, if length is specifiedthe wingwall front tip lengthwill be identical to the heightat joint of wingwall & culvertValid code: 0.00-99.99 FT.


29

I

.

Card Four (Continued)

CARDNUMBER

I

CARDCOLUMN

VARIABLEIFORMATNAME

DESCRIPTION DEFAULTVALUE

4 34 CULEXT II BLANKCULVERT EXTENSIONA calculated tie-in lengthwill be excluded from the newculvert bottom slab at eachside which is connected to theexisting culvertValid code

: New culvert with (BOTH)left and rightwingwalls

1 : New culvert with (BOTH)left and rightwingwalls

2 : New culvert extends (LEFT)I from left side ofexistig culvert withleft wingwall only

3 : New culvert extends (RIGH)from right side ofexistig culvert withright wingwall only

4 : New culvert connects (NONE)existing culvertswith no wingwall

(BOTH)

(LEFT)

(RIGH)

4 35 NOHEAD 11 BLANK

(BOTH)

(BOTH)

;

NUMBER OF HEADWALLiValid code

: Left and rightheadwalls

1 : Left and rightheadwalls

2 : Left headwall only3 : Right headwall only4 : No headwall

(LEFT)(RIGH)(NONE)

4 36-37 F2.1wwcovs2.5 IN3.5 IN

II

COVER FOR OUTSIDE FACE OF WALLSlightly aggressive environmentModerately/Extremely aggressiveenvironmentValid code: Blank-x.xx INCH

38-39 F2.14 IALLCOV2.5 IN3.5 IN

ALL OTHER FACES CONCRETE COVERSlightly aggressive environmentModerately/Extremely aggressiveenvironmentValid code: Blank-x.xx INCH

40-49 A1O4 PROJNO PROJECT NUMBERValid code: Free format

4 50-80 LOCSTA A47 LOCATION & IDENTIFICATIONValid code: Free format

30

IOUTPUT DATA

Three categories of output are available from this program:

The first category is the Standard Box Culvert and Wingwall DesignOutput which may be incorporated into the Florida Department ofTransportation Roadway and Traffic Design Standards Indexes 280 and 290 toproduce a complete design.

The second category is the Special Output which tabulates shear andmoment generated by dead load, live load, soil and water at tenth point ofeach member.

The third category is the Detailed Output which tabulates shearstress at critical sections and reinforcing bar splice lengths.

Combinations of these three output categories may be generated bytriggering either one or both of the Special Print and Minimum keys.

The output data has the following reports:

1.

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 andcorrect any discrepancy. The concrete covers coded and echoed on thispage are the dimensions measured from the center of bar to the face ofconcrete.

2. Standard Output:

2.1 The first part of this output provides a detailed description ofmaterial properties, box culvert and wingwall geometry, calculated designdimensions and concrete quantities. The concrete covers on this page arethe dimensions measured from the face of reinforcing bars to the face ofconcrete 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 onSheet 1 of 5 of Index 290. Based on the wingwall skew angle and drainageconsiderations, the length, height and front tip height of each wingwallare calculated from the equation in Figure 10 on page 16. If all wingwalllengths and front tip heights are identical, a condensed output willautomatically be created. Two sample input coding forms and output reportsare shown on Pages 38 through 53.

I

The total wingwall length with barrel width tabulated on the outputis 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 castwith the bottom slab.

2.2 The second part of this output tabulates the reinforcing barnumber, set, size, spacing, type, length, weight and totalI

mark,

31

I.quantities.

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 individualtotal designed reinforcing bar length by the standard 40 ft. stock length.

In the case of a box culvert extension, the C3 bar will replace theCl bar in the bottom slab to accomodate the reduced length of the new boxculvert bottom slab which will be tied to the existing box culvert bottomslab.

I3. Special OUtput:

The following are column headings and definitions of the SpecialOutput:

3.1 Service Load Design

3.1.1

Moment:

Maximum design moment at the critical section, in kip-it

3.1.2 Axial Force: Axial design load corresponding with maximum momentat the same section in kips.

3.1.3

Shear:

Maximum design shear force at the critical section,in kips. I3.1.4 Concrete Stress: Concrete compressive stress due to design momentand axial force, in psi.

3.1.5 Shear Stress: Shear stress at the section, in psi

3.1.6As:

Required area of steel reinforcement, in square inches.

3.1.7

VA:

Allowable shear stress, in psi.

3.1.8

FCA:

Allowable concrete co~pressive stress, in psi.

3.2 Load Factor Design

3.2.1

Moment:

Maximum loadsection, in kip-ft.

designfactor themoment at critical

3.2.2 Axial Force: Axial design load corresponding with maximum .momentat same section, in kips.

3.2.3

Shear:

Maximum load factor design shear force at the criticalsection, in kips.

