to my - vtechworks.lib.vt.edu · financial support and would proudly dedicate this project to them....
TRANSCRIPT
ENERGY DISSIPATOR DEVICES
by
Mohamad A. Rezvani.B
Project and report submitted to the Faculty of the
Virginia Polytechnic Institute and State University
in partial fulfillment of the requirements for the degree of
MASTER OF ENGINEERING
in
Civil Engineering
APPROVED:
R. ~. Bkrker, Chairman
q~ A , ~ ' ">. tlw' y ,- - " ' 1'1 z_w =n: A. G'cirst T. Ku~p:(l~'amy
December, 1983
Blacksburg, Virginia
J
-ACKNOWLEDGEMENTS
The author wishes to express his gratitude to his major advisor,
Dr. R. M. Barker, and to the other members of his committee for their
aid and patience in the preparation of this report. The author is also
grateful to his parents for their encouragement, continued love, and
financial support and would proudly dedicate this project to them.
The author would also like to express his deepest appreciation to his
fiancee, and all of his friends for their invaluable
assistance and friendship.
ii
To my Parents
iii
TABLE OF CONTENTS
ACKNOWLEDGEMENTS
LIST OF TABLES .
LIST OF FIGURES
CHAPTER 1. INTRODUCTION
Energy Dissipator Devices
CHAPTER 2. ELASTOMERIC BEARING PADS
2.1 General .
2.2 Expansion Bearings
2.3 Fixed Bearings
CHAPTER 3. STEEL HYSTERESIS DAMPERS
3.1 General
3.2 Torsion Beam Devices
3.3 Tapered Steel Cantilever Devices
3.3.1 Tapered Round Type Devices
3.3.2 Tapered Plate Type Devices
3.4 Bent Round Bars ...
3.5 Flexural Beam Dampers
CHAPTER 4. LEAD HYSTERESIS DAMPERS
4.1 Introduction
4.2 Lead Rubber Bearings
4.3 Lead Extrusion Dampers
iv
ii
V.l-
vii
1
1
3
3
3
5
10
10
11
13
14
16
18
20
43
43
43
45
CHAPTER 5.
CHAPTER 6.
REFERENCES .
VITA . . .
DESIGN EXAMPLE PROBLEM
5.1 General . . . . 5.2 Design Criteria
5.3 Designed Model and Developed Charts
5.4 Design Example I, Cromwell Bridge
5.5 Design Example II, South Brighton Bridge
SUMMARY AND CONCLUSIONS
v
Page
54
54
54
56
65
68
98
101
104
LIST OF TABLES
Table
3.1. I Strain history of torsion bar specimens 22
3.3.I Results of tests on tapered steel cantilevers 23
4.2.I Summary of tests conducted at 0.9 Hz with a 400 kN vertical load . . . . . . . . . . . . 48
4.2.II Summary of properties of lead-rubber damper 48
vi
Figure
2.2.I
2.2.II
2.3.I
2.3.II
3.1. I
3.2.I
3.2.II
3.2.III
3.2.IV
3.3.I
3.3.II
3.3.III
3.3.IV
3.3.V
3.3.VI
3.3.VII
3.3.VIII
3.3.IX
LIST OF FIGURES
Earthquake resistant bearing concept (elastomeric pad with slip surface) .
Earthquake resistant bearing concept (visco-elastic material enclosed in a spherical membrane) • . . . . . . . . . . . .
Constant moment simple beam device
Sliding "fixed" bearings at typical bridge abutment
Hysteresis loop
Torsional-bar hysteretic damper
Force-displacement hysteresis loop and cycles plot for torsion beam dissipator
Prototype torsion beam dissipator for South Rangitikei Railway Bridge in test machine
Bilinear hysteresis loop for steel energy dissipator . . . . . . . .
Cyclic load strain relation for steel in bending
Plastic yield stress f in bending p
related to strain level
Low-cycle fatigue relattonship for mild steel in bending . . . . . . . . . .
Round cantilever dissipator
Double cantilever damper machine after testing
Hysteresis loop for cantilever damper .
Double cantilever damper
Hysteresis loop for double cantilever damper
Design curves for round cantilever dissipator
vii
7
8
9
9
24
25
26
26
27
27
28
29
30
30
31
32
32
33
Figure
3.3.X Cantilever dampers
3.3.XI Split type of plate damper LHS seam welded type RHS • • • • • • • • • •
3.3.XII Buttress damper tested during development
3. 3 .XIII Buttress type in test machine
3.3.XIII.A Design curves for plate cantilever dissipater
3.4.I
3.4.II
3.4.III
3.4.IV
3.4.V
3.4.VI
3.4.VII
3.4.VIII
3.5.I
3.5.II
3.5.III
4.2.I
4.2.II
4.3.I
4.3.II
4.3.III
Base isolation method using bent round bars
Loop parameters . .
Proportions of bars tested
Strain gauged bent bar dissipater
Failed bent bars
Forces on bent bars
Force-displacement hysteresis loops for bent bars 25 mm diameter . . . . .
Bilinear hysteresis loop for bent bars
Geometry of flexural beam dissipater
Flexural beam dissipater
Force-displacement hysteresis loop for flexural beam dissipater . . . . .
Lead-rubber shear damper
Force-displacement loops for lead-rubber bearing
Longitudinal section of a constricted tube extrusion energy absorber showing the changes in microstructure of the working material
Typical force-displacement hysteresis loops for (a) 15 kN constricted-tube energy absorber and (b) 30 kN bulged-shaft energy absorber, tested at
1. 7 x io-2 cm/ sec (1 cm/min) . . . . .
Rate dependence of extrus_ion energy absorbers
viii
34
34
35
35
36
37
37
38
39
39
40
40
41
41
42
42
49
50
51
52
53
Figure
5.3.I
5.3.II
5.3.III
5.3.IV
5.3.V
5.3.VI
5. 3. VII
5 .'3. VIII
5.3.IX
5.3.X
5.3.XI
5.3.XII
5.3.XIII
5.3.XIV
5.3.XV
5.3.XVI
5. 3 .XVII
Structural model for parameter studies
Pier and abutment stiffness parameters
Model of elastic structure without dissipators
Elastic structure, no energy dissipators, Skinner4-7 (El Centro 1940 N-S), A= 5% .
Bridge with energy dissipators at abutment only
Energy dissipators on rigid abutment, Qd = 0.03W, El Centro 1940 N-S . . . . . . . . . . . . . .
Energy dissipator on rigid abutment, Qd = o.osw, El Centro 1940 N-S ........ .
Energy dissipators on rigid abutment, Qd = 0.07W, El Centro 1940 N-S . . . . . . . . . . .
Energy dissipators on rigid abutment, Qd = 0.03W, Bl . . . . . . . . . . . . . . . . . . . .
Energy dissipators on rigid abutment, Qd = Bl . . . . . . . . . . . . . . . . Energy dissipators on rigid abutment, Qd = Bl . . . . . . . . . . . Energy dissipators on rigid abutment, Qd = Parkfield . . Bridge with energy dissipators at pier only
00 , Energy dissipators on rigid pier, k p Qd = 0.05W, El Central 1940 N-S ..... \
Energy dissipators on rigid pier, k p Qd = O.OSW, Bl
Energy dissipators on flexible pier,
= 00
'
0.05W, . .
0.07W, . . .
0.05W,
kp = 0.016W/mm, Qd = 0.05W, El Centro 1940 N-S
Energy dissipators on flexible pier, kp = 0.016W/mm, Qd = 0.05W, Bl
5.3.XVIII Energy dissipators on flexible pier, kp = 0.004W/mm, Qd 0.05W, El Centro 1940 N-S
ix
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
Figure
5.3.XIX
5.3.XX
5.3.XXI
5.3.XXII
5.4.I
5.4.II
5.4.III
5.4.IV
5.4.V
5.5.I
5.5.II
5.5.III
6.I
Energy dissipaters on flexible pier, kp = 0.004W/nnn, Qd = 0.05W, Bl
Bridge with energy dissipaters at piers and abutments . . . . . .
Energy dissipaters on rigid pier and abutment, Bl, kp = 00 , Qd = 0.025W; kq = 00 , Qd = 0.025W ....
Energy dissipaters on flexible pier and abutment, Bl, kp = 0.004W/mm, Qd = 0.025W, ka = 0.016W/mm, Qd = 0. 025W . . . . . . . . . . . . . . . .
Flexural beam dissipaters in Cromwell Bridge
General layout, Cromwell Bridge, New Zealand
Cromwell Bridge
Cromwell Bridge
Energy dissipater on rigid abutment, Qd El Centro 1940 N-S . . . . . . .
Bridge details
Pier base-moments, El Centro 1940 N-S
o.osw,
Pier displacement (4.73 rn), El Centro 1940 N-S
Superstructure displacement, New Zealand Bridge
88
89
90
91
92
93
94
94
95
96
97
97
100
Energy Dissipator Devices
Chapter 1
INTRODUCTION
Energy dissipator devices dissipate earthquake energy trans-
ferred to a superstructure from a substructure. These devices act
elastically under the applied forces that the structure normally sees
when in service, namely regular dead and live loads. In case of an
earthquake, lateral movements of the substructure drive the devices
into their inelastic region. Consequently, they behave inelastically,
dissipating the applied forces, and thus do not transfer the forces to
the superstructure.
The devices are usually made of steel or lead, using the
inherent non-linear behavior to dissipate energy in case of
an earthquake. Because of the property of plastic yielding, steel and
lead have been used in the devices. More specifically, the steel
devices are based on absorbing energy by plastic deformation in torsion
or bending. The lead devices utilize plastic extrusion or shear defor-
mation of the material. The combination of rubber with lead has also
been used in recent years. This seems to be the best and most promising
solution to the problem at hand.
Based on possible earthquakes in the area, environmental condi-
tions, economical aspects, space and maintenance limitations, and
engineering judgements, different devices might be adopted. The data
required for design are based on analysis and actual testings carried
1
2
out in the laboratories. The testings are done in full size, where
applicable, while some tests are required to be carried out on a smaller
scale. Due to nonlinear behavior of the devices, the most reliable
results are performed in full size tests based on previous earthquake
information and data.
In this report, various energy dissipating devices will be
described, their performance in laboratory tests summarized, and com-
ments made on their applicability in certain design situations.
2.1 General
Chapter 2
ELASTOMERIC BEARING PADS
Elastomeric bearing pads are made of either natural or synthetic
rubber that can be used in combination with steel sheets to form a
laminated unit. These elastomers act elastically in the normal range
of live load and certain dead load, but when greater displacements are
applied they go into their plastic range and show inelastic behavior.
