AASHTO Lrfd 2014 - CSiBridge

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AASHTO 2014
ISO BRG030315M31 Rev. 0 Proudly developed in the United States of America March 2015
8/19/2019 AASHTO Lrfd 2014 - CSiBridge
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OR THE RELIABILITY OF THIS PRODUCT.
THIS PRODUCT IS A PRACTICAL AND POWERFUL TOOL FOR STRUCTURAL
DESIGN. HOWEVER, THE USER MUST EXPLICITLY UNDERSTAND THE BASIC
ASSUMPTIONS OF THE SOFTWARE MODELING, ANALYSIS, AND DESIGN
ALGORITHMS AND COMPENSATE FOR THE ASPECTS THAT ARE NOT
ADDRESSED.
THE INFORMATION PRODUCED BY THE SOFTWARE MUST BE CHECKED BY A QUALIFIED AND EXPERIENCED ENGINEER. THE ENGINEER MUST
INDEPENDENTLY VERIFY THE RESULTS AND TAKE PROFESSIONAL RESPONSIBILITY FOR THE INFORMATION THAT IS USED.
2.1 Load Pattern Types 2-1
2.2 Design Load Combinations 2-3
2.3 Default Load Combinations 2-5
3 Live Load Distribut ion
3.1 Methods for Determining Live Load Distribution 3-1
3.2 Determine Live Load Distribution Factors 3-2
3.3 Apply LLD Factors 3-3
3.3.1 User Specified 3-4
3.3.2 Calculated by CSiBridge in Accordance
with AASHTO LFRD 3-4 3.3.3 Forces Read Directly from Girders 3-4
3.3.4 Uniformly Distribution to Girders 3-4
3.4 Generate Virtual Combinations 3-5
3.4.1 Stress Check 3-5
3.5 Read Forces/Stresses Directly from Girders 3-6
3.5.1 Stress Check 3-6
3.6 LLD Factor Design Example Using Method 2 3-7
4 Define a Bridge Design Request
4.1 Name and Bridge Object 4-4
4.2 Check Type 4-4
4.3 Station Range 4-6
4.4 Design Parameters 4-6
4.5 Demand Sets 4-18
5.1.1 Capacity Parameters 5-2
5.2 Flexure Design AASHTO LRFD 5-5
5.3 Shear Design AASHTO LRFD 5-15
5.4 Principal Stress Design, AASHTO LRFD 5-31
5.4.2 Demand Parameters 5-31
6.1 Stress Design 6-2
6.2 Shear Design 6-3
7.1 Stress Design 7-1
7.2 Shear Design 7-2
7.2.4 Shear Design Example 7-9
7.3 Flexure Design 7-14
7.3.4 Flexure Capacity Design Example 7-20
8 Design Steel I-Beam Bridge with Composi te Slab
8.1 Section Properties 8-1
8.1.1 Yield Moments 8-1
8.1.2 Plastic Moments 8-3
8.2 Demand Sets 8-11
8.2.1 Demand Flange Stresses f bu and f f 8-12
8.2.2 Demand Flange Lateral Bending
Stress f 1 8-13
8.3 Strength Design Request 8-15
8.3.1 Flexure 8-15
8.3.2 Shear 8-22
8.5 Web Fatigue Design Request 8-26
8.6 Constructability Design Request 8-27
8.6.1 Staged (Steel I Comp Construct Stgd) 8-27
8.6.2 Non-staged (Steel I Comp Construct
Non-staged) 8-27
8.6.4 Flexure 8-28
8.6.5 Shear 8-30
9.1 Section Properties 9-1
9.1.2 Plastic Moments 9-2 9.1.3 Section Classification and Factors 9-7
9.2 Demand Sets 9-9
9.2.2 Demand Flange Lateral Bending
Stress f1 9-11
9.3 Strength Design Request 9-13
9.3.1 Flexure 9-13
9.3.2 Shear 9-16
9.5 Web Fatigue Design Request 9-20
9.6 Constructability Design Request 9-22
9.6.1 Staged (Steel-U Comp Construct Stgd) 9-22
9.6.2 Non-staged (Steel-U Comp Construct NonStgd) 9-22
9.6.3 Slab Status vs Unbraced Length 9-22
9.6.4 Flexure 9-23
9.6.5 Shear 9-27
10.2 Design Preferences 10-3
10.3 Load Combinations 10-3
10.5 Start Design/Check of the Bridge 10-6
v
11.1 Display Results as a Plot 11-1
11.1.1 Additional Display Examples 11-2
11.2 Display Data Tables 11-7
11.3 Advanced Report Writer 11-8
11.4 Verification 11-11
Chapter 1 Introduction
As the ultimate versatile, integrated tool for modeling, analysis, and design of
bridge structures, CSiBridge can apply appropriate code-specific design pro-
cesses to concrete box girder bridge design, design when the superstructure in-
cludes Precast Concrete Box bridges with a composite slab and steel I-beam or
U-tub bridges with composite slabs. The ease with which these tasks can be ac-
complished makes CSiBridge the most productive bridge design package in the
industry.
Design using CSiBridge is based on load patterns, load cases, load combina-
tions and design requests. The design output can then be displayed graphically
and printed using a customized reporting format.
It should be noted that the design of bridge superstructure is a complex subject
and the design codes cover many aspects of this process. CSiBridge is a tool to
help the user with that process. Only the aspects of design documented in this
manual are automated by the CSiBridge design capabilities. The user must
check the results produced and address other aspects not covered by
CSiBridge.
1.1
Organization
This manual is designed to help you become productive using CSiBridge de-
sign in accordance with the available codes when modeling concrete box girder
1 - 1
bridges and precast concrete girder bridges. Chapter 2 describes code-specific
design prerequisites. Chapter 3 describes Live Load Distribution Factors.Chapter 4 describes defining the design request, which includes the design re-
quest name, a bridge object name (i.e., the bridge model), check type (i.e., the
type of design), station range (i.e., portion of the bridge to be designed), design
parameters (i.e., overwrites for default parameters) and demand sets (i.e., load-
ing combinations). Chapter 5 identifies code-specific algorithms used by
CSiBridge in completing concrete box girder bridges. Chapter 6 provides code-
specific algorithms used by CSiBridge in completing concrete box and multi-
cell box girder bridges. Chapter 7 describes code-speicifc design parameters for
precast I and U girder. Chapter 8 explains how to design and optimize a steel I-
beam bridge with composite slab. Chapter 9 describes how to design and opti-
mize a steel U-beam bridge with composite slab. Chapter 10 describes how to run a Design Request using an example that applies the AASHTO LRFD code,
and Chapter 11 describes design output for the example in Chapter 10, which
can be presented graphically as plots, in data tables, and in reports generated
using the Advanced Report Writer feature.
1.2 Recommended Reading/Practice
It is strongly recommended that you read this manual and review any applica-
ble “Watch & Learn” Series™ tutorials, which are found on our web site,
http://www.csiamerica.com, before attempting to design a concrete box girder
or precast concrete bridge using CSiBridge. Additional information can be found in the on-line Help facility available from within the software’s main
menu.
Chapter 2 Define Loads and Load Combinations
This chapter describes the steps that are necessary to define the loads and load
combinations that the user intends to use in the design of the bridge superstruc-
ture. The user may define the load combinations manually or have CSiBridge
automatically generate the code generated load combinations. The appropriate
design code may be selected using the Design/Rating > Superstructure De-
sign > Preference command.
When the code generated load combinations are going to be used, it is im-
portant for users to define the load pattern type in accordance with the applicable code. The load pattern type can be defined using the Loads > Load Pat-
terns command. The user options for defining the load pattern types are sum-
marized in the Tables 2-1 and 2-2 for the AASHTO LRFD code.
2.1 Load Pattern Types
Tables 2-1 and 2-2 show the permanent and transient load pattern types that
can be defined in CSiBridge. The tables also show the AASHTO abbreviation
and the load pattern descriptions. Users may choose any name to identify a
load pattern type.