3.2.4

PO:

Axial designcompression, in kips

load strength of the section in pure

3.2.5

MU:

Design moment strength of the section (pure flexure),in kip-ft.

3.2.6

MB:

Design moment strength of the section when assumed ultimatestrain of concrete and yielding of tension reinforcement occurssimultaneously (balance conditions), in kip-ft.

32

I

.

3.2.7 PB: Axial design load strength of the section when assumedultimate strain of concrete and yielding of tension reinforcementoccurs 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 designload condition, in kip-ft.

in psi3.2.11 VA: Allowable shear stress

I 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 memberas 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, whicheveris the greatest.

5.

Bar Design

This part of output is used for the North Carolina Department ofTransportation Standard and is printed for output verification between theNorth 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.

TSLAB-:

TOp slab top bar, A300

BSLAB+: Bottom slab top bar, A200

BSLAB-:

Bottom slab bottom bar, A300

EXTIN:

Exterior wall inside bar, Bl

EXTOUT: Exterior wall outside bar, B2.

INTWL:

Interior wall bar, B3.

Cl:

Longitudinal bar, Cl.

33

I

.6.

Bar Schedule.

7.

Moment, shear, axial force at tenth points. (option)

8.

Influence Line (option): This is an extensive printout, and should onlybe requested when necessary.

9.

Member reference

I

IM:Member; & Lt. End; R:Rt. End

Fig.

13 Member Reference Diagram

,. 34

I

I BAR SCHEDULE

Normally, the bar schedule is printed with the design option but maybe omitted with the analysis option. The user must refer to the FloridaDOT Roadway and Traffic Design Standards Index No. 290 to determine theexact location of bars.

'AI'

: Top corner bars

'A2' :I Bottom corner bars.

'AIOO' : TOp slab positive (main bars)

'AIOl' to 'AlSO': TOp slab positive, left side cut bars

* 'A151' to 'A199' barsTOp 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

'B2':

Exterior wall outside bars, from construction joint toconstruction joint.

I

'B3':

Interior wall bars

'Cl': Longitudinal bars (Florida Standard)

'C2': Top slab bars

'C3': Longitudinal bars replace Cl at bottom of slab when a new culvertis extended from an existing culvert.

'Gl':

Left side head wall bars, (Florida Standard)

* 'G2': Right side head wall bars,

(N.

C. Standard).

'52':

Left side end bars, (N. ~. Standard)

I * '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

I35

I

I

.

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 willbe a "U-Shaped" bar.

Bar Types

STRAIGHT -BAR

I, 8 -I<..>

lYPE I BAR

TYPE II BAR

I~ B _1

(.,)

TYPE 10 BAR

Fig.

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 thecorner bars will overlap.

Refer to the Florida Department of Transportation Roadway and TrafficDesign Standards Index No. 290, Sheet 1 of 5 for bar splice details.

I

I

I36

I EXAMPLES

Depending upon the desired output, input data can be divided into twocategories. The first category is the mandatory input data to develop theoutput for the design of standard highway box culverts and wingwalls. Thesecond category is the input data required for a special design orstructural analysis. The data in the second category can all be changedfrom preselected defualt values to special values required by user toperform 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 themandatory and special input data is described on Page 43; i.e., the LongCoding 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 aggressiveNumber of -barrels 1Clear 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 degreeSkew angle of right headwall 20 degreeSkewed wingwall angle

Left front ~ 350 degreeLeft back 200 degreeRight front 60 degreeRight back 80 degree

Project number 55030-3418Location Leon county, US 90, Station 220 + 36

Based on this data, a standard coding form is prepared and shown onPage 38.

37

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APPENDIX BVARIABLE LISTING

II 'P' '1'

'2''3''4'AAREAABABARADATEADDSADDWADI(I)AFLOORAHITEALIVEALLCOVANDWILANDWIRARAR(L)AREA(J)IARR(I)ARR(2)ARR(3)ASATASBASPASPBASPMATYPEAl

I A2

A3

A4BARDBBBBARHBDBFILTBNDWILBNDWIRBSLABBTYPEBICECHCUCNCOMM(17)CaMSCOMS(3)COVBCOVINCOVSCOVWCULEXT

A111111111

REINFORCEMENT RATIO CARDCARD NO.1 -MATERIALSCARD NO.2 -LOADINGSCARD NO.3 -BOX CULVERTCARD NO.4 -WINGWALLAREA OF REBARDEPTH OF EQUIV. RECT. STRESS BLOCK AT BALANCED CONDITIONAREA OF REINFORCING BARS IN ARRAY #4-#11I

DATESLAB THICKNESS INCREMENTWALL THICKNESS INCREMENT

..

