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1
Investigation on Effective Parameters for Seismic Dam-
age Control of Steel Moment Frame
Arman Kamalzadeha, Reza Karami Mohammadia*
a Department of Civil Engineering, K.N.Toosi University of Technology, Intersection of Vali-
e-Asr St. and Mirdamad St., 1996715433, Tehran, Iran.
* Corresponding author e-mail: rkarami@kntu.ac.ir
Abstract
In recent building standards, seismic damage of structures represents by local or global dis-
placements and rotations. However, the effect of dissipated energy of members and the whole
structure is not participated directly. Therefore, several damage indices are developed, con-
taining the effect of drifts and dissipated energy including Park and Ang damage index. In
this study, we found the most appropriate design of a one bay and one story steel moment re-
sisting frame using modified Park and Ang damage index (DI) as seismic damage representa-
tive, to satisfy the strong-column weak-beam (SC/WB) criteria and, reach maximum energy
dissipation of the simple frame. Then, the correlation between PGA and DImax occurrence
time is investigated for each record and each design scenario. Finally we examined the effi-
ciency of 4 energy dissipation devices usage in passive and semi-active control systems and
the maximum of modified Park and Ang DI values compared to uncontrolled DImax in several
cases. This paper demonstrates that there is a good time correlation between PGA and DI,
particularly in the range of the appropriate design due to modified Park and Ang DI which di-
rectly take dissipated energy into account. This study also showed that, for mentioned simple
frame and the criteria developed in this paper, passive viscoelastic and viscous dampers are
the most effective devices in dissipating energy.
Keywords: Damage Index; Moment Resisting Frame; Time Correlation; Energy Dissipation
Devices.
1. Introduction
Seismic design of structures has been a long time, a serious concern for civil engineers and re-
searchers. Therefore, primary concepts of structural design are formed to be only on the basis of
structural forces implications (force based seismic design). After several earthquakes shown that,
the previous design concept was not sufficient to undergo these types of seismic excitations, civil
engineering community defined a new concept based on structural responses (mainly roof dis-
3rd International Conference on Acoustics & Vibration (ISAV2013), Tehran, Iran, 25-26 Dec. 2013
2
placement and members rotation) as displacement based seismic design. After that, performance
based seismic design concept was described with modifying displacement based seismic design and
define specific structural responses values to represent the destruction states of structures (perfor-
mance levels).
To design structures on the basis of performance based seismic design, ANSI/AISC 341-10
[1] suggests an approach, strong-column weak-beam (SC/WB). In SC/WB approach, the goal is to
design structures in order to, maximize the energy absorption of members (without general failure
of structure), avoid forming plastic hinges in columns (except columns bottom of first floor) and
avoid incidence of soft story.
As mentioned above, the damage in performance based design defines, due to structural drift.
Park and Ang showed [2] that, considering only drift is not an appropriate representative for struc-
tural damage and, additional to drift, hysteretic energy is participating in this damage. Therefore,
several damage indices are created such as, Modified Park and Ang [3].
However, under some seismic excitations, even designing the structure according to best de-
sign concepts is not enough and, energy dissipation devices are needed to reduce the seismic dam-
age harms. These devices can implement as passive control (without changing presence or proper-
ties of device), active control (presence or properties of device is commutable) and semi-active con-
trol (same as active control but need much less power supply that can provide by a battery) [4].The
active and semi-active control systems need an algorithm (feed-back or feed-forward) with an acti-
vation criterion (depends on uncontrolled structural responses or seismic excitation), to activate the
energy absorption device and, control the responses and damage of structure [5]. The explanation of
passive and semi-active control system is shown in Fig 1. in brief.
(a)
(b)
Figure 1. (a) Passive, (b) Semi-Active Control System [4]
In this study, best design of a one bay and one story steel moment frame by using SC/WB
concept and modified Park and Ang DI, is obtained. Then, in order to find an appropriate criterion
for semi-active control, a correlation with PGA and maximum DI occurrence time is investigated.
Finally, passive and semi-active devices are implemented in the simple frame and the responses are
compared.
2. Methodology
In this paper, initially, a simple steel moment frame (one bay and one story) in Fig 2. is de-
signed only for gravitational loads using IBC2012 [6] and the damping ratio of the structure is as-
sumed to be 2.5%. Then, we performed a kind of incremental dynamic analysis IDA [7] using 12
records (see Table 1.) with 9 Scaled PGAs exerted to 9 frame designs (see Table 2.), these designs
varied with the use of plastic modulus ratio of column to beam (Zc/Zb), which is called Z Ratio. The
earthquake records are chosen to have site classification C (360≤Vs≤760 m/s) [8] and recorded
PGAs more than 0.125g. These records are downloaded from Peer NGA database [9] and ITACA
database [10]. Plenty of nonlinear time history analyses are implemented on a group of simple steel
3rd International Conference on Acoustics & Vibration (ISAV2013), Tehran, Iran, 25-26 Dec. 2013
3
moment frames using open source analysis program OpenSees [11] and, the post-processing out-
comes are calculated using Matlab [12].
