Skew Composite

7/31/2019 Skew Composite

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The Pennsylvania State University

The Graduate School

Department of Civil and Environmental Engineering

Response of a Skewed Composite Steel-Concrete Bridge Floor-

System to Placement of the Deck Slab

A Proposal for a Thesis in

Civil Engineering

by

Elizabeth K. Norton

Submitted in Partial Fulfillment

of the Requirements

for the Degree of

Masters of Science

August 2001


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Table of Contents

1.0 Introduction... 1

1.1 Problem Statement.. 1

1.2 Scope of Research... 2

1.3 Objectives... 3

2.0 Background... 4

2.1 Field Testing... 4

2.2 Laboratory Testing and Analytical Modeling. 6

2.3 V-Load Method...... 9

3.0 Experimental Program.. 10

3.1 Structure Description.. 10

3.2 Field Testing... 12

3.3 Equipment... 13

3.4 Data Reduction... 14

4.0 Analytical Program... 15

4.1 Numerical Analysis of Structure 15

4.2 Construction Sequencing Studies... 16

5.0 Results.. 18

5.1 Preliminary Results. ... 18

5.2 Anticipated Results. 18

A.1 Processing the Data.. 20


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List of Figures:

Figure 1: Plan View... 10

Figure 2: Diaphragms. 11

Figure 3: 12-hour Placement of the Concrete Deck.. 12

Figure 4: Instrument Plan... 13

Figure 5: Initial Screed Position. 17

Figure 6: Comparison of Predicted Response to Actual Response 18


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1.0 Introduction

1.1 Problem Statement

The design of skewed bridges is becoming more commonplace in the United States. It is

more efficient to design bridges with skewed geometries in urban areas due to the lack of space

required for more traditional straight girder bridges. In addition, skewed bridges are common at

highway interchanges, river crossings, and other extreme grade changes where skewed

geometries are necessary due to limitations in space.

The majority of skewed bridges constructed in the United States are designed as modified

right-angle structures. The girders in a right-angle structure are placed perpendicular to the

abutment. The modifications made to convert the right-angle bridge to the skewed bridge do

not efficiently portray the additional torsional effects caused by the angle of skew.

While there have been a multitude of studies on the response of straight, right-angle

steel girder bridges during construction, there has not been a great deal of research on skewed

bridges. Further research must be completed to better understand the behavior of skewed bridges

during construction. Specifically, this research project will study the influence of construction

sequencing and the 12-hour placement process of the concrete deck to determine their effect on

the deflected shape of the skewed bridge and the resulting forces in the girders and diaphragms.

Recommendations for improved analysis methods and construction sequences will lead to more

confident design and construction of skewed bridges.


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1.2 Scope of Research

Further research is required to better understand the behavior of skewed bridges during

construction. From this research, improved methods of analysis and construction procedures of

severely skewed bridges can be determined. The scope of this research includes:

1. Field Test

A skewed bridge was monitored during placement of the concrete deck.

The bridge is made up of seven plate girders with an average length of 74.45 m

(244-3) and a 34 angle of skew measured between the centerline of the bridge

and the perpendicular to the face of the abutments (see Figure 4(c)).

Strains were measured at select locations along some of the seven girders and

cross frames during the 12-hour placement process.

2. Analytical Program

Deflections will be determined using line girder analysis and compared to field

data.

A STAAD model will be created similar to a consultants preliminary STAAD

model and compared to the values determined by analysis.

A more complicated SAP2000 model will be analyzed and compared to the

STAAD model to determine the accuracy of the model.

Construction sequence will be studied in order to determine the most efficient

pour sequencing approach.

A method similar to the V-load method will be developed and examined for use

with skewed bridges.


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1.3 Objectives

The response of the bridge to the placement of the concrete deck was monitored in order

to compare actual response to the predicted response. This comparison will be used to satisfy the

following objectives:

1. Determine theoretical deflections/rotations using analytical models for comparison to

actual deformations monitored during construction.