F3.2F3.2

w.w.

HS20, H2O, HSI5, H15, HSIO, HIO LIVE LOADSWINGWALL CONCRETE COVER EXCEPT FRONT FACELEFT STRAIGHT WINGWALL LENGTH IN INTEGERRIGHT STRbIGHT WINGWALL LENGTH IN INTEGERAREA OF REBAR REQUIRED AT CONTROLLING PT.

If2.1

w.w.w.w.w.

EXTERNAL STIFFNESS MATRIXAREA OF REBAR REQUIRED AT CRITICAL SECTIONTENSION REINFORCEMENT RATIO ASP=AS/bdREINFORCEMENT RATIO IN BALANCED CONDITIONSTRIAL REINFORCEMENT RATIO ASPM=O.5xASPBTYPE OF BARREL; SINGLE, DOUBLE, TRIPLE, QDRPLEAREA OF TOP SLAB SECTIONI

AREA OF EXTERIOR WALL SECTIONAREA OF INTERIOR WALL SECTIONAREA OF BOTTOM SLAB SECTION

--I.-ARRAY OF REINFORCING BAR DIAMETERS, ",FACTOR OF THE WIDTH OF EQUIV. RECT. STRESS BLOCK;

#4-#11

.85

F5.2

F4.2

MAX. DESIGN DL MOMENT/MAX. DESIGN TOTAL MOMENTBOTTOM HAUNCHLEFT END WINGWALL LENGTH -STRAIGHTRIGHT END WINGWALL LENGTH -STRAIGHTBOTTOM SLAB THICKNESS -INPUTTYPE OF WALL; EXT./INT. WALL, TOP/BOTTOM SLABFACTOR OF THE DEPTH OF 'EQUIV. RECT. STRESS BLOCKI

CONCRETE MODULUS OF ELASTICITYREBAR SUPPORT HEIGHT BASED ON BAR DIAMETER IN 1/4" INCRE.

!MODULAR RATIO: STEEL/CONCRETEF3.1

A12 COMMENTS

F3.2F3.2F3.2F3.2

I 13

BOTTOM SLAB CONCRETE COVER (TO CENTER OF BAR)INTERIOR WALL CONCRETE COVER (TO CENTER OF BAR)TOP SLAB CONCRETE COVER (TO CENTER OF BAR)EXTERIOR WALL CONCRETE COVER (TO CENTER OF BAR)CULVERT EXTENSION

56

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ClC2C3C4C5

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I FCONCFEMB

IFEMSFEMLFEMRFEMlFEM2FEWlFEW2FFMFFOOTFIFILLFILLRFMFMOMN

II F3.2

F5.3F5.3F5.3F4.3F3.2F3.2F3.2

I

IF3.0

COEFFICIENT FOR SETTING SLAB THICKNESSCOEFFICIENT FOR SETTING SLAB THICKNESSCOEFFICIENT FOR SETTING SLAB THICKNESSCOEFFICIENT FOR SETTING SLAB THICKNESSCOEFFICIENT FOR SETTING SLAB THICKNESSSTEM WIDTH-CONCRETE COVER W.W.FOOT HEIGHT -CONC. COVER W.W.EQUAL TO D(2) W.W.DISTANCE FROM EXTREME TENSION FIBER TO REBAR CENTROIDDISTANCE FROM EXTREME COMPRESSION FIBER TO REBAR CENTROIDDEVELOPMENT LENGTH OF REINFORCING BARI

WIDTH OF SLAB IN FEET OVER WHICH WHEEL IS DISTRIBUTEDUNI FORM DEAD LOADDESIGN NEGATIVE MOMENT POSITIONC. G. OF WINGWALL HEEL WIDTHC. G. OF STEM AND HEEL W.W.C. G. OF STEM ,HEEL AND TOE W.W.C. G. OF WALL AND FOOT W.W.ECCENTRIC OF RESULTANT W.W.ECCENTRICITY OF RESULTANT LOAD ON A SECTIONMIN. ECCENTRICITY REQUIRED BY COMPRESSION MEMBEREXTRA CONCENTRATED DEAD LOADEXTRA CONCENTRATED DEAD LOAD-2EXTRA CONCENTRATED DEAD LOAD- 3EXTRA UNIFORM DEAD LOADPOSITION OF CONCENTRATED LOADPOSITION OF CONCENTRATED LOAD-2POSITION OF CONCENTRATED LOAD-3EI/L TOP SLABEI/L EXTERIOR WALLEI/L INTERIOR WALLEI/L BOTTOM SLABENVIRONMENT CONDITIONUNIT WEIGHT OF SOILCOMPRESSIVE STRESS IN CONCRETE CAUSED BY FATIGUE DESIGNFATIGUE DESIGN NEGATIVE MOMENTFATIGUE DESIGN POSITIVE MOMENTWINGWALL HEIGHT FT. PARTNEGATIVE MOMENT FOR FATIGUE DESIGNPOSITIVE MOMENT FOR FATIGUE DESIGNSTRESS IN STRAIGHT REINFORCEMENT CAUSED BY FATIGUE DESIGNEXTREME FIBER COMPRESSIVE STRESS IN CONCRETESPECIFIED CONCRETE COMPRESSIVE STRESSDEAD LOAD FIXED END MOMENT AT BOTTOM SLABDEAD LOAD FIXED END MOMENT AT TOP SLAB

