Analytical Collapse Study of Lightly Confined Reinforced Concrete Frames Subjected to Northridge Earthquake Ground Motions

PLEASE SCROLL DOWN FOR ARTICLE

This article was downloaded by: [Ghannoum, Wassim M.]On: 1 October 2008Access details: Access Details: [subscription number 903256142]Publisher Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House,37-41 Mortimer Street, London W1T 3JH, UK

Journal of Earthquake EngineeringPublication details, including instructions for authors and subscription information:http://www.informaworld.com/smpp/title~content=t741771161

Analytical Collapse Study of Lightly Confined Reinforced Concrete FramesSubjected to Northridge Earthquake Ground MotionsWassim M. Ghannoum a; Jack P. Moehle b; Yousef Bozorgnia b

a Department of Civil, Architectural and Environmental Engineering, University of Texas at Austin, Austin,Texas, USA b Pacific Earthquake Engineering Research Center, University of California, Berkeley, California,USA

Online Publication Date: 01 September 2008

To cite this Article Ghannoum, Wassim M., Moehle, Jack P. and Bozorgnia, Yousef(2008)'Analytical Collapse Study of Lightly ConfinedReinforced Concrete Frames Subjected to Northridge Earthquake Ground Motions',Journal of Earthquake Engineering,12:7,1105 —1119

To link to this Article: DOI: 10.1080/13632460802003165

URL: http://dx.doi.org/10.1080/13632460802003165

Full terms and conditions of use: http://www.informaworld.com/terms-and-conditions-of-access.pdf

This article may be used for research, teaching and private study purposes. Any substantial orsystematic reproduction, re-distribution, re-selling, loan or sub-licensing, systematic supply ordistribution in any form to anyone is expressly forbidden.

The publisher does not give any warranty express or implied or make any representation that the contentswill be complete or accurate or up to date. The accuracy of any instructions, formulae and drug dosesshould be independently verified with primary sources. The publisher shall not be liable for any loss,actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directlyor indirectly in connection with or arising out of the use of this material.

http://www.informaworld.com/smpp/title~content=t741771161

http://dx.doi.org/10.1080/13632460802003165

http://www.informaworld.com/terms-and-conditions-of-access.pdf

Journal of Earthquake Engineering, 12:1105–1119, 2008

Copyright � A.S. Elnashai & N.N. Ambraseys

ISSN: 1363-2469 print / 1559-808X online

DOI: 10.1080/13632460802003165

Analytical Collapse Study of Lightly ConfinedReinforced Concrete Frames Subjected toNorthridge Earthquake Ground Motions

WASSIM M. GHANNOUM1, JACK P. MOEHLE2,and YOUSEF BOZORGNIA2

1Department of Civil, Architectural and Environmental Engineering, University

of Texas at Austin, Austin, Texas, USA2Pacific Earthquake Engineering Research Center, University of California,

Berkeley, California, USA

Review of older non seismically detailed reinforced concrete building collapses shows that mostcollapses are triggered by failures in columns, beam-column joints, and slab-column connections.Using data from laboratory studies, failure models have previously been developed to estimateloading conditions that correspond to failure of column components. These failure models havebeen incorporated in nonlinear dynamic analysis software, enabling complete dynamic simulationsof building response including component failure and the progression of collapse. A reinforcedconcrete frame analytical model incorporating column shear and axial failure elements wassubjected to a suite of near-fault ground motions recorded during the 1994 Northridge earthquake.The results of this study show sensitivity of the frame response to ground motions recorded from thesame earthquake, at sites of close proximity, and with similar soil conditions. This suggests that thevariability of ground motion from site to site (so-called intra-event variability) plays an importantrole in determining which buildings will collapse in a given earthquake.

Keywords Collapse; Concrete; Frame; Columns; Shear; Axial

1. Introduction

Post-earthquake studies show that the primary cause of reinforced concrete building collapse

during earthquakes is the loss of vertical-load-carrying capacity in critical building compo-

nents leading to cascading vertical collapse, rather than loss of lateral-load capacity. In cast-

in-place beam-column frames, the most common cause of collapse is failure of columns,

beam-column joints, or both. Once axial failure occurs in one or more components, vertical

loads arising from both gravity and inertial effects are transferred to adjacent framing

components. The ability of the frame to continue to support vertical loads depends on both

the capacity of the framing system to transfer these loads to adjacent components and the

capacity of the adjacent components to support the additional load. When one of these

conditions is deficient, progressive failure of the building can ensue.

