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Incremental dynamic analysis of steel braced frames designedbased on the first, second and third editions of the iranian seismic

code (standard no. 2800)

Behrouz Asgarian and Ali Jalaeefar*,

Civil Engineering Faculty, K.N. Toosi University of Technology, No 1346 Valiasr St Mirdamad Intersection,

Tehran, Iran, P.O Box: 15875-4416

SUMMARY

Incremental dynamic analysis (IDA) is an emerging method in structural analysis which allows evaluationof seismic capacity and demand of structures through a series of nonlinear dynamic analyses using multiplescaled ground motion records.

Seismic behaviour of concentrically braced frames designed based on the first, second and third revisionsof the Iranian seismic code, standard no. 2800, has been evaluated through IDA in the present paper.Besides, a brief comparison is made between seismic behaviour of these frames, frames with differentheights and different bracing types. Seismic capacity and limit states of such structures have been reviewedthrough the paper.

The IDA results imply that frames designed with the first edition are seriously vulnerable and fail beforereaching the acceleration levels predicted in the code. On the other hand, frames designed with the secondand third editions, although behaving better, need partial reinforcement in some cases.

Other results of this study show that chevron braced frames behave seismically better than X-bracedones. Copyright 2009 John Wiley & Sons, Ltd.

1. INTRODUCTION

The first edition of the Iranian seismic code 2800, composed in 1986, was the first code in Iran for

seismic loading and design of structures independent of other load cases. Although the first editionwas a step forward in design of structures, serious defects in its seismic requirements led to the

publishing of the second revision of the code in 1998.

The most important difference between these two revisions is concentrated in six attachments added

to the second edition. Specifically, the second attachment which contains special requirements for

seismic design of steel structures was a great revolution in reinforcement of them.

The third edition of the code, published in 2004, modified the requirements both in earthquake

force calculation and design criteria, and is being widely used by Iranian structural engineers.

On the other hand, looking through steel structures designed and constructed in Iran, it is obvious

that a great percentage of them use concentric bracing as lateral resisting system. Hence, a comparison

between seismic behaviour of concentrically braced frames designed based on the first. second and

third revisions of the Iranian seismic code 2800 has been made in this paper.

Several methods are available to perform such a study. Among them is the incremental dynamicanalysis (IDA), a powerful method that goes through evaluation of structures considering multiple

scaled ground motion records.

Three groups of structures according to their heights are being studied here. Five-storey structures

as representative of low-rise buildings, eight-storey structures as representative of mid-rise build-

ings and 12-storey structure as representative of semi-high-rise buildings.

* Correspondence to: Ali Jalaeefar, No. 22 Narvan Alley, Ghoba St., Dr. Shariati St., Tehran, Iran P.O Box: 19487-64167 E-mail: [email protected]

THE STRUCTURAL DESIGN OF TALL AND SPECIAL BUILDINGSStruct. Design Tall Spec. Build. 20, 190207 (2011)Published online 3 July 2009 in Wiley Online Library (wileyonlinelibrary.com/journal/tal). DOI: 10.1002/tal.528

Copyright 2009 John Wiley & Sons, Ltd.

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IDA OF STEEL BRACED FRAMES 191

Copyright 2009 John Wiley & Sons, Ltd. Struct. Design Tall Spec. Build.20, 190207 (2011)

DOI: 10.1002/tal

For each of the three groups, two types of bracings, chevron and X-bracing, have been designed

based on the three editions of the seismic code 2800. Hence, 18 braced structures with different

heights, bracing types and design codes are being studied using the IDA method.

IDA is an emerging analysis method through which capacity and limit states can be predicted using

a series of nonlinear dynamic analyses (Vamvatsikos, 2002). Ground motion records are scaled in

multiple steps to perform such analyses and to trace the structural behaviour from elasticity to total

failure. IDA diagrams are extracted for each ground motion record according to maximum responseof structure in each step of scaling.

Summarizing the groups of IDA curves using statistical methods and combining the results with

hazard analysis parameters, structural behaviour, capacity and limit state can be studied.