F4.0

SOIL PRESSURE FIXED END MOMENT AT TOP OF WALLSOIL PRESSURE FIXED END MOMENT AT BOTTOM OF WALLWATER PRESSURE FIXED END MOMENT AT TOP OF WALLWATER PRESSURE FIXED END MOMENT AT BOTTOM OF WALLINTERIOR JOINT-FORCE MATRIX, INCLUDE FIXED END MOMENTREAL VALUE OF WINGWALL FOOTING W.W.NBOXDESIGN FILL IN FT.EARTH FILLINTERIOR J~INT-FORCE MATRIXTOTAL NEGATIVE MOMENT

I F4.2

I57

FMOMPFNEELFNLLHTFNOEFNOOTFNOTWIFNOW1FNTEMFOOTFOOTWIFPLDNFPLDP

I1:'S

FSHRFSHRNFSHRP~STIR~STLFYSTHHEELHEELMOHEELPLHEELPPHEELPRHEELSHHHEELHITEHORFO1112IALLHTIBSHIDSNIESTWIFIXBIFIXIIFIXTIFIXWIFOCIFOOTIHAUCHIHEADIHEELIHSIHSIIILOOPINFNINTWILINTWIRIOOTWIIOTWILIOTWIRIPICISAMSISAMWISER

F3.0

IF3. 0F5.0F5.0

TOTAL POSITIVE MOMENTHEEL WIDTH IN. PARTWINGWALL HErGHT IN. PARTTOE WIDTH IN. PARTWINGWALL FOOTING THICKNESS IN. PARTWINGWALL FOOTING WIDTH IN. PARTI WINGWALL KEY AND TOE VOLUMEWINGWALL WALL THICKNESS IN. PARTWINGWALL FOOTING THICKNESSWIDTH OF WINGWALL FOOTING (TOE, STEM, HEEL)TOTAL AXIAL FORCE OCCUR ED WITH FMOMNTOTAL AXIAL FORCE OCCURED WITH FMOMPTENSILE STRESS IN REINFORCEMENT AT SERVICE LOADSALLOWABLE CONCRETE SHEAR STRESSTOTAL NEGATIVE SHEARTOTAL POSITIVE SHEARALLOWABLE CONCRETE SHEAR STRESSALLOWABLE REBAR TENSILE STRESSSPECIFIED YIELD STRENGTH OF REINFORCEMENTFILL+SLABF/2.0+SURCH(FILL+TOP SLAB THICKNESS+SURCHARGE)WINGWALL HEEL WIDTH

w.w.w.w.w.w.

IHEEL PRESSURE

I

REAL VALUE OF HEELDESIGN HEIGHT IN FT. NHITE+(SLABF+SLABBF)*O.5HORIZONTAL FORCE TO WINGWALLNUMBER OF MEMBERSI1+1WINGWALL HEIGHT FT. PARTBAR SCHEDULEDESIGN METHOD

IlIl

BOTTOM SLAB FIXITYINTERIOR WALL FIXITYTOP SLAB FIXITYEXTERIOR WALL FIXITYLOAD FACTOR CASE (IDSN=l,IFOC=O SERVICE LOAD)WINGWALL FOOTING THICKNESS FT. PARTFIXED JOINTCARD HEAD NO.IHEEL WIDTH FT. PART

11

I

THIRD AXLE LOAD

I1 PRINTING LIVE LOAD INFLUENCETOTAL LEFT WINGWALL LENGTHTOTAL RIGHT WINGWALL LENGTHWINGWALL FOOTING WIDTHTOTAL LEFT WINGWALL LENGTHTOTAL RIGHT WINGWALL LENGTH

IN. PARTIN. PARTFT.

