Behavior of Precast Prestressed Concrete Bridge Girders ...

Behavior of precast prestressed concrete bridge girders involving thermal effects

and initial imperfections during construction

Jong-Han Lee ⇑

School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA

a r t i c l e i n f o

Article history:

Received 10 December 2010

Revised 20 January 2012

Accepted 8 April 2012

Keywords:

Precast prestressed concrete

AASHTO-PCI standard girder

Thermal effects

Elastomeric bearing

Nonlinear finite element

a b s t r a c t

The instability of precast prestressed concrete bridge girders during construction have been of particular

concern to bridge engineers. After they are installed on bearing supports, prestressed concrete girders are

immediately subjected to environmental thermal loads that may be exacerbated by fabrication and con-

struction errors. Thus, in this research, the environmental thermal loads, which cause extremes in ther-

mal deformations in precast prestressed concrete girders, were determined. Then a three-dimensional

nonlinear finite element sequential analysis procedure was developed to evaluate the behavior of a pre-

cast prestressed concrete girder subjected to both thermal loads and geometry and support imperfections

during each construction stage. This analysis indicated instability in a 30-m long prestressed concrete BT-

1600 girder when total lateral deformation in the middle height of the girder at mid-span exceeded about

25 cm.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Since the advent of precast prestressed concrete girders in

bridge design and construction, the demand for a more expansive

girder span, which would reduce construction costs and improve

bridge esthetics, has been increasing. However, the lengthening

of girders with deeper precast sections and high-strength concrete

increases the likelihood that the girders will destabilize. Such fail-

ure, one of which is illustrated in Fig. 1, have led to considerable

apprehension about the behavior of precast prestressed concrete

girders during construction, specifically before the addition of the

slab and bracing. One investigation into the collapse of the girders,

Oesterle et al. [1] indicated that a combination of several factors,

including the initial sweep (or lateral deformation), the thermal

sweep, and the support slope, could cause lateral instability of

the girders during construction.

The initial sweep of the girder occurs during fabrication, ship-

ping, and handling. During fabrication, the eccentricity of pre-

stressing strands can create an error that leads to unexpected

initial sweep in the girder. Then shipping and handling can subject

the girder to unaccounted loads or boundary conditions that also

affect the initial sweep. When placed on supports that are not level,

the girder can also experience sweep. In addition, while pre-

stressed concrete girders are resting on a bearing support, thermal

environmental effects can produce additional sweep that may con-

tribute to the instability of the girders prior to the placement of a

bridge deck and diaphragms. For the initial sweep in the girder, the

PCI Bridge Design Manual [2] provides a tolerance of 3 mm per 3 m

(1/8 in per 10 ft) of member length. Nevertheless, in practice, this

small tolerance value has not been adhered to because of the many

unexpected conditions that occur during fabrication and handling,

as mentioned previously. However, no study that evaluates the lat-

eral deformation of the girders has been carried out, especially dur-

ing construction when the girders are subjected to the combined

effects of thermal response, initial sweep, and support slope.

Some relevant initial research was conducted by Mast [3,4],

who calculated the stability of a girder suspended from lifting de-

vices and transported on elastic supports. Mast proposed a method

based on the ratio of a resisting moment at the support to an over-

turning moment induced by the girder sweep and support slope.

The method was adopted in the PCI Bridge Design Manual [2] for

the evaluation of how safe a girder is from rollover (or overturning)

during shipping and lifting. However, the manual provided no spe-

cific method or guideline that analyzes the lateral stability of the

girders placed on elastic bearing supports during construction.

The AASHTO LRFD Bridge Design Specifications [5] and the AASHTO

LRFD Bridge Construction Specifications [6] simply addressed the

importance of considering the safety of precast members during

all construction stages, but they did not provide any specific guide-

lines related to the stability of precast prestressed concrete girders

during construction.