Bridge bearings are used at the superstructure and substructure
interface as a structural support, to allow for relative movements, and
to take care of incompatibility of materials (3).
Most of the failures of these bearings have been due to loss of
vertical support. In exploring potential new bridge design concepts for
earthquake resistance, it is convenient to categorize bearings as
either expansion or fixed, which are covered in sections 2.2 and 2.3.
2.2 Expansion Bearings
Expansion bearings seem to be a good choice for earthquake
resistance. They could be designed so that the elastomeric pads would
act as an energy absorber for moderate earthquakes. In a strong earth-
quake, one surface would slide against the other. The coefficient of
friction in case of sliding is selected so that it would preserve
stability and integrity of the pad, and limit the forces that are trans-
ferred to the portions of structure that could not be checked after
the earthquake. Figure 2.2.I shows a schematic drawing of the
3
4
design concept.
Such a system has the following advantages:
1. A high degree of reliability in maintaining vertical support
2. Protection of the supports from loads which could cause
excessive damage
3. Potential for significant energy dissipation at high dis-
placement levels
4. A high degree of isolation which will tend to limit
structural response
5. Compatibility with current production capabilities of bearing
manufacturers
6. Designer acceptance of elastomeric bearing pads
Figure 2.2.II.a shows a proposed bearing which is maintenance free
and stable under sustained load. It is composed of a reinforced concrete
membrane holding incompressible viscoelastic material in it. The
deformation of membrane is by horizontal forces of earthquake which
causes the device to act like a viscous damper (3). Figures 2.2.II.b
and 2.2.II.c show the developments that could be done to make the pads
more practical. To seal the viscoelastic material in a membrane and
fire proof the concrete cell, a shield could be constructed around the n
~h
cell, Figure 2.2.II.b.
To make the design more effective, the designer could use normal ,2
elastomeric bearing pads as shown in Figure 2.2.II.c. The pads would
support the vertical load and the lateral stiffness of them would induce
sliding at excessive displacements. It should be noticed that the
force displacement curve for the pad, acting as a unit, and the behavior
5
under different temperatures should be studied for a full guideline for
design of flexible bearings.
2.3 Fixed Bearings
Fixed bearings improve the resistance of the structures by one
of the methods listed below:
1.) First method provides nominal fixity in an expansion bear-
ing. The fixity is by applying a fuse at the junction of superstructure
and substructure. The fuse would be stable for lateral load caused by
wind or braking. In an earthquake the fuse would fail and the sub-
structure and the superstructure can act separately. The result would
be a larger displacement, instead of transferring forces. For large
movements, restoring forces might be required to bring the structure to
its zero displacement, after the earthquake.
2.) The second method attempts to mitigate the effect of high
relative displacements experienced in isolated structures. The effect
of energy dissipated by different devices would be used in place of
isolation. The devices dissipate small and large lateral forces caused
by wind, braking, and earthquake. The materials used are steel, lead,
rubber or the combination of them. Figure 2.3.I shows the constant
moment simple beam device that utilizes the advantage of "off-the-
shelf" steel components (3).
Energy is also dissipated due to the sliding of two surfaces.
By selecting the appropriate coefficient of friction, many sliding
expansion bearings in use today could be made to function as "fixed"
bearings. In this type of installation, attention should be given to
6
preventing sliding of the surfaces caused by vibration of the super-
structure under normal loading conditions. A suggested approach to
this problem at a typical bridge abutment is shown in Figure 2.3.II. In
this case, enclosed elastomeric bearings are sloped to keep the
structure in a natural position under normal conditions.
7
SLIP SUfffAC( TO PROT(CT PAO ( sr:.en .. 1TY ANO DISSIPATE ENER:;Y
,--'§--'§--\-~;: \~.~.,.-,~._,.~.,..-..,":~'::--..._,.s;~-. ..-~-'-;:.,...,',-. -,~-, -,~.-'· -. ..,-,,-·,~::::-. --:_-,,~~--==·,,~,---'--! ·i ;; ;i' :=L_~ . ~'---1-.J
--·---:----rr= ~---·DOWEL s OR 30~ TS I .... ,1 ----'-------
TO FIX r.\Q ~o S ; I UBSTRUCTURE ~
Figure 2.2.I Earthquake resistant bearing concept (elastomeric pad with slip surface)
Knurls to prevent filler material from slipping
8
Viscoelastic Filler Material
Figure 2a
Bonded Region
Top I Plate
/Plate
-------------Reinforced spherical membrane
Knurls to preve~n;t~~i;ij!::2:z:::;;z::~~:::;zz::;:::;;;::::(.2:4Z:ZZ:ZZ:::ZZ:~~-:T"'1imit displacement filler material to induce sliding from slipping ~.~.""l"':':,......,~~~~""~~~~-,.;~~?-77'""7.r.-:-
. . Slip surface to protect pad stability dissipate energy and limit force transmitted
Figure 2b Special friction surface--=::; /Plate
~~~~:~~~~i'i~~~~[-:F-~~~~jE~l~a~stomeric bearing pad
Figure 2 . 2 . II
Reinforced elastomeric , membrane
/U U Lviscoelas tic Filler Material ~Dower to fix pad to
bottom plate Figure 2c
Earthquake resistant bearing concept (viscoelastic material enclosed in a spherical membrane)
9
. Rf A·: r 1(.)r.t ~·(l\f; T ·,
. ' I
___ :_ ._'._--l
Figure 2.3.I Constant moment simple beam device
c::::, :--·-1 I! · I I I' i L. ____ J L--·---;: I
Q. '-'SS ~~- : ----··.--,------"" \
\ / ~==-=--~ =·... \ ___,--- ~ I :.;:;,,:Mt:NTB:.CKY .. ~L"'::... _____ L __ / ___ --'.~:?
I :r f '1 rr-7-1 if I l)=.,-;--/77--:1 L:.:'-·--1C) ! l [~
, ~- \ -\) ' • ' - i..ONGllVOINAL
; -......:- ) 0 F"IX(C\ 0 SE.\lllNG
L_ \ ,,· "'""ABUTMEIH SEAT '-..._ TRANVERSC: °FIXE0° BEARING
Figure 2.3.II Sliding "fixed" bearings at typical bridge abutment
Chapter 3
STEEL HYSTERESIS DAMPERS
3.1 General
Steel hysteresis dampers, which are another category of energy
dissipators, capitalize the nonlinear behavior of steel beyond its
elastic capacities, i.e., absorbing energy by plastic deformation in
torsion or bending. The low maintenance requirement has been another
factor in applying steel dissipators.
The name hysteresis is added to the devices because the pattern
that they dissipate energy could be defined by hysteresis loops as
described below. During elastic deformation, especially when it is
accompanied by plastic phenomena, a certain amount of the work done may
be dissipated. This fact will be manifested in the stress-strain
curve, where a somewhat different form is obtained for the loading
than unloading. Figure 3.1.I shows the area that energy is dissipated.
The material used in steel hysteresis dampers is mild steel, that
stays stable at high levels of plastic strain. The steel is normally
stress relieved after fabrication by being heaced for 5 hours at 620°C.
Very low carbon steel, pure aluminum, and spheroidal graphite iron
have been tried, but the results were not as successful as mild steel
(8). Hot dip galvanizing has not so far been recommended as a protec-
tion because of the lack of knowledge of the effects of galvanizing
over long periods on parts subjected to high strains.
10
11
Another important factor is the aging of steel, that does not
affect the level of dissipation. A couple of specimens of black mild
steel were loaded and aged both naturally and artificially. The
results showed, for materials and strain levels that have been adopted
for steel dissipaters, embrittlement is not likely to be a problem
when carried into the plastic range (17). Some results of aging for
the torsion beam dissipaters (section 3.2) are tabulated in Table
3.1.I.
The different kinds of steel energy dissipaters, namely torsion
beam, tapered steel cantilever, tapered round and plate type, bent
round bars, and flexural beam damper devices, are discussed in the
following sections.
3.2 Torsion Beam Devices
In this device energy is dissipated by torsional plastic cyclic
deformation and to some extent in bending. Torsion beam device was
the first steel energy dissipater that was developed in laboratories.
Figure 3.2.I shows a picture of such a device (19).
Some testings were performed and some design formulas were
derived. Figure 3.2.IV shows the parameters considered in design
which could be expressed as below (8).
Kd = RG
kd R(A1 + A2 PY)
Qd = H(B1 + B2 PY)
ym PY
(3.2.1)
(3.2.2)
(3.2.3)
(3.2.4)
12
where: Kd and kd = spring stiffnesses
Qd force required to represent the force displacement
characteristics of energy dissipators
Geometrical Factors:
R in mm {= 0.609
= 0.281
b3 t 3/[r2 (L + 1.5 t)(b2 + t 2)]
b 4 /[r2 (L + 1.5 t)]
for b > 2t
for b = t
(3.2.5)
. -1 {0.912 (b + 0.6 t)bt/[r(L + 1.5 t)(b 2 + t 2) for b > 2t P in mm
0.674 b/[r(L + 1.5 t)] for b t
(3.2.6)
H (3.2.7)
where: b = beam width
t beam thickness
L = beam length
y =nominal maximum strain, varied from 2.3 to 5.75 percent m
r = level length (from mid-beam)
y maximum level deflection
G (effective dynamic shear modulus) 60 GPa
Al 7 GPa
Az = -11 GPa
B1 = 72 GPa
Bz 2.9 GPa
To get more details for the above device the testing was
performed as shown in Figures 3.2.II and 3.2.III. A force of
13
approximately 450 KN for 150 cycles was applied to the dissipator.
The welding was kept well beyond highly strained sections of the beam
between the loading arms.
3.3 Tapered Steel Cantilever Devices
The tapered steel cantilever device is used to dissipate energy
in bridges and other structures. It is used in places where enough
space is provided for the projection of a cantilever arm. Two dif-
ferent models are available (25).
1. The round type, which allows any direction of loading in a
horizontal plane.
