UILU .. ENG .. 2001 .. 2004

CIVIL ENGINEERING STUDIES STRUCTURAL RESEARCH SERIES NO. 633

ISSN: 0442-1744

SEISMIC PEFORMANCE EVALUATI N F ORDINARY MOMENT RESITING CONCRETE FRA ES (OMRCF)

By SANG WHAN HAN OH-SUNG KWON LI-HYUNG LEE

and DOUGLAS A. FOUTCH

A Report on a Research Project Sponsored by the advanced STructural RESearch Station (STRESS) of KOrea Science and Engineering Foundation (KOSEF)

DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN URBANA, ILLINOIS NOVEMBER 2002

50272-101

REPORT DOCUMENTATION 11. REPORT NO.

PAGE UILU-ENG-2001-2004 3. Recipient's Accession No.

4. Title and Subtitle 5. Report Date

SEISMIC PEFORMANCE EVALUATION OF ORDINARY MOMENT RESITING CONCRETE FRAMES (OMRCF)

6.

NOVEMBER 2002

7. Author(s) 8. Performing Organization Report No.

Sang Whan Han, Oh-Sung Kwon, Li-Hyung Lee, and D.A. Foutch SRS 633

9. Performing Organization Name and Address

University of Illinois at Urbana-Champaign Department of Civil and Environmental Engineering 205 N. Mathews Avenue Urbana, Illinois 61801-2352

12. Sponsoring Organization Name and Address

Advanced Structural Research Station (STRESS) Hanyang University Seoul 133-791, Korea

15. Supplementary Notes

16 Abstract (limit 200 wores)

10. ProjectlTaskIWork Unit No.

11. Contract(C) or Grant(G) No.

13. Type of Report & Period Covered

14.

The objective of thiS study is to evaluate the seismic performance of Ordinary Moment Resisting Concrete Frames (OMRCF), which are designed only for gravity loads. For this purpose a 3-story building having OMRCF was designed in compliance 'With the minimum design and detail requirements in ACI 318 (1999) for gravity loads (1.4D+1.7L). Most low to medium rise buildings located in low to moderate seismic regions have been designed only for gravity loads. Accordmg to ACI 318, the detail requirements for OMRCF are less stringent than those for either ~ntermediate or Special Moment Resting Concrete Frames (IMRCF, SMRCF). Particularly, the requirements for ~trong column weak beam design need not be applied to OMRCF. Thus, columns can be more vulnerable than beams ~n an O~1RCF dunng an earthquake. It is important to note that structural details are strongly related to the seismic Ibehavior of structurai members. This study focuses on the behavior of columns and structural frames. For investigating O\lRC~ column behavior, columns in the 1st story are considered since these columns resist the largest axial and lateral for-::es dunng an earthquake. Four two-third-scale test speeimens were constructed representing the IUpper part and the il)\\ ef part of an exterior and an interior column of the 1st story. Based on test results this study estimates defom1.:lth.':L ducullty. strength, and energy absorption capacities as well as plastic hinge length. Three-story frame specimen 0: I .~. <~le was also made for the experiment. For evaluating the seismic performance of this frame, Capacity Spe~trum \ k:tLxl (CSM) is adopted. Capacity curve is obtained from experimental test results, and demand curves are con::.tr~jl·',t"J J'ln~ real earthquake ground motions.

Ordmar:- \L)~llC;l~ Kc-:'tmg Concrete Frame (OMRCF), Details, Gravity Loads, Seismic Performance, Deformation, Ducti lit;., L ;Ie~ .l~' -\ :1" Irptlon Capacity, Plastic Hinge

C. COSATI Field:Group

18. Availability Statement 19. Security'Class (This Report)

UNCLASSIFIED Release UnlimIted 21. Security Class (This Page)

UNCLASSIFIED

(See ANSI-Z39.18)

20. No. of Pages

120

22. Price

OPTIONAL FORM 272 (4-77) Department of Commerce

iii

ACKNOWLEDGEMENTS

This report is based on the results of cooperative research work between Prof. Han

and Prof. Foutch. Financial support from the advanced STructural RESearch Station

(STRESS) of KOSEF is gratefully acknowledged.

IV

To our families

v

T ABLE OF CONTENTS

PART I SEISMIC BEHAVIOR OF OMRCF COLUMNS

CHAPTERl

INTRODUCTION ................................................................................................................... 2

1.1 General remarks ........................................................................................................... 2

1.2 Code requirements for moment frames ....................................................................... 4

CHAPTER 2

DETERMINATION OF DUCTILITY FACTOR CONSIDERING DIFFERENT

HYSTERETIC MODELS ....................................................................................................... 8

2.1 Design. of building frame ............................................................................ : ................ 8

2.2 Material test .................................................................................................................. 9

2.3 Column specimens ....................................................................................................... 9

2.4 Experiments and measurements ................................................................................ 10

2.5 Comparison of the experimental plans ...................................................................... 11

CHAPTER 3

TEST RESULTS AND EVALUATION .............................................................................. 21

3.1 Observations ............................................................................................................... 21

3 .2 Hysteretic performance .............................................................................................. 22

3.3 Maximum strength ..................................................................................................... 23

3.4 Deformation and ductility capacity ........................................................................... 23

3.5 Plastic binge ............................................................................................................... 25

3.6 Evaluation of energy dissipation ............................................................................... 27

Vll

CHAPTERS

SEISMIC PERFORMANCE EVALUATION OF OMRCF USING THE CAPACITY

SPECTRUM METHOD ........................................................................................................ 78

8.1 Introductory remarks .................................................... '" ................................. '" ....... 78

8.2 Capacity spectrum method .......................................... '" ........................................... 80

8.3 Seismic performance evaluation of OI\.1RCF ............................................................ 84

CHAPTER 9 ......................................................................................................................... 97

CONCLUSION ...................................................................................................................... 97

REFERENCES ............................................................................................................................. 99

APPENDIX ................................................................................................................................. 101

A.I Introduction ............................................................................................................. 101

A.2 Comparisons of RJC moment frames in ACI 318-99 ............................................ 102

A.3 Beam desigIl ............................................................................................................ 104

A.4 Colunm desigIl .............................................................. ,;, ......................................... 107

A.S Joint design .............................................................................................................. 108

A.6 Some requirements to improve the toughness of ordinary moment frames in ACI

318-99 ..................................................................................................................... 110

A.7 Joint detailing of ordinary moment frames ............................................................ 112

Vlll

LIST OF TABLES

Table 1.1 Types of moment frames according to seismic rick levels (ACI 318-99) ............. 5

Table 2.1 Concrete properties of the specimens ................................. '" ................................ 13

Table 2.2 Reinforcing steel properties ................................................................................... 13

Table 2.3 Characteristics of the column specimens of STUDy-H ....................................... 13

Table 2.4 Characteristics of the column Specimens of STUDY-R ...................................... 14

Table 2.5 Characteristics of the column Specimens of STUDY-M ..................................... 14

Table 2.6 Comparison of the specimens of STUDIES-H, R, and M .................................... 15

Table 3.1 Test result of specimens ......................................................................................... 28

Table 3.2 Equivalent plastic hinge length at each drift level ... ::' ........................................... 30

Table 6.1 Design loads ........................................................................................................... 54

Table 6.2 Design moments for slab ...................................................................................... 54

Table 6.3 Beam analysis and design results ......................................................................... 55

Table 6.4 Column analysis and design results ..................................................................... 55

Table b.~ \11\ design formula for the concrete model. ........................................................ 56

Tahle 6.b Concrete properties of the model .......................................................................... 56

Table () - Remforcing steel properties of the model ............................................................. 56

Tabk ~ 1 \1oJaJ participation factor and modal mass factor ............................................... 87

Tahk " .: Cakuiation of capacity curve ................................................................................ 87

Tahk I.. 1 f:' .uthyuake catalogue ............................................................................................. 88 .. '

Tahk '-l P::rh)nnance point of three-story OMRCF (DIH, %) .......................................... 89

Table ~" \b\lmUffi story drift at performance points ........................................................ 89

ix

LIST OF FIGURES

Figure 1.1 Three types of moment frames ............................................................................... 6

Figure 1.2 Minimum reinforcement details for columns (Notes on ACI 318-99, Seismic

design of buildings and bridges) .......................................................................... 7

Figure 2.1 Plan view and elevation of the prototype frame building ................................... 16

Figure 2.2 Identification of the column specimens ............................................................... 17

Figure 2.3 Details of 2/3 scale column specimens ................................................................ 18

Figure 2.4 Details for the measurement of defonnation ....................................................... 19

Figure 2.5 Loading history ..................................................................................................... 20

Figure 3.1 Final failure of specimens .................................................................................... 31

Figure 3.2 Measured hysterisis behavior of four specimens ................................................. 32

Figure 3.3 Interaction diagram ............................................................................................... 33

Figure 3.4 Maximum displacement Capacity ............................ , ........................................... 34 .,'

Figure 3.5 Deformation capacity of specimens ..................................................................... 35

Figure 3.6 Displacement ductility capacity of specimens ..................................................... 36

Figure 3.7 Curvature distribution along column at ultimate moment .................................. 37

Figure 3.8 Energy dissipation ................................................................................................ 38

Figure 5.1 Longitudinal reinforcement details in beam for Ol\1RCF ................................... 46

Figure 5.2 Longitudinal reinforcement details in column ..................................................... 46

Figure 6.1 Plan and elevation of prototype structure ........................................................... 57

Figure 6.2 Applied ioads for beam and column analysis ..................................................... 57

Figure 6.3 Rebar layout for beams of prototype structure - beams ..................................... 58

Figure 6.4 Rebar layout for columns of prototype structure - columns .............................. 59

Figure 6.5 Experimental model layout .................................................................................. 60 ,,'

Figure 6.6 Details of the column steel reinforcement .......................................................... 61

Figure 6.7 Details of the beam steel reinforcement ............................................................. 62

Figure 6.8 Stress-strain relationship of the concrete ............................................................ 63

Figure 6.9 Stress-strain relationships of the reinforcing steeL ............................................. 63

PART I

SEISMIC BEHAVIOR OF OMRCF COLUMN

2

CHAPTER 1

INTRODUCTION

1.1 General remarks

The performance of a structure during an earthquake depends on energy absorption

and dissipation capacities. A moment frame is the structural system consisting of

columns, beams and beam-column joints, which can resist flexure, shear and axial forces.