Thus, as an initial study, this research evaluated the behavior of

a precast prestressed concrete girder subjected to the combined ef-

fects of the initial sweep, the thermal response, and the support

slope during construction. For the largest vertical and lateral

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http://dx.doi.org/10.1016/j.engstruct.2012.04.003

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Engineering Structures 42 (2012) 1–8

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thermal response, the thermal effects of seasonal variations and

bridge orientations on vertical and lateral thermal gradients were

evaluated for four AASHTO-PCI standard girder sections in Atlanta,

Georgia. For a 30-m long prestressed BT-1600 girder, which

showed the largest vertical and lateral thermal gradients in the

summer and the winter, respectively, the behavior of the girder

subjected to the thermal response, the initial sweep, and the sup-

port slope was evaluated using three-dimensional (3D) nonlinear

finite element sequential analysis.

2. Determination of thermal loads

The primary environmental parameters causing temperature

variations in bridges are solar radiation, air temperature, and wind

speed. These environmental values were determined from 30-year

(from 1961 to 1990) monthly averaged daily solar radiation and

climatic data provided by the National Renewable Energy Labora-

tory [7] for Atlanta. To account for seasonal variations in environ-

mental conditions, this study chose the daily solar radiation values

of 21.9, 29.4, 22.4, and 11.9 MJ/m2 for March, June, September, and

December, respectively. The months of March, June, September,

and December were defined as representative months of the

spring, summer, fall, and winter. The daily maximum and mini-

mum air temperatures for each season were determined from

the record maximum temperature and the average daily minimum

temperature of the 30-year climatic values, respectively, for the

representative months. The average daily minimum temperature

was used rather than the record daily minimum temperature since

it is highly unlikely that the record maximum and minimum tem-

peratures occurred on the same day. However, since wind speed

was minimal on the days when the largest vertical and lateral ther-

mal gradients occurred, this study neglected the effect of wind

speed on girder temperatures.

The temporal variation in the daily solar radiation was calcu-

lated using the Liu and Jordan equation [8]:

IðtÞ ¼ Hp24

ðaþ b � coswÞ �cosw� cosws

sinws �ws cosws

� �

ð1Þ

in which I(t) is the solar radiation at time t on a horizontal surface, H

the total daily solar radiation, w the solar hour angle, and ws the

sunrise hour angle; a = 0.409 + 0.5016 � sin(ws � 1.047), and

b = 0.6609–0.4767 � sin(ws � 1.047). For other inclined surfaces of

the girder, irradiation was estimated according to the location and

orientation of the girder, the geometry and shadow of the girder,

and the position of the sun. The specific calculation procedures

are outlined in Duffie and Beckman [9].

Variations in the air temperature were calculated using the

sinusoidal Kreith and Kreider equation [10]:

TairðtÞ ¼1

2Tmax þ Tminð Þ �

1

2Tmax � Tminð Þ � sin ðt � 9Þ

p12

h i

ð2Þ

in which Tair(t) is the air temperature as a function of time t, and

Tmax and Tmin are the daily maximum and minimum air tempera-

tures, respectively. In the calculations, the lengths of the 21st of

March, June, September, and December represented the length of

the days in each season.

With the defined seasonal environmental conditions, a two-

dimensional heat transfer analysis was conducted on four AASH-

TO-PCI standard girder sections: Type-I, Type-IV, Type-V, and

BT-1600 [2]. The heat transfer mechanisms involved in this study

are heat irradiation from the sun, heat radiation to the surround-

ings, heat convection between the surroundings and the concrete

surface, and heat conduction in the concrete. In the calculation of

heat gain from the sun and heat loss to the surroundings, the value

of solar absorptivity and surface emissivity of concrete was se-

lected to be 0.50 and 0.85, respectively [11]. The thermal conduc-

tivity and specific heat of concrete, which defines the heat flow

within the body of the concrete girder, were taken as 1.50 W/m K

and 1000 J/kg K, respectively, based on a previous study on the

temperature prediction of concrete pavement [12].

The influence of changes in the girder orientations on tempera-

ture distributions was also evaluated for east–west (E–W), south–

north (S–N), southwest–northeast (SW–NE), and southeast–

northwest (SE–NW) orientations. The largest vertical thermal

gradients, calculated from the largest temperature difference

between the highest and lowest temperatures along the depth of

the sections, were found in the summer and in the E–W orienta-

tion. The largest lateral thermal gradients across the middle of

the top flange, the web, and the bottom flange were found in the

E–W orientation in the winter because of the greater exposure of

the vertical surfaces of the girder to the sun in the E–W orientation.

