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Seismic performance of reinforced concrete moment resisting frames

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Engineering Structures 29 (2007) 2365–2380www.elsevier.com/locate/engstruct
Seismic performance of reinforced concrete moment resisting frames
R. Sadjadi
a
, M.R. Kianoush
a,
∗
, S. Talebi
b
a
Department of Civil Engineering, Ryerson University, Toronto, Ontario, Canada
b
TAG Structural Group Inc., Toronto, Ontario, Canada
Received 14 June 2006; received in revised form 13 October 2006; accepted 27 November 2006Available online 18 January 2007
Abstract
Moment resisting frames (MRF) are typically classiﬁed as “ductile”, “nominally ductile”, and “GLD” (Gravity Load Designed). The seismicperformance of these structures can be evaluated in terms of its lateral load resistance, distribution of interstory drift, and the sequence of yieldingof the members. In this study a typical 5-story frame is designed as (a) ductile, (b) nominally ductile, (c) GLD, and (d) retroﬁtted GLD. Thisstudy presents an analytical approach for seismic assessment of RC frames using nonlinear time history analysis and push-over analysis. Theanalytical models are validated against available experimental results and used in a study to evaluate the seismic behavior of these 5-story frames.It is concluded that both the ductile and the nominally ductile frames behaved very well under the considered earthquake, while the seismicperformance of the GLD structure was not satisfactory. After the damaged GLD frame was retroﬁtted the seismic performance was improved.c
2006 Elsevier Ltd. All rights reserved.
Keywords:
Reinforced concrete; Moment resisting frame; Ductile; Nominally ductile; GLD; Retroﬁtted GLD
1. Introduction
Many multi-story RC frame structures built prior to 1970and located in seismic zones have been designed only forgravity loads without any consideration of lateral loads. Thesestructures are referred to as gravity load designed (GLD)frames. The lack of seismic considerations in GLD structuresresults in non-ductile behavior in which the lateral loadresistance of these buildings may be insufﬁcient for evenmoderate earthquakes. Current seismic codes for reinforcedconcrete structures are based on considerations of inelasticbehavior in the structural members, which requires theformation of a desirable beam side-sway mechanism ratherthan the column side-sway mechanism. According to theCanadian design practice, designers have two options for theseismic design of reinforced concrete frames [1]. The ﬁrst
option is to design a ductile frame, which involves specialdesign and detailing provisions to ensure ductile behavior.The second option is to design a nominally ductile frame.This option involves designing for twice the seismic lateral
∗
Corresponding author. Tel.: +1 416 979 5000x6455; fax: +1 416 979 5122.
E-mail addresses:
rsadjadi@ryerson.ca (R. Sadjadi),kianoush@ryerson.ca (M.R. Kianoush), talebi@taginc.ca (S. Talebi).
load as that of ductile frames, but without taking all thespecial provisions for capacity-based design and good detailingin the design of the frame members. By allowing sucha choice, the code implies that either type of frame willprovide equivalent seismic performance under the design levelearthquake disturbance. The seismic design lateral loads andthe level of seismic reinforcement detailing incorporated in anRC moment resisting frame depend on its available ductilitycapacity. In ductile structures, the design lateral loads reducesigniﬁcantly, but high ductility capacity is enhanced throughstrict detailing requirements to avoid premature modes of brittlefailure.The seismic resistance of existing GLD structures may beinadequate due to weaknesses in the structural system andnon-ductile detailing. To mitigate the seismic hazards, existingdeﬁcient structures should be retroﬁtted.The evaluation of the seismic resistance of existingstructures and their deﬁciencies is essential before anappropriate repair or upgrade system can be designed. Becauseof the economic feasibility of using analytical models insteadof obtaining data from destructive experimental tests, there is aneed for an efﬁcient and reliable analytical tool, which predictsthe real behavior of such structures during an earthquake, andgives comparable results to experimental data.
0141-0296/$ - see front matter c
2006 Elsevier Ltd. All rights reserved.doi:10.1016/j.engstruct.2006.11.029
2366
R. Sadjadi et al. / Engineering Structures 29 (2007) 2365–2380
Heidebrecht and Naumoski [2] conducted an extensiveanalytical investigation on the performance of a six-storyductile moment resisting frame designed based on the NationalBuilding Code of Canada [3], using several different design
variations. Filiatrault et al. [4,5] conducted experimental test
and analytical modeling of a two-story reduced scale framesdesigned as ductile and nominally ductile based on theprovisions of NBCC 1995 [3] and of the Canadian Concrete
Standard [1]. There have also been numerous studies on theseismic performance of the GLD structures such as Bracci et al.[6], Kunnath et al. [7], and Aycardi et al. [8].