2. Several variations on the pour sequence, detailed in Section 4.2, will be examined to

determine the most efficient construction methods.

3. Compare the results of varying levels of analysis to determine the adequacy of the

methods.

4. Recommendations will be made to improve modeling to better predict the response of

the bridge under construction loads.

5. Modify the V-load method commonly used for curved girders and compare to

experimental results from skewed bridges to verify accuracy.


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2.0 Background

2.1 Field Testing

Numerous studies have been performed on the behavior of straight and curved

composite-steel girder bridges (Culver et al, 1969, Fiechtl, 1987, Linzell, 1999); however,

research on the behavior of skewed bridges has been limited. The majority of the studies on

skewed bridges have been focused on the determination of distribution factors, the influence of

the angle of skew on the cross bracing and the behavior of the deck.

Ghali et al. (1969) used both field testing of a skewed bridge and an analytical model to

investigate the validity of the common assumptions used in practice. The reactions at the

supports of an eight span steel-concrete composite bridge were determined by field testing and

compared to reactions found from an analytical model. The bridge is comprised of seven steel

plate girders with a skew angle of 50. Span lengths range from 19.8 m to 40.6 m (65 to 133).

To approximate reactions due to dead loads, a hydraulic jack was used to lift the girders. A

pressure gage was used to verify applied loads measured by a load cell. A 20-ton truck load was

then applied and the corresponding forces were measured by the load cell. The field tests were

validated through the use of an elastic grillage computer model. Due to limitations in the

computer program used in the analysis, the model was divided into eight one span segments.

The results of the tests indicate that there is a 1.8% difference between the theoretical and

experimental values. The method of erection, sequence of casting and time-dependent

deformations of concrete were found to effect the dead load reactions though the reasons for this

are unknown. There were found to be discrepancies between the results of the theoretical and

experimental tests due to the simplification of the analytical model.


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Bishara et al. (1993) conducted a field test of a 41.8 m (137) span four- lane composite

steel-concrete bridge with a skew angle of 58.5. The purpose of the field test was to investigate

the validity of wheel load distribution factor expressions determined from finite element analyses

of 36 bridges of varying geometry. The bridge, located in Columbus, Ohio, was tested using six

dump trucks with known axle loads. Maximum stress occurred at the extreme bottom fiber of

the girder when no more than two lanes were loaded. Once the field test was complete,

sensitivity studies were conducted using several parameters including: span length, number of

girders, number of loaded lanes, skew angle and slab width. It was found that the skew angle has

the highest impact on the wheel-load distribution factor. However, the skew effect is negligible

when the skew angle is less than 30. Distribution factors for interior and exterior girders were

derived from this study and compared to the finite-element modeling scheme and current

AASHTO specifications. The finite-element modeling scheme uses a three-dimensional bridge

deck and assumes that all elements are linearly elastic. The distribution factors from the derived

equations were found to be 5-25% higher than the resulting factors from the finite-element

model. The distribution factors for the interior girders were found to be 30-85% that of the

AASHTO specified factor of S/5.5 and 30-70% of the AASHTO factors for the exterior girders.

The controlling factor in the design of skewed bridges may be the exterior girders because skew

angle has less of an effect on the exterior girders than the interior girders.

Miller et al. (1994) performed a test of a 38 year old, two lane, decommissioned concrete

slab bridge with a skew angle of 30. The purpose of this test was to study the behavior of the

bridge as one lane is incrementally loaded to failure by a hydraulic loading system simulating HS

20-44 trucks. Torsion and out-of-plane sway caused by the unusual geometry were more

accurately portrayed with the use of unsymmetrical loading. Over 150 instruments were used to


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measure the response of the structure to the applied load. A nonlinear finite-element analysis

was used to predict the location of the critical responses in order to determine the most efficient

positioning of the instruments. Results of the field test were compared to the nonlinear finite

element model as well as a linear finite element model and an effective-strip model. The results

of the test indicate: (1) that the boundary conditions had a large impact on the bridge response;

(2) deterioration in the shoulders caused the failure of the slab in punching shear; and (3) the

linear and nonlinear finite-element analyses provided less conservative, more efficient results

than the effective-strip model.

