WisDOTPrestressedGirderDesignStudy (1)

SUPERSTRUCTURE AND SUBSTRUCTURE DESIGN SOFTWARE
COMPARED AGAINST HAND CALCULATIONS AND DESIGN
by
the requirements for the degree of
Master of Science
SUPERSTRUCTURE AND SUBSTRUCTURE DESIGN SOFTWARE
COMPARED AGAINST HAND CALCULATIONS AND DESIGN
APPROVED BY:
University of Wisconsin – Madison
i
Abstract
The purpose of this research was to evaluate and compare the design of bridge
components using automated LRFD bridge design software from Leap Software, Inc. and
hand calculated design. Three example bridges were chosen by the Wisconsin DOT in which
superstructure and substructure components were to be designed using the automated
superstructure design software CONSPAN and substructure design software RC-Pier. These
computer designs were run and comprehensively compared to the results obtained using hand
calculations. Detailed results, discussions, conclusions, and recommendations, particularly
with respect to the design of the prestressed, precast concrete girders, are presented in this
report.
This thesis document describes the process used to design the girders, pier caps, and
pier columns of the example bridges according to AASHTO LRFD Specifications with 2005
Interims using the automated software and using hand calculations, with a comprehensive
comparison between the computer and hand designs. It was determined that both the
CONSPAN and RC-Pier software performed automated design generally correctly, but it
appears that the calculated final values of girder prestress and final girder service stresses are
computed inaccurately in CONSPAN. Slight departures were also noticed in some of the
live load distribution factors and shear and moment envelopes for the prestressed, precast
concrete girders when the CONSPAN calculated values were compared against the hand
calculated values.
4.1.1 Bridge Superstructure Geometry ......................................................................6
4.1.2 Bridge Substructure Geometry .......................................................................11
4.2.1 Bridge Superstructure Geometry ....................................................................14
4.3.1 Bridge Superstructure Geometry ....................................................................22
5.2.1 Microsoft Excel...............................................................................................30
6.1 B-38-91: Two-Span Structure with Sidewalks ..........................................................35
6.1.1 Methodology of Hand Calculations................................................................36
6.1.1.2 Unfactored Composite Design Dead Loads on Bridge........................37
6.1.1.3 Unfactored Composite Design Live Loads on Bridge.........................38
6.1.1.4 Distribution of Unfactored Composite Design Lane and Truck Live
Loads on Interior Girders.................................................................41
6.1.1.5 Distribution of Unfactored Composite Design Lane and Truck Live
Loads on Exterior Girders................................................................44
6.1.1.12 Girder Stresses at Critical Sections....................................................68
6.1.1.13 Moment Capacity at Ultimate Strength .............................................70
6.1.1.14 Additional Calculations and Design ..................................................71

6.1.2.1 Project Tab Screen ...............................................................................74
6.1.2.2 Geometry Tab Screen ..........................................................................75
6.1.2.3 Materials Tab Screen ...........................................................................83
6.1.3.1 Consistency among CONSPAN Output Files......................................95
6.1.3.2 Distribution Factors .............................................................................95
6.1.3.3 Moment Envelopes ..............................................................................97
6.1.3.6 Prestress Losses and Gains ................................................................107
6.2 B-20-163: Three-Span Structure with Varying Span Lengths.................................114
6.2.1 Methodology of Hand Calculations..............................................................114
6.2.1.2 Unfactored Composite Design Dead Loads on Bridge......................116
6.2.1.3 Unfactored Composite Design Live Loads on Bridge.......................116
6.2.1.4 Distribution of Unfactored Composite Design Lane and Truck
Live Loads .....................................................................................117
6.2.1.8 Strand Drape and Strand Debond ......................................................125
6.2.1.10 Moment Capacity at Ultimate Strength ...........................................125
6.2.2 Methodology of CONSPAN Software Use ..................................................126
6.2.2.1 Project Tab Screen.............................................................................126
6.2.3.1 Distribution Factors ...........................................................................133
6.2.3.2 Moment Envelopes ............................................................................135
6.3 B-20-162: Three-Span Structure with Varying Cross Section ................................151
6.3.1 Methodology of Hand Calculations..............................................................152
6.3.3 Comprehensive Comparison between Hand and CONSPAN Results..........156
6.3.3.1 Distribution Factors ...........................................................................156
6.3.3.2 Moment Envelopes ............................................................................157
7. Reinforced Concrete Pier Design Results and Comparisons.............................................173
7.1 B-38-91: Multi-Column Pier....................................................................................174
7.2.1 Project Tab Screen ........................................................................................194
7.2.2 Geometry Tab Screen ...................................................................................195
References..............................................................................................................................222
Appendix................................................................................................................................223
A-1 Exterior Girder Dead Load Shear Hand Calculations ....................................225
A-2 Exterior Girder Live Load Shear Hand Calculations .....................................236
A-3 Exterior Girder Dead Load Moment Hand Calculations................................244
A-4 Exterior Girder Live Load Moment Hand Calculations .................................255
A-5 Exterior Girder Design Hand Calculations.....................................................263
A-6 Interior Girder Dead Load Shear Hand Calculations .....................................327
A-7 Interior Girder Live Load Shear Hand Calculations.......................................337
A-8 Interior Girder Dead Load Moment Hand Calculations.................................345
A-9 Interior Girder Live Load Moment Hand Calculations ..................................355
A-10 Interior Girder Design Hand Calculations....................................................363
B. B-20-163 Girder Hand Calculations .........................................................................426
B-1 Exterior Girder Dead Load Shear Hand Calculations.....................................427
B-2 Exterior Girder Live Load Shear Hand Calculations......................................454
B-3 Exterior Girder Dead Load Moment Hand Calculations ................................467

B-5 Exterior Girder Design Hand Calculations .....................................................507
B-6 Interior Girder Dead Load Shear Hand Calculations......................................558
B-7 Interior Girder Live Load Shear Hand Calculations.......................................585
B-8 Interior Girder Dead Load Moment Hand Calculations .................................598
B-9 Interior Girder Live Load Moment Hand Calculations ..................................625
B-10 Interior Girder Design Hand Calculations....................................................638
C. B-20-162 Girder Hand Calculations .........................................................................688
C-1 Exterior Girder Dead Load Shear Hand Calculations.....................................689
C-2 Exterior Girder Live Load Shear Hand Calculations......................................716
C-3 Exterior Girder Dead Load Moment Hand Calculations ................................729
C-4 Exterior Girder Live Load Moment Hand Calculations .................................756
C-5 Exterior Girder Design Hand Calculations .....................................................769
C-6 Interior Girder Dead Load Shear Hand Calculations......................................804
C-7 Interior Girder Live Load Shear Hand Calculations.......................................831
C-8 Interior Girder Dead Load Moment Hand Calculations .................................844
C-9 Interior Girder Live Load Moment Hand Calculations ..................................871
C-10 Interior Girder Design Hand Calculations....................................................884
D. B-38-91 Pier Hand Calculations ...............................................................................918
E. B-20-163 Pier Hand Calculations..............................................................................934
Figure 4.1.1-1: General plan of structure B-38-91, provided by WisDOT................................7
Figure 4.1.1-2: Cross section and quantities of structure B-38-91, provided by WisDOT. ......8
Figure 4.1.1-3: Superstructure drawing of B-38-91, provided by WisDOT..............................9
Figure 4.1.1-4: Diagram of girder and bridge span lengths. ....................................................10
Figure 4.1.2-1: Pier drawing of B-38-91, provided by WisDOT.............................................12
Figure 4.2.1-1: General plan of structure B-20-163, provided by WisDOT............................15
Figure 4.2.1-2: Cross section and quantities of structure B-20-163, provided by WisDOT. ..16
Figure 4.2.1-3: Superstructure drawing of B-20-163, provided by WisDOT..........................17
Figure 4.2.1-4: Diagram of girder and bridge span lengths. ....................................................18
Figure 4.2.2-1: Pier drawing of B-20-163, provided by WisDOT...........................................20
Figure 4.3.1-1: General plan of structure B-20-162, provided by WisDOT............................23
Figure 4.3.1-2: Cross section and quantities of structure B-20-162, provided by WisDOT. ..24
Figure 4.3.1-3: Superstructure drawing of B-20-162, provided by WisDOT..........................25
Figure 4.3.1-4: Diagram of girder and bridge span lengths and bridge geometry...................26
Figure 6.1.1.3-1: Characteristics of the HL-93 design truck (AASHTO Figure 3.6.1.2.2-1)..40
Figure 6.1.1.4-1: From AASHTO Table 4.6.2.2.2b-1 Distribution of Live Loads Per Lane for
Moment in Interior Beams...........................................................................................41
Figure 6.1.1.4-2: From AASHTO Table 4.6.2.2.3a-1 Distribution of Live Load per Lane for
Shear in Interior Beams. ..............................................................................................42
Figure 6.1.1.4-3: From AASHTO Table 4.6.2.2.3c-1 Correction Factors for Load
Distribution Factors for Support Shear of the Obtuse Corner. ....................................42
Figure 6.1.1.4-4: Excerpt from AASHTO Section 4.6.2.2.1 defining K g................................43

