Precast pretensioned concrete girders

Chapter 8 – Precast Pretensioned Concrete Girders 8-i
BRIDGE DESIGN PRACTICE ● FEBRUARY 2015
CHAPTER 8
PRECAST PRETENSIONED CONCRETE GIRDERS
TABLE OF CONTENTS
8.1 INTRODUCTION ...............................................................................................8-1
8.2 PRECAST GIRDER FEATURES.......................................................................8-3
8.2.1 Typical Sections and Span Ranges..................................................................... 8-3
8.2.2 Primary Characteristics of Precast Girder Design.............................................. 8-7
8.2.3 Methods to Vary Strand Eccentricity and Force .............................................. 8-11
8.3 PRECAST BRIDGE TYPES.............................................................................8-15
8.3.1 Single-Span Bridges......................................................................................... 8-15
8.3.2 Multi-Span Bridges .......................................................................................... 8-16
8.3.3 Spliced Girder Bridges..................................................................................... 8-22
8.4 DESIGN CONSIDERATIONS .........................................................................8-26
8.4.1 Materials........................................................................................................... 8-26
8.4.2 Prestress Losses................................................................................................ 8-27
8.4.3 Flexure.............................................................................................................. 8-30
8.4.4 Shear................................................................................................................. 8-31
8.4.5 Deflection and Camber..................................................................................... 8-32
8.4.6 Anchorage Zones.............................................................................................. 8-37
8.4.7 Diaphragms and End Blocks ............................................................................ 8-37
8.4.8 Lateral Stability................................................................................................ 8-38
8.5 DESIGN FLOW CHART..................................................................................8-39
8.6 DESIGN EXAMPLE.........................................................................................8-41
8.6.1 Problem Statement ........................................................................................... 8-41
8.6.2 Select Girder Depth, Type, and Spacing .......................................................... 8-43
8.6.3 Establish Loading Sequence............................................................................. 8-44
8.6.4 Select Materials................................................................................................ 8-45
8.6.5 Calculate Section Properties............................................................................. 8-46
8.6.6 Determine Loads .............................................................................................. 8-49

Chapter 8 – Precast Pretensioned Concrete Girders 8-ii
8.6.7 Perform Structural Analysis............................................................................. 8-50
8.6.8 Estimate Prestressing Force and Area of Strands............................................. 8-55
8.6.9 Estimate Prestress Losses................................................................................. 8-59
8.6.10 Design for Service Limit State ......................................................................... 8-62
8.6.11 Design for Strength Limit State........................................................................ 8-75
8.6.12 Check Reinforcement Limits............................................................................ 8-80
8.6.13 Design for Shear............................................................................................... 8-82
8.6.14 Design for Interface Shear Transfer between Girder and Deck ....................... 8-93
8.6.15 Check Minimum Longitudinal Reinforcement ................................................ 8-95
8.6.16 Pretensioned Anchorage Zone Reinforcement................................................. 8-96
8.6.17 Deflection and Camber..................................................................................... 8-97
NOTATION.................................................................................................................8-103
REFERENCES ............................................................................................................8-111

Chapter 8 – Precast Pretensioned Concrete Girders 8-1
CHAPTER 8
PRECAST PRETENSIONED CONCRETE GIRDERS
8.1 INTRODUCTION
Precast concrete elements such as girders, piles, deck panels, and pavement are
being used with increasing frequency in California. This chapter focuses exclusively
on precast pretensioned concrete girders, referred to herein as PC girders.
PC girders are a type of prestressed concrete girder that facilitates rapid
construction of a bridge using girders that are fabricated off-site and then transported
and erected into place at the job site. Once the deck is poured, the structural section
becomes composite, minimizing deflections. Because PC girders require little to no
falsework, they are a preferred solution for jobs where Accelerated Bridge
Construction (ABC) is sought, where speed of construction, minimal traffic
disruption, and/or environmental impact is required, and where temporary
construction clearance is limited. PC girders employ high performance concrete for
strength, durability, and/or constructability and tend to be more economical and
competitive when significant repeatability exists on a job (i.e., economy of scale).
The use of PC girders in California highway bridge system has increased rapidly in
recent years (Figure 8.1-1).
A) Pretensioned bulb-tee girders B) Pretensioned wide flange girder
Figure 8.1-1 Example of Precast Pretensioned Concrete Girder Sections
Similar to cast-in-place (CIP) post-tensioned (PT) girders, PC girders are
prestressed to produce a tailored stress distribution along the member at service level
to help prevent flexural cracking. For member efficiency, the girders have
precompressed tensile zones-regions such as the bottom face of the girder at midspan
where compression is induced to counteract tension due to expected gravity loads
(e.g., self-weight, superimposed dead loads such as deck weight, barrier weight, and
overlay, as well as live loads). To achieve this, PC girders employ prestressing

strands that are stressed before the concrete hardens. This is in contrast to PT girders,
in which the tendons are stressed after the concrete hardens. However, PC girders
may also be pretensioned, then post-tensioned, and are sometimes spliced together to
form a single span or continuous superstructure.
As shown in Figure 8.1-2, pretensioning requires the use of a stressing bed, often
several hundred feet long for efficient casting of a series of members in a long line,
and using abutments, stressing stands, jacks, and hold-downs/hold-ups to produce the
desired prestressing profile. The transfer of strand force to the concrete members by
bond is typically evident by the upward deflection (camber) of members when the
strands are detensioned (cut or burned) at the member ends. Steam curing of
members allows for a rapid turnover of forms (typically one-day cycle or less) and
cost efficiency. Control during fabrication of PC girders also permits the use of
quality materials and provides many benefits compared to CIP PT girders, such as
higher strength materials (e.g., f´ci, f´c) and modulus of elasticity, as well as reduced
creep, shrinkage, and permeability. Article 5.5.4.2.1 of CA Amendments to AASHTO
LRFD Bridge Design Specifications (Caltrans, 2014) takes advantage of this higher
quality control and thus increases the resistance factor, , for tensioned-controlled
sections from 0.95 for CIP PT members to 1.0 for PC girders.
Figure 8.1-2 Pretensioning of Members with Straight Strands on
Stressing Bed
L - ES*
B) Strands detensioned
ES = elastic shortening
Removable
abutment
Stressing
jack
End
abutment
FormworkOriginal length, L
Precasting bed
A) Strands tensioned

8.2 PRECAST GIRDER FEATURES
8.2.1 Typical Sections and Span Ranges
The designer may select from a wide variety of standard sections, as described in
Chapter 6 of the Bridge Design Aids (BDA). Girder sections not covered in this
section are considered non-standard and must be approved by the Type Selection
Meeting.
Figure 8.2-1 shows representative PC girder sections, and Table 8.2-1 lists
typical and preferred span lengths for eight common PC girder types, including four
standard California girders (I, bulb-tee, bath-tub, and wide-flange) and the California
voided slab, as well as three other PC girders (box, delta, and double-tee).
Table 8.2-1: PC Girder Types and Span Lengths (Caltrans, 2012)
Girder Type Possible Span Length(ft)
Preferred Span
Length(ft)
California I-girder 50 to 125 50 to 95
California bulb-tee girder 80 to 150 95 to 150
California bath-tub girder 80 to 150 80 to 120
California wide-flange girder 80 to 200 80 to 180
California voided slab 20 to 70 20 to 50
Precast box girder 40 to 120 40 to 100
Precast delta girder 60 to 120 60 to 100
Precast double-tee girder 30 to 100 30 to 60
Among these girders, the I-girder is most commonly used and has been in use in
California for nearly 60 years. With bridge span lengths normally ranging from 50 ft
to 125 ft, the I-girder typically uses a depth-to-span ratio of approximately 0.05 to
0.055 for simple spans and approximately 0.045 to 0.05 for multi-span structures
made continuous for live load.
The bulb-tee and bath-tub (or U-shape) girders are targeted for bridge spans up to
150 ft. The depth-to-span ratio is slightly smaller than that for I-girders: 0.045 to 0.05
for simple spans and 0.04 to 0.045 for continuous structures, respectively. However,
due to the weight limits for economical hauling, the length of bath-tub girders is
usually restricted to a range of 100 ft to 120 ft.
The California wide-flange girder (Figure 8.2-2) was recently developed in
coordination with California precasters to produce more efficient bottom and top
flange areas that permit design for spans up to 200 ft, with a depth-span ratio of 0.045
(simple) and 0.04 (continuous). The larger bottom bulb accommodates nearly 20%
more strands than the standard California bulb tee and, due to its shape, provides
enhanced handling and erection stability at longer spans. Greater economy is also
anticipated due to larger girder spacing and reduction in girder lines. Standard
sections have been developed for both pretensioning alone, as well as combined pre-
and post-tensioned sections. For longer span lengths, special permits for hauling,
trucking routes, and erection must be verified.

Other girders that are less commonly used include girders with trapezoidal,
double-tee, and rectangular cross sections as well as box girders. These are
sometimes used for cost effectiveness and aesthetics. Precast box girders are often
used for railway systems and relatively short span lengths ranging from 40 ft to 100
ft.
It should be noted that using the given bridge depth-to-span ratios to determine
the girder section is approximate but is usually a reasonable starting point for initial
design and cost estimates. Normally, girder spacing is set at approximately 1.25 to
1.75 times the bridge superstructure depth. When a shallow girder depth is required,
girder spacing may have to be reduced to satisfy all design criteria, which may result
in increased cost.
A) I girder

B) Bulb-tee
C) Bath-tub

Figure 8.2-1 Example PC Girder Sections (Caltrans, 2012)
D) Wide-flange

Figure 8.2-2 California Wide-Flange Girders
8.2.2 Primary Characteristics of Precast Girder Design
At the heart of the prestressed concrete design philosophy is the positioning of
the prestressing strands within the PC girder: the center of gravity of the strands
(CGS) is deliberately offset from the center of gravity of the concrete section (CGC)
to establish an eccentricity, defined as the distance between the CGS and CGC at a
section. This eccentricity produces a beneficial tailored flexural stress distribution
along the length of the member to counteract the flexural tension expected from
gravity loads. The largest eccentricity is provided at locations where tension is
expected to be the greatest (e.g., at midspan of simple span girder).
For PC girder design, the following three basic stages are addressed: Transfer,
service, and ultimate.
 Transfer refers to the stage at which the tensile force in the strands is
transferred to the PC girder, by cutting or detensioning the strands after a
minimum girder concrete strength has been verified. Because the girder
is simply supported and only self-weight acts with the prestressing at this
stage, the most critical stresses typically occur at the ends of the girder or
harping points (also known as drape points). Both tensile and
compressive stresses should be checked at these locations against
AASHTO LRFD stress limits.
 Service refers to the stage at which girder and deck self-weight act on the
non-composite girder, together with additional dead loads (e.g., barrier
and wearing surface) and live load on the composite section. This stage
is checked using the AASHTO LRFD Service I and III load
combinations (AASHTO, 2012). Per Caltrans Amendments Table
5.9.4.2.2.-1 (Caltrans, 2014), the girder must also be designed to prevent
tension in the precompressed tensile zones (“zero tension”) due to
permanent loads.

 Ultimate refers to the Strength Limit State. Flexural and shear strengths
are provided to meet all factored load demands, including the Caltrans P-
15 design truck (Strength II load combination).
In service limit state design, the concrete stresses change at various loading
stages. In general, there are three major stages that need to be considered in the
design, and these stages are described in the following sections.
 Stage I: Cast and stress girder (transfer) (Fig. 8.2-3):
o Strands are stressed to jacking force within form. Girder concrete is
cast. Once concrete gains sufficient strength, strands are cut,
transferring prestressing force to the girder.
o Girder self-weight is supported by the PC girder alone.
o This transfer stage is a temporary condition. Tensile stresses are
limited to ksi2.00948.0 '
cif for section without bonded
reinforcement or '
24.0 cif for section with reinforcement sufficient
to resists the tensile force in the concrete per Table 5.9.4.1.2-1
(AASHTO, 2012). The compressive stresses are governed by limits
in Article 5.9.4.1.1 of LRFD Specifications (AASHTO, 2012).
Figure 8.2-3 Representative Concrete Flexural Stress Distribution
at Stage I (Transfer)
TCC
(Mg/S)
- Self wt.
(P/A)
Prestress
CT
(Pe/S)
Prestress
C
Stage I
Concrete
Stresses
Girder
* ksi2.0or0948.0 '
cifT  for section without bonded reinforcement
* '
24.0 cifT  for section with reinforcement sufficient to resist concrete tensile force
T*
'
6.0 c
fC 

 Stage IIA: Erect girder and cast deck slab (Fig. 8.2-4):
o Girders are transported to job site and erected on structure supports.
Diaphragms and concrete deck are cast.
o When deck concrete is wet, deck slab does not contribute to section
modulus for flexural resistance.
o Temporary construction loads for machinery (e.g., Bidwell) need to
be accounted for.
o Girder self-weight plus weight of diaphragms and deck are supported
by the PC girder alone.
o This stage is a temporary condition. Tensile and compressive stresses
are governed by the limits in Article 5.9.4.1 of LRFD Specifications
(AASHTO, 2012).
Figure 8.2-4 Representative Concrete Flexural Stress Distribution
at Stage IIA (Erection and Deck Pour)
 Stage IIB: Construct barrier rails (Fig. 8.2-5)
o Deck concrete hardens and barrier rails are constructed. The girder
and deck act together as a composite section.
by the PC girder alone and additional dead load (haunch and barrier
rails) is supported by the composite section.
o Tensile and compressive stresses are governed by the limits in
Article 5.9.4.1 of LRFD Specifications (AASHTO, 2012).
C
C T
(Slab DL)
CT
S
Mslab
Stage IIA
concrete
stresses
'
6.0 cfC 
Neutral
Axis
Stage I
concrete
stresses

Figure 8.2-5 Representative Concrete Flexural Stress Distribution at Stage
IIB (Barrier Rail Construction).
 Stage III: Open to traffic (Fig. 8.2-6):
o Girder and deck continue to act as a composite section.
by the PC girder alone. Additional dead load (haunch and barrier
rails) and live loads are supported by the composite section.
o This stage is a permanent condition. Compressive and tensile stresses
are governed by the limits in LRFD Specifications Table 5.9.4.2.1-1
and Table 5.9.4.2.2-1 (AASHTO, 2012), respectively.
Figure 8.2-6 Representative Concrete Flexural Stress Distribution at
Stage III (Open to Traffic).
C
CC
C
C T
DC+DW
Service Level
'
19.0 cfT 
S
M LL 1
HL-93
Stage IIB
Stresses Adjusted
for Stage III
Composite
Section of Girder
and DeckGirder
with Wet Deck
C
Stage III
Concrete
Stresses
Neutral
AxisNeut
C
DL ADL 0
(No Tension)
C
S
MADL
ADL on Composite
Section
T
C
C
Stage IIA concrete
stresses
Composite
Section of
Girder and
Deck
C
Stage IIB
Concrete
Stresses
Neutral
Axis
Neutral
Axis (new)
S
M slab

8.2.3 Methods to Vary Strand Eccentricity and Force
Efficient design of PC girders typically requires varying the strand eccentricity
along the length of the member and/or limiting the strand force at transfer. PC girders
are fabricated, transported, and initially installed as simply-supported segments. For a
simply-supported girder with straight strands, the large eccentricity between the CGS
and the CGC section helps reduce tension and possible cracking at midspan at service
level. However, excessive flexural tensile stresses may develop at the top of the
girder segments near the ends, where counteracting flexural stresses due to self-
weight are minimal. Excessive flexural compressive stresses may similarly develop.
The critical location near the ends is at the transfer length, the distance from the end
of the girder at which the strand force is fully developed. For this temporary
condition, Table 5.9.4.1.2-1 of LRFD Specifications (AASHTO, 2012) specifies
appropriate stress limits to mitigate cracking and compression failure.
Figure 8.2-7 Draped Strand Profile (Pritchard, 1992)
Figure 8.2-8 Hold-Down Assembly in Stressing Bed
(Ma and Schendel, 2009)

To reduce the tensile and compressive stresses at the ends of girders, the designer
normally considers two primary methods, both of which are used in California:
 Harping (or draping) strands to reduce the strand eccentricity (Figures
8.2-7 and 8.2-8):.
o Advantages of harping include:
 Flexural design efficiencies due to the strand CGS achieving a
profile corresponding to the moment envelope
 Reduction of eccentricity at member ends to control concrete
stresses at these critical regions at transfer
 Additional shear capacity due to the contribution of the vertical
component of the prestress force in the harped strands
o Disadvantages of harping include:
 Safety issues and precaster ability to economically deflect and
anchor harped strands
 Slightly higher cost for fabrication and embedded hold-down
devices
 Beam form patching to accommodate variable hold down
locations
 Debonding (or shielding) select strands at the member ends to reduce the
transfer prestress force (Figure 8.2-11):
o Advantages of debonding include:
 Reduction in concrete stresses at member ends
 Simpler fabrication by the use of straight strands in the stressing
bed
 Elimination of hold-down devices
o Disadvantages of debonding include:
 Potential increase in design compressive strength of concrete
 Increased design effort to determine debonding patterns, shear
reinforcement, and camber

Figure 8.2-9 Bottom Fiber Stress Distribution at Transfer:
Harping vs. Debonding (PCI Bridge Design Manual 2011)
Figure 8.2-10 Top Fiber Stress Distribution at Transfer:
Harping vs. Debonding (PCI Bridge Design Manual 2011)
By draping the strands in a PC girder, the eccentricity can be varied in linear
segments along the length of the girder by mechanically deflecting some of the
stressed strands in the casting beds prior to casting using hold-downs and hold-ups,
as shown in Figures 8.2-7 and 8.2-8. Although draping is limited to strands within the
web, only a portion of the strands typically needs to be draped to achieve the required
eccentricity at girder ends. Typically, the drape points are located between
approximately 0.33L and 0.4L. Some fabricators may not have suitable equipment for
all drape profiles. In addition, the drape angle must be limited to ensure that jacking
requirements and hold-down forces do not exceed available capacity. The patterns in
Figures 8.2-9 and 8.2-10 provide a comparison of the bottom and top fiber stresses
associated with draped and debonded strands.

A) Single strand sheathing B) Debonded strands in PC girder
Figure 8.2-11 Plastic Sheathing Used for Debonding Strand
Alternatively, the designer may choose to limit transfer stresses by reducing the
prestress force through debonding strands along a portion of the girder length at
member ends. This is known as partial debonding. Figure 8.2-11 shows debonding of
a strand by encasing the strand in a plastic sheathing. Debonding strand prevents the
prestressing force from developing in the debonded region and causes the critical
section for stresses to shift a transfer length (i.e., 60 strand diameters, per LRFD
Specifications) beyond the end of debonding. Caltrans Amendments (Caltrans, 2014)
limit the number of partially debonded strands to 33% of the total number of strands
and the number of debonded strands in any horizontal row to 50% of the strands in
that row. Increases in development length at ultimate are also addressed in Article
5.11.4.3 of LRFD Specifications (AASHTO, 2012).
Due to the limitations in number of debonded strands at the girder bottom, the
temporary stress at girder top at the ends may still exceed the allowable stress limits,
especially for longer span girders. One solution is to use temporary strands at the
girder tops that are shielded along the member length except at the girder ends. These
strands can be cut at a later stage such as erection, when they are no longer needed,
by providing an access pocket formed in the girder top.