2.2 Laboratory Testing and Analytical Modeling

While only a handful of field studies of skewed bridges have been performed, several

laboratory studies have been conducted. These studies generally utilized laboratory testing as a

means to validate an analytical model and included sensitivity studies to predict the effects of

specific parameters. The majority of these laboratory studies have been performed on skewed

concrete bridges.

Newmark et al (1948) conducted a series of laboratory tests on five composite steel-

concrete bridges with skew angles of 30 and 60. Two types of tests were performed: (1)

influence line tests, where influence lines were determined for strains in the beams, deflections

of the beams and strains in the slab reinforcement and (2) tests with simulated wheel loads,

where the concentrated loads of the rear wheels of a truck were simulated to induce strains and

deflections at various locations. These tests were similar to previous tests conducted on right

angle structures. Upon comparison of the tests, it can be noted that the measured beam strains of

the bridges with a skew angle of 60 were 78% to 86% that of the right bridges. In addition, the


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maximum moments in the beams decreased for large angles of skew and the positive moments at

the center of a panel increased.

Davis (1978) investigated the design of a skewed, reinforced concrete box-girder bridge

through the use a finite-element model. The 1:2.82 scale model, which has also been used for

several experimental studies, consisted of reinforced concrete elements. The length of the model

was 25.6 m (84) with a skew angle of 45. The finite element model was created using a

modified version of the CELL program, a computer program specifically designed to analyze

skewed and curved box-girder bridges. The results of this test indicate that the program can be

used to efficiently analyze skewed bridges.

Rahman and George (1980) validated a finite element model by testing a two span slab-

girder bridge with a skew angle of 30. The main focus of this study was to develop an accurate

model portraying thermal stresses developed in skewed bridges. The model proved to be

accurate when results were compared to experimental data.

Gupta and Kumar (1983) tested five small-scale models with skew angles ranging from

0 to 40. Each model consisted of three girders and six cross frames with a total length of 0.125

m (0.41). This study was performed for two reasons: (1) to better understand the effect of the

skew angle on the behavior of the structure; and (2) to evaluate the contribution of the deck slab

to the girders. Analytical models were created based on the stiffness method and a finite element

analysis. Results of the laboratory tests were compared to the analytical results. This report

concluded that careful consideration is necessary for skew angles greater than 30. As the skew

angle increases, deflection increases. Maximum bending moment is not severely affected by the

increase in skew angle.


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Cope and Cope (1989) studied the behavior of two 1:3.5 scale models and compared the

results to a nonlinear finite element model to determine the accuracy of the testing. Both models

were designed and constructed in the same manner with inverted prestressed T-beams, the first

with a 65 skew angle and the second with a 40 skew angle. Simulated traffic loads were

applied to both bridges before loading them to failure. Results of the research indicate that

bridge decks designed with the current British codes possess substantial reserves of strength and

the existing methods of analysis do not accurately predict failure modes.

Helba and Kennedy (1994) studied the ultimate load capacity of composite steel-concrete

skew bridges. Five composite bridge models with a length of 2.1 m (0.64') and skew angles of

45 were tested. All models were tested elastically before loading the bridges to failure.

Deflections and strains were measured during the test and compared to the results of a finite

element model created in ABAQUS. Seven parameters were varied throughout the analytical

studies. These parameters included: skew angle, girder spacing, aspect ratio of the bridge, the

number of transverse diaphragms, ratio of negative to positive moments of resistance, the effect

of composite action between transverse diaphragms and the deck slab, and the number and

position of loads. Using energy equations, the ultimate collapse load of skewed composite

bridges was derived. Collapse loads determined from this equation were compared to

experimental collapse loads. The results indicate that yield- line methods of analysis can

accurately predict the ultimate load capacity of skewed bridges. In addition, results indicate that

the ultimate load is heavily influenced by the longitudinal and transverse moments of resistance.

