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The Professional Journal of the Earthquake Engineering Research Institute
PREPRINT
This preprint is a PDF of a manuscript that has been accepted for publication in Earthquake Spectra. It is the final version that was uploaded and approved by the author(s). While the paper has been through the usual rigorous peer review process for the Journal, it has not been copyedited, nor have the figures and tables been modified for final publication. Please also note that the paper may refer to online Appendices that are not yet available. We have posted this preliminary version of the manuscript online in the interest of making the scientific findings available for distribution and citation as quickly as possible following acceptance. However, readers should be aware that the final, published version will look different from this version and may also have some differences in content.
The DOI for this manuscript and the correct format for citing the paper are given at the top of the online (html) abstract. Once the final, published version of this paper is posted online, it will replace the preliminary version at the specified DOI.
Bayhan et al. 1
SEISMIC RESPONSE OF A CONCRETE FRAME WITH WEAK BEAM-COLUMN JOINTS
B.Bayhan,a)M.EERI, J.P. Moehle,b)
M.EERI, S. Yavari,c) K.J. Elwood,d)M.EERI,
S.H. Lin,e) C.L. Wu,f) and S.J. Hwang,g)
A reduced-scale, planar, two-story by two-bay reinforced concrete frame with
weak beam-column joints was subjected to earthquake simulations on a shaking
table. The beam-column joints did not contain transverse reinforcement, as is
typical in older-type construction designed without attention to detailing for
ductile response. A series of linear and nonlinear analytical models of the frame
were developed in accordance with ASCE 41 and were subjected to the input base
motions. The goodness of fit between analytical and measured results depended
on the details of the analytical model. Reasonably accurate reproduction of the
measured response was obtained only by modeling the inelastic response of both
the columns and the beam-column joints. The results confirm the importance of
modeling nonlinear joint behavior in older-type concrete buildings with deficient
beam-column joints.
INTRODUCTION
Reinforced concrete frames can be made earthquake-resistant by providing appropriate
stiffness, strength, proportions, materials, and reinforcement details. Design procedures for
earthquake-resistant concrete construction based on ductile behavior of the system were
introduced in the 1960s (Blume et al., 1961) and have been adapted to modern building
constructed prior to the adoption of these modern practices may contain deficiencies that
make them especially vulnerable to damage or collapse during earthquake shaking.
a) Assistant Professor, Dept. of Civil Engineering, Bursa Technical University, Bursa, Turkey b) Professor, Dept. of Civil and Environmental Engineering, University of California, Berkeley, USA c) Associate Research Fellow, PhD, Dept. of Civil Eng., University of British Columbia, Vancouver, Canada d) Associate Professor, Dept. of Civil Engineering, University of British Columbia, Vancouver, Canada e) MASc., Dept. of Civil Engineering, National Taiwan University, Taipei, Taiwan f) Associate Research Fellow, PhD, National Center for Research on Earthquake Engineering, Taipei, Taiwan g) Professor, Dept. of Civil Engineering, National Taiwan University, Taipei, Taiwan
Bayhan et al. 2
Procedures for seismic assessment and rehabilitation of such buildings have been developed
(ASCE 31, 2003; ASCE 41, 2008), but these procedures have not been widely tested against
actual response of older-type construction subjected to earthquake motions. In the present
study we examine the seismic response of a deficient reinforced concrete frame that was
tested in a laboratory, and we explore the accuracy of various procedures for analytically
assessing its response.
The test structure was a reduced-scale, planar, two-story by two-bay reinforced concrete
frame constructed without transverse reinforcement in the beam-column joints. The frame
was subjected to earthquake simulations on a shaking table, resulting in severe damage to the
joints. Linear and nonlinear analytical models consistent with the modeling procedures of
ASCE 41 (2008) were implemented and subjected to the input base motions. The results
provide a basis for judging the accuracy of various modeling assumptions and confirm the
importance of modeling nonlinear response, including beam-column joint nonlinearity for the
case of buildings in which joint failures occur.
PRIOR STUDIES
Past earthquake reconnaissance has identified distress and failure in beam-column joints
with inadequate transverse reinforcement, including, in some cases, the appearance that joint
failure contributed to partial or total building collapse. Examples of earthquakes that involved
beam-column joint damage include El-Asnam, Algeria, 1980; Northridge, California, 1994;
*Refers to nominal diameter in mm in accordance with U.S. metric bar sizes
All transverse bars within the footings and beams had 135° end hooks but while those
within the columns had 90° hooks. The concrete clear cover over the transverse
reinforcement was measured as 17 mm and 20 mm for the columns and beams, respectively.
