EARTHQUAKE ENGINEERING & STRUCTURAL DYNAMICS
Earthquake Engng Struct. Dyn. 2014; 43:1935–1954
Published online 16 April 2014 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/eqe.2430
Modeling of the composite action in fully restrained beam-to-column
connections: implications in the seismic design and collapse capacity
of steel special moment frames
Ahmed Elkady and Dimitrios G. Lignos*,†
Department of Civil Engineering and Applied Mechanics, McGill University, Montreal, Canada
SUMMARY
This paper investigates the effect of the composite action on the seismic performance of steel special moment frames (SMFs) through collapse. A rational approach is first proposed to model the hysteretic behavior
of fully restrained composite beam-to-column connections, with reduced beam sections. Using the proposed
modeling recommendations, a system-level analytical study is performed on archetype steel buildings that
utilize perimeter steel SMFs, with different heights, designed in the West-Coast of the USA. It is shown that
in average, the composite action may enhance the seismic performance of steel SMFs. However, bottom
story collapse mechanisms may be triggered leading to rapid deterioration of the global strength of steel
SMFs. Because of composite action, excessive panel zone shear distortion is also observed in interior joints
of steel SMFs designed with strong-column/weak-beam ratios larger than 1.0. It is demonstrated that when
steel SMFs are designed with strong-column/weak-beam ratios larger than 1.5, (i) bottom story collapse
mechanisms are typically avoided; (ii) a tolerable probability of collapse is achieved in a return period of
50 years; and (iii) controlled panel zone yielding is achieved while reducing the required number of welded
doubler plates in interior beam-to-column joints. Copyright © 2014 John Wiley & Sons, Ltd.
Received 29 June 2013; Revised 10 March 2014; Accepted 12 March 2014
KEY WORDS:
composite action; deterioration modeling; steel SMF; panel zone strength; strong-column/
weak-beam ratio; collapse capacity
1. INTRODUCTION
Steel special moment frames (SMFs) are commonly used in highly seismic regions as the primary lateral
load resisting system in steel buildings. Current seismic provisions in the USA, ANSI/AISC 341-10 [1],
employ a series of design rules in order to prevent weak-story collapse mechanisms and unexpected brittle
failure modes associated with weld fractures at the SMF girder flanges. To this end, energy dissipation in
SMFs is achieved through flexural yielding of beams and limited shear yielding of the panel zones. The
latter sometimes requires welding doubler plates in contact with the column web to control the panel
zone shear strength. Flexural yielding of columns is only permitted at the base of a SMF; otherwise,
columns should remain elastic during an earthquake. Columns shall be designed to be stronger than the
fully yielded and strain-hardened beams by employing the strong-column/weak-beam (SCWB)
criterion. In ANSI/AISC 341-10 [1], this is achieved by satisfying the moment ratio (also referred to as
the SCWB ratio) given by Equation (1) at any fully restrained beam-to-column connection. It should be
stated that the current equation in ANSI/AISC 341-10 [1] does not claim to avoid weak column
situations but only minimize their impact on the overall seismic performance of steel SMFs.
*Correspondence to: Dimitrios G. Lignos, Department of Civil Engineering and Applied Mechanics, McGill University,
Montreal, Canada.
†
E-mail: dimitrios.lignos@mcgill.ca
Copyright © 2014 John Wiley & Sons, Ltd.
A. ELKADY AND D. G. LIGNOS
X
X
M pc
M pb
> 1:0
(1)
where ΣM*pc is the sum of the projections of the nominal flexural strengths of the columns above and
below the structural joint to the centerline of the beam and ΣM*pb is the sum of the projections of the
expected flexural strengths of the beams at the plastic hinge location to the centerline of the column.
To calculate M*pb, the expected yield stress, Fye, is employed. Additionally, the expected flexural
strength of the beam is amplified by a factor of 1.1 as per ANSI/AISC 341-10 [1] or alternatively by
a factor, Cpr = 1.15 (for prequalified beam-to-column connections with reduced beam section, RBS)
or Cpr = 1.4 (for welded unreinforced flange welded web prequalified beam-to-column connections)
per ANSI/AISC 358-10 [2] to account for strain hardening. However, in this computation, the
contribution of the concrete floor slab to the beam flexural strength is neglected. The slab would
typically increase the flexural stiffness and strength of the steel beam. In this case, the flexural
strength of the composite beam may exceed that of the column. This will force plastic hinging to
occur in the column. Subsequently, local story collapse mechanisms that involve column plastic
hinging may be triggered. Another consideration is the fact that the shear force demand on the panel
zone increases because of the increase in flexural strength of the composite beam. This could
potentially cause large inelastic shear distortion to the panel zone of interior SMF joints and
eventually fracture of the welds between the bottom flange of the steel beam and the column face [3, 4].
In this case, a rapid drop in the steel beam flexural strength will occur, which is not a desirable energy
dissipation mechanism. However, the undesirability of significant panel zone yielding is still an unsettled
question based on recent experimental data on full-scale prequalified beam-to-column connections as
discussed in [3, 5, 6].
Past experimental studies on full-scale fully restrained beam-to-column connections with composite
slab [7–12] indicate that (i) the flexural strength of a steel beam would typically increase especially
when the slab is in compression (i.e., positive bending); (ii) the strong-axis moment of inertia of a
composite steel beam is typically larger than the one of the bare steel beam; and (iii) because of the
presence of the slab, the cyclic deterioration in strength and stiffness of a composite beam becomes
asymmetric. Nakashima et al. [13] conducted a full-scale test of a two-story composite steel
building with steel SMFs. They demonstrated that the beam flexural strength increased about 1.5
times in the positive bending and 1.2–1.4 times in the negative bending compared to that of the bare
steel beam. More recently, Suita et al. [14] conducted a full-scale collapse test of a four-story steel
building with steel SMFs at the E-Defense facility in Japan. This building collapsed with a first
story mechanism under severe ground-motion shaking. Plastic hinging occurred at the base and top
of the first story columns of the four-story steel SMF. The main reasons were due to (i) the increase
in beam flexural strength due to cyclic strain hardening; (ii) the material variability; (iii) the
composite action; and (iv) excessive panel zone shear distortion. Note that steel SMFs in Japan are
designed with a SCWB ratio >1.5. Lignos et al. [15] developed an analytical model of the same
steel building and demonstrated that when the composite action is neglected, this could lead to a
completely different collapse mechanism. Moreover, Lignos et al. [16] illustrated that if a SCWB
ratio >2.0 was employed, the same building would develop a full four-story collapse mechanism
with plastic hinging concentrated only in the steel beams and at the base of the first story steel
columns. Other analytical studies related to the seismic performance of steel SMFs [17–19] have
mainly focused on the bare frame only. Therefore, there is a need to investigate the effect of composite
action on the dynamic stability of steel SMFs and the implications into seismic design provisions
associated with the SCWB criterion. The same issue has been raised in past experimental and analytical
studies that investigated the seismic performance of composite moment-resisting connections [20, 21].
Similar issues have been left unresolved in concrete buildings until recently [22–24].
In this paper, we first propose a rational way to simulate the effect of composite action on the hysteretic
behavior of prequalified fully restrained beam-to-column connections and panel zones as part of steel
SMFs designed in seismic regions. The modeling approach reflects information from full-scale
experiments with RBS. A set of archetype steel buildings with perimeter steel SMFs ranging from 4 to
20 stories is then designed in accordance with current US seismic provisions [1, 25, 26]. The effect of
Copyright © 2014 John Wiley & Sons, Ltd.