8.3 PRECAST BRIDGE TYPES
There are three main PC bridge types: i) precast pretensioned girders, ii) precast
post-tensioned spliced girders, and iii) precast segmental girders. Table 8.3-1
summarizes the typical span lengths for these bridge types.
Table 8.3-1 Precast Bridge Types and Span Lengths (Caltrans, 2012)
Bridge Type
Possible Span
Length (ft)
Preferred Span
Length (ft)
Precast pretensioned girder 30 to 200 30 to 180
Post-tensioned spliced girder 100 to 325 120 to 250
Precast segmental girder 200 to 450 250 to 400
The selection among these three bridge types is normally decided by span length
requirements. As shown in Table 8.3-1, a single precast, pretensioned girder could be
designed to span from 20 ft to 200 ft. Trucking length, crane capacity, and
transporting routes may limit the girder length (and weight) that could be delivered.
Therefore, a girder may need to be manufactured in two or more segments and
shipped before being spliced together on-site to its full span length. Such splicing
techniques can be applied by using post-tensioning systems for both single-span and
multiple-span bridges, which span up to 325 ft. For span lengths over approximately
250 ft, precast segmental girder bridges may be considered, which is beyond the
scope of this document. Section 8.3.3 further addresses spliced girder bridges.
8.3.1 Single-Span Bridges
As the simplest application of PC girders, single-span bridges normally consist of
single girders. As shown in Figure 8.3-1, girders are set onto bearing pads at seat-
type abutments. Dead and live load effects are based on a simply supported
condition. PC girders obviously lend themselves to being single-span elements
because they are fabricated as single elements. Abutments can be seat-type or end
diaphragm-type.
Figure 8.3-1 Single-Span I Beam Lowered onto Abutments at Mustang Wash
Bridge (Bridge No. 54-1279L, Caltrans)

8.3.2 Multi-Span Bridges
Many design considerations for single-span bridges apply to multi-span bridges
because girders or girder segments exist as single-span elements for several stages,
namely, fabrication, transportation, erection, and deck pour. In addition, some multi-
span bridges or portions thereof are constructed using expansion joints that can
produce a simply supported condition for a span.
Most multi-span bridges are constructed with simple-span girders made
continuous for live load to increase efficiency and redundancy. Limiting expansion
joints, designing deck reinforcement to serve as negative moment reinforcement at
interior bents, and providing girder continuity at bents by using a continuous CIP
deck and/or CIP diaphragms accomplishes this.
In addition, some bridges are detailed to provide an integral connection with full
moment transfer between the superstructure and substructure. To achieve this, use
CIP diaphragms at bent caps; reinforcing bars between the bent cap, diaphragm, and
girders; and/or longitudinal post-tensioning. An integral connection provides not only
longitudinal continuity for live load but also longitudinal continuity for seismic
loading. Due to moment continuity between the superstructure and substructure,
columns in multi-column bents may be designed to be pinned at their base, thus
reducing foundation cost.
The following sections summarize three typical bent cap configurations for
achieving continuity in multi-span bridges:
 Drop caps
 Inverted-tee caps
 Integral caps with precast post-tensioned girders
8.3.2.1 Drop Caps
Figure 8.3-2 Drop Cap at Chuckwalla Wash Bridge
(Bridge No. 54-1278L, Caltrans)

Drop caps are bent caps that provide intermediate supports for girders together
with live-load continuity (Figure 8.3-2). Drop caps are commonly detailed to provide
a non-integral connection-without moment continuity to the substructure but with
moment continuity in the superstructure through negative moment reinforcement in
the deck. Simple-span girders are placed on bearing pads at the top of drop caps.
Girders at the top of drop caps are normally tied together with a CIP diaphragm and
dowels placed through the webs at the ends of the girders. As shown in Figure 8.3-3,
steel pipe shear keys may extend from the top of the drop cap into the CIP
diaphragms at bent caps. With pipe shear keys, moment transfer is prevented between
the superstructure and substructure, and the bearing can more easily be replaced if
needed.
Figure 8.3-3 Nonintegral Drop Cap Detail Using Pipe Shear Key

With proper design and detailing of the diaphragm and bent cap, an integral
connection can be developed between the superstructure and substructure, as shown
in Figure 8.3-4. For example, the system can be designed to emulate seismic
performance of a continuous CIP PT concrete bridge if the joint between girder and
cap (due to positive moment during a seismic event) is prevented from opening. One
method is to extend pretensioning strands through the joint for development within
the cap, in accordance with the requirements of MTD 20-6 (Caltrans, 2001). As
mentioned in the subsequent section on integral caps with post-tensioned precast
girders, post-tensioning of the girders to the cap at intermediate supports can also be
used. The designer is encouraged to clearly detail the reinforcement between the
superstructure, diaphragm, and bent cap so that conditions assumed in design
realistically match field conditions.
Figure 8.3-4 Integral Drop Cap Detail
Adequate seat width must be provided for drop caps to prevent unseating due to
longitudinal displacement in a seismic event. Aesthetics should also be considered in
the use of drop caps, as they lack the clean lines of inverted-tee caps or CIP PT box
girders with integral caps.

8.3.2.2 Inverted-Tee Caps
Using an upside down “T” shaped cross section with a ledge, inverted-tee caps
combine the ability to place precast girders directly on the bent and the aesthetic
appeal of the flush bottom of cap with the precast girders. Hooked reinforcement
extending from side faces of the cap is placed between girders, and a diaphragm is
cast to tie the girders and cap together. A deck is later cast for live-load continuity.
This is shown in Figures 8.3-5 and 8.3-6.
Figure 8.3-5 Dapped End Girder with Inverted-Tee Cap (Snyder, 2010)

Figure 8.3-6 Existing Inverted-Tee to Dapped End
Girder Connection Detail
Designers have commonly modeled this connection as a pin (i.e., non-integral
connection between the superstructure and substructure) due to the assumption that
the connection would degrade to a pin in a seismic event. However, recent research
demonstrated that plastic hinges do indeed form at the column top, confirming that
moment continuity develops due to the use of CIP diaphragm and dowel bars through
the girder webs (Snyder, 2010). For this connection type, continuity at the column
top may be assumed, and joints may be designed for the force transfer associated
with plastic hinging. Confining reinforcement at the column top is required.
Designers should consult with the Caltrans Earthquake Committee for further
Seismic Design Criteria (SDC) updates and instructions for seismic design of invert-
tee cap-girder connections.
8.3.2.3 Integral Caps with Precast Post-Tensioned Girders
Post-tensioning PC girders through a CIP bent creates an integral connection
between the superstructure and substructure as well as a frame that is continuous for
service, strength, and extreme event limit states (Figure 8.3-7). In addition, such a
connection provides a means for bridge widening using PC girders to match the
performance and appearance of an existing CIP PT bridge. Without an integral
connection, continuity is not effectively developed at the bent cap, which would
require columns and foundations to be designed to provide the necessary fixity at the
base of the structure.
If the connection between post-tensioned PC girders and the bent cap is designed
and detailed properly, the system can emulate the seismic performance of a
continuous CIP PT concrete bridge (Holombo et al., 2000; Castrodale and White,
2004). Post-tensioning of the girders to the cap and intermediate supports is intended

to prevent joint opening due to positive moment during a seismic event. Extending
bottom pretensioning strands into the cap for development provides positive moment
capacity.
Figure 8.3-7 Integral Bent Cap Connection Using Longitudinal
Post-tensioning of PC Girders

8.3.3 Spliced Girder Bridges
Due to limitations in transportation length and member weight, as well as
stressing bed size, a girder may need to be fabricated in two or more segments and
shipped before being spliced together on-site to its full span length. Such splicing
techniques can be applied to both single-span and multiple-span bridges. By using
this approach, the designer has significant flexibility in selecting the span length,
number and location of intermediate supports, segment lengths and splice locations.
Splicing is more commonly used for multi-span bridge construction. However,
spliced girders have also been used successfully in the construction of several single-
span bridges in California such as the Angeles Crest Bridge (208 ft).
Splicing of girders is typically conducted on-site, either on the ground adjacent to
or nearby the bridge location, or in place using temporary supports. Figure 8.3-8
shows two precast bathtub girder segments being placed on temporary supports in
preparation for field splicing at midspan.
Figure 8.3-8 Precast Bathtub Girder Segments Spliced Near Midspan Using
Temporary Supports at Harbor Blvd. Overcrossing
(Bridge No. 22-0108, Caltrans)
Full continuity needs to be developed between spliced girder segments. This is
commonly achieved using post-tensioning tendons between segments and mechanical
coupling of reinforcement that is extended from the ends of the girder segments
within a CIP closure pour. Figure 8.3-9 shows these details at the closure pour,
including the use of couplers for PT ducts and ultimate splice couplers for
reinforcement.

Figure 8.3-9 Details of Spliced Girder Closure Pour Using Mechanical
Splices and PT Duct Couplers (Bridge No. 22-0108, Caltrans)
Post-tensioning spliced girders not only provides continuity but also enhances
structural efficiency. Post-tensioning enhances interface shear capacity across the
splice joint (closure pour), which normally includes roughened surfaces or shear keys
(Figure 8.3-9).
When splicing together multiple spans of PC girders, it is critical that the precast
girder placement, post-tensioning sequence, and material properties be properly
defined. Figure 8.3-10 shows the construction sequence of a typical two-span (or
multi-span) spliced girder bridge. At each stage, the following must be checked:
concrete compressive strength and stiffness, creep and shrinkage of concrete, and
tension force in the prestressing steel (and debonded length, if needed). The designer
must consider each stage as the design of an individual bridge with given constraints
and properties defined by the previous stage.

Figure 8.3-10 Spliced Bridge Construction Sequence
(Bridge No. 22-0108, Caltrans)

The simplest multi-span precast spliced girder system includes consideration of a
minimum of four stages or steps after fabrication and before service loads, as
follows:
 Transportation: The girder acts as a simply supported beam, with
supports defined by the locations used by the trucking company.
Typically, the manufacturer or trucking company is responsible for
design and check of loads, stability, and bracing during transportation
and erection of the girder.
 Erection: The girder initially acts as a simply supported beam, with
supports defined by the abutments, bents or temporary falsework
locations. A CIP closure pour is placed after coupling of PT tendons and
reinforcing bars in the splice joint. Optionally, a first stage of post-
tensioning may be applied before the deck pour instead of after the deck
pour (not shown in Figure 8.3-10).
 Deck pour: The deck is poured but not composite with the girders until
attaining full strength. Therefore, the girders alone carry girder self-
weight and the wet deck weight.
 Post-tensioning: The hardened deck and girder act compositely, and the
girders are spliced together longitudinally using post-tensioning. As the
number of girders that are spliced and the stages of post-tensioning
increases, so does the complexity of design.

8.4 DESIGN CONSIDERATIONS
PC girder design must address three basic stages—transfer, service, and
ultimate—as well as additional stages if post-tensioning is introduced. PC girder
design, including section size, prestress force (number and size of strands), strand
layout, and material properties, may be governed by any of these stages. Although
design for flexure dominates the PC girder design process, other aspects must also be
considered, such as prestress losses, girder shear and interface shear strength,
deflection and camber, anchorage zones, diaphragms, and end blocks. The following
sections briefly introduce the various aspects of PC girder design.
The designer is encouraged to read the references cited in the following sections,
particularly LRFD Specifications (AASHTO, 2012), Caltrans Amendments
(Caltrans, 2014), Caltrans Memo To Designers (MTD) 11-8 (Caltrans, 2014),
Caltrans Bridge Design Aids 6-1 (Caltrans, 2012), and Chapters 5 and 6.
8.4.1 Materials
8.4.1.1 Concrete
Concrete used in PC girders produced under plant-controlled conditions is
typically of higher strength and higher quality than for CIP concrete. Per MTD 11-8,
the minimum concrete compressive strength at release, fći, and minimum 28-day
concrete compressive strength, fć, for PC girders is 4 ksi. In addition, the concrete
compressive strength at release, fći, may be selected as large as 7 ksi and fć as large
as 10 ksi. However, designers should verify with local fabricators’ economical ranges
of fći on a project-specific basis, especially for fći and fć exceeding these limits.
Minimum concrete compressive strengths may also be specified at girder erection
and for post tensioning, when used.
In most PC girder design, a relatively large value of fći is used in design, which
typically controls the overall concrete mix design. If an excessively large value of fći
is required in design to resist temporary tensile stresses at transfer in areas other than
the precompressed tensile zone, such as the top flange at girder ends, then bonded
reinforcement or prestress strands may be designed to resist the tensile force in the
concrete, per stress limits in LRFD Specifications Table 5.9.4.1.2-1 (AASHTO,
2012). This helps reduce the required fći used in design.
The relatively large value of fći used in design also results in a relatively large
value of fć (e.g., often in excess of 7 ksi), which is normally larger than that required
to satisfy the concrete compressive strength requirements at the serviceability and/or
ultimate limit state. In cases where a larger fći is required to produce an economical
design (e.g., girders of long span, shallow depth, or wide spacing), high strength
concrete mixes that require longer than the normal 28-day period may be specified.
Current Standard Specifications allow 42 days for achieving specified strength and
56 days for low cement mixes. However, designers should verify the impact of such a
decision on the overall construction schedule.

Advantages of the concrete used in PC girders produced under plant-controlled
conditions are wide ranging. Higher modulus of elasticity and lower creep, shrinkage,
and permeability are by-products of the relatively higher compressive strength and
steam curing process used for PC girders. In addition, reduced effects of creep and
shrinkage for PC girders occur after installation because most creep and shrinkage
occurs prior to erection. Supplementary cementitious materials (SCMs) and regional
materials may also be used for benefits in cost, material properties, and
environmental impact through the use of in-house batch plants, mix designs, and
sustainability practices.
Self-consolidating concrete (SCC), a highly flowable yet cohesive concrete that
consolidates under its own weight, is becoming more commonly used in precast
plants. It provides significant advantages such as elimination of external and internal
vibration for consolidation and reduced manual labor and equipment requirements
resulting in reduced construction time; excellent consolidation, even in congested
regions of reinforcement; higher level of quality control; extremely smooth concrete
surfaces, even in negative draft regions; eliminated need for patching; increased
safety; and lower noise levels, usually combined with higher strength and improved
durability. Some disadvantages of SCC include more costly material, stricter control
on selection and measurement of materials, larger number of trial batches, greater
sensitivity to water content, more rapid hardening, faster drying, higher formwork
design loads (for fluid pressure), as well as greater experience and care in handling
and production of SCC.
8.4.1.2 Steel
For economy, PC girders commonly use 0.6 in. diameter, 270 ksi (Grade 270),
low-relaxation strands. Use of 0.5 in. diameter strands is less common because the
0.6 in. diameter strands provide a significantly higher efficiency due to a 42%
increase in capacity. However, 0.375 in. diameter strands are commonly used for
stay-in-place, precast deck panels. If epoxy coated prestressing strands are required, a
note should be shown on the design plans, and the corresponding section of the
Standard Specifications should be used.
Deformed welded wire reinforcement (WWR), conforming to ASTM A497 and
Caltrans Standard Specifications based on a maximum tensile strength of 60 ksi, is
permitted and commonly used as shear reinforcement in PC girder design.
8.4.2 Prestress Losses
From the time prestressing strands are initially stressed, they undergo changes in
stress that must be accounted for in design. Figure 8.4-1 illustrates the change in
strand stress over time for a typical pretensioned girder.

Figure 8.4-1 Strand Stress vs. Time in Pretensioned Girder
(Tadros et al., 2003)
Prestress losses in prestressed concrete members consist of instantaneous (or
immediate) and time-dependent losses in prestressing strands. Total losses can be
estimated using the LRFD Specifications approach:
∆fpT = ∆fpES  ∆fpLT (AASHTO 5.9.5.1-1)
where:
∆fpT = total change in stress due to losses (ksi)
∆fpES = sum of all losses or gains due to elastic shortening or extension at the time
of application of prestress and/or external loads (ksi)
∆fpLT = losses due to long-term shrinkage and creep of concrete, and relaxation of
the steel (ksi)
Losses are normally defined from the time of initial stress (immediately after
seating of strands for PC girders). Time-dependent losses of prestress include
concrete creep and shrinkage and steel relaxation. LRFD Specifications (AASHTO,
2012) provides an approximate estimate and refined estimate for determining time-
dependent losses. The background can be found in the National Cooperative
Highway Research Program (NCHRP) Report 496, Prestress Losses in Pretensioned
High-Strength Concrete Bridge Girders (Tadros et al., 2003).
For PC girders, instantaneous loss refers to loss of prestress due to elastic
shortening of the girder at transfer. Elastic gain refers to increase in strand stress due
to strand extension related to application of external loads.

A reasonable estimate of prestress losses is critical to properly estimate the
required prestress force (and thus the required number of strands). Overestimating
losses leads to a larger than necessary initial prestress force, which results in larger
initial tensile and compressive stresses and may, in turn, result in cracking and larger
than expected camber. Overestimation of losses tends to reduce design efficiency
because of the increase in number of strands, f´ci cost of the concrete mix, and/or
curing time. In addition, problems in girder placement and haunch height in the field
may result from excessive camber. Although underestimating losses could potentially
produce adverse effects such as flexural cracking in the precompressed tensile zone
at service level, such problems have rarely been found to occur in practice.
8.4.2.1 Instantaneous Losses
In PC girders, the entire prestressing force is applied to the concrete in a single
operation. For pretensioned members, the loss due to elastic shortening can be
calculated from AASHTO Eq. 5.9.5.2.3a-1, as shown below:
cgp
ct
p
pES f
E
E
f  (AASHTO 5.9.5.2.3a-1)
where:
∆fpES = sum of all losses or gains due to elastic shortening or extension at the
time of application of prestress and/or external loads (ksi)
fcgp = the concrete stress at the center of gravity of prestressing tendons due to
the prestressing force immediately after transfer and the self-weight of
the member at the section of maximum moment (ksi)
Ep = modulus of elasticity of prestressing steel (ksi)
Ect = modulus of elasticity of concrete at transfer or time of load application
(ksi)
Calculation of ∆fpES requires iteration for fcgp. However, iteration can be avoided
by using LRFD Specifications Eq. C5.9.5.2.3a-1 (AASHTO, 2012) for ∆fpES. It is
important that LRFD Specifications Articles C5.9.5.2.3a and C5.9.5.3 be consulted
when using transformed section properties in the stress analysis.
8.4.2.2 Time-Dependent Losses
LRFD Specifications (AASHTO, 2012) provides two methods to estimate the
time-dependent prestress losses: approximate method (Article 5.9.5.3) and refined
method (Article 5.9.5.4). This chapter introduces a sample calculation using the
approximate method. However, for cases in which the refined method is required or
preferred, the designer should consult Article 5.9.5.4 of AASHTO LRFD (AASHTO,
2012). Chapter 9 of the PCI Bridge Design Manual (2011) provides useful PC girder
design examples with prestress loss calculations using both the refined and
approximate methods.

Per Article 5.9.5.3, the approximate method is applicable to standard precast,
pretensioned members subject to normal loading and environmental conditions,
where:
 Members are made from normal-weight concrete
 Concrete is either steam- or moist-cured
 Prestressing strands use low relaxation properties
 Average exposure conditions and temperatures characterize the site
In addition, the estimate is intended for sections with composite decks. This
method should not be used for uncommon shapes (volume-to-surface ratios, V/S,
significantly different than 3.5 in.), unusual level of prestressing, or with complex
construction staging.
Long-term prestress losses due to creep and shrinkage of concrete and relaxation
of steel are estimated using the following formula, in which the three terms
corresponds to creep, shrinkage, and relaxation, respectively:
pRsthsth
g
pspi
pLT f
A
Af
f   1210 (AASHTO 5.9.5.3-1)
where:
Ag = gross area of girder section
Aps = area of prestressing steel
fpi = prestressing steel stress immediately prior to transfer (ksi)
H = average annual ambient mean relative humidity (percent)
h = correction factor for relative humidity of ambient air
= 1.7-0.01H
st = correction factor for specified concrete strength time at of prestress
transfer to concrete member
= 5/(1+ f´c)
∆fpR = an estimation of relaxation loss taken as 2.4 ksi for low relaxation strand,
10 ksi for stress relieved strand, and in accordance with manufacturers
recommendation for other types of strand (ksi)
8.4.3 Flexure
Bridge Design Practice provides a detailed summary of flexural design
provisions, with limit states for service (including transfer), strength, and fatigue in
accordance with LRFD Specifications (AASHTO, 2012) and Caltrans Amendments
(Caltrans, 2014). Figures 8.2-3 through 8.2-6 illustrate the change in flexural stress
distribution near midspan for a typical PC girder at transfer, deck pour, and service
level.

MTD 11-8 provides specific guidance for design of PC girders, addressing issues
such as:
 Order of design (service limit state followed by strength check)
 Live load continuity and negative moment reinforcement over the bents
 Determination of Pj and centroid of PS steel (CGS) and their inclusion on
plan sheets
 Harping versus debonding, including tolerances for harping and
debonding provisions
 Use of temporary strands and associated blockouts
 Positive moment reinforcement for continuous spans
 Design modifications for long span girders
In addition, the following practical aspects should also be noted in carrying out
flexural design of PC girders:
 The initial girder section size is typically based on the minimum depth-
to-span ratio required for a given girder type.
 The specified concrete compressive strengths (initial and 28-day) are
commonly governed by the initial compressive strength, f´c , required to
limit stresses at transfer.
 The total prestress force (number and size of strands) and strand layout
are usually determined to satisfy the service limit state (Service III) but
may have to be revised to satisfy flexural strength at ultimate (Strength
II, California P-15 permit truck).
 Girder design is based on the minimum overall depth when computing
capacity of the section.
8.4.4 Shear
8.4.4.1 Shear Design for Girders
Per MTD 11-8, shear design of PC girders is performed using the sectional
method specified in LRFD Specifications Article 5.8.3 (AASHTO, 2012). The
sectional method is based on the Modified Compression Field Theory (MCFT),
which provides a unified approach for shear design for both prestressed and
reinforced concrete components (Collins and Mitchell, 1991). The MCFT is based on
a variable angle truss model in which the diagonal compression field angle varies
continuously, rather than being fixed at 45˚ as assumed in prior codes. For
prestressed girders, the compression field angle for design is typically in the range of
20˚ to 40˚.
Per Article 5.8.3.4.3 of the California Amendments (Caltrans, 2014), the LRFD
Specifications (AASHTO, 2012) simplified shear design procedure cannot be used in
PC girder design.