Ebeido and Kennedy (1995, 1996) performed laboratory studies of girder moments and

shear distribution of six simply supported skew composite steel-concrete bridges with skew

angles of 45. Each bridge was tested both experimentally and analytically. After a series of


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elastic tests conducted with a simulated truck load, the experimental bridge was tested to failure.

In addition to the deflections and strains recorded during the testing, the cracking load of the

deck slab, collapse load of the model and crack pattern of the deck slab were monitored during

the process. A finite-element model was developed using ABAQUS. A sensitivity study was

conducted to investigate the parameters which affect the shear and moment distribution. From

this parametric study, empirical formulas for both moment distribution factors and shear

distribution factors were developed. It was found that the skew angle is the most critical

parameter for the shear distribution and the controlling factor for design is the exterior girder.

2.3 V-Load Method

The V-Load method was developed to provide bridge designers with a relatively

straightforward hand calculation technique to perform preliminary analysis of curved steel girder

bridges. It attempts to account for curvature effects by applying a series of fictitious V-Loads to

the girder. The method was published in 1963 by United States Steel (NSBA, 1996). The

method follows two main steps. The first step involves straightening the curved girders such that

the applied vertical loads only induce bending stresses. The second step involves applying

fictitious forces which result in no net vertical, longitudinal, or transverse forces on the total

structure. These fictitious forces give similar forces as those caused by the curvature effects in a

curved structure. There have been numerous studies completed on the V-load method for use

with horizontally curved girder bridges. Grubb (1984) and Poellot (1986) evaluated the accuracy

of the method by comparing the results of the V-load method with results of MSC/NASTRAN.

While this method is useful for horizontally curved girder bridges, no comparable method is

available for use with skewed bridges except line girder analysis.


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3.0 Experimental Program

3.1 Structure Description

The structure being analyzed, PennDOT Structure #28, is a single span composite steel

multi-girder bridge located on an extension to Interstate 99 in central Pennsylvania (see Figure

1). The bridge is 74.45 m (244 -3) in length with a skew ranging from 33-43-14 to 35-00-

00 measured between the centerline of the bridge and the perpendicular to the face of the

abutments. Seven girders frame into two concrete abutments. Each girder is made up of three

1.75 cm x 240 cm (11/16 x 94) web plates and flange plates ranging from 5.08 cm x 60.96 cm

(2x24) to 7.62 cm x 76.2 cm (3x30). Because of the skewed geometry of the bridge, it was

anticipated that torsional effects due to the deck pour sequence would rotate the girders. Cross

frames were used to force the webs of the girders out-of-plumb in order to compensate for this

additional rotation. Diaphragms are located at the abutments and at varying positions along the

span (see Figure 2).

Figure 1: Plan View

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3.2 Field Testing

The structure was monitored during the twelve-hour deck placement process which began

at 1:25 am on August 31, 2000. The concrete was placed perpendicular to the centerline of the

bridge using two screeds (see Figure 3). The screeds exited the bridge at approximately 11:30

am on September 1, 2000. Strains and displacements were measured using strain transducers

and Linear Variable Differential Transformers (LVDTs). Instruments were placed onto the

structure as indicated in Figure 4.

Figure 3: 12-hour placement of the concrete deck.


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FIGURE 4: INSTRUMENT PLAN

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3.3 Equipment

Strain transducers were placed on the diaphragms and girders (see Figure 4(a)) to record

loads caused by movement of the screed across the bridge as well as the placement of the wet

concrete. The gages recorded one measurement per minute during the twelve-hour placement


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process. LVDTs (see Figure 4(b)) were placed on the diaphragms and girders at the abutments

to record displacements in the members during each phase of construction. All instruments were

connected to a data acquisition system for collection and storage of the data. Stored data was

then transferred to a personal computer where it could be reduced and analyzed.

3.4 Data Reduction

Deflections and rotations will be calculated from data obtained from the LVDTs. Data

obtained from LVDTs can be analyzed directly through the application of calibration factors. In

order to obtain the final values, the measured value is divided by the specified conversion factor.