Bracci et al. [9] studied different retroﬁt techniques for
the seismic performance of the GLD frames. These studiesinclude analytical modeling and experimental test of GLD sub-assemblages, and frames.However, there has not been a study to date which comparesthe seismic performance of RC frames designed based onductile, nominally ductile, GLD, and retroﬁtted GLD options.This study presents an approach for the assessment of seismicbehavior of existing RC frames. Therefore, inelastic modelsof such frames are developed and analyzed using IDARC2D(Version 6.0) [10].Available shake table tests of two half-scale reinforcedconcrete moment resisting frames, designed according toCanadian standards as ductile and nominally ductile [4],
are compared with the predictions of inelastic time-historydynamic analyses following the proposed method. Thereliability of the method is ﬁrst assessed and then the unknownparameters in terms of the hysteretic rule parameters aredetermined so as to achieve more comparable results betweenanalytical results and the experimental evidence. For the GLDand retroﬁtted GLD frames, the information from the researchby Bracci et al. [9] is used. After calibration of the unknown
parameters for each type of frame, analytical investigationis conducted to evaluate the performance of the four typical5-story frame buildings designed as ductile, nominally ductile,GLD, and retroﬁtted GLD. The study includes “non-lineartime-history” analysis and “pushover” analysis. The results interms of ductility, time-history response of the top story, baseshear-top story displacement, sequence of yielding, distributionof interstory drift, and the damage potential are presented.
2. Description of the 5-story building
The plan view and elevation of the 5-story building is shownin Fig. 1. Each frame is assumed to be part of the lateral load
resisting system of a building. The story height is 4 m for theﬁrst story and 3 m for other stories resulting in a total buildingheight of 16 m.In terms of the lateral stiffness and mass distribution, thestructure is almost symmetrical in plan with respect to twoorthogonal axes; therefore analysis may be performed usingtwo planar models, one for each main horizontal direction.The structure is also vertically regular as there is neitherdiscontinuity nor abrupt change in the dimensions and stiffnessof the adjacent stories. It is important to note that if the center
Fig. 1. The 5 story building. (a) Plan, (b) Elevation.
of mass and center of rigidity do not match, torsional responseresults, so 3D models are needed.The material properties are assumed to be identical for thefour structures throughout the height of the structure as: (a)reinforcing steel yield strength,
F
y
=
400 MPa; (b) concretecompressive strength,
f
c
=
35 MPa.In this study the seismic behavior of four types of MRFwith the aforementioned speciﬁcations are discussed. The ﬁrsttwo types correspond to moment resisting frames which aredesigned based on the Canadian code seismic provisions,namely ductile and nominally ductile. The GLD frame isassumed to be built before seismic provisions were included inbuilding codes and this structure is designed based on the ACIcode provisions of ACI 318-63 [11].
2.1. Lateral loads
The NBCC 1995 seismic base shear is given by:
V
=
(
V
e
/
R
)
U
(1)where
V
e
is the equivalent lateral seismic force representingelastic response,
R
is the response modiﬁcation factor (given
R
=
2 for nominally ductile frame and
R
=
4
.
0 for ductilemoment resisting frame structures),
U
=
0
.
6 is a calibrationfactor,
V
e
is the elastic lateral seismic force, which is given by:
V
e
=
v
SIFW (2)
R. Sadjadi et al. / Engineering Structures 29 (2007) 2365–2380
2367Table 1Summary of design seismic loads (for frame B) for ductile and nominally ductile (ND) framesFloor
h
l
(m) Story height
W
l
(MN) Story weight
F
x
(kN) Design baseshear
T
x
Torsion (kN m)
F
xt
Torsionallateral forcesTotal lateralforcesND Ductile ND Ductile ND Ductile ND DuctileRoof 16 2.75 1465.0 732.5 3223.0 1611.5 48.3 24.2 414.6 207.35 13 3.28 1419.0 709.5 3121.8 1560.9 46.8 23.4 401.6 200.84 10 3.28 1091.0 545.5 2400.0 1200.0 36.0 18.0 308.7 154.43 7 3.28 763.3 381.6 1679.3 839.5 25.2 12.6 216.0 108.002 4 2.89 384.7 192.35 846.3 423.2 12.7 6.35 108.9 54.501
=
15
.