Post-earthquake reconnaissance of reinforced concrete buildings provides some insight into

the prevalence of collapse among populations ofheavily shaken buildings. Otani [1999] reported

damage statistics of reinforced concrete buildings, with damage defined in three categories:

Received 4 April 2007; accepted 18 January 2008.

Address correspondence to Wassim M. Ghannoum, Department of Civil, Architectural and Environmental

Engineering, University of Texas at Austin, 1 University Station C1748, Austin, TX 78712-0273, USA; E-mail:

[email protected]

1105

Downloaded By: [Ghannoum, Wassim M.] At: 04:18 1 October 2008

1. operational damage (light to minor damage): columns or structural walls were slightly

damaged in bending, and some shear cracks might be observed in non structural walls;

2. heavy damage (medium to major damage): spalling and crushing of concrete, buckling

of reinforcement, or shear failure in columns were observed, and lateral resistance of

shear walls might be reduced by heavy shear cracking; and

3. collapse (partial and total collapse), which also included those buildings demolished at

the time of investigation.

Figure 1 presents the distribution of damage for four earthquakes reported by Otani

[1999]. For the 1985 Mexico earthquake, data are restricted to the lakebed zone of

Mexico City; for the 1990 Luzon, Philippines earthquake, data are from Baguio City;

for the 1992 Erzincan, Turkey earthquake, data are from two heavily damaged residential

areas of Erzincan; and for the 1995 Kobe earthquake, data are from areas of highest

seismic intensity in Kobe and restricted to buildings constructed before enforcement of

the 1981 Building Standard Law. Figure 1 shows that even in areas of highest damage in

famously damaging earthquakes, the collapse rates of lightly detailed reinforced concrete

buildings are relatively low.

Given the relatively low collapse rate shown in Fig. 1, it is reasonable to postulate that

refined engineering tools might be useful to identify those buildings that are most collapse

prone, so that resources could be focused on seismic mitigation of those buildings. Laboratory

studies of reinforced concrete columns with light transverse reinforcement have identified

primary variables that contribute to loss of column axial-load capacity. These models have

been implemented in nonlinear dynamic analysis software that can be used to simulate

building collapse during earthquake shaking. The software is used in a limited study to

simulate building response to a series of strong ground motions recorded within a relatively

small region during the 1994 Northridge earthquake. The results provide some insight into the

collapse of building frames as well as the influence of local ground motion on collapse.

2. Shear and Axial Load Failure of Reinforced Concrete Columns

The focus of this study was on buildings having reinforced concrete columns with

relatively light transverse reinforcement and with proportions that enable the columns

to yield in flexure prior to developing shear or axial failure. Columns with these details

FIGURE 1 Damage statistics from four earthquakes (adapted from Otani, 1999).

1106 W. M. Ghannoum, J. P. Moehle, and Y. Bozorgnia


and proportions may be able to sustain moderately large lateral deformations prior to

failure; a challenge is to estimate the lateral drift at which failure occurs. Other building

types, while of interest, were not studied here.

For a column that yields in flexure, the lateral strength is limited to the flexural

strength, and therefore can be calculated with relatively high accuracy. The column may

subsequently sustain apparent shear failure. Although the details of the mechanism

leading to shear failure are not fully understood, it is postulated that crack opening and

tensile strains reduce the shear-carrying capacity of the concrete, while spalling and bond

distress lead to degradation of the reinforcement contribution. To identify whether shear

failure is likely, it is necessary to estimate whether the shear strength will degrade to less

than the flexure strength.