2. GENERAL DESCRIPTIONS

2.1. About the code

TheIranian Code of Practice for Seismic Resistant Design of Buildings, standard no. 2800, published

by the Building and Housing Research Center, contains requirements for the seismic design of all

common structures in Iran. All steel, reinforced concrete, masonry and even wooden structures

except special ones such as dams, bridges, marine structures, etc., should be designed using these

requirements.The basic concept of the code is to provide requirements that: (a) cause buildings to remain stable

in severe earthquakes and hence minimize mortality; (b) decrease structural damage due to earth-

quakes with low and moderate intensities in common buildings; and (c) prevent structural damage

due to earthquakes with low and moderate intensities in important buildings.

Severe earthquakes (design earthquakes) are the ones with a probability of occurrence less than

10% in 50 years. Earthquakes with low and moderate intensities are the ones with a probability of

occurrence more than 99.5% in 50 years.

Earthquake lateral forces can be calculated using the following two methods depending on the

structure: (a) equivalent static analysis method; and (b) dynamic analysis method.

Using the equivalent static method is allowed just for regular structures with less than 50 m of

height or irregular ones with less than five stories or 18 m of height. Others must be designed using

dynamic analysis method.Base shear force is calculated according to equation (1) in the equivalent static method, as in

UBC-94.

V C W= (1) (standard no. 2800)

where Vis the base shear force; Cis the base shear coefficient; and W= total dead load +b (liveload), 0 b 1.

The base shear coefficient is calculated from equation (2) as follows:

CABI

R= (2) (standard no. 2800)

where A = 1/g (earthquake design acceleration); B is the reflection factor, which describes thestructures response to the ground motion considering the four soil types introduced in the code and

the structures height;Iis the structural importance factor; andR is the response modification factor.

The base shear V is linearly distributed in the structures height according to its first mode of

vibration.

2.2. Design of structures

2.2.1. Geometric parameters and gravity loading

All of the 18 structures are similar in plan (Figure 1) and storey heights as usual in residential build-

ings. Vertical bracings are placed in middle bays in each side of the plan, making the structure sym-

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192 B. ASGARIAN AND A. JALAEEFAR


DOI: 10.1002/tal

Figure 1. Framing and bracing plan.

metric in plan. Rigid diaphragm can be assumed according to the roof system as in usual structures.

Gravity loads are supposed to be similar to common residential buildings in Iran (standard no. 519.

2000).

2.2.2. Lateral loading (earthquake loads)

The three editions of the seismic code 2800 are used for the design of earthquake-resisting frames.

The most outstanding requirements used in this procedure are as follows.

2.2.2.1. Structural analysis method

Being regular and symmetric in plan and height, as mentioned in the code 2800, equivalent staticanalysis is allowed to be used for the structures (standard no. 2800).

2.2.2.2. Calculation of base shear coefficient

Base shear is calculated according to equation (1) in the equivalent static method.

Table 1 summarizes the steps for calculating the coefficient Caccording to the code.

The earthquake lateral force is distributed linearly in the structures height according to first defor-

mation mode of buildings. To take into account higher modes effect, lateral force Ft should be con-

sidered on the last storey level for structures having main period larger than 0.7 secs.

The base shear coefficient for each of the 18 test structures is listed in Table 2.

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Table 1. Base shear coefficient calculation.

Parameter First edition Second edition Third edition

A 0.35 0.35 0.35R 7 6 6I 1 1 1

TT

HD

H

=

min

.

.

0 09

0 063

4

T H= 0 053

4. T H= 0 05

3

4.

Soil type Type II Type II Type II

B

BT

T= ( )

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P P R P PDL LL E SC+ + ( ) 0 8 0 4. . (4) (Compression control in the second edition)

0 85 0 4. .P R P PD E ST+ ( ) (5) (Tension control in the second edition)

P P P PPL LL E SC+ + 0 8 2 8. . (6) (Compression control in the third edition)

0 85 2 8. .

P P PDL E ST+ (7) (Tension control in the third edition)

where PDL is the axial dead loads, PLL is the axial live loads, PE is the axial earthquake loads, PSC is

the axial strength in compression, PST is the axial strength in tension and R is the response modifica-

tion factor.

2.2.2.5. Bracing member requirements

Special requirements for the design of steel bracing members are recommended in the second attach-

ment of the code. In addition to slenderness and joint requirements, the allowable compressive stress

of the brace member is discussed. According to the code, this stress should be decreased to a lower

limit using the following equations:

F BFas a= (8)

Bkl r

C

=+

1

12 C

(9)

where Fas is the reduced allowable compressive strength, Fa is the allowable compressive strength,B

is the reduction factor, kl/r is the slenderness ratio, CE

FC

y

=2 2

, E is the elastic modulus of steel

and Fy is the steel yield stress.