A moment frame with suitable details can develop plastic hinges that will absorb energy

during a large earthquake so that the frame may survive even after experiencing large

inelastic deformation.

ACI 318 (1999) classifies concrete moment frames into three types: Ordinary \;1

Moment Resisting Concrete Frame (OMRCF), Intermediate Moment Resisting Concrete

Frame (IMRCF), and Special Moment Resisting Concrete Frame (SMRCF).

In this study, the behavior of columns in OMRCF is investigated. The behavior is

estimated in terms of deformation, ductility, strength, and energy dissipation. The design

and details for OMRCF comply with the requirements of Chapters 1 through 18 in ACI

318 (1999).

According to ACI 318 the requirements for a strong column-weak beam design

(Section 21.4.2.2 in ACI 318-99) need not be applied to OMRCF. Thus, plastic hinges

can develop in the columns rather than in the joining beams during an earthquake. This

leads to a weak story mechanism. Moreover, ACI 318 requires the fewest and least

stringent detailing provisions for members of OMRCF among three types of moment

frames. The following are some examples:

(1) Fewest reinforcement requirements for shear and confinement in columns

(2) Lap splice location at the possible plastic hinge region

4

1.2 Code requirements for moment frames

A moment frame consists of beams and columns that are rigidly connected. The

components of a moment frame should resist both gravity and lateral loads. Lateral

forces are distributed according to flexural rigidity of each component. ACI 318 (1999)

provides detailing requirements according to the type of moment frame and an

earthquake (seismic) risk level. Earthquake risk levels are classified into low, moderate

and high seismicity according to the seismic zone provided in UBC (1997), or the seismic

performance category ofNHERP (1997).

The selection of each frame depends on the seismic risk level. Table 1.1 shows the

selection criteria for each type of moment frame. The .:,differences in each type of

moment frame are shown in Figure 1.1. According to this figure, detail requirements

become more stringent in the order ofOMRCF, IMRCF, SMRCF.

It is worthwhile noting that there are no requirements for strong column-weak

beam for OMRCF and IMRCF. Figure 1.2 shows minimum reinforcement details for a

column in OMRCF, IMRCF and SMRCF. As shown in this figure, OMRCF requires the

fewest reinforcement details. In OMRCF and IMRCF, lap splices exist at the base of

columns, where the potential location of plastic hinge during an earthquake is located.

Lap splices in a column of SMRCF must be located in the middle of a column.

More Stringent Detail Requirement

More Ductility . Capacit:t _____ ~

6

+

-. __ . More Stringent -"-, ,Detail Requirement

I

I

" I1)trong Column-L WeakJLeam ____ .

------_._- - .. __ .. ,-------_._-_.-'-_._---_ .. _----------------_.-

i

" I i

~i~~~~~l .... ·1 I T~U:~:~e Modification ! I Reinforcement

Factor ; I inJOint. . ... __________ L_"_' ._;._~

i i

" Djffe.rentTie

Reinf.orcement Spacirigiri Jhe Splic~Region

Figure 1.1 Three types of moment frames

8

CHAPTER 2

DETERMINATION OF DUCTILITY FACTOR CONSIDERING DIFFERENT HYSTERETIC MODELS

2.1 Design of building frame

A typical three-story office building was designed for either gravity loads or

gravity loads with seismic loads (zone 1 in UBC 1997), however the required section and

reinforcement of columns were the same for both designs. The general layout of the

idealized three-story prototype office building is shown in Figure 1.3. Dimensions of the

building were chosen as close as possible to those used by Reinhorn et al. (1994) for the

purpose of the direct comparison of experimental results. The concrete was assumed to

have the specified compressive strength (f'e) of 23.5 Mpa. Longitudinal reinforcement ,;\

and remforcement for hoops and stirrups were assumed to have the yield strength (fy) of

392.3 \1PJ- Design loads for a typical office building were used, which are 52 MPafor

dead loaj and 24 l\IPa for live load. The following load combinations were considered in

desl~

l j ~D-17L

l I, -~( 14D-1.7L+1.87E)

(14D-i.43E

(2.1)

(2.2)

(2.3)

\\-hen the building was designed only for gravity loads, the 1st load combination

(Eq _ (~ 1 I I \\.is used. As mentioned earlier, the column section and amount of reinforcing

bars to r p- J \ It:, loads are the same as those for gravity and seismic loads.

9

2.2 Material test

A design mix was detennined based on concrete trial mixes from various recipes

for attaining the 28day target strength (f'e) of 23.5 Mpa. The maximum size of a

aggregate for two third scale model specimens was 25 mm. Cylinder tests were

performed and the test results are given in Table 2.1. Each concrete cylinder is 20 cm tall

and has a diameter of 10cm.

The longitudinal and transverse hoop reinforcement rebars in column specimens "I

(2/3 scale) are deformed rebar D13 (diameter of 13mm) and D6 (diameter of 6mm),

respectively. The design yield strength (1;,) of these bars is 392.3 MPa. The results of

coupon tests are given in Table 2.2.

2.3 Column specimens

In this study, the 1 st story columns are considered since these columns resist the

largest axial and lateral forces during an earthquake. The exterior column in the 1 st story

of the original prototype frame was designed for an axial force of 644.3 kN and a bending ,,'

moment of 31.4 kN-m. The interior column was designed for an axial load of 1234.7 kN

and a bending moment of 47.1 kN-m. In the prototype frame the column has a 33cm

square section containing four longitudinal reinforcement rebars (D19, 1;, =392.3 MPa).

The column reinforcement ratio (p) is 1.01 %, which slightly exceeds the minimum

longitudinal reinforcing steel of 1.0% (Section 10.9.1 inACI 318-99).

The maximum shear force in the 1st story columns induced by factored gravity

loads is 31.4 kN. According to the equation in Section 11.3.1.2 of the ACI 318, the

concrete shear strength of 1st story columns (~) is calculated as 73.5 kN. Minimum tie

reinforcement (D10) was placed with spacing of 300mm throughout the column in the

11

direction of the lateral loading. The relationship between axial and lateral forces was

obtained using an elastic analysis of a frame, which is P (axial force) = 1.83V (lateral

force) + 17.1 tonf. Axial loads that varied using this relationship were applied to exterior

column specimens throughout the test.

Three pairs of linear transducers were placed at the column faces to capture column .1

curvatures. Four linear transducers were installed to measure the lateral displacements of

the specimen and the slip between the concrete block and the base of the column

specimen (LVDT4) shown in Figure 2.4.

2.5 Comparison of the experimental plans

The results of this experimental study (called STUDY-H hereafter) are compared

with those of Reinhom et al. (1994) and Moehle et al. (1996), which are called STUDY­

Rand STUDY-M from this point on.

STUDY-H and STUDY-R consider the lower and the '~pper part of an exterior and

an interior column (4 test specimens). In these studies constant axial loads were applied

to the interior colurrm specimens, whereas varying axial loads were applied to the exterior

column specimens. One-third scale test specimens were used in STUDY-R, and two­

third scale specimens were used in STUDY-H. The experimental variables of these

studies are the types of axial force (constant and varying, and low and high), and the

existence of lap splices (with or without lap splice). Table 2.4 describes the information

about the specimens in STUDY-R.

In STUDY-M, eight full-scale specimens were made. The experimental variables

of this study are reinforcement ratio, existence of lap splice, size of axial load, and

existence of hoop reinforcement. Constant axial loads wen~:1 applied until the end of the

test for all specimens. Table 2.5 describes the information about the specimens in

STUDY-M.