For reference in this paper, the base corresponds to the top of the footings. Levels 1 and 2
refer to the first and second elevated beams. Columns are identified by their axis letter and
story number; thus, Column A1 is the first-story column at axis A. Joints have similar
Bayhan et al. 8
nomenclature, with the number indicating the level; thus, Joint A1 is the joint immediately
above Column A1.
TEST SETUP
The test specimen was constructed in an upright position in an area outside the testing
laboratory and moved onto the shaking table where it was bolted atop six load cells (two per
column), which were previously bolted to the shaking table (Figure 5).
Elevation
1550
1710
2000 2000
Side View
Top View
Hydraulic Cylinder
Post-tensioned Rod
I Shape Beam
Top Hinge for the Rod
Fixed Clevis ProvidesFree Rotation at the Bottom of theCylinder
750140
5000
750140
310
200
Pin at column topBC A
subsidiarymass
load cells
Figure 5 Test setup showing subsidiary mass, external post-tensioning, and load cells (Yavari 2011).
A stiff steel frame (Figure 6) sandwiched the concrete test frame and provided out-of-
plane stability. A low-friction roller system connecting between the steel and concrete frames
at each level permitted essentially free in-plane motion of the concrete test frame in
horizontal and vertical directions while resisting out-of-plane movement.
Bayhan et al. 9
Inertial masswagon
rigid steelbeamsrollers at mid
span of beams
Elevation view Elevation view Side view
Figure 6 Steel out-of-plane and inertial mass system (Yavari 2011).
Subsidiary mass in the form of lead and steel blocks was attached to the top surfaces of
the beams to simulate tributary gravity and inertial loads at those levels (19.6 kN at Level 1
and 18.9 kN at Level 2) (Figure 6). The connections effectively fixed the mass to the beams
while enabling the beams to deform under applied loads.
As noted previously, the test structure was intended to represent the lower two stories of a
six-story building. Thus, additional measures were necessary to partially simulate effects of
the upper stories. An “inertial mass wagon” weighing 104 kN was positioned above the
second level of the test specimen (Figure 6). The wagon was roller-supported by the steel
out-of-plane frame, with pin-ended links transferring horizontal inertial forces at the second
level. Yavari (2011) provides additional details of the inertial mass wagon.
It was also desirable to increase the column axial loads to values consistent with those in
a taller building. For this purpose, post-tensioning axial forces were applied externally
through pin connections at the tops of the columns. It was intended that the middle column
was initially loaded with a moderate axial load (approximately 0.2fc'Ag) and the exterior
columns with half of that value. Applied axial loads were measured as 0.17fc'Ag and 0.09fc'Ag
for the middle and exterior columns at the beginning of each test, respectively. Pressure-
regulating valves were intended to maintain approximately constant axial force during the
tests. However, maximum variations of 44% and 15% from the target load at peak demand
were recorded for applied load on the exterior and interior columns, respectively. Note that
the aforementioned variations in applied load happened only in a relatively short period of
time and for most of the duration of the tests, the fluctuation in applied load remained less
than 15%.
Bayhan et al. 10
The laboratory simulation procedures do not correctly simulate all effects expected in a
taller building. Such effects include higher-mode responses, overturning effects, and P-delta
effects. However, the primary purpose was not to conduct a proof test on a six-story building,
but instead to provide physical data for testing analytical modeling and simulation
procedures. The laboratory test specimen is reasonably suited for this purpose.
INPUT BASE MOTIONS
Input base motions were scaled from the north-south (NS) component of the TCU047
accelerogram from the 1999 Chi-Chi Taiwan earthquake (Mw=7.6). Station TCU047
(24.6188o N latitude, 120.9387o longitude) was located 33 km from the surface rupture and
recorded a peak ground acceleration (PGA) of 0.41 g in the NS direction. The ground motion
was time-scaled by the square root of 1/2.25 (in consideration of similitude laws for reduced-
scale specimens) and amplitude-scaled to different amplitudes for different tests. In four
shaking table tests the peak table accelerations were recorded as 0.25g, 0.84g, 1.11g, and
1.36g. Figure 7 shows the measured table motion for the 0.84g test and the linear response
spectra (3% damping) for each of the four tests.