CSiBridge Brid ge Superstructure Design
Table 2-1 PERMANENT Load Pattern Types Used in the AASHTO-LRFD Code
CSiBridgeLoad Pattern Type AASHTOReference Description of Load Pattern
CREEP CR Force effects due to creep
DOWNDRAG DD Downdrag force
DEAD DC Dead load of structural components and non- structural attachments
SUPERDEAD DW Superimposed dead load of wearing surfaces and utilities
BRAKING BR Vehicle braking force
HORIZ. EARTH PR EH Horizontal earth pressures
LOCKED IN EL Misc. locked-in force effects resulting from the construction process
EARTH SURCHARGE ES Earth surcharge loads
VERT. EARTH PR EV Vertical earth pressure
PRESTRESS PS Hyperstatic forces from post-tensioning
Table 2-2 TRANSIENT Load Pattern Types Used in the AASHTO LRFD Design Code
CSiBridge Load Pattern Type
BRAKING BR Vehicle braking force
CENTRIFUGAL CE Vehicular centrifugal loads
VEHICLE COLLISION CT Vehicular collision force
VESSEL COLLISION CV Vessel collision force
QUAKE EQ Earthquake
BRIDGE LL LL Vehicular live load
LL SURCHARGE LS Live load surcharge
PEDESTRIAN LL PL Pedestrian live load
SETTLEMENT SE Force effects due settlement
TEMP GRADIENT TG Temperature gradient loads
TEMPERATURE TU Uniform temperature effects
STEAM FLOW WA Water load and steam pressure
WIND–LIVE LOAD WL Wind on live load
WIND WS Wind loads on structure
2 - 2 Load Pattern Types
2.2 Design Load Combinations
The code generated design load combinations make use of the load pattern
types noted in Tables 2-1 and 2-2. Table 2-3 shows the load factors and combi-
nations that are required in accordance with the AASHTO LRFD code.
Table 2-3 Load Combin ations and Load Factors Used in the AASHTO LRFD Code
Load Combo Limit
SH
LL IM CE BR PL LS
LL IM CE WA WS WL FR TU TU SE EQ IC CT CV
Str I γ P 1.75 - 1.00 - - 1.00 0.5/
1.20
1.20
1.20
1.20
Str V γ P 1.35 - 1.00 0.40 1.00 1.00 0.5/
1.20
1.20
1.20
1.20
1.20
- 1.00 - - - -
- 0.875 /1.75
Table 2-4 shows the maximum and minimum factors for the permanent loads
in accordance with the AASHTO LRFD code.
Table 2-4 Load Factors for Permanent Loads, P
γ , AASHTO LRFD Code
1.40
1.05
1.25
0.25
0.30
0.35
EH: Horizontal Earth Pressure
EV: Vertical Earth Pressure
Culverts Flexible Metal Box Culverts
1.00
1.35
1.30
1.35
1.95
1.50
N/A
1.00
0.90
0.90
0.90
0.90
ES: Earth Surcharge 1.50 0.75
Table 2-5 Load Factors for Permanent Loads due to Superimposed Deformations, P
γ ,
Superstructures, Segmental
1.0 See Table 2-5, DC
Concrete Superstructures, non-segmental 1.0 1.0
Substructures supporting non-segmental Superstruc- tures
Using Ig
Chapter 2 - Define Loads and Load Combinations
Table 2-5 Load Factors for Permanent Loads due to Superimposed Deformations, P
γ ,
1.0 1.0
Steel Substructures 1.0 1.0
Two combinations for each permanent load pattern are required because of the
maximum and minimum factors. When the default load combinations are used,
CSiBridge automatically creates both load combinations (one for the maximum
and one for the minimum factor), and then automatically creates a third combi-
nation that represents an enveloped combination of the max/min combos.
2.3 Default Load Combinations
Default design load combinations can be activated using the Design/Rating >
Load Combinations > Add Default command. Users can set the load combi-
nations by selecting the “Bridge” option. Users may select the desired limit
states and load cases using the Code Generated Load Combinations for Bridge
Design form. The form shown in Figure 2-1 illustrates the options when the
AASHTO LRFD code has been selected for design.
Default Load Combinations 2 - 5
Figure 2-1 Code-Generated Load Combinations for Bridge Design Form –
AASHTO LRFD
After the desired limit states and load cases have been selected, CSiBridge will
generate all of the code-required load combinations. These can be viewed us-
ing the Home > Display > Show Tables command or by using the
Show/Modify button on the Define Combinations form, which is shown in
Figure 2-2.
Figure 2-2 Define Load Combinations Form – AASHTO LRFD
The load combinations denoted as Str-I1, Str-I2, and so forth refer to Strength I
load combinations. The load case StrIGroup1 is the name given to enveloped
load combination of all of the Strength I combinations. Enveloped load combi-
nations will allow for some efficiency later when the bridge design requests are
defined (see Chapter 4).
Chapter 3 Live Load Distribution
This chapter describes the algorithms used by CSiBridge to determine the live
load distribution factors used to assign live load demands to individual girders.
An explanation is given with respect to how the distribution factors are applied
in a shear, stress, and moment check.
The live load distribution factors derived using the code-based Method 2 described in Section 3.1 of this manual are applicable only to superstructures of the following types: precast I- or U-girders with composite slabs, steel I-girders
with composite slabs, and multi-cell concrete box girders. These deck section types may also have the live loads distributed based on Methods 1, 3 or 4 de-
scribed in Section 3.1 of this manual.
Legend: Girder = beam + tributary area of composite slab
Section Cut = all girders present in the cross-section at the cut location
LLD = Live Load Distribution
3.1 Methods for Determining Live Load Distribution
CSiBridge gives the user a choice of four methods to address distribution of
live load to individual girders.
Method 1 – The LLD factors are specified directly by the user.
3 - 1
Method 2 – CSiBridge calculates the LLD factors by following procedures out-
lined in AASHTO LRFD Section 4.6.2.2.
Method 3 – CSiBridge reads the calculated live load demands directly from in-
dividual girders (available only for Area models).
Method 4 – CSiBridge distributes the live load uniformly to all girders.
It is important to note that to obtain relevant results, the definition of a Moving
Load case must be adjusted depending on which method is selected.
When the LLD factors are user specified or specified in accordance with the
code (Method 1 or 2), only one lane with a MultiLane Scale Factor = 1
should be loaded into a Moving Load cases included in the demand set combinations.
When CSiBridge reads the LLD factors directly from individual girders
(Method 3, applicable to area and solid models only) or when CSiBridge ap-
plies the LLD factors uniformly (Method 4), multiple traffic lanes with rele-
vant Multilane Scale Factors should be loaded in accordance with code re-
quirements.
3.2 Determine Live Load Distr ibution Factors
At every section cut, the following geometric information is evaluated to determine the LLD factors.
span length the length of span for which moment or shear is being calculat-
ed
the number of girders
girder designation the first and last girder are designated as exterior girders
and the other girders are classified as interior girders
roadway width measured as the distance between curbs/barriers; medians
are ignored
Chapter 3 - Live Load Distributio n
overhang consists of the horizontal distance from the centerline of the exte-
rior web of the left exterior beam at deck level to the interior edge of the curbor traffic barrier
the beams includes the area, moment of inertia, torsion constant, center of
gravity
the thickness of the composite slab t1 and the thickness of concrete slab
haunch t2
the tributary area of the composite slab which is bounded at the interior
girder by the midway distances to neighboring girders and at the exterior
girder; includes the entire overhang on one side, and is bounded by the mid-
way distances to neighboring girder on the other side
Young’s modulus for both the slab and the beams angle of skew support.
CSiBridge then evaluates the longitudinal stiffness parameter, Kg, in accord-
ance with AASHTO LRFD 4.6.2.2 (eq. 4.6.2.2.1-1). The center of gravity of
the composite slab measured from the bottom of the beam is calculated as the
sum of the beam depth, thickness of the concrete slab haunch t2, and one-half
the thickness of the composite slab t1. Spacing of the girders is calculated as
the average distance between the centerlines of neighboring girders.