13

Table 2.1 Concrete properties of the specimens

Design. 28day Strain ,,'

Y ong Modulus Strength Strength at Ultimate Strength

(Mpa) (Mpa) (Mpa) (ceo)

23.5 246 0.003 23,437.9

Table 2.2 Reinforcing steel properties

Yielding Yielding Ultimate Young

Strength Strain Strength Modulus Ductility

Bar .. '

(Mpa) (x10-6 ) (Mpa) (Mpa)

(% )

D6 374 2206 598.4 176,519.7 14.36

D13 396.8 2035 594 194,956.2 15.04

Table 2.3 Characteristics of the column specimens of STUDY-H

Classification Location Specimen

Loading Plan Lap

Name splice

Interior Lower OIL Constant Axial Load d

OMRCF Upper OIN (P=0.28 Agf'e ) x

(STUDY-H) Lower OEL Fluctuation Axial Load d Exterior

Upper OEN (P=1.83V+ 17.1 tf) x

15

Table 2.6 Comparison of the specimens ofSTUDY-H, STUDY-R, and STUDY-M

STUDY-H'" STUDY-R'" STUDY-M'"

Tie Spacing ( em ) 30 30 40(30.5)

Lap Splice Spacing ( em ) 30 15 30.5

Lap Splice Length ( em ) 52.5 46 51(63.5)

Distance of the 1 st Tie from the Base ( em ) 15 15.24 10

Longitudinal bar Ratio (% ) 1.01 ,;1 1.0 2.0,3.0

Concrete Compressive Strength (MPa) 24.1 23.4,30 25.6,27.6,

33.1

Yield Strength of Longitudinal Bars (MPa) 396.8 468.8 330.9

Yield Strength of Transverse Bars (MPa) 374 386.1 399.9

Sectional Area of Column (em 2 ) 33x33 31 x31 46x46

Height (em) 300 320 294

* Note that STUDY-H, STUDY-R and STUDY-M denote the study by Han et al. (2001),

Reinhorn et al (1994), and Moehle et al. (1996), respectively.

17

N tI'\

] 'O' l'I'\

J --!:!,...

~..e-- DEN <-- DIN "'" " .. ~ • H.v'l'1

~ ExtB."iar UPPB." Interior UPPB." Column -~ Column '" r fli - 1"N":1")

-N

~ DEL OIL Exterior Lower Interior Lower Columr

W////~ Column ~ ~ ~

366

Figure 2.2 Identification of the column specimens 'O'

19

Figure 2.4 Details for measurement of deformation

21

CHAPTER 3

TEST RESULTS AND EVALUATION

3.1 Observations

Within a ± 1 % drift, the first flexural crack was observed. The lateral forces

causing the first crack were 23.5 kN, 23.5 kN, 22.6 kN and 26.5 kN for specimen OIN

(interior column without lap splice and with constant axial load (upper part)), OEN

(exterior column without lap splice and with varying axial load), specimen OIL (interior

column without lap splice and with constant axial load (lower part)), and specimen OEL

(exterior column with lap splice and with varying axial load), respectively. At ± 3% drift

all specimens experienced concrete spalling at their bottoms.

In the specimen OEL, spalling and cracking are prominent when the lateral load is

applied in the positive direction. In the positive direction of the lateral loading, axial

forces become larger. This phenomenon is most prominent in the connection at the base

of the column (see Figure 8(a)). Many vertical cracks in the region of lap splice were

observed. The degree of damage varies depending on the direction of loading (more

damage occurs during positive direction loading).

A relatively small nUIJ;lber of vertical cracks were observed in OEN, as compared

with the specimen OEL. Horizontal flexural cracks, which were relatively uniformly

distributed, were also observed. According to this observation, the shapes of cracks are

influenced by the existence of lap-splices. It is important to note that lap splices cause

more vertical cracks, more spalling of cover concrete, and more strength degradation to a

specimen. During the final stage of the test, colunm specimens failed due to loss of the

cover concrete above the spice region, buckling of the longitudinal bar and the crushing

of the core concrete. Figure 3.1 shows the column specimen at failure.

23

3.3 Maximum strength

Figure 3.3 shows P-M interaction curves with a maximum strength Mmax obtained

from experimental tests. Table 3.1 presents the ratio of maximum strength M max to

nominal strength M ACI •

According to Table 3.1, all OMRCF column specimeils have a strength larger than

the calculated nominal strength. All nominal strengths in this study are calculated using

the material strength obtained from material tests.

In specimens OEL and OEN (exterior column specimens), with relatively low axial

loads, the ratio of ultimate strength to nominal strength is relatively lower than those of

the specimens OIL and OIN. The strength ratios of the specimens of STUDY -R and

STUDY-M are lower than those of STUDY-H.

Thus, according to STUDY-H, it is shown that columns designed according to

minimum design and detail requirements in the code (ACI 318(1999)) can attain the

nominal design strength. This also holds for columns with lap splices. It is important,

however, to note that all specimens are governed by flexwe rather than shear. Thus, .,1

different conclusions may be obtained for columns governed by shear.

3.4 Deformation and ductility capacity

The deformation capacities of the specimens in these three studies are presented in

Figure 3.4. Specimen OIN (interior column without lap-splice) has a higher deformation

capacity than specimen OIL (with lap splice). Specimen OEL (with lap-splice) has a

sudden strength drop at 3% drift in the negative direction of the loading. This loading

direction makes the axial force lower.

Specimen OEN (exterior column specimen without lap-splice) has the largest

deformation capacity (4.6% (+) and 6.1 % (-)) among the specimens. The exterior column

specimen with lap splices has the least drift capacity (4.25 (+) and 3.53% (-)). It is

25

specimens of STUDY-R are less than 0.6, which means that the specimens were

governed by flexure. Specimens of STUDY-M have a ratio higher than 0.8. Figure 3.5

(a) and (b) show that the drift capacities of columns generally become larger as the

columns are governed by flexure.

Figure 3.6 shows the displacement ductility capacity with respect to the ratio of

Vp / V.4Cl. Displacement-ductility capacities with respect to the ratio of Vp / VACl have a

similar trend to the drift capacity. The flexure governed specimens have larger ductility

capacities than shear governed specimens in general. This is not as apparent, however,

as the case of drift capacity.

For OMRCF specimens and specimens of STUDY-R, the interior column

specimens have a displacement-ductility ratio larger than 4.0, regardless of lap-splice

existence. The exterior column specimens without lap splices have the largest ductility

capacity among all specimens, whereas ductility capacities of exterior column specimens

with lap splices are inferior to specimens which are not larget than 3.0.

In Figure 3.6(b), with the exception of specimens 2CLH19 and 2SLH18, all

specimens have a ductility ratio in the range of 1.4 ~2.4.

3.5 Plastic hinge

For this study the plastic hinge length is calculated using the relationship among

moment, curvature, and deflection, as shown in Figure 3.7. The procedure follows the

procedure presented in Park (1975) and Pauley (1992). The calculated values are also

compared with the plastic hinge length calculated by SIDDY-R. The formulas for

calculating plastic hinge length are shown in Eq. (3.1 )-(3.4). Detail descriptions of these

formulas are given by STUDY-R.

(3.1)

27

3.6 Evaluation of energy dissipation

The amount of dissipated energy at each loading cycle is shown in Figure 3.8 (a).

According to this figure of interior column specimens, OIL and OIN dissipate the similar

amounts of energy at each loading cycle. Exterior column specimen OEL (with lap

splices), however, dissipates less energy than specimen OEN (without lap splices). Lap

splices, therefore, affect the amount of dissipated energy at each cycle.

Figure 3.8 (b) shows the dissipated cumulative energy of each specimen at each

cycle of the loading. All four specimen$ dissipated almost equal amounts of energy up to

a 2% drift (6th cycle). At a 3% drift, specimen OEL dissipated only 70% of the \;1

cumulative energy of other specimens. It is evident, therefore, that a lap splice has

adverse effects on energy dissipation capacities. This occurs particularly on columns with

a relatively low axial load, such as exterior columns.

29

2CMH18 315.8 30.48 l.7 1.03 4113 1.24 271.6 280.5

3CMH18 338.1 30.48 1.5 1.03 5333 0.91 280.5 360.0

0.35

3CMH12 355.9 45.72 2.4 1.55 5333 1.06 351.1 360.0

3SMD12 378.1 45.72 2.0 1.55 519.8 1.14 3423 351.1

(1) = axial load ratio (2) = maximum shear force (kN) (3) = maximum displacement (mm)

(4) = displacement ductility (5) = drift angle (%)

(6) = the moment capacity calculated using ACI 318-99 procedures (kN-m)

(7) = the ratio of the maximum moment resistance ofthe specimen to M ACI

(8) = the nominal shear strength according to ACI 318-99 (kN)

(9) = the shear or corresponding to flexural yielding with flexural strength M ACI or 2M ACI / I , where I = the column

clear height (kN)

(l 0) = the ratio of Vp to VACI

*Note that STUDY-H, STUDY-R, and STUDY-M denote the study by Han et al. (2001), Reinhorn et aI. (1994), and

Moehle et al. (1996), respectively.

1.03

1.28

1.02

1.03

31

(a) OIL (b) GIN

(c) OEL (d)OEN

Figure 3.1 Final Failure of Specimens

1400

1200

1000

800 z :::; 600 "0 co 0 400 -I

co 200 'x -<

0

-200

-400 -60

1400

1200

1000

800 :2: .,..