Among the four sections, the deeper and wider Type-V and BT-

1600 sections exhibited larger vertical and lateral thermal gradi-

ents. The largest vertical thermal gradients in the summer were

26 �C in the Type-V section and 25 �C in the BT-1600 section. The

largest lateral thermal gradients of the Type-V and BT-1600

sections in the winter were about 20 �C in the top flange, 15 �C

in the web, and 25 �C in the bottom flange. Thus, for the BT-1600

girder in an E–W orientation, the thermal loads in this study were

determined from the summer and winter environmental condi-

tions in Atlanta.

Fig. 1. Stability failure of precast prestressed AASHTO Type-V girders during the

construction of the Red Mountain Freeway in Arizona [1].

Fig. 2. Arrangement of the prestressing strands in the BT-1600.

2 J.-H. Lee / Engineering Structures 42 (2012) 1–8

3. 3D nonlinear finite element thermal response analysis

3.1. 3D finite element model

Based on the preliminary design reference given in the PCI

Bridge Design Manual [2], the BT-1600 girder was designed to be

30 m long with a concrete compressive strength of 48 MPa, girder

spacing of 1.8 m, and 24 low relaxation strands of 12.7 mm in

diameter. As shown in Fig. 2, four strands were placed in the top

flange and twenty strands in the bottom flange. The strands placed

in the top and bottom flanges were each prestressed to 44.5 kN and

150.4 kN, respectively.

The 30-m long BT-1600 girder was modeled with a total of

350,400 linear solid elements of approximately 2.5 cm by 2.5 cm

with 5 cm in the longitudinal direction of the girder per element

in the finite element program Abaqus [13]. The prestressing

strands were modeled using 3D two-node truss elements and de-

fined as embedded elements in the solid concrete elements. The

embedded element technique used in this study constrains the

translational degrees of freedom of the embedded elements to

the interpolated values of the corresponding degrees of freedom

of the host solid elements.

The modulus of elasticity of the concrete used in this study was

calculated to be 28,500 MPa using the ACI Committee 435 [14] for

high-strength concrete. Since the maximum tensile stress of con-

crete due to thermal effects did not exceed the allowable tensile

stress of concrete, 0:63ffiffiffiffi

f icp

, in which f ic represents the compressive

strength of concrete, the concrete materials used in this thermal

response analysis were modeled to be linear elastic. The coefficient

of thermal expansion pertaining to the thermal movement of the

girder was taken as 10.8 � 10�6/�C [5].

The material properties of the 12.7 mm diameter strands were

those listed in the PCI Bridge Design Manual. The design yield

strength of the strands was 1689 MPa. After the yielding of the

strands, or 0.0086 yield strain, the stress and strain relationship

was defined to be perfectly plastic. The coefficient of the thermal

expansion of the strands was defined to be the same as that of

the concrete.

3.2. Support conditions

Precast prestressed concrete bridge girders are generally sup-

ported by steel-reinforced elastomeric bearing pads that provide

vertical support in compression and minimum horizontal resis-

tance to the girder due to friction. According to a recent study on

the elastomeric bearing stiffness of standard precast prestressed

concrete girders [15], the vertical stiffness calculated from the

AASHTO LRFD Bridge Design Specifications [5] provided good agree-

ment with that obtained from the finite element analysis. This

study also recommended that the effects of the horizontal bearing

restraint be ignored in the design of AASHTO precast concrete

bridge girders. Thus, the vertical stiffness of the bearing pad was

evaluated using the AASHTO specifications. This analysis assumed

that the horizontal stiffness of the bearing pad was zero, but in-

cluded the lateral resistance to the girder, provided by the dowel

bar in the middle of the pad.

The size of the bearing pad for the BT-1600 girder, based on the

Georgia Department of Transportation manual [16], was deter-

mined to be 25 cm long and 50 cm wide. A 7.5 cm diameter hole

in the middle of the pad was also designed for the dowel bar.