x
Figure 6.1.1.4-5: AASHTO Table C4.6.2.2.1-1 L for Use in Live Load Distribution Factor
Equations......................................................................................................................44
Figure 6.1.1.5-1: From AASHTO Table 4.6.2.2.2d-1 Distribution of Live Loads Per Lane for
Moment in Exterior Longitudinal Beams. ...................................................................45
Figure 6.1.1.5-2: From AASHTO Table 4.6.2.2.3b-1 Distribution of Live Load per Lane for
Shear in Exterior Beams. .............................................................................................46
Figure 6.1.1.8-1: Standard 54W” girder draped strand arrangement at centerline of span
(Sheet 14 of WisDOT plan set for B-38-91)................................................................54
Figure 6.1.1.8-2: Typical strand pattern for a 54W” girder (Sheet 14 of WisDOT plan set for
B-38-91).......................................................................................................................54
Figure 6.1.1.10-1: Excerpt from AASHTO LRFD section 5.9.5.2.3 Elastic Shortening. .......58
Figure 6.1.2.1-1: The first of six tabs in the CONSPAN program; the Project Tab Screen....74
Figure 6.1.2.2-1: Geometry Tab Screen...................................................................................75
Figure 6.1.2.2-2: Beam section add/edit window where the 54W” beam was defined. ..........78
Figure 6.1.2.2-3: Strand template window where the allowable strand locations were
defined..........................................................................................................................79
Figure 6.1.2.2-4: Strand patterns window where pre-defined strand patterns were inputted. .80
Figure 6.1.2.2-5: Multi-span window where the span and skew dimensions were inputted. ..81
Figure 6.1.2.2-6: Image window showing the layout of the bridge.........................................82
Figure 6.1.2.3-1: Materials Tab Screen. ..................................................................................83
Figure 6.1.2.4-1: Loads Tab Screen.........................................................................................84
Figure 6.1.2.5-1: Analysis Tab Screen.....................................................................................86
Figure 6.1.2.5-2: Analysis Factors window.............................................................................87
Figure 6.1.2.5-3: Resistance Factor/Losses tab in the Project Parameters window. ...............90
Figure 6.1.2.6-1: Beam Tab Screen. ........................................................................................92
Figure 6.1.2.6-2: Strand Pattern window for B-38-91 span 1 exterior girder..........................93
Figure 6.1.3.3-1: Strength I factored interior girder moment envelope...................................98
Figure 6.1.3.3-2: Strength I factored exterior girder moment envelope. .................................98
Figure 6.1.3.3-3: Service I factored interior girder moment envelope. ...................................99
Figure 6.1.3.3-4: Service I factored exterior girder moment envelope....................................99
Figure 6.1.3.3-5: Service III factored interior girder moment envelope................................100
Figure 6.1.3.3-6: Service III factored exterior girder moment envelope. ..............................100
Figure 6.1.3.4-1: Strength I factored interior girder shear envelope. ....................................102
Figure 6.1.3.4-2: Strength I factored exterior girder shear envelope.....................................102
Figure 6.1.3.4-3: Service I factored interior girder shear envelope. ......................................103
Figure 6.1.3.4-4: Service I factored exterior girder shear envelope. .....................................103
Figure 6.1.3.4-5: Service III factored interior girder shear envelope. ...................................104
Figure 6.1.3.4-6: Service III factored exterior girder shear envelope....................................104
Figure 6.2.1.4-1: Points of contraflexure under uniform composite dead load on all spans. 118
Figure 6.2.1.4-2: AASHTO Table 4.6.2.2.2e-1 Reduction of Load Distribution Factors for
Moment in Longitudinal Beams on Skewed Supports. .............................................119
Figure 6.2.1.6-1: Standard 72W” girder draped strand arrangement at centerline of span
(Sheet 11 of WisDOT plan set for B-20-163)............................................................123
Figure 6.2.1.6-2: Typical strand pattern for a 72W” girder (Sheet 11 of WisDOT plan set for
B-20-163)...................................................................................................................124
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Figure 6.2.2.2-2: Actual span geometry and span geometry used in CONSPAN. ................129
Figure 6.2.2.2-6: Multi-span window where the span and skew dimensions were inputted.130
Figure 6.2.2.4-1: Loads Tab Screen.......................................................................................131
Figure 6.2.3.2-2: Strength I factored exterior girder moment envelope. ...............................136
Figure 6.2.3.2-3: Service I factored interior girder moment envelope. .................................137
Figure 6.2.3.2-4: Service I factored exterior girder moment envelope..................................137
Figure 6.2.3.3-1: Strength I factored interior girder shear envelope. ....................................140
Figure 6.2.2-1: AASHTO commentary C4.6.2.2.1................................................................153
Figure 6.3.3.2-1: Strength I factored interior girder moment envelope.................................158
Figure 6.3.3.2-2: Strength I factored exterior girder moment envelope. ...............................158
Figure 6.3.3.2-3: Service I factored interior girder moment envelope. .................................159
Figure 6.3.3.2-4: Service I factored exterior girder moment envelope..................................159

Figure 7.1.1-1: The first of seven tabs in the RC-Pier program; the Project Tab Screen......175
Figure 7.1.2-1: Geometry Tab Screen....................................................................................176
Figure 7.1.2-5: Column input screen. ....................................................................................179
Figure 7.1.2-6: Bearing Line input screen. ............................................................................180
Figure 7.1.2-7: Materials input screen...................................................................................181
Figure 7.1.3-1: Loads Tab Screen..........................................................................................183
Figure 7.1.4-1: Analysis Tab Screen with the A/D Parameters input screen open................185
Figure 7.1.5-1: Cap Tab Screen. ............................................................................................187
Figure 7.1.6-1: Column Tab Screen.......................................................................................190
Figure 7.1.6-1: Pier column interaction diagram and worst-case Strength I column load. ...192
Figure 7.2.1-1: The first of seven tabs in the RC-Pier program; the Project Tab Screen......194
Figure 7.2.2-1: Geometry Tab Screen....................................................................................195

Figure 7.2.2-5: Column input screen. ....................................................................................199
Figure 7.2.2-6: Bearing Line input screen. ............................................................................200
Figure 7.2.2-7: Materials input screen...................................................................................201
Figure 7.2.3-1: Loads Tab Screen..........................................................................................204
Figure 7.2.4-1: Analysis Tab Screen with the A/D Parameters input screen open................206
Figure 7.2.5-1: Cap Tab Screen. ............................................................................................208
Figure 7.2.6-1: Column Tab Screen.......................................................................................211