For disturbed regions, such as those occurring at dapped ends, shear provisions
using the strut and tie method should be used (AASHTO, 2012).
In the sectional method, a component is investigated by comparing the factored
shear force and the factored shear resistance at a number of sections along the
member length. Usually this check is made at a minimum of tenth points along the
span as well as at locations near the supports.
Because shear design typically follows flexural design, certain benefits can be
realized in shear design. For example, when harped strands are used, the vertical
component of the harped strand force contributes to shear resistance. In addition, the
higher strength concrete specified for flexure enhances the Vc term for shear design.
Because flexure-shear interaction must be checked per Article 5.8.3.5 of LRFD
Specifications (AASHTO, 2012), the longitudinal reinforcement—based on flexural
design—must be checked after shear design, to ensure that sufficient longitudinal
reinforcement is provided to resist not only flexure (and any axial forces along the
member), but also the horizontal component of a diagonal compression strut that
generates a demand for longitudinal reinforcement. LRFD Specifications (AASHTO,
2012) includes an upper limit on the nominal shear resistance, Vn, that is independent
of transverse reinforcement, to prevent web crushing prior to yielding of transverse
reinforcement.
For skewed bridges, live load shear demand in the exterior girder of an obtuse
angle must be magnified in accordance with LRFD Specifications (AASHTO, 2012)
Article 4.6.2.2.3c unless a three-dimensional skewed model is used.
To accommodate field bending of stirrups, #4 or #5 stirrups are commonly
preferred. In most cases, the size of stirrups should not exceed #6.
8.4.4.2 Interface Shear Design
Interface shear should be designed based on the shear friction provisions of
LRFD Specifications (AASHTO, 2012) Article 5.8.4 and MTD 11-8.
8.4.5 Deflection and Camber
8.4.5.1 Key Aspects for Design
Designers must address potentially challenging issues related to downward
deflection and upward camber of PC girders. Camber in a PC girder occurs
instantaneously at transfer but can increase to much larger values long-term,
particularly due to creep and shrinkage of the concrete. Excessive camber at erection
may cause potential intrusion of the top flange of the girder into the CIP deck.
Although the contractor is responsible for deflection and camber calculations (per
Caltrans Standard Specifications and MTD 11-8), the designer is responsible for
specifying a midspan haunch thickness and calculating the minimum haunch
thickness at supports, which affects the total bridge depth at both mid-span and at
supports. In order to calculate the minimum haunch thickness at supports, girder
deflections at release and at erection, as well as immediate girder deflection due to

the deck weight, must be considered. To complete the deflection design and provide
better construction support, the following guidelines are recommended:
 Specify unfactored instantaneous girder deflections on plan sheets: Per
Caltrans Standard Specifications, the contractor is responsible for
deflection and camber calculations and any required adjustments for
deck concrete placement to satisfy minimum vertical clearance, deck
profile grades, and cross slope requirements. However, the designer must
provide, on plan sheets, the unfactored instantaneous girder deflections
due to:
o Deck and haunch weight on the non-composite girder
o Weight of barrier rail and future wearing surface on the composite
girder-deck section
These deflection components are used to set screed grades in the field.
For spliced girders, instantaneous upward deflections due to post-
tensioning at different stages should be shown on the design plans.
 Determine minimum haunch thickness and specify on plan sheets: The
haunch is the layer of concrete placed between the top flange of the
girder and bottom of deck to ensure proper bearing. It accommodates
construction tolerances such as unknown camber of the girder at time of
erection. Because camber values vary along the span length, the actual
haunch thickness varies along the span, too. The designer should specify
the haunch thickness at mid-span and then calculate the minimum
required haunch thickness at supports.
The haunch:
o Accommodates variation in actual camber
o Allows the contractor to adjust screed grades
o Eliminates potential intrusion of the top flange of the girder into the
CIP deck
o Establishes the seat elevation at supports
Cross slope and width at the top flange of the girder should be
considered in determining the specified midspan haunch thickness.
The typical section should show:
o Minimum structure depth at centerline of bearing at the supports,
including girder depth, deck thickness, plus calculated haunch
thickness
o Minimum structure depth at mid-span, including girder depth, deck
thickness, plus any haunch thickness the designer specifies
It should be noted that for girders with large flange widths, such as the
CA wide-flange girder, a larger haunch thickness might add a significant
concrete quantity and weight to the design.

 Satisfy LRFD Specifications for live load deflection: Service level
deflections may be checked per Article 2.5.2.6.2 of LRFD Specifications
(AASHTO, 2012), which suggests a limit of L/800 for live load
deflection due to HL-93 vehicular loading. This is an optional check and
not required per LRFD Specifications. Because this is an instantaneous
deflection check, no multipliers for long-term deflection should be used.
The modulus of elasticity should be determined based on Eq. 5.4.2.4-1 of
LRFD Specifications (AASHTO, 2012) and the effective moment of
inertia, Ie, should be used per Article 5.7.3.6.2.
 Verify girder camber is controlled at key stages: The designer may work
with the construction structure representative to ensure that the estimated
PC girder camber and camber growth are controlled throughout all key
stages, such as fabrication, erection, deck placement, and service level.
Camber should not be excessive (i.e., causing concern over intrusion of
the top flange of the girder into the CIP deck) and should be positive
(upward) under both short-term and long-term conditions. This requires
the designer to be aware of girder deflection due to prestress force and
dead loads, as well as the timing of their application. This can be
especially important for bridge widenings. When more accurate camber
values are required for unusual cases such as widening of a long span
bridge, the assumed age of the girder at various stages may need to be
shown on plan sheets.
8.4.5.2 Calculation Approaches
Total deflection of a girder at any stage is the sum of the short-term and long-
term deflections. Short-term deflections are immediate deflections based on the
modulus of elasticity and effective moment of inertia of the appropriate section.
Some loads (such as girder and deck self-weight) are carried by precast girder alone,
while others loads are carried by the much stiffer composite girder-deck system (such
as barriers, overlays, as well as live loads). Long-term deflections consist of long-
term deflections at erection and long-term deflection at final stage (may be assumed
to be approximately 20 years). Long-term deflections at erection are more coarsely
determined because of the highly variable effects of creep and shrinkage. Therefore,
although theoretical values and various procedures to determine instantaneous and
long-term camber and deflection of PC girders are available, calculated values must
be viewed as merely estimates.
Table 8.4-1 lists common equations for instantaneous camber of PC girders for
different prestress configurations. Long-term deflections at erection and final stage
are typically estimated based on one of three approaches:
 Historic multipliers (e.g., Table 8.7.1-1 of PCI Bridge Design Manual
(2011) shown as Table 8.4-2 below)
 Modified multipliers based on regional industry experience
 Detailed time-step analysis accounting for various construction stages
and varying material properties

Table 8.4-1 Camber and Rotation Values for Various Prestress Configurations
(Naaman, 2004)
Case 1
Case 2
Case 3
Case 4

Table 8.4-2 PCI-Recommended Multipliers for Estimating Long-term Camber and
Deflection for Typical PC Members (PCI, 2011)
At Erection
Without
Composite
Topping
With
Composite
Topping
(1)
Deflection () component: Apply to the elastic
deflection due to the member weight at transfer of
prestress
1.85 1.85
(2)
Camber () component: Apply to the elastic camber
due to prestress at the time of transfer of prestress
1.8 1.8
Final
(3)
deflection due to the member weight at transfer of
prestress
2.7 2.4
(4)
Camber () component: Apply to the elastic camber
due to prestress at the time of transfer of prestress
2.45 2.2
(5)
deflection due to superimposed dead load only
3 3
(6)
Deflection caused by the composite topping
--- 2.3
Use of multipliers (either historic or regionally modified) for girders is the most
common approach for estimating long-term deflections at erection of routine bridges
in California. The design example of Section 8.6 uses the historic multiplier method.
Instantaneous deflection due to prestressing force and girder weight is calculated at
release. Long-term deflection of precast concrete girders at erection is then calculated
as the instantaneous deflection multiplied by a multiplier. In performing calculations,
camber due to prestressing force and the self-weight of girder, as well as deflections
due to the weight of deck and haunch are calculated using the initial modulus of
elasticity of concrete and section properties for the non-composite girder. Then,
deflections due to the concrete barrier and future-wearing surface are calculated using
gross composite section properties.
The historic multiplier method is a simple and straightforward method. Even
though it is found to give reasonably accurate prediction of the deflection at time of
erection, it, however, is not recommended for estimating long-term deflection of
bridges comprise of beams that are made composite with cast-in-place deck slab.
This method does not account for the relatively significant effects of cast-in-place
concrete deck, as described here. Once the deck is hardened, it restrains the beam
from creeping upward (due to prestressing). In addition, the differential creep and
shrinkage between girders and cast-in-place concrete deck results in changes of the
bridge member deformation.
The design example in Section 8.6 illustrates the use of Table 8.4-2 to estimate
long-term camber and deflection to determine minimum required haunch thickness at
supports. Chapter 9 of the PCI Bridge Design Manual (2011) provides additional
example calculations for camber and deflection.

8.4.6 Anchorage Zones
8.4.6.1 Splitting Resistance
End splitting can occur along prestressing strands due to local bursting stresses in
the pretensioned anchorage zone. To prevent failure, Article 5.10.10 of LRFD
Specifications (AASHTO, 2012) requires vertical reinforcement, As, to be provided
within a distance h/4 from the end of the girder to provide splitting or bursting
resistance given by the following equation:
Pr = fs As (AASHTO 5.10.10.1-1)
where:
As = total area of vertical reinforcement located within the distance h/4 from end
of beam (in.2
)
fs = stress in steel not to exceed 20 ksi
Pr= factored bursting resistance of pretensioned anchorage zone provided by
transverse reinforcement (kip)
Per LRFD Specifications (AASHTO, 2012) Article 5.10.10.1, fs should not
exceed 20 ksi and Pr should not be taken as less than 4% of the total prestressing
force at transfer.
For spliced precast girders where post-tensioning is directly applied to the girder
end block, general zone reinforcement is required at the end block of the anchorage
area based on Article 5.10.9 of LRFD Specifications (AASHTO, 2012).
8.4.6.2 Confinement Reinforcement
Article 5.10.10.2 of LRFD Specifications (AASHTO, 2012) requires
reinforcement be placed to confine the prestressing steel in the bottom flange, over
the distance 1.5d from the end of the girder, using #3 rebar or larger with spacing not
to exceed 6 in. and shaped to enclose the strands.
8.4.7 Diaphragms and End Blocks
Although intermediate diaphragms may not be required per Article 5.13.2.2 of
LRFD Specifications (AASHTO, 2012), Caltrans practice and MTD 11-8 specify the
use of one or more intermediate diaphragms for girders longer than 80 ft to improve
distribution of loads between girders and to help stabilize the girders during
construction. Also, per Article 5.13.2.2 of LRFD Specifications (AASHTO, 2012),
end diaphragms are required at abutments, piers, and hinge joints. Due to increase in
fabrication inefficiencies, girder weight, and overall cost, end blocks should only be
used where essential for shear resistance. For more information, see MTD 11-8.

8.4.8 Lateral Stability
Because PC girders tend to be rather long slender members, they should be
checked for lateral stability during all construction stages, including handling,
transportation, and erection. Fabricators are normally responsible for all girder
stability checks. However, the designer is encouraged to consider and verify lateral
stability during design, especially when non-standard girders are selected.
Procedures for checking lateral stability were developed by Mast, 1989 and 1993,
and recently summarized in Section 8.10 of the PCI Bridge Design Manual. Some
commercial software incorporates this method. The designer should verify specific
assumed support and stability parameters (e.g., support locations, impact, transport
stiffness, super elevation, height of girder center of gravity and roll center above
road, and transverse distance between centerline of girder and center of dual tire)
with local fabricators, contractors, and other engineers, as appropriate.

8.5 DESIGN FLOW CHART
The following flow chart shows the typical steps for designing single-span precast, prestressed
concrete girders. The example in the next section closely follows this flow chart.
START
DEVELOP GEOMETRY
- Select Girder Type and Spacing
- Determine Structure Depth
- Check Deck Thickness
SELECT MATERIALS
- Select Material Properties for Concrete and Steel
DETERMINE LOADS AND PERFORM STRUCTURAL ANALYSIS
- Calculate DC, DW, LL
- Calculate Distribution Factors
- Calculate Unfactored Shear and Moment Envelopes
DESIGN FOR STRENGTH LIMIT STATE - SHEAR
- Calculate Factored Applied Shear, Vu
- Calculate Concrete Shear Resistance, Vc
- Calculate Required Shear Reinforcement
- Check Spacing and Reinforcement Limits
ESTIMATE PRESTRESS FORCE
- Estimate of PS Force under Service Limit III
- Calculate Required Area of Strands and CGS
CALCULATE SECTION PROPERTIES
- Calculate Precast Section Properties
- Calculate Composite Section Properties
ESTIMATE PRESTRESS LOSSES
- Estimate Elastic Shortening
- Estimate Long-Tem Losses (Approximate or Refined Method)
DESIGN FOR SERVICE LIMIT STATE
- Check Concrete Stress at Release Condition
- Check Concrete Stress at Service Condition
DESIGN FOR STRENGTH LIMIT STATE - FLEXURE
- Calculate Factored Applied Moment, Mu
- Calculate Nominal Flexural Resistance, Mn
- Check Reinforcement Limits
Stress Limits
YES
NO
Mn ≥Mu?
YES
Determine Additional
Required Aps or As
NO
MORE

Figure 8.5-1 Precast/Prestressed Concrete Girder Design Flow Chart
DESIGN FOR INTERFACE SHEAR
- Calculate Interface Shear Reinforcement
- Check Reinforcement Limits
- Check Maximum Nominal Shear Resistance
CHECK MINIMUM LONGITUDINAL REINFORCEMENT
- Check Longitudinal Reinforcement for V-M Interaction
DETERMINE CAMBER, DEFLECTION, AND HAUNCH THICKNESS
- Calculate Deck and Rail Deflections for Contract Plans
- Check Live Load Deflection against AASHTO LRFD criteria
- Determine Minimum Haunch Thickness at Supports for Contract Plans
DESIGN FOR ANCHORAGE ZONE
- Design Pretensioned Anchorage Zone Reinforcement:
Vertical and Confinement
END
CONTINUED

8.6 DESIGN EXAMPLE
This example illustrates the design procedure for a typical PC girder using the
AASHTO Specifications (AASHTO, 2012) and California Amendments (Caltrans,
2014).
To demonstrate the process, a typical interior girder of a 70 ft single-span bridge
with no skew is designed using a standard California PC I girder with composite CIP
deck to resist flexure and shear due to dead and live loads. The design live load used
for service limit design (Service I and III) is the HL-93 design truck, and the Caltrans
P15 design truck is used for the strength limit design (Strength II). Elastic flexural
stresses for initial and final service limit checks are based on transformed sections.
The LRFD Specifications Approximate Method is used to estimate long-term, time-
dependent prestress losses based on gross section properties. Shear design is
performed using the sectional method.
Major design steps include establishing structural geometry, selecting girder type
and spacing, selecting materials, performing structural analysis, estimating prestress
force, estimating prestress losses, service limit state design, strength limit state
design, shear design, anchorage zone design, determining girder deflections and
determining minimum haunch thickness at supports.
8.6.1 Problem Statement
A 70 ft simple-span bridge is proposed to carry highway traffic across a river.
Preliminary studies have resulted in the selection of a PC concrete bridge based on
traffic and environmental constraints at the site. Figures 8.6-1 and 8.6-2 show the
elevation and plan views of the bridge, respectively. The span length (from centerline
of bearing to centerline of bearing) is 70 ft and the girder length is 71 ft.
The required bridge deck width is 35 ft, which includes a 32 ft roadway and two
1.5 ft concrete barriers. Three inches of polyester concrete overlay are assumed to be
placed on the bridge as a future-wearing surface (additional dead load on girders).
Design of a typical interior girder must satisfy all requirements of LRFD
Specifications Bridge Design Specifications (AASHTO, 2012) and California
Amendments (Caltrans, 2014) for all limit states.

Figure 8.6-1 Elevation View of the Example Bridge
Figure 8.6-2 Plan View of Example Bridge
C FreewayL
35-0"
BB EB
Directionof
flow
12-0"
Traffic Lane
shoulder
shoulder
12-0"
Traffic Lane
Girder Length = 71'-0"
Span Length = 70'-0"

8.6.2 Select Girder Depth, Type, and Spacing
For a 70 ft span, the standard California I girder section has been found to be an
efficient section, with a minimum structure depth-to-span length ratio (D/L) of 0.055
for simple spans, based on Chapter 6 of Caltrans Bridge Design Aids (2012). Also for
PC girders, a girder spacing-to-structure depth ratio (S/D) of 1.5 is commonly used.
Span length, L = 70 ft
Assuming:
Structure Depth, Ds
Span Length, L
= 0.055
The minimum depth is: Ds = 0.055 (70) = 3.85 ft
Because the deck thickness is based on girder spacing and girder spacing is based
on structure depth, the concrete slab thickness must be initially assumed. Assume a
slab thickness of 7 in. and later verify this value using Table 10-20.1(a) Deck Slab
Thickness and Reinforcement Schedule in Memo To Designers (Caltrans, 2008b)
after the girder spacing has been determined.
Therefore, the minimum girder height = 3.85 (12) – 7 = 39.2 in.
Select a 42 in. standard California I girder (CA I42) from BDA 6-1, slightly
larger than the minimum height.
Assuming a haunch thickness, th = 1 in. at midspan:
The structure depth, Ds = 42 + 1 + 7 = 50 in. (4.17 ft)
Ds
L
=
4.17
70
=0.060 > 0.055 OK
The center-center girder spacing is determined as follows:
Maximum girder spacing, S = 1.5 Ds = 1.5 (4.17 ft) = 6.26 ft
Total bridge width = 35 ft (assumed)
Try a girder spacing, S = 6 ft
Overhang length=
35 - 6 (5 spacings)
2 overhangs
=2.5 ft
According to MTD 10-20, Attachment 1 (Caltrans, 2013), overhangs should be
less than half the girder spacing (S/2) or 6 ft maximum.
2.5
6
= 0.42 ft < 0.50 ft OK
Therefore, use 6 ft girder spacing.
Determine deck thickness:

From MTD Table 10-20.1(b) Deck Slab Thickness and Reinforcement Schedule
(Caltrans, 2008b), for girder centerline-to-centerline spacing of 6 ft, the required slab
thickness is 7 in. Therefore, a 7 in. deck thickness can be used.
The established typical cross section of the bridge is presented in Figure 8.6-3. It
consists of six standard California 3 ft - 6 in. PC I-girders (CA I42) with a 7 in. CIP
composite deck and two Type 736 concrete barriers.
Figure 8.6-3 Typical Bridge Cross Section.
8.6.3 Establish Loading Sequence
The loading sequence and corresponding stresses for a single-span PC girder are
normally considered at three distinct stages, as summarized in Table 8.6-1. The table
also indicates what section (non-composite versus composite) resists the applied
loading.
Note: Per Caltrans practice, transportation (shipping and handling) is generally the
responsibility of the contractor and PC manufacturer.
1-6 1-6
4'-2"
3'-6""
PC I-Girder, Typ.
Concrete
Barrier
0'-7"

Table 8.6-1 Typical Stages of Loading and Resisting Section for Single-Span
PC Girder
Stage Location
Construction
Activity
Loads Resisting Section
I
Casting
Yard
Cast and Stress
Girder (Transfer)
DC (Girder)
Girder
(Non-composite)
IIA On Site
Erect Girder,
Cast Deck Slab
DC (Girder, Diaphragm,
Slab), Construction Loads
Girder
(Non-composite)
IIB On Site
Construct Barrier
Rails
Slab)
Girder
(Non-composite)
DC (Barrier Rails)
Girder and Deck
(Composite)
III
Final
Location
Open to Traffic
Slab)
Girder
(Non-composite)
DC (Barrier Rails)
DW (Future Wearing
Surface)
LL (Vehicular Loading,
HL-93 or P15)
Girder and Deck
(Composite)
8.6.4 Select Materials
The following materials are selected for the bridge components. The concrete
strengths for PC girders at transfer and at 28 days are assumed at this stage of design
based on common practice in California. However, these values are subsequently
verified during service limit state design:
 Concrete compressive strength and modulus of elasticity:
o PC girder
Concrete unit weight is assumed herein wc = 0.15 kcf
At transfer:
fći = 4.8 ksi (80% of fć at 28 days)
Eci = 33,000 wc
1.5
′ (AASHTO 5.4.2.4)
= 33,000 (0.15)1.5
√4.8 = 4,200 ksi
Eci = modulus of elasticity of concrete at time of transfer
At 28 days:
fć = 6 ksi
Ec=33,000 (0.15)1.5
√6 = 4,696 ksi
o Cast-in-place deck slab:
Concrete unit weight is assumed herein wc = 0.15 kcf
fć = 3.6 ksi (Article 5.4.2.1 of CA; MTD 10-20)

Ec=33,000 (0.15)1.5
√3.6 = 3,637 ksi
o Prestressing steel:
0.6 in. diameter, seven-wire, low-relaxation strands,
Area of each strand, Aps = 0.217 in.2
Grade 270, nominal tensile strength,
fpu = 270 ksi (AASHTO Tab 5.4.4.1-1)
Yield strength, fpy = 0.9 fpu = 243 ksi (AASHTO Tab 5.4.4.1-1)
Initial jacking stress, fpj = 0.75 fpu = 202.5 ksi
(CA Table 5.9.3-1, 2013)
Modulus of elasticity of prestressing steel,
Ep = 28,500 ksi (AASHTO Article 5.4.4.2)
o Mild steel - A706 reinforcing steel:
Nominal yield strength, fy = 60 ksi
Modulus of elasticity of steel, Es = 29,000 ksi
8.6.5 Calculate Section Properties
In calculating section properties, gross sections are used for estimating the
required prestress force (Section 8.6.8) and for estimating prestress losses using the
LRFD Specifications Approximate Method (Section 8.6.9). However, girder flexural
stresses are checked at the service limit state based on transformed section properties
(Section 8.6.10).
8.6.5.1 Precast Section
Figure 8.6-4 shows the standard California Standard 3 ft 6 in. I girder (CA I42)
and gross section properties of the girder. Section properties are obtained from BDA
6-1 (Caltrans, 2012).

