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Efficient Prestressed Concrete-Steel Composite Girder for
Medium-Span Bridges. I: System Description and Design
Yaohua Deng, A.M.ASCE
1
; and George Morcous, P.Eng., A.M.ASCE
2
Abstract: A new prestressed concrete-steel composite (PCSC) girder system is developed to provide a viable alternative for steel and pre-
stressed concrete I-girders in bridges. The PCSC girder is composed of a lightweight W-shaped steel section with shear studs on its top and
bottom flanges to achieve composite action with the pretensioned concrete bottom flange and the cast-in-place concrete deck. The PCSC girder
is lightweight, economical, durable, and easy to fabricate. The proposed fabrication procedure is similar to those of prestressed concrete girders
and does not need specialized equipment, materials, and forms. A service design procedure is proposed using the age-adjusted elasticity mod-
ulus method to evaluate the time-dependent stresses and strains in the PCSC girder caused by creep and shrinkage effects of concrete and re-
laxation of strands. The strength design method is proposed for the design of PCSC girders at prestress release. A design procedure is proposed
to assist engineers to accomplish economic design and production of PCSC girders, and design examples are presented to illustrate the design
procedure. DOI: 10.1061/(ASCE)BE.1943-5592.0000474.©2013 American Society of Civil Engineers.
CE Database subject headings: Prestressed concrete; Steel; Composite materials; Girder bridges; Span bridges; Design.
Author keywords: Prestressed concrete; Steel; Composite girders; Bridges; Design.
Introduction
The stringer/multigirder bridge system consists of steel and pre-
stressed concrete I-shaped girders with a cast-in-place concrete deck.
About 55% of the bridges in the United States are built using the
stringer/multigirder system, based on the statistics of the National
Bridge Inventory of the Federal Highway Administration [DOT-
Federal Highway Administration (DOT-FHWA) 2011]. This system
is popular because of its simplicity of fabrication, speed of con-
struction, and ease of inspection, maintenance, and replacement.
Steel girders are preferred in continuous, curved, and long-span
bridges because of their light weight, flexibility (i.e., curved and
nonprismatic), andstrength. The disadvantagesof steel girders include
high material cost, high maintenance cost, and susceptibility to cor-
rosion caused by chloride-contaminated splashes. Prestressed concrete
girders are preferred in simple-span, straight, and short-medium-span
bridges [i.e., span length less than 61 m (200 ft)] because of their high
stiffness, durability, and low material cost. The disadvantages of
prestressed concrete girders include heavy weight, difficulty of
making them continuous or curved, and susceptibility to concrete
cracking at the end zone and the top flange at prestress release.
To combine the benefits of steel and prestressed concrete girders,
four types of existing prestressed composite girders have been reported
in the literature. The type I prestressed composite girder system is
constructed with corrugated steel webs and top and bottom concrete
flanges (Sayed-Ahmed 2001). In this system, the concrete bottom
flange is usually prestressed, and corrugated steel webs sustain shear
forces without taking any axial stresses caused by flexure, prestressing,
creep, etc. The complexity of fabricating corrugated steel webs and the
high cost of posttensioning operations/hardware hindered the wide use
of this system in North America. The type II prestressed composite
girder system is a prestressed composite floor slab made of semi-
prefabricated prestressed composite steel-concrete beams, precast
prestressed planks, and topping concrete (Bozzo and Torres 2004).
This is an excellent system for building floors with shallow depths, but
the heavy section caused by the fully embedded steel girder in concrete
hinders the application in bridges. The type III prestressed composite
girder system is composed of a concrete deck and the steel beam and
prestressed by embedded strands or external tendons. Embedded
strands are only effective for crack prevention in the negative moment
region (Basu et al. 1987), and external tendons can be easily corroded
(Lorenc and Kubica 2006). The type IV prestressed composite girder
system is the Preflex girder (Hanswille 2011). The system is a steel
girder with the bottom flange encased in RC, while the prestressing is
applied by elastic bending of the steel girder and/or pretensioning
strands. The fabrication procedure is complicated because of drilling
holes in the web of the steel beam to install the stirrups and applying
prebend loads on the top of steel beam during fabrication.
This paper presents the development of a new prestressed
concrete-steel composite (PCSC) girder system as a viable alterna-
tive for steel and prestressed concrete I-girders. Several design and
fabrication issues associated with the PCSC are presented in the
following sections. In the subsequent companion paper (Deng and
Morcous 2013a), finite-element modeling will be introduced to
investigating strain and stress distributions in the composite sections
of PCSC girders and the proposed fabrication and design procedures
will be validated by fabricating and testing a full-scale specimen.
System Description
The PCSC girder system is composed of a pretensioned con-
crete bottom flange, RC deck, and a rolled steel section (usually
1
Postdoctoral Research Associate, Bridge Engineering Center, Institute
for Transportation, Iowa State Univ., Ames, IA 50010 (corresponding
author). E-mail: jimdeng@iastate.edu
2
Associate Professor, Durham School of Architectural Engineering and
Construction, Peter Kiewit Institute, Univ. of Nebraska–Lincoln, Omaha,
NE 68182. E-mail: gmorcous2@unl.edu
Note. This manuscript was submitted on August 22, 2012; approved on
January 30, 2013; published online on February 1, 2013. Discussion period
open until May 1, 2014; separate discussions must be submitted for in-
dividual papers. This paper is part of the Journal of Bridge Engineering,
Vol. 18, No. 12, December 1, 2013. ©ASCE, ISSN 1084-0702/2013/
12-1347–1357/$25.00.