600

- 400

-,. 700 <

0

700

1100

f,O

NOMINAL STRENGTH ~

-40 -20

NOMINAL STRENGTH

~

-40 -20

33

with lap splice

o 20 40

Moment (kN-m)

without lap splice

o 40

Moment (kN-m)

Figure 3.3 Interaction Diagram

60

60

8.0%

~ e..., i:: 6.0%

'C Q

~ 'u u c.. 4.0% CI:I U

c:: 0

:::l CI:I

S r... r£ CI.l Q

2.0%

0.0% n 1

8.0%

0.0% 0.8

l1li OIL

• OEL

0 SPl

0 SP3

35

• OIN

.4. OEN

<> SP2

~ ~ (") 6. SP4

~ 0

• o SP3(-) OEL(-)

R2 0.3 0.4 0.5 0.6

VpNACI

(a) STUDY-H and R

.3CLH18 o2CLH18

3SLH18 !.:,2SLH18

.2CMH18 o3CMH18

11113CMD12 o3SMD12

(>

,--aJ

0 /\

,~

1.2 1.4 1.6

VpNACI

(b) STUDY-M

Figure 3.5 Deformation capacity of specimens

L

V IE h ")1

~v M

(a) Column (b) Moments

37

1<

IE

fe(x)=MxIEde

)IE +y )1

)1

(c) Curvatw-e at Max. Re~nse (d) Defleaions

Figure 3.7 Curvature distribution along column at ultimate moment

39

CHAPTER 4

CONCLUSION

This study investigates the behavior of columns in Ordinary Moment Resisting

Concrete Frames (OMRCF). A frame was designed according to the minimum design

and detail requirements in ACI 318(1999). Four column specimens were made and tested.

Following are the conclusions obtained from this experimental study:

1. The strength of all OMRCF column specimens exceeded the nominal strength calculated

using code formula (ACI 318). Considering the results of these four specimens, it was

determined that the minimum reinforcement detail requirements, including lap splice

length and transverse reinforcement, had a satisfactory amount of strength.

2. All four OMRCF column specimens had drift capacities larger than 3.0%. The

specimens without lap splices provide larger drift capacities than those with lap splices.

The exterior column specimen without lap splices has the largest drift capacity among

the four specimens (4.6% (+) and 6.1% (-)), whereas the exterior column specimen with

lap splices has the least drift capacity (4.25% (+) and 3.53% (-)). To improve the

behavior of OMRCF more stringent details are needed, particularly for exterior columns.

3. A similar observation for drift capacities was made in STUnY-R. The exterior column

specimen with lap splices had a drift capacity of 2.9%. In STUDY-M, the drift

capacities of the specimens were 1 ~2.6%. The deformation capacities of the specimens

in STUDY-M are smaller than those in STUDY-H and STUDY-R. According to the

comparison, the deformation capacity becomes lower as a column is more likely to be

governed by shear. It is also shown that the drift capacity of a column governed by shear

is not as strongly dependent on the existence of lap splice as a column governed by

flexure.

41

PART II

SEISMIC BEBA VIORS OF ORDINARY MOMENT RESISTING CONCRETE FRAMES

42

CHAPTERS

INTRODUCTION

5.1 General remarks

During recent earthquakes such as Northridge Earthquake (U.S., 1994), Kobe

Earthquake (Japan, 1995), and Gi-Gi Earthquake (Taiwan, 1999), many concrete frame

structures experienced substantial damage. Low to mid-rise old concrete buildings were

particularly vulnerable to those earthquakes. The seismic performances of concrete

buildings during such earthquakes generally depend on details of members, building

shape, applied design provisions, etc. Insufficient details can cause unexpected structural

failure during a large earthquake event.

Most low rise buildings in low to moderate seismic zones, and old buildings in high

seismic zones, have been designed primarily for gravity loads (Bracci, 1992). Since such

buildings have less stringent details than those required in high seismic zones (e.g. strong

column weak beam requirements need not be considered), the buildings may behave in a

brittle manner during a large earthquake event. In these cases story failure mechanisms

can develop.

Current design provisions such as ACI 318 (1999) define three types of moment

frames: ordinary moment resisting concrete frames (OMRCF) , intermediate moment

resisting concrete frames (IMRCF) , and special moment resisting concrete frames

(Sl\1RCF). OMRCF is the most popular type of moment frame in mild seismic zones.

Details ofO:t\.1RCF are different from those ofIl\1RCF and SMRCF as follows:

1) Strong column - weak beam requirements need not be satisfied, which causes story

failure mechanisms in OMRCF during a large earthquake event.

44

5.2 Code requirements for OMRCF frame

In this section, detail requirements for beams and columns are described briefly.

Details for OMRCF, IMRCF, and SMRCF are compared in the Appendix 1.

5.2.1 Detail Requirement for OMRCF Beams

The following are the beam details ofOMRCF according to ACI 318:

CD Longitudinal Reinforcement

\\ nere, I, and fc' are in MFa.

At least 114 of the positive moment reinforcement in continuous members shall

extend into the support. In beams, such reinforcement shall extend into the

support at least 6".

\:1

\'.llcn a flexural member is part of a primary lateral load resisting system,

rO:;ltl\ c moment reinforcement shall be anchored to develop the specified yield

strcn;:1h f. in tension at the face of support

·\t k3St 1 '3 the tension reinforcement provided for negative moment at a

"Ur~);t shall have an embedment length beyond the point of inflection not less

th~r: J 12d". 1!16x(clear span)

C0 Deslh-Tfl She3f Strength

. - jf[ For members subject to shear and flexure only, Vc J -6-bwd

46

-rl-~ < ' 'rV-Vs - 4 fc bwd, then If Vs ;;::: 4 fc bwd, -s ~ d/2 or 24" then s ~ d/4 or 12"

~ Avfv/SObw ~ Avfv/SObw --1 ~

fl .. '

L.

s/2 Vu~ O.S~Vc s/2 s/2 l

-iii ~ r--- ~ ---1 ~ ..... r.-

-Lt],1- -Yr Figure 5.1 Longitudinal reinforcement details in beam for OMRCF

s :>; 16db

:>;hmin I ~ 48d,

6 in. max.

Lateral support to column bar provided by enclosure tie having a maximum bend of 135°.

IT] 6 in. max.

- ,i

Figure 5.2 Longitudinal Reinforcement Details in Column

47

CHAPTER 6

EXPERIMENTAL PLAN

6.1 Design of ordinary moment resisting concrete frames

In this study a three-story office building is considereci: The building is assumed to

have 3 and 4 bays in E-W and N-S direction, respectively. The height of a story is 3.5m,

and the width of each bay is 5.5m. Total building height is 10.5m. Figure 6.1 shows the

dimensions of the building, and Table 6.1 shows design loads used in building design.

The compressive strength of concrete (f c) and yield strength of reinforcement (fy) are

assumed to be 23.54 MPa (240 kgf/cm2) and 392.4 MPa (4000 kgf/cm2), respectively.

Structural analysis for member design was carried out using the commercial software

SAP 2000 (2000). Only gravity loads (1.4D+ 1. 7L) were considered for design in this

study.

The slab was designed using the direct design method according to the section 13.6

of ACI 318 (1999). The calculated design moment~\ are given in Table 6.2.

Reinforcement in slabs satisfy the reinforcement required for temperature and shrinkage

(p=0.002) and for design moments. Rebar D10 (diameter of 10 rom) is spaced at 15 cm

for both positive and negative moments.

Cross sections of columns and beams were assumed to be 33x33 cm and 25x50 cm,

respectively. For beam design, dead and live loads from the tributary area of slabs were

converted into triangular loads acting on a beam, as shown in the Figure 6.2. Beam and

column details follow the design procedure for the ordinary moment frame in ACI 318

(1999). The analysis and design results for beams and columns in 1st story are given in

Table 6.3 and 6.4. The design result of beams in the prototype three-story frame is given

49

diameter of 10cm and height of 20cm were cured near the model specimen in the

laboratory. Table 6.6 shows the concrete properties of the model specimen.

Representative stress-strain relationship obtained from the cylinder test is shown in

Figure 6.8.

(2) Reinforcing steel properties

The reinforcing bars used in the prototype building are DIO (lOmm diameter) and

D19 (19mm diameter), with yield strengths (fy) of 294.2 MPa (3,000 kgf/cm2) and 392.3

MPa (4,000kgf/cm2), and cross-sectional rebar areas (Ab) of 0.713 and 2.865cm2,

respectively. The similitude of yield force (AbXfy) for the model reinforcement is

accomplished with a scale factor of 9 (see Table 6.7).

In order to satisfy similitude law for both yield and ultimate strength of rebar, D19

which was used for longitudinal reinforcement in the prototype building, was replaced by

D6 with cross-sectional areas of 0.316cm2 and diameter of 6.35mm in the 1/3-scale

model specimen. A ~3.3mm wire with a cross-sectional area of 0.086cm2 and yield

strength of 345.2MPa (3520kgf/cm2) was used in the modePspecimen for replacing DIO

bars for lateral reinforcement in the prototype frame. Reinforcement for slabs in the

model specimen is a 5cm square mesh composed of ~3 .2mm wire with yield strength of

460.9MPa (4700kgf/cm2). The representative stress-strain relationships of reinforcement

used in the model are shown in Figure 6.9.