Time (sec.)
25 30 35 40 45 50
Acc
eler
atio
n (g
)
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
0.84g
Period (sec.)
0.0 0.5 1.0 1.5 2.0
Spec
tral
acc
eler
atio
n (g
)
0
2
4
6
8
0.25g Test0.84g Test1.11g Test1.36g Test
ξ = 3%
Constant Velocity Region
T f=0.2
9 s
(a) (b)
Figure 7 (a) Base acceleration history recorded on the shaking table for the 0.84g Test and (b) Linear response spectra (3% damping) for the four base motions recorded on the shaking table. (Tf: fundamental period of the test frame)
OBSERVED RESPONSE
Dynamic response of the test structure and its resulting damage were recorded for each of
the four sequential earthquake simulations. Comprehensive observations during the tests and
details of damage to the specimen can be found in the study by Yavari (2011).
Bayhan et al. 11
Figure 8 shows typical results obtained during the second test, during which peak base
acceleration reached 0.84g. The smooth, synchronized appearance of the waveforms suggests
that response was dominated by an apparent first mode, which might be expected considering
the large mass concentrated at Level 2 in the test setup. Based on white noise tests conducted
before the 0.84g test, the period of vibration was approximately 0.29 s. Estimating the
effective period as the time between zero crossings in Figure 8, the effective period had
elongated to approximately 0.46 s at the end of the test, suggesting that the effective
flexibility of the structure had increased by a factor of (0.46/0.29)2 = 2.5.
-505
-2.50.02.5
0.84g Test data
-1000
100
25 30 35 40 45 50
-0.750.000.75
Time (sec.)
(a) Level 2 displacement, cm
(b) Level 1 displacement, cm
(c) Base shear, kN
(d) Level 2 acceleration, g
Figure 8 Measured response histories for 0.84g test (a) 2nd level displacement relative to the base, (b) 1st level displacement relative to the base, (c) base shear, and (d) 2nd level acceleration,
Figure 9 plots relations among peak displacements, peak base shears, and peak base
accelerations measured for each of the four earthquake simulations. Level 2 peak
displacement (relative to the base) increased approximately linearly with increasing peak
base acceleration, which is not unexpected for a reinforced concrete oscillator having
fundamental period in the essentially constant velocity region of the response spectrum
(Figure 7b). In contrast, the relation between peak base shear and peak displacement is highly
nonlinear and suggests that the structure had reached its apparent base-shear strength during
0.84g test and was degrading in strength with subsequent shaking.
Bayhan et al. 12
Level 2 peak displacement, mm
0 50 100 150
PGA
, g
0.0
0.5
1.0
1.5
0.25g Test
1.11g Test
0.84g Test
1.36g Test
Level 2 peak displacement, mm
0 50 100 150
Peak
bas
e sh
ear,
kN
0
50
100
150
200
0.25g Test
1.11g Test0.84g Test
1.36g Test
(a) (b)
Figure 9 Relations between (a) peak base acceleration and Level 2 peak displacement, and (b) peak base shear and Level 2 peak displacement. Peak quantities are the maximum absolute values of the respective quantities recorded during a test.
The test structure was examined visually following each earthquake simulation.
Following the 0.25g test, no cracks were observed on the test structure. In the 0.84g test,
flexural cracks developed at the bottom of first-story columns and diagonal cracks developed
in the Level 1 joints (Figure 10a). The largest residual crack widths were 0.9 mm, 0.2 mm,
and 0.6 mm in joints A1, B1, and C1, respectively. These diagonal cracks propagated into the
top of the first-story columns and, to a lesser extent, into the transverse stubs of joints A1 and
C1. During the 1.11 g test, the extent of flexural cracking in the first-story columns increased,
the cover concrete at the bottom of column B1 partially spalled, and minor flexural cracking
occurred at the top of column B2. Inclined crack residual widths increased to 2.0 mm and 0.8
mm in joints A1 and B1, with no apparent increase in joint C1 (Figure 10b). In the final test
(1.36g test), inclined cracking in joints B1 and C1 increased and joint A1 sustained severe
damage (Figure 10c). The observed damage is consistent with the expected inelastic
mechanism.
Bayhan et al. 13
0.84g Test 1.1g Test 1.36g Test
Jo
int A
1
Join
t B1
Join
t C1
(a) (b) (c)
Figure 10 Damage in first-level joints A1, B1, and C1 after the (a) 0.84 g, (b) 1.11 g, and (c) 1.36 g tests.