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W-shape) in between, as illustrated in Fig. 1. Shear studs are used
to connect the rolled steel section to the bottom flange and later to the
deck, creating a fully composite section. As shown in Fig. 1, the
trapezoidal shape is an alternative option for the concrete bottom
flange to prevent accumulation of water, bird nests, and debris.
However, a rectangular shape will be used for the concrete bottom
flange in this study for simplification.
The PCSC girders can be fabricated using a procedure of five
steps as shown in Fig. 2: Step 1 is to weld studs to the steel beam,
pretension strands, place reinforcements, and install formwork.
Step 2 is to place concrete into the formwork and finish the top
surface of concrete. In Step 3, the steel beam is placed on top of
the fresh concrete and is supported by the supported chairs, and the
studs at the bottom penetrate into the fresh concrete. Step 4 is to strip
the formwork and release and cut the strands. Step 5 is to install
formwork and reinforcement and place concrete for the RC deck.
Steps 2 and 3 can be switched if the width of the bottom flange allows
casting the concrete while the steel girder is in place. This fabrication
procedure is simple, convenient, and similar to that of prestressed
concrete girders. In addition, it does not require specialized equip-
ment, materials, and forms. Other advantages of the PCSC girder
include the following:
•Using a pretensioned bottom flange and a rolled steel section
results in a very economical and lightweight section.
•Using a rolled steel section eliminates the problems associated
with prestress release, such as concrete cracking, which is
common in prestressed concrete girders, and draping strands,
which is taken as a costly and dangerous operation and is not
required in the fabrication of the PCSC girder. Thus, it allows
using a smaller concrete section and higher prestressing force.
•The PCSC girder is more durable than steel girders because it
uses concrete to protect the bottom flange from chloride-
contaminated splashes.
•The PCSC girder can be made continuous by splicing the steel
web and top flange.
•The efficiency of the PCSC girder can be further enhanced by
using 18-mm-diameter (0.7-in.-diameter) strands and ultrahigh-
performance concrete, which have been immensely studied in
earlier research by Morcous et al. (2011).
Service Design
Because of the effects of creep and shrinkage of concrete and re-
laxation of strands, service design at final for a PCSC girder is
significantly different from that for a prestressed concrete girder. For
PCSC girders, the stress and strain redistributions between the
concrete and the steel section and between the concrete and strands
will simultaneously occur along with the change of the time-
dependent stresses and strains in the concrete and strands. To eval-
uate the time-dependent stresses and strains and their redistributions,
the time functions for the stress or strain should be used for each
component of PCSC girders.
Two methods are commonly used, i.e., the step-by-step numerical
method and the age-adjusted elasticity modulus method (AEMM)
(Ghali et al. 2012). Because of the time-consuming computations of
the step-by-step numerical method, it can only be achieved effectively
by using a computer program. However, the AEMM can be performed
similar to conventional elastic analysis and can be carried out by
manual computations. In this study, the AEMM is used for analysis
and design of PCSC girders.
When using the AEMM to determine the time-dependent stress
and strain, age-adjusted transformed section properties is obtained
by using age-adjusted modulus ratios of different materials. The
elasticity modulus of concrete is adjusted by the aging coefficient
and creep coefficient, i.e., age-adjusted elasticity modulus Ecðt,t0Þ,
which can be expressed as (Ghali et al. 2012)
Ecðt,t0Þ¼ Ecðt0Þ
1þxðt,t0Þcðt,t0Þ(1)
where t0and t5ages of concrete when the initial stress is applied
and when the strain is considered, respectively; Ecðt0Þ5modulus of
elasticity of concrete at age t0;xðt,t0Þ5aging coefficient; and
cðt,t0Þ5creep coefficient. Introducing the aging coefficient greatly
simplifies the strain calculations with regard to the stress increments
or decrements. As stated by Ghali et al. (2012), xðt,t0Þis usually
used as a multiplier to cðt,t0Þand rarely accurately determined, and
high accuracy in the derivation of xðt,t0Þis hardly justified. In this
study, the value of the aging coefficient xðt,t0Þis directly obtained
by referring to Ghali et al. (2012). It depends on compressive
strength of the concrete at 28 days, relative humidity, and notional
size (h0), which equals two times the volume-to-surface ratio of the
concrete section (V=S).
The creep coefficient is the ratio of strain caused by creep to the
instantaneous strain and can be expressed in term of age t0and age t.
As recommended by AASHTO (2007), the creep coefficient may be
taken as
cðt,t0Þ¼1:9kvs khc kfktd t20:118
0(2)
where
kvs ¼1:45 20:0051V
S$1:0 (3)
khc ¼1:56 20:008H(4)
kf¼35
7þfci
9(5)
ktd ¼ t2t0
61 20:58fci
9þt2t0!(6)
where H5relative humidity (percentage); kvs 5factor for the effect
of the volume-to-surface ratio of the component; khc 5humidity
factor for creep; kf5factor for the effect of concrete strength;
ktd 5time development factor; V=S5volume-to-surface ratio
(millimeters); fci
95specified compressive strength of concreteat time
Fig. 1. PCSC girder system
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of prestressing for pretensioned members (megapascals). It is
noted that 1 day of accelerated curing by steam or radiant heat is
equivalent to 7 days of normal curing (AASHTO 2007).
For concrete without shrinkage-prone aggregates, the strain
caused by shrinkage occurring between the ages t0and tmay be
taken as (AASHTO 2007)
ɛshðt,t0Þ¼2kvs khs kfktd 0:48 1023(7)
where khs 5humidity factor for shrinkage and can be expressed as
khs ¼2:00 20:014H(8)
Within the range of stresses in service conditions, the super-
position is allowed for the instantaneous strain caused by stress
increments or decrements, the strain caused by creep, and the
strain caused by shrinkage. Namely, with the changes of the ap-
plied stresses, the total strain of concrete is given by (Ghalietal.