Earthquake Engng Struct. Dyn. 2014; 43:1935–1954
DOI: 10.1002/eqe
10969845, 2014, 13, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/eqe.2430 by Tongji University, Wiley Online Library on [25/01/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
1936
1937
the composite action on the collapse potential of these buildings is assessed based on (i) the FEMA
P695 [27] methodology and (ii) the mean annual frequency of collapse, translated to an acceptable
probability of collapse over 50 years per Section 21.2.1, ASCE/SEI 7-10 [25]. Finally, seismic design
recommendations related to the SCWB ratio for steel SMFs are proposed.
2. DETERIORATION MODELING OF COMPOSITE BEAM-TO-COLUMN CONNECTIONS
WITH REDUCED BEAM SECTION
2.1. Modeling of composite beams with reduced beam section
This section proposes an approach to explicitly consider the effect of composite action on the hysteretic
behavior of steel beams with RBS. A steel beam is idealized with an elastic element and a concentrated
plasticity spring at the center of the RBS location. The nonlinear behavior of the rotational spring
utilizes a phenomenological material model, which simulates the cyclic deterioration in flexural
strength and stiffness of the steel beam when subjected to cyclic loading [28, 29]. This model is
referred herein as the modified Ibarra–Medina–Krawinkler (IMK) model. This material model has
been modified to simulate the asymmetric hysteretic behavior because of the composite action, the
residual strength, and ductile tearing [30], which is typically observed in beams with RBS because
of low cycle fatigue [11]. Figure 1 shows the hysteretic behavior of the modified IMK material
model for a bare and a composite steel beam with RBS. In this figure, the experimental data are
retrieved from [11, 31].
The modified IMK model is bounded by a backbone curve as shown in Figure 1. This backbone
curve is defined based on (i) the elastic flexural stiffness Ke of the steel beam; (ii) the effective yield
moment My; (iii) the capping-to-effective yield moment ratio Mc/My (the capping moment, Mc,
represents the maximum flexural strength of a steel component prior to the occurrence of local
buckling, as shown in Figure 1); and (iv) the residual-to-effective yield moment ratio Mr/My. Three
deformation parameters are necessary in order to fully define the backbone curve of the material
model: (i) the precapping rotation θp; (ii) the post-capping rotation θpc; and (iii) the ultimate rotation
θu. These parameters are shown in Figure 1. Three additional parameters define the hysteretic
behavior of the steel beam. These parameters are the reference energy dissipation capacity for a steel
beam (Λ) and the rates of cyclic deterioration in both strength and stiffness in the positive and
negative loading directions (D+ and D) [29]. Different values can be assigned to D+ and D in
order to simulate the asymmetric cyclic deterioration in strength and stiffness of composite beams.
For bare steel beams with RBS, the backbone curve is fully symmetric in both loading directions as
shown in Figure 1(a). In this case, the input model parameters of the backbone curve and the reference
hysteretic energy dissipation capacity Λ can be computed from multivariate regression equations
Figure 1. Modified IMK material model calibrated with (a) bare steel beam with RBS (experimental data
from Uang et al. [31]) and (b) composite beam with RBS (experimental data from Ricles et al. [11]).
Copyright © 2014 John Wiley & Sons, Ltd.
Earthquake Engng Struct. Dyn. 2014; 43:1935–1954
DOI: 10.1002/eqe
10969845, 2014, 13, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/eqe.2430 by Tongji University, Wiley Online Library on [25/01/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
EFFECT OF COMPOSITE ACTION ON STEEL SPECIAL MOMENT FRAMES
A. ELKADY AND D. G. LIGNOS
developed by Lignos and Krawinkler [29, 30] and adopted in PEER/ATC 72-1 [32]. For bare steel
beams, D+ and D are set equal to 1.0 [30, 33].
Due to the presence of the slab, composite steel beams with RBS have an asymmetric hysteretic
behavior as shown in Figure 1(b). Typically, a higher flexural strength and larger plastic rotations,
θp and θpc, are observed in the positive loading direction (i.e., slab in compression) than the
corresponding parameters in the negative loading direction. To quantify these values, the hysteretic
response of the modified IMK model is calibrated with respect to 22 sets of deduced momentrotation hysteretic diagrams from past experimental data of composite beams with RBS [7, 8, 11,
34]. The experimental data are all available from a fully searchable steel W-shape database
(available from http://dimitrios-lignos.research.mcgill.ca/databases/). In summary, most of the
collected tests did not have shear studs installed at the RBS region. Only tests in [34] had studs at
the RBS location. The same tests by [34] only had partially composite action. This is reflected in the
My+/My ratio of the same tests that in average was 1.2 compared to 1.35 for specimens with full
composite action (Table II). Table I indicates the seismic design recommendations that each one of
the collected test specimens complies with. Except for [34], the rest of the tests comply with ANSI/
AISC 358-10 [2] recommendations for RBS design. The calibrated parameters of the modified IMK
model for both the positive and negative loading directions are summarized in Table I. Figure 1(b)
shows a sample calibration of the modified IMK model with respect to the experimental data from
Ricles et al. [11]. From this figure, the material model is able to represent reasonably well the
hysteretic behavior of composite beams.
From Figure 1(b) and Table I, in the positive loading direction (i.e., slab in compression), a higher
effective yield flexural strength (My+), capping flexural strength (Mc+), and precapping plastic rotation
(θp+) are observed compared to the negative loading direction (i.e., slab in tension). The higher
precapping plastic rotation (θp+) is attributed to the lateral restraint provided by the slab to the top
flange of the steel beam, that is, local buckling is delayed. On the other hand, the lower flange of
the steel beam is more susceptible to local and lateral torsional buckling because of its neutral axis
shifting due to the presence of the slab.
The calibrated parameters presented in Table I are normalized with respect to the bare steel beam
deterioration parameters, as computed from the regression equations developed by Lignos and
Krawinkler [29]. Table II summarizes the counted mean of the normalized values for each input
parameter of the modified IMK model. These values can be used to modify the backbone curve of
the bare steel beam with RBS to account for the composite action. In summary, the moment of
inertia, Ic of the composite beams summarized in Table I, is in average 1.225 times larger than that
of the bare steel section, Is based on ANSI/AISC 360-10 [26] (Equation C-I3-3). On the other hand,
for the same composite beams, Ic/Is = 1.70, if the AISC 341-10 [1] (Section C1 and Chapter H) is
used. The difference comes from the fact that the former uses an effective moment of inertia based on
the cracked transformed section; the latter uses the transformed moment of inertia of the beam and
slab by assuming full composite action. Based on independent calibrations of the elastic stiffness of
the composite beam test data summarized in Table I, we found that in average, Ic/Is = 1.40 (Table II).
This value is used later on for the analysis of the archetype steel buildings discussed in detail in
Section 3.
Figure 2(a) shows the calibrated values of θp+ versus the beam depth, db. The parameter θp+ is
statistically insignificant with respect to db based on a standard t-test at a 95% confident interval.
Similar findings hold true for the rest of the calibrated model parameters but are not shown here
because of brevity. This justifies the use of the average values in Table II in order to simulate the
effect of composite action on the hysteretic response of steel beams with RBS.
The nominal flexural strength of the collected composite beams, Mn, is calculated per ANSI/AISC
360-10 [26] when the slab is in compression (i.e., composite beam under positive bending). For this
computation, the following assumptions should be considered: (i) full composite action between
the concrete slab and the steel beam; (ii) the RBS location geometry; (iii) the effective width of the
composite beam as calculated based on [26] (Section I 3.1a); and (iv) the effective stress in the
concrete is taken as 0.85 of the specified concrete stress fc′. The calibrated positive flexural strengths
My+ (i.e., the composite beam flexural strength) are plotted against the nominal flexural strengths Mn
as calculated per ANSI/AISC 360-10 [26] for the composite beams as shown in Figure 2(b).