Figure 8.6-4 Standard CA I42 Girder (BDA 6-1, 2012)
Ag = gross area of girder section (in.2
)
Ig = gross moment of inertia of girder about centroidal axis (in.4
)
yb = distance from neutral axis to extreme bottom fiber of PC girder (in.)
yt = distance from neutral axis to extreme top fiber of PC girder (in.)
Sb = section modulus for bottom extreme fiber of section (in.3
)
St = section modulus for top extreme fiber of section (in.3
)
r = radius of gyration (in.)
8.6.5.2 Effective Flange Width
CA Amendements Article 4.6.2.6 (Caltrans, 2014) state that the effective flange
width, beff, may be taken as the full flange width if 32.0
L
S .
where:
S = spacing of girders or webs (ft)
L = individual span length (ft)
For this example,
32.009.0
70
6

L
S
Therefore, the effective flange width beff = S = 72 in.
D = 42"
yt
yb
SECTION PROPERTIES
Ag = 474 in.2
Icg = 95,400 in.4
yb = 20 in.
yt = 22 in.
Sb = 4,770 in.3
St = 4,336 in.3
r = 14.2 in.

Figure 8.6-5 Effective Flange Width.
8.6.5.3 Composite Section
To compute properties of the composite section, the CIP deck slab and haunch
concrete (same material as deck) are transformed to the higher strength girder
concrete using the modular ratio, n.
D
B
E
E
n  (AASHTO 4.6.2.2.1-2)
where:
n = modular ratio between girder and deck
EB = modulus of elasticity of girder material (ksi)
ED = modulus of elasticity of deck material (ksi)
Using AASHTO Eq.4.6.2.2.1-2:
29.1
637,3
696,4

D
B
E
E
n
Transformed flange width in.8.55
29.1
7272

n
Transformed deck area = 55.8(7) = 391 in.2
Transformed haunch width = in.7.14
29.1
1919

n
Transformed haunch area = 14.7(1) = 14.7 in.2

Table 8.6-2 Section Properties - Gross Composite Section
Section Ai yi Ai (yi ) Io Ai (Y-yi)2
(in.2
) (in.) (in.3
) (in.4
) (in.4
)
Deck 391 46.5 18,182 1,681 79,956
Haunch 14.7 42.5 625 1 1,560
Girder 474 20 9,480 95,400 70,550
Total 879.7 - 28,287 97,082 152,066
Ac = 879.7 in.2
in.32.2
879.7
28,287




i
ii
BC
A
yA
Y
YTC = 50 – 32.2 = 17.8 in.
Ic = 97,082 + 152,066
= 249,148 in.4
3
in.735,7
2.32
148,249

BC
c
BC
Y
I
S
where:
yi = distance from centroid of section i to centroid of composite section
Ac = concrete area of composite section
YTC = distance from centroid of composite section to extreme top fiber of
composite section
Ic = moment of inertia of composite section
SBC = section modulus of the composite section for extreme bottom fiber of PC
girder
8.6.6 Determine Loads
8.6.6.1 Dead Load
PC Girder:
wg=
474
144
(0.15) = 0.494 klf
YTC
Neutral
Axis
YBC
yi

Slab (before reaching design strength):
ws=
504
144
(0.15) = 0.525 klf
Haunch:
wh=
19
144
0.15 = 0.020 klf
Dead loads on composite section:
Type 732 barrier rail on both sides of deck (concrete area = 144 in.2
):
wbr=
444
144
0.15 = 0.463 klf/barrier
Dead load of wearing surfaces and utilities - DW (Article 3.3.2, AASHTO, 2012)
3 in. polyester concrete overlay = 0.035 ksf
8.6.6.2 Live Load
At the Service Limit State, LRFD Specifications requires design for the HL-93
vehicular live load. At the Strength Limit State, LRFD Specifications (AASHTO,
2012) and California Amendments (Caltrans, 2014) require design for both HL-93
vehicular live load and the California P15 permit truck.
 HL-93 vehicular live load consists of these combinations:
o Design truck or design tandem (AASHTO Art. 3.6.1.2.1)
o Design lane load of 0.64 klf without dynamic load allowance (IM)
(AASHTO Art. 3.6.1.2.4)
 California P15 permit truck: The P15 vehicular live load is the California
P15 Permit Design Truck defined in Art. 3.6.1.8 of California
Amendments (Caltrans, 2014).
8.6.7 Perform Structural Analysis
8.6.7.1 Dead Load Distribution Factor
According to LRFD Specifications Art. 4.6.2.2.1 (AASHTO, 2012), permanent
dead loads (including concrete barriers and wearing surface) may be distributed
uniformly among all girders provided all of the following conditions are met:
 Width of deck is constant. (OK)
 Number of girders, Nb, is not less than four; i.e., Nb = 6 (OK)

 Girders are parallel and have approximately the same stiffness. (OK)
 Roadway part of the overhang, de, does not exceed 3 ft de is taken as the
distance from the exterior web of exterior girder to interior edge of curb:
de = 2.5 - 1.5 - 0.5(7/12) = 0.71 ft ≤ 3 ft (OK)
 Bridge is on a tangent line and curvature in plan is zero. (OK)
 Cross-section is consistent with one of the cross-sections shown in
AASHTO Table 4.6.2.2.1-1 (AASHTO, 2012). The superstructure is
type (k). (OK)
Because the design example satisfies the criteria, the concrete barrier and
wearing surface loads can be evenly distributed among the six girders based on the
dead load distribution factor (DFDL), which is determined as:
DFDL=
Tributary Width
Bridge Width
=
6
35
=0.171
Using the DFDL:
Barrier, wbr = DC3 = (0.463)(2)(0.171) = 0.159 klf/girder
DW = dead load of future wearing surface, 0.035 ksf
DW = (0.035)(32)(0.171) = 0.192 klf/girder
8.6.7.2 Unfactored Shear Force and Bending Moment due to DC and DW
Dead load shear and moment can be obtained from structural analysis software or
can be calculated as follows (for simply-supported, single-span bridges):
Shear at x, Vx = w (0.5Lx)
Moment at x, Mx = 0.5wx (Lx)
where:
w = uniform dead load, klf
x = distance from left end of girder (ft)
L = span length = 70 ft

Table 8.6-3 Unfactored Shear Force and Bending Moment due to DC and DW
Location
Girder Weight
(DC1)
Slab, Haunch Wt.
(DC2)
Barrier Weight
(DC3)
Future Wearing
Surface (DW)
Dist/Span Location Shear Moment Shear Moment Shear Moment Shear Moment
(X/L) (ft) (kip) (kip-ft) (kip) (kip-ft) (kip) (kip-ft) (kip) (kip-ft)
0 L 0 17.3 0 19.1 0 5.6 0 6.7 0
0.05L* 3.5 15.6 57.5 17.2 63.4 5 18.5 6 22.3
0.1L 7 13.8 108.9 15.3 120.1 4.4 35 5.4 42.3
0.2L 14 10.4 193.6 11.4 213.6 3.3 62.2 4 75.3
0.3L 21 6.9 254 7.6 280.3 2.2 81.6 2.7 98.8
0.4L 28 3.5 290.3 3.8 320.3 1.1 93.2 1.3 112.9
0.5L 35 0 302.4 0 333.7 0 97.4 0 117.6
*Critical shear section
8.6.7.3 Unfactored Shear Force and Bending Moment due to Live Loads
Live loads are applied to the bridge deck on one or more design lanes. Therefore,
shear forces and bending moments are normally calculated on a per-lane basis.
However, shear forces and moments must then be distributed to individual girders for
girder design. LRFD Specifications permits governing values of shear force and
moment envelopes to be distributed to individual girders using simplified distribution
factor formulas, specified separately for moment and shear (AASHTO Art. 4.6.2.2.2
and Art. 4.6.2.2.3, respectively). As shown previously, the conditions of AASHTO
Art. 4.6.2.2 are satisfied for this example bridge. Therefore, the simplified
distribution factor formulas are applied to the interior girder design in the following
sections.
8.6.7.3.1 Live Load Moment Distribution Factor, DFM (for Interior Girders)
The live load distribution factor for moment (DFM, lanes/girder), for an interior
girder is governed by the larger value for one design lane versus two design lanes
loaded, as shown below.
 One design lane loaded:
 
1.0
3
3.04.0
1214
060.0





















s
g
tL
K
L
SS
DFM
(AASHTO Table 4.6.2.2.2b-1)
Provided the following ranges are met:
3.5  S  16
S = girder spacing = 6 ft (OK)
4.5  ts  12
ts = thickness of concrete slab = 7 in. (OK)
20  L  240

L = span length = 70 ft (OK)
Nb = number of girders  4
Nb = 6 (OK)
10,000  Kg  7,000,000
Longitudinal stiffness parameter, Kg = 552,464 in.4
(OK)
See calculation below:
Kg=n(I + Aeg
2
) (AASHTO 4.6.2.2.1-1)
n = EB / ED = 1.29 (AASHTO 4.6.2.2.1-2)
I = Icg = 95,400 in.4
A = Ag = 474 in.2
eg = distance between centers of gravity of girder and deck
= 46.5 – 20 = 26.5 in.
Kg = 1.29 [95,400 + 474 (26.5)2
] = 552,464 in.4
DFM  0.06 
6
14




0.4
6
70.0




0.3
552,464
12 70  7 3








0.1
== 0.06 + (0.713)(0.479)(1.067) = 0.424 lanes / girder
 Two or more design lanes loaded:
 
1.0
3
2.06.0
125.9
075.0





















s
g
tL
K
L
SS
DFM
(AASHTO Table 4.6.2.2.2b-1)
 
0.1
0.6 0.2
3
6 6 552,464
0.075
9.5 70 12(70) 7
DFM
                  
= 0.075 + (0.759)(0.612)(1.067) = 0.571 lanes / girder
Therefore, DFM for two or more lanes loaded is larger and thus controls.
Use DFM = 0.571 lanes / girder

8.6.7.3.2 Live Load Shear Distribution Factor (DFV) for Interior Girders
 One design lane loaded: (AASHTO Table 4.6.2.2.3a-1)
0.36
25
S
DFV
 
   
 
= 0.36 + 0.24 = 0.6 lanes / girder
 Two or more design lanes loaded:
2
0.2
12 35
S S
DFV
   
     
   
= 0.2 + 0.5 – 0.029 = 0.671 lanes / girder
Therefore, DFV for two or more lanes loaded is larger and thus controls.
Use DFV = 0.671 lanes / girder
Note: The dynamic load allowance factor (IM) is applied to the HL-93 design truck
and P15 permit truck only, not to the HL-93 design lane load. Table 3.6.2.1-1 of
California Amendments (Caltrans, 2014) summarizes the values of IM for various
components and load cases.
The live load moment and shear are commonly calculated at tenth points and can
be obtained from common structure analysis programs. Spreadsheets can also be used
for simple-span structures. In this example, structural analysis software was used to
determine the live load moments. The results are tabulated in Table 8.6-4 for HL-93
loading and Table 8.6-5 for P15 loading, respectively. These tables list the envelope
values for moment and shear per lane, as well as per girder (for design) using the
distribution factors.

Table 8.6-4 Unfactored Live Load Moment and Shear Force Envelope Values due to
HL-93 (LL + IM)
Location Per Lane† DFM DFV Per Girder
(ft)
Moment Shear (Lane per
Girder)
(Lane per
Girder)
M(LL+IM) V(LL+IM)
(kip-ft) (kip) (kip-ft) (kip)
0L* 0 0 102.11 0.571 0.671 0 68.5
0.05L** 3.5 348.5 97.9 0.571 0.671 199 65.7
0.1L 7 655.03 91.56 0.571 0.671 373.8 61.4
0.2L 14 1144.64 78.18 0.571 0.671 653.2 52.4
0.3L 21 1468.82 65.24 0.571 0.671 838.2 43.8
0.4L 28 1657.38 52.75 0.571 0.671 945.8 35.4
0.5L 35 1695.40 -40.87 0.571 0.671 967.5 -27.4
*L = Span Length
** Critical section for shear
†These values were obtained from CT Bridge (Include IM = 33%)
Table 8.6-5 Unfactored Live Load Moment and Shear Force Envelope Values due to
P15 Truck (LL + IM)
Location Per Lane† DFM DFV Per Girder
(ft)
Moment Shear (Lane per
Girder)
(Lane per
Girder)
M(LL+IM) V(LL+IM)
(kip-ft) (kip) (kip-ft) (kip)
0L* 0 0 178.5 0.571 0.671 0 119.8
0.05L** 3 532.4 152.3 0.571 0.671 304 102.2
0.1L 7 972 138.86 0.571 0.671 554.7 93.1
0.2L 14 1566 111.86 0.571 0.671 893.6 75
0.3L 21 2025 89.68 0.571 0.671 1,155.6 60.1
0.4L 28 2349 69.43 0.571 0.671 1,340.5 46.6
0.5L 35 2328.75 -50.14 0.571 0.671 1,328.9 -33.6
*L = Span Length
** Critical section for shear
†These values were obtained from CT Bridge (Include IM = 25%)
8.6.8 Estimate Prestressing Force and Area of Strands
The minimum jacking force, Pj and associated area of prestressing strands, Aps,
can be reaonably estimated based on satisfying the two tensile stress limits at the
bottom fiber of the PC girder at the Service III limit state:
 Case A) No tension under permanent loads
 Case B) Tension limited to prevent cracking under total dead and live
loads
It should be noted that, for Service III, only the HL-93 vehicular live load
applies. P15 applies to Strength II but not Service III. The critical location for
bending moment is normally midspan. However, other locations such as 0.4L (P15

truck) and harp points can govern and must be checked as well. Gross section
properties are used.
Calculations for these two critical cases are provided below.
Note: Compression is taken as positive (+) and tension as negative (-).
 Case A: No tension is allowed for components with bonded prestressing
tendons or reinforcement, subjected to permanent loads (DC, DW) only.
Set the stress at the bottom fiber equal to zero and solve for the required
effective prestress force (at service, i.e., after losses), P, to achieve no
tension.
0321





 



BC
DWDC
b
DCDC
b
c
g S
MM
S
MM
S
Pe
A
P
Rearranging the equation:
b
c
g
BC
DWDC
b
DCDC
S
e
A
S
MM
S
MM
P






 



1
321
As shown in Table 8.6-3 (DC and DW) and Table 8.6-4 (HL-93 vehicular
live load), the maximum moment due dead load and live load occurs at
midspan. Moments on a per girder basis are used for girder design.
MDC1 = unfactored moment due to girder self-weight
= 302.4 kip-ft
MDC2 = unfactored moment due to slab and haunch weight
= 333.7 kip-ft
MDC3 = unfactored moment due to barrier weight
= 97.4 kip-ft
MDW = unfactored moment due to future wearing surface
= 117.6 kip-ft
SBC = section modulus for the bottom extreme fiber of the composite
section = 7,735 in.3
To solve for P, the required effective prestressing force, an estimate of
the eccentricity of the noncomposite girder, ec, is needed. To determine
ec, the centroid of the prestressing force at midspan can be reasonably
estimated to be 4 in. from the bottom of the girder.

Thus, the eccentricity of prestressing force at midspan based on the
noncomposite section is taken as:
ec = 20 – 4 = 16 in.
     
770,4
16
474
1
735,7
126.1174.97
770,4
127.3334.302






 


P
Required effective prestressing force, P = 353.9 kips
 Case B: Allowable tension for components subjected to the Service III
limit state (DC, DW, (0.8) HL-93), subjected to not worse than moderate
corrosion conditions, and located in Environmental Areas I or II =
cf  19.0
.
 
c
BC
HLDWDC
b
DCDC
b
c
g
f
S
MMM
S
MM
S
Pe
A
P
'19.0
8.0. 93321





 



where:
MHL93 = moment due to HL-93 loading at midspan = 967.5 kip-ft
(Table 8.6-4)
 
b
c
g
c
BC
HLDWDC
b
DCDC
S
e
A
f
S
MMM
S
MM
P






 



1
')19.0(
8.0. 93321
     
770,4
16
474
1
619.0
735,7
12)5.967(8.06.1174.97
770,4
127.3334.302






 





 
P
Required effective prestressing force, P = 488.5 kips
The minimum required effective prestressing force, P, at service level for
an interior girder is the larger value from Case A and Case B. Therefore,
P = Pf = 488.5 kips/girder
To determine the minimum required jacking force, an estimate of
prestress losses is needed. Thus, assuming total (immediate and long-
term) prestress losses of 25% (of the jacking force), the required jacking
force (i.e., just before transfer, ignoring minor losses from jacking to de-
tensioning) is:
Minimum Jacking Force, Pj =
488.5
0.75
= 651.3 kips

The required area of prestressing strands, Aps, jacked to 0.75 fpu is:
Required
2
in.22.3
)270(75.0
3.651
psA
Number of 0.6 in. diameter strands required
=
3.22
0.217
= 14.8 strands
14.8 is rounded to 16, an even number provided for symmetry (about a
vertical line through the centroid) to produce a uniform stress distribution
in the member.
Therefore, use sixteen 0.6 in. diameter low relaxation Grade 270 strands.
The actual area of strands is thus:
Aps = 16 (0.217) = 3.42 in.2
Total prestressing force at jacking, Pj = 0.75(270)(3.472) = 703 kips
It is a common practice in Caltrans to provide contractors with the prestressing
force and centroid of prestressing path on contract plans, instead of actual strand
patterns. This gives the contractors flexibility in choosing the location and number of
strands, based on the setup of their casting bed. However, designers are encouraged
to layout an actual strand pattern. This helps ensure the design is constructible and
avoids the possible use of too many strands in one girder.
The strand pattern is shown in Fig. 8.6-6: six strands at 2.5 in., eight at 4.5 in. and
two at 6.5 in.
The CGS from the bottom of the girder is:
CGS =
6(2.5) + 8(4.5) + 2(6.5)
16

= 4 in. from bottom of girder.
The actual eccentricity, ec, at midspan for the girder = 20 – 4 = 16 in., matching
the assumption used in estimating the prestressing force. Normally, the actual value
will vary from the assumption and should be used in subsequent design calculations.

Figure 8.6-6 Strand Pattern in PC Girder at Midspan Section
8.6.9 Estimate Prestress Losses
Prestress losses were previously estimated in a very approximate way to
determine area of strands. With a trial number of strands and layout now determined,
prestress losses can be more accurately approximated.
Per LRFD Specifications, total prestress losses in prestressing strand stress are
assumed to be the sum of immediate and long-term losses. Immediate losses for
strands in a PC girder are due to elastic shortening. Long-term losses are primarily
due to concrete creep and shrinkage as well as steel relaxation.
∆fpT = ∆fpES + ∆fpLT (AASHTO 5.9.5.1-1)
where:
∆fpES = change in stress due to elastic shortening loss (ksi)
∆fpLT = losses due to long-term shrinkage and creep of concrete and relaxation of
prestressing steel (ksi)
∆fpT = total change in stress due to losses (ksi)
8.6.9.1 Elastic Shortening
Immediate elastic shortening losses are easily determined for PC girders using a
closed form solution based on LRFD Specifications Commentary Eq. C5.9.5.2.3a-1:
 
 
p
cigg
gmgps
ggmgmgpbtps
pES
E
EIA
AeIA
AMeAeIfA
f



2
2
where:
Aps = area of prestressing steel = 3.472 in.2
2 @ 6.5
8 @ 4.5
6 @ 2.5
CGS = 4

Ag = gross area of girder section = 474 in.2
fpbt = stress in prestressing steel immediately prior to transfer
= 0.75(270) = 202.5 ksi, ignoring minor relaxation losses after jacking
Eci = 4,200 ksi
Ep = 28,500 ksi
em = eccentricity at midspan = 16 in.
Ig = moment of inertia of gross section = 95,400 in.4
Mg = midspan moment due to self-weight of girder
= MDC1 =302.4 k-ft (12 in./ft) = 3,629 k-in.
500,28
)200,4)(400,95(474
)]474(16400,95[(472.3
)474)(629,3(16)]474(16400,95)[5.202(472.3
2
2


 pESf
ksi84.16 pESf
The initial prestressing stress immediately after transfer = 202.5 – 16.84 = 185.7
ksi.
LRFD Specifications C5.9.5.2.3a notes that when transformed section properties
are used in calculating concrete stresses, the effects of losses and gains due to elastic
deformation are implicitly accounted for. Therefore, fpES should not be used to
reduce the stress in the prestressing strands (and force) for concrete stress
calculations at transfer and service level.
8.6.9.2 Long Term Losses – Approximate Method
LRFD Specifications provides two methods to estimate the time-dependent
prestress losses: Approximate Method (Article 5.9.5.3) and Refined Method (Article
5.9.5.4). This example uses the LRFD Specifications Approximate Method to
estimate long-term, time-dependent prestress losses, based on gross section
properties.
Per Article 5.9.5.3, the approximate method is applicable to standard precast,
pretensioned members subject to normal loading and environmental conditions,
where:
 Members are made from normal-weight concrete (OK)
 Concrete is either steam- or moist-cured (OK)
 Prestressing strands use low relaxation properties (OK)
 Average exposure conditions and temperatures characterize the site
(OK)
Because the girder in this example satisfies all of the criteria, the Approximate
Method can be used.