2012)
ɛcðtÞ¼scðt0Þ1þcðt,t0Þ
Ecðt0ÞþDscðtÞ
Ecðt0Þþɛshðt,t0Þ(9)
where ɛcðtÞ5concrete strain at age t;scðt0Þ5concrete stress at
age t0;andDscðtÞ5increment in concrete stress during the period
from age t0to age t.ThethreetermsinEq.(9) can be explained,
respectively, as strain caused by the stress at age t0and creep
during the period ðt2t0Þ;straincausedbyastressincrementof
magnitude of zero at t0increasing gradually to a final value DscðtÞ
at age t; and strain caused by free shrinkage occurring during the
period ðt2t0Þ.
The prestress losses caused by relaxation of prestressing strands
between time of transfer and deck placement Dfpr1and between time
of deck placement and final time Dfpr2are determined according to
AASHTO (2007)as
Dfpr1¼Dfpr2¼8:62 MPa ð1:25 ksiÞ(10)
The analytical procedure to derive the time-dependent strain and
stress was demonstrated in four analytical steps by Noppakunwijai
et al. (2002) and Ghali et al. (2012). In this study, the analytical
procedure is further elaborated in terms of PCSC girders. According
to AASHTO (2007) and Eq. (10), the prestress losses caused by
strand relaxation are not dependent on the concrete section and only
equal 1.2% of jacking stress [1,397 MPa (202.5 ksi)]. Therefore,
strand relaxation is considered separately, and the prestress losses
caused by strand relaxation are simply evaluated by Eq. (10).To
analyze the creep and shrinkage effects, the total time of loading is
divided into several intervals between different construction stages
or loading stages as described in Fig. 3: Stage 1 at prestress release,
girder sections only/self-weight of girder; Stage 2 during construc-
tion, girder sections only/superimposed dead loads of haunch and
deck; and Stage 3 in service, girder sections with deck/superimposed
dead loads of wearing surface and railing, and moving live loads
(truck 1impact and lane load).
In each interval, the stress and strains caused by different loads
and effects of creep and shrinkage should be derived in four ana-
lytical steps as follows.
Step 1
Calculate the stresses and instantaneous strains induced by sustained
loads at the start of concerned period (such as the initial prestressing
force, self-weight, and dead load) using the transformed section of
the composite section at different ages. Components of the trans-
formed section include the steel section, strands, and concrete sec-
tion. Live load is not a sustained load and induces no time-dependent
stresses/strain. Determine the stresses/strains in the top and bottom
fibers of each concrete component, the stresses/strains in the top and
bottom fibers of each steel component, and prestress losses in the
prestressing strands caused by the sustained loads applied in the start
of the concerned interval.
Detach all the components of the steel section, strands, and
concrete section and allow them to deform freely. Determine the
axial strain and the curvature of each concrete component induced
by the creep and shrinkage in the concerned interval based on
Eqs. (2)–(9),takingintoaccounttheinfluences of all the sustained
loads applied in and before the concerned interval. The time-
dependent stresses obtained in Step 4 should also be considered
as sustained loads and included in the calculations of the axial
strain and the curvature of each concrete component caused by
creep and shrinkage, and the start of the sustained loads is assumed
at the middle of the interval in which the sustained loads was
derived.
Fig. 2. Fabrication procedure of the PCSC girder system
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Step 2
Artificially restrain all the concrete components to counteract the
axial strain and the curvature caused by creep and shrinkage in
Step 1. Calculate the restraining axial force and the corresponding
stress/strain in each concrete component and the restraining moment
and the corresponding stresses/strains in the top and bottom fibers of
each concrete component. In this step, the age-adjusted effective
modulus for each concrete component should be used and can be
determined by Eq. (1). The creep coefficient can be derived from
Eq. (2), and the value of the aging coefficient can be obtained re-
ferring to Ghali et al. (2012).
Step 3
When the artificial restraint is removed, all the components are
reattached, and equilibrium is restored by applying the total re-
straining axial force and the total restraining moment of all the
components to the age-adjusted transformed section in reversed
directions, which are obtained in Step 2. The age-adjusted trans-
formed section properties are obtained by using age-adjusted ef-
fective modulus for each concrete component. Determine the
stresses/strains in the top and bottom fibers of each concrete com-
ponent, the stresses/strains in the top and bottom fibers of each steel
component, and prestress losses in the prestressing strands.
Step 4
The time-dependent stresses and strains caused by creep and
shrinkage in the concerned interval can be obtained by summing up
all the time-dependent values determined in Steps 1–3. The time-
dependent stresses should also be considered as sustained loads and
included into the calculations of the axial strain and the curvature of
each concrete component caused by creep and shrinkage in Step 1 for
the next intervals. The total increment/decrement of stresses and
strains generated in the concerned interval can be obtained by
summing up all the values calculated in Steps 1–3. The total stresses
and strains at the end of the concerned interval can be obtained by
summing up all the values calculated in and before the concerned
interval.
In each interval, increment/decrement of deflection/camber at
midspan of a simply supported girder can be estimated using the
values of curvature at three sections. The three sections consist of
two sections at one-fourth span and one section at midspan. Para-
bolic variation is assumed between these sections. The deflection/
camber at midspan, D, can be expressed as (Ghali et al. 2012)
D¼L2
24 ð2k1þk2Þ(11)
where L5span of the girder; k15curvature of the sections at one-
fourth span; and k25curvature of the section at midspan.