CSiBridge then verifies that the selected LLD factors are compatible with the
type of model: spine, area, or solid. If the LLD factors are read by CSiBridge directly from the individual girders, the model type must be area or solid. This
is the case because with the spine model option, CSiBridge models the entire
cross section as one frame element and there is no way to extract forces on in-
dividual girders. All other model types and LLD factor method permutations
are allowed.
3.3 Apply LLD Factors
The application of live load distribution factors varies, depending on which
method has been selected: user specified; in accordance with code; directly from individual girders; or uniformly distributed onto all girders.
Apply LLD Fac tors 3 - 3
3.3.1 User Specified
When this method is selected, CSiBridge reads the girder designations (i.e., ex-
terior and interior) and assigns live load distribution factors to the individual
girders accordingly.
3.3.2 Calculated by CSiBridge in Accordance with AASHTO LRFD
When this method is selected, CSiBridge considers the data input by the user
for truck wheel spacing, minimum distance from wheel to curb/barrier and
multiple presence factor for one loaded lane.
Depending on the section type, CSiBridge validates several section parameters
against requirements specified in the code (AASHTO LRFD Tables 4.6.2.2.2b-
1, 4.6.2.2.2d-1, 4.6.2.2.3a-1 and 4.6.2.2.3b-1). When any of the parameter val-
ues are outside the range required by the code, the section cut is excluded from
the Design Request.
At every section cut, CSiBridge then evaluates the live load distribution factors
for moment and shear for exterior and interior girders using formulas specified
in the code (AASHTO LRFD Tables 4.6.2.2.2b-1, 4.6.2.2.2d-1, 4.6.2.2.3a-1
and 4.6.2.2.3b-1). After evaluation, the LLD factor values are assigned to indi-
vidual girders based on their designation (exterior, interior). The same valueequal to the average of the LLD factors calculated for the left and right girders
is assigned to both exterior girders. Similarly, all interior girders use the same
LLD factors equal to the average of the LLD factors of all of the individual in-
terior girders.
3.3.3 Forces Read Directly from Girders
When this method is selected, CSiBridge sets the live load distribution factor
for all girders to 1.
3.3.4 Uniformly Distributed to Girders
When this method is selected, the live load distribution factor is equal to 1/n
where n is the number of girders in the section. All girders have identical LLD
3 - 4 Apply LLD Factors
factors disregarding their designation (exterior, interior) and demand type
(shear, moment).
3.4 Generate Virtual Combinations
When the method for determining the live load distribution factors is user-
specified, code-specified, or uniformly distributed (Methods 1, 2 or 4),
CSiBridge generates virtual load combination for every valid section cut se-
lected for design. The virtual combinations are used during a stress check and
check of the shear and moment to calculate the forces on the girders. After
those forces have been calculated, the virtual combinations are deleted. The
process is repeated for all section cuts selected for design.
Four virtual COMBO cases are generated for each COMBO that the user has
specified in the Design Request (see Chapter 4). The program analyzes the de-
sign type of each load case present in the user specified COMBO and multi-
plies all non-moving load case types by 1/ n (where n is the number of girders)
and the moving load case type by the section cut values of the LLD factors (ex-
terior moment, exterior shear, interior moment and interior shear LLD factors).
This ensures that dead load is shared evenly by all girders, while live load is
distributed based on the LLD factors.
The program then completes a stress check and a check of the shear and the
moment for each section cut selected for design.
3.4.1 Stress Check
At the Section Cut being analyzed, the girder stresses at all stress output points
are read from CSiBridge for every virtual COMBO generated. To ensure that
live load demands are shared equally irrespective of lane eccentricity by all
girders, CSiBridge uses averaging when calculating the girder stresses. It cal-
culates the stresses on a beam by integrating axial and M3 moment demands on
all the beams in the entire section cut and dividing the demands by the number
of girders. Similarly, P and M3 forces in the composite slab are integrated and
stresses are calculated in the individual tributary areas of the slab by dividing
the total slab demand by the number of girders.
Generate Virtual Combinations 3 - 5
When stresses are read from analysis into design, the stresses are multiplied by
n (where n is number of girders) to make up for the reduction applied in theVirtual Combinations.
3.4.2 Shear or Moment Check
At the Section Cut being analyzed, the entire section cut forces are read from
CSiBridge for every Virtual COMBO generated. The forces are assigned to in-
dividual girders based on their designation. (Forces from two virtual Combina-
tions one for shear and one for moment generated for exterior beam are as-
signed to both exterior beams, and similarly, Virtual Combinations for interior
beams are assigned to interior beams.)
3.5 Read Forces/Stresses Directly from Girders
When the method for determining the live load distribution is based on forces
read directly from the girders, the method varies based on which Design Check
has been specified in the Design Request (see Chapter 4).
3.5.1 Stress Check
At the Section Cut being analyzed, the girder stresses at all stress output points
are read from CSiBridge for every COMBO specified in the Design Request. CSiBridge calculates the stresses on a beam by integrating axial, M3 and M2
moment demands on the beam at the center of gravity of the beam. Similarly P,
M3 and M2 demands in the composite slab are integrated at the center of gravi-
ty of the slab tributary area.
3.5.2 Shear or Moment Check
At the Section Cut being analyzed, the girder forces are read from CSiBridge
for every COMBO specified in the Design Request. CSiBridge calculates the
demands on a girder by integrating axial, M3 and M2 moment demands on the
girder at the center of gravity of the girder.
3 - 6 Read Forces/Stresses Directl y from Girders
3.6 LLD Factor Design Example Using Method 2
The AASHTO LRFD Specifications allow the use of advanced methods of
analysis to determine the live load distribution factors. However, for typical
bridges, the specifications list equations to calculate the distribution factors for
different types of bridge superstructures. The types of superstructures covered
by these equations are described in AASHTO LRFD Table 4.6.2.2.1-1. From
this table, bridges with concrete decks supported on precast concrete I or bulb-
tee girders are designated as cross-section “K.” Other tables in AASHTO
LRFD 4.6.2.2.2 list the distribution factors for interior and exterior girders in-
cluding cross-section “K.”
The distribution factor equations are largely based on work conducted in the NCHRP Project 12-26 and have been verified to give accurate results com-
pared to 3-dimensional bridge analysis and field measurements. The multiple
presence factors are already included in the distribution factor equations except
when the tables call for the use of the lever rule. In these cases, the computa-
tions need to account for the multiple presence factors. The user is providing
those as part of the Design Request definition together with wheel spacing,
curb to wheel distance and lane width.
Notice that the distribution factor tables include a column with the heading
“range of applicability.” The ranges of applicability listed for each equation are
based on the range for each parameter used in the study leading to the devel-
opment of the equation. When any of the parameters exceeds the listed value in
the “range of applicability” column, CSiBridge reports the incompliance and
excludes the section from design.
AASHTO LRFD Article 4.6.2.2.2d of the specifications states: “In beam-slab
bridge cross-sections with diaphragms or cross-frames, the distribution factor
for the exterior beam shall not be taken less than that which would be obtained
by assuming that the cross-section deflects and rotates as a rigid cross-section.”
This provision was added to the specifications because the original study that
developed the distribution factor equations did not consider intermediate dia-
phragms. Application of this provision requires the presence of a sufficient
number of intermediate diaphragms whose stiffness is adequate to force the
cross section to act as a rigid section. For prestressed girders, different jurisdic-
tions use different types and numbers of intermediate diaphragms. Depending
on the number and stiffness of the intermediate diaphragms, the provisions of
LLD Factor Design Example Using Method 2 3 - 7
AASHTO LRFD 4.6.2.2.2d may not be applicable. If the user specifies option
“Yes” in the “Diaphragms Present” option the program follows the procedureoutlined in the provision AASHTO LRFD 4.6.2.2.2d.
For this example, one deep reinforced concrete diaphragm is located at the
midspan of each span. The stiffness of the diaphragm was deemed sufficient to
force the cross-section to act as a rigid section; therefore, the provisions of
AASHTO LRFD S4.6.2.2.2d apply.
Figure 3-1 General Dimensions
Noncomposite beam moment of inertia, I g = 733,320 in4
Deck slab thickness, t s = 8 in.
Span length, L = 110 ft.
Girder spacing, S = 9 ft.-8 in.