The hole of the bearing pad at the other end of the girder was slot-

ted so that the girder could expand longitudinally. Thus, the dowel

bar, located in the middle of the bearing pad, was modeled with

both lateral and longitudinal restraints at the one end and only a

lateral restraint at the other end.

With the defined geometry of the bearing pad, the compressive

modulus of bearing pad was calculated using the stress and strain

curve given in the AASHTO LRFD Bridge Design Specifications [5].

Since elastomeric bearings become stiffer as strain increases, the

stiffness of the vertical bearings was defined as a bi-linear relation-

ship with one inflection point at 0.028 compressive strain. That is,

the compressive modulus of the elastomeric bearing pad, Es, is ini-

tially 148 MPa up to 0.028 compressive strain, and thereafter in-

creases to 230 MPa. The vertical stiffness of bearing pad, k, was

then derived as follows:

k ¼Es � A

Hð3Þ

in which A is the area of the bearing pad and H the thickness of the

bearing.

The vertical bearing stiffness was modeled using a series of non-

linear spring elements, which provide restraint only when com-

pressed. The compressive stiffness of individual springs was

calculated using the tributary area of the springs categorized as

corner, edge, and center spring elements according to the location

of the springs within the bearing surface. Fig. 3 shows the force and

displacement relationship defined from the calculated compressive

stiffness, in which k1 represents compressive strain up to 0.028 and

k2 represents that greater than 0.028. The vertical spring elements

used to model the bearing pads are illustrated in Fig. 4. The arrows

shown in this figure represent the restrained directions at the both

ends due to the dowel bars located in the middle of the pad.

3.3. Thermal responses

The 3D nonlinear finite element thermal response analysis is

composed of a static analysis and its subsequent nonlinear thermal

stress analysis. First, the 3D static analysis is performed to intro-

duce camber and stresses induced by prestressing forces to the gir-

der. The prestressing forces were defined as the initial stress

conditions and applied uniformly along the strand. The values of

the initial stresses, assigned to the top and bottom strands, were

482 MPa and 1578 MPa, respectively, calculated by dividing the

prestressing forces by a nominal area of the strand. The support

boundary condition in this analysis was defined as a simply sup-

ported condition at the location of the dowel bars. The camber

and stresses obtained from the first static analysis provide the ini-

tial conditions for the start of the subsequent thermal stress anal-

ysis. Then the 3D thermal stress analysis employed the girder

temperatures obtained from heat transfer analysis as sequential

thermal loads to determine the thermal response of the girder.

Since the heat transfer analysis is carried out on a 2D cross-section

of the girder, the temperature distributions are transferred to the

Fig. 3. Relationship between the force and displacement of the spring element.

J.-H. Lee / Engineering Structures 42 (2012) 1–8 3

3D finite element model with a constant temperature variation

along the length of the girder. The support conditions involved in

this analysis were defined to be elastomeric bearing pad conditions

shown in Fig. 4. For the purpose of comparison, the analysis in-

cluded boundary conditions that defined the bearing pads as rigid

vertical restraints. The detailed process of the 3D finite element

thermal response analysis is given in the flowchart shown in Fig. 5.

Fig. 6 shows variations in the vertical and lateral thermal move-

ments at the mid-span of the 30-m long prestressed BT-1600 gir-

der obtained from the 3D thermal response analysis of the

summer and winter environmental conditions in Atlanta. The ini-

tial vertical camber induced by the prestressing strands was

3.28 cm, and it decreased to 0.81 cm due to the self-weight of

the girder. The environmental thermal loads increased the vertical

displacement to 2.67 cm at 3 p.m. in the summer and 1.91 cm at

2 p.m. in the winter under elastomeric bearing pad conditions.

Thus, the total vertical thermal movement was 1.86 cm in the sum-

mer and 1.10 cm in the winter. In the rigid support conditions, the

total vertical thermal movement was 1.07 cm in the summer and

0.46 cm in the winter. In contrast to the vertical thermal move-

ment, lateral thermal movement at mid-span was greater in the

winter due to larger lateral thermal gradients. The lateral thermal

movement was 1.02 cm in the summer and 1.96 cm in the winter.