Sezen and Moehle [2004] reported a model for shear strength of columns that

initially yield in flexure. The empirical model is based on theoretical concepts of shear

resistance but is calibrated to test data. The shear strength is defined as:

Vn ¼ Vs þ Vc ¼ kAstfytd

sþ k

0:5ffiffiffiffif 0c

pa=d

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ P

0:5ffiffiffiffif 0c

pAg

s !0:8Ag ðMPa unitsÞ; (1)

where Vs and Vc are shear contributions assigned to steel and concrete; k is a parameter

equal to 1 for �� 2, equal to 0.7 for �� 6, and varies linearly for intermediate ��values; �� = displacement ductility; Ast = area of shear reinforcement parallel to the

horizontal shear force within spacing s; fyt = yield strength of transverse reinforcement;

d = effective depth (= 0.8 h, where h = section depth parallel shear force); P = axial

compression force; f 0c = concrete compressive strength (MPa); Ag = gross section area,

and a/d = shear span/effective depth (value limited between 2 and 4). Figure 2 compares

measured and calculated shear strengths for the experimental column database used. The

mean ratio of measured to calculated strength and its coefficient of variation are 1.05 and

0.15.

If shear strength degrades to below flexure strength, shear failure is anticipated.

Elwood and Moehle [2005a] developed an empirical model to estimate deformation at

shear failure using the same data, as shown in Fig. 2. For this model, shear failure was

2.0

1.5

1.0

0.5

0.00 2 4 6 8

μ = 1.06

σ = 0.15

Displacement Ductility

Tes

t/mea

sure

d st

reng

th

FIGURE 2 Ratios of strengths measured during tests to strengths calculated by the

strength model [Sezen and Moehle, 2004].

Analytical Collapse Study of Lightly Confined RC Frames 1107


defined as the loss of 20% of the maximum shear strength. The data show that deforma-

tion at shear failure decreases with increasing shear stress, increasing axial stress, and

decreasing transverse reinforcement index. According to the model, deformation at shear

failure is defined as:

�s ¼3

100þ 4�00 � 1

42

�ffiffiffiffif 0c

p � 1

40

P

Agf 0c� 1

100ðMPa UnitsÞ; (2)

where r† = transverse steel ratio and v = nominal shear stress. Figure 3 [Elwood and

Moehle, 2005a] compares results from tests and from Eq. (2). The mean ratio of

measured to calculated drift at shear failure and its coefficient of variation are 0.97 and

0.34, respectively.

Axial load failure may coincide with onset of shear failure or may occur at larger

drift. Elwood and Moehle [2005b] used concepts of shear-friction and experimental data

to derive an expression for the drift at axial load failure of columns initially yielding in

flexure, then developing shear failure, and finally developing axial failure. The drift at

shear failure is estimated as:

�a ¼4

100

1þ tan2 �

tan �þ P sAstfytdc tan �

� � ; (3)

in which y = critical crack angle (assumed = 65�) and dc = depth of the column core

measured parallel to the applied shear. Figure 4 [Elwood and Moehle 2005b] compares

results of tests and Equation 3.

It is important to note that the models presented were for columns with rectangular

cross section, relatively light, and widely spaced transverse reinforcement, subjected to

unidirectional lateral load. Additional data are needed to validate models for other

conditions.

FIGURE 3 Displacement capacity measured and calculated by Eq. (2) [Elwood and

Moehle, 2005a].



3. Implementation of Shear and Axial Failure Models in OpenSEES

Shear and axial failures were modeled in OpenSEES [2004] by adding at the end of the

columns zero-length Limit State spring elements developed by Elwood [2002] (Fig. 5).

These elements have differing backbone curves before and after failures are detected.

Prior to shear failure, the shear springs are elastic with stiffness corresponding to the

shear stiffness of the column. Once the element reaches the limit curve defined by an

empirical shear-drift relation [Elwood and Moehle, 2005a] the shear spring backbone

curve is modified to a degrading hysteretic curve (Fig. 6). The shear degrading slope Kdeg

is calibrated based on observations from previous tests [Nakamura and Yoshimura, 2002],

which have shown that axial failure is initiated when shear strength degrades to about

zero.

FIGURE 5 Zero-length springs [Elwood, 2002].

FIGURE 4 Drift capacity curve based on shear-friction model [Elwood and Moehle,

2005b].



Similarly, the zero-length axial springs have a ‘‘rigid’’ backbone prior to reaching the

axial load versus drift limit curve [Elwood and Moehle, 2005b] (Fig. 6). This limit curve is

defined by the shear-friction model and assumes that shear failure has already occurred in

the element. Once the column element reaches that drift limit curve, its axial load versus

vertical deformation backbone is modified to a degrading hysteretic material model.