Data collected from the strain transducers must undergo a more rigorous conversion into usable

data. To reduce undesirable dynamic and noise effects, raw data is filtered using DasyLab. For

further discussion of the strain transducers and the process used to convert the data see Appendix

A.

In addition to the data from the strain gages and LVDTs, global geometric data collected

from traditional surveys performed before and after the deck placement process will be analyzed

(see Figure 4(c)). The Pennsylvania Department Of Transportation also performed a survey

using a three-dimensional Cyrax laser scanner system (see Figure 4(c)). This system has a

reported accuracy of less than 6 mm and can perform one structure scan in ten minutes (Cyra

Technologies, Inc., 2000). Laser targets were attached to the bottom flanges of girders in 5

locations (see Figure 4(c)). Data collected from this laser measurement system will also be

analyzed. Deflections and rotations will be calculated from elevations determined by the

surveys.


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4.0 Analytical Program

4.1 Numerical Analysis of Structure

Four levels of analysis will be used to determine the accuracy of methods for modeling

skewed bridges. The analyses will include:

1. Hand Calculations.

2. A simplified STAAD model

3. A SAP2000 model

4. The V-load method.

Hand calculations: Deflections in the structure, located at corresponding survey points,

will be determined using the line girder analysis. Deflections from the self-weight of the

structure will first be determined. Then, loads caused by the screed and the wet concrete will be

treated as uniform loads acting over the entire bridge in order to determine the post pour

deflections. Theoretical values will be compared to the values determined by analyzing the raw

data in the previous section. In addition, the effect of the loads on the cross frames will also be

studied by varying the location and makeup of the frames.

STAAD: A simplified STAAD model will be analyzed and compared to the initial

STAAD model used for construction of the bridge. The three-dimensional bridge will be

reduced to a two-dimensional grillage model. The cross frames, diaphragms and abutments,

each containing several members, will be condensed into line segments which possess the

combined material properties of all of the members. The loads used in this model will reflect the

loads applied to the actual structure during construction. The movement of the screed across the

deck will be modeled as uniform loads and moments acting along the bridge. The deflections


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and strains determined through this analysis will be compared to the deflections and strains

determined by the first level of analysis.

SAP2000: The highest level of analysis will be a SAP2000 model. Through the use of

shell elements and 3-D modeling, SAP2000 will provide a more complex model than STAAD.

Similar to the STAAD model, the grillage analogy will be used to create the SAP2000 model.

The wet concrete and the movement of the screed will be modeled as a series of uniform loads

and moments acting along the bridge. Once the SAP2000 model is complete, deflections and

strains will be compared to deflections and strains obtained by the previous two levels of

analysis to determine the accuracy of the model. Several loading sequences will then be applied

to the structure to study the response to the construction sequence, detailed in section 4.2.

V-load: The last level of analysis will be the use of the V-load method. The accuracy of

the V-load method for use on a skewed bridge will be determined through the modification of the

equations to exclude the radius of curvature and include the angle of skew. The V-Loads are

currently determined by the following equation (Highway Structures Design Handbook, 1996):

Mp

V = C*(RD/d)

(4-1)

where:

V = V-load,

Mp = sum of the primary moments in each girder,

C = coefficient which depends on the number of girders,

R = radius of curvature,

D = distance between girders and

d = distance between cross frames.


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Results of the analysis will be compared to results of the previous analyses to determine the

adequacy of the method. If necessary, modifications will be made to better portray the effects of

skew angle on the girders.

4.2 Construction Sequencing Studies

The construction sequence has a significant impact on the structure. Some factors which

influence the final deflected shape include the positioning of the screed on the structure and the

sequence in which the concrete deck is poured. The SAP2000 model will be modified to reflect

the loads caused by the screed when it is placed both parallel to the angle of skew and

perpendicular to the centerline of the bridge. Several pour sequences will be examined and are

listed in Table 1.