List of Tables
Table 6.1.1.1-1: Simply supported dead loads acting on typical interior and exterior
girders. .........................................................................................................................37
Table 6.1.1.2-1: Composite dead loads acting on typical interior and exterior girders...........38
Table 6.1.1.3-1: Composite live loads acting on the bridge. ...................................................39
Table 6.1.1.7-1: Load factors used for Strength I, Service I, and Service III conditions. .......49
Table 6.1.1.7-2: Summary of load cases..................................................................................50
Table 6.1.1.7-3: Summary of load combinations.....................................................................51
Table 6.1.1.10-1: Load step moments used in prestress gain calculations. .............................62
Table 6.1.1.10-2: Variables used in prestress gain calculations for the typical interior
girder............................................................................................................................63
Table 6.1.1.10-3: Gains from load step 1 (additional simply supported dead load) for the
typical interior girder. ..................................................................................................64
Table 6.1.1.10-4: Gains from Load Step 2 (composite dead load) for the typical interior
girder............................................................................................................................65
Table 6.1.1.10-5: Gains from Load Step 3 (composite live load) for the typical interior
girder............................................................................................................................66
Table 6.1.1.12-1: Variables used in girder stress calculations for the midspan girder bottom
and top stresses at transfer and at Service I final condition for the typical interior
girder............................................................................................................................69
Table 6.1.2.2-1: Differences between LEAP defined Wisconsin girder sections and actual
girder sections. .............................................................................................................77

Table 6.1.3.5-2: Calculated composite beam section properties. ..........................................106
Table 6.1.3.5-3: Calculated concrete stress limits. ................................................................106
Table 6.1.3.6-1: Instantaneous loss of prestress. ...................................................................107
Table 6.1.3.6-2: Gains of prestress and adjustments to gains (negative value
indicates a gain). ........................................................................................................108
Table 6.1.3.6-3: Time dependent loss of prestress using the AASHTO Approximate
Method. ......................................................................................................................110
Table 6.1.3.7-1: Computed girder stresses at midspan. .........................................................111
Table 6.1.3.7-2: Computed girder stresses at end of strand transfer length...........................111
Table 6.1.3.7-3: Computed girder stresses at hold down (harp) point...................................112
Table 6.1.3.8-1: Computed girder moment capacity at ultimate strength. ............................113
Table 6.2.1.1-1: Simply supported dead loads acting on span 3 typical interior and exterior
girders. .......................................................................................................................115
Table 6.2.1.2-1: Composite dead loads acting on typical span 3 interior and exterior
girders. .......................................................................................................................116
Table 6.2.1.3-1: Composite live loads acting on the bridge. .................................................116
Table 6.2.1.5-1: Load factors used for Strength I, Service I, and Service III conditions. .....120
Table 6.2.1.5-2: Summary of load cases................................................................................121
Table 6.2.1.5-3: Summary of load combinations...................................................................122
Table 6.2.3.1-1: Comparison of calculated span 3 distribution factors. ................................134
Table 6.2.3.4-1: Calculated concrete properties. ...................................................................144

Table 6.2.3.5-1: Instantaneous loss of prestress for span 3 girders. ......................................145
indicates a gain). ........................................................................................................146
Method. ......................................................................................................................147
Table 6.3.3.1-1: Comparison of calculated span 3 distribution factors. ................................157
Table 6.3.3.4-1: Calculated concrete properties. ...................................................................166
Table 6.3.3.4-2: Calculated composite beam section properties. ..........................................166
Table 6.3.3.5-1: Instantaneous loss of prestress for span 3 girders. ......................................167
indicates a gain). ........................................................................................................168
Method. ......................................................................................................................169


1 INTRODUCTION
The specifications that govern bridge design at agencies in the United States are
constantly being updated as the knowledge base for bridge design and bridge performance
increases. Currently, the U.S. Department of Transportation Federal Highway
Administration (FHWA) is in the process of mandating the use of Load and Resistance
Factor Design (LRFD) for the design of bridges. After October 1, 2007, all new bridges in
which preliminary engineering begins must be designed by the LRFD Specifications.
Culverts, retaining walls, and other standard structures must be designed using the LRFD
Specifications if preliminary engineering of these structures occurs after October 1, 2010
(www.fhwa.dot.gov). The FHWA website provides a very well-written background on the
subject of bridge design specifications, so it is presented here exactly as written:
“Since the adoption of the first AASHTO (American Association of State Highway
and Transportation Officials) Specifications in 1931, the body of knowledge in bridge
research and design has been growing tremendously. A TRB research program (1987)
concluded that the Standard Specifications include gaps and inconsistencies, and do not
utilize the latest design philosophy and knowledge.
When AASHTO began publishing the Standard Specifications for Highway Bridges
in the 1930s, one factor of safety was used. The methodology was called Allowable Stress
Design (ASD). In the 1970s, AASHTO began varying the factor of safety for each load in
relation to the engineer’s ability to predict the corresponding load. This bridge design
methodology was named Load Factor Design (LFD). AASHTO made this change from ASD
to LFD in the form of interim revisions to the Standard Specifications for Highway Bridges.
AASHTO had never totally rewritten its Standard Specifications.
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Today, the bridge engineering profession is moving to Load and Resistance Factor
Design (LRFD) and new specifications with a framework to implement new technology for
decades to come. The new specifications utilize state-of-the-art analysis and design
methodologies, and make use of load and resistance factors based on the known variability of
applied loads and material properties. The load and resistance factors are calibrated from
actual bridge statistics to ensure a uniform level of safety. The designer focuses on a design
objective or limit state, which can lead to a similar probability of failure in each component.
Bridges designed with the LRFD specifications should have more uniform levels of safety,
which should lead to superior serviceability and long-term maintainability.” (Quoted directly
from http://www.fhwa.dot.gov/bridge/lrfd/plan.cfm, accessed on June 22, 2006).
The Wisconsin Department of Transportation is in the process of implementing
AASHTO LRFD Specifications, and as part of this implementation, is searching for new,
automated bridge superstructure and substructure design software. The purpose of this report
is to provide an analysis of two such software packages, the superstructure design software
CONSPAN, and the substructure design software RC-Pier, both from Leap Software, Inc.
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2 PROBLEM STATEMENT
The Wisconsin DOT is in the process of implementing AASHTO LRFD
Specifications for Wisconsin bridge structures, which are currently designed using AASHTO
LFD Standard Specifications. Part of this implementation involves finding new, automated
LRFD superstructure and substructure design software. Two such software programs,
CONSPAN and RC-Pier from Leap Software, Inc., perform automated bridge superstructure
design (CONSPAN) and substructure design (RC-Pier). The requirements for this research
involved hand designing components of three example bridges, including prestressed, precast
concrete girders and reinforced concrete pier caps and pier columns, and comparing the hand
calculated designs with the automated software designs. The heaviest emphasis was placed
on comprehensively comparing the CONSPAN designed prestressed concrete girders against
hand calculations, with less emphasis placed on comparing the RC-Pier pier cap and pier
column designs against hand calculations. The overall purpose of this project is to provide
independent software design testing under the University of Wisconsin-Madison for Leap
Software, Inc. as required by the Wisconsin DOT.
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3 SCOPE OF WORK
The scope of work required for this project includes the hand design and automated
software design for the prestressed, precast concrete girders and reinforced concrete pier caps
and pier columns of three example bridges chosen by WisDOT using AASHTO LRFD
Specifications and comparing the software designs against the hand designs. Following is a
bulleted list detailing the specific scope of work for this project.
• Wisconsin bridge structure B-38-91
o Design worst case interior and exterior girder using hand calculations
o Design worst case interior and exterior girder using CONSPAN
o Perform a fully comprehensive and detailed comparison between hand
calculated and CONSPAN generated girder designs
o Design intermediate pier cap and worst case pier column using RC-Pier
o Design-check the RC-Pier pier cap and pier column designs using hand
calculations and report findings
• Wisconsin bridge structure B-20-163
o Design worst case interior and exterior girder using hand calculations
o
o Perform a fully comprehensive and detailed comparison between hand
calculated and CONSPAN generated girder designs
o Design worst case intermediate pier cap and pier column using RC-Pier
o Design-check the RC-Pier pier cap and pier column designs using hand
calculations and report findings
Design worst case interior and exterior girder using hand calculations
o Design worst case span 3 interior and exterior girder using CONSPAN per
Wisconsin DOT recommendation for software analysis (described in more
detail later)
The scope of work for this project did not include an investigation using AASHTO
Standard LFD Specifications for any bridge components, and it did not include the design of
bridge decks, abutments, footings, diaphragms, bearings, or any other bridge components
outside the bulleted list of items presented in this chapter. This report is intended to be used
as an informational tool that presents the CONSPAN and RC-Pier software in their current
versions, the software designs, the hand calculated designs, and how the designs compare at
the time of this writing. Significant effort was made to ensure the correctness and accuracy
of all calculations presented in this report.
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4 DESCRIPTION OF STRUCTURES
In this chapter, the properties and geometries of the three example bridge structures
will be presented. The first structure, Wisconsin Bridge B-38-91, is a two-span structure
with sidewalks, is designed using Wisconsin 54W” girders, and has an intermediate multi-
column pier. The second structure, Wisconsin Bridge B-20-163, is a three-span structure
with varying span lengths, is designed using Wisconsin 72W” girders, and has intermediate
linearly tapered rectangular piers. The third structure, Wisconsin Bridge B-20-162, is nearly
identical to B-20-163, but has a varying cross-section with splayed girders on the middle
span because of an onramp that merges onto the roadway over part of the bridge. Each
example bridge is presented in this chapter.
4.1 Example Bridge B-38-91 Geometry and Materials
Structure B-38-91 has two equal spans and was designed using Wisconsin 54W”
girders. This bridge also has two pedestrian sidewalks, one on each side of the bridge. The
properties of this bridge are presented in three parts; superstructure geometry, substructure
geometry, and materials of the bridge.
4.1.1 Bridge Superstructure Geometry
Like all three example bridges, B-38-91 is a prestressed concrete girder
superstructure bridge with a reinforced concrete deck supported on simple span prestressed
girders that are made continuous (after the slab cures) for post dead loads and live loads. The
following figures illustrate the geometry of the superstructure.
6
Figure 4.1.1-1: General plan of structure B-38-91, provided by WisDOT.
7