2. The plate type, that is used for unidirectional loading.
Some testings were performed with the results and formulas
derived listed below (8):
K f p
where: f = constant plastic stress p
(3.3.1)
Qd applied load at its ends, defined in hysteresis loop,
at zero strain
X distance from load point to section under consideration
K plastic modulus
d 3 /6 for circular section with
diameter d
Bt 2 /4 for rectangular section of
breadth B and thickness t
(3.3.2)
Qd and fp increase as the cyclic strain increases as shown in Figure
3.3.I. As qn approximation for the design, Figure 3.3.II, which has
14
the plot of f vs. strain, could be used. p
The allowable strain range is figured by using Figure 3.3.II,
keeping in mind the number of cycles to failure that the device has
to go through. Normally a strain range of ± 3%, which corresponds to
80 to 100 cycles is considered. This range of strain leads to value
for f of 350 MPa, which is used for design. p
3.3.1 Tapered Round Type Devices
The round type is used to damp energy in two directions orthogonal
to each other, keeping in mind that the motion is in a horizontal
plane. For all the sections to yield simultaneously,
(3.3.3)
where: x L 1 at the cantilever root d D J
results in 6Qaf fp = D3 /L (3.3.4)
i.e. d n3/x/L (3.3.5)
If the diameter is kept d, as determined by equation (3.3.1), the bar
can be linearly tapered up to 2/3 of its length, without introducing
much error in calculations.
The small undercut at center, due to tapering, promotes failure
within the length of the device rather than at the base (25). To per-
form the test, basal proportions as shown in Figure 3.3.IV were con-
sidered. The cantilever root diameter is D being a push fit in the
cylinder of overall diameter 2D, and height of D. The base plate is
square of 4D and thickness of D/2. The base plate machined flat after
15
welding and stress relieved for 5 hours at 620°C.
Two types of round cantilever, with a diameter of 76.2 mm, were
tested. The first was a single cantilever having a taper over about
1/3 of its length. The second was a double cantilever device, that is
two cantilevers oriented head-to-head and connectec by a sliding joint
as shown in Figures 3.3.V, 3.3.VII.
The first one failed after 132 cycles, in its length. The
strain is about ± 3% and the hysteresis loop is shown in Figure 3.3.VI.
-1 The approximate values for the slopes of the loop, Kd/Qd = 85 m , -1 Kd/Qd = 5 m have been reported. The second type, as shown in Figure
3.3.VII, failed after 1160 cycles, with strain range of± 1%. The loop
for one-half of the cantilever is shown in Figure 3.3.VIII. The test
results are summarized in Table 3.3.I.
For example, for the first cantilever tested equation (3.3.1)
leads to a plastic stress, f of f p p
where Qd 54 KN
L 0.47 m
D 0.076 m 2 2 results in f 344 MN/m . For double cantilever, f = 191 MN/m .
p p
The yield point is calculated to be 290 MN/m2 which indicates the
strain of ± 1% was still elastic.
The percentage rise to peak load in the cycle, (Qmax - Qd)/Qd'
is greater for double cantilever, which is 53%, than the single
cantilever, which is 37%. The reason is due to lower strain level.
To satisfy the strength and deflection conditions, it could be
shown that
DY/ (1. 2 £)
assuming
f = 350 MPa p
£ = 3%
life of 80 to 100 cycles
results in
L 5.270/DY
Qd = 11. 06 71n5 /Y
16
(3.3.6)
(3.3.7)
(3.3.8)
(3.3.9)
The values of L, Qd for a range of ± 75 mm (total of 150 mm) is plotted
on Figure 3.3.IX, which could be used as a basis for design.
3.3.2 Tapered Plate Type Devices
The plate taper was first considered as a unidirectional device
used for bridge decks, but later used for a chimney to step under
earthquake. The breadth, b, at any distance x varies linearly with x,
from point of application of load, with a maximum length of taper of
about 2/31, see Figure 3.3.X. It was desired to provide an adequate
base detail for the inverted "T" type in the bridges, where dissipators
would be attached to the top of the pier or abutment, and loaded with
movement of the deck above. Welding should be kept well beyond points
of high strain to avoid any failure for many number of loading cycles.
Three different butt joints were tested as described below with
the results shown in Table 3.3.I.
17
3.3.2.1 The Split Type
In this joint the plate was split at its wide ends, as shown in
Figure 3.3.XI, opened out and welded. The design was not adopted for
high expenses.
3.3.2.2 The Seam Welded Type
As shown in Figure 3.3.XI, this absorber was fabricated by seam
welding of two L shaped plates back to back down the sloping edges, to
the same taper dimensions and thickness of split type. Due to lower
life cycle of this design relative to split type, the design was not
approved.
3.3.2.3 The Buttressed Type
As shown in Figures 3.3.XII and 3.3.XIII, the joint was rein-
forced with plates and 45° fillets on each side. The vertical plate
has the same taper dimensions and thickness as the previous types.
As summarized in Table 3.3.I, the device had a life cycle of 127
with strain of 4.2%, at 2/3 of the way up the taper. The failure
occurred at a groove caused by roughness in the flame cutting at the
top of the taper. Therefore, better results could be accomplished by
having a smooth finish. Although welding was kept away from the
points of high strains, the welds at the base of the plate had also
failed, but it did not affect the performance.
Based on the results of equations above, the plastic stress, f , p
was calculated. To satisfy the strength and deflection conditions
(25,8):
12 = ty/s
Q = f d p Bt2/4L
with a ratio B to L of
Qd = f p t 2/6
assuming f = 350 MP a p E = 3%
life cycle
results in
L 5. 7721/tY
2 Qd = 58.333 t
18
(3.3.lOa)
(3 .3 .lOb)
2/3 leads to
(3.3.10)
80 to 100
(3.3.11)
(3. 3 .12)
A plot of L and Qd are shown in Figure 3.3.XIII.A for usual range of
thickness and displacements.
3.4 Bent Round Bars
The bent round bars also dissipate the earthquake energy by going
to inelastic force-displacement curve. The possibility of using this
device as an energy dissipater was prompted by considering the
capacity of steel bars to carry the earthquake force after concrete
has failed (8).
The proposed device is shown in Figures 3.4.I, 3.4.III, in which
the columns are mounted on rubber bearings and round steel bars having
a bowed portion. The bars are pushed in between superstructure and sub-
structure and welded at the ends, Figure 3.4.IV. Different types of
bent bars were tested and the results showed that shape of bend was not
19
a critical factor (24).
Either a large number of small diameter bars of short length or a
small number of large diameter bars of longer length will perform the
same function for the chosen movement related to the design earthquake,
except that the shorter the bars the sooner a complete lock-up is
induced, as the length available for straightening is reduced.
To perform the test the bar had vertical projection length of
L = 476 mm and a bowed portion of circular arcs of radius L/4. The
diameter varies from 12 to 38 mm to result in different strain values.
The bars were bent and stress relieved for 5 hours at 620°C to restore
the yield point of steel. The resulting hysteresis loop is shown in
Figure 3.4.II.
For small horizontal deflections, plastic hinges developed at top
and bottom, behaving as a double cantilever that leads to a plastic
moment of QdL/2 where, Qd is the horizontal shear force (8). For large
horizontal deflections, the plastic moment develops at the center equal
to FTL/4, where FT is force created by induced length change (see
Figure 3.4.VI). For the case of Figure 3.4.VI, FT= 2Qd. Figures
3.4.VII and 3.4.VIII have the selection of hysteresis loops for bars of
25 mm in diameter. The failed bars are shown in Figure 3.4.V.
Based on the testings performed, the formula below was found as
a base for design strain range, S
S = 0.063 (D/25.4)(476/L) 2 (T/150) (3.4.1)
where: D diameter
L length (vertical projection)
20
T = horizontal movement
The above value is plotted vs. cycles of failure in Figure 3.3.III.
3.5 Flexural Beam Dampers
In flexural beam damper device, Figures 3.5.I and 3.5.II, loads
are applied to the ends of cranked arms, which causes the circular
beam element, with diameter d, to behave alternately as an eccentrically
loaded strut or tie depending on the direction of loading. Cranking
the loading arm produces a favorable geometry in that the alternate
bowing up and down of the beam is compensated for the change in
leverage, the geometrical effect produces almost a rectangular
hysteresis loop as shown in Figure 3.5.III (17).
The loading arms are of cast steel and welding is confined to
the ends of the beam, where no load would be applied at that length.
The ultimate applicable load, Qd, and the deflection, ± y, are given
by formulas shown below (8)
f d3 Q - __E_ d - 6r
2Lre: y =-d-
where: d = diameter of beam
r = arm length (Figure 3.5.I)
(3.5.1)
(3.5.2)
f = plastic stress for the strain level of ± 3%, for 100 cycles p
with the value of 350 MPa
£ = ± 3%
L = beam length (Figure 3.5.I)
21
It should be noticed that in derivation of the above formulas the
d~rect stresses have been neglected. For a sample test with d = 114 nun,
r = 280 mm, and L = 500 mm, the value of Qd was 309 KN with a deflection
of ± 74 mm, i.e. the stroke with a value of approximately 150 mm.
If for a certain design higher values are required, the ratio
L/d may be increased up to 30% or decreased by 15%. Another alterna-
tive would be reduction of d, but not less than 90 mm. If the last
method is applied the capacity of Qd reduces to 150 KN, while the
stroke increases by about 25%, with a deflection, y, of approximately
185 mm.
Table 3. l.I Strain history of torsion bar specimens
N.B. All specimens rectangular bars in black mild et eel. Carbon content 0.20% except for No. 779 which was 0.02%. No prior heat treatment. Some specimens showed cracks in cycling prior to aging but these did not get noticeably worse subsequently. There were no fractures.
Strain history Strain history Strain history following prior to aging following natural aging artificial aging
Artificial Aging Crose
Specimen Strain* No. of Strain* No. of Time (hrs) Strain* No. of Sect~on No Date (± %) Cycles Date (± %) Cycles Date at 100°C (± %) Cycles (11'111 )
751 12/72 1. 9 400 8/12/78 3.8 22 13/12/78 36 3.8 22 25 x 25 5.7 12 5.7 17 !·)
7.6 4 !,)
752 12/72 3.8 30 7/12/78 3.8 60 " 5.7 10 757 11/73 3.8 407 29/11/78 3.8 128 12.5x50 758 11/73 3.9 300 6/12/78 3.9 30 " 766 2/75 .4 5 5/12/78 1.4 2
. 7 8 2.8 124 1.4 8 4.3 24 2.8 8 4.3 4
778 4/75 2.2 500 1/12/78 2.2 120 11/12/78 12 2.2 42 3.4 7
779 4/75 2.1 500 4/12/78 2.1 120 11/12/78 12 2.1 42 " 3.4 7
*Calculated maximum shear strain
Table 3.3.I Results of tests on taper steel cantilevers
I Cross Length of Section Stroke Cantilever Type Cantilever at Root (mm) (mm)
(mm)
Single round 76.2 mm 470 139 dia.