Because the shear-friction model only describes compression failures, the backbone is

only redefined for compressive axial loads. Beyond the initiation of axial failure, a coupling

effect exists between the horizontal and vertical deformations where an increase in hor-

izontal drift causes an increase in vertical deformation. This effect is modeled in the vertical

spring element with an iterative procedure that keeps the column response on the horizontal

drift versus axial load curve defined by the shear-friction model. When the earthquake

motion reverses direction, the vertical spring backbone is redefined to an elastic response

with a reduced elastic stiffness to account for the damage in the column. This modification

also halts the axial degradation in the column as it is assumed that the critical shear crack

closes and prevents any further sliding along that crack.

Shear Element Response

Axial Element Response

FIGURE 6 Shear and axial zero-length element responses and limit curves [Elwood,

2002].



4. Study of the Dynamic Response of a Building Frame

4.1. Building Frame Description

For this study, a three-bay, three-story reinforced concrete (RC) frame dimensioned to

represent typical 1960s and 1970s office building construction in California was

subjected to a series of ground motions from the Northridge earthquake. The full-

scale building frame shown in Fig. 7 was designed for third-scale, shaking-table testing

at the University of California, Berkeley under an ongoing research effort aimed at

understanding non ductile RC frame collapse mechanisms. Two of the columns in this

frame have non ductile detailing with widely spaced ties and 90� hooks, while the other

two columns have ductile detailing as per ACI 318–2002 recommendations. Since

typical RC building frames contain columns with varying axial loads, dimensions, and

reinforcing details, they sustain a staggered failure mechanism whereby different

columns fail at different drifts. The ductile columns in the test frame, while not

apparently representative of older existing construction, were introduced to simulate

that effect.

Beam dimensions and reinforcements were chosen to create a weak-column strong-

beam mechanism as well as to reduce joint shear stresses. The resulting concentration of

damage in the non ductile columns is intended to force axial collapse in these columns at

high drifts. The beam reinforcement details are typical of those in moment-resisting

frames built in the 1960s and 1970s in California.

Masses added to the frame for the dynamic analysis are equivalent to those expected

considering dead loads from a one-way slab system typical of office building construc-

tion. The masses result in approximately 0.16Agf´c axial load on the first-floor center

columns.

FIGURE 7 Frame details.



As this analytical study was completed prior to the completion of the physical frame

tests, target material properties were used in the modeling. Concrete cylinder strength f´c

is thus taken as 24.6 MPa and target steel yield strength fy as 486 MPa. Beams are

modeled as lumped-plasticity elements with an equivalent flexural stiffness derived from

fiber-section analysis. Columns are modeled as fiber-section elements to account for

variable axial load effects. Concrete for fiber-sections is modeled in OpenSees [2004]

using the concrete01 uniaxial material model (Kent-Scott-Park model with a degraded

unloading/ reloading stiffness according to Karsan and Jirsa, 1969). Concrete is modeled

with no tension strength. Steel for fiber-sections is modeled using the steel01 model

(bilinear with kinematic hardening). Slip of longitudinal reinforcement from joints and

footings is considered using rotational springs at column and beam ends. Effects of

splices are not modeled and joints are considered as rigid. Damping used was mass and

stiffness proportional (first and third modes) with a damping ratio of 5% of the critical

value.

The resulting OpenSEES [2004] analytical structure had an initial elastic first-mode

period T1 = 0.62 s, and a second-mode period T2 = 0.19 s. The effective first-mode period

near collapse of the model was about 1.0 s. The initial elastic periods were obtained from

the eigenvalue solution of the analytical model loaded only with gravity loads. Thus,

these periods were obtained with beams having flexural properties equivalent to a fully

‘‘cracked’’ section (no tension force in the concrete material) while the columns, which

were under gravity compression, had the flexural stiffnesses of effectively ‘‘un-cracked’’

sections. During tests of a physical model of this frame on the University of California,

Berkeley shaking table the equivalent full-scale elastic periods of this frame prior to its

collapse testing were recorded as T1 = 0.61 s and T2 = 0.20 s.