The support conditions of the elastomeric bearing pads did not af-

fect the lateral thermal movements, and the differences in the lat-

eral movements along the depth of the girder were minimal.

Nonlinear thermal strains induced by environmental thermal

loads cause self-equilibrium stresses in the girder due to the strain

difference between the nonlinear thermal strains and the final

(a) One end of the girder (b) Other end of the girder

Fig. 4. Finite element model with spring elements for elastomeric bearing pads and restrained conditions for dowel bars.

Fig. 5. Flowchart of the 3D finite element thermal response analysis.

Fig. 6. Variations in the vertical and lateral thermal movements at the mid-span of the 30-m long prestressed BT-1600 girder under elastomeric bearing pad conditions in the

summer and the winter in Atlanta.


linear strains. The BT-1600 girder initially exhibited longitudinal

compressive stresses of 5723 kPa on the top surface and

7584 kPa on the bottom surface at mid-span due to prestressing

forces and self-weight. In the summer, when the largest vertical

thermal gradients occurred, the concrete longitudinal compressive

stresses increased to 7791 kPa (by 36%) on the top surface and

9170 kPa (by 21%) on the bottom surface. In the winter, the com-

pressive stresses on the top and bottom surfaces only slightly

changed due to the smallest vertical thermal gradients. However,

the middle of the web showed higher longitudinal compressive

stresses due to larger thermal gradients in the web in the winter.

The tensile stresses of the top and bottom strands only slightly

changed (increased by less than 41 MPa) due to environmental

thermal effects.

4. Beam model for the calculation of thermal deformations

4.1. Development of the beam model

Thermal strain distributions induced by environmental thermal

effects are nonlinear. Because of the nonlinear thermal gradients in

the girders, their thermal movements are basically calculated using

3D numerical analysis. Thus, based on beam theory, this study de-

rived an analytical method that could calculate the vertical and

thermal deformations from the nonlinear thermal gradients.

Fig. 7 illustrates vertical strain distributions along the depth of a

prestressed concrete girder section caused by a nonlinear vertical

thermal gradient. The unrestrained plane section tends to expand

in accordance with the vertical thermal gradient shown in

Fig. 7b. However, according to the Navier–Bernoulli hypothesis,

the final strain profile is linear, illustrated in Fig. 7c. Thus, the ver-

tical thermal deformation can be obtained by integrating the cur-

vature, uy, over the length of the girder. For a simple span, the

vertical deformation at mid-span, dy, is

dy ¼uy � L

2

8ð4Þ

in which L is the length of the girder. The curvature of the girder can

be calculated using the following equation:

u ¼

R

½E � a � DTðyÞ �wðyÞ � y�dy

E � Ixð5Þ

in which DT(y) is the vertical thermal gradient at depth y, w(y) the

width of the section, E the concrete modulus of elasticity, a the coef-

ficient of thermal expansion of concrete, and Ix the moment of iner-

tia of the cross-section with respect to the strong x-axis.

Similarly, lateral thermal movement was calculated using the

lateral thermal gradients over the cross-section. However, the lat-

eral thermal gradients vary from the top to the bottom flanges, so

the lateral curvature of the girder, ux, was obtained from three lat-

eral thermal gradients in the middle of the top flange, the web, and

the bottom flange:

ux ¼

X

i

R

½E � a � DTðxÞ � hðxÞ � x�dx

E � Iyð6Þ

in which DT(x) is the lateral thermal gradient at width x, h(x) the

depth of the girder, Iy the moment of inertia of the cross-section

with respect to the weak y-axis, and i (=1,2,3) the lateral thermal

gradients of the top flange, the web, and the bottom flange of the

girder, respectively.

4.2. Comparison of the beam model with the 3D finite element analysis

For the BT-1600 girder, which showed the largest vertical and

lateral thermal gradients among the four AASHTO-PCI standard

girder sections, this study calculated the vertical and lateral

thermal movements in the summer and winter environmental

conditions in Atlanta using the proposed model. The length of

the BT-1600 girder was 30 m, and the material properties of con-

crete were the same as used previously.