Figure 4.1.1-2: Cross section and quantities of structure B-38-91, provided by WisDOT.
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The relevant superstructure geometry that was used for design, which can be seen in
the previous figures, is as follows:
• Two 119’-0” spans
o 75’-0” wide by 0’-8” thick deck
o 68’-0” clear width between sidewalk curbs (total of 5 design lanes)
o 7’-0” wide by 0’-8” thick sidewalk on each side of bridge (1’-0” of each
sidewalk taken by parapet, leaving two 6’-0” wide pedestrian sidewalks)
• Left hand forward skew of 27 degrees
• Wisconsin 54W” girders
o 9 girders spaced at 8’-6” with 3’-6” deck overhang on each side of bridge
o Typical precast beam length of 119’-4 ½”
o Typical simple span beam length of 118’-4 ½”
o Typical continuous span beam length of 119’-0”
• Vertical face parapet “A” with chain link fence on exterior 1’-0” of each sidewalk
• 6’-0” wide by 0’-6” high median
• Two intermediate steel diaphragms per space between girders, per span
4.1.2 Bridge Substructure Geometry
This bridge has an intermediate multi-column bent pier between the two spans, which
is illustrated in the following figure.
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The relevant substructure geometry that was used for design, which can be seen in the
previous figure, is as follows:
• Five 24’-0” tall by 3’-0” diameter columns spaced at 18’-0” on center
• 3’-6” wide by 3’-6” deep (for analysis simplicity) by 81’-0” long bent
4.1.3 Bridge Materials
The main materials used for bridge design were concrete and steel, and the material
properties used for the design of each bridge component are as follows.
• Prestressed girders
o 0.6” diameter grade 270 low relaxation steel prestressing strands
• Deck slab
o Grade 60 steel reinforcing bars
• Pier bent and column
o Grade 60 steel reinforcing bars
13
Structure B-20-163 has three unequal spans and was designed using Wisconsin 72W”
girders. The properties of this bridge are presented in three parts; superstructure geometry,
substructure geometry, and materials of the bridge.
Like all three example bridges, B-20-163 is a prestressed concrete girder
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17
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• Three unequal spans: span 1 = 129’-1”; span 2 = 130’-0”; span 3 = 150’-0”
• Total overall superstructure width of 37’-8”
o 37’-8” wide by 0’-8” thick deck
o 34’-0” clear width between parapets (total of 2 design lanes)
• Right hand forward skew of 47 degrees
• Wisconsin 72W” girders
o 5 girders spaced at 7’-9” with 3’-4” deck overhang on each side of bridge
o Precast beam length: span 1 = 129’-9”; span 2 = 129’-9”; span 3 = 150’-8”
o Simple spans: span 1 = 128’-5 ½”; span 2 = 128’-9”; span 3 = 149’-4 ½”
o Continuous spans: span 1 = 129’-1”; span 2 = 130’-0”, span 3 = 150’-0”
• Sloped face parapet “LF” (modified) barriers
This bridge has two intermediate piers; one between the first and middle span, and
one between the middle and last span. The following figure illustrates the substructure of the
bridge.
19
20

The relevant substructure geometry that was used for design, which can be seen in the
previous figure, is as follows:
• For simplicity, two 20’-0” tall by 3’-9” thick linearly tapered rectangular columns
o Column base width = 8’-3”
o Column top width = 12’-9”
• 4’-0” wide by 4’-0” deep (for analysis simplicity) by 50’-6” long bent
The materials used for this bridge design are the same as the materials used for the
design of structure B-38-91.
Structure B-20-162 has three unequal spans and was designed using Wisconsin 72W”
girders. The geometry of this bridge is unique since an onramp is accommodated by the
bridge cross section to allow the lane to merge into the roadway over the length of the bridge.
Because of this, the girders are splayed in the middle span, and the first span has a larger
spacing of girders than the last span. Also, the bridge deck and cross section vary along the
length of the bridge. The properties of this bridge are presented in three parts; superstructure
geometry, substructure geometry, and materials of the bridge.
Very similar to structure B-20-163, B-20-162 is a prestressed concrete girder
22
23

24
25

Figure 4.3.1-4: Diagram of girder and bridge span lengths (left) and bridge geometry (right).
26

• Three unequal spans: span 1 = 129’-1”; span 2 = 130’-0”; span 3 = 150’-0”
• Varying overall superstructure width
• Wisconsin 72W” girders of varying lengths (see previous figures)
• Sloped face parapet “LF” (modified) barriers
This bridge has two intermediate piers; one between the first and middle span, and
one between the middle and last span. The piers are similar to those on structure B-20-163,
but since they were not designed for this report (refer to the “Scope of Work” chapter), they
are not described in detail here.
The materials used for this bridge design are the same as the materials used for the
design of structure B-38-91 and B-20-163.
27
5 DESCRIPTION OF SOFTWARE
This chapter describes the software used for this project and report, and is divided
into two main parts. The first part of this chapter presents and describes the automated
bridge design software from LEAP Software, Inc. that was used to produce designs of
various bridge components on the example bridges. These designs were compared to the
design results calculated by hand, and the software programs used to aid in hand calculations
are presented and described in the second part of this chapter.
5.1 Bridge Design Software
Two bridge design software programs were provided by LEAP Software, Inc. that
were used to auto-design bridge components, which were compared to hand calculated
designs. The two programs, CONSPAN and RC-Pier, are described in this section.
5.1.1 CONSPAN
CONSPAN Version 4.0.0, published by LEAP Software, Inc., is automated
superstructure design software that was used to produce girder designs for the example
bridges using LRFD. The program can be used for precast/prestressed bridge beam analysis,
design, and load rating per AASHTO Standard or LRFD Specifications. The program
requires user input for bridge geometry, bridge material properties, and bridge design loads.
Many of these values can be auto-generated or left as default, and CONSPAN will run a
structural analysis to produce force envelope values that are then used to design the
prestressing and reinforcing steel.
From the “About CONSPAN” section on page IN-2 of the CONSPAN user manual,
“CONSPAN is a comprehensive program for the AASHTO Standard and LRFD design,
analysis and load rating of simple – and multiple – span precast and prestressed bridge
28