(3) Mass similitude

For proper modeling of gravity loads, mass similitude must be satisfied. Additional

mass must be added to the model to compensate for the difference in required and

provided gravity loads. Mass, m, is defined as the product of the material density, p, and

material volume, V, as follows:

m=pV

51

Ceiling: = 26.67 kN/floor (0.44 kN/m2)

Electric: = 14.81 kN/floor (0.245 kN/m2)

Partitions: = 59.2 kN/floor(0.98 kN/m2)

Total: Wp = 413.9 kN/floor

Therefore the required weight of the test model specimen per floor (Wm) is 46.0 kN/floor

(Wp/9). The self-weight of the model specimen per floor is shown below:

Beams: = 2.16 kN/floor (0.21 kN/m)

Columns: = 1.27 kN/floor (0.28 kN/m)

Slab: = 7.94 kN/floor (1.18 kN/m2)

Total: Wp = 11.38 kN/floor

The additional weight required per floor is, therefore, !l W m =.:.34.62 kN/floor. To make up

for the weight difference due to mass similitude, concrete blocks were made and added to

the specimen. Two different sizes of concrete block were used, which were

OAmxO.3mx1.2m (3.39 kN), and 0.4mxO.3mxO.6m (1.70 kN). These blocks were

mounted at the one sixth point of the span length of the beam to simulate the shear forces

and moments at ends of the beam induced by gravity loads. Figure 6.10 shows concrete

block arrangements on the slabs. The total provided model weight, W m, is 41.87 kN per

floor. The total weight of the model was 376.87 kN, which was 9% less than required

weight, 413.94 kN.

53

instrumented column sections were located at O.5he (he is the column depth) from the face

of the beam. The analog output readings from the instrumentation were r'ecorded

digitally, using a data logger TDS601-A System. Figure 6.14 shows the setup for

potentiometers on the beams and columns.

55

Table 6.3 Beam analysis and design results

Ext. Span Ext. Span Ext. Span Int. Span Int. Span

Left end Mid. Right end Left end Mid.

Re-bar, Top. (em2) 5.73 0.00 8.595 8.595 0.00

Re _bar, Bot. (em2) 5.73 5.73 5.73 5.73 5.73

Neg. I Mu (tf-em) 664.27 0.00 1096.27 1036.83 0.00

I cP Mn (tf-em) 850.92 0.00 1194.01 1194.01 0.00 I I

i Mulcp Mn (tf-em) 0.7807 0.9181 0.8684

Pos. I Mu (tf-em) 0.00 787.73 0.00 0.00 581.16

cP Mn (tf-em) 850.92 850.92 869.38 869.38 850.92

I i\1u/cp M...n (tf-em) 0.00 0.8670 0.00 0.00 0.6830 i I

Table 6.4 Column analysis and design result

Exterior Column Interior Column

Re- haT on one face. (cm2) 5.73 5.73

\1u nfcm) 554.7 470.5 --'--

4 \in ltfcm) 815.4 529.8 >---------.-

\ 1 L1 I;' \ 1n Hfcm) 0.680 0.888 --- - ~~ -

f~u (tt'cm) 63.1 125.7 ----- ~--.--.~-. Pn (tfcm) 92.0 140.4 --_._---

Pu l~ Pn (tfcm) 0.685 0.895

i ..

SLAB(lScm)

I i

-------_.--....

550 550 550

(a) Elevation

Material

Concrete: f c = 240 kg!cm2

Rebar: fy= 4000 kg! cm2

' ...... ,

57

I

S;I "'i

I

I

TEST SPECiMEN

33 x 33cm

01 "'I "'1.1 ALL BEAMS

25x 50cm

Oi

;qi !

(b) Plan

Element sections

Columns: 33cm x 33cm

Beams: 25cm x 50cm

" ======#=== ===# = =====

"

" ==== == #== = = ==# ======

Figure 6.1 Plan and elevation of prototype structure

W=16.3 tonf

Figure 6.2 Applied loads for beam and column analysis

o '" -'"

3-DlO@lSOrrnn

8-D1O @300mm

-3-D10 @lSOrrnn

3-D1O @lSOrrnn I

8-D10 @300mm

3-D1O@lSOrrnn-'-

3-D 10 @lSOrrnn

Y

9-DlO@300mm

4-DlO@lSOrrnn

59

16cm t

l00cm

16cm f

lOOcm

~ 16cm t

Y, +y -

lOOcm

25cm f - I--

rr====114-DI9 lYDIO

33cm

\Ii

5 I 3-D1O@lSOrnm _1_

8-D10 @300nrn

-1- 3-D1O@15Ornm --;-

r 3-D10 @lSOrnm

8-D 10 @300rnm

3-D10@lSOmm

i 3-D10@lSOmm

9-DIO @300rnm

_I 4-D1O@lSOmm

1

Figure 6.4 Rebar layout for columns of prototype structure - Columns

3-D3@S em

8-D3@1 Oem

em 3-D3@S

3-D3@S em

8-D3@10 em

em

I

-I-

I

-I

-

i

--3-D3@S

3-D3@S cm_

y, 9-D3@1O em

I

-4-D3@S cm

I

61

i 1 l' .....,-_i_ 3-D3 @Scm

l- 8-D3@lOcm

_,_ t _i_ 3-D3 @Scm

l- i 16cm f l' 3-D3 @Scm

80em 8-D3@lOcm

\;1

~ f

lOcm 16cm

-

I-

1 i

-i-3-D3 @Scm

-1-

_1_ 3-D3@Scm i

+Y Yf ,Y

80em 9-D3@iOem

li8.Sem

- - t ISem

25em t - --f

-[-4-D3@5~

[

~4-D6 02cm Ilem ~D3 9cm

9cm llcm

Figure 6.6 Details of the column steel reinforcement

400

~ 300 Co)

4:::; b.O

6200 C/l C/l r.il

~100 C/l

o 0.00%

63

0.10% 0.20% 0.30% 0.40%

S1RAIN

Figure 6.8 Stress-Strain Relationship of the Concrete

5000 ~----------------------r-----~

c:::i' 4000 E Co)

~ 3000 ~ '-" C/J ~ 2000 e::: t-C/J 1000 -D6

--- q>3mm

o ~------~------~--------~----~ 0.00% 0.50% 1.00% 1.50% 2.00%

STRAlN

Figure 6.9 Stress-Strain Relationships of the Reinforcing Steel

65

Figure 6.12 Test setup of 113 scale model specimen

67

Dl. 02. D3. D4 tN

i D4 --@ I

i Iii

1)1 I I D3 .. + .. -Q I

1'1 ! Iii i

··f·· --@ I D2

I

I!I I Iii i

I 'Ii

Dl

-@ e~

J

~ VJ

(a) Plan (b) Section 1-1

( C) Section B-B (b) Section D-D

Figure 6.14 Instrumentation Locations

68

CHAPTER 7

TEST RESULTS AND OBSERVATIONS

7.1 Cracks and failure mode

This section presents general observations from the experimental test. Photographs

taken after testing are presented in Figure 7.1.

The first crack was observed at a roof drift ratio of 0.5 % (first cycle). Cracks were

found at both ends of all columns and beams in the first and second story. Third story

cracks were observed at lower ends of all columns and interi~r beam-ends.

Shear cracks were observed at the exterior joint of the first floor at a roof drift ratio

of 2.5%. This occurred at the location where the transverse beam met the longitudinal

beam. At a roof drift ratio of 3.0%, cracks at the upper ends of first story columns were

wider, while the slight concrete crushing was observed at the lower ends of columns in

the same story. The test was terminated at the roof drift ratio of 5.5%, where lateral

strength deteriorated to 67 % of the maximllill strength. After testing, the columns in the

first and second story were severely damaged. At this displacement level, loss of cover

concrete and reinforcement exposing at the column ends in the first-story was observed

(see Figure 7.1). Figure 7.2 illustrates the cracking patterns of the model observed at the

end of the test.

70

columns behaved almost in elastic range. In the negative loading direction damage is

distributed among beams and columns.

For the interior joint hysteretic curves of beams and columns are symmetric.

Columns behaved in the elastic range whereas beams almost remained in the elastic range.

This phenomenon can be predicted by calculating the strength (moment capacities)

ratio between the beams and columns at a joint. At the interior joint, the summation of

nominal moment capacities of the columns is 2x2.363 kN'm = 4.726 kN·m, while the

summation of those of beams is 2x3.413 kN·m=6.826 kN'm (the slab is disregarded and the \~

positive moment capacity is only considered for simplicity). The ratio of the moment

capacities of beams to columns is 1.44, which means the columns are weaker than beams

(strong beam-weak column). Therefore when a large earthquake occurs, columns are more

vulnerable than beams at interior joints. At the exterior joint, however, the ratio is 0.722

(3.413/4.726), which is treated as a strong column - weak beam.

