Transcript of 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
4.2.2 Bridge Substructure Geometry
.......................................................................19
4.3.1 Bridge Superstructure Geometry
....................................................................22
4.3.2 Bridge Substructure Geometry
.......................................................................27
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
6.1.3.7 Girder Stresses at Critical
Sections....................................................111
6.1.3.8 Moment Capacity at Ultimate Strength
.............................................113
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
6.2.1.9 Girder Stresses at Critical
Sections....................................................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
6.2.3.5 Prestress Losses and Gains
................................................................145
6.2.3.6 Girder Stresses at Critical
Sections....................................................148
6.2.3.7 Moment Capacity at Ultimate Strength
.............................................150
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
6.3.3.5 Prestress Losses and Gains
................................................................167
6.3.3.6 Girder Stresses at Critical
Sections....................................................170
6.3.3.7 Moment Capacity at Ultimate Strength
.............................................172
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
xii
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 6.2.3.2-5: Service III factored interior girder moment
envelope................................138
Figure 6.2.3.2-6: Service III factored exterior girder moment
envelope. ..............................138
Figure 6.2.3.3-1: Strength I factored interior girder shear
envelope. ....................................140
Figure 6.2.3.3-2: Strength I factored exterior girder shear
envelope.....................................140
Figure 6.2.3.3-3: Service I factored interior girder shear
envelope. ......................................141
Figure 6.2.3.3-4: Service I factored exterior girder shear
envelope. .....................................141
Figure 6.2.3.3-5: Service III factored interior girder shear
envelope. ...................................142
Figure 6.2.3.3-6: Service III factored exterior girder shear
envelope....................................142
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 6.3.3.2-5: Service III factored interior girder moment
envelope................................160
Figure 6.3.3.2-6: Service III factored exterior girder moment
envelope. ..............................160
Figure 6.3.3.3-2: Strength I factored exterior girder shear
envelope.....................................162
Figure 6.3.3.3-3: Service I factored interior girder shear
envelope. ......................................163
Figure 6.3.3.3-4: Service I factored exterior girder shear
envelope. .....................................163
Figure 6.3.3.3-5: Service III factored interior girder shear
envelope. ...................................164
Figure 6.3.3.3-6: Service III factored exterior girder shear
envelope....................................164
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 6.2.3.4-3: Calculated concrete stress limits.
................................................................144
Table 6.2.3.5-1: Instantaneous loss of prestress for span 3
girders. ......................................145
Table 6.2.3.5-2: Gains of prestress and adjustments to gains
(negative value
indicates a gain).
........................................................................................................146
Table 6.2.3.5-3: Time dependent loss of prestress using the AASHTO
Approximate
Method.
......................................................................................................................147
Table 6.2.3.6-1: Computed girder stresses at midspan.
.........................................................149
Table 6.2.3.6-2: Computed girder stresses at end of strand transfer
length...........................149
Table 6.2.3.6-3: Computed girder stresses at hold down (harp)
point...................................149
Table 6.2.3.7-1: Computed girder moment capacity at ultimate
strength. ............................150
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 6.3.3.4-3: Calculated concrete stress limits.
................................................................166
Table 6.3.3.5-1: Instantaneous loss of prestress for span 3
girders. ......................................167
Table 6.3.3.5-2: Gains of prestress and adjustments to gains
(negative value
indicates a gain).
........................................................................................................168
Table 6.3.3.5-3: Time dependent loss of prestress using the AASHTO
Approximate
Method.
......................................................................................................................169
Table 6.3.3.6-1: Computed girder stresses at midspan.
.........................................................171
Table 6.3.3.6-2: Computed girder stresses at end of strand transfer
length...........................171
Table 6.3.3.6-3: Computed girder stresses at hold down (harp)
point...................................171
Table 6.3.3.7-1: Computed girder moment capacity at ultimate
strength. ............................172
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.
1
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.
2
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.
3
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.
5
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.
8
9
10
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.
11
12
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
4.2 Example Bridge B-20-163 Geometry and Materials
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.
4.2.1 Bridge Superstructure Geometry
Like all three example bridges, B-20-163 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.
14
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
17
18
The relevant superstructure geometry that was used for design,
which can be seen in
the previous figures, is as follows:
• 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
• Two intermediate steel diaphragms per space between
girders, per span
4.2.2 Bridge Substructure Geometry
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
4.2.3 Bridge Materials
The materials used for this bridge design are the same as the
materials used for the
design of structure B-38-91.
4.3 Example Bridge B-20-162 Geometry and Materials
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.
4.3.1 Bridge Superstructure Geometry
Very similar to structure B-20-163, B-20-162 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.
22
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
25
Figure 4.3.1-4: Diagram of girder and bridge span lengths (left)
and bridge geometry (right).
26
The relevant superstructure geometry that was used for design,
which can be seen in
the previous figures, is as follows:
• 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
• Two intermediate steel diaphragms per space between
girders, per span
4.3.2 Bridge Substructure Geometry
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.
4.3.3 Bridge Materials
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
50
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)]
LC16 DC + DW + (Ped 2) + (Lane 1) + Truck
LC17 DC + DW + (Ped 2) + (Lane 1) + Tandem
LC18 DC + DW + (Ped 2) + [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)]
LC22 DC + DW + (Ped 1) + (Lane 2) + Truck
LC23 DC + DW + (Ped 1) + (Lane 2) + Tandem
LC24 DC + DW + (Ped 1) + [90% (Lane 2)] + [90% (Neg. Truck)]
LC25 DC + DW + (Ped 2) + (Lane 2) + Truck
LC26 DC + DW + (Ped 2) + (Lane 2) + Tandem
LC27 DC + DW + (Ped 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.
55
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