Modulus of elasticity of the beam, E B = 4,696 ksi
Modulus of elasticity of the deck, E D = 3,834 ksi
C.G. to top of the basic beam = 35.62 in.
C.G. to bottom of the basic beam = 36.38 in.
1. Calculate n, the modular ratio between the beam and the deck.
3 - 8 LLD Factor Design Example Using Method 2
n = B D E E (AASHTO 2014 4.6.2.2.1-2)
= 4696 3834 = 1.225
2. Calculate eg, the distance between the center of gravity of the noncompo-
site beam and the deck. Ignore the thickness of the haunch in determin-
ing eg
K g = ( )2
gn I Ae+ (4.6.2.2.1-1)
= ( )2 4 1.225 7 33 320 1 0 85 39.62 2 984 704 in + =
4. Interior girder. Calculate the moment distribution factor for an interior
beam with two or more design lanes loaded using AASHTO LRFD Ta-
ble S4.6.2.2.2b-1.
0.075 9.5 12.0g sS S L K Lt +
( ) ( ) ( )( ){ } 0.1
0.6 0.2 3

= 0.796 lane (eq. 1)
5. In accordance with AASHTO LRFD 4.6.2.2.2e, a skew correction factor
for moment may be applied for bridge skews greater than 30 degrees.
The bridge in this example is skewed 20 degrees, and therefore, no skew
correction factor for moment is allowed.
Calculate the moment distribution factor for an interior beam with one
design lane loaded using AASHTO LRFD Table 4.6.2.2.2b-1.
D M = ( ) ( ) ( ) 0.10.4 0.3 3
0.06 14 12.0g sS S L K Lt +
= ( ) ( ) ( )( ){ } 0.1

Notice that the distribution factor calculated above for a single lane load-
ed already includes the 1.2 multiple presence factor for a single lane,therefore, this value may be used for the service and strength limit states.
However, multiple presence factors should not be used for the fatigue
limit state. Therefore, the multiple presence factor of 1.2 for the single
lane is required to be removed from the value calculated above to deter-
mine the factor used for the fatigue limit state.
6. Skew correction factor for shear.
In accordance with AASHTO LRFD 4.6.2.2.3c, a skew correction factor
for support shear at the obtuse corner must be applied to the distribution
factor of all skewed bridges. The value of the correction factor is calcu-
lated using AASHTO LRFD Table 4.6.2.2.3c-1.
S C = ( ) 0.3
= ( )( )( ) 0.3
3 1.0 0.20 12.0 110 8 2 984 704 tan20+
= 1.047
7. Calculate the shear distribution factor for an interior beam with two or
more design lanes loaded using AASHTO LRFD Table S4.6.2.2.3a-1.
DV = ( ) ( ) 2
= 0.929 lane
DV = ( )1.047 0.929 0.973= lane (eq. 4)
8. Calculate the shear distribution factor for an interior beam with one de-
sign lane loaded using AASHTO LRFD Table S4.6.2.2.3a-1.
DV = ( )0.36 25.0S +
= ( )0.36 9.667 25.0+
= 0.747 lane
DV = ( )1.047 0.747
= 0.782 lane (eq. 5)
9. From (1) and (2), the service and strength limit state moment distribution
factor for the interior girder is equal to the larger of 0.796 and 0.542 lane.
Therefore, the moment distribution factor is 0.796 lane.
From (4) and (5), the service and strength limit state shear distribution
factor for the interior girder is equal to the larger of 0.973 and 0.782 lane.
Therefore, the shear distribution factor is 0.973 lane.
10. Exterior girder
11. Calculate the moment distribution factor for an exterior beam with two
or more design lanes using AASHTO LRFD Table 4.6.2.2.2d-1.
D M = e DV interior
e = 0.77 9.1de+
where de is the distance from the centerline of the exterior girder to the
inside face of the curb or barrier.
e = 0.77 + 1.83/9.1 = 0.97
D M = 0.97(0.796) = 0.772 lane (eq. (7)
12. Calculate the moment distribution factor for an exterior beam with one
design lane using the lever rule in accordance with AASHTO LRFD Ta-
ble 4.6.2.2.2d-1.
Figure 3-2 Lever Rule
= 0.672 lane (eq. 8)
Notice that this value does not include the multiple presence factor,
therefore, it is adequate for use with the fatigue limit state. For service
and strength limit states, the multiple presence factor for a single lane
loaded needs to be included.
D M = ( )0.672 1.2
= 0.806 lane (eq. 9) (Strength and Service)
13. Calculate the shear distribution factor for an exterior beam with two or more design lanes loaded using AASHTO LRFD Table 4.6.2.2.3b-1.
DV = e DV interior
where:
= 0.762 lane (eq. 10)
14. Calculate the shear distribution factor for an exterior beam with one
design lane loaded using the lever rule in accordance with AASHTO
LRFD Table 4.6.2.2.3b-1. This value will be the same as the moment
distribution factor with the skew correction factor applied.
DV = ( )1.047 0.806
Notice that AASHTO LRFD 4.6.2.2.2d includes additional requirements
for the calculation of the distribution factors for exterior girders when the
girders are connected with relatively stiff cross-frames that force the
cross-section to act as a rigid section. As indicated in the introduction,
these provisions are applied to this example; the calculations are shown
below.
4.6.2.2.2d)
The multiple presence factor, m, is applied to the reaction of the exterior
beam (AASHTO LRFD Table 3.6.1.1.2-1)
m1 = 1.20
m2 = 1.00
m3 = 0.85
R = ( ) 2 L b ext N N X e x+ ∑ ∑ (4.6.2.2.2d-1)
where:
R = reaction on exterior beam in terms of lanes
N L = number of loaded lanes under consideration
e = eccentricity of a design truck or a design land load from
the center of gravity of the pattern of girders (ft.)
x = horizontal distance from the center of gravity of the pat-
tern of girders to each girder (ft.)
X ext = horizontal distance from the center of gravity of the pat-
tern to the exterior girder (ft.) See Figure 1 for dimen-
sions.
R = ( ) ( ) ( ) ( )( )2 2 2
= 0.1667 + 0.310
= 0.477 (Fatigue)
Add the multiple presence factor of 1.2 for a single lane:
R = ( )1.2 0.477
= 0.333 + 0.443
= 0.776
Add the multiple presence factor of 1.0 for two lanes loaded:
R = ( )1.0 0.776
Three lanes loaded:
3 6 24.167 21 9 3 2 24.1672 14.52 4.8332 + + − + +
= 0.5 + 0.399
= 0.899
Add the multiple presence factor of 0.85 for three or more lanes loaded:
R = ( )0.85 0.899
= 0.764 (Strength)
These values do not control over the distribution factors summarized in
Design Step 16.
16. From (7) and (9), the service and strength limit state moment distribution
factor for the exterior girder is equal to the larger of 0.772 and 0.806
lane. Therefore, the moment distribution factor is 0.806 lane.
From (10) and (12), the service and strength limit state shear distribution
factor for the exterior girder is equal to the larger of 0.762 and 0.845
lane. Therefore, the shear distribution factor is 0.845 lane.
Table 3-1 Summary of Service and Strength Limit State Distribut ion Factors -- AASHTO LRFD
Load Case
Multiple lanes loaded
0.796 0.772 0.973 0.762
Additional check for rigidly connected girders
Multiple lanes loaded
NA 0.776 NA 0.776
Design Value 0.796 0.806 0.973 0.845
Value reported byCSiBridge 0.796 0.807 0.973 0.845
LLD Factor Design Example Using Method 2 3 - 15
Figure 4-1 shows the Bridge Design Request form when the bridge object is for
a concrete box girder bridge, and the check type is concrete box stress. Figure4-2 shows the Bridge Design Request form when the bridge object is for a
Composite I or U girder bridge and the check type is precast composite stress.
Figure 4-3 shows the Bridge Design Request form when the bridge object is for
a Steel I-Beam bridge and the check type is composite strength.
Figure 4-1 Bridge Design
4.1 Name and Bridge Object
Each Bridge Design Request must have unique name. Any name can be used.
