II ~I ~ I · 2009. 12. 3. · Mr. Saber Abdel-Ghaffar,a Doctoral student, and Mr. Dan O'Connor,a...
76
II I PB93-167153 Evaluation of the Current CALTRANS Seismic Restrainer Design Method Nevada Univ., Reno Prepared for: California State Dept. of Transportation, Sacramento Oct 92 I u.s. DEPARTMENT OF COMMERCE National Technical Information Service NTIS
Transcript of II ~I ~ I · 2009. 12. 3. · Mr. Saber Abdel-Ghaffar,a Doctoral student, and Mr. Dan O'Connor,a...
~ II ~I ~ IPB93-167153
Evaluation of the Current CALTRANS Seismic Restrainer Design Method
Nevada Univ., Reno
Prepared for:
California State Dept. of Transportation, Sacramento
Oct 92
I~ I
u.s. DEPARTMENT OF COMMERCENational Technical Information Service
NTIS
BIBLIOGRAPHIC INFORMATION
PB93-167153
Report Nos: CCEER-92-8
Title: Evaluation of the Current CALTRANS Seismic Restrainer Design Method.
Date: Oct 92
Authors: M. Saiidi, E. Maragakis, and S. Feng.
Performing Organization: Nevada Univ., Reno. Center for Civil EngineeringEarthquake Research.
Sponsoring Organization: *California State Dept. of Transportation, Sacramento.*National Science Foundation, Washington, DC. *Nevada Dept. of Transportation,Carson City.
Supplementary Notes: See also PB84-103035. Sponsored by California State Dept. ofTransportation, Sacramento, National Science Foundation, Washington, DC., andNevada Dept. of Transportation, Carson City.
NTIS Field/Group Codes: 50A
Price: PC A04/MF A01
Availability: Available from the National Technical Information Service,Springfield, VA. 22161
Number of Pages: 72p
Keywords: *Highway bridges, *Earthquake resistant structures, *Hinges, *Bridgedesign, Dynamic response, Earthquakes, Computer programs, Nonlinear systems,Displacement, Earthquake engineering, Stress analysis, Dynamic structural analysis,Stiffness, Design standards, Bearings, Seismic effects, *Restrainers.
Abstract: The primary objective of the study was to develop an understanding of theimplications of the current Cal trans hinge restrainer design procedure. Two aspectsof the problem were studied. One was the effects of changing (1) the crosssectional area of restrainers and (2) the restrainer gap on the nonlinear responseof a bridge with several hinges. The other was the sensitivity of the number ofrequired restrainers to changes in some of the simplifying assumptions which aremade in the current Cal trans restrainer design method. Computer program NEABS-86was used in the nonlinear analyses. The focus of this part of the study was therelative displacements at the joints, restrainer forces, and restrainer stresses.Three earthquake records, the El Centro 1940, Eureka 1954, and Saratoga 1989. Inaddition to input earthquakes, the number of restrainers at each hinge, therestrainer gaps, and the hinge gaps were varied. It was found that when arestrainer gap of 0.75 in. is assumed, the number of restrainers does not affectthe response significantly. It is recommended that the design should be based oncases with and without restrainer gaps to encompass all the critical forces,stresses, and displacements. To study the effects of design assumptions on the
i Continued on next page
Continued ••.
BIBLIOGRAPHIC INFORMATION
PB93-167153
required number of cables, several manual calculations of the example in theCaltrans restrainer design guidelines were carried out. The deviations from themethod included the treatment of mass and stiffness of bridge segments as differenthinges closed.
11
Report No. CCEER 92-8
AN EVALUATION OF THE CURRENT CALTRANSSEISMIC RESTRAINER DESIGN METHOD
M. Saiidi, E. Maragakis, and S. Feng
A Report to the
California Department of TransportationNational Science Foundation
Nevada Department of Transportation
Civil Engineering DepartmentUniversity of Nevada, Reno
October 1992
ABSTRACT
The primary objective of this study was to develop an understanding of the implications
of the current Caltrans hinge restrainer design procedure. Two aspects of the problem were
studied. One was the effects of changing (a) the cross sectional area of restrainers and (b) the
restrainer gap on the nonlinear response of a bridge with several hinges. The other was the
sensitivity of the number of required restrainers to changes in some of the simplifying
assumptions which are made in the current Caltrans restrainer design method.
Computer program NEABS-86 was used in the nonlinear analyses [3]. The focus of this
part of the study was the relative displacements at the joints, restrainer forces, and restrainer
stresses. Three earthquake records, the El Centro 1940, Eureka 1954, and Saratoga 1989. In
addition to input earthquakes, the number of restrainers at each hinge, the restrainer gaps, and
the hinge gaps were varied. It was found that when a restrainer gap of 0.75 in. is assumed, the
number of restrainers does not affect the response significantly. It is recommended that the
design should be based on cases with and without restrainer gaps to encompass all the critical
forces, stresses, and displacements .
To study the effects of design assumptions on the required number of cables, several
manual calculations of the example in the Caltrans restrainer design guidelines were carried out.
The deviations from the method included the treatment of mass and stiffness of bridge segments
as different hinges closed. Another variable was the simultaneous reduction in the restrainer gap
and increase in the hinge gap. The results indicated that slight variation in some of the
assumptions can change the number of restrainers significantly. A more streamlined design
method that incorporates the nonlinear response of bridge components needs to be developed.
ACKNOWLEDGEMENTS
The study presented in this report was part of a project which has been mainly funded
by the California Department ofTransportation. Additional funds were provided by the National
Science Foundation and the Nevada Department of Transportation (NOOT). All the funding
agencies are thanked for providing their support. Mr. Mark Yashinsky, the Caltrans project
monitor, Dr. C. H. Liu, the program manager at the National Science Foundation, Mr. Floyd
Marcucci, the Chief Bridge Engineer at NDOT, and Mr. R. Obisanya, a staff engineer at
Caltrans, are thanked for providing helpful comments.
Other members of the project team at the University of Nevada, Reno, provided
significant assistance in the study. Mr. Saber Abdel-Ghaffar, a Doctoral student, and Mr. Dan
O'Connor, a research engineer, are thanked for their valuable input to the modeling aspects of
the study.
TABLE OF CONTENTS
Page
CHAPTER 1 - INmODUCTION 1
1.1 Background. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 1
1.2 Object and Scope 1
CHAPTER 2 - RESTRAINER DESIGN METHOD AND THEEXAMPLE BRIDGE 3
2.1 Summary of Restrainer Design Method . . . . . . . . . . . . . . . . . . 3
2.2 Example Bridge 3
CHAPTER 3 - NONLINEAR MODELING OF THE EXAMPLE BRIDGE 5
3.1 Introductory Remarks 5
3.2 Description of the Bridge Model . . . . . . . . . . . . . . . . . . . . . . . 5
3.3 Input Earthquake Records 7
3.4 Variation of Parameters 7
CHAPTER 4 - RESULTS OF THE NONLINEAR RESPONSE STUDIES 9
4.1 General Characteristics of the Dynamic Results 9
4.2 Results of Parametric Studies (Cable Gap = 0.75 in.) 104.2.1 Hinge Movements 104.2.2 Restrainer Forces and Stresses 104.2.3 Abutment Displacements 114.2.4 Abutment Forces 11
4.3 Results of Parametric Studies (Cable Gap = 0 in.) 124.3.1 Hinge Movements 124.3.2 Restrainer Forces and Stresses 124.3.3 Abutment Displacements 134.3.4 Abutment Forces 14
iii
4.4 Effects of Reduction in the Restrainer Gap 144.4.1 Hinge Movements 144.4.2 Restrainer Forces and Stresses 154.4.3 Abutment Displacements 154.4.4 Abutment Forces 15
4.5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 16
CHAPTER 5 - SENSmVITY OF THE EQUIVALENT STATIC DESIGNRESULTS TO CHANGES IN DESIGN ASSUMPTIONS 17
5.1 Introductory Remarks 17
5.2 Influence of Changes in the Stiffness 17
5.3 Influence of Changes in Stiffness and Mass 19
5.4 Influence of Reducing Restrainer Gap to Zero 19
5.5 Concluding Remarks 20
CHAPTER 6 - SUMMARY, CONCLUSIONS~ AND RECOMMENDATIONS . . .. 21
6.1 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 21
6.2 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 226.2.1 Conclusions from the Nonlinear Analyses 226.2.2 Conclusions from the Redesigns
of the Example Bridge 22
6.3 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 23
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 24
TABLES 25
FIGURES 27
APPENDIX A - SUMMARY OF RESTRAINER DESIGN METHOD [1] 57
APPENDIX B - SAMPLE NEABS-86 INPUT FOR THE REFRENCE CASE . . . .. 58
APPENDIX C - LIST OF CCEER PUBLICATIONS 63
iv
Chapter 1
INTRODUCTION
1.1 Background
Since the San Fernando earthquake in 1971, restrainers have been generally incorporated
in highway bridges in the State of California to avoid excessive displacements at hinges during
strong earthquakes. The design of restrainers has been based on a relatively simple equivalent
static analysis method that incorporates many of the primary factors affecting the seismic
response of bridges [1]. Many simplifying assumptions are made some of which are based on
engineering judgement and expectations, while others reflect the general observations made
during past strong earthquakes.
Although the performance of restrainers which have been designed using the current
methodology has been generally satisfactory during recent moderate earthquakes [2], many
aspects of the restrainer design method have not been studied in detail. For example, it is not
known what the effects of variation in the simplifying assumptions are. Furthermore, no studies
have been conducted to evaluate the nonlinear response history of a bridge with restrainers which
are designed using the current method. The purpose of the study presented in this report was
to address some of these aspects of the hinge restrainer design method.
In writing this report, it was assumed that the reader is familiar or otherwise has access
to Caltrans design guidelines and documents and has, at least, a general familiarity with dynamic
nonlinear analysis of bridge structures.
1.2 Object and Scope
The primary objective of the research presented in this report was to provide a better
insight into the implications of the current Caltrans hinge restrainer design method. Two aspects
of the problem were studied. One was the effect of changing the number of restrainers and the
restrainer gap on the nonlinear response of a bridge which includes several hinges. The other
was the influence of changing some of the assumptions which are made in the restrainer design
method on the number of required restrainers. In all the studies, the example bridge described
1
in the Caltrans design manual was used as the reference case. Only straight bridges were
considered in this study.
The focus of the nonlinear analyses was the relative displacements at the joints, restrainer
forces, and restrainer stresses. The level of ductility demand in the piers was also examined to
identify the extent of nonlinearity. Different earthquake records were used to insure that
conclusions reflect the effects of a variety of ground excitations. In addition to the input
earthquake, the number of restrainers at each hinge, the restrainer gap, and the hinge gap were
also varied. Only longitudinal bridge response was considered to be consistent with the design
method.
To study the effects of design assumptions on the required number of cables, several
manual calculations of the design example in the Caltrans restrainer design guidelines were
carried out. The general procedure was the same as that outlined in Ref. 1. The deviations
from the method included a different treatment of mass and stiffness as different hinges closed
as a result of earthquakes. Another variable was the simultaneous change in the restrcliner and
the hinge gaps.
2
Chapter 2
RFSTRAINER DESIGN METHOD AND THE EXAMPLE BRIDGE
2.1 Summary of Restrainer Design Method
An equivalent linear static analysis method is currently used to design longitudinal hinge
restrainers [1]. The primary features of the design are:
1) Restrainers are designed so that they will not yield even in the event of the maximum
probable ground motion.
2) The formation of plastic hinges in the piers and the resulting reduction in the
horizontal stiffness is accounted for.
3) The failure of the soil behind the abutment at certain displacements is taken into
account.
4) The bridge is divided into a series of frames at the hinges. These frames may
oscillate independently or in concert with adjacent frames depending on the expected
maximum displacement and the hinge and restrainer gaps.
S) The displacement response of each frame is determined using the response spectrum
method, based on the effective period of one or more frames. The seismicity and the
characteristics of the site are accounted for in the smoothed acceleration spectra used for
this purpose.
6) Restrainers are designed to avoid excessive relative displacements at the hinges so that
a minimum bearing width is maintained.
A step-by-step summary of the restrainer design method extracted from Ref. 1 is
presented in Appendix A.
2.2 Example Bridge
Figure 2.1 shows the elevation of the example bridge which is the subject of all the
studies presented in this report. No span lengths are specified in Ref. 1 because only the
superstructure weight and not the length enters the calculations. The span lengths shown in Fig.