48
where,
v
is zonal velocity ratio. It is assumed that the buildingis located in the highest seismic zone (i.e.
v
=
0
.
4),
S
is theseismic response factor
=
1
.
5
√
T
for
T
≥
0
.
5 s (given
T
=
0
.
1
N
=
0
.
5 s,
S
=
2
.
121), where
T
is the fundamental periodof vibration,
N
is the total number of stories above grade,
I
isthe seismic importance factor assumed to be 1.0 as the buildingis intended for typical ofﬁce occupancy,
F
is the foundationfactor assumed to be equal to 1.3, as the structure is assumed tobe built on soft base soil.According to the Canadian Concrete Standard, the use of
R
=
4 for the ductile structure was justiﬁed by implementingthe strict seismic detailing requirements. The structure withnominal ductility (
R
=
2) incorporated only nominal detailing,since its design lateral loads were higher than the ductilestructure.Thedeadload(W)ofthebuildingiscalculatedas15482kN.The calculated base shears are 5122 and 2561 kN for thenominally ductile and the ductile frames, respectively.NBCC 1995 requires that the lateral load to be distributedover the building height as:
F
x
=
(
V
−
F
t
)
h
x
W
x
h
i
W
i
(3)where,
F
x
is lateral force applied at level
x
,
F
t
=
additionallateral force applied to the top of building (
F
t
=
0
.
0 if
T
≤
0
.
7 s),
W
i
and
W
x
are portions of
W
at levels
i
and
x
respectively,
h
i
and
h
x
are the heights above the base to levels
i
and
x
respectively. NBCC 1995 requires that the effects of torsional moments be included in the design of the lateral forceresisting system. Since there is no eccentricity in the building,the accidental applied torsional moment is calculated using thefollowing formula at each level (
x
):
T
x
=
(
F
x
)(
±
0
.
1
D
nx
)
=
2
.
2
F
x
(4)where
D
nx
=
22 m is the plan dimension of the building in thedirection of the computed eccentricity.
2.2. Analysis and design of the frames
Initial elastic analyses of the frames were performed inorder to determine the structural element seismic design forcesusing SAP2000 [12]. A summary of the design seismiclateral loads on frame-B as shown in Fig. 1 for ductileand nominally ductile (ND) frames is shown in Table 1.The ductile and nominally ductile structures are designedaccording to provisions of NBCC 1995 and of the CanadianConcrete Standard. Summaries of designed beam sections andreinforcement for the ductile, nominally ductile, and GLDstructures are shown in Table 2.For the ductile frame, the interior columns are 800
×
800 mmwith12No.30bars,andexteriorcolumnsare600
×
600mmwith12No.20 bars.For the nominally ductile frame, columns are 600
×
600 mm.The bars are 12No.30 bars at 1st, and 2nd story, 8No.30 bars at3rd, and 8No.25 bars at 4th, and 5th stories.Although the design lateral load for the ductile structure wasreduced to half of that of the nominally ductile structure, thesizes of the columns were determined based on the applicationof capacity design at the joints, adopted by the CanadianConcrete Standard, which imposes the requirement that:
M
rc
≥
1
.
1
M
nb
,
(5)where
M
rc
is the sum of moments at the center of the joint,corresponding to the factored resistance of the columns framinginto the joint, and
M
nb
is the sum of moments at the centerof the joint, corresponding to the nominal ﬂexural resistance of the beams framing into the joint.
2.3. Design of the GLD frame
The GLD frame has the same conﬁguration and geometryas the other two cases of study. The structure was assumed tobe constructed prior to 1970 and therefore designed accordingto the provisions of ACI 318-63 [11]. Since the code did notinclude seismic requirements, the framing system is assumedto be located in a Sandspit-BC with high-risk seismic zone andis designed for a wind load pressure of 0.63 kPa on verticalsurfaces, and the same gravity loads as the other cases of study.All columns are 350
×
350 mm with 6No.20 bars throughoutthe height of the GLD structure.