If multiple Bridge Objects are used to define a bridge model, select the bridge
object to be designed for the Design Request. If a bridge model contains only a
single bridge object, the name of that bridge object will be the only item avail-
able from the Bridge Object drop-down list.
4.2 Check Type
The Check Type refers to the type of design to be performed and the available options depend on the type of bridge deck being modeled.
For a Concrete Box Girder bridge, CSiBridge provides the following check
type options:
Concrete Box Principal
Concrete Box Stress
Concrete Box Flexure
Concrete Box Shear
For Multi-Cell Concrete Box Girder bridge, CSiBridge provides the following
check type options:
AASHTO LRFD, CAN/CSA S6, EN 1992-1-1, and IRC: 112
Concrete Box Stress
Concrete Box Shear
For bridge models with precast I or U Beams with Composite Slabs,
CSiBridge provides three check type options, as follows:
AASHTO LRFD, CAN/CSA S6, EN 1992-1-1, and IRC: 112
Precast Comp Stress
Precast Comp Shear
Precast Comp Flexure
For bridge models with steel I-beam with composite slab superstructures,
CSiBridge provides the following check type option:
AASHTO LRFD
Steel Comp Constructability NonStaged
For bridge models with steel U-tub with composite slab superstructures,
CSiBridge provides the following check type option:
AASHTO LRFD
Steel Comp Constructability Staged
Steel Comp Constructability NonStaged
The bold type denotes the name that appears in the check type drop-down list.
A detailed description of the design algorithm can be found in Chapter 5 for
concrete box girder bridges, in Chapter 6 for multi-cell box girder bridges, in
Chapter 7 for precast I or U beam with composite slabs, and in Chapter 8 for
steel I-beam with composite slab.
4.3 Station Range
The station range refers to the particular zone or portion of the bridge that is to
be designed. The user may choose the entire length of the bridge, or specify
specific zones using station ranges. Multiple zones (i.e., station ranges) may be
specified as part of a single design request.
When defining a station range, the user specifies the Location Type, which de-
termines if the superstructure forces are to be considered before or at a station
point. The user may choose the location type as before the point, after the
point, or both.
4.4 Design Parameters Design parameters are overwrites that can be used to change the default values
set automatically by the program. The parameters are specific to each code,
4 - 6 Station Range
Chapter 4 - Define a Bridge Design Request
deck type, and check type. Figure 4-4 shows the Superstructure Design Re-
quest Parameters form.
Figure 4-3 Superstructure Design Request Parameters form
Table 4-1 shows the parameters for concrete box girder bridges. Table 4-2
shows the parameters for multi-cell concrete box bridges. Table 4-3 shows the
parameters applicable when the superstructure has a deck that includes precast
I or U girders with composite slabs. Table 4-4 shows the parameters applicable
when the superstructure has a deck that includes steel I-beams.
Table 4-1 Design Request Parameters for Concrete Box Girders
AASHTO STD 2002
Concrete Box Stress Resistance Factor - multiplies both compression and tension
stress limits
Multiplier on sqrt( ′cf ) to calculate the tension stress limit,
given in the units specified
The tension limit factor may be specified using either MPa or
ksi units for ′cf and the resulting tension limit
Design Parameters 4 - 7
AASHTO LRFD Concrete Box Stress Concrete Box Stress, PhiC, - Resistance Factor that multi-
plies both compression and tension stress limits
Concrete Box Stress Factor Compression Limit - Multiplier
on ′cf to calculate the compression stress limit
Concrete Box Stress Factor Tension Limit Units - Multiplier
on sqrt( ′cf ) to calculate the tension stress limit, given in the
units specified
Concrete Box Stress Factor Tension Limit - The tension limit
factor may be specified using either MPa or ksi units for ′cf
and the resulting tension limit
Concrete Box Shear Concrete Box Shear, PhiC, - Resistance Factor that multiplies both compression and tension stress limits
Concrete Box Shear, PhiC, Lightweight Resistance Factor that multiplies nominal shear resistance to obtain factored resistance for light-weight concrete
Include Resal (Hunching-girder) shear effects – Yes or No. Specifies whether the component of inclined flexural compression or tension, in the direction of the applied shear, in variable depth members shall or shall not be considered when determining the design factored shear force in accordance with Article 5.8.6.2.
Concrete Box Shear Rebar Material - A previously defined rebar material label that will be used to determine the area
of shear rebar required Longitudinal Torsional Rebar Material - A previously defined
rebar material that will be used to determine the area of longitudinal torsional rebar required
Concrete Box Flexure, PhiC, - Resistance Factor that multiplies both compression and tension stress limits
Concrete Box Principal
CAN/CSA S6
Concrete Box Stress Multi-Cell Concrete Box Stress Factor Compression Limit -
Multiplier on ′cf to calculate the compression stress limit
Multi-Cell Concrete Box Stress Factor Tension Limit - The tension limit factor may be specified using either MPa or ksi
units for ′cf and the resulting tension limit
Concrete Box Shear Phi Concrete c -- Resistance factor for concrete (see CSA
4 - 8 Design Parameters
Clause 8.4.6)
Phi PT p -- Resistance factor for tendons (see CSA Clause 8.4.6)
Cracking Strength Factor – Multiplies sqrt( ′cf ) to obtain
cracking strength
EpsilonX Negative Limit -- Longitudinal negative strain limit (see Clause 8.9.3.8)
EpsilonX Positive Limit -- Longitudinal positive strain limit (see Clause 8.9.3.8)
Tab slab rebar cover – Distance from the outside face of the top slab to the centerline of the exterior closed transverse torsion reinforcement
Web rebar cover – Distance from the outside face of the web to the centerline of the exterior closed transverse torsion reinforcement
Bottom Slab rebar cover – Distance from the outside face of the bottoms lab to the centerline of the exterior closed transverse torsion reinforcement
Shear Rebar Material – A previously defined rebar material label that will be used to determine the required area of transverse rebar in the girder
Longitudinal Rebar Material – A previously defined rebar material that will be used to determine the required area of longitudinal rebar in the girder
Phi Concrete c -- Resistance factor for concrete (see CSA Clause 8.4.6)
Phi Pt p -- Resistance factor for tendons (see CSA Clause 8.4.6)
Phi Rebar s -- Resistance factor for reinforcing bars (see CSA Clause 8.4.6)
Eurocode EN 1992
Concrete Box Stress Compression limit – Multiplier on f c k to calculate the compression stress limit
Tension limit – Multiplier on f c k to calculate the tension stress limit
Concrete Box Shear Gamma C for Concrete – Partial factor for concrete.
Gamma C for Rebar – Partial safety factor for reinforcing
steel. Gamma C for PT – Partial safety factor for prestressing
steel.
Angle Theta – The angle between the concrete compression strut and the beam axis perpendicular to the shear force.
The value must be between 21.8 degrees and 45 degrees.
Factor for PT Duct Diameter – Factor that multiplies post- tensioning duct diameter when evaluating the nominal web thickness in accordance with section 6.2.3(6) of the code. Typical values 0.5 to 1.2.
Factor for PT Transmission Length – Factor for the transmission length of the post tensioning used in shear resistance equation 6.4 of the code. Typical value 1.0 for post tensioning.
Inner Arm Method – The method used to calculate the inner lever arm “z” of the section (integer).
Inner Arm Limit – Factor that multiplies the depth of the section to get the lower limit of the inner lever arm “z” of the section.
Effective Depth Limit – Factor that multiplies the depth of the section to get the lower limit of the effective depth to the tensile reinforcement “d” of the section.
Type of Section – Type of section for shear design.
Determining Factor Nu1 – Method that will be used to calcu-
late the η1 factor.
Factor Nu1 – η1 factor
calculate the αcw factor.
Factor AlphaCW – αcw factor
Factor Fywk – Multiplier of vertical shear rebar characteristic yield strength to obtain a stress limit in shear rebar used in 6.10.aN. Typical value 0.8 to 1.0.
Shear Rebar Material – A previously defined material label that will be used to determine the required area of transverse rebar in the girder.
Longitudinal Rebar Material – A previously defined material that will be used to determine the required area of longitudinal rebar in the girder.