3
2.1 were estimated for the purpose of the nonlinear analyses which are described in Chapter 3.
The column height is 24 ft. and the bridge "active" width at the abutments is 40 ft. The
superstructure depth is assumed to be 5 ft. The diaphragm at the right abutment is assumed to
be 5 ft. high and is assumed to shear off at a longitudinal displacement of 2 in. The stiffness
of the spring representing the abutment soil is taken as 200 K/in. per linear foot of the abutment
width for an 8-ft. deep soil wedge. For the same soil wedge, the soil is assumed to fail at a
pressure of 7.7 Ksf. Because the superstructure depth is only 5 ft., this stiffness and the
capacity of abutment spring is reduced by a factor of 5/8.
One half of the columns in each frame are assumed to behave as pinned members at both
ends due the expected inadequacies in the column bar embedment lengths, lap splice lengths, and
foundation. The gross moment of inertia of the columns about the transverse axis of the bridge
is assumed to be 26 ft4. The actual compressive strength of concrete is estimated at 5000 psi.
It is assumed that the bridge is at an alluvium site with a depth of 10 to 80 ft and a peak bed
rock acceleration of sixty percent of gravity.
The example bridge represents the pre-1971 designs in which the typical hinge width was
6 in. The hinge gap and the restrainer gap are both assumed to be 0.75 in. Figure 2.2 shows
the hinge detail and the assumed minimum required seat width.
4
Chapter 3
NONLINEAR MODELING OF TIlE EXAMPLE BRIDGE
3.1 Introductory Remarks
A series of nonlinear response history analyses were carried out on the example bridge
described in the previous chapter. The purpose of the study was to determine the restrainer
forces and stresses as well as relative displacements at hinges as a function of the number of
restrainers, the input earthquake record, and the restrainer gap. Because the properties specified
in Ref. 1 for the example bridge were suited only for an equivalent static analysis, many
assumptions had to be made about geometric and section properties of different bridge
components in order to perform the nonlinear analyses. This chapter first explains these
assumptions and the model used in the analysis, followed by a description of the parameters
which were studied.
3.2 Description of the Bridge Model
The nonlinear response history analysis of the bridge was performed using computer
program NEABS-86 [3] which is a modified version of program NEABS (Nonlinear Earthquake
Analysis of Bridge Systems) [4]. In the equivalent static analysis method, each frame is treated
as a single-degree-of-freedom (SDOF) system which consists of a single rigid mass representing
the superstructure. As a result, span lengths are not needed. To analyze the example bridge
using NEABS-86, however, the span lengths and hinge locations had to be given as input.
These values were estimated based on the weight of each frame and the superstructure width and
height as presented in the design example. The concrete was assumed to be normal weight with
a unit weight of 150 pef. It was further assumed that the superstructure weight is uniformly
distributed along its length. Each pier was assumed to consist of three square columns with a
side dimension of 3.2 ft. The combined moment of inertia of each pier in the longitudinal
direction is hence 26.2 ft4 which is very close to the specified value of 26 ft4. To determine the
yield properties of the column sections, it was assumed that the longitudinal steel ratio in each
column is one percent and that the steel has a yield stress of 60 ksi.
5
The computer model of the bridge is shown in Figs. 3.1 and 3.2. The adjacent nodes
at the base of each column (Fig. 3.1) allowed the modeling of the nonlinear response at the base
of the columns using the five-spring element [3]. To be consistent with the design example, all
the pier footings and abutments were assumed to be fixed except for the degree of freedom of
the abutments in the longitudinal direction of the bridge.
To model the nonlinear effects at the abutments, fictitious restrainer elements had to be
assumed because the boundary spring elements in NEABS-86 which are intended to represent
the flexibility of the abutments and foundation are~. At each abutment, two expansion joint
elements were needed, one to model the nonlinearity of the abutment soil and the other to model
the impact between the superstructure and the abutment. Ordinarily, a single hinge element
would be sufficient to model both the impact effect and the nonlinearity of the restrainer. This
would work in hinges where openin~ of the hinge would activate the restrainer but~~ of
the hinge would activate the impact spring. In the fictitious element at the abutment, however,
both the impact spring and the abutment soil spring (modeled by a restrainer) nec;~ to be
activated when the gap closes. Therefore, two separate hinge elements had to be used.
In the hinge element representing the abutment soil, the input hinge node numbers were specified
in such a way that closing of the gap would put the "restrainer" in tension. The impact spring
in this case was deactivated. The hinge element modeling the impact effect had no restrainers.
Only the intermediate hinges incorporated true hinge restrainers.
Only cable restrainers were assumed in the study with a yield stress of 176.1 ksi [1].
The stiffness of impact springs was determined based on the guidelines recommended in Ref.
5. According to these guidelines, the spring stiffness should approximately be the sanle as the
axial stiffness of the superstructure segment on each side of the hinge. It is reasonable to use
the larger of the two values when superstructure stiffnesses on both sides of a hinge are
different. In the example bridge, impact stiffness values in the range of 8.4xl<f klft to 9.1xHP
klft were used (See Appendix B).
The differential equation of motion in NEABS-86 is formed in incremental form and is
integrated using constant or linear variation of acceleration over each time interval. In the
studies, the constant acceleration method was used to obtain stable results. The time interval
for numerical integration can affect the convergence of the results. Because the bridge model
6
can be highly nonlinear, the appropriate time interval was determined by attempting different
values and study their effect on the relative displacements at the hinges and abutments. The
relative displacement at these locations was believed to be the most critical response parameter
as it can directly affect the restrainer forces. The results of the trial analyses are listed in Table
3.1. It can be seen that no appreciable improvement could be realized by reducing the time
interval below 0.005 second. This time interval was used throughout the study.
A sample input data for the "reference" bridge (the bridge with the same number of
cables as those sPeCified in the Caltrans design example) used in the NEABS-86 analysis is
shown in Appendix B.
3.3 Input Earthquake Records
Three earthquake records were used in the nonlinear analyses. These were the north
south component of the 1940 El Centro earthquake, the north-south component of the Eureka
earthquake of 1954, and the east-west component of the 1989 Loma Prieta earthquake recorded
at the Saratoga station. All the records were normalized to a peak ground acceleration (pGA)
of 0.6g, and were applied in the longitudinal direction of the bridge. The PGA of 0.6g is the
same as that used in the example bridge in Ref. 1. The first ten seconds of each record were
used. Figure 3.3 shows the acceleration sPeCtrum for the three earthquakes calculated at a
damping ratio of five percent. The sPeCtra show notable differences particularly when the
vibration period is less than one second. The estimated periods for different frames in the
example bridge are close to 0.5 second according to Ref. 1.
3.4 Variation of Parameters
Two parameters were studied. One was the hinge restrainer cross sectional area and the
other was the restrainer initial gap. Because only 3/4-in. cable restrainers were considered, the
first parameter was studied by changing the number of restrainers. The restrainer gaps included
in the study represented the condition of the bridge during the extremely high and extremely low
temperatures.
Table 3.2 shows the number of restrainers for different cases. It can be seen that the
restrainers were used in sets of ten cables to be consistent with the design example [1]. The
7
number of cables in Case 1 is the same as that used in the example. Note that the abutments
had no restrainers. In Cases 2 to 5, the numbers were arbitrarily reduced for all three hinges.
The restrainers were completely eliminated in Case 6. Because NEABS-86 allows for a
maximum of only six restrainers at each hinge, groups of the cables had to be lumped. As a
result "equivalent cables" were assigned at different hinges. The number of equivalent cables
in Hinges 1, 2, and 3, is 4, 3, and 5, respectively. The cables were all 7 ft. long and were
placed in a symmetric pattern relative to the longitudinal axis of the bridge.
The specified restrainer gap of 0.75 in. in Ref. 1 is for the "hottest ambient
temperature." The corresponding hinge gap is assumed to be 0.75 in. During the extreme low
ambient temperature, the restrainer gap is expected to become very small and even approach
zero. Under this condition, the hinge gap will reach 1.5 in. The cases listed in Table 3.2 were
analyzed for both the extreme high (restrainer gap of 0.75 in.) and extreme low (restrainer gap
of zero) ambient temperatures.
8
Chapter 4
RESULTS OF TIlE NONLINEAR RESPONSE STUDIES
4.1 General Characteristics of the Dynamic Results
The bridge model discussed in Chapter 3 was analyzed for 36 combinations of restrainer
numbers, input earthquakes, and restrainer gaps using computer program NEABS-86 [3]. In all
the analyses, a 5 percent damping ratio and a time interval of 0.005 second were used. The
focus of the study was the effect of the change in parameters on relative movements at the
hinges and abutments, restrainer forces and stresses, and abutment movements and forces.
Before these effects are discussed, however, sample response histories and the extent of ductility
demand in the piers are discussed in this section to demonstrate the extent of nonlinearity that
the example bridge experienced in the parametric studies.
It will be seen in the next section that the response at hinge 2 was typically more critical
than others. Figure 4.1 shows the relative displacement response history at hinge 2 due to the
El Centro record when the restrainer gap was 0.75 in. A positive value indicates that the two
segments of the superstructure adjacent to the hinge move away from each other. Also shown
is the restrainer force history. The number of the restrainers is the same as that in Case 1
(Table 3.2). Note that a relative displacement of 0.0625 ft. (0.75 in.) is necessary to activate
the restrainers. It can be seen that during the earthquake, the restrainers experienced tension
eight times, each when the relative hinge movement exceeded 0.0625 ft. The force magnitude
was different depending on the relative displacement in each case. The maximum restrainer
force was far below the yield force. For the same case, the relative displacement history and
the force history at abutment 2 are shown in Fig. 4.2. The hinge gap at this abutment is 0.167
ft. The results show that this displacement was exceeded three times during the earthquake.
At t = 5.1 sec., the abutment force reached the yield level which was 1000 kips.
In all the parametric studies, the piers experienced a moderate level of yielding. The
displacement ductility demand for all the cases ranged between 1.8 to 2.2. The ductility demand
is defined as the ratio of the maximum pier top horizontal displacement divided by displacement
when the base moment reaches the yield level. In establishing the yield displacement, shear
9
deformation of the column was ignored because the column aspect ratio (ratio of column height
to its width) was 7.5.
4.2 Results of Parametric Studies (Cable Gap=O.75 in.)
Restrainers are used in bridges to limit the relative hinge displacements below a tolerable
limit. With a restrainer gap of 0.75 in., the permissible relative displacement at the hinge is
2.25 in. (Fig. 2.2). The performance of restrainers is considered to be satisfactory when the
displacement is kept below the permissible limit without any yielding of the restrainers and any
damage to the hinge region. Therefore, the restrainer stresses and hinge movements are of
primary concern. Also important are the movements at the abutments and the resulting forces
because of the close interaction of displacement at the abutments and at hinges, even though
abutments are not equipped with restrainers. This section presents hinge and abutment
movements and forces for different earthquakes and different number of restrainers when the
restrainer gap is 0.75 in.
4.2.1 Hinge Movements
Shown in Fig. 4.3 is the maximum relative displacement of the two segments of the
superstructure adjacent to each hinge. The general observations on this figure are:
1) The relative hinge displacements were insensitive to the changes in the number of cables
including Case 6 in which no restrainers had been used. This was true regardless of the
input ground motion.
2) The maximum relative movement at hinges varied depending on the earthquake.
3) Hinge 2 experienced the largest relative displacement in all earthquakes. This is because
the proximity of the two other hinges to the abutments helped reduce their movement and
because Hinge 2 has the smallest number of restrainers. The estimated hinge movement
in Ref. 1 is the smallest for Hinge 2 which indicates that a revision in the design method
may be necessary.
4) The permissible relative displacement at the hinges when restrainer gap is 0.75 in. is
2.25 in. (0.1875 ft.). It can be seen in Fig. 4.3 that this limit was not reached even
when no restrainers were used.
10
4.2.2 Restrainer Forces and Stresses
Figures 4.4 and 4.5 show the maximum restrainer forces and stresses, respectively. The
forces shown are for each "equivalent cable" at each hinge. These forces need to be multiplied
by 4, 3, and 5, to obtain the total restrainer forces at hinges 1, 2, and 3, respectively. The
equivalent cables had to be used due to the restriction in NEABS-86 on the number of restrainers
at each hinge (See Sec. 3.4). Note that Case 6 had no restrainers. The following observations
are made:
1) Restrainer forces generally decreased as the number of restrainers was reduced. This
was particularly clear for Hinge 2 which experienced the largest relative displacements.