Design Examples of Prestressed Concrete-Steel
Composite Girders and Comparisons
A 24.4-m-long (80-ft-long) simple-span bridge was designed using
the PCSC girder. The bridge has a width of 17.8 m (38 ft and 8 in.)
and is composed of five girders with center-to-center spacing of
2.44 m (8 ft) and a 178-mm-thick (7-in.-thick) deck. For the purpose
of comparison, a prestressed concrete girder (NU900) and a steel
girder (W36 3232) were also alternatively designed for this bridge
while keeping the identical structural depth of the bridge, i.e.,
around 1,092 mm (43 in.).
The cross sections of the designed PCSC-36 girder, prestressed
concrete girder, and steel girder are shown in Figs. 4(a–c), re-
spectively. Design parameters, self-weight, and cost of the girders
are summarized in Table 1. The detailed design calculations for the
PCSC-36 girder can be found in Deng (2012). Table 1indicates that
the self-weight of the PCSC-36 girder is 375 kg=mð0:252 kip=ftÞ,
which is much less than that of the prestressed concrete girder,
i.e., 1,005 kg=mð0:675 kip=ftÞ, and is close to that of the steel
girder, i.e., 346 kg=mð0:232 kip=ftÞ. The unit cost of shear stud is
estimated at $4/one stud including labor cost (Bonenfant 2009).
According to the Florida DOT (FDOT 2012), the unit costs of
a prestressed concrete solid flat slab less than 1,219 3305 mm
ð48 312 in:Þand the straight steel beam with rolled wide flange
section are $492=m section ($150=ft) and $2:98=kg ð$1:35=lbÞ,
respectively. The unit cost of a NU girder is estimated at
$820=mð$250=ftÞbased on the estimation of the Precasters in
Omaha. The labor cost is included into all unit costs. Table 1
indicates that the fabrication cost of the PCSC girder is estimated at
$932=mð$284=ftÞ, which is a little more than that of a prestressed
concrete girder, i.e., $820=mð$250=ftÞand less expensive than that
of a steel girder, i.e., $1,053=mð$321=ftÞ.
Intervals 1–3 are defined between Stages 1 and 2, between Stages
2 and 3, and between Stage 3 and infinity, respectively. Stress
profiles in the midspan section of the PCSC girder induced during
intervals are described in detail in Fig. 5. As shown in Fig. 5, the
final stress in the bottom of the concrete bottom flange equals
23:24 MPa ð20:47 ksiÞ, which is less than the tensile stress limit
of 24:14 MPa ð20:60 ksiÞ. The stress profile in the midspan
section caused by the total effects of creep and shrinkage in all
intervals is described in Fig. 6. Fig. 6indicates that average stresses
of 29:7, 77.2, and 21:45 MPa ð21:4, 11:2, and 20:21 ksiÞ
(negative in tension) are induced by those effects in the concrete
bottom flange, steel beam, and top deck, respectively. Because of the
significant tensile stress generated in the concrete bottom flange,
Fig. 3. Concrete ages at different stages and intervals
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Service III design is always dominant over other design consid-
erations. Namely, the stresses in concrete bottom flange induced by
creep and shrinkage should be recognized very well during the
design of the PCSC girder.
To further prove the feasibility of PCSC girders, different PCSC
girder sections were designed for bridges with different spans. The
bridges have a width of 17.8 m (38 ft and 8 in.) and are composed of
five girders with the center-to-center spacing of 2.44 m (8 ft) and
a 178-mm-thick (7-in.-thick) deck. The concrete strength of the
concrete bottom flange is 55 and 69 MPa (8 and 10 ksi) at prestress
release and 28 days, respectively. The deck has a 28-day strength of
28 MPa (4 ksi). The PCSC girder sections, PCSC-38, PCSC-44, and
PCSC-53, for a 29-, 38-, and 47-m (95-, 125-, and 155-ft) span are
shown in Figs. 7(a–c), respectively. The maximum span-to-depth
ratio is equal to 29.6. It is found that if a longer span is designed, more
strands and higher depth of the steel beam are required for the PCSC
girder section.
To provide the designer with an excellent starting point for
preliminary design, a summary chart was developed to display the
maximum attainable span versus girder spacing [1.83, 2.44, 3.05,
and 3.66 m (6, 8, 10, and 12 ft, respectively)] for different girder
sections, PCSC-38, PCSC-44, and PCSC-53, as shown in Fig. 8.
The chart shows the largest possible span length allowed when girder
spacing, and PCSC girder sections are given.
Strength Design at Prestress Release
Current design specifications such as American Concrete Institute
(ACI) Committee 318 (2011), AASHTO LRFD (AASHTO 2007),
Precast/Prestressed Concrete Institute (PCI) Design Handbook (PCI
Industry Handbook Committee 2010), and PCI Bridge Design
Manual (PCI 2011) generally only adopt a working stress design
method for designing pretensioned flexural concrete members.
Table 2lists the compressive and tensile stress limits according to
those specifications at different sections immediately after prestress
release. Table 2indicates that current design specifications are not in
a full agreement with respect to compressive and tensile stress limits.
These allowable stress limits are used to satisfy the serviceability
criteria, such as deflection, camber, and cracking (Noppakunwijai
et al. 2001). However, it is a common perception among design
engineers that compressive stress limits are provided to prevent the
Fig. 4. Cross sections of PCSC-36, prestressed concrete and steel girders (1 in. 525.4 mm): (a) PCSC girder (PCSC-36); (b) prestressed concrete
girder (NU900); (c) steel girder
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crushing of concrete at release, which is in fact a strength requirement
and not a serviceability requirement. This is especially true for PCSC
girders, because no tensile stress is induced in the concrete bottom
flange at prestress release. Because of the preceding reasons, the
strength design method, taken as a rational approach replacing the
current working stress method, was developed for pretensioned
flexural concrete membersat prestress releaseby Noppakunwijai etal.