Copyright © 2014 John Wiley & Sons, Ltd.
Earthquake Engng Struct. Dyn. 2014; 43:1935–1954
DOI: 10.1002/eqe
10969845, 2014, 13, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/eqe.2430 by Tongji University, Wiley Online Library on [25/01/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
1938
Copyright © 2014 John Wiley & Sons, Ltd.
DBBWC-N
DBBWC-S
DBWWC-N
DBWWC-S
DBBWSPZC-N
DBBWSPZC-S
TRSC2
TRSC1
SPEC1-E
SPEC1-W
SPEC2-E
SPEC2-W
SPEC3-E
SPEC3-W
SPEC4-E
SPEC4-W
SPEC5-E
SPEC5-W
1C Beam1
1C Beam 2
3C Beam1
3C Beam 2
[8]
163,835
163,835
203,380
214,680
192,080
214,680
84,740
90,955
451,960
451,960
395,465
395,465
361,570
361,570
384,165
395,465
259,880
259,880
203,380
203,380
203,380
203,380
Ke (kN.m/rad)
2485
2485
2540
2655
2485
2430
645
590
2925
3220
3140
3445
2790
3275
2825
3335
2090
2090
2260
2260
2370
2370
My+ (kN.m)
2485
2370
2315
2370
2315
2370
620
620
2825
3220
3030
3220
2735
3050
2770
2995
1750
1955
2035
1920
2315
2260
My (kN.m)
1.20
1.30
1.20
1.20
1.15
1.20
1.35
1.35
1.20
1.35
1.05
1.05
1.35
1.20
1.30
1.30
1.35
1.30
1.35
1.35
1.45
1.40
Mc þ
My
1.05
1.10
1.10
1.10
1.05
1.10
1.10
1.05
1.05
1.05
1.05
1.05
1.05
1.05
1.05
1.05
1.05
1.05
1.10
1.10
1.05
1.05
Mc
My
0.40
0.40
0.40
0.35
0.25
0.20
*
0.40
0.20
0.20
0.00
0.00
0.30
0.40
0.30
0.30
0.30
0.40
*
*
*
0.30
Mr þ
My
0.30
0.20
0.35
0.35
0.10
0.30
*
0.40
0.20
0.20
0.00
0.00
0.25
0.20
0.20
0.20
0.20
0.20
*
*
*
0.30
Mr
My
0.050
0.055
0.038
0.038
0.035
0.035
0.028
0.035
0.030
0.045
0.014
0.014
0.045
0.035
0.045
0.033
0.036
0.043
0.020
0.020
0.033
0.033
θ p+
0.035
0.040
0.030
0.027
0.026
0.028
0.011
0.013
0.010
0.010
0.014
0.014
0.010
0.010
0.010
0.010
0.010
0.010
0.020
0.020
0.020
0.023
θ p
0.25
0.25
0.25
0.25
0.25
0.25
*
0.20
0.20
0.20
0.15
0.15
0.25
0.25
0.25
0.25
0.23
0.35
*
*
0.20
0.20
θpc+
0.20
0.20
0.16
0.18
0.17
0.17
*
0.20
0.15
0.15
0.15
0.15
0.13
0.20
0.15
0.18
0.13
0.15
*
*
0.15
0.15
θpc
1.50
1.60
1.10
0.97
1.40
1.00
*
1.30
0.70
0.60
0.60
0.60
0.85
0.90
0.85
0.70
0.90
0.90
*
*
1.30
1.40
Λ
0.80
0.70
1.10
1.12
1.10
0.80
*
1.00
1.40
1.20
1.40
1.40
1.20
1.35
1.40
1.30
1.20
1.00
*
*
1.00
1.00
D+
1.00
1.00
1.00
1.00
1.00
1.00
*
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
*
*
1.00
1.00
D
1939
Earthquake Engng Struct. Dyn. 2014; 43:1935–1954
DOI: 10.1002/eqe
10969845, 2014, 13, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/eqe.2430 by Tongji University, Wiley Online Library on [25/01/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
*Parameter could not be identified from experimental data.
Test specimens by [8] comply with Engelhardt [35] design recommendations and AISC 1997 provisions [36].
Test specimens by [7] comply with AISC 1997 provisions [36].
Test specimens by [11] comply with Engelhardt [35] design recommendations and ANSI/AISC 341-02 [37].
Test specimens by [34] comply with UBC 1985 [38] and rehabilitated with RBS at the bottom flange only.
[34]
[11]
[7]
Specimen notation
Reference
Table I. Calibrated parameters of the modified IMK material model for composite steel beams with RBS.
EFFECT OF COMPOSITE ACTION ON STEEL SPECIAL MOMENT FRAMES
A. ELKADY AND D. G. LIGNOS
Table II. Normalized deterioration parameters of composite steel beams with RBS.
Ic
Is
My þ
My
My
My
Mc þ
My
Mc
My
Mr þ
My
Mr
My
θp þ
θp
θp θp
θpc þ
θpc
θpc θpc
Λ
D+
D
1.40
1.35
1.25
1.30
1.05
0.30
0.20
1.80
0.95
1.35
0.95
1.0
1.15
1.0
Figure 2. (a) Precapping plastic rotation θp+ with respect to beam depth db and (b) calibrated flexural yield
strength, My+, when slab is in compression versus composite beam nominal flexural strength, Mn, per ANSI/
AISC 360-10 [26].
This figure shows that the calibrated flexural strengths of the composite beam are more or less equal to
those calculated according to [26]. Therefore, if a designer knows the geometric and material properties
of the steel deck and concrete slab, the composite beam flexural strength can be directly calculated
from [26] and then implemented in the SCWB ratio calculation as part of the design process.
However, if the composite action is neglected, a higher SCWB ratio may need to be considered during
the design process in order to consider the expected increase in the beam flexural strength due to the
composite action. This is discussed in Sections 3 to 6. It should also be pointed out that the amount
of continuous slab reinforcement primarily affects the flexural strength of the composite beam when
the slab is in tension (i.e., negative bending). This is inherently captured by a 25% increase of the
My compared to that of the bare steel beam, My, as indicated in Table II (i.e., My/My ratio).
2.2. Modeling of the panel zone in the presence of the slab
Based on prior experimental studies, it has been shown that the cyclic behavior of panel zones is affected
by the presence of the slab. Several researchers have proposed different expressions for modeling the
panel zone shear force (V) – shear distortion (γ) hysteretic behavior [39–42]. In this paper, the
parallelogram model proposed in [19] is utilized to represent the panel zone element within an
analytical model of a steel SMF. This model consists of rigid elements connected with flexural hinges
at three corners and with a nonlinear rotational spring at the fourth corner. A trilinear backbone curve
proposed by Krawinkler [40] is employed to simulate the backbone curve of a panel zone as shown in
Figure 3(a). The first region of this curve, where elastic shear strains are predominant, is fully defined
using the equivalent shear yield force, Vy, the shear elastic stiffness, Ke, and the yield rotation, γy. In the
second region, a post-yield slope, Kp, provides additional strength because of the contribution of
surrounding elements (i.e., column flanges and continuity plates). In the third region, when the full
plastic shear resistance, Vp, is reached at a shear distortion angle, γ2, equal to four times γy, a
considerable decrease in panel zone shear stiffness is observed. This is typically accompanied by high
strains as captured by the second post-yielding slope, Ksh. The shear force and shear distortion
parameters of the trilinear backbone can be calculated using the equations given in [32]. The deduced
moment-rotation relation that is assigned to the panel zone rotational spring is computed from the shear
force parameters (i.e., Vy and Vp) multiplied by the effective depth, deff, of the panel zone.