4.2. Selected Earthquake Ground Motions

The structural model is subjected separately to both components of seven ground motions

recorded during the 1994 Northridge, California, earthquake. By choosing the records

from a single earthquake, the earthquake-to-earthquake variability of ground motions is

excluded from the analysis. Additionally, by selecting a set of recording sites located in

the same general area, spatial variability of the recorded ground motion is relatively

reduced. The selected strong motion recording stations are listed in Table 1.

The locations of the recording stations, along with the epicenter and the surface

projection of the fault rupture plane are mapped in Fig. 8. As provided in Table 1, the

selected recording stations constitute a closely spaced cluster of sites located between 5.2

and 6.5 km from the fault plane. The sites have either NEHRP (ICC 2003) site class ‘C’

or ‘D’. The shear-wave velocity in the top 30 m of soil is in the range of 251–441 m/s (see

Table 1).

Figure 9 shows 5% damped elastic response spectra of the horizontal ground motions

at the selected sites. This figure shows the variability of the ground motion in terms of a

linearly elastic structural response intensity measure. The effects of such variability on

nonlinear dynamic response of the structural models will be discussed in the next section.

4.3. Analysis Results

Dimensioning and detailing of the frame were chosen to concentrate damage in the non

ductile columns at the first floor level, with little or no damage in the upper floor columns

prior to collapse. To get a sense of the damage sequence of the frame up to collapse, the

frame model was subjected to a pushover analysis driven by lateral forces with a first



mode vertical distribution acting from the ductile column side of the frame toward the

‘‘non ductile’’ side. The observed response and damage sequence for the frame are

summarized in Fig. 10, which plots the base shear versus first-story drift ratio for this

analysis. This figure also marks the various damage milestones, which are described next.

1. Yielding of all first-story column longitudinal steel occurs at a first floor horizontal

drift between approximately 0.7 and 1.0%.

2. At higher drifts, shear failures initiate in the yielded regions of both non ductile

columns. This occurs at about 2.2% horizontal drift.

TABLE 1 Strong ground motion records used in this study

Station

Ground motion

horizontal

components 1

Ground motion

horizontal

components 2

Rrup

(km)

Nehrp

site class

VS30

(m/s)

Rinaldi Receiving Sta RRS228 RRS318 6.5 D 282

Sylmar – Converter Sta SCS142 SCS052 5.3 D 251

Newhall – Fire Sta NWH360 NWH090 5.9 D 269

Sylmar – Converter

Sta East

SCE018 SCE288 5.2 C 371

Sylmar – Olive View

Med FF

SYL360 SYL090 5.3 C 441

Jensen Filter Plant JEN292 JEN022 5.4 C 373

Newhall – W Pico

Canyon Rd.

WPI046 WPI316 5.5 D 286

Notes: Rrup = Distance to fault rupture plane.NEHRP = U.S. National Earthquake Hazard Reduction Program (ICC 2003).Vs30 = Average shear-wave velocity in the top 30-m of soil.Ground motion horizontal components are presented in two sets, components 1 and 2 whichcorrespond to the components that produce higher and lower damage to the frame, respectively.

FIGURE 8 The 1994 Northridge, California, earthquake: Epicenter (star symbol),

surface projection of the fault plane, and locations of the selected recording stations

(solid circles) are marked.



3. Between approximately 2.2 and 5.5% horizontal drift, there is a gradual loss of shear

resistance in the non ductile columns until the point where the residual shear capacity

degrades to the capacity required to support axial loads.

4. At that drift level, axial failure is initiated in the nonductile columns. It is important to

note here that these high failure drift levels are mainly a function of the low axial load

on the columns as well as the flexure-then-shear failure sequence in the columns.

5. As the structure is pushed to even higher drifts, it collapses on the non ductile side of

the frame dragging the ductile side with it. A drift of 8% on the first floor was assessed

as the complete collapse drift for this frame.

0

20

40

60

80

100

120

Drift Ratio (%)

Bas

e Sh

ear F

orce

(KN

)

Long. steelyielding

Shear failureinitiation

Residual shearstrengths

SpallingNon-DuctileOuter Col.

DuctileOuter Col.

Non-DuctileInner Col.

DuctileInner Col.

First Floor Columns

Axial failureinitiation Projected behavior

XCollapse

0 1 2 3 4 5 6 7 8 9

FIGURE 10 Frame first–story pushover curve.