Double cantilever .. 470 47 round each each
Fork ended plate 38.1 mm 305 83 x 213
Seam welded plate .. .. 70
l:!uttress plate .. .. 127
fp Cycles Qmax-Qd Measured strain
Qd Qmax range (peak to (HN/m2) to (kN) (kN) Qd peak) failure
(\) (\)
54 344 132 74 37 6.0 +
30 191 1160 46 53 2.0
75 296 75 llO 46 3.5
46 181 70 85 86 2.4
78 308 144 . 110 41 4.2
- -·---
+ this value estimated from fatigue relationship
(Fig 2-6) for 132 cycles to failure.
N w
b
24
Area proportional to dissipated energy
E (in/in)
Figure 3.1.I Hysteresis loop
25
Pier anchor
Superstructure anchor
Figure 3.2.I Torsional-bar hysteretic damper
26
~· · 1 \ ; : : '
, : ; ·: .;I 1.i t -Figure 3.2.II Force-displacement hysteresis loop and cycles plot for
torsion beam dissipator
\ ~
·\
\ ,,
Figure 3.2.III Prototype torsion beam dissipator fo r South Rangitikei Railway Bridge in test machine
27
Figure 3.2.IV Bilinear hysteresis loop for steel energy dissipater
f p
l I
I ~ ~1
I I !
_J....:::::::.::;___------j------ - t
Figure 3.3.I Cyclic load strain relation for steel in bending
Figure 3.3.II
28
0 400 -!-------,--
E Bui tr us
~L Fork end•~\X - JOO -t------t .. --t------"' " ... .. .. "O
Ci
0 I i I
~200-+-----r--+-----r-- -i ~ .. .. 0
I\.
100
0
0 Bani bar tuts
CJ Rosul t for round top tr cantlltv•r
x Results for toptr plate cant 1 levtrs
e Range al strain C •Jo)
0
a 10
Plastic yield stress f related to strain level in bending p
29
10,000 --r
! !! .. • u
"' u
Figure 3.3.III
I
0
But1r1111........._ \
'x' 0,
0 Bent bar hsh - votuea hom table I
C Rnull for round toper ) cont1hver
····~·'0 X :;~~l!!.,'.o,r1 tao., 0101•
Curve previo..,aly derived for 1tt1oolh round bars
' 100.+----.'--.-.~n~o-eo"°/-r--· - 0,
x ,. a, r-s .... I o , wtld•d
d ob' 0 i Btnl bar r1lot1on1l'lip
10+..~~~+---~~----i~~--r~---;----+----• •• " Range of st,.oin {9f.)
Low-cycle fatigue relationship for mild steel in bend-ing
ro,_, ,., yi•ld 4,,., .,..,. ,.,...,,.
30
~ i
----. ---L _ t J-aL__.~~ ....... a' L_ - -- _l
... -r I •• ,.,; ! Io •'16-2 di~
I I~ : I I ~-~ 1--- 40 _ _j
Figure 3.3.IV Round cantilever dissipater
- - -· f t :)~•o - ..
_/. .. -~
Figure 3.3.V Double cantilever damper machine after testing
I I
I .t "Q"
31
-
S trok• 139 mm
Figure 3.3.VI Hysteresis loop for cantilever damper
... .... "' Q "'":·
32
Figure 3.3.VII Double cantilever damper
( ,.,., I 4 t,
o •• ,•d•t1..,. d"''"• l•1t1 fR.ce••,••t• o ... ,.,,., •• ,.
Figure 3.3.VIII Hysteresis loop for double cantilever damper
1 o y
il 4 00
lOO
0 9 r-,, -,-I I ... -
I I -' o a - . I -' u I
N,~
I
! ~ I
0 Jr )', { I
D -:z ... 0 6 L _______ E ... 0
<LJ w a:: 0 200 u..
-'
I :i: f-
~-+· w :z u.J a s -' F-I
a 4
100 al L ___ 0 l -
0 \ 25 IQ
33
fp = 350 MN/m2
E =!0·03
DIAMETER 0 lmml
: .
. ~;
0
"' .. '" ·"-
"' " ' .. '" "
"' ~ .,
" ..... ..
""' ::::-., ::.:::~
" .. , "' "''\,,, •,
.:: ~';:'(;:;
'50
Figure 3.3.IX Design curves for round cantilever dissipater
Figure 3.3.XI
i ! ·
(a)
,. ., .
34
4_01• .
x, ! ___ j - -:1
i -! ~ 1--- -I --
Round Type lb) Plate T:tE'-,
Figure 3.3.X Cantilever dampers
Split type of plate damper LHS seam welded type RHS
r
I I
i L-
I'
''
35
SECTION A- A
-· ''" N • .,.. : I I
267
Figure 3.3.XII Buttress damper tested during development
Figure 3.3.XIII Buttress type in test machine
z .>it.
o"'
~00
3CO
~ zoo ._, a: 0 u...
tGO
e
0 8 If ! ...JI
...J'
0·7 '
I as L
! I
a 20 l 0 •O
36
fp : 350 MN /m 2
E = 0 03
so 60
PLATE THICKNESS t {mml
-- _ _J
70 !O
Figure 3.3.XIII.A Design curves for plate cantilever dissipator
8tf'll "'t1Cl ,,, •• !)or, (IS ffi;j\,11 tf~
/
37
Coiu1tu•
I 7 I -t-
0os•"'•"I llOOf' 1lob
L uowl 1poc•
Figure 3.4.I Base isolation method using bent round bars
Force
" ~r f ,, / I ----- / I
I ___.,-/ a mox.
al I r 1 ( :,t y It' 141 I I
a'I Typical "•tJE>rimpntol d I loup
-! I I
I D1splocC?ment
;j.. ! I
I - -:::--
I -I
I ~ ~.tr lJk f> T
Figure 3.4.II Loop parameters
I ~I
,, M
38
~ _J I I : '--~~~~~-t--TI~'~~~~
i .. n.1?10.1~
L 11• 11·1
J'u.":: h I 1 ~
ill ]
t
"'' C"- ~ _,I
11 !
i t
Figure 3.4.III Proportions of bars tested
39
Figure 3.4.iv Strain gauged bent bar dissipator
Figure 3.4.V Fail~d bent bars
Figure 3. 4. VII
v
- a t - "' l .
40
I • I
Figure 3.4.VI Forces on bent bars
,. I .. I'
[,~:· .. ~ Col Strain gauge test
, . ..J.'
-~ ... -· I
. f, .. - - _, ...... •&"'"' -- __ jl__
- (
.. ....~ .~r
(C) Movement ot 4~· to oione of ~end
(b) Movement at rlgnt angles to olone of bend
(di Movement for bar with comolete tul"'n at centre
Force-displacement hysteresis loops for bent bars 25 mm diameter
'1111cot ••O•'•"'•"IOI
_J_-r
I'. a. o'
·~•---/ ;oi J
~ 1-~-1~1 -----I
I I
41
Stroir• T
a "'O•.
r_
I I
I
Figure 3.4.VIII Bilinear hysteresis loop for bent bars
L
... Arm
a -
~1
~ range of deflection : 2y
0
Figure 3.5.I Geometry of flexural beam dissipater
42
Flexure! Beam
Anchor
Figure 3.5.II Flexural beam dissipator
T Qmax
322 kN = 36'5 kl'o
19"' mm 7•1. Str-an r-ange
/
Figure 3.5.III Force-displacement hysteresis loop for flexural beam dissipator
Chapter 4
LEAD HYSTERESIS DAMPERS
4.1 Introduction
Another series of devices which are used in bridges to dissipate
the earthquake energy are lead hysteresis devices. The researchers
take advantage of properties of recrystalization in room temperature,
a typical value of 20°C to 25°C, and the plastic extrusion or shear
deformation of lead in designing the devices.
The combination of rubber with lead has also been used in recent
years. This seems to be the best and most promising solution to the
problem at hand. In addition, bridge bearings of rubber have
also been the subjects of tests, as a knowledge of its characteristics
is required for their use in conventional ductile design of bridge
decks and also in base isolation systems.
The devices discussed in this chapter use either lead or its
combination with other materials and are listed below:
1) Lead rubber bearings
2) Lead extrusion dampers
4.2 Lead Rubber Bearings
The lead rubber damped bearings combine the properties of a
bearing and a shear damper in one unit to dissipate energy. As a
device which may be based on either a round or a square laminated
rubber bearing, allows for any direction of movement in a horizontal
plane, it is very well suited to the isolation of bridge decks and
43
44
buildings. A typical device is shown in Figure 4.2.I (13).
The testings performed, as will be discussed in the following
paragraphs, resulted in force-displacement diagram that is plotted in
Figure 4.2.II for rubber-lead and rubber alone. To linearize the
hysteresis loop, a parallelogram can be considered that passes through
points a,b,c (see Figure 4.2.II). This area is 98% of the loop area,
keeping the sides of the parallelogram close to slopes of the loop.
The lead rubber device has many characteristics suitable for use
in a base isolated system. It functions through the strain pattern
of the load, forcing it to act through pure shear. The bearing also
provides a horizontally flexible mount and an elastic centering force.
Furthermore at ambient temperature load is being "hot worked", meaning
during its deformation the l~d recovers most of its mechanical
properties almost immediately. The easy installation and low main-
tenance requirements of this device have made a wider range for its
use in bridges.
To study the details of the device some tests were performed
with the data as described below (8). The lead rubber shear damper was
constructed by taking a 356 x 356 x 140 mm bounded elastomeric bridge
bearings, containing seven 3 mm thick steel plates and six 16 mm \.
rubber plates. A hole was drilled through its center, filling the hole
with a lead insert, with a diameter of 100 mm, Figure 4.2.I. Table
4.2.I has some typical values of the performed test.
45
4.3 Lead Extrusion Dampers
This device works by extruding lead back and forth through an
orifice. The property of lead that could recrystalize in room tempera-
ture and gain its properties back has made it an ideal material for
this device. On being extruded the deformed lead recrystalizes im-
mediately, thereby recovering its original mechanical properties before
the next extrusion or stroke (Fig. 4.3.I) (12). The amount of energy
absorbed is not limited by work hardening or fatigue, but the heat
capacity of the device. The recrystalization temperature, the tempera-
ture which is sufficient to cause 50% recrystalization, during one
hour is well below 20°C for lead. For comparison it could be men-
tioned that for iron the value is 450°C. As a result the operational
temperature for lead is well below the melting point of the lead, i.e.
the melting point of the lead stands for the upper limit temperature.
The extrusion damper is manufactured from a steel tube with an
extrusion orifice at its mid-points. Two pistons are joined by a tie
rod which is extended from one piston to form a push rod, with lead
surrounding the tie rod and filling the volume contained between the
pistons. The interface between lead and steel is lubricated and the
lubricant is retained by chevron seals mounted in the piston. One
piston is effectively part of a connecting rod which extends beyond
one end of the cylinder, and opposite end of the cylinder is fixed to
another part of the structure. When the two parts of the structure
oscillate due to earthquake, the lead extrudes back and forth (8). The
device works like a Coulomb damper, while being extruded through the
46
orifice it does not absorb much energy, which makes it possible to be
used for any number of earthquakes.