PARTFT. PART

FT. PARTI

IIII

SAME TOP & BOTTOM SLAB DESIGNSAME EXTERIOR & INTERIOR WALL DESIGNSERVICE LOAD CASE (IDSN=2, ISER=O LOAD FACTOR)

58

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II

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IWINGWALL WALL THICKNESS

FT.

PART

II SPECIAL PRINTOUT[ TOE WIDTH FT. PARTINTERIOR WALL THICKNESS IN. -SEEDED VALUEINTERIOR WALL THICKNESS IN.ZERO FILL STRESS CHECKNUMBER OF MEMBERSISER=O, 11=211 + 1IFOC=O, 12=2SELECTIONS OF DESIGN, SPECIAL L.L. FILL OR ZERO FILL, *,

'

I ;U:PORT JOINT

'4'JOINT TYPE- BOTTOM SLABINTERIOR WALL JOINT TYPEJOINT TYPE-TOP SLABJOINT TYPE-EXTERIOR WALLHAUNCHHEADWALLINPUT CARD CODE *, 1, 2, 3, 4, P1

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IN FT.IN FT.IN FT.IN FT.IN FT.

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w.w.DEAD LOAD MOMENTECCENTRIC MOMENTFACTORED WALL MOMENTFACTORED TOE MOMENTFACTORED HEEL MOMENT

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MTENNBOXNBlNCARDNFILLNHITENNUMBNOHEADNOPNNPlNP2NP3NP4NP5NP6NRNSE(L)NSPANNSZNUMBNX

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PALOADPASPBPINFPLDMNPLDMPPMINPOPRESSPROJNOPWATRESULTROERSKESHEARASHEARHSHEARTSHEARWSHRSHRDLSHRSPSHRWPSIDBEVSKLTSKRTSLABSLABBSLABBF

ISLABBZ

IIII

FS.2F4.2

III

[MAX. LIVE LOAD POSITIVE MOMENTMAX. LIVE LOAD NEGATIVE MOMENTISOIL

PRESSURE MOMENTWATER PRESSURE MOMENTPRINT M, V, P @ 1/10 POINTSNUMBER OF BOXESNBOX+1INPUT CARD NUMBERDESIGN FILLCLEAR HEIGHT 2-14 FT.NUMBER OF REBARNUMBER OF HEADWALLTOTAL NUMBER OF THE DEGREE OF FREEDOMNO. OF DEGREE OF FREEDOM FOR ROTATION AT INITIAL PT.NO.

OF DEGREE OF FREEDOM FOR H-TRANSLATION AT INITIAL PNO. OF DEGREE OF FREEDOM FOR V-TRANSLATION AT INITIAL PNO. OF DEGREE OF FREEDOM FOR ROTATION AT TERMINAL PT.NO. OF DEGREE OF FREEDOM FOR H-TRANSLATION AT TERMINALNO. OF DEGREE OF FREEDOM FOR V-TRANSLATION AT TERMINALNO.

OF INFLUENCE LINE ORDINATES

II

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ICLEAR SPANSIZES OF REINFORCING BARS AT CRITICAL SECTIONSA SET OF SIZE NUMBERS OF REINFORCING BARS

F4.2 I

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OVERSTRESS FACTORLEFTS IDE OFFSETOVERLOAD STANDARD TRUCK AXLEEXTERNAL JOINT-FORCE MATRIXPRESSURE ON WINGWALL FOOTINGREINFORCEMENT RATIOAXIAL DESIGN LOAD AT BALANCE CONDITIONAXIAL FORCE INFLUENCE LINE AT 1/20 PT. OF EACH MEMBERDESIGN AXIAL FORCE OCCURED WITH SMOMNDESIGN AXIAL FORCE OCCURED WITH SMOMPMIN.

SOIL EQUIVALENT FLUID PRESSUREAXIAL DESIGN LOAD IN PURE COMPRESSIONMAX. SOIL EQUIVALENT" FLUID PRESSUREPROJECT NUMBERWATER WEIGHTRESULTANT OF ALL MOMENTS W.W.REINFORCEMENT RATIO W. W.RIGHT CULVERT SKEW ANGLEALLOWABLE SHEAR ~J~

I13w.w.w.w.w.w.w.w.