0

0.5

1

1.5

2

2.5

3

Ground Motion Horizontal Components 1

Period (sec)

Spe

ctra

l Acc

eler

atio

n (g

) T1 = 0.62 secRRS228SCS142NWH360SCE018SYL360JEN292WPI046Mean


RRS318SCS052NWH090SCE288SYL090JEN022WPI316Mean

0 0.5 1 1.5 2 2.5

T2 = 0.19 sec

Period (sec)0 0.5 1 1.5 2 2.5

0

0.5

1

1.5

2

2.5

3

Spe

ctra

l Acc

eler

atio

n (g

) T1 = 0.62 sec

T2 = 0.19 sec

FIGURE 9 Elastic response spectra for 5% damping for both horizontal components of

the selected 1994 Northridge records.



As the first-story columns yield in flexure and sustain significant damage, a first

mode pushover load pattern is no longer representative of seismic excitation. However,

since damage and inelastic deformations are concentrated at the first-story level (Fig. 11),

the effect of pushover load distribution is minimal on first-story damage sequence and

drifts presented in Fig. 10. Similar failure sequences and drifts were observed in dynamic

analyses.

The relatively large drift capacity of this frame is not generally applicable to this

class of buildings, but is a result of the specific conditions of the frame studied. Drift

capacity is sensitive to the amount of axial load on the columns, which drives the axial

failure, as well as the amount of longitudinal steel in the columns, which affects the

flexure-shear failure sequence and provides additional axial resistance [Elwood and

Moehle, 2005b]. Neither of these factors is accounted for in current codes of practice,

particularly the more recent performance-based FEMA 356 [FEMA 356, 2000].

This displacement-controlled behavior prompted the use of the first-story drift ratio

as the damage parameter for comparison between the different ground motion simula-

tions. Figure 12 shows the first-story drift ratio responses of the frame when subjected

to each of the components of the seven ground records individually. Table 2 sum-

marizes the absolute value of the maximum first-story drift ratios for each of the ground

motions.

As can be seen in Fig. 12, there is high variability in the frame response when

subjected to ground motions obtained from the same earthquake at sites of close proxi-

mity with similar soil conditions. These responses ranged from complete collapse of the

frame to almost no yielding of the first-story column longitudinal steel. It is evident here

that local geological and soil conditions have significant effects on the earthquake

response of a structure. As well, a high variability in response is observed in Fig. 12

when considering the frame response to either of the two components of each ground

motion. This suggests that the orientation of the structure can have a significant effect on

its response. While this might relate in part to differences in ground motion associated

with fault normal and fault parallel directions, this is not the sole source of the difference.

To demonstrate this point, the frame was subjected to the SCS142 ground motion in both

the East-West direction as well rotated 180� in the West-East direction. For the EW

direction, frame action resulted in increased axial load in the non ductile columns at peak

0

2

4

6

8

10

12

0 2 4 6 8Normalized Floor Displacements (%)

Floo

r Hei

ght (

m)

ElasticAt Shear Failure InitiationAt Residual Shear

FIGURE 11 Normalized horizontal floor displacements from pushover analysis (displa-

cements are normalized by story height = 3.96 m).



drift response, leading to loss of axial load carrying capacity. For the rotated ground

motion, frame action resulted in uplift on the non ductile columns at peak drift, in which

case axial failure did not occur.

To better understand why the frame sustained such a wide range of damage due to

these ground motions, several ground motion intensity measures (IMs) are investigated

with relation to the frame maximum first-story drift ratios (absolute values). These IMs

are the peak ground acceleration (PGA), peak ground velocity (PGV), spectral accelera-

tion at the first-mode elastic period (T1) of the structure (SaT1), and two modified

Housner velocity spectrum intensity measures [Housner 1959]. These measures are

derived by integrating the spectral velocity curve over a period range. In this work, the

4 2 0

2 0

6 8 12

Time (sec)

RRS228 SCS142 SCS142neg NWH360 SCE018 SYL360 JEN292 WPI046

X

Initiation of shear failure at +/-2.2% drift

Yielding at +/-0.7% drift


Initiation of axial load loss at +5.5% drift

–6

–4

–2

0

2

4

6

4 6 8 1JEN022 12Time (sec)