Gamma c for Rebar – Partial safety factor for reinforcing steel.
Gamma c for PT – Partial safety factor for prestressing steel.
PT pre-strain – Factor to estimate pre-strain in the post- tensioning. Multiplies f pk to obtain the stress in the tendons after losses. Typical value between 0.4 and 0.9.
Table 4-2 Design Request Parameters for Multi-Cell Concrete Box
AASHTO LRFD
Multi-Cell Concrete Box Stress, PhiC, - Resistance Factor that multiplies both compression and tension stress limits
Multi-Cell Concrete Box Stress Factor Compression Limit -
Multi-Cell Concrete Box Stress Factor Tension Limit Units -
Multiplier on sqrt ( )′cf to calculate the tension stress limit,
given in the units specified
units for ′ c
Multi-Cell Concrete Box Shear
Multi-Cell Concrete Box Shear, PhiC, - Resistance Factor that multiplies both compression and tension stress limits
Multi-Cell Concrete Box Shear, PhiC, Lightweight Re- sistance Factor that multiplies nominal shear resistance to obtain factored resistance for light-weight concrete
Negative limit on strain in nonprestressed longitudinal reinforcement – in accordance with section 5.8.3.4.2; Default Value = -0.4x10-3, Typical value(s): 0 to -0.4x10-3
Positive limit on strain in nonprestressed longitudinal reinforcement - in accordance with section 5.8.3.4.2; Default Value = 6.0x10-3, Typical value(s): 6.0x10-3
PhiC for Nu - Resistance Factor used in equation 5.8.3.5-1;
Default Value = 1.0, Typical value(s): 0.75 to 1.0 Phif for Mu - Resistance Factor used in equation 5.8.3.5-1;
Default Value = 0.9, Typical value(s): 0.9 to 1.0
Specifies which method for shear design will be used – either Modified Compression Field Theory (MCFT) in accordance with 5.8.3.4.2 or Vci Vcw method in accordance with 5.8.3.4.3. Currently only the MCFT option is available.
A previously defined rebar material label that will be used to determine the required area of transverse rebar in the girder.
A previously defined rebar material that will be used to de-
termine the required area of longitudinal rebar in the girder
Multi-Cell Concrete
Box Flexure
that multiplies both compression and tension stress limits
CAN/CSA S6
Multi-Cell Concrete
Box Stress Multi-Cell Concrete Box Stress Factor Compression Limit -
units for ′cf and the resulting tension limit
Highway Class – The highway class shall be determined in accordance with CSA Clause 1.4.2.2, Table 1.1 for the average daily traffic and average daily truck traffic volumes for which the structure is designed
Cracking Strength Factor -- Multiplies sqrt( ′cf ) to obtain
cracking strength
Shear Rebar Material – A previously defined rebar material that will be used to determine the required area of transverse rebar in the girder
Longitudinal Rebar Material – A previously defined rebar
material that will be used to determine the required area of longitudinal rebar in the girder
Multi-Cell Concrete Box Flexure
Highway Class – The highway class shall be determined in accordance with CSA Clause 1.4.2.2, Table 1.1 for the average daily traffic and average daily truck traffic volumes for which the structure is designed
Eurocode EN 1992
Multi-Cell Concrete Box Stress
Compression limit – Multiplier on f c k to calculate the compression stress limit
Gamma C for Rebar – Partial safety factor for reinforcing steel.
Gamma C for PT – Partial safety factor for prestressing steel.
Angle Theta – The angle between the concrete compression strut and the beam axis perpendicular to the shear force. The value must be between 21.8 degrees and 45 degrees.
Factor for PT Duct Diameter – Factor that multiplies post- tensioning duct diameter when evaluating the nominal web thickness in accordance with section 6.2.3(6) of the code.
Typical values 0.5 to 1.2.
Factor for PT Transmission Length – Factor for the transmission length of the post tensioning used in shear resistance equation 6.4 of the code. Typical value 1.0 for post tensioning.
calculate the αcw factor.
Factor AlphaCW – αcw factor
Factor Fywk – Multiplier of vertical shear rebar characteristic yield strength to obtain a stress limit in shear rebar used in 6.10.aN. Typical value 0.8 to 1.0.
Shear Rebar Material – A previously defined material label that will be used to determine the required area of transverse
rebar in the girder.
Longitudinal Rebar Material – A previously defined material that will be used to determine the required area of longitudinal rebar in the girder.
Multi-Cell Concrete
Box Flexure Gamma c for Concrete – Partial safety factor for concrete.
Gamma c for Rebar – Partial safety factor for reinforcing steel.
Gamma c for PT – Partial safety factor for prestressing steel.
PT pre-strain – Factor to estimate pre-strain in the post- tensioning. Multiplies f pk to obtain the stress in the tendons after losses. Typical value between 0.4 and 0.9.
Table 4-3 Design Request Parameters for Precast I or U Beams
AASHTO LRFD
Precast Comp
Precast Comp Stress, PhiC, - Resistance Factor that multi-
plies both compression and tension stress limits Precast Comp Stress Factor Compression Limit - Multiplier
on f ′c to calculate the compression stress limit
Precast Comp Stress Factor Tension Limit Units - Multiplier
on sqrt(f ′ c) to calculate the tension stress limit, given in the units specified
Precast Comp Stress Factor Tension Limit - The tension limit
factor may be specified using either MPa or ksi units for f ′c and the resulting tension limit
Precast Comp Shear
PhiC, - Resistance Factor that multiplies both compression and tension stress limits
PhiC, Lightweight Resistance Factor that multiplies nominal shear resistance to obtain factored resistance for light-weight concrete
Negative limit on strain in nonprestressed longitudinal reinforcement – in accordance with section 5.8.3.4.2; Default Value = -0.4x10-3, Typical value(s): 0 to -0.4x10-3
Chapter 4 - Define a Bridge Design Request

Positive limit on strain in nonprestressed longitudinal rein-forcement - in accordance with section 5.8.3.4.2; Default Val- ue = 6.0x10-3, Typical value(s): 6.0x10-3
PhiC for Nu - Resistance Factor used in equation 5.8.3.5-1; Default Value = 1.0, Typical value(s): 0.75 to 1.0
Phif for Mu - Resistance Factor used in equation 5.8.3.5-1; Default Value = 0.9, Typical value(s): 0.9 to 1.0
Specifies what method for shear design will be used - either Modified Compression Field Theory (MCFT) in accordance with 5.8.3.4.2 or Vci Vcw method in accordance with 5.8.3.4.3 Currently only the MCFT option is available.
A previously defined rebar material label that will be used to determine the required area of transverse rebar in the girder
A previously defined rebar material that will be used to determine the required area of longitudinal rebar in the girder
Precast Comp Flexure, PhiC, - Resistance Factor that multiplies both compression and tension stress limits
CAN/CSA S6
on f ′c to calculate the compression stress limit
Precast Comp Stress Factor Tension Limit - The tension limit
factor may be specified using either MPa or ksi units for f ′c and the resulting tension limit
Precast Comp Shear
Highway Class – The highway class shall be determined in accordance with CSA Clause 1.4.2.2, Table 1.1 for the average daily traffic and average daily truck traffic volumes for
which the structure is designed
Cracking Strength Factor -- Multiplies sqrt( ′cf ) to obtain
cracking strength
Shear Rebar Material – A previously defined rebar material label that will be used to determine the required area of transverse rebar in the girder.

Longitudinal Rebar Material – A previously defined rebar ma-terial that will be used to determine the required area of longitudinal rebar n the girder
Highway Class – The highway class shall be determined in accordance with CSA Clause 1.4.2.2, Table 1.1 for the average daily traffic and average daily truck traffic volumes for which the structure is designed
Eurocode EN 1992 Precast Comp Stress
Compression limit – Multiplier on f c k to calculate the compression stress limit
Precast Comp Shear
Gamma C for Rebar – Partial safety factor for reinforcing steel.
Gamma C for PT – Partial safety factor for prestressing steel.
Angle Theta – The angle between the concrete compression strut and the beam axis perpendicular to the shear force. The value must be between 21.8 degrees and 45 degrees.