The vertical and lateral thermal movements calculated using

the beam model were compared with those obtained from the

3D finite element thermal stress analysis for simply supported

boundary conditions. Fig. 8 shows that the thermal movements

calculated from the beammodel correlate well with those obtained

from the 3D finite element analysis. Differences between the max-

imum vertical and lateral thermal movements of the beam model

and those of the 3D finite element analysis were less than 0.08 cm

(5.3%).

4.3. Equations for calculating maximum thermal movements in

AASHTO-PCI standard girders

The beam model was further used to propose simple equations

that are capable of calculating the vertical and lateral thermal

movements with the design span of precast prestressed concrete

bridge girders. For the four AASHTO-PCI standard girder sections,

Type-I, Type-IV, Type-V, and BT-1600 sections, Table 1 summarizes

the equations in terms of the span length of the girder. The equa-

tions can be used to calculate the maximum vertical and lateral

thermal movements of the girders located in Atlanta. The thermal

(a) Cross-section (b) Thermal strain (c) Final strain

Fig. 7. Strain distributions induced by a nonlinear vertical thermal gradient in a simply supported prestressed concrete girder section.


loads were based on summer and winter environmental conditions

that yield the largest vertical and lateral thermal movements,

respectively.

Since the behavior of the girders mainly depends on the mo-

ment of inertia of the cross-section, the Type-I section, which has

the smallest moment of inertia with respect to the strong x-axis,

has the largest vertical thermal movement. For a Type-I girder de-

signed to be a maximum span of 15 m, the maximum vertical ther-

mal movement was calculated to be 0.71 cm in the summer in

Atlanta. The largest lateral thermal movements occurred in the

Type-V and BT-1600 sections, which have the largest lateral ther-

mal gradients and a small amount of moment of inertia with re-

spect to the weak y-axis.

5. Behavior of a precast prestressed concrete girder involving

thermal effects with geometry and support imperfections

5.1. 3D nonlinear finite element sequential analysis procedure

The environmental thermal effects are combined with fabrica-

tion and construction errors to affect the behavior of precast pre-

stressed concrete girders during construction, especially prior to

the placement of cross bracing and the deck slab. This study found

that the main imperfection was initial lateral deformation in the

girder at mid-span and the bearing slope in the lateral direction.

To analyze the combined effects of the initial sweep, the bearing

support slope, and thermal loads on the prestressed concrete gir-

der, a 3D nonlinear finite element sequential analysis procedure

was developed which could update the geometry and stresses of

the girder during each construction state. The flowchart of the

sequential analysis procedure is depicted in Fig. 9.

The first static analysis shown in Fig. 9 was performed to gener-

ate the sweep in the girder and camber and stresses due to pre-

stressing forces. As mentioned previously, the camber and

stresses are obtained from prestressing forces, defined as the initial

stress conditions. The shape of the initial sweep, defined in the first

static analysis, is obtained from another previous static analysis

with the self-weight of the girder applying to the lateral direction.

The magnitude of the initial sweep is specified by scaling the

Fig. 8. Comparisons of the vertical and lateral thermal movements calculated using the beam model with those obtained from the 3D finite element analysis.

Table 1

Maximum vertical and lateral thermal movements of the four AASHTO-PCI standard girder sections in the summer and the winter (Units: � 2.73 � 10�5 m).

AASHTO-PCI standard sections Max. vertical movement a Max. lateral movement a Max. span (m) [2]

Summer Winter Summer Winter

Type-I 117�L2 71�L2 53�L2 63�L2 15

Type-IV 39�L2 23�L2 123�L2 153�L2 37

Type-V 59�L2 26�L2 40�L2 82�L2 44

BT-1600 55�L2 20�L2 40�L2 83�L2 40

a L is the span of the girder in meters.

Fig. 9. Flowchart of the 3D nonlinear finite element sequential analysis.


maximum lateral deformation obtained from the static analysis to

a target sweep value. Since the sweep and the camber occur prior

to the placement of the girder on the bearing supports, the support

boundary condition in this first static analysis was assumed to be a

simply supported condition.