7.3 Maximum base shear and yield drift

The maximum base shear force from the quasi-static test was 0.157 W where W is ,;\

the total weight of the model. This shear force is attained at the roof drift ratio of 0.015

(see Figure 7.5).

The design base shear for similar structural layout in Seismic Zone 2A, can be

calculated as the following according to UBC (1997):

v = CJ W = (0.15)·(1.0) = 0.10W RT (3.5)· (0.426)

where, Cv is the seismic coefficient. For soil type SB and seismic zone 2A, Cv is 0.15.

I is the seismic importance factor. For standard occupancy structure, I is 1.00. R is the

72

fIrst story, and 40% was dissipated in the second story. According to Figure 7.7 (b), most

of the inelastic deforrnations occurred in the first and second stories, while the third story

behaved mainly in the elastic region.

74

11 IR

17;;. t::::, m ~ If.'I E 10 ri IN f:

!filii ....

I I

• and m denote significant and moderate damage, respectively. ,;1

Figure 7.2 Crack Patterns in the Model

5 ----.---.-----.-

4

3

2

~

C3 0 Q.)

.!:: UJ -1

Q.) (f)

-2 co OJ

-3

-4

-5 , .

~.--.--- .. ----I------·-··~-~I>-l-------1--....:

-0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08

Roof Drift (L':./H)

Figure 7.3 Base Shear Force-Roof Drift Responses

0.18

~ 0.15

---o ~

0.12

a: co 0.09 Q)

..c. Cf)

Q) 0.06 (f)

co co

0.03

0.00 o

76

Hu

I •••••• r, ••• »;>'-+---:--+-~

--.tiP'-___

I ., ............. "'He' = 0.75 Hu ------------1

I I

I

~u ~rrax I .,1

0.01 0.02 0.03 0.04 0.05

Roof Drift (t6/H)