Copyright © 2014 John Wiley & Sons, Ltd.
Earthquake Engng Struct. Dyn. 2014; 43:1935–1954
DOI: 10.1002/eqe
10969845, 2014, 13, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/eqe.2430 by Tongji University, Wiley Online Library on [25/01/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
1940
1941
Figure 3. (a) Panel zone hysteretic material model (experimental data from Engelhardt et al. [8) and (b)
boundary forces acting on an interior composite panel zone.
In the case of a bare steel panel zone, the effective depth is equal to the distance between the
centroids of the bare steel beam flanges. Therefore, the yield and full plastic moments, My and Mp,
can be calculated using Equations (2) and (3), respectively, where db is the depth of the beam and tf
is the thickness of the beam flange.
M y ¼ V y deff ¼ V y d b t f
(2)
h
i M p ¼ V p d eff ¼ V y þ K p γ2 γy
db tf
(3)
For panel zones in the presence of a slab, the effective depth depends on the loading direction as
shown in Figure 3(b). In the negative loading direction, the slab is in tension, and therefore, the
effective depth is similar to that of the bare steel panel zone; hence, the negative yield moment of
the panel zone should be calculated using Equation (4). In the positive loading direction, the slab is
in compression; therefore, the effective depth becomes larger than that of the bare steel panel zone.
The positive yield moment is calculated using Equation (5), where, drib is the depth of the ribbed
section of the steel deck and ts is the thickness of the slab. This increase in the effective depth
reflects the higher stiffness and yield moments of the panel zone due to the presence of the
composite action. The procedure outlined here was first proposed by Kim and Engelhardt [42].
M
y ¼ V y d eff ¼ V y d b t f
(4)
þ
Mþ
y ¼ V y d eff ¼ V y d b d rib þ 0:5t s 0:5t f
(5)
For interior composite panel zones, their backbone curve is symmetric because in both loading
directions, the slab is effective (Figure 3(b)). However, for exterior composite panel zones, their
backbone curve is asymmetric as discussed earlier.
3. ARCHETYPE STEEL BUILDINGS
In order to quantify the composite effect on the seismic performance of steel SMFs as part of steel
buildings designed in seismic regions, four archetype steel buildings, with different heights of 4, 8,
12, and 20 stories, are designed in accordance with ANSI/AISC 341-10 [1], ANSI/AISC 358-10 [2],
and ASCE/SEI 7-10 [25]. The response spectrum analysis procedure was employed as the basis for
Copyright © 2014 John Wiley & Sons, Ltd.
Earthquake Engng Struct. Dyn. 2014; 43:1935–1954
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EFFECT OF COMPOSITE ACTION ON STEEL SPECIAL MOMENT FRAMES
A. ELKADY AND D. G. LIGNOS
the design of these frames (see Section 12.9 in [25]). The SMFs are designed with typical RBS
connections as discussed in ANSI/AISC 358-10 [2]. The archetype steel buildings have a
rectangular plan view and perimeter three-bay steel SMFs in each loading direction as shown in
Figure 4(a). This plan view is the same with the archetype buildings summarized in [17, 18]. The
archetype steel buildings are located in urban California (seismic design category: SDC = Dmax; soil
class D). A typical elevation view of the eight-story steel SMF, including its geometric properties, in
the East–West (EW) loading direction is shown in Figure 4(b). The columns are spliced at the midheight of odd-numbered stories except for the first story. Beams and columns are fabricated from
steel ASTM A992 Gr. 50 (Fy,nominal = 345 MPa). In the seismic design of the archetype steel SMFs,
the expected yield stress (i.e., 380 MPa) was used for the steel beams and the minimum specified
yield stress (i.e., 345 MPa) was used for the columns and panel zones.
Two-dimensional (2D) nonlinear models of the steel SMFs in the EW direction are developed in the
open-source simulation platform OpenSEES [43]. In order to quantify the effect of composite action on
the dynamic response of a steel SMF from the onset of structural damage through collapse, two types
of numerical models are employed; the first one represents the bare frame only (noted herein as the
‘bare model’); the second one considers the effect of the composite action on the hysteretic behavior
of steel beams and panel zones of the steel SMFs (noted herein as ‘composite model’). The 2D
models are idealized based on the concentrated plasticity approach. Rotational springs, located at the
plastic hinge regions, are used to model the nonlinear behavior of the columns, beams, and panel
zones (Section 2).
P-Delta effects are considered by using a fictitious column (noted as ‘leaning column’) connected to
the steel SMF by axially rigid truss elements. The leaning column is loaded at each floor with a vertical
load equal to half of the seismic gravity load of the building minus the tributary load that is directly
assigned to the SMF columns. The contribution of the interior gravity framing to the lateral strength
and stiffness of the steel SMFs is not considered in the present study. Rayleigh damping is
incorporated in the 2D models. The Rayleigh damping stiffness-proportional term is assigned only
to the elastic column and beam elements while the mass-proportional term is assigned to all the
frame nodes with masses as discussed by Zareian and Medina [44]. This method of assigning
damping to the frame model helps avoiding fictitious damping forces when the frame is subjected to
severe ground-motions. Two percent damping ratio (ζ = 2%) is assumed at the first and third mode
of the SMFs.
Based on the eigenvalue analysis, the first mode periods (T1) of the bare and composite models for
all the SMFs are summarized in Table III. From this table, the composite frames are about 20% stiffer
Figure 4. (a) Typical plan view of the archetype buildings and (b) elevation of the eight-story SMF.
Copyright © 2014 John Wiley & Sons, Ltd.
Earthquake Engng Struct. Dyn. 2014; 43:1935–1954
DOI: 10.1002/eqe
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1942
Table III. Archetype steel SMFs: first mode periods and global performance factors.
4-story
Bare
SCWB ratio
T1 (s)
Ω
μT
1.0
1.51
2.00
4.60
8-story
Composite
1.0
1.37
2.29
4.57
1.5
1.33
2.41
4.56
Bare
2.0
1.30
2.57
4.91
1.0
2.00
2.63
3.30
12-story
Composite
1.0
1.82
3.13
2.91
1.5
1.75
3.32
3.41
2.0
1.69
3.52
3.62
Bare
1.0
2.70
2.09
2.70
20-story
Composite
1.0
2.46
2.52
2.38
1.5
2.41
2.52
2.93
2.0
2.25
2.77
3.36
Bare
1.0
3.44
1.89
2.61
Composite
1.0
3.17
2.27
2.21
1.5
3.05
2.34
2.62
2.0
2.94
2.39
2.81
than the bare ones. This is indicated by the shorter periods of the composite models compared to the
corresponding values of the bare ones. This difference is attributed to the 40% average increase in
moment of inertia Ic of the composite beams as opposed to the bare ones (Table II). The effect of
composite action on the seismic performance of steel SMFs is discussed in more detail in the
following sections. To facilitate the discussion in this paper, results from the eight-story steel SMF
are employed for illustration purposes.