The pressure applied to the ram forces the material to flow
through the orifice, producing a microstructure of elongated grains
containing many crystal lattice defects. A proportion of the energy
required to extrude the material appears immediately as heat, and some
stored in deformed material, which is the primary driving force for
the three processes of recovery, recrystalization, and grain growth,
which returns the material back to its original condition. The micro-
scopic process is shown in Figure 4.3.I.
To draw the force displacement loop for the device, the sizes
and testing conditions as described below were used. The sample
device of outside diameter of 150 mm and total length of 1500 mm, with
a total weight of 100 kg was shaken in a 250 KN Instron Universal
Testing Machine for two lead filled extrusion energy absorbers. The
experiment was performed at a frequency of 0.9 Hz. The force-dis-
placement diagram is plotted in Figure 4.3.II, and as it can be ob-
served from the figure, the hysteresis loop is almost a rectangular
one. The ratio of curve area to enclosing area, performance factor, is
79%. The device is not rate dependent (8). A number of extrusion
-8 1 energy absorbers were tested at speeds ranging from 2xl0 to 6xl0
cm/sec. - -1
At l.7xl0 cm/sec and less, the results were obtained using
Instron Machine, at 1.7 cm/sec the results were obtained using
PACRA's 450 KN, and at 6xl0 cm/sec a 62 kg weight drop on a 20 KN
energy absorber was used to perform the experiment.
47
The results are normalized and plotted in Figure 4.3.III (12,11)
using equation below.
where: F force to operate absorber
v = speed
constant {: .12 for v < -3 cm/sec 1. 7xl0
b = .03 for v > -3 cm/sec l.7xl0
For first value of b, load increases 32% for a ten fold increase
in operating speed. For b = 0.03, 7% increase in load is observed
for a rate increase by a factor of 10. As a result of this plot, for
an earthquake like speed the energy absorber is rate-independent.
48
Table 4.2.I Summary of tests conducted at 0.9 Hz with a 400 kN vertical load
Test No. Stroke/mm ·y Temp/°C No. of Cycles
2S, JO ! 68 o.sa +ls 3,S J3 ! 62 O.SJ +lS s 36 + 48 0.41
I +ls s SJ :t 2 0.01 +lS 10,000 S4 + 68 o.sa +4S +S 10 I SS ! 68 o.sa -ls +2 s S9 :!: 68 o.sa -3S +S s 62,64,6S,66 ! 68 o.sa +ls 20,SO,lOO,SO.
69,70 +llS +0.99 +ls 6S,20 -21 -0.18
Table 4.2.II Summary of properties of lead-rubber damper
F/F' F/F {vertl ~tiffness Stiffness Co-ordinates y { b ( F /F I l I~ y l (kN/mm)
a l. 76 0.128 0 a-b = J.4 a.as b J.S6 0.2S8 0.53 b-d = 24 6.0 c 0.86 0.062 0.42 o-c = 2.00 0.50 d 0 0 O.JS o-d = 0 0
Size 356 x J56 x 140 mm ~ass = 82 kg
F' = Force exerted by rubber at a strain of O.S 29 kN
F(vert) = 13.SF' 400 kN
Design Stroke (y 0.5) = ! 58 mm
49
__ F_.~
Lead
tF(vert) 11
F
Figure 4.2.I Lead-rubber shear damper
50
·Stroke/mm -60 -40 -20 0 20 40 60
4.0 b 100
3.0 ~
2.0 50 1 .o
z .. LL\LL 0 o~
-1. 0
-2.0 50 .....--:::
-3.0 .....-".'.
100 -4.0
-0 5 0 05 Shear Strain 0
Figure 4.2.II Force-displacement loops for lead-rubber bearing
51
ORIGINAL GRAINS
EL.ONGATEO GRAINS
RE:CRYSIAL-IZ.AT\ON
GRAIN GROWTH
Figure 4.3.I Longitudinal section of a constricted tube extrusion energy absorber showing the changes in microstructure of the working material
52
2.0
1'5
10
r 5 FORCE' E' x TENSION c l<N) o -t-:;======--=-2-c_"'_ ----------------_ -_ -.... """.r-
10
20 Ca) IS kN CoNST"' c.~o- Tuss:
. 1 '0 FORCE (KN)) O
10
EX"TENSION
----15·2. Cm
Cb) 30 kN B UL.Q~- .Sr!AFT
Figure 4.3.II Typical force-displacement hysteresis loops for (a) 15 kN constricted-tube energy absorber and (b) 30 kN bulged-shaft energy absorber, tested at
1.7 x 10-2 cm/sec (1 cm/min)
53
F / F (1 cm/ rnin)
9 Q 0 6 l"I)
0. N ti\ 0 "
l"I 3 - 0, a ~ " rJ. ~
0 6, ..
~ U1 '"'O
(J) 111 "O - fT1 Ill - OJ. o J'TI 0 0 ,Ja .........
() -- -~ () < 6, q I/)
" lb 3 "' n 5 \ -.......... '
~ 0 0 ~
.I.
I 6 <j ;.
5 + 6!.
6 0 ..
\ 0 0 ...
0 0
0. ..
KEY: SYMBOL TYPE OPERA TING FORCE TEST METHOD
0 CONSTRICTED-TU BE 150 kN CONSTANT RATE It CONSTRICTED-TUBE 15 kN SHOCK LOADING 0 BULGED-SHAFT 30 kN CONSTANT RATE 6. BULGED-SHAFT 9 kN CONSTANT LOAD 'V CONSTANT RATE
Figure 4.3.III Rate dependence of extrusion energy absorbers
5.1 General
Chapter 5
EXAMPLE PROBLEM
Many studies were undertaken by research groups to evaluate the
advantages and disadvantages of using elastic method, elastomeric
bearings, energy dissipaters or other combinations of the above. The
dynamic analysis was carried out based on known and most probable
earthquakes. In this chapter the factors, variables and constants,
considered and calculated for design are investigated. The
computer model and idealizations made are described, and the design
charts developed based on computer output are supplemented (8).
The first design example, Cromwell Bridge, (10) of section 5.4
utilizes the above data applicable to it, for an economical and safe
design. In this example the energy dissipaters were used at the
abutments and elastomeric bearings at both abutments and piers.
The second example (21) reveals the fact that choices of elastic
solution, bearing, or bearing plus dissipaters should be investigated
before final solution is adopted. In this example as described with
more detail in section 5.5 it is shown that using bearings was suf-
ficient for the use of bridge and expected quakes in the bridge life-
time.
5.2 Design Criteria
The dissipators are effective if used in one of the situations
listed below
54
55
a) In regions of high seismicity
b) Mounted on a stiff substructure
c) Mounted on a substructure to remain elastic
It might have disadvantages if used in regions of low seismicity or
where mounted on a flexible or flexurally yielding substructure.
Three different levels of earthquakes were specified as described
below. These are earthquakes possible to happen in the lifetime of
bridges. The bridges are expected to tolerate each of them to some
extent, based on the severity of the earthquake.
a) Moderate Earthquake
It is expected to happen 2 or 3 times in the lifetime of the
structure, varying from 100 to 150 years. If energy dissipater is
the adopted solution, the earthquake energy should be absorbed with no
damage to structural members.
b) Design Earthquake
Bridges are designed based on this earthquake. The designer must
find the optimum solution considering construction economies and
anticipated frequency of earthquake induced damage. For a safer
design, it is advised that protection against yielding should be at
least as much as values adopted for conventional methods of seismic
design.
c) Extreme Earthquake
Failure is expected in extreme earthquake, but in a desired level
for foundation and structural members that will preclude a brittle
56
collapse. The brittle collapse could be gained by suitable margins of
strength between nonductile and ductile members and with attention to
detail.
5.3 Designed Model and Developed Charts
A series of research was carried out to develop charts to be used
rather than dynamic analysis for structures, incorporating energy
dissipating devices where the structural form did not comprise any
unusual features (8).
5.3.1 Computer Program and Computer Model
For analysis the computer program DRAIN-2D which has dynamic
response analysis ability for planar structures deforming inelastically
under earthquake excitation was used and run on MWD's IBM 370/168
computer. The elements were beam/column, with flexural and axial
deformation, and truss, with axial deformation only. The structure mass
is assumed to be lumped at the nodes, and the static loads can be
applied before dynamic loads. The structure is idealized as a planar
assemblage of discrete elements. When the members yield, the plastic
hinges occur at the end of elements.
The computer model is shown in Figure 5.3.I.b. It idealizes the
half of the bridge shown in Figure 5.3.I.a, by a mass representing the
superstructure mass, connected from one side to a truss element,
representing the combined stiffness and strength effect of abutment,
bearings, and dissipators, and from the other side to a combination of
truss and beam/column elements, representing stiffness and strength of
pier bearings, and dissipators. The pile mass is applied at 0.65 ~
57
which is the center of inertial mass. The mass at the base of pier is
the pile cap mass and surrounding soil around the cap that vibrates with
it.
The cases listed below could be considered for stiffness and
strength characteristics of abutment and pier:
a) Energy dissipater at abutment only; in this case truss element 1
of Figure 5.3.I.b is bilinear hysteresis and truss element 2 is
elastic
b) Energy dissipater at pier only; in this case we have bilinear
hysteresis in element 2, and truss element 1 is elastic
c) Energy dissipater at both abutment and pier; in this case both
trusses 1 and 2 are bilinear hysteresis
d) Elastomeric bearings only at both abutment and pier; in this case
both elements 1 and 2 are elastic
e) Sliding bearings at abutment and elastomeric bearings at pier; in
this case element 1 is a Columb damper and element 2 is elastic
5.3.2 Constants and Variables
5.3.2.1 Constants
a) Masses - The studies showed that the results are not very sensitive
to the mass. But it has to be considered that the results are not
useful if the pile cap and pier mass are the same as superstructure
mass. The relative masses of pier, pile cap, and superstructure
relative to each other are shown in Figure 5.3.I.b. The effects
of rotational inertia of pier and pile cap could be neglected, but
for superstructure under transverse response the period would
58
increase, and for an elastic structure it increases the maximum
pier moments by 10%.
b) Damping - The viscous damping ratio of 5% was assumed for the first
mode and 8% for the second mode, expecting the stiffer structural
members to yield at that ratio. Studies showed that 5% and 8% lead
to similar results so the ratio is not critical. The value of 5%
is normally used.
c) Post-yield stiffness ratio - If a section with uniformly distributed
reinforcement of Grade 275 MPa is used, the flexural stiffness of
the piers after yielding could be assumed to be 5% of the stiffness
prior to yielding. The 5% could be varied based on the strain
hardening of the reinforcing steel, the section shape, and the
distribution of steel.