Figure 7.5 Yield drift and maximum base shear

~~~ 1· "=:,,c-='r·;-·-,;--'''':·~;:'::· 7.~~~~' fId:-7~~::::-'::' -~-.-c;·- """,::":-'::'- rn;1::: .--

,,; .,;.u~; .• '- V!L"2::-:::' •• _ •. ,._ ... ,~~.~ ..... "~"::-~7"", . ..... •.••. - '~~' ..••.• ~.::....:.::.1!IilI ._ \11 .,

.~... •. , "--

Figure 7.6 Base shear force-curvature curve

78

CHAPTERS

SEISMIC PERFORMANCE EVALUATION OF OMRCF USING CAPACITY SPECTRUM METHOD

S.l Introductory remarks "I

In low and moderate seismic zones most buildings, particularly old buildings, have

been designed only for gravity loads. Details of those buildings are inferior to those used

for buildings in strong seismic zones. These details are close to the details of Ordinary

Concrete Moment Frames in current design code provisions such as ACI 318 (1999). In

recent large earthquakes, such buildings have experienced serious damage and collapse.

This study attempts to evaluate the seismic performance of low-rise concrete

moment frames, which are designed for gravity loads and detailed in compliance to the

detail requirements for OMRCF in ACI 318 (1999). For this purpose, the three-story

OMRCF structure was designed in accordance with the designing and detailing

requirements specified in ACI 318 (1999). The structure was assumed to be located in

SB soil type in the seismic region of 1, 2A, 2B, 3, and 4 as classified in the Uniform

Building Code 1997 (UBC 1997).

There are several methods to evaluate the seismic performance of a structure.

Currently~ the most popular methods are the secant method (City of Los Angeles,

Division 95 (COLA 95)), the capacity spectrum method (Freeman 1998, ATC-40 1996,

Chopra 1999, Fajfar 1999), the displacement coefficient method (FEMA-273 (ATC

1996a)), etc. Such methods are generally simple, since they do not require nonlinear

dynamic history analysis for calculating seismic demand. In this study, the capacity

spectrum method is adopted.

80

8.2 Capacity spectrum method

This section presents the proc.edures of CSM suggested in ATe 40 (1996) and

introduces an improved CSM suggested by Chopra (1999).

CSM represents the seismic demand and structural capacity as spectral acceleration

(Sa) and spectral displacement (Sd). This method was fIrst suggested by Mahaney and

Freeman (1993). The CSM is applicable to a wide range of evaluations from new

building designs to seismic evaluation of existing buildings. This study evaluates the

seismic performance of OMRCF using CSM. The graphical procedure of CSM is given

in Figure S.l.

8.2.1 Construction of bilinear representation of capacity s:pectrum

A bilinear representation of the capacity spectrum is needed to estimate the

effective damping (ATC 40 1997) or the post yield stiffness and ductility of the

equi\'alent smgle degree of freedom (SDOF) system (Chopra 1999) as shown in Figure

8.2. Construction of the bilinear representation requires defmition of the point api, dpi.

This r{lm: I~ the trial performance point at which the development of a reduced demand

respon\l' ~pedrum occurs. If the reduced response spectrum is found to intersect the

cap:.l.:It\ "r':..'ctrum at the estimated api, dpi point, then that point is the performance point.

"Y l\ C'\ ln~truct the bilinear representation, draw one line up from the origin at the

mlllJl q!ltnl':'~ of the building using element stiffness. Draw a second line back from the

tnal rt."rlu;Truncc point, api, dpi. Slope the second line such that when it intersects the first

line. at pl..llnt J .. d: .. the area designated AI in the figure is approximately equal to the area

designated A= The intent of setting area Al equal to area A2 is to have equal area under

the capacity spectrum and its bilinear representation, that is, to have equal energy

associated v·;ith each curve.

82

Thus, fJe(j becomes

The idealized hysteresis loop shown in Figure 8.3 is a reasonable approximation for

a ductily detailed building subjected to a ground motion of relatively short duration. The

reinforced concrete buildings, however, are not typically ductile structures. For such

buildings, the above equivalent viscous damping yields results that overestimate the

realistic levels of damping. The ATC-40 document suggested effective viscous damping

( fJef!) using a damping coefficient factor, K, to enable the simulation of imperfect ,;\

hysteresis loops.

(2) Demand reduction using constant ductility (Chopra 1999)

Seismic demand in ATC 40 is represented by a demand spectrum, which is reduced

using effective damping coefficient, fJef!' to consider the inelastic behavior of structures.

In various codes, the inelastic deformation capacity of a structure is usually considered

using displacement ductility f.1. It is therefore necessary to evaluate the validity of

seismic demand reduction using either effective damping coefficient or displacement

ductility. Chopra (1999) examined the procedures suggested in ATC 40 using the

effective damping coefficient to determine that the procedures have the following flaws:

The procedure A of ATC-40 did not converge for some of the systems.

The peak deformation of inelastic systems, determined by A TC-40 procedures, when

compared against results of nonlinear response history analysis for several ground

motions were shown to be inaccurate.

The damping modification factor, K , in ATC-40 procedures improves the deformation

estimate only marginally.

84

8.3 Seismic performance evaluation of OMRCF

8.3.1 Capacity spectrum

To evaluate the seismic demand of a given stru.9ture, the structure's load­

deformation relationship and structural capacity should be defined. The structural

capacity can be calculated using simplified nonlinear static analysis. Pushover analysis

may be done for simple two-dimensional structures using nonlinear analysis software

such as DRAIN 2D (1993) and IDARC (1994). Alternatively, the capacity can be

measured from the experiment for a more realistic and accurate evaluation. In this study,

the capacity of a three-story OMRCF structure was measured from a quasi-static cyclic

test of a 113 scale representative model specimen. The experiment specimen and testing

conditions were given in Part II.

From the experiment, the roof drift-base shear relationship was measured, as shown

in Figure 7.3. As the experiment was conducted using a 1:3 scale model, the roof drift­

base shear relationship of a full-scale structure should be scciled from the test result. The

capacity curve from this scaled load-deformation relationship was taken by connecting

the plateaus of each cycle, as shown in the Figure 8.6. The obtained capacity curve is

given in Figure 8.7 (a).

The measured capacity curve needs to be converted into spectral displacement and

spectral acceleration. This conversion requires the dynamic properties of the structure.

To identify the dynamic properties of the structure, modal analysis was conducted using

the nonlinear dynamic analysis software IDARC (Reinhorn, A. et al. 1994). Since micro­

cracking is present in reinforced concrete members, the stiffness of members were

reduced as specified in the ATC-40 document. For columns and beams, reduction factors

of 0.7 and 0.5 were used, respectively. The modal analysis results, the corresponding .. '

modal participation factors, and the modal mass factors are as shown in Table 8.1. The

capacity curve was converted using modal analysis and is shown in Figure 8.7(b).

86

8.3.3 Evaluation results

From the structural capacity (Section 8.2) and seismic demand (Section 8.3), roof .,1

drift was calculated using CSM as shown in Table 8.4. The displacements of each story

at the performance points were found using the experimental result. The maximum story

drift ratios for each performance point are shown in Table 8.5 and Figure 8.9.

The ATC 40 document specifies that the structural displacement should satisfy both

the life safety limit for design earthquakes, and the structural stability limit for maximum

considered earthquakes. The response limits are defined in the view of both global

responses and component responses. The component response criteria are not checked in

this study, as the member forces could not be measured from this experiment. In the

ATC 40, the global response limit, the inter-story drift is 0.02 for life safety level and

O.33V/P for structural stability level, which is approximately 0.04.

Table 8.5 shows that the OMRCF designed only for :gravity loads can sustain the

seismic load of every seismic zone with soil condition SB, zone 1, 2A, 2B, and 3 with

soil condition SC, and zone 1 and 2A with soil condition SD. As seismic demand of soil

condition SA is smaller than that of soil condition SB, it can be inferred that the OMRCF

designed for gravity loads also sustain the seismic load of every seismic zone with soil

condition SA. The UBC (1997) specifies that only structures in seismic zone 1 can be

designed with OMRCF detail.

88

Table 8.3 Earthquake catalogue

(a) Soil Type SB

Event name Station name Date Comp PGA

Mchoacan Calete De Campo 21108/85 N90W 0.083

Helena Federal Bleg, Helena 31110/35 EW 0.145

Kern County Taft 21107/52 N21E 0.156

Mammoth lakes Long Valley Dam, Bed Rock 25/05/80 90 0.137

Borrego Min SCE Power Plant, San Onofre 08/04/68 N33E 0.041

Mammoth lakes Long Valley Dam, Right Crest CI4 25/05/80 90 0.474

San Fernando Cal. Tech. Seism. Lab. 09/02171 EW 0.192

Imperial Valley EICentro 18/05/40 NS 0.318

San Fernando Santa Felicia Dam(Outlet) 09/02171 S08E 0.217

Whittier Pacoima-Kagel Canyon 01/10/87 90 0.158

(b) Soil Type Sc

Event name Station name I Date Comp PGA

Whittier Narrows Mt. Gleason Ave. 01110/87 S90W 0.098

Whittier Narrows Kagel Canyon Ave. 01110/87 N45E 0.12

Landers N. Figueroa St. 28/06/92 N58E 0.028

Landers Mel Canyon Rd. 28/06/92 N90E 0.030

Landers Willoughby Ave. 28/01/92 SOOE 0.024

San Fernando Water And Power Building 09/02171 S40W 0.172

San Fernando South Olive Ave. 09/02171 S37W 0.196

Northridge Mel Canyon Rd. 17/01194 SOOE 0.026

Northridge S. Alta Dr. 17/01/94 NOOE 0.074

Northridge N. Figueroa St. 17/01/94 N32W 0.158

(c) Soil Type SD

Event name Station name Date Comp PGA

Landers Colima Rd. 01110/87 S90W 0.046

Landers Palma Ave. 01110/87 N40W 0.045

Landers Del Arno Blvd. 28/06/92 N58E 0.054

N011hridge Manhattan Beach Blvd. 28/06/92 N90E 0.158

Northridge Willoughby Av. 28/01192 N90W 0.250

Northridge S. Orange Ave. 09/02171 S40W 0.065

Whittier Water St. 09/02171 N38E 0.111

Whittier Colma Rd. 17/01194 SOOE 0.197

Whittier Sunset Blvd. 17/01194 NOOE 0.036

San Fernando Via Tejon 17/01/94 N32W 0.025

90

A-I Pushover Curve

"I~

V )

+-- Vo Un

(a) Detennination of structural capacity \,i

Capacity Diagram

(b) Conversion to capacity spectrum

D

(c) Detennination of seismic demand

50' D d Demand Point 10 eman I

Diagram j' l17y //Demand Diagram

1/ \"" A Hi-----",llr

o

Cd) Reduction of demand and finding perfonnance point

Figure 8.1 Procedures of capacity spectrum method

92

Develop response spectrum (5% damping)

: ... I i Transform the capacity curve Into a capacity spectrurTi

y y

Plot the capacity curve together with response spectrum

Select a New.perl"rmance

!

I n t~~~:~ti~~dp6 int : Select a trial performance point. %i·dpi i

--~-----------------------'

v Develop a bilinear representation of the capacity

spectrum

y

fJifJ

equal displacement "approximation

'--____ c_a_lc_u_la_te_t_h_e _s_pe_c_tr_a_1 r_e_du_c_ti_o_n _Ia_c_to_r_s ___ H Sf' =3.21-16itb1()9·k)

! .' .2.3J-c0.411Il(.Beff) y SRr .. = ....... ' ·.·.1:65

Develop the reduced demand spectrum

Draw the demand spectrum together with the capacity' spectrum ;

: ~ .. :" ~~ Intersects the capacity _ - a: r-e point 't,.d"

displacement. d. is within acceptable toler~nce of d,i

--------yes---------------yes;-----

y

The trial point a,. do,. is the performance point

h~urt' '" ..l Flowchart for determining performance point, ATe 40 Procedure A

94

-D.05

-300

Figure 8.6 Roof displacement and base shear relation of full-scale structure

30 0.20 ----.. ------ ..• ~---.--------------

i 25

- 20 0.15

ro 1! 15 Ul

Cii ~ 0.10

~ 10 ClJ

(/)

0.05

0 0.00 0 10 20 30 40 50 o 10 20 30 40 50

Roof Drift (em) SO (em)

(a) Backbone curve (b) Capacity curve

Figure 8.7 Conversion of backbone curve to capacity curve

o en

o en

96

Siory Dri1t(Oeslon EO, Site S8) Story orifl(Maxirrum EO. Site SS)

0.01

V ule safety ~~~sne 1

, -Zone2A

, =!:;:r

0.02 Story drilt

0.03 0.04 0.01