4. PUSHOVER ANALYSIS OF ARCHETYPE STEEL SPECIAL MOMENT FRAMES
Nonlinear static analysis (pushover) is conducted for all the steel SMFs by using a first mode lateral load
pattern. Figure 5(a) shows the global pushover curves for the bare and composite models of the eightstory SMF. These curves are presented in terms of the normalized base shear force V1/W, where W is
Figure 5. (a) Comparison of pushover curves for the eight-story SMF bare and composite models; (b) illustration of performance factors obtained from pushover curve; (c) normalized floor displacement profile for
the eight-story composite model at different roof drift ratios; and (d) collapse mechanism for the eight-story
composite model.
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1943
EFFECT OF COMPOSITE ACTION ON STEEL SPECIAL MOMENT FRAMES
A. ELKADY AND D. G. LIGNOS
the seismic weight of the building per frame, versus the roof drift ratio θr = δr/H, where δr is the roof
displacement and H is the total height of the SMF. This figure shows that when the slab is considered
as part of the analytical modeling of a steel SMF, both the lateral stiffness and strength of the eightstory SMF is increased by 17% and 19%, respectively.
Table III summarizes the values for the overstrength factor, Ω, and period-based ductility factor, μT,
obtained from the pushover curves of both the bare and composite models of the archetype steel SMFs.
Table III also includes the performance parameters for the composite models of the same SMFs
designed with higher SCWB ratios as discussed later in Section 6.
The overstrength factor (Ω) is defined in Figure 5(b) as the ratio between the maximum base shear
strength (Vmax) to the code-design base shear strength (Vdesign). This definition is consistent with
FEMA P695 [27]. From Table III, it is evident that Ω increases when the composite action is
considered. This is primarily attributed to the higher flexural strength of the beams and higher shear
strength of the panel zones within the composite model as opposed to the bare model. The
overstrength factors appear to be lower than the recommended overstrength Ωo = 3.0 by ASCE/SEI
7-10 [25] regardless of the fact that all the steel SMF designs presented herein were controlled by
the allowable drift or P-Delta stiffness criteria. This is attributed to two primary reasons: (i) the fact
that all the SMF designs did not incorporate any wind considerations and (ii) the interior gravity
framing was not considered as part of the analytical model.
Table III summarizes the period-based ductility factor μT for each steel SMF. Based on Figure 5(b),
this factor is defined as the ratio of the global roof drift of a steel SMF corresponding to a 20% drop in
the global maximum base shear strength (δu) to the global yield drift (δy,eff) as shown in Figure 5(b).
From Table III, the corresponding ductility factors for code compliant steel SMFs with SCWB ratio
higher than 1.0 decrease once the composite action is considered in the analytical model. This can
be explained from Figure 5(a) that shows a comparison of the pushover curves for the bare and
composite models of the eight-story steel SMF. When the slab is considered as part of the analytical
model (i.e., composite model), a two-story collapse mechanism is developed compared to the threestory one of the bare model; thus, the post-capping global stiffness of the composite model is
steeper compared to the one of the bare model (Figure 5(a)). The progression of the collapse
mechanism is shown in Figure 5(c). This figure shows the normalized floor displacements along the
height of the eight-story composite steel SMF at various roof drift ratios ranging from 0.5% to 3.0%
radians. The corresponding floor displacements in the same figure are normalized with respect to the
total height of the eight-story steel SMF (i.e., 31,931 mm). The final collapse mechanism of the
same steel SMF is shown in Figure 5(d). The reason for the two-story collapse mechanism in
the case of the composite model is attributed to the increased flexural strength of the composite
beams. This increase is not considered during the design process when Equation (1) is applied. This
necessitates further investigation of the seismic performance of steel SMFs with the use of nonlinear
response history analysis through collapse. This is discussed in the following section.
5. COLLAPSE ASSESSMENT OF ARCHETYPE STEEL SPECIAL MOMENT FRAMES
This section discusses the effect of composite action on the collapse capacity of SMFs based on two
approaches: (i) the FEMA P695 [27] methodology and (ii) the mean annual frequency of collapse (λc).
The former defines a collapse margin ratio (CMR) based on the median collapse intensity of a steel
SMF to the intensity associated with a maximum considered earthquake (MCE) at the design location.
The latter defines a collapse risk that is estimated by combining the probability of collapse of a steel
SMF, given a ground-motion intensity, with a seismic hazard curve. The hazard curve describes how
frequently each intensity level is exceeded at a specific site. The mean annual frequency of collapse can
be translated to a corresponding probability of collapse over 50 years. This probability of collapse is
compared to the acceptable probability of collapse limit given by ASCE/SEI 7-10 [25] (Section 21.2.1).
The computation of λc (Section 5.2) is more complicated than the CMR; however, λc is a more precise
collapse metric than CMR because it takes into account all intensities that contribute to the collapse risk
of a steel SMF compared to CMR that only considers two intensities; the one associated with collapse
and the one associated with the 2% in 50 hazard at a given site.
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Earthquake Engng Struct. Dyn. 2014; 43:1935–1954
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1944
1945
The Far-Field ground-motion record set, specified by FEMA P695 [27], is employed for the collapse
evaluation of the steel SMFs. The set includes 22 component pairs of horizontal ground-motions
(i.e., total of 44 records). These ground-motions are scaled incrementally based on incremental
dynamic analysis (IDA: Vamvatsikos and Cornell [45]) till the steel SMFs become dynamically
unstable, that is, collapse occurs. The IDA is performed using the hunt and fill algorithm as
discussed in [45]. Each ground-motion record is incrementally scaled with respect to the first mode,
5% damped, spectral acceleration Sa(T1, 5%) of the bare steel frame model through collapse.
Collapse is simulated explicitly. The collapse intensity is defined as the intensity at which a story or
a number of stories of the steel SMF displaces sufficiently and the story shear becomes zero
because of P-Delta effects accelerated by steel component deterioration in strength and stiffness.
Figure 6(a) shows the normalized base shear force versus the first story drift ratio for the 8-story
composite model when subjected to the collapse intensity, SCT(T1, 5%) = 0.84 g, of the Plaster City
record from the 1994 Imperial Valley earthquake. This definition of collapse is consistent with
recent small and full-scale collapse experiments of steel SMFs [14–16, 46].
Figure 6(b) shows the IDA curves (44 ground-motions) for the eight-story composite model in terms
of Sa(T1, 5%) versus maximum story drift ratio (SDRmax) along with the median, 16th, and 84th
percentiles. The cumulative probabilities of collapse corresponding to the 44 collapse intensities,
obtained from the IDA, are calculated and then fitted with a lognormal cumulative distribution
(i.e., the collapse fragility curve) as shown in Figure 6(c) for both the bare and composite models of
the eight-story SMF. The median collapse intensities ( S^CT ) and standard deviations of the natural
logarithm of the collapse intensities (i.e., the record-to-record variability, βRTR) for the bare and
composite models of all the steel SMFs considered in this paper are summarized in Table IV. These
values are comparable with reported ones for moment-resisting frames [18, 27].
Figure 6. (a) Normalized base shear force versus first story drift at collapse intensity; (b) IDA curves for the
eight-story SMF composite model; (c) comparison of collapse fragility curves for the eight-story SMF bare
and composite models; and (d) comparison of median maximum story drift profile at collapse for the eightstory SMF bare and composite models.
Copyright © 2014 John Wiley & Sons, Ltd.
Earthquake Engng Struct. Dyn. 2014; 43:1935–1954
DOI: 10.1002/eqe
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EFFECT OF COMPOSITE ACTION ON STEEL SPECIAL MOMENT FRAMES
A. ELKADY AND D. G. LIGNOS
Table IV. Median collapse intensity and standard deviation of the collapse fragility curve for bare and
composite models.