2.4. The retroﬁtted GLD frame
There are several methods for retroﬁtting an RC framewhich can be applied to an either damaged or undamaged
2368
R. Sadjadi et al. / Engineering Structures 29 (2007) 2365–2380
Table 2Summary of designed section for ductile frame beamsType Story Location Dimensions (mm) As (mm
2
) ElevationDuctile 1st Int & Ext Support
(
−
)
600
×
600 3000 TopInt & Ext Support
(
+
)
1500 BotMid-span 1200 Bot2nd Int & Ext Support
(
−
)
600
×
600 3000 TopInt & Ext Support
(
+
)
1500 BotMid-span 1200 Bot3rd Int & Ext Support
(
−
)
500
×
500 2700 TopInt & Ext Support
(
+
)
1400 BotMid-span 1500 Bot4th and 5th Int & Ext Support
(
−
)
500
×
500 2000 TopInt & Ext Support
(
+
)
1000 BotMid-span 1500 BotNominally Ductile 1st Int & Ext Support
(
−
)
600
×
600 5700 TopInt & Ext Support
(
+
)
4200 BotMid-span 1400 Bot2nd Int & Ext Support
(
−
)
600
×
600 5700 TopInt & Ext Support
(
+
)
4200 BotMid-span 1400 Bot3rd Int & Ext Support
(
−
)
500
×
500 5900 TopInt & Ext Support
(
+
)
3100 BotMid-span 1400 Bot4th and 5th Int & Ext Support
(
−
)
500
×
500 4200 TopInt & Ext Support
(
+
)
2100 BotMid-span 2100 BotGLD All ﬂoors Interior Support
(
−
)
250
×
450 2000 TopExterior Support
(
−
)
1500 TopMid-span 2000 Bot
structure such as “improved concrete jacketing”, “masonryblock jacketing”, and “partial masonry inﬁll” (Bracci et al. [9]).Column retroﬁtting is often critical to the seismicperformance of a structure. To prevent the column-swaymechanism during earthquakes, columns should never be theweakest components in the building structure. The response of a column in a building structure is controlled by its combinedaxial load, ﬂexure, and shear. Therefore, improved concrete jacketing is used to increase column shear and ﬂexural strengthso that columns do not conform to the weak-column strongbeam undesirable mechanism.In this study it is decided to evaluate the application of the “improved concrete jacketing” to all columns of the GLDframe. In this method all the 350
×
350 mm columns areencased in a concrete jacket with additional longitudinal andtransverse reinforcement and the column size is increased to500
×
500 mm. This will increase the moment of resistanceof the columns relative to the beams. The reinforcement isnot anchored to the foundation to avoid the transmission of additional stresses to the foundation and, more importantly,to force the desirable mechanism of column base hinging incase of the seismic force. The longitudinal bars are then post-tensioned, and an RC ﬁllet is provided in the beam column jointzone. This will enhance the shear capacity of the beam-column joint by increasing the axial load and also will increase the bondcondition between the beam reinforcement and the concrete atthe joint zone (Bracci et al. [9]).
3. Nonlinear modeling
A number of computer programs are available for non-linear analysis of reinforced concrete structures. Some of theseprograms such as LARSA, SAP2000, ABAQUS, NISA, andANSYS implement ﬁnite element methods (FEM) for theanalysis of the structures. The application of FEM for seismicanalysis of a multistory reinforced concrete structure is avery time-consuming and complicated task. On the other handapplication of simple and reliable modeling schemes such asmacro-modeling that permits efﬁcient seismic analysis of theentire multistory frame is more justiﬁed. Therefore programssuchasIDARC2D,DRAIN-2DX,andRUAUMOKOhavebeenused widely for the seismic analysis of structures. The mainadvantage of such programs is their simplicity, and the speed of analysis, which is important in the case of analysis of structureswith several members.The inelastic dynamic analysis of reinforced concretebuilding structures program IDARC2D (Version 6.0) [10] isused to observe the response of the structure to nonlineartime history and pushover analyses. It has the capability of using both lumped plasticity, and spread plasticity concepts.The formulations are based on macro-models in which mostof the elements are represented as a comprehensive elementwith nonlinear behavior. Columns and beams are macro-modeled with inelastic ﬂexural deformation and elastic sheardeformation. The load-deformation of the structure is simulated

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