The reduction in restrainer forces is attributed to the reduction in the stiffness of the links
between adjacent superstructure segments.
2) The maximum restrainer forces changed as the input earthquake motion varied.
3) Unlike forces, the restrainer stresses were generally insensitive to the number of cables.
This is because of the reduction in cross sectional area of the restrainers as the number
of cables decreased.
4) The maximum restrainer stress was well below the yield stress of 176.1 ksi in all cases.
4.2.3 Abutment Displacements
The maximum relative displacements between the abutments and the superstructure are
shown in Fig. 4.6. The negative sign of the displacement amplitudes signifies the movement
of the superstructure toward the abutment. Only displacements that tend to reduce or close the
abutment gap were considered, because only the gap closure affects abutment forces. The
following trends can be noted:
1) The maximum displacement of the superstructure relative to the abutment was not
affected by the number of restrainers.
2) Different input earthquakes resulted in different maximum displacements.
3) The movement at Abutment 2 was always larger than that in Abutment 1 because the gap
in the former was 2 in., while in the latter was 1 in. The larger gap allowed the
superstructure to move more.
11
4.2.4 Abutment Forces
The maximum abutment back fill forces in the longitudinal direction of the bridge are
shown in Fig. 4.7. Note that for the abutment to experience any forces, it is necessary that the
hinge gap at the abutment be closed. The yield force for both abutments was 1000 kilPS. The
figure indicates the following:
1) Except for the Eureka earthquake, the number of cables did not influence the abutment
forces significantly.
2) The abutment forces were sensitive to the input ground motion. While the El Centro
earthquake caused the yielding of Abutment 2, the Saratoga earthquake caused only small
forces in the abutments.
4.3 Results of Parametric Studies (Cable Gap=O in.)
All the computer analyses discussed in Sec. 4.2 were repeated for bridge models without
any gap at the restrainers. A reduction in the restrainer gap led to an increase in to hinge gap
to 1.5 in. (0.125 ft.). Because the total seat width is 6 in. (Fig. 2.2), to maintain a minimum
of 3 in. bearing (a criterion set in the design example in Ref. 1) the maximum permissible
relative displacement between the two segments of the superstructure adjacent to each hinge is
1.5 in. (0.125 ft.). The permissible limit was 2.25 in. in the cases presented in Sec. 4.2.
4.3.1 Hin" Movements
Shown in Fig. 4.8 are the maximum relative superstructure movements at different
hinges. The following general observations can be made on this figure:
1) In most cases, the relative hinge displacements increased as a result of reduction in the
number of cables. When no restrainers were used (Case 6), the displacements in Hinges
2 and 3 exceeded the permissible limit. This was true regardless of the input ground
motion.
2) The maximum relative movement at Hinge 1 varied depending on the earthquake.
3) Hinge 2 experienced the largest relative displacement in all earthquakes. This is because
Hinge 2 is away from the abutments and movements at this hinge are not directly
restricted by the abutments.
12
4.3.2 Restrainer Forces and Stresses
Figures 4.9 and 4.10 show the maximum restrainer forces and stresses, respectively.
Note that the forces shown are per "equivalent cable". The results indicate the following:
1) Restrainer forces generally decreased as the number of restrainers was reduced. This
was particularly clear at Hinge 2 which experienced the largest relative displacement.
The reduction in restrainer forces is attributed to the reduction in the stiffness of the
cables connecting the adjacent superstructure segments.
2) The maximum restrainer forces depended on the input earthquake.
3) Unlike forces, the restrainer stresses generally increased as the number of cables was
reduced. This is because of the reduction in cross sectional area of the restrainers and
the increase in the relative displacements (Fig. 4.8) as the number of cables decreased.
4) The maximum restrainer stresses were below the yield stress of 176.1 ksi in all cases.
However, the cable stresses in Case 5 were close to 85 percent of this limit.
4.3.3 Abutment Displacements
The maximum relative displacements between the abutments and the superstructure are
shown in Fig. 4.11. Note that the values are for displacement that tended to reduce or close the
abutment gap. Because the bridge is considered to be under the extreme low ambient
temperature, the gaps are 1.375 in. (0.115 ft.) and 2.375 in. (0.198 ft.) at Abutments 1, and 2,
respectively. The following trends can be noted:
1) The maximum displacement of the superstructure relative to the abutment was only
slightly affected by the number of restrainers.
2) Different input earthquakes resulted in different maximum displacements. The maximum
displacement in most cases was sufficiently large to close the abutment gap and activate
the back fill soil.
3) The movement at Abutment 2 was always larger than that in Abutment 1 because the gap
in the former was 2.375 in., while in the latter was 1.375 in. The larger gap allowed
the superstructure to move more.
13
4.3.4 Abutment Forces
The maximum abutment back fill forces in the longitudinal direction of the bridge are
shown in Fig. 4.12. Note that for the abutment to experience any forces, it is necessary that
the hinge gap at the abutment be closed. The figure indicates the following:
1) The effect of reduction in the number of cables on the abutment forces appears to be
non-uniform. This is true for all three earthquake records, although the pattern varies
from one earthquake to another.
2) The abutment forces were sensitive to the input ground motion. However, in all cases
the forces remained well below the yield force of 1000 kips. The increase in the
abutment gaps and the tightening of the restrainers appears to have reduced the demand
on the abutments.
4.4 Effects of Reduction in the Restrainer Gap
One of the· primary factors considered in the parametric studies was to determine the
effect of reducing the restrainer gap. The design of restrainers according to Ref. 1 is carried
out for the highest ambient temperature with an assumed restrainer gap of 0.75 in. The gap can
reduce to zero during low temperatures due to the contraction of the superstructure. The results
presented in Sec. 4.2 and 4.3 are compared and discussed in this section. To facilitate the
comparisons, the envelopes of the results for different earthquakes are considered. These
envelopes present the largest of the response maxima caused by different input ground motions.
4.4.1 Hin" Movements
Figure 4.13 shows the maximum relative superstructure displacements adjacent to each
hinge. It can be observed that, by eliminating the restrainer gap, the displacements were
sensitive to the number of cables. The results for Case 6, in which no restrainers were
present, show that the relative displacements would exceed the permissible movement of 0.125
ft. at all hinges, and would potentially lead to the collapse of the superstructure. The beneficial
effects of using a large number of restrainers (Cases 1 to 3) to reduce hinge movements is
realized only when the restrainer gap is zero.
The most critical relative hinge movements may correspond to zero or a non-zero
14
restrainer gap depending on the number of restrainers. An improved design method would need
to account for both the extreme temperature conditions to determine the maximum hinge
movements.
4.4.2 Restrainer Forces and Stresses
The total restrainer forces and stresses are compared for different hinge gaps in Figs.
4.14 and 4.15, respectively. It can be seen that the forces generally tend to decrease when the
number of cables is reduced regardless of the gap. The reduction in the stiffness of the
connection between the adjacent superstructure segments is believed to cause the decrease in the
force. The slight deviations from this trend observed in Hinge 1 and 3 are due to the fact that
the bridge model is nonlinear and effects can not always be explained using elastic theory. The
forces corresponding to no restrainer gap condition were always considerably higher than those
in cases with a gap.
Figure 4.15 shows that restrainer stresses are sensitive to the number of cables when no
gap is present. A reduction in the number of cables generally increased the magnitude of
stresses. The maximum stress at hinge 2 in Case 5 reached nearly 85 percent of the yield stress.
The data clearly indicate that the most critical condition for cable stresses is when the restrainer
gap is reduced to zero due to low temperatures.
4.4.3 Abutment Displacements
The envelopes of the maximum closing relative displacements between the superstructure
and the abutments are shown in Fig. 4.16. In all cases, the superstructure moved sufficiently
to close the abutment gap. Note that the gap in Abutment 2 is nearly twice that in Abutment
1. The presence or the number of the cables did not appear to influence the movements. The
relative displacements for the low temperature condition (no restrainer gap) were always higher.
This is due to the fact that the abutment gap is larger by 0.375 in. for this condition. Therefore,
larger displacements are allowed before the abutment gap is closed.
4.4.4 Abutment Forces
The larger openings at abutments in cold temperatures resulted in generally smaller forces
15
in the back fill soil (Fig. 4.17). This is evident in both abutments, although it is very
pronounced in Abutment 2 where the gap is larger. Abutment 2 yielded regardless of the
number of cables when the restrainer gap was 0.75 in. Considering the fact that the trend was
not uniform at Abutment 1, it is concluded that to determine the most critical abutment forces,
it is necessary to analyze the bridge for both the extreme cold and extreme high ambient
temperature condition.
4.5 Concluding Remarks
The results presented in this chapter pointed out the need to consider the extreme low
ambient temperature condition (zero restrainer gap) to determine critical restrainer stresses. The
maximum relative superstructure displacements at hinges and abutments, however, may develop
for the case of zero or non-zero restrainer gap depending on the number of restrainers. It is
therefore recommended that the design of restrainers include both the extreme high and low
temperatures conditions.
The current design procedure [1] predicted that Hinge 2 will experience the minimum
relative displacement, and hence, the lowest number of restrainers was used at this hinge. The
dynamic results presented in this Chapter, however, showed that Hinge 2 would experience the
largest amount of displacement among the three hinges. The design method described in Ref.
1 needs to be modified to better represent the dynamic behavior of the bridge.
16
Chapter 5
SENSITIVITY OF THE EQUIVALENT STATIC DESIGN RESULTS
TO CHANGES IN DESIGN ASSUMPI10NS
5.1 Introductory Remarks
The equivalent static analysis method for restrainer systems is intended to be a rational
yet practical procedure for manual design of hinge restrainers [1]. The primary features of the
method were discussed in Chapter 2. Several simplifying and judgmental assumptions are
incorporated in calculating the effective stiffness and mass which in turn influences the effective
vibration period of different frames or groups of frames. Furthermore, the initial restrainer gap
is assumed to be 0.75 in. which corresponds to extreme high ambient temperature.
The purpose of the study presented in this chapter was to determine the effect of (1) the
changes in the way the effective stiffness and mass is calculated and (2) the elimination of the
restrainer gap. The criterion to measure the effect of these variations is the number of required
restrainers. The example bridge presented in Ref. 1 (Fig. 2.1) was used to illustrate the effects.
The design procedure and the properties used in the study were the same as those in Ref. 1
except as noted.
5.2 Influence of Changes in the Stiffness
To determine the movements that must be resisted by hinge restrainers, the bridge
structure on each side of the hinge is considered separately. A "frame" is defined as the part
of the bridge which is in between two adjacent hinges, or is between a hinge and the adjacent
abutment. On each side of each hinge, the movement of the frame away from the hinge is
considered. As the frame moves away from the hinge, it closes the gap at an adjacent hinge,
thus mobilizing a second frame. If the displacement continues to increase, another hinge may
close which leads to the mobilization of a third frame or the abutment. The design method [1]
accounts for the closure of only one adjacent hinge and permits the mobilization of only one
adjacent frame. This assumption is intended to be conservative and simple. It is also assumed
that the mass for only one frame should be used in computing the effective period of vibration
17
for the segments, even though more than one frame may be mobilized. The purpose of this
section is to discuss the effect of allowing more than one adjacent frame to contribute to stiffness
when displacements are sufficiently large to permit gap closure. The mass calculation in this
section followed the procedure used in Ref. 1.
Two cable lengths of 5 ft. and 7 ft. are considered in the design example. The maximum
restrainer "deflections" for these are 1.81 in. and 2.25 in., respectively, including a restrainer
gap of 0.75 in. At either side of each hinge, the movement of the bridge segment is considered
and the force-displacement relationship is plotted. The effective stiffness of each segment (or
segments, when the gap at the adjacent hinge closes) is the slope of the line connecting the origin
to the point on the curve corresponding to the maximum restrainer elongation. Figure 5.1 shows
the stiffness chart for the left side of Hinge 1 as it is presented in Ref. 1 and as refined in this
study. The differences between Charts (a) and (b) are:
1) Chart (b) uses a stiffness of 1100 k/in which is specified for this frame in Ref. 1, while
Chart (a) rounds this stiffness down to 1000 k/in.