Bayhan et al. 14
ANALYTICAL MODELS OF THE SIMULATION
Three analytical models were developed without considering the shaking table test results
in order to provide a “blind” comparison of the measured and analytical results and to
objectively evaluate the accuracy of existing procedures. Analytical models were
implemented in the software platform OpenSees (2005) based on as-built geometrical and
material properties of the test structure. The first model follows the linear modeling
recommendations of ASCE 41 (2008), the second model introduces nonlinear column
elements with slip springs to represent column behavior, and the third model is the same as
the second model but with relatively simple nonlinear rotational springs at joints representing
the expected shear force-deformation relationship of the joint. More refined models likely
could be developed by “tuning” the model to obtain improved correlation; development of
such “tuned” models, however, is not pursued in this study.
For each analytical model, numerical response simulations were conducted by subjecting
the analytical model sequentially to the four measured shaking table motions, with time
between each shaking table motion to allow the analytical model to come to rest. Thus, the
analytical models accumulated damage from one test to the next in a manner similar to the
sequence that occurred during the shaking table tests. Analyses of white noise test data (after
applying the pre-stress axial load on the columns and before subjecting to ground motion
records) indicated that the equivalent viscous damping value was approximately 3% of
critical. Therefore, Rayleigh damping was introduced to the all models through mass and
stiffness-proportional coefficients resulting in 3% damping ratio for the first and second
modes.
MODEL 1 - LINEARLY ELASTIC MODEL
The first analytical model (Model 1) implements the linear modeling recommendations of
ASCE 41 (2008). The model (Figure 11) consists of linear-elastic line elements connected at
the joints. Beam and column flexural stiffnesses are reduced from gross-section values to
account approximately for effects of concrete cracking and reinforcement slip from adjacent
anchorages. Following the ASCE 41 procedures, effective stiffnesses of beams, exterior
columns (P/ fc'Ag = 0.1), and interior columns (P/ fc'Ag = 0.2) are defined as 0.3EcIg, 0.3EcIg
and 0.4EcIg, respectively, where Ec is concrete modulus of elasticity and Ig is the gross
section moment of inertia. Effects of joint shear deformations are approximated by extending
the column flexibility into the joint as prescribed by ASCE 41 for ΣMnc/ΣMnb < 0.8, where
Bayhan et al. 15
ΣMnc and ΣMnb are the sums of the nominal moment strengths of the columns and beams,
respectively, at a beam-column connection. Beam elements are taken as rigid within the
dimensions of the joint. Footings and supporting load cells also are modeled, though their
flexibility is found to be negligible. Beams and supported lead are considered as point gravity
loads and lumped masses at the beam nodes. Inertial mass of the inertial mass wagons is also
considered.
0.3E
cIg
0.3E
cIg
0.4E
cIg
0.4E
cIg
0.3E
cIg
0.3E
cIg
A B C
0.3E cIg 0.3E cIg
0.3E cIg 0.3E cIg
Rigid end zone Linear element
Figure 11 Model 1 implements the linear modeling recommendations of ASCE 41 (2008)
The calculated fundamental period of Model 1 is 0.36 s, which is longer than the initial
period of 0.29 s (estimated from a white noise test after the first earthquake simulation test).
The longer calculated period is expected, because the structure responded well below the
yield point at this stage of testing whereas the ASCE 41 (2008) modeling procedures are
intended to model response near the yield point. During subsequent earthquake simulations,
the calculated period was shorter than the ever elongating apparent periods achieved during
those tests. Because the vibration period of the analytical model did not match the apparent
periods in any of the tests, it is not surprising that the calculated displacement waveforms
mismatched all the measured displacement waveforms (Figure 12).
Bayhan et al. 16
Leve
l 2 r
elat
ive
disp
lace
men
t, c
m-505
MeasuredCalculated
-505
-10-505
10
25 30 35 40 45 50
-10-505
10
Time (sec.)
(a) 0.25g test
(b) 0.84g test
(c) 1.11g test
(d) 1.36g test
Figure 12 Measured and calculated (Model 1) relative displacement response histories for Level 2 measured during (a) 0.25 g, (b) 0.84 g, (c) 1.11 g, and (d) 1.36 g tests.