Brace members are designed with the decreased compressive strength.

2.3. Modelling the structures

Each of the 18 structures selected for the study is loaded, analysed and designed according to men-

tioned assumptions. AISC-ASD89 design rules are used in the design procedure.

OpenSees finite element programme, generated and developed in West American universities, is

used for modelling and IDA of the structures. IDA is performed for a two-dimensional (2D) frame of

each structure which is located on axis A of the plan.

Most important assumptions in modelling of the 2D frames are as follows:

2.3.1. Geometric and material nonlinearity (Crisfield, 1991)

The main structural elements are supposed to yield or buckle during severe earthquakes. Hence, both

geometric and material nonlinearity should be taken into account while modelling the structures.Using finite element method based on uniaxial elements is a way to face the matter. Both lumped

and distributed plasticity can be used for modelling material nonlinearity. The latter is used in the

present study.

To solve geometrically nonlinear problems in beams or uniaxial elements, Lagrangian method,

modified Lagrangian method and corotational method are available. Corotational method, which

is used in this study, is more efficient and less time consuming than the others. Equilibrium equations

are solved based on the deformed shaped coordinate system as in modified Lagrangian method.

Besides assuming only the degrees of freedom related to deformations, and not rigid movements, a

basic system of coordinates is generated. Using such a system of coordinates, equilibrium equations

are solved while stiffness matrices are updated in each step of solution.

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Figure 2. Stressstrain curve for steel material.

To model the St-37 steel behaviour, steel 02 stressstrain curve is used from the library of materi-

als introduced in OpenSees. The stressstrain curve is shown in Figure 2.

2.3.2. Elements used

A force-based beamcolumn element, consists of fibre elements, is used for beams, columns and

braces. Using St-37 stressstrain curve, stress is calculated in parts of the element section according

to the imposed strain. Integrating on section area, total stress, forcedeformation and momentcurva-

ture curves are calculated. At last, taking all integration points into account, forces and deformations

are calculated.

2.3.2.1. Modelling beams

Beams in braced frames are modelled as moment-released beams at both ends. Therefore, beams are

not parts of lateral resisting system and will behave elastically under gravity loads.

2.3.2.2. Modelling columns

Columns in braced frames are parts of a lateral resisting system and are supposed to enter nonlinear

region in severe earthquakes. Hence, both geometric and material nonlinearity should be taken into

account for them.

An initial deflection equal to 1/1000 of the element span is considered to provide geometric non-

linearity conditions as shown in Figure 3. This will make in-plan buckling of columns possible under

severe earthquake loads.

Buckling occurs around the weaker axis of column section. Considering the weaker axis in theframe plan, 2D modelling of the structure will be similar to real conditions.

Besides, material nonlinearity is provided using fibre elements as mentioned in the previous section.

2.3.2.3. Modelling braces

Braces are modelled as moment-released elements at both ends and are supposed to behave as axial

members.

Geometric nonlinearity is provided in the same way as columns, considering initial deflection in

midspan of the brace element. Thus, buckling is assumed to occur around the weaker axis of the brace

section in the frame plan.

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Figure 3. Initial imperfection in columns and braces.

2.4. Behaviour of axial members under cyclic loads

The behaviour of axial members under cyclic loads, both in linear and nonlinear regions, should be

studied to make sure that modelling assumptions are similar to real conditions. Figure 4(ac) shows

the hysteretic curves for sample braces modelled using different slenderness.

The results are similar to buckling loads calculated using AISC-ASD89 requirement as shown in

Table 3. Hysteretic curves are also similar to experimental results of Black and Popov (1980) Zayas

and Popov (1981). Thus, modelling assumptions of axial members are close to reality.

2.5. IDA parameters2.5.1. Acceleration time histories used

Twenty acceleration time histories are selected for IDA of frames. Soil condition is assumed to be

similar to type II of soil classification in the standard 2800.

Table 4 summarizes the information for the selected 20 records.

2.5.2. Intensity (IM) and damage measures (DM)

Suitable IM and DM are other basic parameters of an IDA study.

The IM selected for IDA is an important factor in reflecting the real behaviour of an acceleration

time history to the structure.