(2001,2003). To assist engineers to accomplish economic design and
production of PCSC girders, the strength design method is further
extended for the design of PCSC girders at prestress release.
The formulation of design equations for the strength design
method at release was conducted using the strain compatibility ap-
proach and was based on the following assumptions: (1) plane
sections remain plane; (2) a perfect bond exists between the concrete
and strands and between the concrete and steel; (3) elastic-perfectly
plastic behavior and linear elastic behavior are assumed for steel and
prestressing strands, respectively, whereas the stresses of the con-
crete are calculated based on its stress-strain curve; and (4) the
neutral axis of the girder section is located at the web of the steel
section and the bottom flange of the steel section yields, because of
the shallow section of the concrete bottom flange and the deep
W-shaped steel section. Actually, the bottom of the web and the
bottom flange of the steel section always yield when using the
strength design of PCSC girders at prestress release.
The concrete strength at release, fci
9, and distance from extreme
compression fiber to neutral axis, c, are the only two unknown
variables. The solutions for fci
9and ccan be derived based on the
formulation of design equations of axial force and bending moment
for both applied load and section resistance. Applied axial force and
bending moment as shown in Fig. 9can be formulated as follows:
Qsp ¼Aps fpj (12)
QsM ¼Aps fpj dp(13)
QswM ¼Msw (14)
where QsP 5axial force caused by prestressing strands; QsM
5bending moment caused by eccentricities of prestressing strands;
QswM 5bending moment caused by self-weight; Aps 5area of
prestressing strands; fpj 5jacking stress of strands; dp5centroidal
distance of strands from bottom fiber; and Msw 5moment caused by
self-weight.
Section resistance is defined as the total axial force and moment
that the section can resist. Fig. 9shows the components of the section
resistance for the section. Based on Fig. 9, the strain changes in
strands and the strains of fibers in steel beam can be derived as
Dɛps ¼c2dp
cɛcu (15)
ɛs1¼hsþhc2c
cɛcu (16)
ɛs2¼hsþhc2c2tf
cɛcu (17)
ɛs3¼c2hc2tf
cɛcu .ɛs(18)
ɛs4¼c2hc
cɛcu .ɛs(19)
where c5distance from extreme compression fiber to neutral axis;
hs5depth of steel section; hc5depth of concrete bottom flange;
tf5thickness of flanges of steel section; ɛcu 5ultimate concrete
compression strain 50.003; Dɛps 5strain change in strands; ɛs1
5strain in the top fiber of top flange of steel section; ɛs25strain in
the bottom fiber of top flange of steel section; ɛs35strain at the top
fiber of bottom flange of steel section; ɛs45strain in the bottom fiber
of bottom flange of steel section; and ɛs5yielding strain of steel
50.00172 for 345 MPa (50 ksi) steel. ɛs3and ɛs4should be verified
and should be larger than ɛs. Because yielding stress should be used
for the value of stresses in the bottom flange of the steel section, the
following equations are used for ɛs3and ɛs4:
ɛs3¼ɛs(20)
ɛs4¼ɛs(21)
Meanwhile, because of the small thickness of the steel web, the strain
in the steel web is assumed to be linear and the strain in the bottom
Table 1. Design Parameters, Self-Weight, and Cost of Different Girders
PCSC-36 girder
Prestressed concrete girder
NU900
Steel girder
Components
Concrete bottom flange,
610 3165 mm
(24 36:5in:) W30 390 Studs, 10/m (3=ft) W36 3232 Studs, 7/m (2=ft)
Self-weight, kg/m (klf)
Separate 241 (0.162) 134 (0.090) —1,005 (0.675) 345 (0.232) —
Total 375 (0.252) 1,005 (0.675) 345 (0.232)
Approximate cost, dollars/m
(dollars=ft)
Separate 492 (150) 400 (122) 39 (12) 820 (250) 1,026 (313) 26 (8)
Total 931 (284) 820 (250) 1,052 (321)
Strands
Number 18–18 mm (18–0.7 in.) 26–15 mm (26–0.6 in.) N/A
Area, mm (in:2) 3,414 (5.292) 3,649 (5.642)
Concrete strength, MPa (ksi)
Girder (7-day) 55 (8) 34 (5) N/A
Girder (28-day) 69 (10) 48 (7)
Deck (28-day) 28 (4)
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fiber of the steel web is equal to yielding strain of steel, ɛs. The stresses
in the top and bottom fibers of the steel web are calculated usingstrains
ɛs2and ɛs3from Eqs. (17) and (20), respectively.
Distances from the force components on the steel beam section to
the bottom fiber can be expressed as follows:
ds1¼hsþhc2tf
2(22)
ds2¼2hsþhc2tfþc
3(23)
ds3¼cþ2hcþtf
3(24)
ds4¼hcþtf
2(25)
where ds15distance from Ts1to bottom fiber of section; ds2
5distance from Ts2to bottom fiber of section; ds35distance from
Cs3to bottom fiber of section; and ds45distance from Cs4to bottom
fiber of section.