4-story
S^CT (g)
βRTR
8-story
12-story
20-story
Bare
Composite
Bare
Composite
Bare
Composite
Bare
Composite
1.030
0.45
1.509
0.44
0.784
0.39
0.967
0.42
0.533
0.39
0.790
0.42
0.388
0.43
0.622
0.42
Figure 6(c) shows that the median collapse intensity of the eight-story SMF composite model is 23%
higher than the one predicted from the bare model. This increase in the median collapse intensity is
observed in all the SMFs when the composite action is considered as part of the analytical modeling
(Table IV). The reasons for this increase are discussed later.
Similarly to the results of the pushover analysis, the collapse mechanism for all the composite
models of the archetype steel SMFs involved lesser number of stories than the corresponding ones
from the bare models. This can be seen from Figure 6(d), which shows a comparison of the median
maximum story drift profiles at collapse for the bare and composite models of the eight-story SMF.
Because plastic deformations are concentrated to less number of stories in the case of the composite
model, one would expect that the composite models would have a smaller median collapse intensity
compared to the bare models. In order to explain this issue, a close inspection of the hysteretic
response of various structural components (i.e., beams, columns, and panel zones) within a story of
the eight-story steel SMF is needed.
Figure 7 shows the hysteretic response of the steel column, beam with RBS, and panel zone in terms
of moment-rotation at the second floor interior joint at the collapse intensity, SCT(T1, 5%) = 1.08 g, of
the Canoga Park record from the 1994 Northridge earthquake. Results are presented for the bare (top
part of Figure 7) and composite (bottom part of Figure 7) models of the eight-story SMF. In this figure,
the moment-rotation of the column is the one at the bottom of the second floor interior joint.
For the bare frame model (Figures 7(a)–(c)), the column and the panel zone remain elastic while
plastic hinging and energy dissipation primarily occur in the RBS region of the second floor beams.
From Figure 7(c), it is clear that once the chord rotation of the steel beam exceeds about 3% rad, the
beam strength deteriorates. From the same figure, the steel SMF, prior to collapse, ratchets in one
Figure 7. Moment-rotation response of a second story interior joint at collapse intensity for the eight-story
bare model (top) and composite model (bottom).
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1946
loading direction; therefore, the amplitude of inelastic cycles in the opposite loading direction is not
large; thus, the cyclic deterioration in strength and stiffness of the same component is not significant
as shown in the same figure.
For the composite frame model, the column yields and eventually deteriorates in strength as shown
in Figure 7(d). This is attributed to the higher flexural strength of the composite beams compared to the
ones of the bare frame beams with RBS; another reason is the change of the column moment gradient
once plastification occurs (i.e., the inflection points in the columns do not remain constant during the
response history). In addition, due to the higher flexural strength of the composite beams, the panel
zone becomes the ‘weak link’ of the interior joint. This can be seen from Figure 7(e) that shows the
deduced moment-rotation of the panel zone at the same joint. As a result, the composite beam
experiences minor yielding in flexure (Figure 7(f)). Despite the fact that the composite model
developed a collapse mechanism that involved plastic hinging of the columns at lower story, the
collapse capacity of this frame increased because plastic deformations were concentrated in the
panel zones. This is a stable energy dissipation mechanism even at large plastic deformations [11,
40, 42]. However, excessive panel zone yielding at interior joints of steel SMFs should be treated
with caution. The reason is that when the panel zone shear distortion angle becomes larger than 4%
rad, fracture may occur between the bottom flange of the steel beam and the column face [3, 9, 40].
This would cause a sudden drop in the beam flexural strength in the negative loading direction. This
failure mode is not desirable. Given the randomness of these fractures, one should examine carefully
how close are the probabilities of collapse of the composite frames with respect to established limits
based on FEMA P695 [27] and ASCE/SEI 7-10 [25] for the archetype steel SMFs. In addition, a
strategy to reduce excessive panel zone shear distortion in steel SMFs should be considered.
5.1. Collapse assessment based on the FEMA P695 methodology
In this section, the seismic performance of the bare and composite steel SMFs is evaluated according to
FEMA P695 methodology. This methodology compares the adjusted collapse margin ratio (ACMR) for
a given structural system to the minimum acceptable CMR for a 10% probability of collapse,
ACMR10%. The ACMR is computed as follows:
ACMR ¼
S^CT
SSF
SMT
(6)
where SMT is the spectral acceleration intensity of the MCE at the fundamental period (T) and SSF is
the spectral shape factor used to account for the frequency content (spectral shape) of the groundmotion record set. The SSF is based on the period-based ductility factor and the fundamental period
of the frame. The fundamental period (T) used in the FEMA P695 [27] evaluation methodology is
the one given by Section 12.8 of ASCE/SEI 7-10 [25] (i.e., the strength-based period). The
calculated values of the fundamental period for the four archetype buildings are tabulated in Table V.
In order to compute the ACMR10%, the total system uncertainty (βTOT) is quantified based on the
following assumptions: (i) the design requirements uncertainty is assigned ‘A-Superior’ quality
rating (βDR = 0.1) and (ii) the test data and numerical modeling uncertainty are both assigned ‘B-Good’
quality rating (βTD and βMDL = 0.2). The modeling uncertainty is rated ‘B-Good’ given the absence of
certain modeling features such as the interior gravity framing. Table V summarizes the computed
ACMR and ACMR10% values for the bare and composite models of the archetype SMFs. According to
Table V. Evaluation of bare and composite models according to FEMA P695 methodology.
4-story
T (s)
ACMR
ACMR10%
Pass/fail
8-story
12-story
20-story
Bare
Composite
Bare
Composite
Bare
Composite
Bare
Composite
0.95
1.92
1.90
Pass
0.95
2.64
1.90
Pass
1.64
2.52
1.90
Pass
1.64
2.60
1.88
Pass
2.25
2.42
1.84
Pass
2.25
2.96
1.78
Pass
3.37
3.35
1.83
Pass
3.37
4.39
1.75
Pass
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Earthquake Engng Struct. Dyn. 2014; 43:1935–1954
DOI: 10.1002/eqe
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1947
EFFECT OF COMPOSITE ACTION ON STEEL SPECIAL MOMENT FRAMES
A. ELKADY AND D. G. LIGNOS
the FEMA P695 procedure, both the bare and composite models of the archetype SMFs pass the
performance evaluation criteria (i.e., ACMR > ACMR10%). Looking at low to mid-rise steel SMFs, the
margin against collapse is not much; thus, the mean annual frequency of collapse (λc), discussed in
the following section, is also employed to examine the collapse risk of the same archetype steel
SMFs (Section 5.2).
5.2. Mean annual frequency of collapse
In this section, the effect of the composite action on the seismic performance of steel SMFs is evaluated
based on λc. The λc considers the entire collapse hazard arising from all possible seismic events. The
performance evaluation is based on comparing the probability of collapse over 50 years
corresponding to a given mean annual frequency of collapse with the acceptable limit given by
ASCE/SEI 7-10 [25]. The mean annual frequency of collapse, λc, for a given structural system is
computed numerically by integrating the collapse fragility curve of the structural system over the
corresponding hazard curve using Equation (7) [47–49], where, Pc|Sa is the probability of collapse
at a given spectral acceleration and dλSa(Sa)/d(Sa) is the slope of the seismic hazard curve given this
spectral acceleration. Assuming that the earthquake occurrence follows a Poisson distribution, the
probability of collapse for a given number of n years, Pc(50 years), can be computed as Pc
(n years) = 1 exp(λc n). This Pc(50 years) is compared to the 1% limit specified in Section 21.2.1,
ASCE/SEI 7-10 [25] for the archetype steel buildings under consideration.
dλSa ðSaÞ
:dðSaÞ
λc ¼ ∫ ðPc jSaÞ:
dðSaÞ 0
∞
(7)
The hazard data used to calculate λc are obtained from the USGS website (2008 update of the US
national seismic hazard maps). The data correspond to the gridded coordinates (34.000, 118.150)
for a location south of downtown Los Angeles, California and a site condition with shear wave
velocity Vs30 = 259 m/s equivalent to NEHRP ‘D’ site condition (183 < Vs30 < 366 m/s). A fourth
order polynomial curve is fitted to the discrete hazard data points in the log-log space in order to be
used in the integration process for the λc calculation. Figure 8 shows the hazard curves for the bare
models of the 4-, 8-, 12-, and 20-story steel SMFs.