Base shears were over-estimated for all tests (Table 2). This is expected for the second,
third, and fourth tests, because the analytical model assumed linear behavior whereas for
those tests the base shear was limited by nonlinear response.
Table 2 Measured and calculated absolute max. base accelerations(PBA), Level 2 displacements (Δ2), Level 1 displacements (Δ1), base shears (Vb), and Level 2 accelerations (A2) for all models (M1 = Model 1; M2 = Model 2; M3 = Model 3) and earthquake simulations. All displacements are measured relative to the base. Accelerations are absolute. Errors (%) shown below the calculated values in gray color are calculated as the absolute value of (calculated – measured)/measured for each quantity.
An apparent shortcoming in Model 1 is that all components were modeled as being
linear-elastic whereas the test structure responded inelastically for some of the tests. As a first
step in modeling inelastic response, Model 2 introduces nonlinear elements for the columns,
including linear springs to represent rigid body rotations associated with reinforcement slip
from anchorages. Beams were expected to respond in the effectively linear range of response,
so they are modeled using linear elements with effective flexural stiffness 0.3EcIg as in Model
1. Joints are assumed rigid along beam and column depths. Figure 13 depicts the model
configuration.
NC
NC
NC
NC
NC
NC
A B C
0.3E cIg 0.3E cIg
0.3E cIg 0.3E cIg
Rigid end zone Linear element Slip spring
NC Nonlinear column
Figure 13 Model 2 implements linear beam elements, nonlinear column elements, and linear slip springs at both ends of columns.
Column flexure is represented by force-based, fiber nonlinear beam-column elements
with five integration points. The formulation of these elements assumes that plane sections
remain plane and normal to the longitudinal axis at each integration point. Spread of
plasticity is modeled using the Gauss-Lobatto quadrature rule through the element presented
in Spacone et al. (1996). Column shear deformations are ignored. Unconfined concrete and
confined concrete are modeled using the stress-strain model of Mander et al. (1998).
Confined concrete strength was calculated as 43.5 MPa. Longitudinal reinforcement is
modeled using a hysteretic material with tri-linear backbone (OpenSees 2005).
Zero length linear-elastic section elements are added to both ends of columns to simulate
rotations due to slip of reinforcement from adjacent anchorages. The rotational stiffness of
the slip springs, kslip, is calculated by assuming a constant bond stress of u = 0.8 'cf (MPa)
Bayhan et al. 18
along the column longitudinal bars within the footings and the beam-column joints until the
calculated stress drops to zero, estimating bar slip as the total elongation of the bar along this
stressed anchorage length, and assuming section rotation occurs about the cracked section
neutral axis. With these assumptions, the rotational spring stiffness is (Elwood and Eberhard,
2009)
flex
ybyybslip EI
fd
uM
fd
uk
88 004.0 ==φ
(2)
where db is the nominal diameter of the longitudinal reinforcement, fy is the longitudinal
reinforcement yield stress, M0.004 is the calculated moment strength corresponding to strain
0.004 in the extreme compression fiber of concrete, φy is the yield curvature for the cracked
section, and EIflex is effective flexural rigidity of the cracked section.
The fundamental period of vibration of Model 2 (0.28 s) is shorter than that of Model 1
(0.36 s), and very close to the initial period of 0.29 s measured in white noise tests. The
calculated responses for the 0.25 and 0.84g tests are relatively well synchronized with the
measured responses (Figures 14a and 14b).
-505
-505
-10-505
10
25 30 35 40 45 50
-10-505
10
MeasuredCalculated
Leve
l 2 re
lativ
e di
spla
cem
ent,
cm
Time (sec.)
(a) 0.25g test
(b) 0.84g test
(c) 1.11g test
(d) 1.36g test
Figure 14 Measured and calculated (Model 2) relative displacement response histories for Level 2 measured during (a) 0.25 g, (b) 0.84 g, (c) 1.11 g, and (d) 1.36 g tests.
Bayhan et al. 19
For subsequent earthquake simulation tests in which joint cracking increased, however,
the apparent period of the analytical model with rigid joints is shorter than the apparent
period of the test structure, such that calculated and measured waveforms are poorly
synchronized (Figures 14c and 14d). As summarized in Table 2, estimates of peak
displacement are inconsistent especially for the 0.84g test. The calculated errors are 40% and
44% for Level 2 and Level 1 displacements, respectively. Peak base shears were fairly
estimated for the 0.25g and 0.84g earthquake simulations. For the 1.11g and 1.36g tests,
however, the calculated base shears exceeded the measured values by a considerable margin.