The initial sweep in the girder and the camber and stresses in-

duced by prestressing forces are employed to update the geometry

and stress states of the girder for the next analysis. Then the slope

of the bearing support is produced by applying displacement

boundary conditions corresponding to the support slope to the up-

graded 3D finite element model. Since the support slope is a stress-

free behavior, the stress states in the concrete and prestressing

strands are the same as those defined in the first static analysis.

Finally, the prestressed concrete girder updated from the previ-

ous analyses—the first static analysis for the initial sweep of the

girder and the effects of prestressing forces and the second static

analysis for the support slope of the girder—provides a reference

configuration of the next 3D nonlinear finite element analysis.

The self-weight of the girder and the thermal loads obtained from

the 2D heat transfer analysis are applied to assess the behavior of

the prestressed concrete girder during construction. This analysis

accounted for the nonlinearity of the geometry and the nonlinear

behavior of the elastomeric bearing pads.

5.2. Structural analyses with the support slope and the initial sweep

Since the stability of prestressed concrete girders during con-

struction mainly depends on their lateral behavior, the thermal

load involved in this 3D sequential nonlinear analysis was based

on the winter environmental conditions showing the largest lateral

thermal gradients in Atlanta. Among the four AASHTO-PCI sections,

this study selected the 30-m long prestressed BT-1600 girder.

The initial evaluation of the support slope on the behavior of the

prestressed BT-1600 girder was conducted with no initial sweep.

The support slopes chosen for this study were 0�, 2.5�, and 5�.

The angle of 0� represents a perfectly flat condition between the

girder and the supports. The maximum value of the support slope

of 5� was chosen based on the maximum measured support slope

of 0.0079 rad. (4.5�) on the collapsed girders in Arizona [1].

For a support slope of 5� at both ends of the girder, this study

examined the vertical and lateral responses of the prestressed

BT-1600 girder with increases in initial sweep at 3, 6, 9, 11, and

13 cm. The initial sweep of 3 cm was the sweep tolerance of

3 mm per 3 m length of prestressed concrete beam provided in

the PCI Bridge Design Manual [2].

5.3. Vertical behavior of the prestressed concrete girder

For the geometrically perfect structure, or the 30-m long BT-

1600 girder with no initial sweep, Fig. 10a shows variations in

the vertical movements due to thermal loads and self-weight for

the support slope of 0�, 2.5�, and 5�. Fig. 10b shows the variations

in the vertical movements of the girder with increases in the initial

sweep from 3 cm to 13 cm with a constant 5� support slope. From

Fig. 10, we can see that the girder, after being installed on the bear-

ing supports, underwent slight increases in vertical movement

with increases in the support slope or the initial sweep. In partic-

ular, for the initial sweep of 11 and 13 cm, the 3D nonlinear finite

element analysis stopped at 2 p.m. and at 10 a.m., respectively, as

shown in Fig. 10b. The failure of this numerical analysis was due

to the larger increases in lateral movements with increases in the

initial sweep in the sloped girder. The lateral behavior of the girder

with increases in the initial sweep and support slope will be dis-

cussed below.

Fig. 10. Variations in the vertical movements of the 30-m long BT-1600 girder at

mid-span with increases in (a) support slope with no initial sweep and (b) initial

sweep for a 5� support slope.

Fig. 11. Variations in the lateral movements at the mid-height of the 30-m long BT-

1600 girder web at mid-span with increases in (a) support slope with no initial

sweep and (b) initial sweep for a 5� support slope.


5.4. Lateral behavior of the prestressed concrete girder

For the lateral behavior of the 30-m long prestressed BT-1600

girder during construction, Fig. 11 exhibit variations in the lateral

movements at the middle height of the girder web with increases

in the support slope and the initial sweep. Increases in the support

slope with no initial sweep, illustrated in Fig. 11a, only slightly

changed the lateral deformations due to the combination of ther-

mal effects and self-weight, as was found in the vertical behavior

of the girder. However, with increases in the initial sweep for a

constant support slope of 5�, Fig. 11b reveals increases in the lat-

eral movements at the middle height of the web at mid-span. For

the 30-m long prestressed BT-1600 girder with an initial sweep

of 11 and 13 cm, the lateral movements were about 12 cm imme-

diately after the girder was installed on the sloped bearing support.