Force components of the resistance can be derived as follows:
Ts1¼bftfEs
ðɛs1þɛs2Þ
2(26)
Ts2¼twhsþhc2c2tfEs
ɛs2
2(27)
Cs3¼twc2hc2tfEs
ɛs3
2(28)
Cs4¼bftfEs
ðɛs3þɛs4Þ
2(29)
Cc¼afci
9hcbc(30)
Fig. 5. Stress profiles in the midspan section of PCSC-36 girder during different intervals (stress in kilopounds per square inch, negative in tension,
1 ksi 56.895 MPa)
Fig. 6. Stress profile in the midspan section of PCSC-36 girder caused
by total creep and shrinkage effects (stress in kilopounds per square inch,
negative in tension, 1 ksi 56.895 MPa)
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Cps ¼ApsDɛps Eps 2afci
9(31)
where Ts15tensile force on the top flange of steel section; Ts2
5tensile force on the web of steel section; Cs35compressive force
on the web of steel section; Cs45compressive force on the bottom
flange of steel section; Ccf 5compressive force on concrete flange;
Cps 5compressive force on strands; bf5width of flange; Es
5elastic modulus of steel; Eps 5elastic modulus of strands; tw
5thickness of web; Aps 5area of strands; and a5factor relating to
compressive stress, fci
9. For fci
9521e35 MPa ð3e5 ksiÞ,a50:90;
for fci
9535e69 MPa ð5e10 ksiÞ,a50:85. The values of aare
developed based on the expression for the stress-strain curve of
concrete proposed by Wee et al. (1996)as
fc¼fci
9
2
4
k1bɛ
ɛo
k1b21þɛ
ɛok2b
3
5
(32)
where fcand ɛ5stress and strain on concrete, respectively; strain at
peak stress is expressed as
ɛo¼0:00078fci
91=4ðin MPaÞ(33)
b¼1
12fci
9=ðɛoEitÞ(34)
where initial tangent modulus is expressed as
Eit ¼10,200fci
91=3ðin MPaÞ(35)
and when fci
9#50 MPa ð7:25 ksiÞ,k151andk251; when
fci
9.50 MPa ð7:25 ksiÞ, for ascending branch of the curve, k151
and k251, and for descending branch of the curve, the following
equations should be used as
k1¼50
fci
93:0
(36)
k2¼50
fci
91:3
(37)
As previously assumed, the strain of the top fiber of concrete
bottom flange is larger than the yielding strain of steel, ɛs. For
conservative consideration, the yielding strain is used at the top fiber.
The strain of the bottom fiber of concrete bottom flange is equal to
ultimate concrete compression strain, 0.003. Substitution of strains
on the top and bottom fibers of concrete bottom flange into Eq. (30)
gives stresses. Factor, a, is used to simplify the stresses on concrete
bottom flange as a rectangular stress block. The average stress of the
top and bottom fibers of the concrete bottom flange divided by fci
9
yields the value of a.
Axial force resistance and moment resistance are found as
follows:
RP¼CcþCps þCs3þCs42Ts12Ts2(38)
RM¼Cchc
2þCps dpþCs3ds3þCs4ds42Ts1ds12Ts2ds2
(39)
Fig. 7. Application of PCSC girder sections for bridges with different
spans (1 in. 525.4 mm; 1 ft 50.305 m; 1 ksi 56.895 MPa): (a) PCSC-
38: 95-ft span (span-to-depth ratio: 25.6); (b) PCSC-44: 125-ft span
(span-to-depth ratio: 29.6); (c) PCSC-53: 155-ft span (span-to-depth
ratio: 29.1)
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According to ACI Committee 318 (2011), the design strength at
the sections shall not be less than the required strength with com-
binations of factored loads. The strength design requirement can be
expressed as follows:
fRPn$QPu(40)
fRMn$QMu(41)
where fRPnand fRMn5design strengths; RPn5nominal values for
axial force strength; RMn5nominal bending moment strength; f
5resistance factor (or strength reduction factor), as suggested by
Deng and Morcous (2013b), equals 0.75 for fci
9521 MPa ð3 ksiÞand
0.70 for fci
9535 MPa ð5 ksiÞ; and QPuand QMu5required
strengths calculated from the factored load effect. The required axial
force strength and bending moment strength, i.e., QPuand QMu, can
be expressed with load factors as follows:
QPu¼gpQsPn(42)
QMu¼gpQsMnþgmQswMn(43)
where QsPn5nominal axial force caused by prestressing strands;
QsMn5nominal bending moment caused by prestressing strands;
QswMn5nominal bending moment caused by self-weight; gp
5initial prestress load factor 51.2 (Deng and Morcous 2013b);
and gm5self-weight moment load factor 50.9 when self-weight
moment counteracts the moment because of prestress relative to
neutral axis of the section or 1.2 when the self-weight moment is in
the same direction as the moment because of prestress relative to
neutral axis of the section (Deng and Morcous 2013b). However, the
moments in the formulation of design equations are calculated
relative to the bottom fiber of the section. For calculation purpose,
self-weight moment is positive when it induces compressive stress
on the top fibers and negative when it induces compressive stress on
the bottom fibers.