2) Upon closure of the gap (part "c" on the Chart), Chart (b) adds the abutment stiffness
to the frame stiffness, whereas in the original design, the abutment stiffness is used for
the total stiffness.
The consequence of the above modifications is that the effective stiffnesses in Chart (b)
are approximately ten percent larger than those in Chart (a).
The differences are more pronounced when the movement of the bridge to the right of
Hinge 1 is considered (Fig. 5.2). Chart (b) accounts for the fact that at a displacement of 1.5
in. both Hinges 2 and 3 are closed and all three frames move together. As a result the refined
effective stiffnesses are 20 percent and 29 percent larger than those in Ref. 1 for the 5-ft. and
7-ft. cables, respectively.
A more accurate plot of stiffnesses in Fig. 5.3 for movement on the left side of Hinge
2 led to an increase in the equivalent stiffness of 26 percent and 11 percent for the 5-ft. and 7-ft.
cables, respectively. The differences for movement on the right side, however, are only 4
percent or less (Fig. 5.4).
When movement of the bridge on the right side of Hinge 3 is considered (Fig. 5.5) and
the 5-ft. cables are used, the equivalent stiffness is the same in both Charts. For the 7-ft. cable,
18
however, the abutment is mobilized. In the refined analysis, the abutment stiffness was added
to the frame stiffness, while in Ref. 1 the abutment stiffness was substituted for the total stiffness
of the frame and the abutment. The result was an increase of 9 percent in the equivalent
stiffness corresponding to the 7-ft. cable.
Following the above refined stiffnesses and the procedure used in Ref. 1, the restrainers
were designed and checked to insure that the maximum displacements are within the permissible
limits. The number of required ten-cable units of 3/4 in. cables is shown in Table 5.1. Column
3 in the table lists the number of units as determined in the original design. It can be seen that
the refinements in the equivalent stiffnesses led to a significant reduction in the number of
required cables, especially for the 7-ft. cables.
5.3 Influence of Changes in Stiffness and Mass
When hinge gaps are closed as a result of the movement of one or more frames, it is
reasonable to assume that the effective period is affected by both the stiffness and mass of all
the segments. In calculating the cable forces in between the segments, however, the mass of
individual segments need to be used. The design method of Ref. 1 uses the mass for only one
segment even in computing the effective period of two segments. To determine the effect of
changing the mass to the total mass of all the contributing segments, the restrainers in the
example bridge were redesigned. The modified stiffnesses discussed in Sec. 5.2 were used. The
number of required restrainers is shown in Col. 5 of Table 5.1 for different hinges. Hinge 1
did not need a restrainer when 7-ft. cables were used. It can be observed that, by changing the
treatment of the mass, the number of cables is reduced drastically. The general explanation for
this reduction is the fact that added masses increased the effective period considerably. The
period elongation, in tum, reduced the acceleration response spectrum (ARS) value, and the
reduced ARS led to smaller displacements. Because restrainers are designed to control relative
movements at hinges, smaller displacements required fewer cables.
5.4 Influence of Reducing Restrainer Gap to Zero
During the extreme low ambient temperatures, the superstructure segments become
shorter. As a result, the restrainer gap may diminish while the hinge and abutment gaps may
19
increase. When restrainer gap in the example bridge is reduced to zero~ the gap will increase
to 1.5 in.~ 1.375 in.~ and 2.375 in. in hinges~ Abutment 1~ and Abutment 2~ respectively.
(Recall that during the hottest ambient temperature~ the gaps in the hinges~ abutment 1~ and
abutment 2 were 0.75 in. ~ 1 in. ~ and 2 in. ~ respectively) This will reduce the allowable cable
"deflection" and the seat width to maintain a 3-in. minimum bearing. The effect of these
changes on the number of required restrainers is presented in this section.
The maximum cable deflection is 1.06 in. for the 5-ft. cable and 1.48 in. for the 7-ft.
cable. The maximum allowable movement is 1.5 in. in order to maintain a minimum seat width
of 3 in. Figures 5.6 to 5.10 show the stiffness charts for different conditions. It can be seen
that because of the small permissible cable deflections and because of large hinge gaps~ none of
the gaps can be closed without yielding the restrainers. As a result~ each segment of the bridge
oscillates individually.
As expected~ a large number of restrainers are required to limit the displacements to the
above levels. Column 6 in Table 5.1 shows the results of the design. It can be seen that the
numbers are substantially higher than those of other conditions~ suggesting that the critical
condition for the design of restrainers is when the restrainer gaps are zero.
5.5 Concluding Remarks
The results discussed in Sec. 5.2 and 5.3, indicate that the simplifying and judgmental
assumptions made in the design of restrainers can greatly change the outcome of the design
method presented in Ref. 1. The high degree of sensitivity of the results to these assumptions
strongly suggests that an alternate design method may have to be developed.
The considerable increase in the required number of cables as a results of the elimination
of the restrainer gaps shows that the worst condition for restrainer design is under low ambient
temperatures. This conclusion is in complete agreement with the observations in the results of
the nonlinear analyses presented in Chapter 4.
20
Chapter 6
SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS
6.1 Summary
The primary objective of this study was to develop an understanding of the implications
of Caltrans' current hinge restrainer design practice. Two aspects of the problem were studied.
One was the effects of changing (a) the cross sectional area of restrainers and (b) the restrainer
gap on the nonlinear response of a bridge with several hinges. The other was the sensitivity of
the number of required restrainers to changes in some of the simplifying assumptions which are
made in the restrainer design method. In all the studies, the example bridge described in the
Caltrans design manual [1] was used as the reference case. The study was limited to the
longitudinal response of straight bridges which utilized cable restrainers.
The compu~er program NEABS-86 was used in the nonlinear analyses [3]. The focus of
this part of the study was the relative displacements at the joints, restrainer forces, and restrainer
stresses. The level of displacement ductility demand in the piers was also examined to identify
the extent of nonlinearity. Three earthquake records, the El Centro 1940, Eureka 1954, and
Saratoga 1989, were used to insure that conclusions reflect the effects of a collection of
earthquakes with different response spectra. In addition to the input earthquake, the number of
restrainers at each hinge, the restrainer gap, and the hinge gap were varied. Only longitudinal
bridge response was considered to be consistent with the design method.
To study the effects of simplifying assumptions incorporated in the design method on the
required number of cables, several manual calculations of the example in the Caltrans restrainer
design guidelines were carried out. The general procedure was the same as that outlined in Ref.
1. The deviations from the method included the treatment of mass and stiffness of bridge
segments as different hinges closed. Another variable was the simultaneous the reduction in the
restrainer and increase in the hinge gap. This condition would represent the effect of low
ambient temperatures on the gaps.
21
6.2 Conclusions
The following conclusions were drawn based on the results of the study.
6.2.1 Conclusions from the Nonlinear Analyses
I) The relative hinge displacements are insensitive to the changes in the number of cables
when restrainers have a gap. When the restrainer gap was eliminated, the relative
displacements reduced as a result of an increase in the number of restrainers.
2) The equivalent static analysis method does not necessarily represent the dynamic response
of the bridge. In the example bridge, the former predicted the least displacement at the
middle hinge while the dynamic result showed that this hinge would experience the
largest maximum relative displacement.
3) Unlike forces, the restrainer stresses were generally insensitive to the number of cables
when a restrainer gap of 0.75 in. was present. When the gap was reduced to zero, a
reduction in the number of restrainers increased the restrainer stresses.
4) The maximum displacement of the superstructure relative to the abutment was not
affected by the number of restrainers regardless of the restrainer gap.
5) Abutment forces are sensitive to the input ground motion. Therefore, it is necessary that
the bridge be analyzed for a variety of earthquake records representing the characteristics
of the site at which the bridge is located.
6) The use of computer program NEABS for nonlinear earthquake response history analysis
is very cumbersome. The nonlinearity of boundary elements has to be 3.1tificially
modeled by assumptions that do not represent the true behavior. In addition, the
program is outdated in terms of software development techniques. A simpler, more
realistic computer program for nonlinear seismic response history analysis of bridges is
urgently needed.
6.2.2 Conclusions from the Redesigns of the Example Bridge
1) When a restrainer gap of 0.75 in. was present, changes in the equivalent stiffnesses led
to a significant reduction in the number of required restrainers, particularly for 7-ft.
cables.
22
2) By changing the treatment of the mass in the restrainer design method, the number of
cables were reduced drastically. This was for the restrainer gap of 0.75 in.
3) The number of required hinge restrainers became substantially higher when the restrainer
gap was reduced to zero.
6.3 Recommendations
The results presented in this report pointed out the need to consider the extreme low
ambient temperature condition (zero restrainer gap) to determine critical restrainer stresses. The
maximum relative superstructure displacements at hinges and abutments, however, may develop
for the case of zero or non-zero restrainer gap depending on the number of restrainers. It is
therefore recommended that the design of restrainers include both the extreme high and low
temperatures conditions.
The current design procedure [1] predicted that Hinge 2 will experience the minimum
relative displacement, and hence, the lowest number of restrainers was designed at this hinge.
The dynamic results presented in this report, however, showed that Hinge 2 would experience
the largest amount of displacement among the three hinges. The design method described in
Ref. 1 needs to be modified to better represent the dynamic behavior of the bridge.
The results discussed in Sec. 5.2 and 5.3, indicate that the simplifying and judgmental
assumptions made in the design of restrainers can greatly change the outcome of the design
method presented in Ref. 1. The high degree of sensitivity of the results to these assumptions
strongly suggests that an alternate design method may be need.
The considerable increase in the required number of cables as a result of the elimination
of the restrainer gaps shows that the worse condition for restrainer design is under low ambient
temperatures, if the current Caltrans restrainer is to be used. A more rational nonlinear dynamic
analysis would need to consider both zero and non-zero restrainer gaps to determine the critical
forces at abutments as well as restrainers.
23
REFERENCES
1. tlSeismic Design References" State of California, Department of Transportation Divisionof Structure, July, 1990, and the Restrainer Design Example Update, July 1991.
2. Saiidi, M., E. Maragakis, S. Abdel-Ghaffar, and D. O'Connor, "Effect of HingeRestrainers on the Response of Highway Bridges during the Lorna Prieta Earthquake, "Proceedings, Third Workshop on Bridge Engineering Research in Progress, San Diego,California, November 1992.
3. Saiidi, M., G. Ghusn, and Y. Jiang, tlFive-Spring Element for Biaxially Bent RICColumns," Journal of Structural En~ineerin~, ASCE, Vol. 115, No.2, February 1989,pp. 398-416.
4. tlEarthquake Resistant Bridge Bearing, Vol. 2, NEABS Computer Program" U.S.departmentofTransportation, Federal Highway Administration, FHWA/RD-82/166, May1983.
5. Kawashima K. and J. Penzien, "Correlative Investigations on Theoretical andExperimental Dynamic Behavior of a Model Bridge Structure" Report No. 76-26,Earthquake Engineering Research Center, University of California, Berkeley, July 1976.
24
Table 3.1 - Maximum Relative Displacements (ft)(t= Time interval for integration)
Time t=0.02 t=O.Ol t=0.OO5 t=0.OO2 t=O.OOlInterval (sec.) (sec.) (sec.) (sec.) (sec.)
Abut. 1 0.1803 0.1572 0.1569 0.1568 0.1568
Hinge 1 0.1237 0.07066 0.07084 0.06744 0.06718
Hinge 2 0.1038 0.08653 0.07567 0.07508 0.07499
Hinge 3 0.0751 0.08424 0.07109 0.06864 0.06848
Abut. 2 0.2176 0.2230 0.1993 0.1928 0.1931
Table 3.2 Number of Cables in Different Cases
CASE NO. NUMBER OF CABLES
HINGE 1 HINGE 2 HINGE 3
1 8X10 6XlO 10X10
2 7XlO 5XlO 9XlO
3 6XlO 4XlO 8XIO
4 5X10 3XlO 7X10
5 4X10 2XIO 6XlO
6 0 0 0
25
Table 5.1 - Number of Required Ten-Cable Unitsfor Different Analyses
-
(1) (2) (3) (4) (5) (6)HINGE CABLE REF. 1 MODIFIED MODIFIED ZERO
LENGTH EQ. STIFF. EQ. STIFF. REST. GAP(ft.) & MASS
1 5 10 9 4 157 8 5 - 13
2 5 12 9 7 157 7 5 2 14
3 5 13 11 6 167 11 10 2 15
26
3/4" GAP3/4' GAPI' GAP 314' GAP
Ii t1 Ii n DtAPHRAGM-TYPEII \01=4,0001< II \oI=3,aOOI< II \oI=4,.400K "'=~,OOOK ABUTMENT
SEAT-~JT~ -.-----.- nlzjABUTME~~~1 1 1 1
J<-15_'f-!_100_'--i!~1-,-5'+=-~1=-2'~__1_00_'----.}~ 22" } 100' ~10'~ 100'
Fig. 2.1 - The Elevation of the Example Bridge (Ref. 1).