Factor for PT Transmission Length – Factor for the transmission length of the post tensioning used in shear resistance equation 6.4 of the code. Typical value 1.0 for post tensioning.
Table 4-4 Design Request Parameters for Steel I-Beam
Steel-I Comp - Fatigue
Steel I Comp Construct Stgd
Resistance factor Phi for flexure
Resistance factor Phi for shear
Resistance factor Phi for Concrete in Tension
Do webs have longitudinal stiffeners?
Concrete modulus of rupture factor in accordance with AASHTO LRFD Section 5.4.2.6, factor that multiplies sqrt of f 'c to obtain modulus of rupture, default value 0.24 (ksi) or 0.63 (MPa), must be > 0
The modulus of rupture factor may be specified using either
MPa or ksi units
Resistance factor Phi for flexure
Resistance factor Phi for shear
Resistance factor Phi for Concrete in Tension
Do webs have longitudinal stiffeners?
Concrete modulus of rupture factor in accordance with AASHTO LRFD Section 5.4.2.6, factor that multiplies sqrt of f 'c to obtain modulus of rupture, default value 0.24 (ksi) or 0.63 (MPa), must be > 0
The modulus of rupture factor may be specified using either MPa or ksi units
4.5 Demand Sets
A demand set name is required for each load combination that is to be consid-
ered in a design request. The load combinations may be selected from a list of
user defined or default load combinations that are program determined (see
Chapter 2).
4.6 Live Load Distribution Factors
When the superstructure has a deck that includes precast I or U girders with
composite slabs or multi-cell boxes, Live Load Distribution Factors can be
specified. LLD factors are described in Chapter 3.
4 - 18 Demand Sets
Chapter 5 Design Concrete Box Girder Bridges
This chapter describes the algorithms applied in accordance with the AASHTO
LRFD 2014 (AASHTO LRFD) for design and stress check of the superstruc-
ture of a concrete box type bridge deck section.
When interim revisions of the codes are published by the relevant authorities,
and (when applicable) they are subsequently incorporated into CSiBridge, the
program gives the user an option to select what type of interims shall be used
for the design. The interims can be selected by clicking on the Code Prefer-
ences button.
In CSiBridge, when distributing loads for concrete box design, the section is
always treated as one beam; all load demands (permanent and transient) are
distributed evenly to the webs for stress and flexure and proportionally to the
slope of the web for shear. Torsion effects are always considered and assigned
to the outer webs and the top and bottom slabs.
With respect to shear and torsion check, in accordance with AASHTO Article
5.8.6, torsion is considered.
The user has an option to select “No Interims” or “YYYY Interims” on theBridge Design Preferences form. The form can be opened by clicking the Code
Preferences button.
5 - 1
The revisions published in the 2015 interims were incorporated into the Flex-
ure Design.
5.1.1 Capacity Parameters
PhiC – Resistance Factor; Default Value = 1.0, Typical value: 1.0
The compression and tension limits are multiplied by the φC factor
FactorCompLim – c f ′ multiplier; Default Value = 0.4; Typical values: 0.4 to
0.6. The c f ′ is multiplied by the FactorCompLim to obtain the compression limit.
FactorTensLim – c f ′ multiplier; Default Values = 0.19 (ksi), 0.5(MPa);
Typical values: 0 to 0.24 (ksi), 0 to 0.63 (MPa). The c f ′ is multiplied by the
FactorTensLim to obtain the tension limit.
5.1.2 Algori thm
The stresses are evaluated at three points at the top fiber and three points at the
bottom fiber: extreme left, Bridge Layout Line, and extreme right. The stresses assume linear distribution and take into account axial (P) and both bending
moments (M2 and M3).
The stresses are evaluated for each demand set (Chapter 4). If the demand set
contains live load, the program positions the load to capture extreme stress at
each of the evaluation points.
Extremes are found for each point and the controlling demand set name is rec-
orded.
The stress limits are evaluated by applying the Capacity Parameters (see Sec-
tion 5.2.1).
Figure 5-2 Reinforcement, AASHTO LRFD Stress Design
AASHTO Box Beam, Type BIII-48
Reinforcing bars:
Section Properties
A = area of cross-section of beam = 826 in2
h = overall depth of precast beam = 39 in I = moment of inertia about centroid of the beam = 170812 in4
yb, yt = distance from centroid to the extreme
bottom (top) fiber of the beam = 19.5 in
Demand forces from Dead and PT (COMB1) at station 570:
P = −856.51 kip
M3 = −897.599 kip-in
Top fiber stress =
3 top top
f py Yield tensile strength of prestressing steel (area weighted average of all
tendons in the tensile zone)
f y Yield strength of rebar
k PT material constant (AASHTO LRFD eq. 5.7.3.1.1-2)
M n Nominal flexural resistance
M r Factored flexural resistance
t slabeq Equivalent thickness of the slab
1 Stress block factor, as specified in AASHTO LRFD 2015 Interim Sec-
tion 5.7.2.2.
β1 Stress block factor, as specified in AASHTO LRFD Section 5.7.2.2.
φ Resistance factor for flexure
5.2.3 Design Process
The derivation of the moment resistance of the section is based on the approx-
imate stress distribution specified in AASHTO LRFD Article 5.7.2.2. The nat-
ural relationship between concrete stress and strain is considered satisfied by
an equivalent rectangular concrete compressive stress block of 1 ′ over a zone bounded by the edges of the cross-section and a straight line located par-
allel to the neutral axis at the distance a = β1c from the extreme compression
fiber. If the AASHTO LRFD 2015 interim is selected the factor 1 is taken as
0.85 for specified compressive strengths not exceeding 10.0 ksi. For specified
concrete compressive strengths exceeding 10.0ksi, 1is reduced at rate of 0.02
for each 1.0ksi of strength in excess of 10.0ksi, except that 1 is not taken less
than 0.75. For AASHTO LRFD no interim the 1is always taken as 0.85 inde-
pendent of concrete compressive strength. The factor The distance c is meas-
ured perpendicular to the neutral axis. The factor β1 is taken as 0.85 for con-
crete strengths not exceeding 4.0 ksi. For concrete strengths exceeding 4.0 ksi,
β1 is reduced at a rate of 0.05 for each 1.0 ksi of strength in excess of 4.0 ksi, except that β1 is not to be taken to be less than 0.65.
5 - 6 Flexure Design AASHTO LRFD
Chapter 5 - Design Concrete Box Girder Brid ges
The flexural resistance is determined in accordance with AASHTO LRFD Par-
agraph 5.7.3.2. The resistance is evaluated for bending about horizontal axis 3only. Separate capacity is calculated for positive and negative moment. The
capacity is based on bonded tendons and mild steel located in the tension zone
as defined in the Bridge Object. Tendons and mild steel reinforcement located
in the compression zone are not considered. It is assumed that all defined ten-
dons in a section, stressed or not, have f pe (effective stress after loses) larger
than 0.5 f pu (specified tensile strength). If a certain tendon should not be con-
sidered for the flexural capacity calculation, its area must be set to zero.
The section properties are calculated for the section before skew, grade, and
superelevation have been applied. This is consistent with the demands being
reported in the section local axis. It is assumed that the effective width of the
flange (slab) in compression is equal to the width of the slab.
5.2.4 Algori thm
At each section:
All section properties and demands are converted from CSiBridge model
units to N, mm.
The equivalent slab thickness is evaluated based on the slab area and slab
width, assuming a rectangular shape.
slab slabeq
b =
The equivalent web thickness is evaluated as the summation of all web hori-
zontal thicknesses.
The
1 stress block factor is evaluated in accordance with AASHTO LRFD
5.7.2.2 based on section c f ′
– For AASHTO LRFD 2015 Interim
Flexure Design AASHTO LRFD 5 - 7

1 = 0.85
The β1 stress block factor is evaluated in accordance with AASHTO LRFD
5.7.2.2 based on section c f ′
– If c f ′ > 28 MPa, then 1
28 max 0.85 0.05; 0.65 ;
7 c f ′ −
else 1 0.85.β =
The tendon and rebar location, area, and material are read. Only bonded ten-
dons are processed; unbonded tendons are ignored.