Simplified Solutions
The unknown variables, fci
9and c, can thus be determined by sub-
stitutions of Eqs. (15)–(17) and (20)–(25) into Eqs. (26)–(31);
Eqs. (26)–(31) into Eqs. (38) and (39); Eqs. (12)–(14) into Eqs. (42)
and (43); and substitution of Eqs. (38),(39),(42), and (43) into
Eqs. (40) and (41). To derive the solutions to fci
9and c, the following
two equations need to be solved:
Fig. 8. Summary chart for PCSC girder sections with the maximum attainable span versus girder spacing
Table 2. Stress Limits at Prestress Release for Different Specifications
Compressive stress
limits
Tensile stress
limits, MPa (psi)
Specifications Midsections
End
sections
Other
sections
End
sections
ACI 318 (ACI Committee 318 2011)0:6fci
90:7fci
90:25 ffiffiffiffiffi
fci
9
p3ffiffiffiffiffi
fci
9
p0:50 ffiffiffiffiffi
fci
9
p6ffiffiffiffiffi
fci
9
p
AASHTO LRFD (AASHTO 2007)0:6fci
90:6fci
90:25 ffiffiffiffiffi
fci
9
p3ffiffiffiffiffi
fci
9
p0:25 ffiffiffiffiffi
fci
9
p3ffiffiffiffiffi
fci
9
p
PCI Design Handbook (PCI Industry Handbook Committee 2010)0:7fci
90:7fci
90:58 ffiffiffiffiffi
fci
9
p7:5ffiffiffiffiffi
fci
9
p0:58 ffiffiffiffiffi
fci
9
p7:5ffiffiffiffiffi
fci
9
p
PCI Bridge Design Manual (PCI 2011)0:6fci
90:6fci
90:25 ffiffiffiffiffi
fci
9
p3ffiffiffiffiffi
fci
9
p0:25 ffiffiffiffiffi
fci
9
p3ffiffiffiffiffi
fci
9
p
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fci
9¼
Apsgp
ffpj 2Dɛps EpsþEstw
2c2hc2tfɛs2hsþhc2c2tfɛs2þbftf
tw
ð2ɛs2ɛs12ɛs2Þ
ahcbc2Aps(44)
fci
9¼
Aps dpgp
ffpj 2Dɛps Epsþgm
fMsw þEstw
2c2hc2tfɛsds32hsþhc2c2tfɛs2ds2þbftf
tw
½2ɛsds42ðɛs1þɛs2Þds1
ahcbchc
22Aps dp(45)
The distances of the bottom fiber and top fiber of steel web to the
bottom fiber of the section are taken as the lower bound and upper
bound for c, respectively. Trials of different values of cinto Eqs. (44)
and (45) give the two values of fci
9. The correct value of cis the one
that results in the same value of fci
9.
Closed Form Solutions
The closed form solutions to the unknown variables, fci
9and c, were
also derived by Deng (2012). Because of the complicated formulas,
these solutions are not presented herein.
Proposed Design Procedure
To assist designers in using the developed formulas for strength
design of PCSC girders at release, the following procedure is
proposed:
1. Determine the following parameters: bf,hs,tf,tw,bc,hc,dp,
Aps,fpj ,fy,L, and wsw (self-weight of the girder).
2. Calculate the self-weight moment, Msw , and determine the
value of load factor gmfor Msw.gmequals 0.9 when Msw
counteracts the moment because of prestress or 1.2 when Msw
is in the same direction as the moment because of prestress
both relative to neutral axis of the section. Select the value for
resistance factor, f, which equals 0.75 and 0.70 for the
concrete strength at release of 20.7 and 34.5 MPa (3 and
5 ksi), respectively.
3. Two methods can be adopted as described in the following
sections.
Simplified Solutions
Trials of different values of cmay be required to obtain the solution
to fci
9. Choose a value of c, which is larger than the distance from the
bottom fiber of the steel web to the bottom fiber of the section
(i.e., hc1tf) and less than the distance from the top fiber of the steel
web to the bottom fiber of the section (i.e., hc1hs2tf). Substitute
the value of cinto Eqs. (44) and (45) to find two solutions for fci
9.If
Fig. 9. Applied load, strains, and section resistance of the section
Table 3. Comparisons of Strength Design and Working Stress Design for the End Sections of the PCSC Girders at Release
fci
9, MPa (ksi)
Working stress design using different compressive stress limits
Girder sections Span, m (ft) Strength design
ACI (ACI Committee 318
2011)(0:7fci
9)
AASHTO (2007) or PCI
(2011)(0:6fci
9)
PCI (PCI Industry
Handbook Committee 2010)
(0:7fci
9)
PCSC-36 24.4 (80) 52 (7.6) 54 (7.8) 63 (9.1) 54 (7.8)
PCSC-38 29.0 (95) 53 (7.7) 55 (8.0) 64 (9.1) 55 (8.0)
PCSC-44 38.1 (125) 55 (8.0) 55 (8.0) 64 (9.1) 55 (8.0)
PCSC-53 38.1 (125) 55 (8.0) 57 (8.2) 66 (9.1) 57 (8.2)
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the solutions of fci
9obtained from Eqs. (44) and (45) are almost
identical, the correct solution of fci
9is obtained. If the solutions of fci
9
obtained from Eqs. (44) and (45) are significantly different, another
trial is made using a different value of c.
Closed Form Solutions
The design solutions to fci
9and ccan also be obtained using the
formulas of closed form solutions by Deng (2012).
1. Design the required amount of shear studs between steel beam
and concrete bottom flange from end to transfer length, which
is determined based on the horizontal shear force; and
2. Check the design results.
Design Examples and Comparison with Working Stress
Design Method
To help designers to understand the proposed design procedure,
design examples were developed using the PCSC girder sections.
Girder sections PCSC-36, PCSC-38, PCSC-44, and PCSC-53,
shown in Figs. 4and 7(a–c), respectively, were designed for
bridges with spans of 24, 29, 38, and 47 m (80, 95, 125, and 155 ft),
respectively. For the purpose of comparisons, those girders were
designed using the strength design method and the working stress
design method. An example with detailed design calculations for
girder section PCSC-36 can be found in Appendix B in Deng (2012),
including the strength design method with simplified solutions and
closed form solutions and the working stress design method.
The required concrete strengths at release, fci
9, at the end sections
of those girders (at transfer length) aresummarized in Table3. The end
section is the critical section because of the self-weight of the girders
using the strength design at release. Table 3indicates that the required
concrete strengths at release, fci
9, at the end sections using the strength
design method are no more than those using the working stress design
method with different design specifications. Because the production
cycle is highly dependent on achieving the minimum required con-
crete strength at prestress release, failure to achieve the strength might
cause significant delays in production and increase the product cost.