5.3.2.2 Variables
The variables as partly shown in Figure 5.3.I are as follows:
a) Energy dissipater strength, Qd
b) Energy dissipator stiffness, kd
c) Elastomeric bearing stiffness, kb
d) Pier stiffness, I pier
e) Foundation translation, and rotational stiffness, k0 and k8
respectively
f)
g)
Flexural yield strength of the pier, M y
Design earthquakes - The three earthquakes listed below are used
to run samples on the computer as design earthquakes:
59
1) El Centro 1940 N-S - El Centro was recorded on stiff aluvium
in 1940 with a Richter magnitude of 6.4. The maximum accelera-
tion was 0.33 g, and the period of strong shaking of about 12
seconds.
2) Artificial Bl - This is a simulated earthquake with a period
of strong shaking of about 20 seconds. The maximum accelera-
tion is 0.37 g, and a Richter value of 7 or more.
3) Parkfield - Parkfield was recorded in June 1966 in California.
It had a Richter magnitude of 5.5, and period of 2 seconds. It
was an impulsive earthquake with acceleration of 0.50 g.
5.3.3 Design Charts for Elastic Structures with Dissipators
5.3.3.1 General
The subsections of this section will consider the possible designs
below:
a) No dissipators, i.e., elastic structure
b) Dissipators at abutment only
c) Dissipators at piers only
d) Dissipators at piers and abutment
Using the design charts requires the knowledge of the values described
below that are also shown in Figures 5.3.I, 5.3.II.
kdb combined post-yield stiffness of dissipators plus elastomeric
bearings. If lead-rubber device is used kdb is the post-yield
of composite unit
60
where: ~ = dynamic shear stiffness of elastomeric bearings, about
20% higher than quoted shear stiffness
kd post-yield stiffness of dissipators which could be
calculated as below
a) for steel cantilever and bent bar devices,
b)
-1 m
-1 for torsional beam device, kd/Qd = 7 m
kpb = total elastic stiffness of piers, including foundations,
and elastomeric bearings
..!._+..!._+£+ i 3 h k k_ k k k k 3EI ' were o' -o• 8' and I . are 0 b e pier pier
described in section 5.3.2.2.
kab = total elastic stiffness of abutment plus elastomeric
bearings
The value of kab may be considere~ as the horizontal force, Fa' per
unit deflection, 6, as shown in Figure 5.3.II.c. For a rigid abutment,
kab is equal to kb. For a free standing abutment, with an independent
back wall, as shown in Figures 5.3.II.b, 5.3.II.c, kab could be deter-
mined in the same manner as pier in Figure 5.3.II.d.
5.3.3.2 No Dissipators - Elastic Structure
For a bridge structure, acting elastically and restrained at
piers and abutment as shown in Figure 5.3.III, the design charts of
Figure 5.3.IV could be used. The curve is drawn for El Centro 1940
N-S earthquake and the procedure below should be applied to utilize the
curve to find the forces on pier.
61
Procedure:
a) Calculate weight of superstructure, W.
b) Calculate stiffness of abutment plus elastomeric bearings, kab'
and determine kab/W with units of l/mm
c) Calculate stiffness of pier plus elastomeric bearings (or pier
alone where superstructure is built-in to pier) kpb' and determine
kpb/W with units of l/mm.
d) From top half of chart, determine intersection of kab/W line and
kpb/W curve to give force on abutment on vertical axis and super-
structure displacement on horizontal axis.
e) Determine force on pier by:
1) Either multiply superstruture displacement derived from (d)
above by the calculated pier stiffness, kpb
2) or from bottom half of chart, determine intersection of kpb/W
line and kab/W curve.
5.3.3.3 Energy Dissipaters at Abutment Only
The given charts in Figures 5.3.VI to 5.3.XII are design charts
for bridge structures with dissipaters located only at the abutment and
elastic bearing at piers. Figure 5.3.V shows such a structure with
force-deflection characteristics loop. The procedure for using the
charts is as follows:
Procedure:
a) Choose design earthquake.
b) Select from choice of energy dissipater yield strength, Qd
c) Calculate weight of supe~structure, W
62
d) Calculate combined stiffness of dissipater plus elastomeric bearings
at abutment, kab/W with units of l/mm.
e) Calculate stiffness of pier plus elastomeric bearings (or pier
alone where superstructure is built into pier), kpb' and determine
kpb/W with units of l/nnn.
f) From top half of chart, determine intersection of kab/W line and
kpb/W curve to give force on abutment on vertical axis and super-
structure displacement on horizontal axis.
g) Determine force on pier by
1) Either multiply superstructure displacement from (f) above by
the calculated pier stiffness, kph
2) or from bottom half of chart, determine intersection of kpb/W
line and kdb/W curve.
5.3.3.4 Energy Dissipaters at Piers Only
In this case elastic restraint is at abutment and dissipaters at
piers only, as shown in Figure 5.3.XIII. Figures 5.3.XIV to 5.3.XIX
have design charts for this case with specifications given beneath
the charts and procedure listed below.
Procedure:
a) Calculate weight of superstructure, W.
b) Calculate stiffness of pier (not including bearings and dissipators),
k /W in units of l/mm p
c) Select chart with pier stiffness closest to calculated value
d) Choose design earthquake
63
e) Calculate combined stiffness of dissipater plus elastomeric bear-
ings, kdb' at pier and determine kdb/W in units of l/mm.
f) Calculate elastic stiffness of abutment plus elastomeric bearings,
kab' and determine kab/W in units of l/mm.
g) From top half of chart
1) Both determine intersection of full kdb/W line and kab/W curve
to give force on pier on vertical axis and displacement of
superstructure relative to top of pier (deflection of dissipa-
ters and bearings) on horizontal axis,
2) and for flexible pier case determine intersection of dashed
kdb/W line and kab/W curve to give total displacement of super-
structure on horizontal axis.
h) Determine force on abutment by:
1) Either multiply total superstructure displacement derived from
(g)(2) above (or (g)(l) for rigid pier case) by the calculated
abutment plus bearing stiffness, kab
2) or from bottom half of chart, determine intersection of kab/W
line and kdb/W curve.
i) Repeat (g) and (h) above, if necessary, for chart with next closest
pier stiffness and interpolate to estimate design values.
5.3.3.5 Energy Dissipater at Piers and Abutment
As shown in Figure 5.3.XX, the dissipater is located at both
piers and abutment. Figures 5.3.XXI and 5.3.XXII with the procedure
below leads to forces in piers.
64
Procedure:
a) Calculate weight of superstructure, W.
b) Calculate stiffness of pier (not including bearings and dissipaters),
k /W in units of l/mm. p
c) Calculate stiffness of abutment (not including bearings and dis-
sipators), k /Win units of l/mm. a
d) Select chart with appropriate pier and abutment stiffness and
design earthquake.
e) Calculate combined stiffness of dissipater plus elastomeric bear-
ings at abutment, kdb' and determine abutment kdb/W in units of
l/mm.
f) Calculate combined stiffness of dissipater plus elastomeric bear-
ings at pier, kdb' and determine pier kdb/W in units of l/mm.
g) From top half of chart
1) Both determine intersection of full abutment kdb/W line and
pier kdb/W curve to give force on abutment on vertical axis and
displacement of superstructure relative to top of abutment
(deflection of abutment dissipaters and bearings) on hori-
zontal axis,
2) and determine intersection of dashed abutment kdb/W line and
pier kdb/W curve to give total displacement of superstructure
on horizontal axis.
h) From bottom half of chart determine intersection of full pier
kdb/W line and abutment kdb/W curve to give force on pier on
vertical axis and displacement of superstructure relative to top
of pier (deflection of pier dissipaters and bearings) on
65
horizontal axis.
5.4 Design Example I, Cromwell Bridge
The design example utilizes the values calculated for Cromwell
bridge crossing Clutha river upstream of Cromwell, New Zealand. It is
a five span bridge with spans of length 44-56-60-56-40 meters with 8-
meter footpaths on each side, leading to a total length of 272 meters
(21). The superstructure weighs 25,500 kN.
Figure 5.4.I shows elevation and plan view of the bridge, as well
as a section at pier and the flexural beam device used in it as
dissipator device. Figure 5.4.II has more details of the bridge, and
the bridge after completion is shown in Figures 5.4.III, 5.4.IV.
The substructure is concrete piers 11 meters wide x 1 meter
thick with variable heights of 20, 32, 33, and 16 meters, as shown in
Figure 5.4.I. The bridge is located in a most active region, region A,
of earthquake specifications.
It was approved that the structure should be anchored to rock at
the east abutment and all temperature movement accommodated at the
west end, by multiseal deck joint. The bearings used were thick multi-
layer elastomeric bearings at all truss supports, with small sliding
bearing at the landspan ends.
The flexural beam devices were used as dissipators that act
longitudinally only and hinge under transverse load. The hysteresis
loop for this device is shown in Figure 3.5.III. Based on 5% of super-
structure weight as a basis for the value of Qd' which happens to be
almost 300 kN for flexural device, 4 dissipators were used.
66
The calculation is shown below.
W weight = 25500 kN
QdT = (5%)(W) = 1275 kN
n = # of dissipators 1275 300 = 4.25 - 4 dissipators
The El Centro 1940 N-S earthquake was used for analysis and the
charts described in section 5.3.3 were used to find the force on pier.
The force on pier is required for the case that dissipators are
located in abutment and elastomeric bearing pads at piers. This leads
to section 5.3.3.3, and the procedure of that section is closely
followed with the appropriate design chart. For Qd .OS W, and El
Centro 1940 N-S, the design chart of Figure 5.3.VII is applicable (8).
Procedure:
a) The El Centro 1940 N-S earthquake was chosen to be the designed
earthquake with specifications given in section 5.3.2.2.
b) The value of Qd was chosen to be equal to 300 kN which is read
from hysteresis loop of flexural beam device, Figure 3.5.III.
It could also be calculated from 5% of the weight of superstructure,
which would be:
(6375 kN)(0.05) = 318.75 kN ~ 300 kN . +
For this design the conservative value of 300 kN was chosen.
c) The superstructure weight was estimated to be 25500 kN which for
each dissipator would be 1/4 of the total weight.