Peak ground acceleration (PGA) was at first used for IM, but linear scaling of the time history

records using PGA caused a great dispersion in the results of analysis with different records. Thus,

first-mode spectral acceleration (SA) is used as scalable IM in this study. Considering the structuresmain period, earthquake duration, damping effects, etc., in calculating a spectrum, make SA a more

powerful IM than PGA in reflecting the time history effects to the structure. But, it seems that using

other parameters such as energy content of records may cause the results to be more exact and real.

Besides, maximum inter-storey drift is selected as DM according to seismic code 2800, in the

present study.

2.5.3. Scaling acceleration time histories

The 20 selected records are linearly scaled in 14 steps, from 0.1 g to 2.4 g according to first-mode

SA. For each of the test frames, the SA corresponding to the first mode of vibration is extracted from

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Figure 4. Cyclic behaviour of brace members.

Table 3. Analytical and American Institute of Steel Construction (AISC) buckling loads.

Slenderness Analytical buckling load (kg/cm2) AISC buckling load (kg/cm2)

40 2309 222880 1997 1955120 1373 1399

1 kg/cm2= 104 kg/m2= 2048.16 lb/ft2= 98 066.5 N/m2.

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the time history record. Using this quantity, the record is linearly scaled so that its SA becomes 0.1 g,

0.2 g, 0.3 g, 0.4 g, 0.6 g, 0.8 g, 1.0 g . . . 2.4 g. This means that in each step of scaling, all points are

multiplied by a unique scaling factor as follows.

a t a a a

A t ba t ba

n( ) = ( )

( ) = ( ) =

1 2, , , original time history record

11 2, , ,ba ban( ) scaled time history record

Considering this range, structural behaviour can be traced from elasticity to total failure.

3. IDA OF FRAMES USING 20 RECORDS

IDA is performed for the 18 selected frames using the assumptions mentioned before, and IDA curves

are extracted for each of the 20 records. The IDA curves display a wide range of behaviour, showing

large record-to-record variability, thus making it essential to summarize such data and quantify the

randomness introduced by the records. We need to employ appropriate summarization techniques that

will reduce these data to the distribution of DM given IM. Mean value is not a good choice due to

infinite values of DM at high levels of IM.

Thus, statistical 16, 50 and 84% fractiles are used for summarizing the DM values. Median is the

most famous and common form of fractile, and half of all quantities are greater than the median.

Similarly, 16% of all quantities are greater than the 16% fractile, and 84% of all quantities are greaterthan the 84% fractile.

Hence, each group of the curves is summarized to three individual ones. Figures 5(a, b), 6(a, b)

and 7(a, b) show sample results of IDA for X-braced frames designed with the third edition of

the seismic code 2800. The median or the 50% fractile is used for comparing the results. Obviously,

other fractiles could also be used instead, but as mentioned above, median is the most common

of all.

As shown in the figures, the initial stiffness decreases by increasing the structures height, and taller

frames reach higher displacement levels in lower SAs.

The same procedure can be seen in curves related to frames designed based on the first and second

editions of the code, and frames with different bracing types.

Table 4. Acceleration time histories used.

Number Location Date Station PGA (g)

1 Tabas 16/9/78 9101 Tabas 0.8522 Kobe 16/1/95 Nishi Akashi 0.5093 Loma Prieta 18/10/89 Agnews State Hospital 0.1594 Loma Prieta 18/10/89 Hollister Clif Alley 0.279

5 Loma Prieta 18/10/89 Anderson Dam 0.2446 Loma Prieta 18/10/89 Koyote Lake 0.1797 Loma Prieta 18/10/89 Sunnyvale Colton 0.2078 Loma Prieta 18/10/89 Hollister South 0.3719 Loma Prieta 18/10/89 Sunnyvale Colton 0.20910 Loma Prieta 18/10/89 WAHO 0.3711 Loma Prieta 18/10/89 WAHO 0.63812 Loma Prieta 18/10/89 Hollister Clif Alley 0.26913 Imperial Valley 15/10/79 Plaster City 0.05714 Imperial Valley 15/10/79 Cucapah 0.30915 Imperial Valley 15/10/79 El-Centro Array 3 0.11716 Imperial Valley 15/10/79 Westmorland 5 0.07417 Imperial Valley 15/10/79 Chihuahua 0.25418 Imperial Valley 15/10/79 El-Centro Array 3 0.13919 Imperial Valley 15/10/79 Westmorland 5 0.1120 Imperial Valley 15/10/79 Plaster City 0.042

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4. CAPACITY AND LIMIT STATESDifferent methods are available for calculating capacity points in IDA curves, one of which is the

20% slope criteria (Vamvatsikos, 2002). The capacity point in this method is the first point on the

IDA curve in which the tangent slope will be equal to 20% of the initial elastic slope. But, this study

is based on the seismic code 2800; thus, capacity points are determined using the code requirements

for damage prevention. The two concepts introduced in section 2.1.2.3 for lateral storey drift control

(real lateral drift and design lateral drift) are considered as damage limits. These limits are calculated

for each of the frames, and are summarized in Table 5.