Table 1: Pour Sequences (see Figure 5)

Screed Position

(a) 2 screeds placed side by side at East end

(b) 1 screed spanning the width of the bridgePerpendicular to skew angle

(c) 2 screeds placed at opposite ends of bridge

(d) 2 screeds placed side by side at East end(e) 1 screed spanning the width of the bridgePerpendicular to centerline of bridge

(f) 2 screeds placed at opposite ends of bridge

The cross bracing can also influence the final shape of the structure. While the cross

bracing proves to be beneficial during construction, several studies, including Azizinamini et al

(1995), have found that cross bracing can actually hinder the performance of the bridges once

construction is complete. Cracking in the girder web has been observed in the areas surrounding

the cross bracing. Several variations in cross bracing location will be studied in order to

determine a more efficient design and construction of skewed bridges.


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FIGURE 5: STARTING SCREED POSITION

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5.0 Results

5.1 Preliminary Results

Measured data obtained from the surveys was analyzed and compared to predicted data

obtained from drawings and details used in the construction of the structure (see Figure 6 for an

example of a typical girder). The results indicate that predicted elevations of the girders under

only the self-weight of the structure tend to be higher than the actual elevations of the girders

determined by the surveys. However, the predicted elevations of the girders under both the self-

weight and the concrete deck tend to be similar to the actual elevations of the girders. This data

will be compared to the data obtained from hand calculations and analytical models.

Figure 6: Comparison of Predicted Response to Actual Response.

5.2 Anticipated Results

Four levels of analysis will be compared to determine the accuracy of each level. These

results will be compared to results of the initial, pre-construction analysis and to experimental

data. Upon comparison of results from Section 4.0 to the results of the initial analysis,

Girder 1

Measured (Steel)

Measured (Steel +

Deck)

Predicted (Steel)

Predicted (Steel +

Deck)

Predicted (Vertical

Curve)

3592.00

3594.00

3596.00

3598.00

3600.00

3602.00

0.00 100.00 200.00 300.00 400.00 500.00 600.00 700.00

Distance From West BRG. (Ft.)

Bottom

ofGirderElevation

(m)


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recommendations for improving analysis will be provided. Once the accuracy of the models is

determined, the effect of varying construction sequences can be determined and

recommendations for improved methods can be made. The modified V-load method may prove

to be a simple and reasonably accurate method of analysis for skewed bridges.


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A.1 Processing the Data

The strain transducers record all static and dynamic responses during the twelve-hour

placement of the concrete deck including the movement of the screed across the bridge. In order

to translate the raw data from the strain transducers into usable data, any unnecessary dynamic

frequencies must first be filtered. Using DASYLab, a Fast Fourier Transform (FFT) must be

performed in order to determine the frequency at which the data will eventually be filtered. The

FFT identifies frequencies that are equal to or less than one half of the sampling frequency. The

sampling frequency used in this study was 166.67 Hz.

Once the FFT has been performed, a 10

th

order, low pass, Butterworth filter will be used

to remove the dynamic frequencies. The Butterworth response is defined in the following

equation (Johnson, Johnson and Moore, 1980):

A

| H(jw) | = (1 + (w/wc)2n)0.5 (A-1)

Where |H(jw)| is the amplitude or magnitude, A = 1, wc is the cutoff frequency and n is the order

of the filter. The response decreases as the frequency increases and improves as the order

increases. The 10th order Butterworth filter was chosen because it is the largest order filter

allowed in DASYLab.

After all dynamic responses have been filtered out of the data obtained from the strain

transducers, the data will be converted from volts to microstrain. Microstrain can be obtained by

applying the appropriate conversion factors - similar to those applied to the LVDTs and

tiltmeters. The following equation describes the conversion:


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GGF*Vout*1000*Gaine =

Vext

(A-2)

Where GGF is the manufacturer specified conversion factor, the gain is based on the inputted

instrument settings, Vext is the excitation voltage and Vout is the filtered voltage.