RRS318 SCS052 NWH090 SCE228 SYL090

WPI316


Yielding at +/-0.7% drift

Initiation of shear failure at +/-2.2% drift

Initiation of axial load loss at +5.5% drift

Firs

t-Sto

ry D

rift R

atio

s (%

)

–6

–8

–4

–2

0

2

4

6

8

Firs

t-Sto

ry D

rift R

atio

s (%

)

FIGURE 12 First-story drift ratio histories.



period ranges considered were T1 to 1.5 T1 and T2 to 1.5T1 (dubbed SIVT1 and SIVT2).

These IMs are summarized in Table 2 along with the maximum absolute first-story

drift ratios. Figure 13 plots these data with a least-squares linear regression fit through

them and presents the coefficients of determination (R2) for the fits. The results for

PGA were not reported in Fig. 13 as PGA showed least correlation with frame drift

with a coefficient of determination R2 = 0.08. While different relations can be

expected between the IMs presented here and the frame drift ratios for either the

elastic or inelastic drift ranges, it is the intent of this work to only investigate these

relations for inelastic frame deformations. As all the ground motions in this study

pushed the frame into the inelastic range a simple linear regression fit is used here for

quantitative comparison between the different IMs.

As can be seen in Fig. 13, the intensity measure SIVT1 shows a strong linear relation

with respect to maximum first-story drift with an R2 = 0.81. This correlation level is followed

by that of SaT1 and PGV which showed more dispersion with several outliers and R2 values

of 0.57 and 0.51, respectively. SIVT2 did not show much relation to the first-story drift ratios

as the response of this frame is mostly dominated by the first mode.

TABLE 2 Summary table of first-story maximum drift ratios and ground motion

intensity measures

Ground Motion

Maximum

Absolute

First-Story

Drift Ratio

(%)

PGA

(g)

PGV

(cm/s)

Elastic

SaT1 (g)

SIVT1 (cm)

T1!1.5T1

SIVT2 (cm)

T2!1.5T1

RRS 228 8.00* 0.83 160 1.96 5.17 18.0

318 2.41 0.49 74 0.92 2.31 12.0

SCS 142 5.78 0.61 117 1.37 4.04 11.7

142neg 6.55 0.61 117 1.37 4.04 11.7

052 4.89 0.90 102 1.48 3.55 13.6

NWH 360 4.36 0.59 97 2.00 4.36 16.4

090 1.31 0.58 75 1.17 2.17 14.6

SCE 018 2.18 0.83 117 1.11 3.34 14.0

288 1.55 0.49 75 0.76 2.11 9.2

SYL 090 2.20 0.60 78 1.14 2.58 10.6

360 1.36 0.84 129 1.35 2.91 18.1

JEN 292 2.09 0.57 76 0.73 2.04 11.3

022 1.66 1.02 67 1.17 2.98 19.2

WPI 046 0.93 0.45 93 0.65 2.02 7.2

316 0.80 0.33 67 0.56 1.56 6.5

*Limited to 8% drift corresponding to collapse.Notes:PGA = Peak ground acceleration.PGV = Peak ground velocity.SaT1 = Elastic response spectrum value at 1st mode period T1.SIVT1 = Modified Housner [Housner, 1959] Spectrum Intensity =

R 1:5T1

T1SvðT; 5%ÞdT With

Sv(T,n) = velocity response spectrum value corresponding to period T and 5% damping.SIVT2 = same as above with integration bounds ranging from T2 to 1.5T1.



5. Conclusions

The use of a model for shear and axial failure of lightly confined reinforced concrete

columns is explored for columns that develop shear and axial failure following initial

flexural yielding. Lateral strength can be estimated relatively accurately as the lateral

force corresponding to flexural yield. Propensity for shear failure can be identified using

a shear strength model in which shear strength following flexural yield degrades with

increasing deformation demand. The drift at shear failure varies with transverse reinfor-

cement amount and inversely with nominal axial and shear stresses. Drift at axial failure

varies with transverse reinforcement and inversely with axial load.