beams.” Also in this section of the user manual is a bulleted list of some of the main features
of the program.
RC-Pier Version 4.1.0, published by LEAP Software, Inc., is automated substructure
and foundation design software that was used to produce pier cap and pier column designs
for the example bridges using LRFD. The program can be used for AASHTO LFD and
LRFD analysis and design of reinforced concrete bridge substructures and foundations. The
program requires user input for pier geometry, pier material properties, and pier design loads.
Many of these values can be auto-generated or left as default, and RC-Pier will run a
structural analysis to produce force envelope values that are then used to design the concrete
cap, column, or footing reinforcing steel.
From the “About RC-Pier” section on page IN-1 of the RC-Pier user manual, “RC-
Pier is an integrated tool for the AASHTO Standard and LRFD analysis and design of
reinforced concrete bridge substructures and foundations. By incorporating both LFD and
LRFD specifications in one interface, RC-Pier makes the transition to LRFD simple and
efficient. RC-Pier allows users to design multi-column and hammerhead piers, straight,
tapered or variable caps, and circular, rectangular (tapered and non-tapered) or drilled-shaft
columns. Footing types include isolated or combined, supported on either soil or piles.
There is no limit to the number of loads, bearings and piles that may be included in the
design. Analysis results are presented in a variety of easy-to-view formats.” Also in this
section of the user manual is a bulleted list of some of the main features of the program.
29
5.2 Software Used for Hand Calculations
Several software programs were used to aid in the hand calculation process that was
used to produce design results that were compared to the automated software designs. These
programs are briefly described in this section.
5.2.1 Microsoft Excel
Microsoft Excel 2000, a spreadsheet and data manipulation software program, was
used extensively for hand calculations. This program was used for data entry, equation
calculations, plot generation, and importation of data from structural analysis programs and
results files.
A pre-written Excel spreadsheet was also used for hand calculations. Available free
for use from www.yakpol.net, a spreadsheet called ShortCol was used for pier column
calculations. The spreadsheet calculates the axial force – bending moment interaction
diagram for short reinforced concrete columns.
5.2.2 PC Bridge
PC Bridge Version 2.60 is a bridge analysis program that generates load envelopes
for moving loads across a continuous beam. This program was used to produce unfactored,
undistributed shear, moment, and reaction envelopes for moving truck loads and/or
composite dead and live loads along the length of a given bridge superstructure.
From the PC Bridge user manual, “PC Bridge analyzes the forces on a continuous
beam over simple supports. Each span can have a different flexural stiffness EI. A series of
concentrated loads is “stepped” along the beam and maximum moment (positive and
negative), shear (absolute), and deflection (negative) are stored for presentation as load
ENVELOPES. PC Bridge can also analyze a single span bridge and/or stationary load(s).
30

PC Bridge employs a matrix method of structural analysis, specifically the three-moment
method of solution along with singularity functions to calculate shear, moment and deflection
at any location along the bridge.”
5.2.3 RISA 3D
RISA 3D Version 4.5 is a powerful structural analysis program that was used mainly
to supplement PC Bridge for girder hand calculations. For trapezoidal distributed composite
loads, like those seen in the example bridge B-20-162 because of the splayed girders and
inconsistent cross section, RISA 3D was used to produce shears, moments, and reactions
where PC Bridge was unable to due to the limitations of PC Bridge. RISA 3D was also used
to aid hand calculation and analysis of piers.
5.2.4 Microstation
Microstation Version 08.05.01.25 is a computer aided drafting program, similar to the
more popular AutoCAD, that was used to produce various drawings used in this report. It
was also used to create geometrically accurate drawings of various bridge components or
layouts in order measure accurate dimensions for use in hand or computer calculations and
designs.
5.2.5 MathCAD
MathCAD Version 13.0 is a powerful mathematical tool that was used extensively for
hand calculations. This program was used to perform the bulk of the hand calculations in
order to clearly present the equations and calculation process used while minimizing
calculation and unit errors.
Paraphrased from the built-in MathCAD “Help” menu, MathCAD can be used to
perform, document, and share calculations and design work. It has a “visual format and a
31
worksheet – making MathCAD ideal for knowledge capture, calculation reuse, and
engineering collaboration.” MathCAD allows for the design and documentation of
engineering work with unit-aware calculations.
32
6 PRESTRESSED GIRDER DESIGN RESULTS AND COMPARISONS
In this chapter, prestressed girder designs for three bridge structures will be presented
and compared. Typical interior and exterior prestressed concrete girders for each of the three
bridge structures described earlier (B-38-91, B-20-163, and B-20-162) were designed using
the CONSPAN software and using hand calculations. CONSPAN was set to design using
“AASHTO LRFD Bridge Design Specifications” and hand calculations were also done
according to the same specifications.
Initially, hand calculations were done independently of the CONSPAN analysis.
However, once the CONSPAN results were produced, it was clear that the hand calculations
needed to be revised in order to be more comprehensively compared to the CONSPAN
results. The main reason for the new hand calculations was a difference in design
philosophies between CONSPAN design and hand design. Further explanation and details of
these differences will be presented in this chapter.
For each bridge structure, the hand calculated results and CONSPAN calculated
results will be separately presented, then comparatively presented and discussed. Results
from independent hand calculations will be mentioned, however, the revised hand
calculations will be used in this comparison. As mentioned, the difference in design
philosophies will be explained in this chapter, primarily along with the results and
comparisons of structure B-38-91 in the next section. Since this bridge structure will be the
first bridge presented in this chapter, and because the difference in design philosophies is the
same among all bridges, the design differences will be presented and explained thoroughly
within the girder design results comparison of B-38-91, but will not be presented in depth in
the sections for the other two structures. This should help to clarify the design steps and
33

differences by presenting them in the order in which calculations and differences were
discovered. Also, the key hand calculation design steps will be presented in detail as well as
key observations and considerations found or needed while operating CONSPAN. Full
calculations can be found in the Appendix.
34
6.1 B-38-91: Two-Span Structure with Sidewalks
This structure, as mentioned earlier, has two equal spans and was designed using
Wisconsin 54W” girders. This bridge also has two pedestrian sidewalks; one on each side of
the bridge. “AASHTO LRFD Bridge Design Specifications” is not explicit or clear on how
to incorporate sidewalk considerations in design, so a detailed discussion and solution to this
issue is presented. B-38-91 was the first bridge in which the hand calculated and
CONPSPAN designs were compared, so special attention was paid to design details and
eliminating any inconsistencies between hand calculations and CONSPAN input. Also, the
consistency between similar CONSPAN girder designs was checked to ensure all CONSPAN
designed exterior girders were identical, as well as all CONSPAN designed interior girders.
Furthermore, if any input calculated by CONSPAN did not match identically with its hand
calculated counterpart, if it could be adjusted in CONSPAN, it was. This primarily occurred
with distribution factors for moment and shear, and will be covered in more detail later.
35
6.1.1 Methodology of Hand Calculations
Hand calculations were done in two main parts. The first part was to calculate the
moment and shear envelopes, and the second part was to design the interior and exterior
girders using the calculated moment and shear envelope values from part one. These two
main parts are broken down for this report into individual design components, which are
presented in this fashion for easy reference.
6.1.1.1 Unfactored Simply-Supported Design Dead Loads on Bridge
Three sets of loads were applied to each typical interior and exterior girder. The first
set included all non-composite dead loads, which are defined as the self-weight of bridge
components that act on the simply supported girder before and up to the installation of the
deck slab. The second set included composite dead loads, which are defined as the self-
weight of bridge components that act on the continuous composite girder after the deck has
been placed and the girder has become composite with the deck. These loads are treated as
composite loads, meaning that once the girders and deck slab are in place, they are
considered to be one continuous beam spanning the entire bridge distance. The third set of
loads included composite live loads, which in this case are defined as the additional loads on
the bridge from traffic. Since traffic loads are not constant, these live loads can be anywhere
on the bridge surface, and were analyzed in order to produce the worst possible loading
situations.
The following table lists the non-composite dead loads acting on a typical interior and
exterior girder for B-39-91. These loads were used to produce unfactored simply supported
dead load moment and shear values along the length of each girder, which were calculated by
hand using shear and moment equations for a simply supported, uniformly loaded beam.
36