In order to find a set of design that, satisfies SC/WB criteria and causes economical design, in-
stead of drift (local/global displacement/rotation), modified Park and Ang DI values of each mem-
ber at possible plastic hinges are computed (plastic hinges are set to be at member ends in which,
responses were the most, see Fig 2.). To reach this purpose, DImax values for each Z Ratios and
each 12 records and, for a specific Scaled PGA are compared. At last, using this comparison and
averaging the results of each 12 records, we found the best design (range of Z Ratios) for a specific
Scaled PGA. This procedure is iterated for each of 9 Scaled PGAs in Table 3. to find best design for
each of these cases.
With Comparison of earthquake records accelerations and the modified Park and Ang DI time
histories, we saw that, there could be a correlation between PGA occurrence time (tPGA) and exceed-
ance of DImax (tDIm) and 0.5DImax (t0.5DIm) occurrence time. After this, with the best range of Z Ratios
obtained and, choosing the smallest Scaled PGA that, caused noticeable damage in frames for all 12
earthquake records, time correlation between tPGA and tDIm and t0.5DIm is investigated, separately.
This time correlation could lead us to an appropriate criterion for semi-active control activation.
Because, for DI>1.0, the structure is collapsed, DImax values are set to be 1.0 .
Figure 2. Simple Frame Model (Primarily Design due to Gravity Loads)
Finally, to control damage values, four energy dissipation devices are used diagonal in the
frame (see Fig 2.), once in passive control and once in semi-active control system. Then, the results
are compared to see which one had the most effective role in reducing damage.
3. Best Design Survey
To find the most appropriate design of the frame, we just changed the column section and let
the beam remain unchanged. We chose Modified Park and Ang damage index [3] in order to esti-
mate the damage capacity of columns and beam.
(1)
In the above equation φm is maximum curvature during excitation obtained from analyses, φr
is recoverable curvature at unloading, φu is the ultimate curvature capacity (obtained from pushover
analysis or code criteria), β is the energy participant factor (this factor is taken 0.025 [13]), My is the
yield moment of member and is the hysteretic energy calculates from moment-curvature hys-
teresis curve. One can rewrite this equation as follows:
(2)
In which, mC.P. is the ratio of ultimate curvature to recoverable curvature corresponding to
Collapse Prevention performance level [14].
3rd International Conference on Acoustics & Vibration (ISAV2013), Tehran, Iran, 25-26 Dec. 2013
4
To find the most appropriate sections, nonlinear time history analyses are utilized using 12
earthquake records which are scaled to nine Scaled PGAs and these set of records are applied to
nine different designs of steel moment frames (beam remained unchanged and column sections var-
ied).
Table 1. Earthquake Records Characteristics
Earthquake
Component
PGA
PGA Time
Duration
Significant Duration
Bracketed Duration
ElCentro
180
0.3129
2.15
39.99
24.1
28.83
Friuli 1st Shock
NSC
0.3458
4.03
36.385
4.25
7.425
Friuli 3rd Shock
NSC
0.2636
3.8
21.99
4.46
4.76
Friuli 4th Shock
NSC
0.3493
3.43
24.59
3.645
5.925
Kern County
21
0.156
9.14
54.15
30.3
19.6
Irpinia Bagnoli
NSC
0.1294
6.23
79.145
40.75
41.175
Irpinia Brienza
NSC
0.2178
12.075
78.83
29.215
8.51
Irpinia Sturno
NSC
0.2253
4.53
70.755
38.865
43.655
Northridge
180
0.2447
11.92
19.9
8.47
11
San Fernando
205
0.3234
2.62
29.99
14.53
15
Sierra Madre
1155
0.302
1.98
39.98
2.74
4.16
Tabas
LN
0.8358
10.5
32.82
16.48
27.24
Hereinafter, using the results of all these analyses, modified Park and Ang damage index is
computed for each case at two ends of each member (see Fig 2.). Then, DImax of plastic hinge 1 and
6 as column bottom damage index (DImColBot), maximum DI of plastic hinge 2 and 5 as column top
damage index (DImColTop) and, maximum DI of plastic hinge 3 and 4 as beam damage index (DIm-
Beam), are sketched versus Z Ratio for 12 records with specific scaled PGA value and after this, the
average for these 12 records could be obtained. Therefore, we got 9 average graphs (for 9 Scaled
PGAs).