DESIGN SHEAR STRESSDEAD LOAD SHEAR FORCE$OIL PRESSURE SHEAR FORCEWATER PRESSURE SHEAR FORCESIDE BEVEL IN IN.LEFT SKEWED WINGWALL LENGTHRIGHT SKEWED WINGWALL LENGTHTOP SLAB THICKNESSBOTTOM SLAB THICKNESSBOTTOM SLAB THICKNESS IN FT.BOTTOM SLAB THICKNESS

IN.-SEEDED VALUEIN.-SEEDED VALUE

-SEEDED VALUE-DEFAULT OR INPUT

I

60

SLABF

SLABZ

SLOPEE

SMOMN

SMOMP

SPACMAX

SPACMIN

SPAN

SPCG

SPG

SPG(L)

SPLDN

SPLDP

SPM

SPRl

SPR2

SPl

SP2

SSPCG

SSTEM

STEEL

STEM

SUMVET

SURCH

TI TEMS TFILT

TOE

TOEMOM

TOEPRA

TOEPRS

TOESHR

TOPBEV

TOTWIL

TOTWIR

TSLABI

TTOE

TVOLl

TVOL2

TVOL3

TWALLH

UMOMN

UMOMP

UPLDN

UPLDP

USHRN

USHRP

VVIMP

VINF

VOLUM

VOLll

VOL12

VOLUMl

VOLUM2

VOLUM3

VOLUM4IVOLUM5

TOP SLAB THICKNESS IN FT. -SEEDED VALUETOP SLAB THICKNESS -DEFAULT OR INPUTTWISTING COUPLE ON FOOTINGTOTAL NEGATIVE MOMENT FOR SERVICE LOAD DESIGNTOTAL POSITIVE MOMENT FOR SERVICE LOAD DESIGNMAX. BAR SPACINGI

MIN. BAR SPACINGNSPAN+(EXTERIOR WALL+INTERIOR WALL)/2 IN FT.A SET OF REINFORCEMENT SPACINGSREINFORCEMENT SPACINGS AT CRITICAL SECTIONS

I

IF3.1'F3.1

w.w.

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F3.1

LIVE LOAD AXIAL FORCE OCCURED WITH MOMLDTLIVE LOAD AXIAL FORCE OCCURED WITH MOMLDC(FEM2-FEM1)/HITESP1 * HITE/2.0 + SP2 * HITE/6.0 -SPMSP1 * HITE/2.0 + SP2 * HITE/3.0 + SPMPRESS * H / 1000.0PRESS * HITE / 1000.0SPACING OF REBARREAL VALUE OF STEM THICKNESSSTEEL WEIGHTWINGWALL STEM THICKNESSSUM OF VERTICAL FORCES W1,W2,W3LIVE LOAD SURCHARGEINTERIOR WALL THICKNESSINTERMEDIATE SLAB THICKNESSTOP HAUNCHWINGWALL TOE WIDTHMOMENT AT TOETOE PRESSUREjTOE PRESSURE

F5.2

W.W.PSF

W.W.W.W.

TOP BEVEL IN IN.TOTAL LEFT WINGWALL LENGTH IN DECIMAL FT.TOTAL RIGHT WINGWALL LENGTH IN DECIMAL FT.TOP SLAB THICKNESSREAL VALUE OF TOETOTAL CONCRETE VOLUME OF BARRELTOTAL CONCRETE VOLUME OF WINGWALLTOTAL CONCRETE VOLUME OF BARREL+WINGWALLTOTAL WINGWALL HEIGHTTOTAL NEGATIVE MOMENT FOR LOAD FACTOR DESIGNTOTAL POSITIVE MOMENT FOR LOAD FACTOR DESIGNAXIAL FORCE OCCURED WITH UMOMNAXIAL FORCE OCCURED WITH UMOMP,TOTAL NEGATIVE SHEAR FOR LOAD FACTOR DESIGNI TOTAL POSITIVE SHEAR FOR LOAD FACTOR DESIGNSPANIMPACT FACTOR

I

SHEAR INFLUENCE LINE MATRIXCONCRETE VOLUMEUNIT VOLUME OF BARREL BOTTOM SLABUNIT VOLUME OF BARREL SIDE AND TOPBOTTOM SLAB CONCRETE VOLUMEBARREL WALL CONCRETE VOLUMETOP SLAB CONCRETE VOLUMELEFT HEADWAL CONCRETE VOLUMERIGHT HEADWALL CONCRETE VOLUME

F4.2 -INPUTw.w.