5. ANALYZING THE IDA RESULTS

Considering the 18 frames, 20 acceleration time histories and 14 steps of scaling, 5040 nonlinear

dynamic analyses are performed.After summarizing the results, three types of comparison can be made as follows.

5.1. Studying behaviour of frames with similar heights and different design codes

Figure 8(af) shows IDA curves for X-braced five-storey frames designed based on the first, second

and third editions of the code. IDA curves are based on the maximum inter-storey drifts or maximum

roof displacement.

Studying the curves, it is obvious that frames designed with the third edition of the code have higher

stiffness, and therefore less displacement occurs in them than frames designed with the second and

first editions.

Figure 5. Summarizing incremental dynamic analysis curves for X-braced five-storey frame

designed by the third edition (H= 17 m).

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The difference between frames designed with the third and second editions is almost negligible,

while frames designed with the first edition of the code are completely distinct.

Fifty per cent fractile curves (median) for each of the X-braced five-storey frames are calculated

from which the following results are concluded:

(a) The initial tangent slope (say, elastic stiffness) of the curves increases from the first edition to

the third, and frames behave with higher stiffness.

(b) The elastic stiffness for the five-storey X-braced frame designed with the first edition of the

code is 19.32, while for the frames designed with the second and third editions, the stiffnesses

are 35.63 and 35.89 (similar stiffness of the latter frames is considerable).

(c) The design lateral displacement of the roof for the frames designed with the second and third

editions occurs in 0.57 g, while in the first edition frame it occurs in 0.2 g. Real lateral storey

drifts in the first, second and third edition frames occur in 1.11 g, 1.92 g and 2.0 g, while

predicted acceleration for linear and nonlinear behaviour of the structures are 0.16 g and

0.962 g (AB/R= 0.16 g ,AB= 0.962 g; see Table 1).

(d) The lateral inter-storey drifts have almost the same behaviour. Considering the damage criteria

summarized in Table 6, the lateral design storey drift predicted in the code for the five-storey

frame designed based on the first edition occurs in 0.28 g, while this quantity is 0.37 g for the

second edition frame and 0.39 g for the third. Real lateral storey drifts predicted in the code

for the five-storey frames designed based on the first, second and third editions occur in 0.79 g,

Figure 6. Summarizing incremental dynamic analysis curves for X-braced eight-storey frame

designed by the third edition (H= 27.5 m).

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Figure 7. Summarizing incremental dynamic analysis curves for X-braced 12-storey frame designed

by the third edition (H= 41.5 m).

Table 5. Code capacity points (standard no. 2800).

Stories Bracing CodeHeight(cm)

Period(s)

Designlateraldrift

Reallateraldrift

Design roofdisplacement

(cm)

Real roofdisplacement

(cm)

5 X-bracing 1 1700 0.87 0.00408 0.02 6.93 342 1700 0.69 0.0059 0.025 10.11 42.53 1700 0.67 0.0059 0.025 10.11 42.5

8 X-bracing 1 2750 1.5 0.00408 0.02 11.22 552 2750 1.1 0.0047 0.02 13.09 553 2750 1.04 0.0047 0.02 13.09 55

12 X-bracing 1 4150 2.37 0.00408 0.02 16.93 832 4150 1.68 0.0047 0.02 19.76 833 4150 1.65 0.0047 0.02 19.76 83

5 Chevron 1 1700 0.85 0.00408 0.02 6.93 342 1700 0.63 0.0059 0.025 10.11 42.53 1700 0.61 0.0059 0.025 10.11 42.5

8 Chevron 1 2750 1.47 0.00408 0.02 11.22 552 2750 1.02 0.0047 0.02 13.09 553 2750 0.95 0.0047 0.02 13.09 55

12 Chevron 1 4150 2.33 0.00408 0.02 16.93 832 4150 1.65 0.0047 0.02 19.76 833 4150 1.53 0.0047 0.02 19.76 83

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1.0 g and 1.05 g. The little difference between capacity levels of the second and third edition

frames is related to stronger columns in the third edition frames, while braces are exactly the

same in both. (As mentioned in section 2.1.2.4, the load combinations used for axial control

of columns are different in the two editions.) On the other hand, frames designed with the first

edition of the code are seriously more vulnerable than the other two. One important reason is

the soft and weak first storey which increases the lateral displacement of above stories.