Fig 3. shows, Averages of DImColBot, DImColTop and DImBeam for two Scaled PGAs (1.25g and
3g). It is illustrated, with increasing Z Ratio values, DImColBot and DImColTop decrease and, even
DImColTop became zero at some point of Z Ratio (for nine Scaled PGAs, this Z ratio range differs
from 1 to 1.3). Furthermore, DImBeam increased and then, decreased at some point. As it can be seen
from Fig 3.a., when the Z Ratio is 1.3 and from Fig 3.b., when the Z Ratio is about 1.1 the column
bottom and beam DImax intersected. Which means at these points the damage value of beam is equal
to column bottom.
(a)
(b)
Figure 3. Average DImax of 12 Earthquake Records Scaled to (a) 1.25g and (b) 3g, both cases Applied to 9
Set of Designs
It is noticeable in Fig 3.a., that from Z Ratio=0.75 to 1.3 and in Fig 3.b., from Z Ratio=0.75 to
1.1, the bottom column damage is dominant and from Z Ratio=1.3 to 2.0 and Z Ratio=1.1 to 2.0,
beam damage is dominant, respectively. Note that for this kind of frame, top column damage is not
ever predominant. After investigation for nine Scaled PGAs, the results showed that, the best Z Ra-
tio range to meet the SC/WB criteria with considering economical design, is from 1.1 to 1.3 in gen-
eral.
3rd International Conference on Acoustics & Vibration (ISAV2013), Tehran, Iran, 25-26 Dec. 2013
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4. Time Correlation Investigation
In this section, the time correlation of Park and Ang damage index and PGA occurrence is in-
vestigated for all cases. This correlation is investigated on tPGA with tDIm and t0.5DIm, separately.
Table 2. Set of Scaling PGAs and, Different Z Ratios with Periods Corresponding to Z Ratios
Scaling PGAs (g)
Z Ratios
Period (s)
0.5
0.75
0.2208
0.75
0.9
0.2005
1
1
0.1901
1.25
1.1
0.1814
1.5
1.2
0.1741
2
1.3
0.1665
2.5
1.5
0.1542
3
1.75
0.1421
4
2
0.1324
For all cases including 12 records which is scaled to 9 scaled PGAs, that is exerted to 9 sets of
design (see Table 1. and Table 2.), the correlation between the time in which PGA value occurs and,
the time in which the exceedance of DImax and 0.5DImax occur have been investigated, separately
and, the results for exceeding of DImax and 0.5DImax have been illustrated in Fig 4.a. and Fig 4.b.
(Scaled PGA=0.5g is not mentioned here because, did not cause any particular damage in frames.).
(a)
(b)
Figure 4. Time Correlation between tPGA and, (a) tDIm, (b) t0.5DIm
As it can be seen from Fig 4. after Z Ratio=1.0, almost for all Scaled PGAs we have accepta-
ble correlation between PGA occurrence time and both DImax and 0.5DImax occurrence time. Note
that the best range of Z Ratios mentioned in Section 3. embraced in this range. Also notice, there is
no correlation available for Scaled PGA=0.75 after Z Ratio=1.1 because, all seismic excitations
cause low damage that, is not enough for investigating correlation. And, the average correlation of
these tPGA (except Scaling PGA=0.5) for tDIm and t0.5DIm are shown in Fig 4. with wide red line.
Fig 4. even shows, for DImax, the average of all Scaled PGA correlations, resulted in accepta-
ble correlation after Z Ratio=0.95 which is above 0.85 . This figure also shows, for 0.5DImax, the
average of all Scaled PGA correlations, gave us even much more appropriate correlation in all rang-
es of Z Ratios that is more than 0.8 (note that in this case for Z Ratios above 0.95 is approximately
near 0.9) .
3rd International Conference on Acoustics & Vibration (ISAV2013), Tehran, Iran, 25-26 Dec. 2013
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5. Comparison of Semi-Active and Passive Control
Eventually, analyses are carried out for Scaled PGA=1.5g the lowest PGA value, we were
certain that the frame under all earthquake records, undergo serious damage, due to results of Sec-
tion 4. also, a range of design of columns (Z Ratio={1.1 1.2 1.3}) is used, according to Section 3.
outcomes.