Table 6.1.1.1-1: Simply supported dead loads acting on typical interior and exterior girders.
Girder Self-Wt Slab Self-Wt Steel Diaphragm Haunch Self-Wt
Interior Girder 831 lb/ft 850 lb/ft 6.14 lb/ft 31 lb/ft
Exterior Girder 831 lb/ft 775 lb/ft 3.07 lb/ft 31 lb/ft
These calculations were based on a concrete density of 150 lb/ft 3 for reinforced
concrete (AASHTO T3.5.1-1 and 3.5.1), a deck thickness of 8 inches per design, and a
minimum haunch depth of 2 inches. The girder self-weight is given by the girder properties
of a 54W” typical girder, and the slab self-weight is based on the tributary fraction of the
deck imposed on the girder. For example, the interior girders are spaced 8.5 ft. from one
another, so each girder takes 8.5 ft. of tributary width from the deck. The exterior girder
takes the entire overhang load (3.5 ft.) and half the deck load between the 8.5 ft. spaced
girders (4.25 ft.) for a tributary width of 7.75 ft. The steel diaphragm weight was estimated
for each diaphragm based on the amount of steel used, then totaled and treated as a
distributed load along the length of each girder equally, with exception of the exterior girders
which only see half the diaphragm load since only one side of the exterior girder is connected
to steel diaphragms. Assuming a bridge deck cross-slope of 2% and a minimum haunch of 2
inches as specified in section 19.3 of the Wisconsin Bridge Manual, which states that the
present practice is to use a 2 inch minimum haunch for design but an average of 2.5 inches
for computing quantities, the haunch weight was computed for a 4 ft. girder flange width.
6.1.1.2 Unfactored Composite Design Dead Loads on Bridge
Composite dead loads are applied after the composite deck slab is poured and cured.
The separate spans of the structure are now considered to be one continuous span with
37

intermediate supports. The following table lists the composite dead loads acting on a typical
interior and exterior girder for B-39-91. These loads were used to produce unfactored
composite dead load moment and shear values along the length of each girder using the
PCBridge structural analysis software.
Table 6.1.1.2-1: Composite dead loads acting on typical interior and exterior girders.
FWS Sdwk Self-Wt Median Self-Wt Rail/Fence
Interior Girder 137.8 lb/ft 155.6 lb/ft 50 lb/ft 86 lb/ft
Exterior Girder 137.8 lb/ft 155.6 lb/ft 50 lb/ft 86 lb/ft
Based on the same concrete density used for non-composite dead loads, each
composite dead load was totaled and distributed evenly among all girders as permitted by
section 4.6.2.2.1 of “AASHTO LRFD Bridge Design Specifications”. The future wearing
surface (FWS) was taken as 20 psf over the bridge surface, excepting the area taken by the
median and sidewalk. Both the sidewalk and median self-weight were calculated using the
cross-sectional dimensions of each. The rail and fence were lumped together as a load of 387
lb/ft for each, which accounts for the vertical face parapet “A” weight of 345 lb/ft and an
estimate of the linear weight of the fence. The load of 387 lb/ft was specifically chosen since
it is the weight of an “LF” type parapet, so the future replacement of the current parapet with
an “LF” type parapet could be accommodated.
6.1.1.3 Unfactored Composite Design Live Loads on Bridge
Composite live loads are also applied after the composite deck slab is poured and
cured, but these loads can be applied in patterns on the bridge in order to produce the worst
loading scenario, and are also subject to applicable distribution factors. The following table
38
and figure illustrates the undistributed and unfactored composite live loads acting on the
bridge. These loads were used to produce unfactored composite live load moment and shear
values along the length of the bridge using the PCBridge structural analysis software.
Table 6.1.1.3-1: Composite live loads acting on the bridge.
Total Pedestrian Load Design Lane Load (Per Lane) Design Truck Loads
900 lb/ft 640 lb/ft Explained Below
The pedestrian load was calculated using a pedestrian live load of 75 psf (AASHTO
3.6.1.6) over two 6’-0” sidewalks, yielding an unfactored, undistributed pedestrian live load
of 900 lb per foot of bridge length. The unfactored, undistributed design lane live load is
specified by AASHTO 3.6.1.2.4 as 640 lb/ft per design lane.
39

There are three design truck loads that were used in design; the HL-93 design truck,
the design tandem, and the negative moment truck. The HL-93 design truck is illustrated in
the following figure, with three axles; the first two are spaced 14 feet apart and are 8 kips and
32 kips of load, respectively. The third axle is spaced anywhere from 14 feet to 30 feet,
whichever results in the most extreme load event, and has a load of 32 kips.
Figure 6.1.1.3-1: Characteristics of the HL-93
design truck (AASHTO Figure 3.6.1.2.2-1).
The design tandem (not illustrated), also called the alternate military load, consists of
two axles spaced 4 feet apart at 25 kips per axle. Lastly, the negative moment truck consists
of 90 percent of two HL-93 design trucks, each having their rear axles spaced at 14 feet. The
two trucks are separated by 50 feet, measured from the rear axle of the forward-most truck to
the front axle of the following truck. The vehicular live loading on the bridge consists of the
combination of either the HL-93 truck or tandem truck and design lane load, or 90 percent of
40

the negative moment truck combined with 90 percent of the design lane load (AASHTO
3.6.1.3.1). Using the PCBridge software, the moments and shears caused by each design
truck were calculated every six inches as the truck moved along the length of the bridge, in
either direction, in order to find the maximum and minimum moments and maximum shear at
each increment along the bridge length.
6.1.1.4 Distribution of Unfactored Composite Design Lane and Truck Live Loads on Interior
Girders
Both the truck loads and design lane loads are applied to individual girders based on a
distribution factor calculated using AASHTO equations. For the interior girders, the
distribution factor for moments was calculated using the equations provided for a type “K”
bridge in AASHTO Table 4.3.2.2.2b-1, and the distribution factor for shear was calculated
using the equations provided for a type “K” bridge in AASHTO Table 4.6.2.2.3a-1 with a
correction factor for skewed bridges applied, which was calculated using the equation
provided in AASHTO Table 4.6.2.2.3c-1. The following figures from AASHTO show the
equations used for truck and lane load distribution to each interior girder.
Figure 6.1.1.4-1: From AASHTO Table 4.6.2.2.2b-1 Distribution of Live Loads Per Lane for
Moment in Interior Beams.

Figure 6.1.1.4-2: From AASHTO Table 4.6.2.2.3a-1 Distribution of Live Load per Lane for Shear in Interior Beams.
Figure 6.1.1.4-3: From AASHTO Table 4.6.2.2.3c-1 Correction Factors for Load
Distribution Factors for Support Shear of the Obtuse Corner.
Using the equations from AASHTO, the distribution factors for moment and shear to
the interior girders were calculated and multiplied by the moment and shear values,
respectively, obtained from the PCBridge analysis of the design lane load and design truck
loads. The variables in the AASHTO formulas are defined as follows:
S = spacing of beams = 8.5 ft.
ts = effective depth of concrete slab = 7.5 in.
θ = skew angle = 27 degrees
Kg = longitudinal stiffness parameter (in 4 )
L = span of beam (ft)
42

The variables “Kg” and “L” are defined in AASHTO section 4.6.2.2.1 and by
AASHTO Table C4.6.2.2.1-1, respectively, and are presented in the following figures.
Figure 6.1.1.4-4: Excerpt from AASHTO Section 4.6.2.2.1 defining K g.