MODEL 3 – NONLINEAR COLUMN AND JOINT MODEL
Test photographs (Figure 10) show that beam-column joints of the test structure sustained
notable damage during earthquake simulations. Model 3, illustrated in Figure 15, was
developed from Model 2 by adding a nonlinear beam-column joint element to represent
observed behavior in the first-level joints.
The scissors model proposed by Alath and Kunnath (1995) was implemented because it
offered essential features of nonlinear behavior while using a relatively simple analytical
representation. In the scissors model, the finite size of the joint panel is modeled by two rigid
links interconnected by an inelastic rotational spring. When the spring is subjected to
moment, the rigid links rotate relative to one another at an angle that represents the shear
distortion of the beam-column joint.
A B C
Rigid end zoneLinear element
0.3 EcIg 0.3 EcIg
NC
NC
NC
NC
NC
NC
0.3 EcIg 0.3 EcIgSlip springNonlinear columnNCJoint spring
Figure 15 Model 3 implements linear beam elements, nonlinear column elements, linear slip springs at column ends, and nonlinear joint springs at Level 1.
Bayhan et al. 20
The relation between moment Mj at the center of the joint and the nominal joint shear
stress τjh is (Celik, 2007):
c
bcjhjhj
Ljd
LhAM
1/11
−−
= τ
(3)
where nominal joint shear stress τjh and joint area Ajh are calculated according to ACI 318
(2011), hc is the column depth parallel to the beam span, Lb and Lc are the total length of the
beams and columns, respectively, and jd is the internal moment arm of the beam (assumed
constant throughout the test).
The relative rotation of the two rigid links in the scissors model represents the change in
angle between two adjacent edges of the panel zone assumed to exist in the beam-column
connection. Thus, rotation of the spring equals the joint shear strain, that is,
jj γθ =
(4)
Pinching4 hysteretic material, a uniaxial material model proposed by Lowes and Altoontash
(2003) and implemented in OpenSees (2005), was used to model the hysteretic behavior of
the joint spring. It has a multi-linear envelope exhibiting degradation and a tri-linear
unloading-reloading path representing a pinched hysteresis.
The moment-rotation envelope relationship for the pinching4 material was determined
empirically from the previous laboratory tests reported by Pantelides et al. (2002a) and
Walker (2001). Mean values of τjh and γ were chosen from the reported experimental results.
These tests were selected from among other test data because the tested joints were deemed
most similar to those in the shaking table specimen. None of the selected test units had any
transverse reinforcement in the panel zone. The beam bottom bars were continuous and axial
load level in the joint was 0.1fc'Ag. However, it is noted that the columns in the tests of
Walker (2001) were stronger than the beams (contrary to the shaking table specimen) and the
column axial stresses were lower than those in the shaking table specimen. For the exterior
columns; test unit 3 from Pantelides et al. (2002a) was taken as being representative of joints
in the shaking table structure. In this joint, beam bottom bars were extended 360mm (14 in.)
into the joint having a width of 400mm (16 in.), resulting in good anchorage of the bottom
bars.
Bayhan et al. 21
The pinching4 backbone parameters suggested by Celik and Ellingwood (2009) for
nonductile joints were adopted in this study; namely:
uforceP = uForceN = -0.10 (5)
rForceP = rDispP = rForceN = rDispN = 0.15
The current study also adopted, without calibration, the pinching4 cyclic stiffness and
strength degradation parameters used for examples in the Opensees Manual (2005). Since the
blind test is intended to evaluate the accuracy of existing procedures; no adjustment was
made to improve goodness of fit for the test structure.
Figure 16 illustrates the resulting hysteresis obtained for Joint A1 in analysis of the test
structure subjected to the 0.84g table motion. The obtained hysteresis is similar to that
commonly observed for unreinforced joints, within the limits of the analytical model, and
suggests that the model was reasonably implemented in the simulation. Joint instrumentation
during this test indicated peak negative joint shear strain of -0.015, which is close to the peak
negative value obtained in the joint analytical model.
Figure 16 Behavior of the moment-rotation spring at joint A1 for the 0.84g test
Figure 17 shows the measured and calculated Level 2 relative displacement histories for
the four sequential earthquake simulations. The analytical results closely follow the measured
displacement histories from the beginning of the test through the time of maximum response
(around 35 s), with poorer correlation in the subsequent lower-amplitude response.