The combined thermal effects then increased the lateral move-

ments, including the initial sweep of 11 cm and 13 cm, to

25.7 cm at 1 p.m. and 25.9 cm at 9 a.m., respectively, at the middle

height of the girder web at mid-span, shown in Fig. 11b. After that,

as mentioned previously, the 3D finite element analyses halted due

to error messages of ‘‘largest increment of displacement’’ in the lat-

eral direction at the top flange of the girder at mid-span and

‘‘excessive distortion’’ in solid concrete elements. According to

the messages, the failure of this numerical solution to converge

is an indication of instability in the structure due to the large in-

crease in lateral deformations.

6. Conclusions and discussions

Using the 3D nonlinear finite element analysis, this initial study

evaluated the behavior of a precast prestressed concrete bridge gir-

der during construction, particularly before the placement of the

slab deck and bracing. This analysis included initial sweep in the

girder and the slope of the support, which occur during fabrication,

handling, and construction, and environmental thermal loads to

the girders immediately after resting on bearing supports.

To determine thermal loads, this study first evaluated vertical

and lateral thermal gradients using seasonal variations in environ-

mental conditions from 30-year (from 1961 to 1990) monthly daily

climatic values for Atlanta. The study then examined the influence

of girder orientations on the thermal gradients for four AASHTO-

PCI standard girder sections. The maximum vertical thermal gradi-

ents were found in the summer in an east–west orientation, and

the maximum lateral thermal gradients were found in the winter

in an east–west orientation. Among the four AASHTO-PCI sections,

the deeper and wider Type-V and BT-1600 sections exhibited the

largest vertical and lateral thermal gradients. Thus, the thermal

loads involved in this study were determined from the summer

and winter environmental conditions for Atlanta.

For a 30-m long prestressed BT-1600 girder, the 3D finite ele-

ment thermal response analysis was performed which consisted

of two sequential analyses: A 3D static analysis with a simply sup-

ported boundary condition and a 3D thermal stress analysis with

elastomeric bearing pads. The bearing pads were modeled as non-

linear springs with the effective vertical stiffness of the bearing

pads. Results of the analyses showed no instability in the girder

due to the combined effects of self-weight and thermal loads with-

out any initial sweep or support rotation.

In the following analysis, to combine thermal effects with fabri-

cation and construction errors, this study developed a 3D finite ele-

ment sequential nonlinear analysis procedure that accounted for

the changes in the geometry and stress states of the girder. This

analysis included the nonlinear behavior of the girder and the elas-

tomeric bearing pads. The analyses indicated possible instability in

the 30-m BT-1600 girder when lateral deformations due to the

combination of thermal effects, the initial sweep, and the support

slope exceeded about 25 cm at the middle height of the girder,

close to the centroid of the girder cross-section.

In addition, this study proposed a beammodel to calculate envi-

ronmentally-induced vertical and lateral thermal deformations for

simply supported girders. The vertical deformation is based on a

vertical thermal gradient along the depth of the cross-section,

and because the lateral thermal gradients vary from the top to

the bottom flanges, the lateral deformation is defined from three

lateral temperature gradients of the middle of the top flange, the

web, and the bottom flange. A comparison showed that the vertical

and lateral movements of the beam were within 0.08 cm (6%) of

those determined by the 3D finite element analysis. Furthermore,

this study proposed simple equations for calculating the maximum

vertical and lateral thermal movements in terms of the span length

of the girders for simply supported four AASHTO-PCI standard

girders located in Atlanta: Type-I, Type-IV, Type-V, and BT-1600

girders.

To provide more generalized conclusions on the lateral behavior

of precast prestressed concrete girders, including the initial sweep

and the support slope during conduction, the development of the

3D and simplified models should include more girders under vari-

ous environmental conditions.

References

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