A = 798 in 2 (from 54W” girder properties, Wisconsin Bridge Manual)
eg = (COG beam) + 2 in. haunch + ts /2 = 27.7 in. + 2 in. + (7.5 in.)/2 = 33.45 in.
EB = 5422.453 ksi (calculated using AASHTO Eq. 5.4.2.4-1)
ED = 3834.254 ksi (calculated using AASHTO Eq. 5.4.2.4-1)
43

Figure 6.1.1.4-5: AASHTO Table C4.6.2.2.1-1 L for Use in Live Load
Distribution Factor Equations.
The resulting calculation of Kg yields Kg = 1,716,760.8 in 4 , and the calculation for the
moment distribution factor yields a value of 0.6877 for interior girders, with the equation for
two or more loaded design lanes controlling. Because both spans are equal in length, the
factor “L” is 119 ft. for positive moment, negative moment, and shear distribution
calculations. Similarly, the two or more design lanes loaded case controlled for shear, which
had a distribution factor of 0.8494 and an adjustment factor of 1.0744 for skew, for a shear
distribution factor of 0.9126.
6.1.1.5 Distribution of Unfactored Composite Design Lane and Truck Live Loads on
Exterior Girders
For exterior girders, the moment distribution factor was calculated in accordance with
AASHTO Table 4.6.2.2.2d-1, and the shear distribution factor was calculated in accordance
with AASHTO Table 4.6.2.2.3b-1, with the shear correction factor calculated the same as
with interior girders. For all distribution factor calculations, AASHTO Table C4.6.2.2.1-1
44

was adhered to, which defines the length variable “L” for use in the live load distribution
factor equations, and was presented in the previous section for interior girder distribution
factors. The following figures from AASHTO show the equations used for truck and lane
load distribution to each exterior girder. The same variable definitions and values presented
for the interior girder distribution factor calculations apply.
Figure 6.1.1.5-1: From AASHTO Table 4.6.2.2.2d-1 Distribution of Live Loads Per Lane for
Moment in Exterior Longitudinal Beams.
The variable de is defined as the distance from the exterior web of the exterior beam
to the interior edge of the curb or traffic barrier, and since the value of d e was slightly
negative, a conservative value of d e = 0 ft. was used in hand calculations. The lever rule for
one design lane loaded was based on an axle width of 6 ft. at a distance of 2 ft. from the
inside of the curb edge to the first wheel, and a multipresence factor of 1.2 was also applied
per AASHTO Table 3.6.1.1.2-1. The variable ginterior is the distribution factor calculated for
the interior beam (before any applicable adjustment factors for skew). The following figure
shows the equations used to calculate the shear distribution factor for shear on the exterior
girder.
45

Figure 6.1.1.5-2: From AASHTO Table 4.6.2.2.3b-1 Distribution of Live Load per Lane for Shear in Exterior Beams.
Using the equations from AASHTO, the distribution factors for moment and shear to
the exterior girders were calculated and multiplied by the moment and shear values,
respectively, obtained from the PCBridge analysis of the design lane load and design truck
loads to produce the actual moments and shears seen in the individual girder. The variables
in the AASHTO formulas are defined the same as for the interior girder, as are the variable
values. The moment distribution factor yields a value of 0.5396 for exterior girders, with the
equation for two or more loaded design lanes controlling. Similarly, the two or more design
lanes loaded case controlled for shear, which had a distribution factor of 0.5475 after
the1.0744 adjustment factor for skew.
6.1.1.6 Pedestrian Live Load
The pedestrian live load application presented a unique challenge since AASHTO
LRFD provides little guidance or discussion on how to properly analyze pedestrian live
loads. According to AASHTO 3.6.1.6, “A pedestrian load of 0.075 ksf shall be applied to all
sidewalks wider than 2.0 ft. and considered simultaneously with the vehicular design live
load.” Applying this surface load to both sidewalks resulted in the previously stated load of
46

900 pounds per linear foot of bridge length, but determining the proper distribution of this
load presented a problem.
The first necessary decision to make regarding how to apply the pedestrian load was
whether or not it could or should be reduced to reflect multipresence of loads. Since the
pedestrian load is to be considered simultaneously with the vehicular design live load, it is
unlikely the full load would be seen on the bridge at a given time. Therefore, it was decided
that reduction of pedestrian load due to multipresence of loads should be done. This is
supported by the AASHTO 3.6.1.1.2 commentary, which states, “The consideration of
pedestrian loads counting as a ‘loaded lane’ for the purpose of determining a multiple
presence factor (m) is based on the assumption that simultaneous occupancy by a dense
loading of people combined with a 75-year design live load is remote. For the purpose of
this provision, it has been assumed that if a bridge is used as a viewing stand for eight hours
each year for a total time of about one month, the appropriate live load to combine with it
would have a one-month recurrence interval. This is reasonably approximated by use of the
multiple presence factors, even though they are originally developed for vehicular live load.”
This bridge, with a 68 ft. clear roadway width, can fit five design lanes of 12 ft. each.
Since the live load distribution factors used in analysis already consider multiple presence
factors, and the controlling equation in all cases was for two or more lanes, the multiple
presence factor that was applied to sidewalk loads was 0.65 for more than 3 loaded lanes
(AASHTO Table 3.6.1.1.2-1) since loading all five design lanes would result in the worst
loading condition the bridge would conceivably see. After application of the multiple
presence factor, the sidewalk design load became 585 lb/ft.
47

The next challenge with respect to pedestrian loads was how to distribute the load
among the girders. AASHTO provides no distribution equations for pedestrian live loads,
but since the current practice at the DOT is to evenly distribute pedestrian live loads to each
girder, the same approach was taken in hand calculations. Furthermore, CONSPAN treats
pedestrian live loads in the same fashion, so evenly distributing pedestrian live loads to all
girders in the bridge cross-section was necessary in order for hand calculations to be
comparable with CONSPAN results. It should be noted, however, that using the lever rule
for distributing pedestrian live loads may cause a more extreme load on the exterior girder
than the approach that was used. The impact of using the lever rule for pedestrian live load
distribution was ignored in favor of evenly distributing the load to all the girders in the bridge
cross-section. This approach could potentially be unconservative, so an ideal design would
investigate the load effects of distributing the pedestrian live load to the exterior girder using
the lever rule, and use the worst case loading event in design.
6.1.1.7 Load Combinations
With all the loads defined, the next step in hand calculations was to define load
combinations that would encompass all conceivable loading states of the bridge. For this
bridge, eleven load cases were identified and combined in twenty-seven load combinations,
which were analyzed and factored per AASHTO Tables 3.4.1-1 and 3.4.1-2 in order to
produce shear and moment envelopes for typical interior and exterior girders of the bridge for
Strength I, Service I, and Service III conditions. The following table lists the load factors for
each condition.