The same procedure can be seen comparing eight-storey (Figure 9(af)) and 12-storey frames

designed with different editions of the code. The results for other frames are summarized in Table 6.

As seen in Table 6:

(a) Elastic stiffness increases from the first edition frames to the third.

(b) Lateral design storey drifts occur in lower acceleration levels in the first edition frames than

in the second and third edition ones.

(c) The second and third edition frames behave almost similarly, although the third edition frames

are usually more efficient reducing lateral displacements.

Figure 8. Summarized incremental dynamic analysis curves for X-braced five-storey frame

designed with the three editions of the code.

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Table 6. Summary of incremental dynamic analysis results for 18 frames.

Stories Bracing CodeElastic

stiffness

SAcorrespondingdesign lateral

drift (g)

SAcorresponding

real lateraldrift (g)

SAcorresponding

design roofdisplacement

(g)

SAcorresponding

real roofdisplacement

(g)

5 X-brace 1 19.32 0.28 0.79 0.20 1.112 35.63 0.37 1.00 0.57 1.923 35.89 0.39 1.05 0.57 2.00

8 X-brace 1 5.74 0.10 0.25 0.07 0.562 13.88 0.46 1.03 0.18 1.023 13.88 0.47 1.15 0.18 1.18

12 X-brace 1 3.42 0.09 0.23 0.05 0.402 5.35 0.21 0.75 0.10 0.803 5.35 0.18 0.79 0.10 0.85

5 Chevron 1 19.42 0.22 0.57 0.2 0.972 29.80 0.82 1.93 0.31 >2.43 35.09 0.81 2.03 0.27 >2.4

8 Chevron 1 8.25 0.13 0.41 0.08 0.532 11.97 0.38 1.35 0.20 1.193 15.15 0.34 1.31 0.24 1.58

12 Chevron 1 3.87 0.09 0.18 0.06 0.422 4.65 0.19 1.00 0.08 0.853 5.73 0.19 0.94 0.10 0.85

SA, spectral acceleration.

(d) Design and real lateral displacements and drifts of 12-storey frames designed with the third

edition occur in lower acceleration levels than what is specified in the code (AB/R= 0.16 g,

AB= 0.962 g; see Table 1). Thus, reinforcement is required for such frames.

5.2. Studying behaviour of frames with similar design codes and different heights

Figure 10(ae) shows IDA curves for 5-, 8- and 12-storey X-braced frames designed with the third

edition of the code. The DM in Figure 10 is maximum inter-storey drift in typical stories. Typical

stories are defined according to Table 7 to make comparison between frames possible.

The following conclusions can be made in studying the IDA curves in Figure 10(ae):

(a) Elastic stiffness decreases while number of stories increases, and lateral displacements in taller

frames are more than others in the same acceleration level.

(b) Although the behaviour of first typical stories in 5-, 8- and 12-storey frames are almost similar,

but the little difference between curves increases moving to higher stories. This may be related

to higher mode effect which is considerable in taller buildings. The different distribution of

lateral forces in taller frames causes different damage distribution in the structures height.

The same procedure can be seen in frames designed with different codes and bracing types.

5.3. Studying behaviour of frames with similar design codes, similar heights

and different bracing types

Although it is not possible to find a special rule governing the behaviour of the frames with different

bracing types, but it can be claimed that in most cases chevron bracing is more efficient in reducing

lateral displacements than X-bracing. As shown in Figure 11(af), this difference is considerable in

some cases and negligible in others. But, it is obvious that in most cases, chevron braced frames

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Figure 9. Summarized incremental dynamic analysis curves for X-braced eight-storey frame

designed with the three editions of the code.

behave better specially in higher stories. This may be because of the beam axial stiffness in the storey

level which contributes in lateral resistance of the frame.