Table VI summarizes the values for λc and the corresponding Pc(50 years) for the bare and composite
models of all SMFs. From this table, the corresponding probability of collapse over 50 years decreases
when the composite action is considered compared to the bare steel frame. However, for low and midrise steel SMFs (i.e., 4 to 12 stories), the probability of collapse over 50 years exceeds the 1% limit
imposed by ASCE/SEI 7-10 [25]. For high-rise steel SMFs (i.e., 20 stories), the Pc(50 years) is
Figure 8. Seismic hazard curves for bare models of all SMFs.
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1948
Table VI. Mean annual frequency of collapse and the corresponding probability of collapse in 50 years for
bare and composite models.
4-story
λc [1/year]
Pc(50 years)
8-story
12-story
20-story
Bare
Composite
Bare
Composite
Bare
Composite
Bare
Composite
6.37e-4
3.14%
2.40e-4
1.19%
2.79e-4
1.39%
2.25e-4
1.12%
2.98e-4
1.48%
2.20e-4
1.07%
3.48e-5
0.17%
1.10e-5
0.05%
noticeably lower than 1%. This is primarily attributed to the low seismic hazard associated with long
periods (Figure 8). A comparison of the results in this section with the ones presented based on the
FEMA P695 [27] methodology illustrates the importance of considering all the intensities that
contribute to the collapse risk compared to CMR.
Based on the aforementioned results, the composite action can benefit the steel SMF seismic
performance at large deformations; however, two very important issues should also be addressed: (i)
how to avoid bottom story collapse mechanisms that are triggered due to the presence of the
concrete slab so that we can achieve a tolerable probability of collapse over a certain period of time
(i.e., 50 years) and (ii) how to achieve controlled panel zone yielding in beam-to-column joints of
steel SMFs after considering the composite action without using thicker doubler plates to achieve
the panel zone strength requirements per ANSI/AISC 360-10 [26]. A reasonable approach would be
to consider SCWB ratios larger than 1.0. This is examined in the following section.
6. EVALUATION OF COMPOSITE SPECIAL MOMENT FRAMES DESIGNED WITH HIGHER
STRONG-COLUMN/WEAK-BEAM RATIOS
This section discusses the seismic evaluation through collapse of the same archetype steel SMFs
discussed in Section 3 after we redesigned them by using a SCWB ratio > 1.5 and > 2.0. Figures 9
(a) and (b) show the column and beam sections for the eight-story steel SMFs designed a SCWB
ratio > 1.5 and > 2.0, respectively. The discussion in this section focuses only on the steel SMFs
when the slab is considered as part of their analytical models (i.e., composite models).
The collapse capacities of the composite models of the redesigned steel SMFs are evaluated as
discussed in Sections 4 and 5. The first mode period, T1, and the system performance parameters
(Ω and μT) of the redesigned steel SMFs are summarized in Table I. As expected, steel SMFs
designed with higher SCWB ratios have shorter first mode periods and higher overstrength factors
compared to the steel SMFs designed with SCWB ratio >1.0. Higher values are also observed for
the period-based ductility factors implying that column plastic hinging did not concentrate in the
bottom stories of the redesigned steel SMFs. This resulted in a less steep post-capping slope
compared to steel SMFs designed with SCWB ratio >1.0.
Incremental dynamic analysis is performed for the composite models of the redesigned SMFs. For
comparison purposes, for each composite model, the first mode period of the corresponding bare steel
SMF designed with SCWB >1.0 is used to scale the ground-motion records as discussed in Section 5.
Figure 10(a) shows the collapse fragility curves for the composite models of the eight-story SMFs
designed with different SCWB ratios. From this figure, it is evident that the median collapse
intensity of the eight-story steel SMF when designed with SCWB ratio >1.5 or >2.0 increased by
35% and 63%, respectively, compared to the median collapse intensity of the eight-story steel SMF
designed with SCWB ratio > 1.0. Because the steel columns of the redesigned SMFs have thicker
webs, their panel zones experienced lower levels of shear distortion compared to the original
designs, for the same spectral intensity. This implies that the likelihood of bottom flange fracture
due to excessive panel zone shear distortion is reduced. The thicker column webs also help reducing
the dependency on welded doubler plates. Many researchers have questioned the efficiency of the
doubler plates [42, 50, 51]. Therefore, fabrication costs are likely to be reduced with an average
column weight increase of not more than 149 kg/m (100 lbs/ft).
Copyright © 2014 John Wiley & Sons, Ltd.
Earthquake Engng Struct. Dyn. 2014; 43:1935–1954
DOI: 10.1002/eqe
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EFFECT OF COMPOSITE ACTION ON STEEL SPECIAL MOMENT FRAMES
A. ELKADY AND D. G. LIGNOS
Figure 9. Column and beam sections of the eight-story SMF, designed with SCWB ratios larger than 1.5 and 2.0.
Figure 10. (a) Collapse fragility curves for the composite models of the eight-story SMF designed with
different SCWB ratios and (b) mean annual frequency of collapse versus SCWB ratio for all composite
models (FEMA P695 Far-Field ground-motion set).
Figure 10(b) shows the effect of the SCWB ratio on the mean annual frequency of collapse, λc, and the
corresponding probability of collapse in 50 years, Pc(50 years), for the composite models of all the
archetype steel SMFs. From this figure, once a SCWB ratio >1.5 is employed, the mid-rise steel SMFs
achieve a tolerable Pc(50 years), which is less than 1%. This implies that the corresponding limit per
ASCE/SEI 7-10 [25] is satisfied. For the low-rise four-story SMF, a small increase in the probability of
collapse is observed at SCWB ratio >1.5. This is attributed to the minor change in column sizes when
the four-story SMF is designed with a SCWB >1.5 versus SCWB > 1.0. Figure 10(b) also shows that
for SCWB ratios larger than 1.5, an almost uniform probability of collapse is achieved for all the
archetype steel SMFs considered in this paper. Note that for high-rise steel SMFs (i.e., 20 stories), an
increase in the SCWB ratio of more than 2.0 is not effective. This is attributed to the fact that P-Delta
effects mostly control the sidesway collapse mechanism in these cases.
Copyright © 2014 John Wiley & Sons, Ltd.
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DOI: 10.1002/eqe
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1950
Figure 11. (a) Collapse fragility curves for the eight-story composite models designed with different SCWB
ratios and (b) mean annual frequency of collapse versus SCWB ratio for all composite models (LMSR-N
ground-motion set).
Table VII. Change in column weight and number of doubler plates for SMFs designed with SCWB ratios
>1.5 and >2.0 with respect to SMFs designed with SCWB ratio >1.0.