WT W=;iofd .. 1r issipators
67
25500 kN 4 6375 kN . +
d) kdb/W = ?
e)
f)
g)
kdb = kd + kb
kb= (1.2)(4.85 kN )( 1000 nun) mm 1 m 5820 kN/m
-1 m => 1500 kN/m
kdb kd + kb = 1500 + 5820 = 7320 kN/m
7320/6375 =
k /W = ? pb
1.148 -1 m = .00ll5 -1 nun
The formula in Figure 5.3.II should be used. In this case the
value is calculated and given as 10.1 kN/nun.
kph (lO.l kN )( 1000 mm) mm 1 m = 10100 kN/m
kpb/W 10100/6375 1.584 -1 . 001584 -1 = m = nun +
F = ? 8 ? abut . ' s/s
Fabut/W = 0.128 +
Fabut = 0.128 x W = 0.128 x 6375 kN = 816 kN +
8 I = superstructure displacement = 70 mm + s s
The above values are read from top part of chart on vertical and
horizontal axis respectively. Figure 5.4.V is a copy of Figure
5.3.VII with the intersection of kpb and kdb specified
F . pier ?
68
F . (70 mm)(lOlOO kN )( 1 m ) 707 kN + pier m 1000 mm
ii) Bottom half of the chart
F . /W = 0.11 pier
F . (O.ll)(W) (0.11)(6375 kN) 701.25 - 701 kN + pier
5.5 Design Example II, South Brighton Bridge
The design of a Christchurch Bridge in New Zealand, South
Brighton Bridge, is discussed in this section. Initial design was
based on supporting the superstructure on elastomeric bearing pads and
steel cantilever dampers. Dynamic analysis showed that the dampers were
relatively ineffective, and that the seismic response was dictated by
the characteristics of the bearing pads.
In this design (8) the elastomeric bearings support the super-
structure at abutments and internal hammerheads. This was possibly the
best choice because of its maintenance free nature in the aggressive
salt water environment. Figure 5.5.I has more details of the bridge.
The earthquake forces will be resisted in each direction by single
column octagonal piers acting as vertical cantilevers from rigid pile
caps.
For analysis purposes it was elected to examine the use of steel
cantilever dissipaters between the superstructure and pier hammerhead
to reduce structural ductility requirements under earthquake. So
initial design used eight dissipaters, two at each support, with a total
yield force of 5% of the superstructure weight. It was expected that
the dissipators would greatly reduce pier hinging, and hopefully
69
eliminate the need for ductile pier design. Resulting benefits would
be possible economics in pier reinforcement, and limitation of damage
to the dissipaters by moderate earthquake to the replaceable energy
dissipators.
A computer model was made for the bridge above and both trans-
verse and longitudinal analyses were performed based on El Centro 1940
N-S earthquake. From the graph, one could see that transverse analysis
was the dominant one and so the pier base moment and pier displacement
were considered for that case as shown in Figures 5.5.II and 5.5.III.
Figure 5.5.II the monolithic design reaches yield on seven
points, but the combination of dissipators and bearings have peak well
below yield. The use of elastomeric bearings and no dissipators is
also below yield, and almost close to the one with dissipators. Based
on this data designers wondered whether the use of dissipators are
necessary or not. The displacement response, Figure 5.5.III, as
expected for elastically responding systems is qualitatively similar
to the moment response, with the results of the two designs using bear-
ings being similar, and the improvement resulting from incorporation
of the dissipators being relatively insignificant.
On the basis of the results presented in Figures 5.5.II, 5.5.III
it was concluded that the beneficial effects of the dissipators in
reducing response were at best marginal, and rather uncertain. It is
significant to note that, based on the El Centro response above,
possible savings in reinforcement costs of less than $500 are only a
fractionof the estimated installed cost of the dissipaters of $10,000.
So the final design was using bearings only.
70
(a) Typical Structure
abutment 0·35L
0·075m
t I pier
0·65t
(bl Structural Model
F
(c ) Force - Deflection ldealisorion of Oissipator plus BearinQ
Figure 5.3.I Structural model for parameter studies
71
(a) Rigid Abutment Cose
(b) Fle)(ible Abutment Cose
A I!.
Fa r; - I I I I I I I I I
Fa kob= ~
(cl Abutment Stiffness
A Fp -
F kpb= t
!
( 2 t 3 I i"-?- +-
k(} 3EIµer kb
(d) Pier Stiffness
Figure 5.3.II Pier and abutment stiffness parameters
(a l Structure
F F
abutment pier
(bl Farce - Deflection Characteristics
Figure 5.3.III Model of elastic structure without dissipators
c .!' • ! i. ~ s c • , : ~
-
Figure 5.3.IV
73
°'40
Oo50
0-20
o·•~
Elastic structure, no energy dissipators, (El Centro 1940 N-S), A= 5%
4-7 Skinner
74
energy dissipater
(a) Structure
F F
abutment pier
lb) Force - Deflection Characteristics
Figure 5.3.V Bridge with energy dissipators at abutment only
j i ~ ! 'S.
J ~
; !
s.. O·t~ .;:
:
Figure 5.3.VI
75
;: "' j ~
" u
~ . . ~
" "' ~ c . ! " " <(
c 0 . ... ~
Energy dissipators on rigid abutment, Qd El Centro 1940 N-S
O.OJW,
76
:c "' .i .. , u
E . ~ C> , "' :; ;; a: c 0 . ~ 0 ... ,,
Figure 5.3.VII Energy dissipater on rigid abutment, Qd El Centro 1940 N-S
/
o.osw,
0·25
.t:.
.~ 0-20 ~ .. ~ u E .. .. C> ~ 0•15 ~ c .. E ~
.0 <l
.t:. .,. ;; ~
0•07
0•05
~ 0•05 .;! u
f .. . C> ~ Vl
.. 0•10 Q: e 0 .. u 0 ...
77
Superstructure Oisplocemenl, mm
10 20 30 40 50 60 70 80 90
Figure 5.3.VIII Energy dissipators on rigid abutment, Qd El Centro 1940 N-S
0.07W,
78
3
i
g, 0-0!.
• • (
O·•J_
1 s. ;:
0·1~
~
<>"r f
Figure 5.3.IX Energy dissipators on rigid abutment, Qd = 0.03W, Bl
. , v ,
79
0-30
; o-~ en
s. c
~ .. .. . v 0 ...
. v 0 ...
Figure 5 . 3 . X
0•1
Energy dissipators on rigid abutment, Qd
j
l
0. OSW, Bl
Figure 5.3.XI
:c .!' l . • u ! f .. s. c i • " c c 0
~ :.
c .. i . t . .. s.. . .:: c 0 . u 0 ..
80
0-25
0•20
Energy dissipators on rigid abutment, Qd 0.07W, Bl
c 'r ~ r 2
i .,.. s. ~
i l '
·~
~ ... i ~
l .. '.::". .! . O•?O
! O·lO
Figure 5.3.XII Energy dissipators on rigid abutment, Qd Parkfield
o.osw,
82
(a l Structure
F F
I
abutment pier
(bl Force- Deflection Characteristics
Figure 5.3.XIII Bridge with energy dissipators at pier only
Figure 5.3.XIV
.. ,
c 0 .. u
~
83
0·05
Energy dissipaters on rigid pier, k El Centro 1940 N-S p
o.osw,
84
O·Z~
~
~
,,., ~
~ s .. o ...
2
o .. o
. ~'
~ >O 60 ro 60 90 <JO "o
~ 0-()!11
~
5
0-0
: .. O' l
0·1~ '-----'-·
Figure 5.3.XV Energy dissipators on rigid pier, k 00 Qd o.osw, Bl p '
;: .'? i e .: u
~ .. 0. , "' -s . a: c 0 . u
~
c 0 . u
~
Figure 5.3.XVI
85
0·25
Oisplocement relative to pier
0•20
0·15
0•10
0•10''----1--...L.-.....l...--L----L-
Energy dissipaters on ~lexible pier, k Qd = 0.05W, El Centro 1940 N-S P
0.016W/mm,
Figure 5.3.XVII
86
Energy dissipators on flexible pier, k p Qd = 0.05W, Bl
0.016W/mm,
Figure 5.3.XVIII
. ii: c 0 .. ~ if
.. ~2 - " l ~ 0·05
~~ .. ~ c"' o-.. " if
0•10 --
87
40 50 60
.'? _.__ _ _._;:;__~---1.-::::.J
.,.fl
Energy dissipaters .on flexible pier, k p Qd = O.OSW, El Centro 1940 N-S
0.004W/mm,
Figure 5.3.XIX
88
Energy dissipators on flexible pier, k p Qd = 0.0SW, Bl
0.004W/mm,
89
(a ) Structure
F
abutment pier
(b) Force - Deflection Characteristics
Figure 5.3.XX Bridge with energy dissipators at piers and abutments
90
0-2,
~ 0-20 ~ ,
. .l "' :::. • ~ 4
0•10~
~
~ i
. , "' 0·•5t-::; ~ .. ~
... ~ ~
t I
0·2~1-
Figure 5.3.XXI Energy dissipators on rigid k = 00 , Qd = 0.025W,· k oo
p . a '
....,
' ~ i
~ i 1 " I
pier and abutment, Qd = 0.025W
Bl,
u
: u
f ~ .. 0.
" "'
c 0
~ 0 u.
;: "' ;; 3 .. ~
~ ~ .. ~
CJ>
'-. u a: c 0 .. u :; u.
91
0•30.--~~~~~~~~~~~~~~~~---r~~~-.--~~--,~--.-~~-/'-.,..~~
0·25
0-20
0•10
0·025
0·05
0•10
0•15
0•20
kdb: 0•000 25 W/mm 0•0005
0•0010 0•0015
Displacement relative __ _+-~~'"\"'\ to abutment
30 40 50 60 70 80 90 100 110 Superstructure Oisploc.ement, mm
01splocement
'+-6'0
120 130
/'
/ /
.tl
"' ~
140 150 E
~
/ /
160
Figure 5.3.XXII Energy dissipators kp 0.004W/rnrn, Qd Qd 0.025W
on flexible pier and abutment, Bl, = 0.025W, k = 0.016W/mm, a
111 ,.i.,r upl ilL cff.,cts. TOTAL SUPERSTRUCTURE MASS= 2500 TONNES t-- ----·---------- ---------------- 272m -----------------. _____ _
~t---4~m-r·-----~Ei~---r·---~~ -t--~~~---r- 40rn TE:. Mf T fl A'I Llf(f MOVEMENl
ic, -'" .:r. ___________ ~
· ..•. • ..•. ·... ~ . ·,,: .. . : .. :.·· --·-·!hWh'll"/\V'f{C\.