Long-term prestress losses due to creep and shrinkage of concrete and relaxation
of steel are estimated using the following formula, in which the three terms
corresponds to creep, shrinkage, and relaxation, respectively:
∆fpLT
=10
fpi
Aps
Ag
γh
γst
+ 12γh
γst
+ ∆fpR
(AASHTO 5.9.5.3-1)
where:
fpi = prestressing steel stress immediately prior to transfer (ksi)
H = the average annual ambient relative humidity (%)
h = correction factor for relative humidity of ambient air
= 1.7-0.01H
st = correction factor for specified concrete strength time at of prestress transfer
to concrete member
= 5/(1+ fci)
∆fpR an estimation of relaxation loss taken as 2.4 ksi for low relaxation strand,
10 ksi or stress-relieved strand, and in accordance with manufacturers
recommendation for other types of strand (ksi)
For this calculation:
fpi = 202.5 ksi
H = Average annual ambient relative humidity = 70%
h = 1.7 – 0.01H = 1.7 = 0.01 (70) = 1 (AASHTO 5.9.5.3-2)
   
862.0
8.41
5
1
5





ci
st
f
 (AASHTO 5.9.5.3-3)
∆fpR = 2.4 ksi for low relaxation strands
         
ksi5.254.23.108.1
4.2862.0112862.01
474
472.35.202
10

 pRf
Total prestress losses: ∆fpT = 16.85 + 25.5 = 42.3 ksi
%24%)100(
5.202
3.42
 pTf
Effective prestress used with gross non-transformed section:
fpe = effective stress in prestressing strands (service level)
= 202.5 – 42.3 = 160.2 ksi
Check prestressing stress limit at service limit state:
0.8 fpy ≥ fpe (AASHTO Table 5.9.3-1)

0.8 (270)(0.9) = 194.4 ksi > 160.2 ksi, (OK)
For gross non-transformed sections, the effective prestressing force after all
losses, Pf = 3.472 (160.2) = 556.2 kips
Regarding transformed sections, note that with transformed sections used in
subsequent sections of this design example, the prestressing force to be used in
concrete stress calculations at transfer is the jacking force, Pj, and the prestressing
force to be used in concrete stress calculations at service level is the final prestressing
force, Pf , based on long-term losses only:
Effective prestress used with transformed section:
fpe = 0.75 fpu – ∆fpLT = 0.75 (270) – 25.5 = 177 ksi
Pf = fpe (Aps) = 177(3.472) = 614.5 kips
8.6.10 Design for Service Limit State
Design for the Service Limit State addresses the suitability of the previously
estimated strand force and profile based on Stages I, IIA, and III. Concrete stresses
are checked at transfer, which may lead to design modifications such as adjusting the
strand profile or initial concrete compressive strength fci. The most critical check of
stresses at the Service Limit State is normally the check of the tensile stress at the
bottom of the girder to prevent possible cracking at Service III (HL-93 vehicular live
load).

8.6.10.1 Calculate Transformed Section Properties
The use of transformed concrete section properties generally leads to more
accurate calculations than use of gross section properties. As this is recognized by
LRFD Specifications C5.9.5.2.3a, calculations use transformed section properties.
Three sets of transformed section properties are needed for the service limit state
design. These include transformed section properties of the noncomposite girder at
transfer (Stage I), erection, and deck casting (Stage IIA, before deck hardening), as
well as the composite section of the girder and deck at service (Stage III). The section
property calculations for these stages are presented below. A minor difference in final
and initial transformed noncomposite properties results from the use of Ec versus Eci.
However, the difference between the composite and noncomposite final properties is
significant due to the additional deck area.
Table 8.6-6 Transformed Section Properties: Girders and Strands (Initial, Transfer)
Section Ai yi Ai ( yi ) Ii Ai (Y-yi)2
(in.2
) (in.) (in.3
) (in.4
) (in.4
)
Girder 474 20 9,480 95,400 200
Strands 20.1‡
4 80.4 ≈ 0 4,736
Total 494.1 -- 9,560.4 95,400 4,936
8.51
200,4
500,28
11 
ci
ps
E
E
n
Total Ac = 494.1 in.2
in.4.19
1.494
4.560,9
BtiY
YTti = 42 – 19.35 = 22.6 in.
Iti = 95,4000 + 4,936
= 100,336 in.4
3
in.185,5
4.19
336,100

Bti
ti
Bti
Y
I
S
3
in.430,4
6.22
336,100

Tti
ti
Tti
Y
I
S
eti = 19.4 - 4 = 15.4 in.
‡
Strands are transformed using (n – 1)
YTti
YBti
yi
eti
CGS
Neutral
Axis

Table 8.6-7 Transformed Section Properties: Girders and Strands (Final)
Section Ai yi Ai ( yi ) Ii Ai (Y-yi)2
(in.2
) (in.) (in.3
) (in.4
) (in.4
)
Girder 474 20 9,480 95,400 154
Strands 17.7‡
4 70.8 ≈ 0 4,190
Total 491.7 -- 9,550.8 95,400 4,344
1.51
696,4
500,28
11 
c
ps
E
E
n
in.4.19
7.491
8.550,9
BtfY
YTti = 42 – 19.35 = 22.6 in.
Iti = 95,4000 + 4,344
= 99,744 in.4
3
in.135,5
4.19
744,99

Btf
tf
Btf
Y
I
S
3
in.419,4
6.22
744,99

Ttf
tf
Ttf
Y
I
S
et = 19.4 - 4 = 15.4 in.
‡
Strands are transformed using (n – 1)
CGS
YTtf
YBtf
etf
Neutral Axis

Table 8.6-8 Transformed Section Properties: Composite Girder and Deck (Final)
Section Ai yi Ai (yi ) Ii Ai (Y-yi)2
(in.2
) (in.) (in.3
) (in.4
) (in.4
)
Girder 474 20 9,480 95,400 63,671
Strands 17.7 4 70.8 ≈ 0 13,473
Deck 391** 46.5 18,182 1,595 86,922
Haunch 14.7** 42.5 624.8 1 1,750
Total 897.4 - 28,357.6 96,996 165,816
77.0
696,4
637,3

girder
deck
E
E
n
Ac = 897.4 in.2
in.6.31
4.897
6.357,28
BCtY
YTGCt = 42 – 31.6 = 10.4 in
YTCt = 50 – 31.6 = 18.4 in
ICt = 96,996 + 165,816 = 262,806 in.4
3
in.317,8
6.31
806,262

BCt
Ct
BCt
Y
I
S
3
in.271,25
4.10
806,262

TCt
Ct
TGCt
Y
I
S
3
in.425,18
)77.0(4.18
806,262

DCt
Ct
TDCt
Y
I
S
eCt = 31.6 – 4 = 27.6 in.
**Deck and haunch are transformed using (n = 0.77)
YTGCt
YBCt
YTCt
CGS
eCt
Neutral Axis

8.6.10.2 Check Concrete Stresses at Transfer Condition
The check of concrete stresses at transfer investigates the suitability of both the
prestressing force and the strand profile for the assumed section. Commonly, strands
must be harped or debonded to produce an efficient design that does not overstress
the section. In addition, the initial concrete compressive strength, fci may be
modified.
 Concrete stress limits:
o Compressive stress limit:
Stress limit = 0.6fci = 0.6 (4.8) = 2.880 ksi (AASHTO 5.9.4.1.1)
o Tensile stress limit: (AASHTO Table 5.9.4.1.2-1)
 In area other than precompressed tensile zone without bonded
auxiliary reinforcement:
Stress Limit ksi200.00948.0  cf
Stress Limit = 0.0948√4.8 = 0.208 ksi
Since 0.208 ksi is larger than 0.200 ksi, 0.200 ksi is taken as the
limit.
 In areas with bonded auxiliary reinforcement sufficient to resist
the tensile force
Stress Limit=0.24√4.8=0.526 ksi
Per AASHTO Commentary C5.9.5.2.3a, when checking concrete stresses using
transformed section properties, the effects of losses and gains due to elastic
deformations are implicitly accounted for. Therefore, the elastic shortening loss,
∆fpES, should not be subtracted from the strand stress in calculating the prestressing
force at transfer (taken as Pj because relaxation losses between jacking and transfer
are ignored).
Check concrete stresses at transfer length section: (straight strands)
Transfer length = 60(db) = 60(0.6) = 36 in. = 3 ft (LRFD 5.11.4.1)
db = nominal strand diameter (in.)
Pj = 703 kips
Ati = 494 in.2
Where Ati = Gross area of girder concrete at time of force transfer
Eccentricity at 3 ft with CGS strands = 4 in. from bottom
Eti = 15.4 in.
SBti = 5,185 in.3
STti = 4,430 in.3

MDC1 = moment at transfer length section due to girder weight, based on total
girder length
= 0.5(0.494)(3)(71 - 3) = 49.8 kip-ft = 598 kip-in.
Calculate concrete stress at top of girder at transfer length:
(Tensile)ksi886.0
430,4
598
430,4
)4.15(703
494
703
1



Tti
DC
Tti
tij
ti
j
top
S
M
S
eP
A
P
f
Because the tensile stress exceeds the upper limit of the allowable tensile stress
(0.526 ksi, assuming bonded reinforcement), the effect of prestressing must be
reduced. Either harping or debonding a portion of strands near the end of the girders
can accomplish this.
Note: Selection of harping versus debonding should be discussed with fabricators.
For this example, two point harping is selected. Harp points are usually located
between 0.33L and 0.4L from girder ends. 0.4L is chosen as the harp point. The
calculations below investigate stressses along the member by the use of four strands
harped with a profile at the girder ends as follows: two strands at 28.5 in. from
bottom and two strands 30.5 in. from bottom. A suitable configuation of harping is
easily arrived at by iteration using spreadsheets or commercially available software.
From midspan to the harped point (0.4L), CGS is 4 in. from the girder bottom, and at
the girder ends, the CGS is 10 in. from the bottom. The strand pattern at the harp
points and girder ends are shown in Figure 8.6-7. Hold-down forces and harp angle
are normally calculated and checked against limits by local precast producers.

Figure 8.6-7 Strand Patterns at Midspan and Ends of Girder
 Check concrete stresses at transfer length section (harped strands):
The eccentricity at transfer length (3 ft) with harped strands:
ve)(Compressiksi066.0
430,4
598
430,4
)4.9(703
494
703
in.4.90.4)0.40.10(
28
328
1






Tti
DC
Tti
tij
ti
j
top
ti
S
M
S
eP
A
P
f
e
ftop
=
Pj
Ati
-
Pjeti
STti
+
MDC1
STti
=
703
494
-
703(9.4)
4,430
+
598
4,430
= 0.66 ksi (Compressive) < 2.880 ksi (OK)
Note that the transformed section properties at midspan are used in the
calculations above. It is not necessary to check the stresses at transfer
length using transformed properties at transfer length since the stress
level is very low.
2 at 30.5 in.
2 at 28.5 in.
Strand pattern at ends
CGS = 10 in.
6 at 4.5 in.
6 at 2.5 in.
Strand pattern at 0.4L
CGS = 4 in.
2 at 6.5 in.
8 at 4.5 in.
6 at 2.5 in.

 Check concrete stresses at harp points:
Harped point location = 0.4L =0.4(70) = 28 ft
Pj = 703 kips
Ati = 494 in.2
Eccentricity at 0.4L, eti = 15.4 in.
SBti = 5,158 in.3
STti = 4,430 in.3
MDC1 = moment at 0.4L due to girder weight, based on total girder length
MDC1 = 0.5 (0.494) (28) (70 – 28) = 290.3 kip – ft = 3,484 kip – in. (Table
8.6-3)
Calculate concrete stress at top of girder at transfer at 0.4L:
ftop
=
Pj
Ati
-
Pjeti
STti
+
MDC1
STti
=
703
494
-
703(15.4)
4,430
+
3,484
4,430
= -0.227 ksi (Tensile)
Since the tensile stress at top of girder exceeded the limit of 0.200 ksi,
auxiliary (mild) reinforcement must be provided at the tensile face (top)
to resist the total tensile force.
 Determine auxiliary reinforcement:
To find the neutral axis of the section, it is necessary to determine:
fbot
=
Pj
Ati
-
Pjeti
SBti
+
MDC1
SBti
=
703
494
-
703(15.4)
5,185
+
3,4884
5,185
= 2.832 ksi (compressive) < 2.889 ksi (OK)
Locate neutral axis, x, from similar triangles.

Figure 8.6-8 Concrete Stress Distribution
in.12.3
832.2227.0
)227.0(42


x
The neutral axis is slightly below the 3 in. rectangular section of the top
flange. The value 3.12 in. can be conservatively used to calculate the
total tension force as the area of concrete times the average tensile stress.
Required tension capacity, FT = 0.5 (0.227) (3.12) (19) = 6.73 kips
Using non-prestressed reinforcement (mild steel) at a working stress of
24 ksi
Area of mild steel required:
6.73
24
0.28 in.
Provide two #4 bars at top flange for entire length of girder,
As,provided = 2 (0.2) = 0.4 in.2
> 0.28 in.2
(OK)
 Check concrete stresses at midspan:
Midspan is not expected to govern over the harp points at transfer
because of the beneficial effects of self-weight. However, the calculation
is demonstrated herein. The values for Pj, eti, Ati, SBti, and Stti at midspan
are the same as at 0.4L.
MDC1 = moment at midspan due to girder weight, based on total girder
length = (0.494)(70)2
/8 = 302.4 kip-ft = 3,629 kip-in. (Table
8.6-3)
- 0.227 ksi
(tension)
2.832 ksi (compression)
x
42"

ftop
=
Pj
Ati
-
Pjeti
STti
+
MDC1
STti
=
703
494
-
703 15.4
4,430
+
3,629
4,430
= -0.194 ksi (Tensile)
This is within the tensile limit of 0.2 ksi (OK)
botf =
Tti
DC
Tti
tij
ti
j
S
M
S
eP
A
P 1

=
703
494
-
703 15.4
5,185
+
3,629
5,185
8.6.10.3 Check Concrete Stresses at Service Condition
The check of concrete stresses at service level investigates the suitability of the
section to resist service level loads. Of particular importance is the prevention of
flexural cracking of the section at midspan for Service Level III due to the LRFD
Specifications HL-93 Vehicular Live Load. In addition, per requirements of the
California Amendments (Caltrans, 2014), the section must not develop any tension
under permanent loads (only).
 Effective prestressing force, Pf :
Because transformed section properties are used, the effective
prestressing force (Pf) acting on the section is calculated using the force
at transfer, Pj, less long-term losses that were estimated using the
Approximate Method:
fpe = 0.75 fpu – ∆fpLT = 0.75 (270) – 25.5 = 177 ksi
Pf = fpe (Aps ) = 177 (3.472) = 614.5 kips
 Concrete stress limits:
o Compressive stress limits (AASHTO Table 5.9.4.2.1-1)
 Compressive stress limits due to unfactored permanent loads
(including girder, slab and haunch, barrier, and future wearing
surface) and prestressing force.
Load combination: PS + Perm
PC girder: 0.45 f´c = 0.45(6) = 2.700 ksi
CIP deck: 0.45 f´c,deck = 0.45(3.6) = 1.62 ksi
 Compression stress limit due to effective prestress, permanent,
and transient loads (including all dead and live loads).
Load combination: Service I = PS + Perm + (LL + IM)HL-93

PC girder: 0.6w fci = 0.6(1.0)(6) = 3.600 ksi
CIP deck: 0.6 w fc,deck = 0.6(1.0)(3.6) = 2.160 ksi
 Tensile stress limit (Table 5.9.4.2.2-1, Caltrans 2014)
o For components with bonded prestressing tendons or
reinforcement subjected to permanent loads only.
Load combination: PS + Perm
PC girder: 0 ksi (no tension allowed)
o For components with bonded prestressing tendons or
reinforcement.
Load combination:
Service III = PS + Perm + 0.8(LL+IM)HL-93
PC girder: -0.19 f c
' = -0.19√6 = -0.465 ksi
 Check concrete stresses at midspan:
Bending moments at midspan are given in Table 8.6-9.
Table 8.6-9 Unfactored Bending Moments at 0.4L and Midspan (per Girder).
Location *MDC1 *MDC2 *MDC3 *MDW **M(LL+IM)HL93
(kip-ft) (kip-ft) (kip-ft) (kip-ft) (kip-ft)
0.4L 290.3 320.3 93.2 112.9 945.8
0.5L 302.4 333.7 97.4 117.6 967.5
*From Table 8.6-3
** From Table 8.6-4
 Check compressive stresses at midspan:
PC girders are checked for compressive stresses under the following two
load combinations:
o Load combination PS + Perm
 Stress at top of PC girder:
tgf =
TGCt
DWDC
Ttf
DCDC
Ttf
tf
tf
f
S
MM
S
MM
S
Pe
A
P )()( 321 



25,271
117.6)(12)(97.4
4,418
333.7)(12)(302.4
4,418
)614.5(15.4
491.7
614.5 



= 0.938 ksi (compression) < 2.7 ksi (OK)
 Stress at bottom of PC girder:
bf =
BCt
DWDC
Btf
DCDC
Btf
tf
tf
f
S
MM
S
MM
S
Pe
A
P )()( 321 




8,317
117.6)(12)(97.4
5,137
333.7)(12)(302.4
5,137
)614.5(15.4
491.7
614.5 



= 1.299 ksi (compressive) < 2.7 ksi (OK)
Note that both the top and bottom fibers are in compression. This
satisfies the requirement of no tension for components subjected
to permanent loads only per California Amendments Table
5.9.4.2.2-1 (Caltrans, 2014).
o Load combination PS + Perm + (LL+IM)HL-93 (Service I)
 Compressive stress at top of PC girder:
tgf
TGCt
HLIMLL
TGCt
DWDC
Ttf
DCDC
Ttf
tf
tf
f
S
M
S
MM
S
MM
S
Pe
A
P 93)(321 )()( 





25,271
967.5(12)
25,271
117.6)(12)(97.1
4,418
333.7)(12)(302.4
4,418
)614.5(15.4
491.7
614.5





 Compressive stress at top fiber of deck:
This check is not normally required. The deck resists all loads
compositely, so that even with a lower compressive strength, the
concrete deck is rarely subjected to significant compressive stress.
However, designers may desire to check Service I (PS + Perm + (LL +
IM)HL-93) for completeness, applying wearing surface, barrier loads, and
HL-93 truck and lane loads to the composite section.
 Check tensile stresses at bottom of girder at midspan: (Service III)
This check to prevent cracking at midspan is normally a critical check
that can govern the prestressing force and thus area of prestressing
strand.
Load combination PS + Perm + 0.8L:
bf
BCt
HLIMLL
BCt
DWDC
Btf
DCDC
Btf
tf
tf
f
S
M
S
MM
S
MM
S
Pe
A
P )(8.0)()( 93)(321 





8,317
(12)0.8(967.5)
8,317
117.6)(12)(97.1
5,137
333.7)(12)(302.4
5,137
)614.5(15.4
491.7
614.5





In this case, not only is the check satisfied, but the girder remained in
compression at the bottom fiber.