Table 6.1.1.7-1: Load factors used for Strength I, Service I, and Service III conditions.
Type of Load Strength I Factor Service I Factor Service III Factor
DC 0.90 to 1.25 1.00 1.00
DW 0.65 to 1.50 1.00 1.00
IM 1.33 1.33 1.33
LL 1.75 1.00 0.80
PL 1.75 1.00 0.80
The definitions of the abbreviations in the “Type of Load” column in the previous
table are as follows (from AASHTO 3.3.2):
DC = dead load of structural components and nonstructural attachments
DW = dead load of wearing surfaces and utilities
IM = vehicular dynamic load allowance
LL = vehicular live load
PL = pedestrian live load
For DC and DW loads, the load factor for Strength I can vary, and the load factor within the
allowable range that produced the most extreme loading forces on the bridge was used in
design. The following tables list the load cases and load combinations that were used in
design. Each load case was factored accordingly within each load combination to produce a
shear and moment envelope for the Strength I condition, Service I condition, and Service III
condition for interior and exterior girders.
49
Dead (DC) Girder, Slab, Diaphragm, Haunch, Sidewalk, Median, Rail&Fence
FWS (DW) Future Wearing Surface (FWS)
Ped 1&2 (PL) Pedestrian live load on spans 1 and 2
Ped 1 (PL) Pedestrian live load on span 1 only
Ped 2 (PL) Pedestrian live load on span 2 only
Lane 1&2 (LL) Lane live load on spans 1 and 2
Lane 1 (LL) Lane live load on span 1 only
Lane 2 (LL) Lane live load on span 2 only
Truck (LL, IM) HL-93 truck load, driving across the bridge in either direction
Tandem (LL, IM) Tandem truck load (also known as alternate military load)
Neg. Truck (LL, IM) Load from negative moment truck pair
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Name Load combination
LC1 DC + DW + (Ped 1&2) + (Lane 1&2) + Truck
LC2 DC + DW + (Ped 1&2) + (Lane 1&2) + Tandem
LC3 DC + DW + (Ped 1&2) + [90% (Lane 1&2)] + [90% (Neg. Truck)]
LC4 DC + DW + (Ped 1) + (Lane 1&2) + Truck
LC5 DC + DW + (Ped 1) + (Lane 1&2) + Tandem
LC6 DC + DW + (Ped 1) + [90% (Lane 1&2)] + [90% (Neg. Truck)]
LC7 DC + DW + (Ped 2) + (Lane 1&2) + Truck
LC8 DC + DW + (Ped 2) + (Lane 1&2) + Tandem
LC9 DC + DW + (Ped 2) + [90% (Lane 1&2)] + [90% (Neg. Truck)]
LC10 DC + DW + (Ped 1&2) + (Lane 1) + Truck
LC11 DC + DW + (Ped 1&2) + (Lane 1) + Tandem
LC12 DC + DW + (Ped 1&2) + [90% (Lane 1)] + [90% (Neg. Truck)]
LC13 DC + DW + (Ped 1) + (Lane 1) + Truck
LC14 DC + DW + (Ped 1) + (Lane 1) + Tandem
LC15 DC + DW + (Ped 1) + [90% (Lane 1)] + [90% (Neg. Truck)]
LC19 DC + DW + (Ped 1&2) + (Lane 2) + Truck
LC20 DC + DW + (Ped 1&2) + (Lane 2) + Tandem
LC21 DC + DW + (Ped 1&2) + [90% (Lane 2)] + [90% (Neg. Truck)]
51

Each load combination was factored for Strength I, Service I, and Service III
conditions in order to produce a maximum and minimum moment envelope graph and
maximum shear graph for typical interior and exterior girders along the bridge length. Refer
to the results comparison section for the graphs of both the hand calculated and CONSPAN
calculated shear and moment graphs for each condition for each girder.
6.1.1.8 Design of Prestress
The preliminary design steps used in hand calculations for design of prestressing
began by calculating the amount of prestress needed to prevent tension at the bottom of the
beam under the full Service III loads at midspan after 50 years. This required an estimate of
loss of prestress in order to calculate the number of strands and strand pattern needed to
avoid excessive tension stresses in the beam. Next, revisions and adjustments to the prestress
design were done, if they were necessary, in order to avoid premature failure at midspan at
the time of transfer. The condition near the girder ends was then checked to avoid excessive
tension or compression at transfer, and the design was adjusted again, if necessary.
When the bridge girder is constructed, prestressing strands are placed in a form,
stressed to 202.5 ksi (AASHTO Table 5.9.3-1), and the girder concrete is poured into the
form. After the concrete has sufficiently cured, the prestressing strands are released, and the
girder cambers upward due to the force in the prestressing strands. At this time, the girder
also elastically shortens due to the prestress force, and as a result, there is an associated loss
of prestress due to elastic shortening. After the girder is used in bridge construction,
additional time dependent losses of prestress also occur from concrete creep, steel relaxation,
and concrete shrinkage.

The first step in designing the prestressing for a typical interior or exterior girder is to
estimate the loss of prestressing from elastic shortening and time dependent loss. This is
needed in order to choose the number and configuration of prestressing strands necessary to
prevent the girder from reaching its maximum allowable service stresses during its service
life. Based on AASHTO Table 5.9.5.3-1, which provides an equation to estimate time
dependent prestress loss, and assuming a value for elastic shortening of 18 ksi, a total loss
was conservatively estimated at 58 ksi for both the interior and exterior girders (refer to
calculations for B-38-91 in the Appendix). Since the AASHTO equation used for estimating
time dependent prestress loss was developed for use with “I” girders, a higher time
dependent loss estimate was taken for the 54W” girder since wide flanged girders allow the
use of much higher levels of prestress, and thus tend to develop higher losses due to concrete
creep and elastic shortening.
With the properties of the non-composite girder section known (given in the
Wisconsin Bridge Manual), the parallel axis theorem was used to calculate the properties of
the composite section, and the desired amount of prestress was able to be calculated. Using
the maximum Service III moment and the girder properties, the stress at the bottom of the
beam was calculated assuming the absence of prestressing. The difference in the AASHTO
Service III tension stress limit of 0.537 ksi (AASHTO Table 5.9.4.2.2-1) and the tension
stress caused by the maximum Service III moment was used to calculate the required initial
prestress compression force needed to avoid excessive Service III tension.
Independent hand calculations required a minimum of 40 draped prestressing strands
for the interior girders and 36 draped prestressing strands for the exterior girders, but since
the CONSPAN software designed the interior girders with 34 draped strands and the exterior
53

girders with 30 strands, the hand calculations were revised to use the same strand
configuration as designed by the software. This was done in order to more comprehensively
compare hand design results with CONSPAN software design results. The Wisconsin DOT
standard patterns for 30, 34, 36, and 40 strands are shown in the following figure, and a
typical strand pattern illustration is also presented.
Figure 6.1.1.8-1: Standard 54W” girder draped strand arrangement at centerline of span (Sheet 14 of WisDOT plan set for B-38-91).
Figure 6.1.1.8-2: Typical strand pattern for a 54W” girder (Sheet 14 of WisDOT plan set for B-38-91).
54

Clearly there is a substantial difference between 40 and 34 strands for interior girders,
and between 36 and 30 strands for exterior girders. The main explanation for this difference
lies in the difference in design philosophies between hand calculations and the CONSPAN
software. Independent hand calculations used the traditional approach when calculating
prestress losses, in that only elastic shortening and time dependent losses were accounted for
in terms of the overall changes in prestress force. The CONSPAN software, in addition to
these losses, uses a more exact approach and also calculates gains in prestressing for different
load steps on the bridge. This will be explained in more detail later, but both design
approaches are correct, and thus the hand calculations were revised to follow the same design
approach used by the CONSPAN software.
6.1.1.9 Prestress Losses
With the prestressing strand pattern known, a more accurate estimate of prestress loss
was calculated. Using AASHTO Equation 5.9.5.2.3a-1, with the assumption that the
prestress is 90% of the prestress just before transfer (AASHTO 5.9.5.2.3a), a new estimate of
elastic shortening loss was calculated to be 15.287 ksi for interior girders and 12.94 ksi for
exterior girders. Next, the time dependent loss of prestress was calculated for each girder.
Time dependent prestress loss comes primarily from three sources; concrete
shrinkage, concrete creep, and steel relaxation. Concrete shrinkage is caused by the natural
shortening of concrete as it hardens over time. Concrete creep results from the permanent
compression stresses in the beam causing the slow shortening of concrete over time, and
relaxation of the steel occurs as the steel prestressing tendons slowly accommodate to the
induced stretch, and the internal prestress drops over time.
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AASHTO provides two approaches for estimating time dependent losses; a quick
approximate method (AASHTO 5.9.5.3) and a more refined method (AASHTO 5.9.5.4).
The approximate method was selected for use in the CONSPAN software since it was the
only method available for calculating time dependent prestress loss that included the 2005
AASHTO LRFD interims (the refined method used pre-2005 interims). For this reason, the
approximate method results were used in hand calculations even though both approaches
were calculated by hand. The time dependent loss of prestress as calculated using the
approximate method was 22.221 ksi for interior girders and 20.807 ksi for exterior girders.
Using the more refined method, the time dependent loss of prestress for interior girders was
calculated to be 30.527 ksi and 27.794 ksi for exterior girders. In this case, the more refined
method p

WisDOTPrestressedGirderDesignStudy (1)

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