Bayhan et al. 22
-505
-505
-10-505
10
25 30 35 40 45 50
-10-505
10
MeasuredCalculated
Leve
l 2 r
elat
ive
disp
lace
men
t, c
m
Time (sec.)
(a) 0.25g test
(b) 0.84g test
(c) 1.11g test
(d) 1.36g test
Figure 17 Measured and calculated (Model 3) relative displacement response histories for Level 2 measured during (a) 0.25 g, (b) 0.84 g, (c) 1.11 g, and (d) 1.36 g tests.
Figure 18 compares the measured and calculated base shear response histories for the
0.84g test for all models. Model 3, which includes column and joint nonlinear models,
produces consistently more accurate results than either of Models 1 or 2. Similarly good
correlation was obtained by Model 3 for the other earthquake simulations (not shown).
-300-150
0150300
-1500
150
25 30 35 40 45 50-300-150
0150300
Time (sec.)
MeasuredCalculated
Base
she
ar, k
N
(a) Model 1
(b) Model 2
(c) Model 3
0.84g test
Figure 18 Measured and calculated base shear response histories measured during the 0.84g Test for (a) Model 1 (b) Model 2 (c) Model 3.
Bayhan et al. 23
Although Model 3 analysis results match the measured results fairly well, the peak base
shears were consistently underestimated. It is possible that this strength difference may be
related to the strain rate. Dynamic tests on reinforcing steel (Malvar 1998) have shown yield
strength increase on the order of 20% for the strain rates achieved during these tests (around
0.14/s). Although dynamic loading similarly affects concrete strength, the effects on strength
of beam-column joints are unknown. It is also plausible that other inaccuracies in the models
used to estimate column and beam-column joint strengths were at cause. It is not possible to
isolate the source with the available data.
SUMMARY AND CONCLUSION
Shaking table tests were conducted on a 1/2.25 scale, planar, two-bay by two-story
reinforced concrete frame without transverse reinforcement in the first-level beam-column
joints. During the shaking tests, the joints sustained considerable damage indicating
occurrence of inelastic joint response. Analytical models of the test structure were developed
based on recommendations of ASCE 41 (2008). The analytical models and their analyses
used measured geometries, material properties, and input base motions, but otherwise the
analyses were intended as “blind analyses” in the sense that “tuning” of model parameters to
improve correlation was not pursued. Within the limitations of these tests and analyses, the
following conclusions are made:
1. The test structure responded essentially elastically for a first shaking test (0.25g peak base
acceleration). During subsequent tests, the response was highly nonlinear. As was
intended during the design phase, damage to the components suggested that inelastic
behavior was concentrated mainly in the first-story beam-column joints.
2. A linear model incorporating stiffness modeling recommendations of ASCE 41 (2008) had
fundamental period longer than the effective period measured during the 0.25g test. The
longer calculated period is attributed to the ASCE 41 member effective stiffnesses, which
are intended to represent response near yield, whereas the structure responded well below
the yield point in that test. The calculated period was shorter than the apparent period
during subsequent tests. Consequently, the analytical simulation using Model 1 did not
match well with the measured simulations for any of the tests.
3. The addition of nonlinear column models to the analytical model improved the correlation
with all tests, but the model was too stiff and strong for shaking tests that drove the
structure well into the inelastic range of response.
Bayhan et al. 24
4. The addition of a relatively simple nonlinear joint model produced excellent correlation
with all four shaking tests. This study confirms the importance of incorporating effects of
joint nonlinearity in analytical models for buildings with weak beam-column joints.
Furthermore, the analytical implementation used in this study was demonstrated to be
effective for the limited conditions in which it was applied.
ACKNOWLEDGMENTS
This study was funded by the U.S. National Science Foundation as part of the NEES
Grand Challenge Project on Mitigation of Collapse Risk in Vulnerable Concrete Buildings,
under Award No. 0618804 to the Pacific Earthquake Engineering Research Center,
University of California, Berkeley. The laboratory tests were funded in part by the National
Science Council of Taiwan under Award No. NSC94-2625-Z-492-005. The funding,
facilities, and technical support from the National Center for Research on Earthquake
Engineering of Taiwan are gratefully acknowledged. All opinions expressed are solely those
of the authors and do not necessarily represent the views of the funding agencies.
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