Thus, the lower required concrete strength at release benefits the
production of the PCSC girder. Based on the required concrete
strength at release using the strength design method shown in Table 3,
it can be concluded that a concrete strength of 55 MPa (8 ksi)at release
was safely designed for concrete bottom flanges of girder sections
PCSC-36, PCSC-38, PCSC-44, and PCSC-53.
Summary and Conclusions
A new PCSC girder system is developed. A procedure of five steps is
introduced to fabricate PCSC girders. A service design procedure is
proposed using the AEMM to evaluate the time-dependent stresses
and strains in the PCSC girder caused by the creep and shrinkage
effects of concrete and relaxation of strands. The strength design
method is proposed for the design of PCSC girders at prestress re-
lease, and a design procedure is also proposed to assist engineers to
accomplish economic design and production of PCSC girders. The
following conclusions can be drawn:
•The PCSC girder is a viable alternative for steel and prestressed
concrete I-girders in bridges; it is lightweight, economical, du-
rable, and easy to produce.
•The proposed PCSC girder fabrication procedure is simple and
follows the standard procedure of fabricating prestressed con-
crete girders without the need for specialized equipment, materi-
als, or forms.
•The PCSC girder can be designed using AASHTO LRFD bridge
specifications, the AEMM for Service III, and the strength design
method at release. Service III design is always dominant over
other design considerations because of the significant tensile
stress generated in the concrete bottom flange caused by the
effects of creep and shrinkage.
•The required concrete strengths at release at end sections using
the strength design method are no more than those using working
stress design method, and thus, their lower values benefit the
production of PCSC girders.
References
AASHTO. (2007). AASHTO LRFD bridge design specifications, 4th Ed.
with 2008 interim revisions, Washington, DC.
American Concrete Institute (ACI) Committee 318. (2011). “Building code
requirements for structural concrete”and “Commentary,”ACI 318-11
and ACI 318R-11, Farmington Hills, MI.
Basu, P. K., Sharif, A. M., and Ahmed, N. U. (1987). “Partially prestressed
composite beams. I.”J. Struct. Eng., 113(9), 1909–1925.
Bonenfant, R. R., Jr. (2009). “How to estimate the cost of structural steel.”
Estimating Today,15–23, Æhttp://www.aspenational.org/userfiles/file/
Technical%20Papers/2009/TechPaper_January2009.pdfæ.
Bozzo, L. M., and Torres, L. (2004). “A proposed semi-prefabricated pre-
stressed composite steel–concrete slab.”Struct. Build., 157(5), 309–
318.
Deng, Y. (2012). “Efficient prestressed concrete-steel composite girder for
medium-span bridges.”Ph.D. dissertation, Univ. of Nebraska–Lincoln,
Lincoln, NE.
Deng, Y., and Morcous, G. (2013a). “Efficient prestressed concrete-steel
composite girder for medium-span bridges. II: Finite-element analysis
and experimental investigation.”J. Bridge Eng., 18(12), 1358–1372.
Deng, Y., and Morcous, G. (2013b). “Reliability calibration of strength
design for prestressed concrete members at transfer.”Reliability Eng.
Syst. Safety, in press.
DOT-Federal Highway Administration (DOT-FHWA). (2011). “National
bridge inventory (NBI)—Count of bridges by structure type.”Æhttp://
www.fhwa.dot.gov/bridge/struct.cfmæ(Jan. 22, 2012).
Florida DOT (FDOT). (2012). “FDOT structures manual, Vol. 2, structures
design guidelines.”Topic No. 625-020-018, Tallahassee, FL.
Ghali, A., Favre, R., and Elbadry, M. (2012). Concrete structures: Stresses
and deformations, 4th Ed., Spon Press, London.
Hanswille, I. G. (2011). “Composite bridges in Germany—State of the art.”
Proc., Workshop on Eurocode 4-2, composite bridges.
Lorenc, W., and Kubica, E. (2006). “Behavior of composite beams pre-
stressed with external tendons: Experimental study.”J. Constr. Steel
Res., 62(12), 1353–1366.
Morcous, G., Hanna, K., and Tadros, M. K. (2011). “Impact of 0.7 inch
diameter strands on NU I-girders.”Final Rep. to Nebraska Dept. of
Roads (NDOR), No. SPR-1(08) P311, Univ. of Nebraska–Lincoln,
Omaha, NE.
Noppakunwijai, P., Al-Omaishi, N., Tadros, M. K., and Krause, G. L.
(2002). “Elimination of prestressed concrete compression limits at
service load.”PCI J., 47(6), 2–19.
Noppakunwijai, P., Tadros, M. K., Ma, Z., and Mast, R. F. (2001). “Strength
design of pretensioned flexural concrete members at prestress transfer.”
PCI J.,46(1),34–52.
Noppakunwijai, P., Tadros, M. K., and Sun, C. (2003). “Application of the
strength design method for flexural members at prestress transfer.”PCI
J., 48(5), 62–75.
Precast/Prestressed Concrete Institute (PCI). (2011). Precast prestressed
concrete bridge design manual, 3rd Ed., Chicago.
Precast/Prestressed Concrete Institute (PCI) Industry Handbook Committee.
(2010). PCI design handbook2Precast/prestressed concrete, 7th Ed.,
Chicago.
Sayed-Ahmed, E. Y. (2001). “Behaviour of steel and (or) composite girders
with corrugated steel webs.”Can. J. Civ. Eng., 28(4), 656–672.
Wee, T. H., Chin, M. S., and Mansur, M. A. (1996). “Stress-strain re-
lationship of high-strength concrete in compression.”J. Mater. Civ.
Eng., 8(2), 70–76.
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