4-story
SCWB ratio
Percentage increase in columns weight
Percentage decrease in number of doubler plates
1.5
9
25
8-story
2.0
24
50
1.5
17
30
2.0
35
60
12-story
1.5
18
25
2.0
37
63
20-story
1.5
16
31
2.0
31
56
The analysis and evaluation process discussed herein was also repeated using a different ground-motion
record set compiled by Medina and Krawinkler [48]. This set covers ground-motion records with large
moment-magnitude, 6.5 ≤ Mw ≤ 7 and short closest-to-fault-rupture distance, 13 km < Rrup < 40 km. This
ground-motion set is labeled as the LMSR-N set. The LMSR-N set yielded very similar results to the
Far-Field set. For example, the difference in the median collapse intensity, obtained from the two
ground-motion sets for a given model, was below 20%. This can be seen if we compare Figures 10 and
11 that correspond to the eight-story steel SMF when the FEMA P695 Far-Field and the LMSR-N sets
are employed, respectively. Similarly to the results of the Far-Field set, the Pc(50 years) also exceeded
the 1% limit for low-rise and mid-rise steel SMFs, when the LMSR-N set is implemented (Figure 11(b)).
Note that the effect of long duration records on the seismic collapse capacity of steel SMFs and
implications on seismic design is not considered as part of this paper.
It is worth mentioning that heavier column sections, associated with higher SCWB ratios, might
raise a cost-associated issue. Table VII summarizes the percentage change in column weight and
number of doubler plates for the redesigned steel SMFs with respect to steel SMFs designed with
SCWB ratio >1.0. In average, designing a steel SMF with a SCWB ratio >1.5 or SCWB ratio >2.0
increased the column weight by 15% and 32%, respectively. However, this increase in column
weight lead to a considerable reduction in the number of required welded doubler plates to satisfy
the panel zone strength requirements per ANSI/AISC 360-10 [26]. The reduction in number of
doubler plates reduces the cost of steel fabrication and the likelihood of welding related failures [52].
7. CONCLUSIONS
This paper investigates the effect of the composite action on the seismic performance of SMFs designed in
highly seismic regions. A rational approach is first proposed to model the cyclic behavior of steel beams
and panel zones in the presence of a slab. A state-of-the-art deterioration model was calibrated with
available experimental data on composite RBS connections, and modification factors are proposed to
Copyright © 2014 John Wiley & Sons, Ltd.
Earthquake Engng Struct. Dyn. 2014; 43:1935–1954
DOI: 10.1002/eqe
10969845, 2014, 13, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/eqe.2430 by Tongji University, Wiley Online Library on [25/01/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
1951
EFFECT OF COMPOSITE ACTION ON STEEL SPECIAL MOMENT FRAMES
A. ELKADY AND D. G. LIGNOS
simulate the asymmetric hysteretic behavior of composite beams with RBS. Based on the component
modeling assessment,
(1) The flexural strength of a composite beam with RBS in the positive loading direction (i.e. slab in
compression) and the negative loading direction is 35% and 25% higher than that of the bare
steel beam, respectively.
(2) The precapping and post-capping plastic rotations of a composite beam with RBS in the positive
loading direction increase by 80% and 35%, respectively, compared to those of the bare steel
beam with RBS. This is attributed to the lateral restraint provided by the slab to the top flange
of the steel beam.
(3) The corresponding precapping and post-capping plastic rotations of a composite beam with RBS
in the negative loading direction (slab in tension) decrease by no more than 5% compared to the
bare steel beam with RBS. The reason is that the lower flange of a composite beam is more susceptible to local and lateral torsional buckling because the neutral axis of the composite beam is
shifted up because of the presence of the slab.
(4) If the slab geometric and material properties are known, a designer can use the approach
outlined in ANSI/AISC 360-10 [26] to compute the flexural strength of a composite beam in
order to account for the composite action during the computation of the SCWB ratio.
Using the proposed component models, the effect of the composite action on the global performance
of archetype steel buildings that utilize perimeter steel SMFs, designed based on the current seismic
provisions in the USA, was investigated. The steel SMFs, under evaluation, ranged from 4 to 20
stories. Both pushover and nonlinear response history analysis were conducted. The main findings
for the cases analyzed as part of this paper are summarized as follows:
(1) The composite action decreases the computer-based first mode period of all the steel SMFs by
about 20% compared to the bare frames. This decrease is attributed to the 40% average increase
in flexural stiffness of the steel beams in the presence of slab.
(2) An average increase of 10% to 20% was observed in the overstrength factor (Ω) of all the steel
SMFs when the composite action is considered.
(3) Bottom story collapse mechanisms are triggered when the composite action is considered as part
of the analytical modeling of steel SMFs. This is attributed to the increased beam flexural
strength due to the presence of slab, which is not considered as part of the SCWB ratio
calculation.
(4) For steel SMFs designed with a SCWB ratio >1.0, excessive panel zone shear distortions (γ > 5%)
were observed because of the increased flexural strength of composite beams. This is likely to trigger brittle fracture at the bottom flanges of beam-to-column welds. Controlled panel zone yielding
is achieved if a SCWB ratio >1.5 or 2.0 is employed as part of the design process.
(5) Both the bare and composite models of low-rise and mid-rise SMFs designed with SCWB ratio
>1.0 achieved a probability of collapse in 50 years that exceeded the 1% limit specified by
ASCE/SEI 7-10 [25]. The same steel SMFs pass the ACMR10% per FEMA P695 methodology.
This indicates the importance of considering a collapse metric that takes into account all the
intensities that contribute to the collapse risk (i.e., the mean annual frequency of collapse, λc)
instead of considering only two intensities that contribute to the collapse risk (i.e., ACMR).
However, the ACMR is a simpler collapse metric than λc. The same findings were confirmed
with a set of ground-motions other than the FEMA P695 Far-Field ground-motion record set.
(6) In all cases, when the steel SMFs are redesigned with a SCWB >1.5 or >2.0, they achieve a
uniform and acceptable probability of collapse over 50 years as per [25].
(7) Steel SMFs designed with SCWB ratios >1.5 or 2.0 typically employ columns with thicker
webs. This increases the column weight by 149–298 kg/m (100–200 lbs/ft) depending on the
SCWB ratio that is selected. Fabrication costs are reduced because the number of required
welded doubler plates is considerably reduced.
In the authors’ opinion, few of the system-level findings discussed in this paper may be ‘designoffice’ dependent. The authors believe that the SCWB ratio is a very challenging problem to handle
from the design standpoint; however, a larger value of the moment ratio compared to the one that is
Copyright © 2014 John Wiley & Sons, Ltd.
Earthquake Engng Struct. Dyn. 2014; 43:1935–1954
DOI: 10.1002/eqe
10969845, 2014, 13, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/eqe.2430 by Tongji University, Wiley Online Library on [25/01/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
1952
1953
currently used in the seismic design of steel SMFs substantially reduces their collapse potential during
extreme earthquake loading at relatively little costs. It is recommended that the analytical study
discussed in this paper be extended to different structural configurations and steel SMFs that utilize
other types of fully restrained beam-to-column connections in order to identify the optimum SCWB
ratios to be used in seismic design of steel SMFs.
ACKNOWLEDGEMENTS
This study is based on work supported by the National Science and Engineering Research Council of
Canada (NSERC) under the Discovery Grant Program. Funding is also provided by the Steel Structures
Education Foundation (SSEF). This financial support is gratefully acknowledged. Any opinions, findings,
and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily
reflect the views of sponsors. Feedback from two anonymous reviewers is appreciated.
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