CY/FTCY/FTCY/FTCY/FTCY/FTCY/FTCY/FTCY/FTI

61

I

VOLUM6VOLUM7VSHRLNVSHRLPVSHRNVSHRPVWATWALLWALLHTWALLIZWALLMOWALLRWALLSHWALLZWCWDWDLFWDLBWDRFWDRBWDWWGTNWHEELWHEERWIDTHWIDTHLWIDTHRWIDTHFWINDRPWINGAWINGA

,WINGTYWLDRPBWLDRPFWLDRPFWLDRPFWLFSWLBSWRFSWRBSWLSKEBWLSKEFWRSKEBWRSKEFWSKLFWSKLBWSKRFWSKRBWSLFRWSLBRWSRFRWSRBRWSKLFJWSKLBJWSKRFJWSKRBJWTWVLFl

CY/FTCY/FT

TOTAL HEADWALL CONCRETE VOLUMETOTAL BARREL CONCRETE VOLUMENEGATIVE LIVE LOAD SHEAR FORCEPOSITIVE LIVE LOAD SHEAR FORCETOTAL NEGATIVE SHEAR OF SERVICE LOAD DESIGN

!TOTAL POSITIVE SHEAR OF SERVICE LOAD DESIGN

EXTERIOR WALL THICKNESSWINGWALL HEIGHTINTERIOR WALL THICKNESSWINGWALL MOMENTEXTERIOR WALL THICKNESS

IN.-SEEDED VALUEFT.

-DEFAULT OR INPUT

F4.2

F5.3

II

W.W.EXTERIOR WALL THICKNESS -DEFAULT OR INPUTWDW = (FI + 1.0) * WALLF* HITE * 150.0/(SPAN * FI)UNIFORM DEAD LOAD DUE TO FILL AND TOP SLABL F WINGWALL LENGTH FROM C J TO BOX FACEL B WINGWALL LENGTH FROM C J TO BOX FACER F WINGWALL LENGTH FROM C J TO BOX FACER B WINGWALL LENGTH FROM C J TO BOX FACEUNIFORM DEAD LOAD DUE TO WALLSA SET OF REINFORCING BARS UNIT WEIGHT IN PLF.ONE WHEEL LIVE LOADSPECIAL WHEEL LIVE LOADSTRAIGHT WINGWALL FACE WIDTH IN IN.STRAIGHT WINGWALL FACE WIDTH -LEFT SIDE IN IN.STRAIGHT WINGWALL FACE WIDTH -RIGHT SIDE IN IN.STRAIGHT WINGWALL FRONT FACE WIDTH IN FT.WINGWALL TOP DROP YES OR NOWINGWALLDATEHEADWALL TYPELEFT BACK WINGWALL TOP DROP IN FT.

I RIGHT FRONT WINGWALL TOP DROP IN FT.RIGHT BACK WINGWALL TOP DROP IN FT.LEFT FRONT WINGWALL TOP DROP IN FT.LEFT FRONT WINGWALL LENGTH IN INTEGER IN FT.LEFT BACK WINGWALL LENGTH IN INTEGER IN FT.RIGHT FRONT WINGWALL LENGTH IN INTEGER IN FT.RIGHT BACK WINGWALL LENGTH IN INTEGER IN FT.LEFT BACK WING WALL SKEW ANGLE INTEGER IN DEGREELEFT FRONT WING WALL SKEW ANGLE INTEGER IN DEGREERIGHT BACK WING WALL SKEW ANGLE INTEGER IN DEGREERIGHT FRONT WING WALL SKEW ANGLE INTEGER IN DEGREELEFT FRONT SKEWED WINGWALL LENGTH FT.lEFT BACK SKEWED WINGWALL LENGTH FT.RIGHT FRONT SKEWED WINGWALL LENGTH FT.RIGHT BACK SKEWED WINGWALL LENGTH FT.LEFT FRONT WINGWALL SKEW ANGLE IN RADIANLEFT BACK WINGWALL SKEW ANGLE IN RADIANRIGHT FRONT WINGWALL SKEW ANGLE IN RADIANRIGHT BACK WINGWALL SKEW ANGLE IN RADIANL F WINGWALL DISTANCE FROM CONSTRUCTION JOINTL B WINGWALL DISTANCE FROM CONSTRUCTION JOINTR F WINGWALL DISTANCE FROM CONSTRUCTION JOINTR B WINGWALL DISTANCE FROM CONSTRUCTION JOINTWD = FILL * EWGT + SLABF * 150.0 + (EDLU * 1000.0)LEFT FRONT WINGWALL CONCRETE VOLUME