3" MIN.EDGE
DISTANCE
MIN.AVAILABLE
SEAT
SUPERSTRUCTURE
6' HINGE SEAT~NGE
GAP
---------
Fig. 2.2 - The Hinge Detail in the Example Bridge.
27
12 3
1920
2122
-4 567
2324
2526
8 910 11
27 228 30
12 131415
3132
16 1718
3334
Fig. 3.1 - Node Numbers in the NEABS-86 Model.
1
(2)31
2 2
1
31
2 2
3
2
1
2
3
2 2
(2)3
1 - lIneQr StrQignt Bea.M EleMent)
2 - FIve Spring BendIng Elel"\en1:J
3 - Nonlinenr EXPQnSIOn Joint EleMent]
Fig. 3.2 - Element Types in the NEABS-86 Model.
28
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f-
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-
-
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(b) Force at Hinge 2
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30
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.....+l4-l 0.2
p.U'l 0.'
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,..-l
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Fig. 4.2 - Response at Abut. 2 due to the El centro Earthquake.
31
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thq
uak
esa
rato
ga
Ear
thq
uak
e
Fig
.4
.4-
Max
imum
Rest
ra
iner
Fo
rces
(Rest
ra
iner
Gap
=O
.75
in.)
.
•H
ING
E3
oH
ING
E2
0
~0
255
00
500
00
0flJ
HIN
GE
10
0r-
.0
(\J
2040
•H
ING
E3
40Z
00
00
0o
HIN
GE
2
f
•H
ING
E3
........
.........
15•
30~
HIN
GE
130
oH
ING
E2
~•
'-/
•()
0(6
HIN
GE
1•
•10
20t>
20(/
)(/
)•
05
0'"
10e
•10
W•
~•
0,0
~0
l-0.
00
0,0
i•
•e
~L
V0
00
"'"(/
)
-5-1
0-1
0
01
23
45
60
12
34
56
01
23
45
6
CASE
NO
.CA
SEN
O.
CASE
NO
.
EL
-Cen
tro
Ear
thq
uak
eE
ure
ka
Ear
thq
uak
eS
ara
tog
aE
arth
qu
ake
Fiq
.4
.5-
Max
imum
Rest
ra
iner
str
esses
(Rest
ra
iner
Gap
=O
.75
in.)
.
-0.2
0l
-0.2
0I
I-0
.20
••
••
••
-0.1
8t
-0.1
8•
••
••
•-0
.18
'" +'-0
.16
I•
••
••
•4
--0
.16
•A
BU
T.2
-0.1
6'"
•A
BU
T,2
0...
-0.1
4o
AB
UT.
1-0
.14
oA
BU
T.1
-0,1
4[
V?
•A
BU
T,
2.....
-0,1
2o
AB
UT
.1
Q-0
.12
-0.1
2
w<
[-0
.10
-0.1
0-0
.10
VI
...J
00
00
0W
00
00
00
0-o
.oe
l0
00
00
0~
-0.0
8-0
,08
01
23
45
60
12
34
56
01
23
45
6
CASE
NO
,CA
SEN
O.
CASE
NO
,
EL
-Cen
tro
Eart
hq
uak
eE
ure
ka
Ear
thq
uak
eS
ara
tog
aE
arth
qu
ake
Fig
.4
.6-
Max
imum
Rela
tiv
eA
bu
tmen
tD
isp
lacem
en
ts(R
est
ra
iner
Gap
=O
.75
in.)
.
12
00
1200
•A
BU
T.
2"-
oA
BU
T,
1lJ
l10
00•
••
••
•10
005
00
[0
.•
••
•A
BU
T,
2•
..Y8
00
••
40
0o
AB
UT
,1
'-/
•A
BU
T.
28
00
W6
00
oA
BU
T.
16
00
0
I3
00
U0
~0
00
20
0I
"0
00
0"
04
00
400
u...
00
w2
00
00
20
0I
100
L•
••
••
•O
'l0
00
o1
23
45
6
CA
SE
NO
.
EL
-Cen
tro
Ear
thq
uak
e
a1
23
45
6
CA
SE
NO.
Eu
rek
aE
arth
qu
ake
o2
34
56
CA
SE
NO
.
sara
tog
aE
arth
qu
ake
Fig
.4
.7-
Max
imum
Ab
utm
ent
Fo
rces
(Rest
ra
iner
Gap
=O
.75
in.)
.
0.15
•H
ING
E3
0.15
•H
ING
E3
00.
15•
HIN
GE
30
0o
HIN
GE
2o
HIN
GE
2I"
".o
HIN
GE
2•
•of-
>o
HIN
GE
1•
4-
"H
ING
E1
0o
HIN
GE
1.....
..0.
100.
10a
a0.
100
0-
0a
e
VI
aa
00
0a
ig
......
00
S0
Q0
i0
0.05
00.
05;
"i
•0.
05•
0"
•0
w<
I:0
•-..
.1-..
.1•
••
••
••
W ~0.
0\
I0.
0I
I0.
0,
,I
,,
.,
,,
.I
.0
12
34
56
01
23
45
60
12
34
56
CASE
NO.
CA
SEN
O.
CASE
NO
,
EL
-cen
tro
Ear
thq
uak
eE
ure
ka
Ear
thq
uak
eS
ara
tog
aE
arth
qu
ake
Fig
.4
.8-
Max
imum
Rela
tiv
eD
isp
lacem
en
tsa
tH
ing
es(R
est
ra
iner
Gap
=Oin
.).
50
050
050
0•
HIN
GE
3
'"0
00
oH
ING
E2
l/)
400
040
040
0o
HIN
GE
1Q
.0
00
¢l
.::t.
30
00
300
ev
030
00
0i
i•
ew
20
0•
0~
0e
0•
••
200
•0
20
0j
U,
••
••
~10
010
010
00
•H
ING
E3
•H
ING
E3
u...
oH
ING
E2
oH
ING
E2
w0,
00.
0o
HIN
GE
1I
0,0
OJ
oH
ING
E1
-10
0-1
00-1
00
0'
12
34
56
01
23
45
60
12
34
56
CA
SE
NO
,C
AS
ENO
,C
AS
EN
O.
EL
-Cen
tro
Ear
thq
uak
eE
ure
ka
Ear
thq
uak
esa
rato
ga
Ear
thq
uak
e
Fig
.4
.9-
Max
imum
Rest
ra
iner
Fo
rces
(Rest
ra
iner
Gap
=o
in.)
.
150
015
0I
150
~0
0A
0
nz0
00
0
-0
00
100
00
"10
010
00
00
00
0•
0~
00
"-/
•0
0•
•(/
)0
0•
•0
i0
•(/)
50•
••
•H
ING
E3
50•
HIN
GE
350
•W
•o
HIN
GE
2•
••
HIN
GE
3w~
oH
ING
E2
'!l
I-
oH
ING
Et
oH
ING
E2
(.I)
oH
ING
E1
oH
ING
E1
01
23
45
60
12
34
56
01
23
45
6
CASE
NO
.CA
SEN
O.
CA
SEN
O.
EL
-cen
tro
Ear
thq
uak
eE
ure
ka
Ear
thq
uak
eS
ara
tog
aE
arth
qu
ake
Fig
.4
.10
-M
axim
umR
est
ra
iner
str
esses
(Rest
ra
iner
Gap
=o
in.)
.
-0.2
0l
••
••
••
I-0
.20
••
•-0
,201
••
••
••
~-0
.18
t-0
,18
•-0
.18
+'
•A
BU
T.2
••
4-
-0.1
6-0
.16
•A
BU
T.2
-0.1
6f
•A
BU
T.2
'-/
oA
BU
T.1
oA
BU
T.1
-0.1
40
AB
UT.
1a...
-0.1
4L
-0.1
4
"">-4
-0.
12l
-0.1
2t
00
-0.1
2~
p0
00
00
00
00
00
00
00
0
"'"<
[-0
,10
l-0
.10
-0.1
00
....J w
-0.0
81.
I-0
.08
1I
-0,0
8~
..
,.
.,
I.
!I
I
0.
12
34
56
01
23
45
60
12
34
56
CA
SE
NO
.C
AS
EN
O.
CA
SE
NO
.
EL
-Cen
tro
Ear
thq
uak
eE
ure
ka
Ear
thq
uak
eS
ara
tog
aE
arth
qu
ake
Pig
.4
.11
-M
axim
umR
ela
tiv
eA
bu
tmen
tD
isp
lacem
en
ts(R
est
ra
iner
Gap
=Oin
.).
1200
1000
•A
BU
T.2
500
00
"0
lfl
1000
800
oA
BU
T.
140
00
-0
..Y8
00
•A
BU
T.
260
03
00
0'-
"o
AB
UT
.1
00
00
w6
00
400
00
200
0
U•
AB
UT
.2
•~
40
02
00
100
oA
BU
T.
10
00
•e
u...
i•
0•
20
0•
•0
a.j:
>i
••
••
••
••
I->
0•
-20
0I
..
..
.I
I-1
00
01
23
45
61
23
45
61
23
45
6
CASE
NO.
CASE
NO
.CA
SEN
O,
EL
-Cen
tro
Ear
thq
uak
eE
ure
ka
Ear
thq
uak
eS
ara
tog
aE
arth
qu
ake
Fig
.4
.12
-M
axim
umA
bu
tmen
tF
orces
(Rest
ra
iner
Gap
=o
in.)
.
0.15
0,15
•I
0.15
"-
0.10
[
•+
'o
RT,
GA
P=
3/4
'~
•o
RT.
GA
P=
3/4
"'\
.../
0,10
•R
T.G
AP
=Q
'0,
10e
0•
RT,
GA
P=O
vci
00
0i
•(.
/)0
0~
••
I-i
0•
••
0
0.05
f0
00
0•
0q
••
-0,
050
.05
•<I
:o
RT,
GA
P=
3/4
'•
J:>~
•N
W•
RT,
GA
P=O
"0::
::0,
00,
00,
0
01
23
45
60
12
34
56
01
23
45
6
CA
SE
NO
,C
AS
EN
O,
CA
SE
NO
,(H
ING
ED
(HIN
GE
2)
(HIN
GE
3)
Fig
.4
.13
-M
axim
umR
ela
tiv
eD
isp
lacem
en
tsa
tH
ing
es.
20
00
oR
T.G
AP
=3
/4v
1500
oR
T.G
AP
=3
/4v
I2
50
0
/""0
.•
RT,
GA
P=O
"•
•R
T.GAP=O~
1!I16
00•
•12
00•
2000
r:RT
GA
P:3
:4'
_9-
••
.::t:.
1200
1500
RT.
GA
P-O
\../
900
••
••
••
•W
80
060
00
•10
00•
U0
Ck:
0
04
00
300
05
00
00
0
I0
LL0
00
0,j:
:>0.
00.
00
00
w0,
0
-40
0I
,,
,,
I,
I-3
00
-50
0
01
23
45
60
12
34
56
01
23
45
6
CASE
NO
,C
ASE
NO
,C
ASE
NO
,
(HIN
GE
1)
(HIN
GE
2)
<HIN
GE
3)
Fig
.4
.14
-M
axim
umR
est
ra
iner
Fo
rces.
150
oR
T.G
AP
=3
/4'
150
•15
0,....
•R
T,G
AP
=O
"o
RT,
GA
P=
3/4
'(\j
•Z
••
RT,
GA
P=Q
Vt-1 '"
••
•10
0~
100
••
•10
0•
'-"
•o
RT
.G
AP
=3
/4V
•(I
)•
RT.
GA
P=
O'
•(/
)•
5050
00
50w
00
0•
fr:
"""f-
~0
0"""
(I)
0
II
II
00
00
00
0I
.,
,.