-4-1·8 l'o
.fLE'{[ITIOf>i
-41 ii :: " :: :73EkN ~· " " ,, " ~~ DIRECTION OF ACTION OF
_PLA!i_ ENERGY DISSIPATORS
12 Om ,--·- - --- ------- --1 ~ . _ II. _____ ----- - -- __ 1L_~
I><1~~1 ~~j~lll-~r:Jl~' · (' 3 '.,n, riu 1·/ ;'!l1':l __ :!,_1 __ ;i ['l;1._H_1;'·'· '. )1·1_1_'','i' 1[!_·1· .. '. li_.li'.I ; __ !Ii \ELA_,TOMLRIC Sl/\NflAfUl ·l,,,:1:1111 I' :J:I:,' '''.!IV !ii', I'·· j flEAHINGS
sru.L rnuss :ii~~~] 1m1~ m~ ''ji'' '~I ;1''1
1"4---- ll·Om ----i
SECTION ~LE!~ft
FLEXURAL
BEAM "''
,., ,x"' ,
_,,
A NC HOH
/113U 11-ll'Nl AN CHOP
FLEXURAL BEAM DEVICE
Figure 5.4.I Flexural beam dissipators in Cromwell Bridge
\0 N
93
~i ,
1 -..,
~t !
I I
-.---I
0
---
94
Figure 5. 4. III Cromwell Bridge View
Figure 5.4.IV Cromwell Bridge View
. " u
0·30
0•25
g 0·20 . Q.
" "' ~ c . ! " "' C(
"' .,.
0•15
0.10
i Q.05
. ~ 0 0•15 ...
4-0
95
I .. " l <> ...
I 7o 50 60 70 80 90
Figure 5.4.V Energy dissipater on rigid abutment, Qd El Centro 1940 N-S
0.05W,
96
\ I
6JM
PLAN
LONG!TUD!NA l SECTION si:ole 1. ~oo
Figure 5.5.I Bridge details
97
10 ---;;- --- --- -- ,..--'' ': '' 1
5 : ~
E z ~
c 0 1JJ E 0 :I:
-5 ' ' r
' .,
' 'J ' r
: r ' : ' "
-10
J 'r : : ~
., ·,
' " '', , "
,, 'I
-('---·--yield (: ~ : 1 I
1 'r
I\ 1 l I I 11 1 1 ,1 :: \I
'•
,, ,, ,,
r r
' r r I' ,, ,, 'I
" r r '' '
.., ___ _ ---yrQld
sec
Figure 5.5.II Pier base-moments, El Centro 1940 N-S
20
c
·' •'
i: " •'
r,
"' '
~ o~~~--+:-t~;.-lf--t.:...~~~~:--tt--t-t-'rr~\:"T~\--:f'!':::'l'i":-t?\t::_t-:-tr:'"7T1i"I';1-t"i~s~e~c 1JJ L) 0 0.. "' C:i -10
-20
Figure 5.5.III
"J r r ' ' r ' r r
' I r : r 1 r ' ' r ' I I I 1
' r 'J r l r r' ' '
')
: r
'' v v v ' I 1 r 1 r 1 I 1 1
I I 1 I I I ,, 'I
,, ,1
' I 1 v v 'I I 'J '• 'J
,, 1,
" ' - munvi 1 ttl tc. -- bee1r1n9s • c.i.moQr:S
Pier displacement (4.73 m), El Centro 1940 N-S
Chapter 6
SUMMARY AND CONCLUSION
This project has been a review of various energy dissipators in-
vestigated and used in bridges. In regions of high seismicity it seems
to be a safe and economical solution relative to the old elastic solu-
tion. The computer outputs for displacements under earthquake show that
energy dissipators used in combination with elastomeric bearings reduce
the displacement to a much lower value.
Figure 6.I shows the displacement of Cromwell Bridge with and
without energy dissipators under artificial Bl earthquake. The dis-
placement has a much lower value when dissipators are used (8). The
problem encountered in investigation of devices is testing them that
should be carried through using the actual size of the dissipator, if
exact values are required. The research is still going on to find some
combination of lead, rubber, and steel for better dissipators.
The facts that most energy dissipators are maintenance free and
have the ability to be replaced if required after a moderate to severe
earthquake, and ~ot affected by aging, especially for steel in the last
case, have attracted many engineers toward conducting research for ideal
devices to be used in bridges and other structures.
In this report the dissipators available on the market today,
with a general description of their nature and their behavior in testing
machines have been covered. The hysteresis loops available for them
are drawn for the samples tested, with dimensions and testing conditions
98
99
described in the test.
The first design example, Cromwell Bridge, uses the data
available for abutment and bridge and utilizes the design charts to
find forces in pier and abutment when flexural beam dissipators are
used.
There have also been cases, such as South Brighton Bridge, that
use of energy dissipators were not considered necessary. The con-
ventional ductile approach was found to be more economical, without
significant increase to seismic risk.
400
300
200
100
200
400
0
Figure 6.1
f\
\0
... : ~ . .....
100
without eneri;y diss1i:ioror1
with ener'll dls:\lpatora,Oci::OiQ W
• S1.4>9"tructute Oisplacement
I'S"
Time, seconds
Superstructure displacement, Cromwell Bridge
REFERENCES
1. J. L. Beck, R. I. Skinner, "The Seismic Response of a Reinforced Concrete Bridge Pier Designed to Step," Earthquake Engineering and Structural Dynamics, Vol. 2, 1974.
2. R. W. G. Blakeley, A. W. Charleson, H. C. Hitchcock, L. M. Megget, M. J. N. Priestley, R. D. Sharpe, R. I. Skinner, "Recom-mendations for the Design and Construction of Base Isolated Structures," Bulletin of the New Zealand National Society for Earthquake Engineering, Volume 12, 1979.
3. Roy A. Imbsen, "Improved Bearing Design Concepts for Increased Seismic Resistance of Highway Bridges."
4. James M. Kelly, "Aseismic Base Isolation, Its History and Prospects."
5. J. M. Kelly, "Aseismic Base Isolation," The Shock and Vibration Digest, Vol. 14, No. 5, May 1982.
6. D. M. Lee, I. C. Medland, "Base Isolation, An Historical Develop-ment and the Influence of Higher Mode Responses," Bulletin of the New Zealand National Society for Earthquake Engineering, 1978.
7. L. M. Megget, "Analysis and Design of a Base-Isolated Reinforce-ment Concrete Frame Building," Bulletin of the New Zealand National Society for Earthquake Engineering, Dec. 1978.
8. R. Park, R. W. G. Blakeley, "Seismic Design of Bridges," Bridge Seminar 1978, Vol. 3, Wellington, New Zealand.
9. T. Paulay, "An Application of Capacity Design Philosophy to Gravity Load Dominated Ductile Reinforced Concrete Frames," Bulletin of the New Zealand National Society for Earthquake Engineering, Vol. 11, No. 1, March 1978.
10. M. J. N. Priestley, M. J. Stockwell, "Seismic Design of South Brighton Bridge, A Decision Against Mechanical Energy Dissipators," Bulletin of the New Zealand National Society for Earthquake Engineering, Vol. 11, No. 2, June 1978.
11. W. H. Robinson, L. R. Greenbank, "An Extrusion Energy Absorber Suitable for the Protection of Structures During an Earthquake," Earthquake Engineering and Structural Dynamics, Vol. 4, 1976.
12. W. H. Robinson, L. R. Greenbank, "Properties of an Extrusion Energy Absorber, 11 Bulletin of the New Zealand Society for Earthquake Engineering, Vol. 8, No. 3,. Sept. 1975.
101
102
13. W. H. Robinson, A. G. Tucker, "A Lead-Rubber Shear Damper," Bulletin of the New Zealand Society for Earthquake Engineering, Vol. 10, No. 3, Sept. 1977.
14. R. D. Sharp, J. R. Binney, D. J. McNaughton, "The Development of the Anz. Head Office Building, Lambton, Wellington," Bulletin of the New Zealand National Society for Earthquake Engineering, Vol. 2, No. 3, Sept. 1979.
15. R. I. Skinner, J. L. Beck, G. N. Bycroft, "A Practical System for Isolating Structures from Earthquake Attack," Earthquake Engineer-ing and Structural Dynamics, Volume 3, 1975.
16. R. I. Skinner, J. M. Kelly, A. J. Heine, "Hysteretic Dampers for Earthquake Resistant Structures," Earthquake Engineering and Structural Dynamics, Volume 3, 1975.
17. R. I. Skinner, R. G. Tyler, A. J. Heine, W. H. Robinson, "Hysteretic Dampers for the Protection of Structures from Earth-quake," Bulletin of the New Zealand National Society for Earth-quake Engineering, Vol. 13, No. 1, March 1980.
18. R. I. Skinner, A. J. Heine, R. G. Tyler, "Hysteretic Dampers to Provide Structures with Increased Earthquake Resistance," Proceeding 6th World Conference on Earthquake, Vol. 2, 1977, New Dehli, India.
19. R. I. Skinner, G. H. McVerry, "Base Isolation for Increased Earth-quake Resistance of Buildings," Bulletin of the New Zealand National Society for Earthquake Engineering, Vol. 8, No. 2, June 1975.
20. P. Sotirov, "Determination of Damping of Real Structures," Pro-ceedings 6th World Conference on Earthquake, Volume II, 1977, New Dehli, India.
21. A. G. Stirrat, Chief Civil Engineer,"Cromwell Bridge - Seismic Design Aspects," Ministry of Works and Development, Civil Engineer-ing Head Office, May 1978.
22. R. G. Tyler, "Damping in Building Structures by Means of PTFE Sliding Joints," Bulletin of the New Zealand Society for Earth-quake Engineering, Vol. 10, No. 3, Sept. 1977.
23. R. G. Tyler, "Dynamic Tests on PTFE Sliding Layers under Earth-quake Conditions," Bulletin of the New Zealand National Society for Earthquake Engineering, Vol. 10, No. 3, Sept. 1977.
24. R. G. Tyler, "A Tenacious Base Isolation System Using Round Steel Bars," Bulletin of the New Zealand National Society for Earth-quake Engineering, Oct. 1978.
103
25. R. G. Tyler, "Tapered Steel Energy Dissipaters for Earthquake Resistant Structures," Bulletin of the New Zealand National Society for Earthquake Engineering, Vol. 11, No. 4, December 1978.
26. Minoru Yamada, Hiroshi Kawamura, "Resonance Capacity Method for Earthquake Response Analysis of Hysteretic Structures," Earth-quake Engineering and Structural Dynamics, Volume 8, 1980.
The vita has been removed from the scanned document