(a) Site Condition, SB

structura: stablity lim!s ..... ~ ....... .

---t"-Zone 1

--+-Zone2P.. -+Zone2E ---!-Zone3

1'-' 0.02 0.03 0.04 0.05

Story d'ilt

Story Orift(Deslcn EQ. Site SCI Story Drift(Moxirrum EO. Site SCI

Lile~lety.lirri.I~ .............. . V' -Zone 1

: ==~~:~ ...u...--r----,--r-~'..., -_-_-~~: ~

0.01 0.02

Story drill

0.03 0.04 0.01

(b) Site Condition, SC

0.02 0.03 0.04 0.05

Slory drift

Story ori1t{Desion EO. Site SO) Story orill{Maxirrum Ea, SIte SO)

0.01 0.02 Siory erift

0.03 0.04

o en

0.01

( C) Site Condition, SD

. '''.tr.~~~~I~~II~ty lirrits

----;-Zone 1 ---t- Zone 2A

--+zone2B

0.02 0.03 0.04 0.05 Story drilt

Figure 8.9 Global structural response at perfonnance point

97

CHAPTER 9

CONCLUSION

This study investigates the behavior of moment frames designed for gravity loads and

detailed by the requirements for OMRCF. The test for this study was conducted using a

113 scale model specimen with the quasi-static cyclic loading. The performance of the 3

story OMRCF was evaluated using the capacity spectrum method. The capacity of the

OMRCF was also obtained from the experiment. Various seismic demands according to

soil types and seismic zones were applied for the capacity spectrum method. The test and

evaluation results are as follows:

1. At a 0.5 % roof drift ratio, the first crack was observed at both ends of all columns

and beams in the 1 st and 2nd stories, and at the bottom of all columns and interior

beams in the 3rd story. At the roof drift ratio of 2.5 %, shear cracks were observed

at the transverse exterior beams of the 1 st floor.

2. The OMRCF structure showed a very stable energy dissipation capacity without

abrupt strength deterioration, even if the structure was designed only for gravity

loads and detailed for the requirements of OMRCF.

3. At the final loading stage, interior columns in the 1st story were severely damaged,

while the beams had not experienced any apparent d~mage. At the exterior joints

of the 1 st story, damage was distributed to the exterior columns and beams. This

shows that in an OMRCF designed only for gravity loads interior joints have the

mechanism of a weak column and strong beam whereas exterior joints have that of

a strong column and weak beam. This could be referred to as a hybrid failure

mechanism.

4. The maximum lateral strength of the frame was 0.157 W, which occurred at the

roof drift ratio of 0.015. The design base shear of the building required for seismic

zone 1, 2A, and 2B, is 0.05W, O.lOW, and 0.13W. Thus the OMRCF designed

99

REFERENCE

American Concrete Institute (1995, 1999), Building code requirements for reinforced concrete, ACI 318-95, 99, Detroit, Michigan

Aycardi, L.E., Mander, lB., and Reinhorn, A. M, "Seismic Resistance of Reinforced Concrete Frame Structures Designed Only for Gravity Loads : Experimental Performance of Sub assemblages, ACI Structural Journal, pp 552-563, September­October, 1994

Lynn, A., Moehle, J., Mahin, S. A., and Holmes, W. T., "Seismic Evaluation of Existing RC Building Columns," Earthquake Spectra, Vol 12, No.4, pp. 715-739,1996.

Uniform Building Code (UBC), International Conference on Building Officials, Whittier, California. 1994

Building Seismic Safety Council, NEHRP Recommended Provisions for the Development of Seismic Regulation for New Buildings, Part 1 and 2, Provisions and Commentary, FEMA, Washington, D.C., 1994, 1997

Portland Cement Association (1999), Notes on ACI 318-99 Building Code Requirements for Structural Concrete, Skokie, Illinois.

Alan Williams, Seismic Design of Buildings and Bridges, Engineering Press, Austin, Texas, 1998, pp. 274-283.

Computers and Structures inc., SAP2000, Berkeley, California, 1997.

Park, R. and Paulay, T, Reinforce Concrete Structures, John Wiley and Sons, 1975.

Paulay, T and Priestley, M. Seismic Design of Reinforced Concrete and Masonry Buildings, John Wiley and Sons, 1992.

Akshay Gupta and Helmut Krawinkler, " Estimation of seicmic drift demands for frames structures" Earthquake Engineering and Structural Dynamics, March 2000.

Applied Technology Council, ATC 40: Seismic Evaluation and Retrofit of Concrete Buildings Vol. 1 & Vol. 2, California Seismic Safety Commission No. SSC 96-01, NOV. 1996.

Bracci, 1 M., Reinhom, A. M., and Mander, 1 B., "Seismic resistance of reinforced concrete frame structures designed for gravity loads: performance of structural system," ACI Structural Journal, 92, 5, Sept.-Oct. 1995, pages 597-60

Bracci, 1 M., Reinhom, A. M., and Mander, J. B., "Seismic resistance of reinforced concrete frame structures designed only for gravity loads: Part I -- design and properties of a one third scale model structure," NCEER-92-0027, National Center for Earthquake Engineering Research, Buffalo, N.Y., Dec. t;, 1992, vol 1.

101

APPENDIX

DESIGN PROCEDURE AND COMMENTARY

FOR RIC MOMENT FRAMES

A.I Introduction

Moment frames develop their resistance to lateral forces through the flexural strength and

continuity of beam and column elements. In an earthquake, a frame with suitable proportions and

details can develop plastic hinges that will absorb energy and allow the frame to survive

displacements larger than the frame was designed for on an elastic basis. A strong earthquake

induces forces and displacements in a typical building structure which could greatly exceed those

induced by an earthquake specified in standard building codes; buildings designed for normal code

lateral forces could be stressed beyond the elastic limit by a major earthquake. Therefore, in

designing a building to withstand severe earthquakes, it is necessary that the large seismic energy

input be absorbed and dissipated through large but controllable inelastic deformations of the

structure. The sources of potential structural brittle failure must, therefore, be eliminated. Thus, it is

necessary to prevent: premature crushing and shearing of concrete; sudden cracking and

simultaneous fracturing of steel; sudden loss of bond and anchorage; premature crushing and/or

splitting of concrete cover accompanied by local buckling of main reinforcement; and premature

dynamic instability resulting from large lateral drifts. Degradation of stiffuess and strength under

repeated loading must also be minimized or delayed long enough to permit sufficient energy to be

dissipated through stable hysteretic behavior.

It is, however, uneconomical to apply single provisions to withstand severe earthquakes without

considering the frequency or magnitude of possible earthquakes in various regions. For this reason,

the ACI 318-99 code requires different provisions on reinforced concrete moment frames that resist

seismic forces according to seismic risk levels. The ACI 318-99 proportioning and detailing

requirements for lateral force resisting systems of reinforced concrete are summarized in Table A.I.

Seismic risk levels and seismic zones generally correlate as shown in Table A.I.

103

The NEHRP Evaluation Handbook (FEMA-178, 1992) provides the comparisons ofr~inforced

concrete frames based on the ACI 318-89 as sho\V11 in Table A.3. Although some detailed

provisions are changed in ACI 318-99, Table A.3 describes the deficiencies of ordinary and

intennediate frames, comparing with special frames.

Table A.3 Evaluation Statement Used to Determine the Appropriate Frame

Intennediate Statement Special Frame Ordinary Frame

Frame

Ko shear failures T T "I F

Strong column/weak beam T F F

StIrrup and tie hooks I T F F

Column-bar splices2 T F F

Column-tie spacing3 T * F

Beam bars .; T * F

Beam bar splIces) T F F

StIrrup spacmg6 T T F

JOInt rClntl.1rcmg T F F

1. Sttrrup,> J:ld tlc:-, ;Ue anchored into the member cores with hooks of 135° or more. 2 Ali ,.-"\u:nr t--J! IJp splice lengths are greater than 35db long, and are enclosed by ties spaced at 8db or

Ie"" :: f-r~HT)t.· dliun1T1'> h..!\ e ties spaced at d/4 or less throughout their length and at 8db or less at all potential

pi..!,l:, hlll).".' le~lons. .,1

... ·\1 k..i°,i t,'Illr:",ltudinal top and two longitudinal bottom bars extend continuously throughout the 1~T1~t' [I' "'..l, r trame beam. At least 25% of the steel provided at the joints for wither positive or nq:..ll:" e m(':Tlt"nl IS continuous throughout the member.

S. Ttlr i..:~ <,p:.:e" tor longitudinal beam reinforcing are located within the center half of the member kn~:tn ..If j 110t In the vicinity of potential plastic hinges.

6. AI: be,liTl- h.J. t' stIrrups spaced at dl2 or less throughout their length, and at 8db or less at potential

The e mdk.lle-, th..!! the numerical criterion for intermediate and special frames is different, but that the same concertuJI n:quIrement exists.

Transverse Reinforcements

refer to Fig. Al(a)

Lateral reinforcement for tlexural framing members subject to stress reversals or to torsion at supports shall consist of closed ties, closed stirrups, or spirals extending around the flexural reinforcement.

Closed ties or stirrups shall be formed in one piece by overlapping standard stirrup or tie end hooks around a longitudinal bar. or formed in one or two pieces lap spliced with a Class B splice (lap of l.31d) or anchored in accordance with 12.13.

Other Requirements

Beams at the perimeter of the structure

refser to Fig. A2(a)

Stirrups anchored around the negative moment reinforcement with a hook having a bend of at least 135°

In other than perimeter beams, when closed stirrups are not provided

refer to Fig. A2(b)

105

refer to Fig. A.I (b) refer to Fig. A.I(c)

where hoops and stirrups shall be fonned as follows:

~i'b [] '[1 r}= ! ...

'.

'= '= - =: -Transverse reinforcement over probable hinge regions identified above shall be proportioned assuming Vc=O when both of the following conditions occur:

(Mpr~Mpr,.)/2 :?: V CJIkL/2

The factored axial compressive force including earthquake effects ::; Agf rl20

ORDINARY MOMENT FRAME

Conditions

Design Shear Strength

107

AA Column Design

INTERMEDIATE MOMENT FRAME

For members subject to axial compression, Larger of

Transverse Reinforcements

refer to Fig. A.3(a)

Ties shall be arranged such that every comer and alternated longitudinal bar shall have lateral support provided by the comer of a tie with an included angle of not more than 135° and no bar shall be farther than 6" clear on each side along the tie from such a laterally supported bar

Ma.,"Ximum shear obtained from

U=0.75[l.4D+ 1.7L+2(l.87E)]

refer to Fig. A.3(b)

SPECIAL MOMENT FRAME

hmin;::: 12"

hmill / hpctp;::: 0.4

0.01 ~ pg~ 0.06

IMc;::: 1.:Z~Mg

where column flexural strength shall be calculated for the factored axial force, consistent with the direction of the lateral forces considered, resulting in the lowest flexural strength

where Mpr is based on fs = 1.25 fy

tylpr need not be greater than Mpr of the beams framing into the joint

refer to Fig. A.3 ( c)

Transverse reinforcement over probable hinge regions identified above shall be proportioned assuming Vc=O when both of the following conditions occur:

(Mprl+Mprr)/2 ;::: V CJlJa/2

The factored axial compressive force including earthquake effects ~ Agfcl20

I:"or rectangular hoop reinforcement "I

ASh = 0.3(sh/~ / fyh)[(Ag / A ch ) -1]

ASh = 0.09shcf~ I fyh

For spiral or circular hoop reinforcement

where Ps = O.l2f~ Ifyh

109

~i

H,

(a) Ordinary moment frame (b) Intermediate moment frame

( c) Special moment frame

Fig. A.3 Longitudinal reinforcement details in column

111

lateral reinforcement required by Eq. (11-13) within the column for a depth more than that of

the deepest cOlmection of framing elements to the columns. (introduced in ACI 318-95)

Eq. (11.13) - minimum area of shear reinforcement

A = 50 bws v f

y

(11.13)

Chapter 12 - Development and splices of reinforcement (modi:q.ed in ACI 318-71 to improve in .. '

bar anchorage and splicing details)

12.11 Development of positive moment reinforcement (introduced in ACI 318-95)

12.11.1 - At least one-third the positive moment reinforcement in simple members and one­

fourth the positive moment reinforcement in continuous members shall extend along the same

face of member into the support. In beams, such reinforcement shall extend into the support

at least 6 in.(I5.24CI1l)

12.11.2 - When a flexural member is part of a primary lateral load resisting system, positive

moment reinforcement required to be extended into the support by 12.11.1 shall be anchored

to develop the specified yield strength fy in tension at the face of support.