.I
,I
,I
,
01
23
45
60
12
34
56
01
23
45
6
CASE
NO
.C
ASE
NO
,C
ASE
NO
,(H
ING
ED
(HIN
GE
2)
(HIN
GE
3)
Fig
.4
.15
-M
axim
umR
est
ra
iner
str
esses.
-0,1
8L
oR
T,G
AP
=3
/4A
I-0
.20r
e•
••
••
00
00
0
"-0
.16
-0.1
8-P
•R
T.G
AP=O
A4
--0
,14
1-0
.16
'-/
0-
-0,1
2•
••
••
-0.1
4~
oR
T,G
AP
=3
/4A
•(/
)•
RT,
GAP
=OA
~ l=1
-0,1
0-0
,12
00
00
00
.l'><t
-0,0
8I
-0.1
0V
1-.
J w-0
,06
1I
-0,0
8n::
,,
.,
,,
01
23
45
60
12
34.
56
CA
SE
NO
,C
AS
EN
O,
(AB
UT
ME
NT
D(A
BU
TM
EN
T2)
Fig
.4
.16
-M
axim
umR
ela
tiv
eA
bu
tmen
tD
isp
lacem
en
ts.
Fiq
.4
.17
-M
axim
umA
bu
tmen
tF
orc
es.
Hin
ge
ID
esig
nF
ra
m.
Im
ov
ing
aw
ay
fro
mH
Im
ob
iliz
In
ga
bu
tm.n
tI.
HIN
GE
1D
ES
IGN
f"ro
ne
IM
ov
ing
nw
o.y
f('O
MH
I
Mo
bil
iZin
ga
bu
tMe
nt
1
I·o
ap
LA
A/L
Jr
W~k
~yy
y~TTrame
IK
=S
OO
Ok/ln
'H
\F
ma
x=
IOO
Ok
AI
11
00
k/l
n
-i"f
\.I=
40
00
K
r-M
!'-L
:jl:
H\
1l00
k/1n
K=S
OO
Ok/'
nF
nQ
x=I
OO
Ok
Fra
ne
I
60
00
5I
1213
4IA
but.1
Dr7
=2.
25"
I'g
op
DrS
=1.
8!"
DIS
P.
(;n
)
a
1000
4000
II
I/1
/1
I
50
00
II
II
/1
I
"- Vl
Q.
~30
00I
~~
II
-U
VV
'""'I
\~
I·
w u [520
00L.
..
Li(
fn
)0"
5'=
•.8
1"
40
00
-;;3
00
0
W u a:
"'"0
-..J
h.
20
00
10
00
Eq
uiv
ale
nt
Stl
ffn•••
:
®W
llh
5'
ca
ble
s_
Z70
0'>
{1
50
0k/l
n-
T:8
I-
®W
llh
7'
ca
ble
s=
.310
0'¥
14
00
k/i
n2
.25
©A
bu
tme
nt
Sti
ffn
es
s=
50
00
k/i
n
Eq
uiv
ale
nt
Sti
ffn
es
s'
®\.
lith
5'
ca
ble
s=~
=1
65
3k/'
n1.
81
®\l
ith
7'
ca
ble
s=
~4;i
=1
54
4k/'
n
©S
t'ff
ne
ss
=6
10
0k/'
n
(a)
orig
ina
lD
esi
gn
(b)
Refi
ned
Desi
gn
Fig
.5
.1-
sti
ffn
ess
for
Mov
emen
to
fth
eB
rid
ge
on
the
Left
Sid
eo
fH
ing
e1
.
Hin
ge
I&
3D
esig
ns
Fro
me
2m
ov
ing
aw
ay
fro
mH
Ic
los
ing
H2
an
dm
ob
iliz
ing
Fro
me
3.
J"
4g
op
HIN
GE
1&
.3D
ES
IGN
S
r,..
.on
e2
nO
vio
ga
wa
yfr
"'O
MH
.l
clo
sin
gH
2a
nd
Mo
bil
izin
gfr
o.n
e3.
clo
sin
gH
3Q
odM
ob
iliz
ing
fro
.Me
4.
HI 11
00
kiln
Fram
e3
H3 1
10
0kiln
J/4
'9G
P
HI
V=3
BO
OK11
1""r
--r-
----
r-H
2r=
44
00
KI
!1'
....,.
H3
\J=
4000
K
frn
ne
2~,~
I1::
:fr
oM
.e3
1l00
k/ln
fra
ne
-4
54
32 ,
,Dr
7=
2.2
5'
DrS
=1.
81'
DIS
P(I
n)
1
~ 3/4
'3
/4'
a
1000
5000
4000
6000
~
\Il 0. o3
000
w u g§20
00I
,41
,III
II
II
1.L
-r'-
3
ll.(
inO
rs'=
1.8
1"
.00
0
30
00
w U 0: 02
00
0",
10
00
ol'>
CD
Eq
ui
....o
len
tS
tiff
ne
ss
:
®W
i't>
S'
ca
bl
es
=2
90
0'?
!1
60
0k
/in
1,8
1
®W
itt>
.380
01
70
0T
ca
ble
s=--
'?!k
/in
2.2
5
(a)
orig
ina
lD
esi
gn
EQ
viv
ole
n't
St:
ffn
es
s:
®I.
nth
5'
cn
ble
s=
34
98
=1
93
3kiln
1.81
®\.
lith
7'
cn
ble
s=
49
50
=22
00kiln
2.2
5
©S
tiff
ne
ss
=2
20
0k/;
n
@S
tiff
ne
ss
=33
00k/;
n
(b)
Refi
ned
Desi
gn
Fig
.5
.2-
sti
ffn
ess
for
Mov
emen
to
fth
eB
rid
ge
on
the
Rig
ht
sid
eo
fH
ing
e1
.
Hin
ge
2D
esig
nF
ro
m.
2m
ov
ing
aw
ay
for
HZ
clo
sin
gH
Im
ob
Iliz
ing
Fra
me
,&.
Ab
utm
ent
I.
4'..~"gop
LM~~nr
W,=
38
00
k~
IYY
Fram
eI
---
K=
SO
OO
kiln
/T
$ro
me
Zfm
ox=
IOQ
Ok
AI
HI
HZ
11
00
kiln
11
00
kiln
HIN
GE
2D
ES
IGN
frO
Me
2M
ov
ing
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an
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ob
iliz
ing
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Me
1.M
ob
iliz
ing
a.bu
tne
nt
1.
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40
00
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80
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rMf'
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K-5
00
0kiln
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1,,'·1<
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00
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22
78
kiln
19
10
kiln
1(21
34
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go
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rS=
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DIS
P.
(In
)
EQ
Uiv
ale
nt
Sti
ffn
e-s
s:
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;th
5'
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ble
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81
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7'
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ble
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51
25
=2
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(C)S
tlff
n"s
s=
22
00
kiln
o
1000
400
0I
1\/11
II
I
50
00
60
00
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II
III
II
II
C3
00
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w u 152
00
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II
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3
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Eq
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ith
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ble
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15
20
k/i
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81
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ith
46
00
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ca
ble
s=
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50
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o
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i
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00
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10
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(a)
orig
ina
lD
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gn
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ss
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20
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(b)
Refi
ned
Desi
gn
Fig
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ess
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rid
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IGN
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4
11
00
kiln
50
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Eq
uiv
ale
nt
Sti
ffn
ess:
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ith
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co
bl•
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80
0kiln
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7'
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ca
ble
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S=
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kiln
(a)
orig
ina
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gn
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P.(i
n)
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34
5
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o
(b)
Refi
ned
Desi
gn
1000
60
00
50
00
4000
Eq
uiv
o.l
en
tS
-tif
'f'n
es
sl 31
57
@V
lth
5'
ca
ble
s=
--=
17
44
kIl
n1.
81
®V
lth
7'
ca
ble
s=
41
25
=1
83
3kIl
n2
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(C)
Sti
ffn
ess
=22
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n'
w U gj20
00L.
.
VI 0. ;g
3000
No
te:
Ab
utm
ent
.prln
gd
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tb
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me
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ized
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of
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)
Ot"
r=2
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oX
30
00
LU UU
1a:
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20
00
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10
00
Fig
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-sti
ffn
ess
for
Mov
emen
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rid
ge
on
the
Rig
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sid
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ing
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ge
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rom
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GE
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ES
IGN
frO
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ov
ing
o.w
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(,..0
1"'1
H3
clo
sin
gA
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nd
Mo
bil
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ga
bu
tMe
nt
10.
V=
40
00
K-1
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frO
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4~::"~~Il\..
11
00
k/l
n
DrS
=1.
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P.G
n)
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gn
p
V/
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/
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23
45
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ut.
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o
6000
,]I
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00
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~2~~~11
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w U n:: o20
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10
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1000 a
Eq
uiv
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nt
Stl
ffn
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s:
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ith
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eo
ble
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11
00
k/i
nI.
BI
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ith
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co
blo
s=~
'l(
14
20
k/l
n2
.25
EQ
Uiv
ale
nt
Sti
f"F
'ne
ss
:
@V
;th
S'
co
btp
s:;~
=11
00k
/in
1.01
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co.b
les
:3
47
5=
15
44
k/;
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t'ff
ness
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n
(a)
oriq
ina
lD
esi
gn
(b)
Refi
ned
Desi
gn
Fiq
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sti
ffn
ess
for
Mov
emen
to
fth
eB
rid
ge
on
the
Rig
ht
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ing
e3
.
6000
HIN
GE
1D
ESI
GN
1.3
75
'F
hM
J'-I
\.I=
40
00
K
L~HI
Al
K=
50
00
k/i
nn
OO
k/"
,
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X=l
OO
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1
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IM
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ng
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I
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go
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tMe
nt
1
Eq
uiv
o.l
en
tS
tiff
ne
ss: 11
66®
\.lith
5'
Co
.ble
s=--
=H
OO
k/i
n1.
06
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lith
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co
.ble
s=
2 115 84
=1
45
5k/i
n.
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©S
tiff
ne
ss
=61
00kiln
5
f'ro.
.Me
1=
11
00
k/in
43
1.48
#
DIS
P.
(in
)
o_
111
2_
D r5
,=1.
06"
I.Dr7
-
~ 1.3
75
'g
np
5000
4000
/"'. Vl
Q.
~30
00w u gj
2000
1.L
V'1
N
1000
Fig
.5
.6-
sti
ffn
ess
for
Mov
emen
to
fth
eB
rid
ge
on
the
Left
Sid
eo
fH
ing
e1
wh
enR
est
ra
iner
Gap
isZ
ero
.
HIN
GE
1&
3D
ESIG
NS
Fra
Me
2M
ovin
ga
wa
yF
rOM
Hl
ISg
ap
\.I=
38
00
KI
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I=4
40
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HII'-
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1-F
raM
e2
fra
Me
3
Eq
uiv
ale
nt
Sti
ffn
ess: 11
66®
\.lith
5'
ca
ble
s=-
-=
1100
k/i
n1.
06
®\.
lith
7'
ca
ble
s=
16
28
=11
00k/i
n1.
48
5
~fro.Me
2=
11
00
k/in
1o D
rS=
1.06
04I
Dr7
=1.
48
Ihin
ge
21•
•D
ISP.
(in
)1.
5'"g
ap
5000
6000
4000
r.. VI Q C
3000
w u g§20
00L
..(J
l
w
1000
Fig
.5
.7-
sti
ffn
ess
for
Mov
emen
to
fth
eB
rid
ge
on
the
Rig
ht
Sid
eo
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ing
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wh
enR
est
ra
iner
Gap
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ero
.
6000
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GE
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ES
IGN
S
FrO
Me
2M
ovin
go
wo
yF
rOM
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ISgo
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\.,I
=40
00K~
I\.
,I=
38
00
K
---r
---r
-HI-
--r-
--r-
H2~
1!
lUO
Ok
/1n
fro
Me
1fr
oM
e2
Eq
uiV
o.l
en
tS
tiff
ne
ss: 11
66®
\.,l
ith
5'
co
.ble
s=-
-=
HO
Ok/i
n1.
06
®\.
,lit
h7
'co
.ble
s=
16
28
=H
OO
k/i
o1,
485
~fro.Me
2=
11
00
k/in
a_
11I
2_
3If
4DrS
-1.
06Dr7
-1
.48
lhin
ge
1JD
ISP
.<
in)
l.Slfg
o.p
50
00
4000
r-.. VI
Q ~30
00w u gj
20
00
L...
U1 .c.