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References:

Bishara, A. G., Liu, M. C., and El-Ali, N. D. (1993), Wheel Load Distribution on Simply

Supported Skew I-Beam Composite Bridges,ASCE Journal of Structural Engineering,

v119, n2, pp. 399-419.

Cope, R. J. and Cope, M. (1989), Skewed, Concrete, Composite Bridge Decks, The Structural

Engineer, v67, n4, pp. 61-67.

Culver, C.G. and Christiano, P.P. (1969), Static Model Tests of Curved Girder Bridge,ASCE

Journal of the Structural Division, August, v95, nST8, pp. 1599-1614.

Cyra Technologies, Inc., Cyrax 2500 Laser Scanner, Cyrax 2500 Product specifications,

Endwell, New York

Davis, R. (1982), Design of a Skew, Reinforced Concrete Box-Girder Bridge Model,

Transportation Research Record, n871, pp. 52-57.

Ebeido, T. and Kennedy, J. B. (1995), Shear Distribution in Simply Supported Skew Composite

Bridges, Canadian Journal of Civil Engineering, v22, pp. 1143-1154.

Ebeido, T. and Kennedy, J. B. (1996), Girder Moments in Simply Supported Skew Composite

Bridges, Canadian Journal of Civil Engineering, v23, n4 pp. 904-916.


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Fiechtl, A. L. (1987), Analysis of Horizontally Curved Girder Bridges, M. S. thesis, University

of Texas at Austin, Austin, Texas.

Ghali, Strong and Bathe (1969), Field Measurement of End Support Reactions of a Continuous

Multi-Girder Skew Bridge, Second International Symposium on Concrete Bridge

Design, American Concrete Institute, SP-26, Chicago, Ill., pp. 260-271.

Grubb, M. (1984), Horizontally Curved I-Girder Bridge Analysis: V-Load Method,

Transportation Research Record, n982, pp. 26-36.

Gupta, Y. P. and Kumar, A. (1983), Structural Behavior of Interconnected Skew Slab-Girder

Bridges,Journal of the Institution of Engineers (India), Civil Engineering Division, v64,

pp. 119-124.

Helba, A. and Kennedy, J. B. (1994), Collapse Loads of Continuous Skew Composite Bridges,

ASCE Journal of Structural Engineering, v120, n5, pp. 1395-1414.

Highway Structures Design Handbook. National Steel Bridge Alliance, Chicago, Il., 1996, Vol.

1, Chapter 12.

Johnson, D. E., Johnson, J. R., and Moore, H. P. (1980),A Handbook of Active Filters, Prentice-

Hall Inc., Englewood Cliffs, New Jersey.


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Kostem, C. N. (1986), Approximations and Errors in the Grillage Analysis of Multibeam

Bridges, The Conference on Bridges Official Proceedings: 3rdAnnual International

Bridge Conference, IBC, Pittsburgh, PA, pp. 214-218.

Linzell, D.G. (1999), Studies of a Full-Scale Horizontally Curved Steel I-Girder Bridge System

Under Self-Weight, Ph.D. Dissertation, School of Civil and Environmental Engineering,

Georgia Institute of Technology.

Miller, R. A., Aktan, A. E. and Shahrooz, B. M. (1992), Destructive Testing of a

Decommissioned Slab Bridge,ASCE Journal of Structural Engineering, v120, n7, pp.

2176-2198.

Newmark, N. M., Peckham, W. M. (1948), "Studies of Slab and Beam Highway Bridges- Part II:

Tests of Simple-Span Skew I-Beam Bridges," University of Illinois Bulletin Engineering

Experiment Station, No. 375.

Poillot, W. (1986), Computer-aided Design of Horizontally Curved Girders by the V-Load

Method, Proceedings - Solutions in Steel, The National Engineering Conference, AISC

Chicago, IL, pp. 1-30.

Rahman, F. and Gearoge, K. P. (1980), Thermal Stresses in Skew Bridge by Model Test,

ASCE Journal of the Structural Division, v104, n1, pp. 39-58.

Documents

Skew Composite