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.

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