1000
'Pig
.5
.8-
sti
ffn
ess
for
Mo
vem
ent
of
the
Bri
dg
eo
nth
eL
eft
Sid
eo
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ing
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wh
enR
estr
ain
er
Gap
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ero
.
60
00
HIN
GE
2D
ES
IGN
S
Fro
.Me
3M
ovi
ng
o.w
o.y
frO
MH
2
Eq
uiv
o.l
en
tS
tiff
ne
ss: 11
66
®\.
lith
5'
co
.ble
s=
-=
1100
k/i
n1.
06
®\.
lith
]'
co
.ble
s=
16
28
=11
00k/i
n1,
48
I.S
·g
op
\.I=
44
00
KI
I\.
I=4
00
0K
H2
I1~
~3I
1---
fro
.Me
3fr
o.M
e4
54
/fro
.Me
3=
11
00
k/in
o_
11I
2_
3"
Dr5
-1.
06D
r7
-1.
48
Ihin
ge
31•
DIS
P.
(in
)
1.5"
'go.
p
50
00
40
00
" V\ 0..
~3
00
0w u gj
20
00
L-
V'
V'
1000
Fiq
.5
.9-
sti
ffn
ess
for
Mov
emen
to
fth
eB
rid
qe
on
the
Riq
ht
sid
eo
fH
inq
e2
wh
enR
est
ra
iner
Gap
isZ
ero
.
6000
5000
II
II
II
K&
SOO
O1<
1...
r.....
"&IO
OO
k
C-t
HIN
GE
3D
ES
IGN
S
2.37
S·g
o.p
\/=
40
00
K~
I1I00
k/1nl
fro
.ME
'4
tro
.'''H
?4
Mo
vin
go.
wo.
ytr
OM
H3
Eq
uiV
o.l
eo
tS
tiff
ne
ss:
.11
66®
'Wit
h5
'co
.ble
s=--:::
llOO
k/i
n1.
06
®'W
ith
7'
co
.ble
s=
16
28
=llO
Ok/i
n1
.48
5
/.fr
o.M
E?
4=
11
00
k/i
n
o_
111
2_
3If
4D
rS-
1.06
Dr7
-1.
48
IAbut
.10
j.
•D
ISP
.(i
n)
2.3
7S
'gu
p
4000
r'\ \J'
I 0.
~30
00w u
V1gj
2000
0'1L
..
1000
Fiq
.5
.10
-sti
ffn
ess
for
Mov
emen
to
fth
eB
rid
ge
on
the
Rig
ht
Sid
eo
fH
ing
e3
wh
enR
est
ra
iner
Gap
isZ
ero
.
APPENDIX A - SUMMARY OF RESTRAINER DESIGN METiiOD [1]
1. Maximum permissible restrainer deflection, Q~.
Dr 5' = 1.81" D 7' = 2.25"r
2. Ku = the unrestrained total system stiffness
Where Ku = the equivalent stiffness of the total system
considering the stiffness of all sub-structures
mobilized and any gaps in the system.
3. T = 0.32 x
4. Compute the longitudinal deflection Deq = ARS(W)/Ku (in)
Where 01 = the longitudinal earthquake deflection of the
unrestrained system;
ARS = the acceleration in g. for given period of
vibration, T (sec). Where T = 0.32 X the square
root of (W/Ku ) (Ref. Bridge Design Specifications,
Figures 3.21.4.3 A-D and Section 3.21.6.1);
W = weight of the segment (k);
Ku = the unrestrained system stiffness (k/in)
5. Determine the number of restrainers required.
57
APPENDIX B - SAMPLE NEABS-86 INPUT FOR THE REFERENCE CASE
48 4 37 1 1 2016 11 (I 1 0 1 1 1 0.0 24.0 0.0
2 0.0 24.0 0.0
3 15.0 24.0 0.0
4 115.0 24.0 0.0
5 130.0 24.0 0.0
6 130.0 24.0 0.0
7 142.0 24.0 0.0
8 242.0 24.0 0.0
9 254.0 24.0 0.0
10 254.0 24.0 0.0
11 276.0 24.0 0.0
12 376.0 24.0 .0.0
13 398.0 24.0 0.0
14 398.0 24.0 0.0
15 408.0 24.0 0.0
16 508.0 24.0 0.0
17 528.0 24.0 0.0
18 0 1 0 1 1 1 528.0 24.0 0.0
19 15.0 0.1 0.0
20 1 1 1 1 1 1 15.0 0.0 O.21 115.0 0.1 0.0
22 1 1 1 1 1 1 115.0 0.0 0.0
23 142.0 0.1 0.0
24 1 1 1 1 1 1 142.0 0.0 0.0
25 242.0 0.1 0.0
26 1 1 1 1 1 1 242.0 0.0 0.027 276.0 0.1 0.028 1 1 1 1 1 1 276.0 0.0 0.029 376.0 0.1 0.0
30 1 1 1 1 1 1 376.0 0.0 0.0
31 408.0 0.1 0.0
32 1 1 1 1 1. 1 400.0 0.0 0.033 508.0 0.1 0.034 1 1 1 1 1 1 508.0 0.0 0.035 1 1 1 1 1 1 0.0 24.0 100.036 1 1 1 1 1 1 15.0 24.0 100.037 1 1 1 1 1 1 115.0 24.0 100.038 1 1 1 1 1 1 142.0 24.0 100.039 1 1 1 1 1 1 242.0 24.0 100.040 1 1 1 1 1 1 276.0 24.0 100.041 1 1 1 1 1 1 376.0 24.0 100.042 1 1 1 1 1 1 408.0 24.0 100.043 1 1 1 1 1 1 508.0 24.0 100.044 1 1 1 1 1 1 528.0 24.0 100.045 1 1 1 1 1 1 528.0 24.0 -100.046 1 1 1 1 1 1 130.0 24.0 100.047 1 1 1 1 1 1 254.0 24.0 100.048 1 1 1 1 1 1 398.0 24.0 100.0
58
2 20 2 0 1
1 576000.0 0.18 0.0046581 30.7 44.4 26.0 78.02 200.0 1405.3 416.7 26667.0
0.0-32.0
0.01 19 3 36 1 12 21 4 37 1 13 23 7 38 1 14 25 8 39 1 15 27 11 40 1 16 29 12 41 1 17 31 15 42 1 18 33 16 43 1 19 2 3 36 1 2
10 3 4 37 1 211 4 5 38 1 212 6 7 38 1 213 7 8 39 1 214 8 9 40 1 215 10 11 40 1 216 11 12 41 1 217 12 13 42 1 218 14 15 42 1 219 15 16 43 1 220 16 17 44 1 2
4 2 1 11 60000.0 1-0 1-0 1.0 1.0 1.01 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0
10. 10. 10. 10. 10. 10.1 1 4 35 1 (I
2 18 16 45 1 0C" 7 1 7.J
1 1458.0 1.0 14580.0 1.0 1.0 1.01· 0.0 1.0 0.0625 0.0625 6337.0 792.0
909000. 4-20.0 -10.0 10.0 20.0
2 0.0 1.0 0.0625 0.0625 6337.0 792.0B650oo. 3
-20.0 0.0 20.03 0.0 1.0 0.0625 0.0625 6337.0 792.0
843000. 5-20.0 -10.0 0.0 10.0 20.0
4 0.0 1.0 0.0 0.0833 60000.0 1000.0o. 1
0.05 0.0 1.0 0.0 o. :1.666 60000.0 1000.0
O. 10.0
59
6 0.0 i .0 0.0833 O.OO(l() j .0 :l000.0
886000. 00.07 0.0 1.0 0.1666 0.0000 1.0 1000.0
886000. 00.01 2- 1 35 15 011100 1 4
40.0 0.02 5 6 46 15 000000 1
40.0 0.03 9 10 47 15 000000 2
40.0 0.04 13 14 48 15 000000 3
40.0 0.05 17 18 45 15 011100 1 t=
..J
40.0 0.06 1 2 35 15 011100 1 6
40.0 0.07 18 17 45 15 011100 1 7
40.0 0.06 8 1 11 720.0 8640.01 30.72 0.4 0.48598.0 10934.0 32817.01 0.3071 1.9114 11 20 19 36 12 22 21 37 13 24 23 38 14 26 25 39 15 28 27 40 16 30 29 41 17 32 31 42 18 34 33 43 1
10.0050 0.6533 0.003580 0.70 1 0.01 0.0051 1.0
EL CENTRO EARTHQUAKE504 5.65 0.02
0.000 -0.108 -().101 -0.088 -0.095 -0.102 -0.142 -0.128-0.110 -0.085 -0.085 -0.131 -0.176 -0.194 -0.162 -0.144-(>.108 -0.082 -0.042 -0.066 -0.131 -0.190 -0.196 -0.0660.030 0.141 -0.049 -0.128 -0.144 -(1.203 -0.260 -0.325
-0 .. 306 -0.172 -0.197 -0.163 -0.164 -0.067 0.025 0.3.500.236 0.252 0.336 0.463 0.492· 0.419 0.359 0.2710.235 0.339 0.412 0.530· 0.639 0.732 . 0.652 0.5990.400 0.4<>0 0.063 -0.515 -0.787 -0.603 -0.484 -0.250
-0.059 0.134 0.308 0.499 0.710 0.995 1.219 1.5291.449 1.155 0.935 0.892 0.926 0.839 0 .. 901 0 .. 9931 .. 209 0.328 -1.475 -2.066 -j .989 -2._034 -1.816 -1.752
60
-1.752 -1.753 -1.8'-1:') -1.630 -1.34"7 -1.087 -0.782 -0.429-0.017 0.360 0.785 1.164 1.598 1.9bO 2.412 2.7293.036 3.200 3.417 2.821 2.324 -1.198- --2.373 -1.640
-1.865 -1.095 -0.753 -0.173 0.113 0.533 0.895 1.1861.757 0.576 -2.631 -1.547 -1.729 -1.012 -0.579 0.237
-0.670 -1.980 -1.641 -1.685 -1.48i -1..231 -1.001 --0.751-0.523 -0.271 -0.044 0.188 -0.095 "0.433 -0.838 -0.951-0.716 -0.599 -0.334 -0.108 0.185 0.420 0.673 -0.097-0.372 -0.040 0.011 0.344 0.565 0.833 1.130 1.3630.219 0.241 0.683 0.689 1.318 1.353 2.040 -0.931
-1.308 -0.692 -0.546 0.072 0.675 -1.067 -1.488 -1.071-1.162 -0.762 -0.559 -0.215 -0.126 -0.674 -0.324 -0.337-0.109 0.017 0.299 0.488 0.608 0.222 -0.032 -0.245
0.077 0.211 0.568 0.826 1.206 1.478 1.737 0.4210.029 0.259 0.293 -0.055 -0.147 0.143 0.201..: 0.4990.645 0.957 1.128 1.447 1.629 1.945 1.856 1.9841.769 1.250 -1.207 -0.542 -0.384 -0.31t -1.118 -1.6612.464 -2.205 -1.836 -1.317 -0.960 -0.325 0.154 0.8161.319 1.818 -0.058 -0.169 0.285 0.447 . 0.983 1.4241.853 2.456 1.685 -1.380 -0.999 -1.089 -0.907 -0.469
-1.250 -2.111 -1.617 -1.692 -1.306 -1.111 -0.773 --0.510-0.544 -1.200 -1.209 -1.158 -1.145 -0.717 -0.546 0.064-0.804 -1.634 -0.859 -0.961 -0.369 -0.147 0.319 0.6480.876 0.472 0.198 -0.027 0.292 0.445 0.785 1.0331.352 1.606 1.861 1.281 0.640 0.204 0.314 0.3730.496 0.235 -0.084 -0.168 -0.113 -0.229 -0.248 -0.157
-0.069 0.147 0.379 0.579 0.255 -0.041 -0.420 -0.1330.095 0.230 -0.129 -0.050 0.080 0.210 0.380 0.5100.157 -0.032 -0.111 0.005 0.076 0.035 -0.095 -0.036
-0.016 0.038 0.085 -0.056 -0.304 -0.421 -0.244 -0.236-0.177 -0.129 -0.018 0.203 -0.108 -0.091 -0.034 -0.10b-0.111 -0.099 -0.002 0.073 0.235 0.355 0.705 0.7790.184 -0.263 -0.124 -0.042 0.159 0.048 -0.219 -0.467
-0.428 -0.216 -0.043 0.159 0.320 0.419 0.123 -0.160-0.204 -0.082 -0.206 -0.137 -0.055 0.053 0.134 0.2660.232 0.079 -0.008 0.200 0.435 0.492 0.191 0.092
-0.022 -0.021 0.052 0.093 0.255 0.368 0.525 0.5410.425 0.398 0.559 0.756 0.365 0.411 0.098 -0.204
-0.249 -0.405 -0.413 -0.471 -0.433 -0.458 -0.057 0.178-0.208 -0.492 -0.530 -0.362 -0.405 -0.308 -0.316 -0.265-0.265 -0.269 -0.345 -0.309 -0.217 -0.078 0.087 0.2810.031 0.358 0.341 0.358 0.287 0.305 0.112 0.2140.136 0.384 -0.861 -1.349 -1.342 :-1.354 -1.193 -1.042
-0.829 -0.651 -0.444 -0.258 -0.060 -0.091 -0.182 -0.1470.085 0.163 0.050 0.264 0.582 0.867 1.200 1.6951.111 -1.100 -0.366 -0.445 -0.236 -0.960 -0.656 '-0.597
-0.670 -0.552 -0.027 0.378 1.072 1.669 0.947 0.4030.667 0.132 -0.095 -0.520 -0.827 -1.15? -1.150 -0.803
-0.369 0.029 0.545 1.178 1.610 -0.270 0.034 -0.0560.020 0.146 0.537 0.798 -0.205 -0.5ao -0.169 -0.175
-0.028 0.074 0.382. 0.567 0.753 0.801 0.592 0.3040.023 0.064 -0.406 -0.451 -0.079 0.168 0.567 0.093
61
31 1 2 3
2 1 2 34 1 2 3
6 1 2 ~...:>
7 1 2 3
8 1 2 310 1 2 312 1 2 3
13 1 2 3
14 1 2 316 1 2 318 1 2 3
19 1 2 :3
20 1 2 3
22 1 2 324 1 2 3
25 1 2 326 1 2 3
41 1 2 3 4 5 6
42 1 2 3 4 5 6
43 1 2 3 4 5 6
44 1 2 3 4 5 6
45 1 2 3 4 5 646 1 2 3 4 5 647 1 2 3 4 5 648 1 2 3 4 5 6
32 1 1 2 3 4 5 6 7 8 9 10 11 12
2 2 1 2 3 4 5 6 7 8 9 10 11 12
2 3 i 2 3 4 5 6 "7 (] 9 10 11 12..2 4 1 2 3 4 c 6 7 i-j 9 10 11 12
d
2 5 1 2 3 4 5 6 7 8 9 10 11 12
2 6 1 2 " 4 c 6 .-, 8 s· 10 11 1~,"') <oJ .. .-
2 7 1 2 r; 4 5 6....., 8 9 10 11- 12
,::; ..2 8 1 2 ~. 4 c= 6 7 •. C:' 10 11 12
,"') .J ~:.;
4 1 1 2 3 4 5 b
4 2 1. 2 3 4 5 6
5 1 1 2 3 4 5 6 7 8 9 10 11 12c= 2 i. 2 .. 4 5 6 7 8 9 10 11 12,J .:1
5 3 1 2 3 4 5 6 7 8 9 10 1.1 12
5 4 1 2 3 4 5 6 7 8 9 10 11 12
5 5 1 2 3 4 5 6 7 8 9 10 11 12
62
APPENDIX C - LIST OF CCEER PUBLICATIONS
Report No. Publication
CCEER-84-1 Saiidi, Mehdi and Renee A. Lawver, "User's Manual for LZAK-C64, A Computer Program toImplement the Q-Model on Commodore 64, " Civil Engineering Department, Report No. CCEER84-1, University of Nevada, Reno, January 1984.