 Check concrete stress at harped point (0.4L):
The concrete stresses at the harp point (0.4L) should also be checked.
These can be checked using the same procedures as for midspan. The
calculations are not repeated here, but final results are shown.
 Check compressive stresses at 0.4L:
o Load combination PS + Perm
ftg = 0.861 ksi (compressive) < 2.7 ksi (OK)
fb = 1.369 ksi (compressive) < 2.7 ksi (OK)
Thus also satisfies the requirement of no tension.
o Load combination PS + Perm + LL
ftg = 1.309 ksi (compressive) < 3.6 ksi (OK)
fb = 0.278 ksi (compressive) < 3.6 ksi (OK)
8.6.10.4 Fatigue Stress Limit
Although fatigue-related compression in concrete deck slabs with multiple PC
girders rarely governs design (because of internal arching action), a check of the
compressive stress in the deck for the Fatigue I load combination is required per
LRFD Specifications Article 5.5.3.1. The compression due to the Fatigue I load
combination and one half of the sum of effective prestress and permanent loads
cannot exceed 0.4 fc.
Per C5.5.3.1, the net concrete stress is usually significantly less than the concrete
tensile stress limit for cracking, leading to very small steel stress ranges in the
prestressing steel less than limiting values.
Fatigue is not likely to control the design and therefore is not checked in this
example. Readers are referred to the PCI Bridge Design Manual for more information
on how to perform fatigue check.

8.6.10.5 Effect of Deck Shrinkage
Article 5.9.5.4.3d of LRFD Specifications (AASHTO, 2012) shows the
procedure to calculate prestress gain due to shrinkage of deck composite section.
However, it is Caltrans practice to ignore this prestress gain due to the fact that the
deck is designed as reinforced concrete, and cracks are allowed to form in the
section. The calculations will not be presented in this example. The readers are
referred to the PCI Bridge Design Manual for information and procedure in
estimating prestress gain due to deck shrinkage.
8.6.11 Design for Strength Limit State
Design of PC girders for the service limit state may produce an adequate design
for the strength limit state. However, this must be checked because of the significant
additional live load design requirement for the Strength II load combination—the
P-15 permit truck.
8.6.11.1 Determine Factored Moment
The factored moment at ultimate, Mu, is based on the unfactored moments
previously given in Table 8.6-9, shown below:
Table 8.6-10 Unfactored Bending Moments at 0.4L and Midspan (per Girder).
Location
*MDC1
(kip-ft)
*MDC2
(kip-ft)
*MDC3
(kip-ft)
*MDW
(kip-ft)
**M(LL+IM)HL93
(kip-ft)
†M(LL+IM)P15
(kip-ft)
0.4L 290.3 320.3 93.2 112.9 945.8 1,340.5
0.5L 302.4 333.7 97.4 117.6 967.5 1,328.9
*Table 8.6-3; **Table 8.6-4; † Table 8.6-5
Mu is taken as the larger of Strength I and II combinations, per Article 3.4.1 of
California Amendments (Caltrans, 2014). Strength I uses the LRFD Specifications
(AASHTO, 2012) HL-93 vehicular live load, whereas Strength II uses the California
P-15 permit truck.
Determine the controlling factored ultimate moment, Mu:
By inspection, moments at midspan govern for Strength I.
 Strength I:
Mu = 1.25 [MDC1 + MDC2 + MDC3] + 1.5 MDW + 1.75 [M (LL+IM)HL93]
Mu(LL+IM)HL93 = 1.25 (302.4 + 333.7 + 97.4) + 1.5 (117.6) + 1.75 (967.5)
= 2,786.4 kip-ft/girder
 Strength II:
Mu = 1.25 [MDC1 + MDC2 + MDC3] + 1.5 MDW + 1.35 [M (LL+IM)P15]
Since live load moment is larger at 0.4L, it is necessary to check both 0.4L and
0.5L sections to find the critical moment demand.
 At 0.4L:

Mu(LL+IM)P15 = 1.25 (290.3 + 320.3 + 93.2) + 1.50 (112.9) + 1.35 (1,340.5)
= 2,858.8 kip-ft
 At 0.5L:
Mu(LL+IM)P15 = 1.25 (302.4 + 333.7 + 97.4) + 1.50(117.6) +1.35(1,328.9)
= 2,887.3 kip-ft / girder  controls
 Strength II governs. Mu = 2,887.3 kip-ft/girder
8.6.11.2 Calculate Nominal Flexural Resistance
Based on AASHTO 5.7.3.1 and 5.7.3.2, compute nominal flexural resistance of
the section, as shown in Figure 8.6-9.
Figure 8.6-9 Bridge Section at Midspan
 Determine average prestressing steel stress at ultimate:
In most applications, the average prestressing steel stress at ultimate
can be easily determined from AASHTO Eq. 5.7.3.1.1-1, applicable to
typical PC girder sections that use bonded tendons and have an effective
stress with fpe ≥ 0.5 fpu. If more precise calculations are required,
conditions of equilibrium and strain compatibility can be used
(AASHTO 5.7.3.2.5).
For this example, the effective prestress (after all losses),
fpe = 160.2 ksi > 0.5 fpu= 135 ksi, thus Eq. 5.7.3.1.1-1 is applicable.
2-#5
@ 5.5”
2-#5 @ 3.5”
CGS
ybtsybts
cg rebars
de
cg tensile
reinf
dp
a/2










p
pups
d
c
kff 1 (AASHTO 5.7.3.1.1-1)
For low relaxation strand, fpy/fpu = 0.9 (Table C5.7.3.1.1-1), thus the
value k is determined as follows:
2 1.04 (AASHTO 5.7.3.1.1-2)
= 2(1.04 – 0.9) = 0.28
Assuming the compressive stress lies solely within the deck
(rectangular stress block develops at ultimate), the neutral axis depth, c,
is determined from the following:
)45.7.3.1.1(AASHTO
85.0
'
1
'
'










p
pu
psc
ssspups
d
f
kAbf
fAfAfA
c s

where:
Aps = area of prestressing steel = 3.472 in.2
fpu = specified tensile strength of prestressing steel = 270 ksi
fpy = yield strength of prestressing steel = 243 ksi
As = area of mild steel tension reinforcement
= four #5 for longitudinal steel requirement
= 4 (0.31) = 1.24 in.2
Note that there are four #5 longitudinal bars added to the bottom
bulb of the girder as illustrated in Section 8.6.15.
As = area of mild steel compression reinforcement = 0
fs = stress in the mild steel tension reinforcement at nominal
flexure resistance = 60 ksi
fs = stress in the mild steel compression reinforcement at nominal
flexure resistance
b = effective width of flange in compression (deck) = 72 in.
fc = compressive strength in deck concrete at midspan = 3.6 ksi
dp = distance from extreme compression fiber (deck) to centroid of
prestressing tendon
= 50 – 4 = 46 in.

From AASHTO 5.7.2.2,
for fc ≤ 4 ksi
1 = 0.85
for fc > 4 ksi
0.85 – 0.05(f’c – 4) 0.65
fc = 3.6 ksi
Therefore, 1 = 0.85
c = distance from extreme compression fiber to the neutral axis
assuming tendon prestressing steel has yielded (in.)
Assuming that mild reinforcement has also yielded, c is calculated as
follows:









46
270
)472.3(28.0)72)(85.0)(6.3(85.0
)60(24.1)270(472.3
c
= 5.24 in. < 7 in. (deck thickness)
Because compressive stresses lie entirely within the slab thickness,
the assumption of rectangular section behavior is valid.
psf 






46
24.5
)28.0(1270
= 261.4 ksi
Determine factored flexural resistance, Mr
Mr = Mn (AASHTO 5.7.3.2.1-1)
where:
Mr = factored flexural resistance
 = resistance factor per AASHTO 5.5.4.2
Mn = nominal flexural resistance
For rectangular sections:













22
a
dfA
a
dfAM sssppspsn
where:
ds = distance from extreme compression fiber (deck) to centroid of
mild steel
= 50 – 4.5 = 45.5 in.
a = depth of equivalent rectangular stress block, in.

= 1 (c) = 0.85(5.24) = 4.46 in.
nM 












2
46.4
5.45)60(26.1
2
46.4
46)4.261(472.3
= 42,944 kip-in. = 3,578.7 kip.-ft
 Determine resistance factor, :
According to the AASHTO C5.7.3.3.1 and Figure C5.5.4.2.1-1 of
California Amendments (Caltrans, 2014) as shown in Figure 8.6-10 if the
net tensile strain, t ≥ 0.005, then the section is defined as tension-
controlled and  =1 for flexure.
Figure 8.6-10 Variation of  with Net Tensile Strain, t, for Grade 60 Reinforcement and
Prestressed Members (Figure C5.5.4.2.1-1, California Amendments (Caltrans, 2014)
The net tensile strain is calculated using similar triangles based on the
assumed strain distribution through the depth of the section at ultimate,
as shown in Figure 8.6-11.
Figure 8.6-11 Assumed Strain Distribution through Section Depth at Ultimate
cu = 0.003
c
de-c
t

Variables in Figure 8.6-11 are defined as follows:
c = distance from extreme compression fiber to the neutral axis (in.)
de = effective depth from extreme compression fiber to the centroid of
the tensile force in the tensile reinforcement (in.) (AASHTO
5.7.3.3.1)
cu = failure strain of concrete in compression (in./in.) (AASHTO
C5.7.3.1.2 and 5.7.4.4)
t = net tensile strain in extreme tension steel at nominal resistance
(in./in.) (AASHTO C5.5.4.2.1)
yspsps
sysppsps
e
fAfA
dfAdfA
d



0
=
3.472 261.4 (46) + 1.24(60)(45.5)
3.472(261.4) + 1.24(60)
= 45.96 in.
By similar triangles:
cdc e
tcu


εε
εt=
εcu
c
de - c =
0.003
5.24
45.96-5.24 = 0.023 ≥ 0.005
Therefore, the section is tension-controlled, and thus,  = 1.
Check flexural capacity of section:
Mr = Mn = 1 (3,578.7) = 3,578.7 kip-ft > Mu = 2,877.3 kip-ft (OK)
8.6.12 Check Reinforcement Limits
8.6.12.1 Maximum Reinforcement
AASHTO Art. 5.7.3.3.1, which defined a maximum limit for flexural tension
reinforcement to prevent over-reinforced sections, was eliminated in the 2006
interims. As of 2012, the current approach involves reducing the flexural resistance
factor when the net tensile strain in the extreme reinforcement is less than 0.005.
Although this approach permits sections with less ductility than previous editions if a
smaller resistance factor is applied, sections with a net tensile strain less than 0.004
are not recommended because they have a reduced ductility and are generally
uneconomical. Rather, superstructure members shoud be designed for a net tensile
strain of at least 0.004, preferrably 0.005 (for which the resistance factor is 1). The
net tensile strain can alternatively be checked, ensuring that the c/dt (or c/de) ratio for
the section is not greater than 0.375 (which corresponds to a net tensile strain of
0.005).

8.6.12.2 Minimum Reinforcement
To prevent a brittle failure at intial flexural cracking, AASHTO Article 5.7.3.3.2
(2012) requires that all flexural components have sufficient amount of prestressed
and non-prestressed tensile reinforcement to develop a factored flexural resistance,
Mr, at least equal to the lesser of: (i) 1.33Mu and (ii) Mcr
where:
Mu = controlling factored moment demand
Mcr = cracking moment as defined in Eqn. 5.7.3.3.2-1
For this example,
(i) The controlling factored moment occurs at midspan due to Strength II
combination.
Mu = 2,887.3 kip-ft
1.33 Mu = 3,849.0 kip-ft
(ii)  














 1γγγ 213
nc
c
dncccpercr
S
S
MSffM (AASHTO 5.7.3.3.2-1)
where:
fr = modulus of rupture of concrete specified in Article 5.4.2.6
fcpe = compressive stress in concrete due to effective prestress forces
only (after allowance for all prestress losses) at extreme fiber of
section where tensile stress is caused by externally applied loads
(ksi)
Mdnc = total unfactored dead load moment acting on the noncomposite
section (kip-in.)
Sc = section modulus for extreme the fiber of the composite section
where tensile is caused by externally applied loads (in.3
)
Snc = section modulus for extreme the fiber of the noncomposite section
where tensile is caused by externally applied loads (in.3
)
1 = flexural cracking variability factor
= 1.6 for other than PC segmental structures
2 = prestress variability factor
= 1.1 for bonded tendons
3 = ratio of specified minimum yield strength to ultimate tensile
strength of reinforcement
= 1 for prestressed concrete structures
ksi588.0624.024.0 '
 cr ff (AASHTO 5.4.2.6)

cpe =
Pf
Ag
+
Pf (e
c
)
Sb

556.2
474

556.2 16
4,770
= 3.039 ksi
Mdnc = MDC1 + MDC2 = 302.4 + 333.7 = 636.1 kip-ft = 7,633 kip-in.
Sc = SBC = 7,735 in.3
Snc = Sb = 4,770 in.3
Mcr = 1 1.6 0.558 + 1.1 3.039 7,735 - 7,633
7,735
4,770
-1
= 28,389 kip-in. = 2,366 kip-ft
Since 1.33Mu (= 3,849 kip-ft) > Mcr (= 2,366 kip-ft)  Mcr controls.
Mn = 3,578.7 kip-ft ≥ Mcr = 2,366 kip-ft (OK)
8.6.13 Design for Shear
Shear design of PC girders in this example is performed using the sectional
design method of Article 5.8.3 (AASHTO 2012). However, the General Procedure
for Shear Design with Tables is used to determine β and , per Appendix B5 of
LRFD Specifications (AASHTO, 2012) and California Amendment 5.8.3.4.2
(Caltrans, 2014). A design flow chart is provided in Figure CB5.2-5 of Appendix B5
of the LRFD Specifications (AASHTO, 2012).
Note: California Amendment 5.8.3.4.3 (Caltrans, 2014) prohibits the use of LRFD
Specifications (AASHTO, 2012) Article 5.8.3.4.1, Simplified Procedure for
Nonprestressed Sections, for both prestressed and nonprestressed sections.
PC girders are designed by comparing the factored shear force (envelope value)
and the factored shear resistance at a number of sections along their length, typically
at tenth points along the member length and at additional locations near supports. Per
LRFD Specifications (AASHTO, 2012), the shear resistance, Vn, may be taken to
consist of the sum of three components:
 Concrete component, Vc, that relies on tensile stresses in the concrete
 Steel component, Vs, that relies on the tensile stresses in the transverse
reinforcement
 Prestressing component, Vp, the vertical component of the prestressing
force for harped strands
This example illlustrates shear design only at the critical section.
8.6.13.1 Determine Critical Section for Shear Design
For the common situation near supports where the reaction force in the direction
of the applied shear introduces compression into the end region of a member, Article

5.8.3.2 of LRFD Specifications (AASHTO, 2012) allows the location of the critical
section for shear to be taken at a distance, dv, the effective shear depth, from the
internal face of the support.
Determine effective shear depth, dv :
dv = distance between resultants of tensile and compressive forces due to flexure
= de  a/2, but not less than the greater of (0.9de, 0.72h)(AASHTO 5.8.2.9)
where:
h = hc, overall depth of composite section
de = effective depth from extreme compression fiber to centroid of tensile
reinforcement = hc - ybts
where:
ybts = centroid of all tensile reinforcement
a = depth of compression block (taken at midspan for simplicity)
Because harped strands are used, de varies near the ends. Thus, either initially
assume de based on the straight strands or a location equal to 0.05L for dv to calculate
de.
Using the latter approach:
dv = 0.05 (70) = 3.5 ft from face of internal support.
The centroid of the tensile reinforcement from the bottom fiber, including both
prestressing steel (straight strands only) and mild reinforcement, is calculated based
on the following, Figure 8.6-12 and Table 8.6-11:
Figure 8.6-12 Definitions of ybts, de, and dv at Section Located Near Support
dv
Centroid of tensile
reinforcement
ybts
a/2
2 - #5 @5.5
2 - #5 @ 3.5
hc
PS Steel
de

Table 8.6-11 Centroid of Tensile Reinforcement
Layer
As
(in.2
)
yi
(in.)
(As)(yi)
(in.3
)
1 Two #5 = 0.62 3.5 2.2
2 Two #5 = 0.62 5.5 3.4
3 12(0.217)(270/60) = 11.72 3.5* 41
Total 12.96 - 46.6
*Centroid of 12 straight strands on the tension side.
in.6.3
96.12
6.46
btsy
de = hc - ybts = 50 – 3.6 = 46.4 in.
The depth of compression block, a, at dv can be computed using the procedure
presented in the flexure design section. It is found that a = 4.46 in.
in.23.2
2
46.4
2

a
 
 








in.0.360.5072.07.0
in.8.414.469.09.0
in.2.442.24.462/
max
h
d
ad
d e
e
v
dv = 44.2 in.= 3.7 ft
Because 3.7 ft is larger than the initially assumed value of 3.5 ft, it is
conservative to simply use the smaller value for dv (and larger shear) rather than
continue iteration. Also, because the bearing pad size has not yet been determined at
this stage, it is conservative to assume that the support width equals zero.
Therefore, use dv = 3.5 ft from centerline of the support.
8.6.13.2 Determine Shear Force Demand
Determine factored shear force demand and corresponding factored moment
demand at dv away from the face of the support, which is taken as 3.5 ft from the
centerline of the support.
Table 8.6-12 Unfactored Shear Forces and Associated Moments at dv from Face of
Support
Shear VDC1 VDC2 VDC3 VDW V(LL+IM)HL93 V(LL+IM)P15
(kip) 15.6 17.2 5 6 65.7 102.2
Associated Moment MDC1 MDC2 MDC3 MDW M(LL+IM)HL93 M(LL+IM)P15
(kip-ft) 57.5 63.4 18.5 22.3 199 304
Table 8.6-3 Table 8.6-4 Table 8.6-5

Apply Strength I and Strength II Load Combinations to determine which governs
for Vu:
Strength I:
Vu = 1.25(VDC1 + VDC2 + VDC3) + 1.5 VDW + 1.75 V(LL+IM)HL93
= 1.25(15.6 + 17.2 + 5) + 1.5(6) +1.75(75.7)
= 171.2 kips
Strength II:
Vu = 1.25(VDC1 + VDC2 + VDC3) + 1.5 VDW + 1.35 V(LL+IM)P15
= 1.25(15.6 + 17.2 + 5) + 1.5(6) +1.35(102.2)
= 194.2 kips  controls
Corresponding Strength II factored moment:
Mu = 1.25 [57.5 + 63.4 +18.5] + 1.5[22.3] + 1.35[304]
= 618.1 kip-ft
8.6.13.3 Determine Contribution of Concrete
The concrete contribution to shear resistance is determined from the following
equation:
Vc=0.0316 β bvdv (AASHTO 5.8.3.3-3)
where:
 = factor indicating the ability of diagonally cracked concrete to transmit
tension and shear
bv = effective web width taken as the minimum web width within the depth, dv
(in.)
dv = effective shear depth (in.)
For the General Procedure of LRFD Specifications Appendix B5 (AASHTO
2012), the value of  is based on the net longitudinal tensile strain, x, at the middepth
of the section for the normal case in which code-minimum transverse reinforcement
is provided. This is because such members have the capacity to redistribute shear
stresses.