Tendons and rebar are split into two groups depending on which sign of mo-
ment they resist negative or positive. A tendon or rebar is considered to re-
sist a positive moment when it is located outside of the top fiber compression
stress block and is considered to resist a negative moment when it is located
outside of the bottom fiber compression stress block. The compression stress
block extends over a zone bounded by the edges of the cross-section and a straight line located parallel to the neutral axis at the distance a = β1c from
the extreme compression fiber. The distance c is measured perpendicular to
the neutral axis.
For each tendon group, an area weighted average of the following values is
determined:
– sum of the tendon areas, APS
– distance from the extreme compression fiber to the centroid of prestress-
ing tendons, d P
– constant k (AASHTO LRFD eq. 5.7.3.1.1-2)
5 - 8 Flexure Design AASHTO LRFD
For each rebar group, the following values are determined:
–
sum of the tension rebar areas, As
– distance from the extreme compression fiber to the centroid of the ten-
sion rebar, d s
The distance c between the neutral axis and the compressive face is evaluated
in accordance with (AASHTO LRFD eq. 5.7.3.1.1-4).
1 1 slab
f f b kA
′α β +
The distance c is compared against requirement of Section 5.7.2.1 to verify if
stress in mild reinforcement f s can be taken as equal to f y. The limit on ratio
c/d s is calculated depending on what kind of code and its interim are speci-
fied in the Bridge Design Preferences form as shown in the table below:
Code AASHTO LRFD 2012
≤ 0.6 0.003 0.003 +
where the compression control strain limit is per AASHTO LRFD 2013
Interims table C5.7.2.1-1
When the limit is not satisfied the stress in mild reinforcement f s is reduced
to satisfy the requirement of Section 5.7.2.1.
The distance c is compared to the equivalent slab thickness to determine if
the section is a T-section or rectangular section.
– If 1 slabeq ,c t β > the section is a T-section.
If the section is a T-section, the distance c is recalculated in accordance with
(AASHTO LRFD eq. 5.7.3.1.1-3).
( )1 slab webeq slabeq
pu
f f b kA
′α β +
Average stress in prestressing steel f ps is calculated in accordance with
d
Nominal flexural resistance M n is calculated in accordance with (AASHTO
LRFD eq. 5.7.3.2.2-1).
( ) slabeq 1 1 1 1 slab webeq slabeq ;
2 2 2 2 n PS PS p S s s c
t c c c M A f d A f d f b b t
β β β ′= − + − + α − −
β β = − + −

Factored flexural resistance is obtained by multiplying M n by φ.
M r = φ M n
Extreme moment M3 demands are found from the specified demand sets and
the controlling demand set name is recorded.
5.2.5 Flexure Design Example
Cross Section: AASHTO Box Beam, Type BIII-48, as shown in Figure 5-3.
Concrete unit weight, wc = 0.150 kcf
Concrete strength at 28 days, c f ′ = 5.0 ksi (~34.473 MPa)
Design span = 95.0 ft
Prestressing strands: ½ in. dia., seven wire, low relaxation
Area of one strand = 0.153 in
2
f pu = 243 ksi
Figure 5-3 LRFD Flexure Design
Cross-Section, AASHTO Box Beam, Type BIII-48
Figure 5-4 Reinforcement, AASHTO LRFD Flexure Design
Cross-Section, AASHTO Box Beam, Type BIII-48
Section Properties
A = area of cross-section of beam = 826 in2
h = overall depth of precast beam = 39 in
I = moment of inertia about centroid of the beam = 170812 in4
yb, y t = distance from centroid to the extreme
bottom (top) fiber of the beam = 19.5 in
Demand forces from Dead and PT (COMB1) at station 570:
P = −856.51 kip
M 3 = −897.599 kip-in
The equivalent slab thickness is evaluated based on the slab area and slab
width, assuming a rectangular shape.
slab slabeq
Value reported by CSiBridge = 5.5 in
The equivalent web thickness is evaluated as the summation of all web hori-
zontal thicknesses.
web
b b= = + =
Tendons are split into two groups depending on which sign of moment they
resist negative or positive. A tendon is considered to resist a positive mo-
ment when it is located outside of the top fiber compression stress block and
is considered to resist a negative moment when it is located outside of the
bottom fiber compression stress block. The compression stress block extends
over a zone bounded by the edges of the cross-section and a straight line lo-
cated parallel to the neutral axis at the distance a = β1c from the extreme
compression fiber. The distance c is measured perpendicular to the neutral
axis.
For each tendon group, an area weighted average of the following values is
determined:
– sum of the tendon areas, ( ) 2
bottom 0.153 6 23 4.437inPT A = + =
Value reported by CSiBridge = 4.437 in2
– distance from the center of gravity of the tendons to the extreme com-
pression fiber, bottom
23 6 PT y
– specified tensile strength of prestressing steel, 270kip pu f =
Value reported by CSiBridge = 270 kip
– constant k (AASHTO LRFD eq. 5.7.3.1.1-2)
243 2 1.04 2 1.04 0.28
270
py
pu
Value reported by CSiBridge = 0.28
The β1 stress block factor is evaluated in accordance with AASHTO LRFD
5.7.2.2 based on section .c f ′
– If c f ′ > 28 MPa, then
1
7
Value calculated by CSiBridge = 0.8037 (not reported)
The distance c between the neutral axis and the compressive face is evaluated
in accordance with (AASHTO LRFD eq. 5.7.3.1.1-4).
1 slab
270 36.586
PT pu
=
Value calculated by CSiBridge = 6.919 in (not reported)
The distance c is compared to the equivalent slab thickness to determine if
the section is a T-section or a rectangular section.
– If 1 slabeq 6.91 0.80376 5.56in 5.5inc t β > → × = > , the section is a
T-section.
Value reported by CSiBridge, section = T-section
– If the section is a T-section, the distance c is recalculated in accordance
with (AASHTO LRFD eq. 5.7.3.1.1-3).
slab webeq slabeq
PT pu c
f f b kA
Average stress in prestressing steel f ps is calculated in accordance with
7.149 1 270 1 0.28 255.23 ksi
36.586
Value reported by CSiBridge = 255.228 ksi
Nominal flexural resistance M n is calculated in accordance with (AASHTO
LRFD 5.7.3.2.2-1).
( )
( )
2 2 2
2 7.149 0.80376 5.5
38287.42kip-in
n PT ps PT c
t c c M A f y f b b t
β β ′= − + − −
Value calculated by CSiBridge = 38287.721 kip-in (not reported)
Factored flexural resistance is obtained by multiplying M n by φ.
1.0 38287.42 38287.42 kip-inr n M M = φ = × =
Value reported by CSiBridge = 38287.721 kip-in
5.3
5.3.1 Capacity Parameters
PhiC – Resistance Factor; Default Value = 0.9, Typical value: 0.7 to 0.9. The
nominal shear capacity of normal weight concrete sections is multiplied by the
resistance factor to obtain factored resistance.
PhiC (Lightweight) – Resistance Factor for light-weight concrete; Default Val-
ue = 0.7, Typical values: 0.7 to 0.9. The nominal shear capacity of light-weight
concrete sections is multiplied by the resistance factor to obtain factored re-
sistance.
Include Resal (haunched girder) Shear Effect – Typical value: Yes. Specifies
whether the component of inclined flexural compression or tension, in the di-rection of the applied shear, in variable depth members shall or shall not be
considered when determining the design factored shear force.
Shear Rebar Material – A previously defined rebar material label that will be
used to determine the area of shear rebar required.
Longitudinal Torsional Rebar Material – A previously defined rebar material label that will be used to determine the required area of longitudinal torsional rebar.
5.3.2
Variables A Gross area of the section
AO Area enclosed by the shear flow path, including the area of holes, if any
Al Area of longitudinal torsion reinforcement
Avsweb Area of shear reinforcement in web per unit length
Avt web Area of transverse torsion reinforcement in web per unit length
b&nb

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AASHTO Lrfd 2014 - CSiBridge