CCEER-84-2 Douglas, Bruce M. and Toshio Iwasaki, "Proceedings of the First USA-Japan Bridge EngineeringWorkshop," held at the Public Works Research Institute, Tsukuba, Japan, Civil EngineeringDepartment, Report No. CCEER-84-2, University of Nevada, Reno, April 1984.
CCEER-84-3 Saiidi, Mehdi, James D. Hart, and Bruce M. Douglas, "Inelastic Static and Dynamic Analysis ofShort RIC Bridges Subjected to Lateral Loads," Civil Engineering Department, Report No.CCEER-84-3, University of Nevada, Reno, July 1984.
CCEER-84-4 Douglas, B., "A Proposed Plan for a National Bridge Engineering Laboratory, " Civil EngineeringDepartment, Report No. CCEER-84-4, University of Nevada, Reno, December 1984.
CCEER-85-1 Norris, Gary M. and Pirouze Abdollaholiaee, "Laterally Loaded Pile Response: Studies with theStrain Wedge Model," Civil Engineering Department, Report No. CCEER-85-1, University ofNevada, Reno, April 1985.
CCEER-86-1 Ghusn, George E. and Mehdi Saiidi, "A Simple Hysteretic Element for Biaxial Bending of RICColumns and Implementation in NEABS-86, " Civil Engineering Department, Report No. CCEER86-1, University of Nevada, Reno, July 1986.
CCEER-86-2 Saiidi, Mehdi, Renee A. Lawver, and James D. Hart, "User's Manual of ISADAB and SIBA,Computer Programs for Nonlinear Transverse Analysis of Highway Bridges Subjected to Staticand Dynamic Lateral Loads, " Civil Engineering Department, Report No. CCEER-86-2, Universityof Nevada, Reno, September 1986.
CCEER-87-1 Siddharthan, Raj, "Dynamic Effective Stress Response of Surface and Embedded Footings inSand," Civil engineering Department, Report No. CCEER-86-2, University of Nevada, Reno,June 1987.
CCEER-87-2 Norris, Gary and Robert Sack, "Lateral and Rotational Stiffness of Pile Groups for SeismicAnalysis of Highway Bridges," Civil Engineering Department, Report No. CCEER-87-1,University of Nevada, Reno, June 1987.
CCEER-88-1 Orie, James and Mehdi Saiidi, "A Preliminary Study of One-Way Reinforced Concrete PierHinges Subjected to Shear and Flexure," Civil Engineering Department, Report No. CCEER-87-3,University of Nevada, Reno, January 1988.
CCEER-88-2 Orie, Donald, Mehdi Saiidi, and Bruce Douglas, "A Micro-CAD System for Seismic Design ofRegular Highway Bridges, " Civil Engineering Department, Report No. CCEER-88-2, Universityof Nevada, Reno, June 1988.
CCEER-88-3 Orie, Donald and Mehdi Saiidi, "User's Manual for Micro-SARB, a Microcomputer Program forSeismic Analysis of Regular Highway Bridges," Civil Engineering Department, Report No.CCEER-88-3, University of Nevada, Reno, October 1988.
63
CCEER-89-1 Douglas, Bruce, Mehdi Saiidi, Robert Hayes, and Grove Holcomb, "A Comprehensive Study ofthe Loads and Pressures Exerted on Wall Forms by the Placement of Concrete, " Civil EngineeringDepartment, Report No. CCEER-89-1, University of Nevada, Reno, February 1989.
CCEER-89-2 Richardson, James and Bruce Douglas, "Dynamic Response Analysis of the Dominion RoadBridge Test Data," Civil Engineering Department, Report No. CCEER-89-2, University ofNevada, Reno, March 1989.
CCEER-89-2 Vrontinos, Spiridon, Mehdi Saiidi, and Bruce Douglas, "A Simple Model to Predict the UltimateResponse of RIC Beams with Concrete Overlays," Civil Engineering Department, Report NO.CCEER-89-2, University of Nevada, Reno, June 1989.
CCEER-89-3 Ebrahimpour, Arya and Jagadish, Puttanna, "Statistical Modeling of Bridge Traffic Loads - ACase Study," Civil Engineering Department, Report No. CCEER-89-3, University of Nevada,Reno, December 1989.
CCEER-89-4 Shields, Joseph and M. "Saiid" Saiidi, "Direct Field Measurement of Prestress Losses in BoxGirder Bridges," Civil Engineering Department, Report No. CCEER-89-4, University of Nevada,Reno, December 1989.
CCEER-90-1 Saiidi, M. "Saiid", E. "Manos" Maragakis, George Ghusn, Jr., Yang Jiang, David Schwartz,"Survey and Evaluation of Nevada's Transportation Infrastructure, Task 7.2 - Highway Bridges,FinaJ, Report," Civil Engineering Department, Report No. CCEER 90-1, University of Nevada,Reno, October 1990.
CCEER-90-2 Abdel-Ghaffar, Saber, Emmanuel A. Maragakis, and Mehdi Saiidi, "Analysis of the Response ofReinforced Concrete Structures During the Whittier Earthquake 1987," Civil EngineeringDepartment, Report No. CCEER 90-2, University of Nevada, Reno, October 1990.
CCEER-91-1 Saiidi, M., E. Hwang, E. Maragakis, and B. Douglas, "Dynamic Testing and the Analysis of theFlamingo Road Interchange, " Civil Engineering Department, Report No. CCEER-91-1, Universityof Nevada, Reno, February 1991.
CCEER-91-2 Norris, G, R. Siddharthan, Z. Zatir, S. Abdel-Ghaffar, andP. Gowda, "Soil-Foundation-StructureBehavior at the Oakland Outer Harbor Wharf," Civil Engineering Department, Report No.CCEER-91-2, University of Nevada, Reno, July 1991.
CCEER-91-3 Norris, G.M., "Seismic Lateral and Rotational Pile Foundation Stiffnesses at Cypress," CivilEngineering Department, Report No. CCEER-91-3, University of Nevada, Reno, August 1991.
CCEER-91-4 O'Connor, D.N. and M. "Saiid" Saiidi, "A Study of Protective Overlays for Highway BridgeDecks in Nevada, with Emphasis on Polyester-Styrene Polymer Concrete," Civil EngineeringDepartment, Report No. CCEER-91-4, University of Nevada, Reno, October 1991.
CCEER-91-5 O'Connor, D.N. and M. "Saiid" Saiidi, "Laboratory Studies of Polyester-Styrene PolymerConcrete Engineering Properties," Civil Engineering Department, Report No. CCEER-91-5,University of Nevada, Reno, November 1991.
CCEER-92-1 Straw, D.L. and M. "Saiid" Saiidi, ·Scale Model Testing of One-Way Reinforced Concrete PierHinges Subject to Combined Axial Force, Shear and Flexure," edited by D.N. O'Connor, CivilEngineering Department, Report No. CCEER-92-1, University of Nevada, Reno, March 1992.
64
CCEER-92-2 Wehbe, N., M. Saiidi, and F. Gordaninejad, "Basic Behavior of Composite Sections Made ofConcrete Slabs and Graphite Epoxy Beams," Civil Engineering Department, Report No. CCEER92-2, University of Nevada, Reno, August 1992.
CCEER-92-3 Saiidi, M. "Saiid" and Eric Hutchens, "A Study ofPrestress Changes in A Post-Tensioned BridgeDuring the First 30 Months, " Civil Engineering Department, Report No. CCEER-92-3, Universityof Nevada, Reno, April 1992.
CCEER-92-4 Saiidi, M., B. Douglas, and S. Feng, E. Hwang, and E. Maragakis, "Effects of Axial Force onFrequency of Prestressed Concrete Bridges," Civil Engineering Department, Report No. CCEER92-4, University of Nevada, Reno, August 1992.
CCEER-92-5 Siddharthan, R., and Zafir, Z., "Response of Layered Deposits to Traveling Surface PressureWaves," Civil Engineering Department, Report No. CCEER-92-5, University of Nevada, Reno,September 1992.
CCEER-92-6 Norris, G., and Zafir, Z., "Liquefaction and Residual Strength of Loose Sands from DrainedTriaxial Tests, " Civil Engineering Department, Report No. CCEER-92-6, University of Nevada,Reno, September 1992.
CCEER-92-7 Douglas, B., "Some Thoughts Regarding the Improvement of the University of Nevada, Reno'sNational Academic Standing," Civil Engineering Department, Report, Report No. CCEER-92-7,Uni~ersity of Nevada, Reno, September 1992.
CCEER-92-8 Saiidi, M., E. Maragakis, and S. Feng, "An Evaluation of the Current ealtrans Seismic RestrainerDesign Method," Civil Engineering Department, Report, Report No. CCEER-92-8, Universityof Nevada, Reno, October 1992.
65