Figure 8.6-13 Shear Parameters for Section Containing at Least Minimum Amount of
Transverse Reinforcement, Vp = 0 (Figure B5.2-1 (AASHTO, 2012)
 Determine x:
For the General Procedure, the longitudinal strain, , at middepth of the
section is typically determined using one of the two equations:
o Eq. B5.2-1 when the strain is tensile (positive)
o Eq. B5.2-3 when the strain is compressive (negative)
The value of 0.5 cot may be taken equal to 1 (i.e.,  may be taken as
26.6) initially during iterations for  and β, and may also be assumed
constant to avoid iterations, without significant loss of accuracy
(AASHTO, 2012).
Note that for some situations (e.g., PC girders made continuous for live
load), using Eq. B5.2-1 may be overly conservative when applied near
supports because the prestressing strands will be located on the flexural
compression side. In such cases, Eq. CB5.2-1 may be used for greater
accuracy (AASHTO, 2012).
εx=
|Mu|
dv
+ 0.5Nu + 0.5 Vu - Vp cot θ - Apsfpo
2 EsAs + EpAps
where:
| Mu | = absolute value of factored moment corresponding to the factored
shear force, not to be taken less than | Vu – Vp | dv
= maximum of (618.1 k-ft, | Vu – Vp | dv)
Vu = factored shear force =194.2 kips
Vp = component in the direction of the applied shear of the effective
prestressing force; positive if resisting the applied shear (kip)
Pf = total strand force = 556.2 kips (Section 8.6.9.2, Pfg, non-
transformed section)

 = angle of harped strands, from Figure 8.6-14
= tan-1
10 - 4
28 x 12
=1.02o
Figure 8.6-14 Girder Elevation Near Support and Critical Section for Shear
(Ignoring Bearing Pad)
Vp = 556.2 sin (1.02º) = 9.9 kips
| Vu – Vp | dv = |194.2 – 9.9 | 3.5 = 645.2 kip-ft > 618.1 kip-ft
Therefore, | Mu | = 645.1 kip-ft = 7,741 kip-in.
Nu = factored axial force, taken as positive if tensile and negative is
compressive
= 0 kips
 = angle of inclination of diagonal compressive stresses
= 26.5 initially assumed, based on taking 0.5 (cot ) = 1
fpo = a parameter taken as modulus of elasticity of prestressing tendons
multiplied by the locked-in difference in strain between the
prestressing tendons and the surrounding concrete. For the usual
levels of prestressing, a value of 0.7fpu is appropriate for
pretensioned members.
= 0.7 (270) = 189 ksi
Aps= area of prestressing strands on flexural tension side at section
= 3.472 in.2
As = 1.24 in.2
dv
Critical Section

CG =
10
28'-0"
CG = 4
Centroid of
prestressing steel

xε
)]472.3(500,28)24.1(000,29[2
)189(472.3)5.26cot(9.92.1945.0)0(5.0
42
741,7



  3
10x07.1
820,269
288 



Since x is negative at this location at middepth, the section is in
compression. Therefore, x must be calculated using Eq. B5.2-3, which
accounts for the presence of concrete in compression.
xε
)(2
θcot5.05.0
pspsscc
popspuu
v
u
AEAEAE
fAVVN
d
M









Ac = area of concrete on the flexural tension side
= 6 (19) + 0.5 (2) (6) (6) + 7 (50/2-6)
= 283 in.2
Figure 8.6-15 Definition of Ac
xε
)]472.3(500,28)24.1(000,29)283(696,4[2
)189(472.3)6.62cot(9.92.1945.0)0(5.0
42
741,7









  3
10x098.0
760,927,2
288 



h/2 = 25"
h = 50"
= Ac

 Determine  and 
For sections with transverse reinforcement equal to or larger than
minimum transverse reinforcement, the value of  (factor for concrete
shear contribution) and  (angle of inclination of diagonal compressive
stresses) are estimated through iteration from Table B5.2-1 of LRFD
Specifications (AASHTO, 2012), shown as Table 8.6-13. To use this, the
ratio (vu / fc) is required in addition to x.
Using  = 0.9 for shear per LRFD Specifications,
uv
vv
pu
db
VV



ksi700.0
)42()7(9.0
)9.9(9.02.194



c
u
f
v
'
117.0
6
700.0

Table 8.6-13 Values of and  for Sections with Transverse Reinforcement (Table B5.2-1
(AASHTO 2012)
vu
fc′
εx × 1,000
≤−0.2 ≤−0.1 ≤−0.05 ≤0 ≤0.125 ≤0.25 ≤0.5 ≤0.75 ≤1
≤0.075 22.3
6.32
20.4
4.75
21
4.1
21.8
3.75
24.3
3.24
26.6
2.94
30.5
2.59
33.7
2.38
36.4
2.23
≤0.1 18.1
3.79
20.4
3.38
21.4
3.24
22.5
3.14
24.9
2.91
27.1
2.75
30.8
2.5
34
2.32
36.7
2.18
≤0.125 19.9
3.18
21.9
2.99
22.8
2.94
23.7
2.87
25.9
2.74
27.9
2.62
31.4
2.42
34.4
2.26
37
2.13
≤0.15 21.6
2.88
23.3
2.79
24.2
2.78
25
2.72
26.9
2.6
28.8
2.52
32.1
2.36
34.9
2.21
37.3
2.08
≤0.175 23.2
2.73
24.7
2.66
25.5
2.65
26.2
2.6
28
2.52
29.7
2.44
32.7
2.28
35.2
2.14
36.8
1.96
≤0.2 24.7
2.63
26.1
2.59
26.7
2.52
27.4
2.51
29
2.43
30.6
2.37
32.8
2.14
34.5
1.94
36.1
1.79
≤0.225 26.1
2.53
27.3
2.45
27.9
2.42
28.5
2.4
30
2.34
30.8
2.14
32.3
1.86
34
1.73
35.7
1.64
≤0.25 27.5
2.39
28.6
2.39
29.1
2.33
29.7
2.33
30.6
2.12
31.3
1.93
32.8
1.7
34.3
1.58
35.8
1.5
From Table 8.6-13 with x = -0.098  10-3
and vu / fc = 0.117, the values
of and  could be determined. Although the values to be selected fall
between two choices (boxes) in the table, for hand calculations, it is

normally simpler and conservative to use the value of  in the lower row
(larger vu / fc ) and value of in column to the right (larger x) of the
computed value in the table.
For this design example, first iteration yields:
 = 22.8
 = 2.94
The angle  was initially assumed to be 26.5, significantly larger than
22.8. Therefore, another iteration is performed using the angle of 22.8.
xε
)]472.3(500,28)24.1(000,29)283(696,4[2
)189(472.3).822cot(9.92.1945.0)0(5.0
42
741,7









  3
10x086.0
760,927,2
253 



From Table 8.6-13, Iteration 2 yields the same values for and .
Therefore, no further iteration is required and the following values are
used in design at this section:
 = 22.8
 = 2.94
 Compute concrete contribution to shear resistance, Vc :
cV vvc dbf 'β0316.0 (AASHTO 5.8.3.3-3)
)42()7(6)94.2(0316.0
= 66.9 kips
8.6.13.4 Requirement for Transverse Reinforcement
Check if shear reinforcement is required, i.e., when Vc  0.5 (Vc – Vp)
Vu = 194.2 kips > 0.5 (0.9) (66.9 + 9.9) = 34.6 kips
Therefore, transverse shear reinforcement is required at the critical section.
8.6.13.4.1 Required Area of Transverse Reinforcement
The required area of transverse reinforcement is based on satisfying the
following design relationship:

≤ Vn = Vc+ Vp+ Vs (AASHTO 5.8.3.3-1)
Solving this equation for Vs leads to:

Vs =
Vu

Vc Vp
Therefore, the required contribution of the transverse reinforcement, Vs, is:
Vs =
194.2
0.9
- 66.9 - 9.9 = 139 kips
The required area of transverse reinforcement can conveniently be expressed in
design as an area per length, i.e., (Av/s) based on rearrangement of AASHTO Eq.
5.8.3.3-4:
Vs =
Av fy
dv cot  + cot  sin 
s
Av
s
=
Vs
fy
dv cot  + cot  sin 
where:
s = spacing of transverse reinforcement measured in a direction parallel to the
longitudinal reinforcement
Av = area of shear reinforcement within a distance s
 = angle of inclination of diagonal compressive stresses
 = angle of inclination of transverse reinforcement to longitudinal axis
= 90 for vertical stirrups
fy = yield strength of transverse reinforcement
Av
s
=
139
60(42) cot 22.8o
+ cot 90o
sin 90o
= 0.023
in.2
in.
Using #5 double-leg stirrups for transverse reinforcement,
Av = 0.31 (2) = 0.62 in.2
Spacing, s =
0.62
0.023
= 27 in.
Using # 5 double-leg stirrups at 12 in. on center (s = 12 in.) near supports.
Note: Larger spacing, up to the maximum permitted by LRFD Specifications, may be
selected for section beyond 4 ft at the discretion of the designer.
This corresponds to a contribution of transverse reinforcement, Vs, to nominal
shear resistance:
Vs,provided =
0.62(60)(42) cot 22.8o
12
= 309.7 kips
Vn = Vc + Vp + Vs

Vn = 66.9 + 9.9 + 309.7 = 386.5 kips >
Vu

= 215.8 kips (OK)
8.6.13.5 Determine Maximum Spacing for Transverse Reinforcement
Per Article 5.8.2.7 of LRFD Specifications (AASHTO, 2012), the spacing of
transverse reinforcement, s, cannot exceed the maximum permissible spacing, smax
(i.e., s ≤ smax). The maximum spacing, smax, depends on the level of shear stress, vu.
From previous calculation,
vu=
Vu - Vp
 bv dv
= 0.700 ksi
If vu < 0.125 fć, smax = 0.8 dv ≤ 18 in. (CA 5.8.2.7-1)
0.125 fć = 0.126 (6) = 0.75 ksi > vu = 0.7 ksi
smax = 0.8 dv = 33.6 in.
smax = 18 in.  controls
Therefore, smax = 18 in.
Spacing provided s = 6 in. < 18 in. (OK)
Note that tighter spacing per Eq. 5.8.2.7-2 applies for cases in which
vu  0.125fc.
8.6.13.6 Check Minimum Transverse Reinforcement
The area of transverse reinforcement, Av, provided cannot be less than that
required by Eq. 5.8.2.5-1:
y
vc
v
f
sbf
A


0316.0
(AASHTO 5.8.2.5-1)
For s = 12 in. as provided:
Av = 0.62 in.2
> 0.0316√6
7(12)
60
= 0.108 in.2
Therefore, #5 double-leg stirrups at 12 in. on center satisfy the minimum
transverse reinforcement requirement.
8.6.13.7 Check Maximum Nominal Shear Resistance
To ensure that the web concrete will not crush prior to yielding of transverse
reinforcement, LRFD Specifications (AASHTO, 2012) requires that the nominal
shear resistance, Vn, be limited to the smaller of Eq. 5.8.3.3-1 and Eq. 5.8.3.3-2:
Vn = Vc + Vs + Vp = 386.5 kips (AASHTO 5.8.3.3-1)
Vn = 0.25 fćbvdv + Vp = 0.25 (6) (7) (42) + 9.9 = 450.9 kips (AASHTO 5.8.3.3-2)
Therefore, the nominal shear resistance is 386.5 kips.

Using the above procedure, the transverse reinforcement along the entire girder
can be similarly determined.
8.6.14 Design for Interface Shear Transfer between Girder and Deck
The interface shear transfer between precast concrete girder and cast-in-place
deck shall be designed according to AASHTO Article 5.8.4. The interface resistance
shall satisfy
Vri =  Vni ≥ Vui (AASHTO 5.8.4.1-1 & 5.8.4.1-2)
where
Vri = factored interface shear resistance (kip)
Vni = nominal interface shear resistance (kip)
Vui = factored interface shear (kip)
 = resistance factor = 0.9
Using AASHTO Eq. (C5.8.4.2-7), the factored interface shear can be taken as:
v
u
uihi
d
V
VV 
where
Vu = factored vertical shear under Strength Limit State
dv = effective depth for shear
All sections along the entire length of the girder are required to satisfy the Article
5.8.4 requirement. For this example, the interface shear design is only demonstrated
at the dv (= 42 in.) location from face of support.
From Section 8.6.13.2, the factored shear Vu = 194.2 kips at dv. The factored
interface shear,
kip/in.62.4
42
2.194
uiV
 cvfcvni PAcAV   (AASHTO 5.8.4.1-3)
Acv = bvi Lvi (AASHTO 5.8.4.1-6)
where
c = cohesion factor from AASHTO Art 5.8.4.3 (ksi)
Acv = area of concrete engaged in interface shear transfer (in.2
)
Avf = area of interface shear reinforcing crossing the shear plane within Acv (in.2
)
fy = yield stress of interface shear reinforcement (ksi)
Pc = permanent compressive force (kip)
bvi = interface width (in.)

Lvi = interface length (in.)
For CIP concrete slab on clean concrete girder surfaces, free of laitance and with
surface roughened to an amplitude of 0.25 in.:
c = 0.28 ksi (AASHTO Art 5.8.4.3)
µ = 1 (AASHTO Art 5.8.4.3)
Acv = 19 (1) = 19 in.2
The amount of vertical shear reinforcement provided at dv is #5 bar, double legs,
at 6 in. spacing (Sect. 8.6.13), acting as interface shear reinforcement extended into
the deck.
Avf =
0.31
6
= 0.052 in.2
in.⁄
Vni = 0.28(19) + 1[(0.052)(60) + 0] = 8.44 kip/in.
Vni= 0.9 (8.44) = 7.6 kip/in. > Vui = 4.62 kip/in. (OK)
8.6.14.1 Check Minimum Interface Shear Reinforcement
The minimum interface shear reinforcement required is
Avf, min =
0.05Acv
fy
=
0.05(19)
60
0.016 in.2
in.⁄
Provided Avf = 0.052 in.2
in.⁄ > 0.016 in.2
in.⁄
Therefore minimum interface shear reinforcement requirement is met.
8.6.14.2 Check Maximum Nominal Shear Resistance
The maximum nominal shear resistance used in design shall be the lesser of the
two:
 Vni ≤ K1 f´c Acv (AASHTO 5.8.4.1-4)
 Vni ≤ K2 Acv (AASHTO 5.8.4.1-5)
where:
fc = concrete compressive strength of deck slab (ksi)
K1 = fraction of concrete strength available to resist shear
K2 = limiting interface shear resistance
For CIP concrete slab on clean concrete girder surfaces, free of laitance with
surface roughened to an amplitude of 0.25 in.:
K1 = 0.3 (AASHTO Article 5.8.4.3)
K2 = 1.8 ksi for normal weight concrete (AASHTO Article 5.8.4.3)
 Vni ≤ 0.3 (3.6) (19) = 20.5 kip/in.  controls

 Vni ≤ 1.8 (19) = 34.2 kip/in.
The Vni provided = 8.44 kip/in. < 20.5 kip/in. (OK).
8.6.15 Check Minimum Longitudinal Reinforcement
The minimum longitudinal reinforcement (including both prestressed and non-
prestressed reinforcement on the flexural tension side) at all locations along the
girder shall be proportioned to satisfy:


cot5.05.0








 sp
c
u
c
u
fv
u
yspsps VV
VN
d
M
fAfA
(AASHTO 5.8.3.5-1)
At dv from the face of the support:
Mu = 618.1 kip-ft
Vu = 194.2 kips
Vs = 309.7 kips, but not to exceed
Vu
 v
where:
Vu
 v
=
194.2
0.9
= 218.5 kips
Therefore, Vs = 215.8 kips
Vp = 9.9 kips
Nu = 0 kips
dv = 42 in.
 = 22.8
fps = fpe = 160.2 ksi (from Section 8.6.9.2)
The determination of minimum longitudinal reinforcement at dv from face of
support is illustrated below.
|Mu|
dv f
0.5
Nu
c
Vu
v
- Vp -0.5Vs cot 
  kips7.4098.22cot5.2185.09.9
9.0
2.194
0.1
0.0
5.0
)0.1)(42(
)12(2.618












 o
Transfer length, Lt, from girder end is taken as 30(strand diameters) = 30(0.6) =
18 in. This is less than the distance dv from the end. Therefore, the strands have
developed the full prestressing force and the effective prestress fps = 160.2 ksi is used.
Aps = area of 12 straight strands = 12(0.217) = 2.604 in.2

As = area of four #5 rebar = 4(0.31) = 1.24 in.2
Aps fps + As fy = 2.604(160.2) + 1.24(60) = 491.6 kips > 409.7 kips
Therefore, the minimum reinforcement requirement is satisfied.
Note that the minimum reinforcement requirement needs to be satisfied in all
locations along the girder. Eq. 5.8.3.5-2 of LRFD Specifications (AASHTO, 2012)
must also be satisfied at the inside edge of bearing of simple end supports to the
section of critical shear
8.6.16 Pretensioned Anchorage Zone Reinforcement
 Splitting resistance:
Article 5.10.10.1 of LRFD Specifications (AASHTO, 2012) requires the
following vertical reinforcement be provided within the distance h/4
from the end of the girder to provide splitting resistance to bursting
stresses.
ssr AfP  (AASHTO 5.10.10.1-1)
where:
fs = stress in steel not to exceed 20 ksi
As = total area of vertical reinforcement located within the distance h/4
from end of beam (in.2
)
h = overall dimension (height) of the precast I girder in the direction in
which splitting resistance is being evaluated (in.)
Pr = factored bursting resistance of pretensioned anchorage zone
provided by transverse reinforcement (kip), not less than 4% of
prestressing force at transfer, Pi
Pr = 0.4 (Pi) = 0.04 (0.75) (270) (3.472) = 28.1 kips
2
in.41.1
20
1.28
sA
Using #5 bars with 2 vertical legs,
Number of bars required = 3.2
)2(31.1
41.1

Therefore, use three #5 double legs within h/4 (42/4 = 10.5 in.) from end
of girder.
 Confinement reinforcement:
Article 5.10.10.2 of LRFD Specifications (AASHTO, 2012) requires
reinforcement be placed to confine the prestressing steel in the bottom
flange, over the distance 1.5d from the end of the girder, using #4 rebar
with spacing not to exceed 6 in. and shaped to enclose the strands.

Place #4 rebar at no more than 6 in. on center over the distance
1.5h = 1.5(42) = 63 in. (conservative) from the end of the girder to
confine the prestressing strands in the bottom flange.
Figure 8.6-16 Transverse, Longitudinal, and Confinement Reinforcement
Details
8.6.17 Deflection and Camber
The following three aspects of deflection and camber are addressed in this design
example:
 Determine and specify unfactored instantaneous girder deflections due to
deck and rail for plan sheets
 Check live load deflection against AASHTO LRFD deflection criteria
 Determine and specify minimum haunch thickness at supports for plan
sheets
Total deflection of the girder is estimated as the sum of the short-term and long-
term deflections. Short-term deflections are immediate and are based on an estimate
of the modulus of elasticity and the effective moment of inertia. Girder and deck slab
self-weight are carried non-compositely by the girder alone, while dead loads such as
barriers and overlays as well as live loads are carried by the composite girder-deck
system. Long-term deflections consist of long-term deflections at erection and long-
term deflection at final stage (may be assumed to be approximately 20 years).
#5 stirrup
4-#5 cont.
(longitudinal reinforcement)
#4 confinement
reinforcement
Note: See XS Sheet XS1-120 for standard reinforcement (not shown).

8.6.17.1 Calculate Girder Deflections due to Deck and Rail
In this section, the instantaneous, unfactored girder camber and deflections due to
prestressing force and self-weight of the deck, haunch, barrier, and future wearing
surface are calculated for the contract plans.
 Initial camber due to prestressing force at midspan can be estimated
using case (4) of Table 8.4-1. After simplifying, the deflection, ∆p, is
expressed as,









6
)('
8
22
bLeLe
IE
P c
ci
i
p
where:
Pi = total prestressing force immediately in prestress strands after
transfer (kips)
= Pj – ES = (202.5 – 16.84) (3.472) = 644.6 kips
ciE = modulus of elasticity of concrete at initial (ksi) = 4,200 ksi
I = initial gross (non-transformed) moment of inertia of the girder (in.4
)
= 95,400 in.4
ec = eccentricity of prestressing strands at midspan (in.) = 20 – 4 = 16 in.
e' = difference between eccentricity of prestressing strands at midspan
and at end of girder (in.) = 10 – 4 = 6 in.
L = girder length = 71(12) = 852 in.
bL = distance from end of girder to harped point (in.) = 28(12) = 336 in.
in.15.2
6
)336(0.6
9
)852(0.16
)400,95(200,4
6.644 22









 p (upward)
 Immediate deflection due to girder self-weight at midspan:
The equation for deflection of a simply supported girder with a
distributed load:









IE
Lw
ci
g
g
4
384
5
where:
wg = distributed weight of the girder= 0.494 kip/ft = 0.041 kip/in.
Deflection due to beam self weight to be used in computing deflection at
erection (with span = 70 ft = 840 in.),

g=
5
384
0.041 840 4
4,200 95,400
= 0.66 in. (downward)
 Immediate deflection due to weight of deck and haunch at midspan (non-
composite section):
ws = 0.525 + 0.02 = 0.545 kip-ft = 0.045 kip-in.
Ec = 4,696 ksi
s=
5
384
0.045 840 4
4,696 95,400
 Immediate deflection due to barrier weight at midspan (composite
section):
wbr = 0.159 kip-ft = 0.013 kip-in.
Ec = 4,696 ksi, and I = 249,148 in.4
(gross composite section)
br=
5
384
0.013 840 4
4,696 249,184
 Immediate deflection due to future wearing surface at midspan
(composite section):
wfw = 0.195 kip-ft = 0.016 kip-in.
Ec = 4,696 ksi, and I = 249,148 in.4
(gross composite section)
fw=
5
384
0.016 840 4
4,696 249,184
 Immediate deflections for plans (deck and haunch; barrier rails and
future wearing surface):
The following unfactored instantaneous girder deflection values at
midspan should be shown on the contract plans.
o Deck: Unfactored instantaneous girder deflection due to deck and
haunch = ∆s = 0.65 in.
o Rail: Unfactored instantaneous girder deflection due to barrier rail
and future wearing surface = ∆br∆fw= 0.07 + 0.09 = 0.16 in.
8.6.17.2 Compare Live Load Deflection to AASHTO LRFD Limit
Girder live load deflection check is estimated using composite section properties
and concrete strength at service, and compared to the AASHTO LRFD limit per
Section 2.5.2.6.2. It should be noted that the deflection criteria in LRFD Section
2.5.2.6.2 is optional for California bridges. However, for specific situations, such as
bridge widening where the deflection may impair the minimum vertical clearance,
the deflection must be accounted for in the design.