62

WVLBlWVRFlWVRBlWVOLLFWVOLLBWVOLRFWVOLRBWVOLlWVOL2WVOL3WWCOVSWVSLFWVSLBWVSRFWVSRBWWHTLFWWHTLBWWHTRFWWHTRBWlW2w3XXDYZZFILL

LEFT BACK WINGWALL'CONCRETE VOLUMERIGHT FRONT WINGWALL CONCRETE VOLUME

I RIGHT BACK WINGWALL CONCRETE VOLUMELEFT FRONT WINGWALL CONCRETE VOLUMELEFT BACK WINGWALL CONCRETE VOLUMERIGHT FRONT WINGWALL CONCRETE VOLUMERIGHT. BACK WINGWALL CONCRETE VOLUMEUNIT CONCRETE VOLUME OF WINGWALL FOOTINGUNIT CONCRETE VOLUME OF WINGWALL WALLTOTAL CONCRETE VOLUME OF WINGWALLWINGWALL FRONT FACE CONCRETE COVERLEFT FRONT WINGWALL CONCRETE VOLUMELEFT BACK WINGWALL CONCRETE VOLUMERIGHT FRONT WINGWALL CONCRETE VOLUMERIGHT BACK WINGWALL CONCRETE VOLUMELEFT FRONT END WINGWALL HEIGHTLEFT BACK END WINGWALL HEIGHTRIGHT FRONT END WINGWALL HEIGHTRIGHT BACK END WINGWALL HEIGHTEARTH WEIGHT ON WINGWALL HEELWINGWALL STEM WEIGHTWINGWALL FOOT WEIGHTSLAB THICKNESSJOINT-DISPLACEMENT MATRIXINTERIOR WALL SLENDERNESS RATIO

I

C.Y./FT.C.Y./FT.C.Y./FT.C.Y./FT.

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CALCULATED FILL

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APPENDIX C

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allowable shear 60axle. 20, 60

axle weight. 6bar schedule. 19, 23, 34, 35, 41, 47, 58block.

56Boundary. iv, 1

contitions 1check. 20, 59compressive stress 57cover 22,30,39,44,56,57,63crack control. 14critical sections 60,61dead load. 24, 57degree of freedom 60environment. 22, 40, 41, 46, 47extension. 30, 56fatigue stress limits 14fill 20,24,25,57,59,60,63force matrix. 57, 60haunch 27,31,39,44,56,59,61headwall. 25, 27-31, 37, 39-42, 44, 46-48, 59-62height. ..vii, 6, 15, 16, 20, 25, 29, 31, 36, 37, 39, 40, 44, 46, 56-58,

60-63influence lines 21,50-53internal matrix. 5lateraldisplacem~nt 1level. vii, 14linear. 7live load. 6, 20, 24, 39, 44, 59, 62live load surcharge 27,61load 6,20,24,39,44,57-59,62load factor design. 10, 21, 32, 61matrix. iv, 1-5, 56, 57, 59-61, 63member. iv, 1-8, 10, 31, 33, 34, 50, 52, 53, 57, 59, 60member reference 34method vii,1,2,5,21,58minimum. vii, 8, 14, 15, 23, 26-28, 31, 59moment. 7, 15, 27, 32, 39, 44, 49, 50, 56-60, 62pressure. 6, 27, 40, 46, 58, 60, 61range. 14reinforcement ratio. 13, 24, 56, 60service load design. 7, 21, 32, 61, 62shear. 6, 8, 13, 21, 31-34, 39, 44, 49, 52, 58-62skew angle. 25, 28, 29, 40, 46, 59, 60slab. 24, 25, 39, 41, 44, 47, 56, 57, 59-62slenderness. 15soil weight. 21span. vii, 6, 20, 25, 33, 36, 37, 39, 40, 44, 46, 59-62steel. 7, 8, 10, 14, 21-23, 32, 39-42, 44, 46-48, 56, 61Stiffness. 1

matrix 2,56method. 1... 56stJ.ffnessmatrJ.x J.V,

stress. 21, 57, 58, 60, 33allowable. 14block. 7, 56check. 20

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compressive. 32, 57concrete 8,10,21,32fatigue. 14, 57level. 14linear. 7minimum. 14range. 14service load. 14shear 8,13,21,31-33,58,60

steel. 7, 21tensile. 58Stresses.

1tension. 8tensile.

14, 58tension 7,8,10,14,32,3'3,56tension steel. 10thickness 22,26,40,46,58,61tie-in length. 30truck.

6, 20, 32, 60wall. 12, 22, 25, 30, 39-41, 44, 46, 47, 57, 59, 62, 63water 6,10,27,31,39,44,57,60Weight. 6, 20, 21, 24, 27, 31, 41, 42, 47, 48, 57, 60-63wheel loads. 6width 6,31,40,46,56-59,61,62wingwall 17, 18, 29, 30, 39, 40, 42, 44, 46, 48, 56, 58, 61-63wingwallskewangle 28,29

~

76

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Mail to : Structures Design OfficeFlorida Department of Transportation605 Suwannee St., MS 33Tallahassee, Florida 32399-0450Attn: Liang Y. Hsia, P .E.Tel: (904) 488-6424, Fax: (904) 488-6352 November 1992

REINFORCED CONCRETE BOX CULVERT AND WINGWALL DESIGN · PDF filei i reinforced concrete box...

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