The same procedure can be seen in frames designed with different codes and different heights.

6. CONCLUSIONS

(a) IDA is completely dependent on acceleration time histories selected, and results are different

from one record to the other. Many parameters such as earthquake duration, acceleration peak

points, frequency content and energy content of the record are effective in analysis results.

(b) The IM selected for IDA (first-mode SA in the present study) is an important factor in reflecting

the real behaviour of an acceleration time history to the structure. Although SA is more effi-

cient than PGA in this process, it seems that using other parameters such as energy content

of records may cause the results to be more exact and real.

(c) Although it is not possible to find a special rule governing the behaviour of the frames with

different bracing types, it can be claimed that in most cases chevron bracing is more efficient

in reducing lateral displacements than X-bracing. In other cases, the difference is negligible.

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Table 7. Definition of typical stories.

Typicalstorey

Compared storeyin five-storey

frames

Compared storeyin eight-storey

frames

Compared storeyin 12-storey

frames

First First First FirstSecond Second Second ThirdThird Third Fourth FifthFourth Fourth Sixth SeventhFifth Fifth Eighth Ninth

Figure 10. Summarized incremental dynamic analysis curves comparing 5-, 8- and 12-storey

X-braced frames, designed with the third edition of the code.

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(d) The first edition of the Iranian seismic code 2800 does not introduce any special requirements

for steel braced frame reinforcement. Thus, frames designed with the first edition reach capacity

limits in lower acceleration levels and do not satisfy the codes requirements for lateral drifts

and displacements.

(e) Although five-storey frames showed lower displacements than 8- and 12-storey ones in the

same acceleration levels, it is obvious that optimum height of a structure depends also on other

parameters such as site soil classification and its interaction with the structure, frequency content

of the earthquake records, etc., which needs a more detailed study.(f) Higher mode effects in mid-rise and high-rise buildings are of great importance, and it is neces-

sary to take these effects into account as mentioned in the seismic code.

(g) Although frames designed based on the third edition of the seismic code (standard no. 2800)

are more efficient in controlling of lateral displacements than the others, they still need seismic

reinforcement in some cases, specially in high-rise structures according to Table 6.

(h) Great changes have been made in estimation of earthquake forces comparing different editions

of the code. More detailed classification of seismic zones, more conservative calculation of soil

effects and importance factor of structures are some of the steps forward in this procedure.

Besides, the response modification factor of concentrically braced frames is reduced fromR= 7toR= 6 in the second and third editions, which leads to higher estimation of base shear.

Figure 11. Summarized incremental dynamic analysis curves comparing five-storey frames,

designed with the third edition of the code, with X-bracing and chevron bracing.

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(i) The second attachment added to the second and third editions of the seismic code (standard

no. 2800) has made a great revolution in design of columns and bracing members. Although

most of the code requirements in the second and third editions are the same, small differences

such as axial control of columns make the third edition distinct.

REFERENCES

AISC (American Institute of Steel Construction). 1989. Manual of Steel Construction. Allowable Stress Design 1989. AISC

ASD89. AISC: Chicago, IL.

BHRC (Building and Housing Research Center). 1986. Iranian Code of Practice for Seismic Resistant Design of Buildings.

Standard No. 2800, 1st edn. BHRC: Tehran.


Standard No. 2800, 2nd edn. BHRC: Tehran.


Standard No. 2800, 3rd edn. BHRC: Tehran.

Black RG, Popov E. 1980. Inelastic buckling of steel struts under cyclic load reversals. Report Number UCB/EERC. 80/40,

University of California, Berkeley.

Crisfield MA. 1991.Nonlinear Finite Element Analysis of Solids and Structures, Vol. 1. John Wiley & Sons: New York.

Mazzoni S. 2006. Manual of OpenSees 1.73. University of California: Berkeley, CA.

Ministry of Housing. 2000.National Iranian Code of Minimum Building Loads. Standard No 519. Ministry of Housing: Tehran.

Vamvatsikos D. 2002. Seismic Performance, Capacity and Reliability of Structures as Seen Through Incremental Dynamic

Analysis. Department of Civil and Environmental Engineering, Stanford University: California.

Zayas V, Popov E. 1981. Inelastic structural modeling of braced offshore platforms for seismic loading. UCB/EERC-81/04 ,

Earthquake Engineering Research Center, University of California, Berkeley, CA.

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