The instantaneous live load deflection for a simple span bridge occurs at midspan
due to the HL-93 truck axles placed in the location shown below in Figure 8.6-17,
together with the HL-93 lane load (not shown).
Figure 8.6-17 Position of Truck to Produce Maximum Moment
The live load for each lane can be obtained from any structural analysis software
program, such as CT Bridge. The deflection for each girder is calculated by
multiplying the deflection per lane by the ratio of (number of lanes/number of
girders). This ratio can also be estimated using the moment distribution factor (DFM)
shown in Sec. 8.6.7.3, which is the simpler way.
Since the deck concrete and girder concrete differ in strength, transformed
properties are used to calculate the live load deflection. As shown in Sec. 8.6.7.3, the
DFM for this bridge is 0.571.
∆LL = DFM (∆LL per lane) = 0.571 (∆LL per lane)
From structural analysis software, ∆LL per lane = 1.01 in. (downward)
∆LL = 0.571 (1.01) = 0.58 in. (downward)
This instantaneous live load deflection is compared to the AASHTO LRFD
recommended limitation of L/800 for general vehicular loading.
800
70(12)
800
1.05 in.
The live load deflection is less than the AASHTO limit and therefore acceptable.
8.6.17.3 Determine Minimum Haunch Thickness
The minimum haunch thickness at supports is intended to help ensure that the
specified haunch at midspan is achieved in the field. (See Section 8.4.5.1 for
discussion on importance of the haunch.)
8 kips
2- 4"
Midspan
14- 0" 14'-0"
32 kips32 kips

The midspan haunch thickness is first specified by the designer (note that this is
no recommended minimum value). Based on this, the designer would calculate the
minimum haunch thickness at the supports. Both the minimum haunch thickness at
the supports and the designer-specified midspan haunch thickness should be shown
on the plans.
At erection, the net upward camber of the girder at midspan due to prestressing
force plus self-weight, ∆g,erect, is calculated based on the instantaneous deflection
components multiplied by the PCI factors. These factors account for the time-
dependent effects between girder casting and erection.
∆g,erect = (MPCIerect ∆p – MPCIerect ∆g)
where:
∆g,erect = camber at midspan at erection, due to long-term effects of
prestressing force and girder self-weight (in.)
MPCIerect = PCI multiplier for long-term effects at erection (Table 8.4-2)
∆p = immediate camber of girder at transfer due to prestressing force (in.)
∆g = immediate deflection of girder at midspan at transfer due to self -
weight (in.)
As shown in Figure 8.6-18, the minimum haunch thickness at the supports, THsup,
is then calculated as the difference (at the centerline of the girder) between the long-
term camber at midspan at erection, ∆g,erect and the instantaneous deflection of the
girder at midspan due to the weight of the deck and haunch, plus the designer-
specified haunch at midspan, THmid.
midserectg THTH  ,sup
where:
THsup = haunch thickness at supports
∆g,erect = camber at midspan at erection, due to long-term effects of prestressing
force and girder self-weight (in.)
∆s = immediate deflection at midspan due to deck weight (in.)
THmid = designer-specified haunch thickness at midspan (in.)

Figure 8.6-18 Relationship between Specified Haunch Thickness
at Midspan and Minimum Haunch Thickness at Supports
For this example:
∆g,erect = 1.8∆p – 1.85∆g = 1.8 (2.15) – 1.85 (0.66) = 2.65 in. (upward)
Specifying a haunch thickness of 1 in. at midspan, the minimum haunch
thickness required at the supports is determined as follows:
THsup = ∆g,erect + ∆s + THmid = 2.65 + (-0.65) + 1 = 3 in.
Therefore, the following should be specified on contract plans:
Haunch thickness at midspan: 1 in.
Minimum haunch thickness at supports: 3 in.
Note that the deck cross slope and girder top flange width do not affect the
specified midspan haunch thickness. For situations where the cross slope is relatively
large and/or the top flange is very wide (such as the wide flange girders), thickness of
the haunch at midspan on both sides of the girder flange must be carefully
considered.
THsup
Bottom of
Deck
Top of
Girder
Midspan
THmid
Camber after deck
placement
g,erect
s
Deformed shape (before deck placement)
Un-deformed shape
Deformed shape (after deck placement)
Legends:

NOTATION
a = depth of equivalent rectangular compression stress block (in.) (8.6.11.2)
A = area of stringer, beam, or component (in.2
) (8.2.2)
Ac = concrete area of composite section (8.6.5.3)
Acv = area of concrete engaged in interface shear transfer (in.2
) (8.6.14)
Ag = gross area of girder section (in.2
) (8.4.2.2)
Ai = area of individual component (Table 8.6-2)
Aps = area of prestressing steel (in2
) (8.4.2.2)
As = area of non-prestressed tension reinforcement (in.2
) (8.4.6.1)
A´s = area of compression reinforcement (in.2
) (8.6.11.2)
Atf = area of transformed section, at final (8.6.10.3)
Ati = (8.6.10.2)
Av = area of transverse reinforcement within distance s (in.2
) (8.6.13.5)
Avf = area of interface shear reinforcing crossing the shear plane within Acv (in.2
)
(8.6.14)
ADL = added dead load (kips) (8.2.2)
b = width of the compression face of a member (in.) (8.6.11.2)
beff = effective flange width (in.) (8.6.5.2)
bL = distance from end of girder to harped point (in.) (8.6.17.1)
bv = effective web width taken as the minimum web width, measured parallel to the
neutral axis, between resultants of the tensile and compressive forces due to
flexure; this value lies within the depth, dv (in.) (8.6.13.3)
bvi = interface width (in.) (8.6.14)
c = distance from extreme compression fiber to the neutral axis (in.) (8.6.11.2);
cohesion factor from AASHTO Art 5.8.4.3 (ksi) (8.6.14)
cg = center of gravity
CGC = center of gravity of the concrete section (8.2.2)
CGS = center of gravity of the strands (8.2.2)
D = structure depth (ft) or height of standard shape of PC girder given in BDA 6-1
(in.) (8.2.1)
DC = weight of supported structures (kip) (8.2.2)
db = nominal strand diameter (in.) (8.6.10.2)
de = effective depth from extreme compression fiber to the centroid of the tensile
force in the tensile reinforcement (in.) (8.6.7.1)

DFDL = dead load distribution factor (8.6.7.1)
DFM = live load moment distribution factor (8.6.7.3.1)
DFV = live load shear distribution factor (8.6.7.3.2)
dp = distance from extreme compression fiber to the centroid of the prestressing
tendons (in.) (8.6.11.2)
ds = distance from extreme compression fiber to the centriod of the nonprestressed
tensile reinforcement (in.) (8.6.11.2)
Ds = superstructure depth (ft) (8.6.2)
dt = distance from extreme compression fiber to the centroid of tensile
reinforcement (8.6.12.1)
dv = the effective shear depth taken as the distance, measured perpendicular to the
neutral axis, between the resultants of the tensile and compressive forces due to
flexure (in.) (8.6.13.1)
DW = superimposed dead load (kip) (8.2.2)
e = eccentricity of the anchorage device or group of devices with respect to the
centroid of the cross section; always taken as positive (ft); also the base of
Napierian logarithms (8.2.1)
e' = difference between eccentricity of prestressing steel at midspan and at end (in.)
(8.6.17.1)
EB, Ec = modulus of elasticity of girder material (ksi) (8.6.5.3)
ec = eccentricity of strands measured from center of gravity of girder at midspan
(in.) (8.6.8)
Eci = modulus of elasticity of concrete at initial time (ksi) (8.6.4)
Ect = modulus of elasticity of concrete at transfer or time of load application (ksi)
(8.4.2.1)
Ecu = failure strain of concrete in compression (in./in.) (8.6.11.2)
ED = modulus of elasticity of deck material (ksi) (8.6.5.3)
eg = distance between centers of gravity of girder and deck (in.) (8.6.7.3.1)
em = eccentricity at midspan (8.6.9.1)
Ep, Eps = modulus of elasticity of prestressing tendons (ksi) (8.4.2.1)
Es = modulus of elasticity of mild reinforcing steel (ksi) (8.6.4)
etf = distance between centers of gravity of strands and concrete section at time of
service (8.6.10.1)
eti = distance between centers of gravity of strands and concrete section at time of
transfer (in.) (8.6.10.1)
fb = concrete flexural stress at extreme bottom fiber (8.6.10.3)

fć = specified compressive strength of concrete used in design (ksi) (8.1)
fći = specified compressive strength of concrete at time of initial loading or
prestressing (ksi); nominal concrete strength at time of application of tendon
force (ksi) (8.1)
fcgp = concrete stress at the center of gravity of prestressing tensonds that results from
the prestressing force at either transfer or jacking and the self-weight of the
member at sections maximum moment (ksi) (8.4.2.1)
fcpe = compressive stress in concrete due to effective prestress forces only (after
allowance for all prestress losses) at extreme fiber of section where tensile
stress is caused by externally applied loads (ksi) (8.6.12.2)
fg = stress in the member from dead load (ksi) (8.6.9.2)
fpbt = stress in prestressing steel immediately prior to transfer (8.6.9.1)
fpe = effective stress in the prestressing steel after losses (8.6.9.2)
fpi = prestressing steel stress immediately prior to transfer (ksi) (8.4.2.2)
fpj = stress in prestressing steel at initial jacking (ksi) (8.6.4)
fpo = a parameter taken as modulus of elasticity of prestressing tendons multiplied by
the locked-in difference in strain between the prestressing tendons and the
surrounding concrete (ksi) (8.6.13.3)
fps = average stress in prestressing steel at the time for which the nominal resistance
is required (ksi) (8.6.11.2)
fpu = specified tensile strength of prestressing steel (8.6.4)
fpy = yield strength of prestressing steel (8.6.4)
fr = modulus of rupture of concrete (ksi) (8.6.12.2)
fs = stress in mild tension reinforcement at nominal flexural resistance (ksi)
(8.4.6.1)
f´s = stress in the mild steel compression reinforcement at nominal flexure resistance
(8.6.11.2)
FT = required tension capacity provided by reinforcement (8.6.10.2)
ftg = concrete stress at top of precast girder (ksi) (8.6.10.3)
fy = yield strength of mild steel (ksi) (8.6.11.2)
fý = specified minimum yield strength of compression reinforcment (ksi) (8.6.4)
H = average annual ambient mean relative humidity (percent) (8.4.2.2)
h = web dimension of PC girder (in.) (8.2.1)
hc = overall depth of composite section (in.) (8.6.13.1)
I = initial gross (non-transformed) moment of inertia of the girder (in.4
) (8.6.17.1)

Ic = moment of inertia of composite section about centroidal axis, neglecting
reinforcement (in.4
) (8.6.5.3)
Icg, Ig = moment of inertia of the girder concrete section about the centroidal axis,
neglecting reinforcement (in.4
) (8.6.5.1)
ICt = moment of inertia of composite transformed section (in.4
) (8.6.10.1)
Ie = effective moment of inertia (in.4
) (8.4.5)
Ig = gross moment of inertia of girder (in.4
) (8.6.5.1)
Io = moment of inertia of individual component (in.4
) (Table 8.6-2)
Iti = moment of inertia of concrete section at initial stage, transformed (in.4
)
(8.6.10.1)
K1 = fraction of concrete strength available to resist shear (8.6.14.2)
K2 = limiting interface shear resistance (8.6.14.2)
Kg = longitudinal stiffness parameter (in.4
) (8.6.7.3.1)
L = span length or girder length (ft) (8.1)
LL = live load (kip) (8.6.7.3.2)
Mcr = cracking moment (kip-in.) (8.6.12.2)
MADL = moment due to added dead loads (kip-ft) (8.2.2)
MDC1 = moment due to self-weight of beam (kip-ft) (8.6.8)
MDC2 = moment due to self-weight of deck (kip-ft) (8.6.8)
MDC3 = moment due to self-weight of barrier (kip-ft) (8.6.8)
Mdnc = total unfactored dead load moment action on the monolithic or noncomposite
section (kip-ft) (8.6.12.2)
MDW = moment due to future wearing surface (kip-ft) (8.6.8)
Mg = midspan moment due to self-weight of girder (8.2.2)
MHL93 = moment due to enveloped HL-93 trucks (kip-ft) (8.6.8)
MLL = moment due to live loads (8.2.2)
Mn = nominal flexure resistance (kip-in.) (8.6.11.2)
MP15 = moment due to enveloped P15 truck (8.6.11.1)
MPCIerect = PCI Multipliers for camber/deflection at time of erection (8.6.17.3)
Mr = factored flexural resistance of a section in bending (kip-in.) (8.6.11.2)
Mslab = moment due to weight of deck slab (8.2.2)
Mu = controlling factored moment demand (8.6.11.1)
Mx = moment at location x (kip-ft) (8.6.7.2)
n = modular ratio between beam and deck (8.6.5.3)

Nb = number of beams, stringers, or girders (8.6.7.1)
Nu = factored axial force, taken as positive if tensile and negative is compressive
(kip) (8.6.13.3)
P, Pe = Effective force in prestress strands after all losses (kip) (8.2.2)
Pc = permanent compressive force (kip) (8.6.14)
Pf = force in prestress strands after losses (kip) (8.6.13.3)
Pfg = effective force in prestress strands after all losses for gross section design (kip)
(8.6.9.2)
Pi = force in prestress strands after elastic shortening loss (kip) (8.6.17.1)
Pj = force in prestress strands before losses (kip) (8.6.8)
Pr = factored bearing resistance of anchorages (kip) (8.4.6.1)
r = radius (in.) (8.6.5.1)
S = spacing of girders or webs (ft) (8.2.2)
S = surface of girder section (8.4.2.2)
s = spacing of reinforcing bars (in.)
Sb = section modulus for the bottom extreme fiber of the girder where tensile stress
is caused by externally applied loads (in.3
) (8.6.8)
SBC = section modulus for the bottom extreme fiber of the composite section where
tensile stress is caused by externally applied loads (in.3
) (8.6.5.3)
SBCt = section modulus for the bottom extreme fiber of the composite section -
transformed (in. 3
) (8.6.10.1)
SBtf = section modulus for the bottom extreme fiber of the composite section -
transformed, at service stage (in. 3
) (8.6.10.3)
Sc = section modulus for the extreme fiber of the composite sections where tensile
stress is caused by externally applied loads (in.3
) (8.6.12.2)
Snc = section modulus for the extreme fiber of the monolithic or noncomposite
sections where tensile stress is caused by externally applied loads (in.3
)
(8.6.12.2)
St = section modulus for the top extreme fiber of the sections where tensile stress is
caused by externally applied loads (in.3
) (8.6.5.1)
Stc = section modulus for the top extreme fiber of the composite sections where
tensile stress is caused by externally applied loads (in.3
)
STDCt = section modulus for the top extreme fiber of the composite sections at top of
deck level, at service, transformed (in.3
) (8.6.10.1)
STGCt = section modulus for the top extreme fiber of the composite sections at top of
girder level, at service, transformed (in.3
) (8.6.10.1)

STtf = section modulus for the top extreme fiber of the composite sections at top of
girder level, at service, transformed (in.3
) (8.6.10.3)
STti = section modulus for the top extreme fiber precast girder, at initial, transformed
(in.3
) (8.6.10.2)
T = tensile stress in concrete (ksi) (8.2.2)
ts = thickness of concrete deck slab (in.) (8.6.7.3.1)
th = haunch thickness at midspan (in.) (8.6.2)
THmid = haunch thickness at midspan (in.) (8.6.17.3)
THsup = haunch thickness at support (in.) (8.6.17.3)
w = uniform dead load, k/ft (8.6.7.2)
wbr = uniform dead load—weight of barrier (klf) (8.6.6.1)
wfw = uniform dead load—weight of future wearing surface (klf) (8.6.6.1)
wg = uniform dead load—weight of girder (klf) (8.6.6.1)
wh = uniform dead load—weight of haunch (klf) (8.6.6.1)
ws = uniform dead load—weight of deck slab (klf) (8.6.6.1)
V = volume of girder (in.3
) (8.4.2.2)
Vc = nominal shear resistance provided by tensile stresses in the concrete (kip)
(8.6.13)
Vn = nominal shear resistance of the section considered (kip) (8.6.13)
Vni = nominal interface shear resistance (kip) (8.6.14)
Vri = factored interface shear resistance (kip) (8.6.14)
Vp = component in the direction of the applied shear of the effective prestressing
force; positive if resisting the applied shear (kip) (8.6.13)
Vs = shear resistance provided by the transverse reinforcement at the section under
investigation as given by AASHTO 5.8.3.3-4, except Vs shall not be less than
Vu/ (kip) (8.6.13)
Vu = factored shear force (kip) (8.6.13.3)
vu = average factored shear stress on the concrete (ksi) (8.6.13.3)
Vui = factored interface shear resistance (kip/in.) (8.6.14)
x = distance from left end of girder (ft) (8.2.1)
Y = distance from the neutral axis to a point on individual component (in.)
(Table 8.6-2)
yb = distance from the neutral axis to the extreme bottom fiber of PC girder (in.)
(8.2.1)

YBC = distance from the centroid to extreme bottom fiber of composite section (in.)
(8.6.5.3)
YBCt = section modulus for the bottom extreme fiber of the composite, at service,
transformed (in.3
) (8.6.10.1)
YBtf = section modulus for bottom extreme fiber of PC girder, at service, transformed
(in.3
) (8.6.10.1)
YBti = section modulus for bottom extreme fiber of PC girder, at initial, transformed
(in.3
) (8.6.10.1)
ybts = centroid of all tensile reinforcement (in.) (8.6.13.1)
yi = distance from centroid of section i to centroid of composite section (8.6.5.3)
yt = distance from the neutral axis to the extreme top fiber of PC girder (in.) (8.2.1)
YTC = distance from the centroid to extreme top fiber of composite section (in.)
(8.6.5.3)
Ytg = distance from centroid of the composite section to the extreme top fiber of the
PC girder (in.) (8.6.10.1)
YTGCt = distance from centroid of the composite section to the extreme top fiber of the
PC girder (in.) (8.6.10.1)
YTti = distance neutral axis to the extreme top fiber of the PC girder, transformed (in.)
(8.6.10.1)
 = angle of inclination of transverse reinforcement to longitudinal axis (º) total
angular change of prestressing steel path from jacking end to a point under
investigation (rad) (8.6.13.4.2)
 = factor relating effect of longitudinal strain on the shear capacity of concrete, as
indicated by the ability of diagonally cracked concrete to transmit tension
(unitless) (8.6.13.3)
1 = ratio of the depth of the equivalent uniformly stressed compression zone
assumed in the strength limit state to the depth of the actual compression zone
(5.7.2.2) (8.6.11.2)
∆br = deflection due to barrier weight (in.) (8.6.17.1)
∆g = camber at midspan at erection due to girder self-weight (in.) (8.6.17.3)
∆g,erect = camber at midspan at erection due to long-term effects of prestressing force
and girder self-weight (in.) (8.6.17.3)
∆ES = change in length due to elastic shortening (8.1)
∆fpES = sum of all losses or gains due to elastic shortening or extension at the time of
application of prestress and/or external loads (ksi) (8.4.2)
∆fpLT = losses due to long-term shrinkage and creep of concrete and relaxation of
prestressing steel (ksi) (8.4.2)

∆fpR = an estimation of relaxation loss taken as 2.4 ksi for low relaxation strand, 10
ksi for stress relieved strand, and in accordance with manufacturers
recommendation for other types of strand (ksi) (8.4.2.2)
∆fpT = total change in stress due to losses (ksi) (8.4.2)
∆fw = deflection due to future wearing surface (in.) (8.6.17.1)
∆p = camber at midspan due to prestressing force at release (in.) (8.6.17.3)
∆s = instantaneous deflection due to weight of deck slab (in.) (8.6.17.3)
cu = failure strain of concrete in compression (in./in.) (8.6.11.2)
t = net tensile strain in extreme tension steel at nominal resistance (in./in.)
(8.6.11.2)
x = longitudinal strain in the web reinforcement on the flexural tension side of the
member (in./in.) (8.6.13.3)
 = angle of inclination of diagonal compressive stresses (8.6.13.3)
1 = flexural cracking variability factor (8.6.12.2)
2 = prestress variability factor (8.6.12.2)
3 = ratio of specified minimum yield strength to ultimate tensile strength of
reinforcement (8.6.12.2)
h = correction factor for relative humidity of ambient air. (8.4.2.2)
st = correction factor for specified concrete strength time at of prestress transfer to
concrete member (8.4.2.2)
 = resistance factor (8.6.11.2)
 = coefficient of friction (unitless) (8.6.14)
 = angle of harped strands (8.6.13.3)
c = unit weight of concrete (kcf) (8.6.4)

REFERENCES
1. AASHTO, (2012). AASHTO LRFD Bridge Design Specifications, American Association of
State Highway and Transportation Officials, 6th Edition, Washington, D.C.
2. Caltrans, (2014). California Amendments to AASHTO LRFD Bridge Design Specifications
— Sixth Edition 2012, California Department of Transportation, Sacramento, CA.
3. Caltrans, (2014). Memos to Designers 11-8 Design of Precast, Prestressed Girders,
California Department of Transportation, Sacramento, CA.
4. Caltrans, (2013). Memos to Designers 10-20 Attachment 1: Deck Slab Reinforcement
Details, California Department of Transportation, Sacramento, CA.
5. Caltrans, (2012). Bridge Design Aids Chapter 6-1: Precast Prestressed Concrete Girders,
6. Caltrans, (2010). Memos to Designers 11-3 Designer’s Checklist for Prestressed Concrete,
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