The model is implemented in nonlinear dynamic analysis software to demonstrate the

feasibility of conducting nonlinear dynamic analysis including shear and axial failure of

columns. A three-story building model is subjected numerically to a series of ground

motions recorded at stations located between 5.2 and 6.5 km from the fault plane of the

1994 Northridge earthquake and which had similar soft soil conditions. Response of the

frame is found to be very sensitive to the ground motions, with responses to individual

ground motions varying from almost no yielding of longitudinal steel to total collapse.

The response of the frame was very sensitive to its orientation and the component of the

ground motion to which it is subjected. Thus, the variability of ground motion from site to

site (so called intra-event variability) was found to play an important role in analytical

prediction of structural collapse. A modified Housner spectrum intensity measure with

integration bounds between T1 and 1.5T1 was found to correlate well with damage of the

frame.

Experimental studies to validate the numerical results, and additional numerical

studies to validate the ground motion intensity measures that best correlate with collapse,

are needed.

0 50 100 1500

2

4

6

8

R2 = 0.51

PGV (cm/sec.)

Firs

t-S

tory

Drif

t Rat

io (

%)

0 1 2 30

2

4

6

8

R2 = 0.57

Spectral Acceleration at T1 (g)

Firs

t-S

tory

Drif

t Rat

io (

%)

0 1 2 3 4 50

2

4

6

8

R2 = 0.81

SIVT1 (cm)

Firs

t-S

tory

Drif

t Rat

io (

%)

0 5 10 15 200

2

4

6

8

R2 = 0.1

SIVT2 (cm)

Firs

t-S

tory

Drif

t Rat

io (

%)

FIGURE 13 First-story absolute drift ratios vs. ground motion IMs. Circles mark the

horizontal component 1 motions and diamonds the horizontal component 2 motions.



Acknowledgments

This work was supported by the Pacific Earthquake Engineering Research Center through

the Earthquake Engineering Research Centers Program of the National Science Founda-

tion under award number EEC-9701568. Any opinions, findings, and conclusions or

recommendations expressed are those of the authors and do not necessarily reflect

those of the National Science Foundation. Ground motion data were obtained from the

PEER ground motion database (http://peer.berkeley.edu).

References

Elwood, K. [2002] ‘‘Shake table tests and analytical studies on the gravity load collapse of

reinforced concrete frames,’’ Doctoral Dissertation, University of California, Berkeley.

Elwood, K. and Moehle, J. [2005a] ‘‘Drift capacity of reinforced concrete columns with light

transverse reinforcement,’’ Earthquake Spectra, Earthquake Engineering Research Institute,

21(1), 71–89.

Elwood, K. and Moehle, J. [2005b] ‘‘Axial capacity model for shear-damaged columns,’’ Structural

Journal, American Concrete Institute, 102(4), 578–587.

FEMA 356 [2000] ‘‘Prestandard and commentary for the seismic rehabilitation of buildings,’’

Federal Emergency Management Agency, Washington, D.C.

Housner, G. W. [1959] ‘‘Behavior of structures during earthquakes,’’ Journal of the Engineering

Mechanics Division, ASCE, 85(EM4), 108–129.

ICC [2003] ‘‘International Building Code,’’ International Code Council, Falls Church, VA.

Karsan, I. D. and Jirsa, J. O. [1969] ‘‘Behavior of concrete under compressive loadings,’’ Journal of

the Structural Division, ASCE, 95(ST12), 2543–2564.

Nakamura, T. and Yoshimura, M. [2002] ‘‘Gravity load collapse of reinforced concrete columns

with brittle failure modes,’’Journal of Asian Architecture and Building Engineering 1(1), 21–27.

OpenSEES [2004] Open system for earthquake engineering simulation, http://opensees.berkeley.

edu, Pacific Earthquake Engineering Research Center, University of California, Berkeley.

Otani, S. [1999] ‘‘RC building damage statistics and SDF response with design seismic forces,’’

Earthquake Spectra, Earthquake Engineering Research Institute, 15(3), 485–501.

Sezen, H. and Moehle, J. P. [2004] ‘‘Shear strength model for lightly reinforced concrete columns,’’

Journal of Structural Engineering, ASCE, 130(1), 1692–1703.



Documents

Analytical Collapse Study of Lightly Confined Reinforced Concrete Frames Subjected to Northridge Earthquake Ground Motions