It is seen, the most significant proportion of damage, occur about the time in which, peak
ground acceleration occurred (see Fig 4.). Therefore, these two control systems are used to reduce
structural damage:
Passive Control: energy dissipation devices installed and their characteristics and
presence remain unchanged.
Semi-Active Control: energy dissipation installed and, it is activated when, the re-
sponse of the structure met the criteria and, deactivated when, the response of the
structure is under the criteria.
Four kinds of energy dissipation devices are used in this analyses, adding stiffness (see Fig
3.a.), viscoelastic solid damper using Kelvin-Voight model (see Fig 3.b.), fluid viscous damper us-
ing Maxwell model (see Fig 3.c.) and, viscous damper without any additional stiffness (see Fig 3.d.)
[5].
(a)
(b)
(c)
(d)
Figure 5. Energy Dissipation Devices: (a) Additional Stiffness, (b) Solid Viscoelastic Damper, (c) Fluid
Viscous Damper, (d) Viscous Damper [4,5]
The criteria for all the semi-active cases was so that, these devices participate in bearing seis-
mic excitation when, the roof displacement exceeded the Immediate Occupancy performance level
(I.O.) [15]. So, a feedback algorithm is used to satisfy this criterion.
We used viscous damping of the devices as Cd=4.0 tonf.s/cm, stiffness of the devices Kd=1.9
tonf.s/cm and α=0.6 according to Zhang and Soong [16] and, L.M.Moreschi [17]. These devices are
used diagonal in the simple frame of Fig 2. . Then, the analysis results are compared to see which
one of the energy dissipation devices reduce the structure responses (Park and Ang DI), more.
To compare responses of frames, analyses are done for all of 12 earthquake records (Table 1.)
with Scaling PGA=1.5g and for Frame Period={0.1814; 0.1741; 0.1665} (see Table 2.). Nine
types of frames are analysed including uncontrolled frame and frames with additional stiffness, vis-
coelastic damper, Maxwell damper and viscous damper once in passive control and once in semi-
active control system.
The activation criterion of semi-active devices is chosen to be 0.5% of frame height [15] that
is 3.5m according to Fig 2. (which is 1.75 cm) to correspond the I.O. performance level, approxi-
mately. The results are listed as DImax in Table 3. .
For all cases in Table 3. in comparison with uncontrolled frame, it is shown that passive vis-
coelastic (Kelvin-Voight) damper and passive viscous damper are the most effective devices used to
decrease seismic damage more. Additional passive stiffness damper had appropriate effect on heal-
3rd International Conference on Acoustics & Vibration (ISAV2013), Tehran, Iran, 25-26 Dec. 2013
7
ing damages for 4 cases but had destructive effect on 2 cases. Passive fluid viscous damper, semi-
active fluid viscous damper and semi-active additional stiffness, had small effect on reducing dam-
age values. Finally, semi-active viscoelastic and semi-active viscous damper unlike their passive
usage, not only had effective influence on decreasing damage values, but also exaggerated damages.
To be more precise, for all analyzed cases passive viscoelastic damper in 52% cases reduced
damage and in 48% cases completely removed the harms of damage. Passive viscous damper in
52% cases decreased damage, in 46.67% of cases made damage to zero and in 1.33% cases made no
difference.
Table 3. DImax for Passive and Semi-Active Energy Dissipation Devices
6. Concluding Remarks
According to results of Section 3. range of plastic modulus ratio of column to beam (Z Ra-
tio) that satisfied the weak beam-strong column design and let the design to still be econom-
ical, is from Z Ratio=1.1 to Z Ratio=1.3 .
In order to find a new and an appropriate criterion for activation of semi-active control de-
vices, the correlation of occurrence time of peak ground acceleration and occurrence time of
maximum modified Park and Ang damage index (DImax) and the exceed from half of maxi-
mum modified Park and Ang damage index (0.5DImax), is investigated in Section 4. respec-
tively. It was shown in mentioned section, the results of correlation were so good, specially
the correlation with 0.5DImax (for all set of frame designs, the correlation value was above
0.8).
To carry out the efficiency of semi-active devices on the studied frame, 4 passive devices
and their semi-active usages are implemented as a diagonal member in the frame. It was
shown in Section 5. that, passive viscoelastic damper and passive viscous damper had the
most effective influence in all scenarios to reduce damage and, semi-active viscoelastic and
semi-active viscous had the most destructive effects on studied frames. Therefore, with the
mentioned criterion and these types of frames, the passive devices were much more effective
than the semi-active devices.
3rd International Conference on Acoustics & Vibration (ISAV2013), Tehran, Iran, 25-26 Dec. 2013
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