comparison of displacement based and force based method for seismic analysis of concentrically...

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CHAPTER 1

Introduction

1.1 General:

Steel Concentrically Braced Frame (CBF) is commonly used structural system

(Figure 1.1), developed for resisting forces and deformations induced by severe

earthquake ground motions and wind loads. This system offers significant energy

dissipation, ductility, moderate initial stiffness, which render it an efficient lateral load

resisting system. Concentrically braced frames are defined as those where the centre lines

of all intersecting members meet at a point as shown in Fig.1.1. This traditional form of

bracing is widely used for all kinds of construction such as towers, bridges, and buildings,

creating stiffness with great economy of materials in two dimensional space frames.

1.1.1 Advantages of using Steel Concentrically Braced Frame (CBF)

Following are advantages of using CBF as a lateral load resisting system in

comparison with traditional lateral load resisting systems:

1. Due to light weight of CBF, it reduces the seismic loads which are directly

proportional to the mass of the structure.

2. From architectural point of view, CBF increases versatility and space savings

because of the smaller cross section as compared to reinforced concrete section.

3. By using hot rolled Steel section, high quality control is achieved and speed of

construction is faster as compared to reinforced concrete structure.

4. Lateral loading on a building is reversible, braces thus will be subjected in turn to

both tension and compression, and consequently, they are usually designed for the

more stringent case of compression.

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1.1.2 Limitations of Steel Concentrically Braced Frame Systems (CBF)

Following are limitations associated with CBF as a lateral load resisting system:

1. CBF systems are usually more flexible in comparison to traditional lateral load

resisting systems.

2. As compared to other reinforced concrete structure, CBF increases its vulnerability

to fire hazards.

3. The inability to provide reversible inelastic deformation is the principal

disadvantage of CBF.

4. Ordinary concentrically braced frames are not allowed in Seismic zones IV and V

and for buildings with an importance factor greater than unity (I > 1.0) in zone III.

5. K bracing is not permitted in earthquake zones by the code. The inelastic

deformation and buckling of K bracing members may produce lateral deflection of

the connected columns, causing collapse.

1.1.3 Design provisions:

Current code-based seismic design provisions, IS 1893 Part1: Criteria for Earthquake

Resistant Design of Structures, Part 1: General Provisions and Buildings (Fifth Revision

2002) & AISC Seismic Provision for Structural Steel Buildings, (ASCE7 2005) adopts

elastic force/strength-based approach and implicitly accounts for inelastic behavior of

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structural system through a response reduction factor R. Generally for ductile design, the

code-based provision adopted value of R for Steel CBF is between 3-4.

1.1.4. The performance-based seismic design (PBSD):

The performance-based seismic design (PBSD) method is a more general, reliable

and efficient method which explicitly considers the inelastic behavior of a lateral load

resisting system. The Performance Based Plastic Design (PBPD), a displacement-based

approach of PBSD. It is based on a target displacement ductility ratio and pre-selected

yield mechanism and it uses plastic analysis and design provisions. This approach was

proposed by Chao and Goel (2006).

1.2 Objectives:

Limitations of code-based design method

1. No consideration of inelastic response:

The current seismic design codes for lateral load resisting systems are still not

based on proper inelastic design methodology. As a result, the significant inelastic

displacement capacity of these systems cannot be fully explored. Elastic design

methodology applied on Steel CBF does not recognize the redistribution of moments in

the inelastic range.

2. Unpredictable failure:

The design procedures do not always lead to the intended failure mode and the

expected ductility under severe ground motions

3. Insufficient energy dissipation capacity:

The energy dissipation capacity of structure designed by current seismic code

procedure can be less than that required for preventing collapse under severe ground

motion.

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Performance Based Plastic Design (PBPD) is an emerging seismic design method for

next generation. It is of upmost importance to evaluate or to check the advantage of PBPD

over traditional code based method through a design case study. Hence following

objectives are considered for this study:

1. Design a four storey Steel CBF for high seismicity by using force/strength based

approach of current Indian design standard IS: 1893-2002 (BIS: 2002).

2. Obtaining similar design by using displacement base approach of recent PBPD

method proposed by Chao and Goel (2001).

3. Comparing design as well as their seismic performance through nonlinear static

push over analysis (NSPA).

1.3 Scope of the project:

A four storey Steel CBF under high seismic condition is considered for seismic

design. Due to lack of high capacity/strength of Indian standard hot rolled Steel

sections (SP:6(1)-1964), American Institute of Steel Construction standard

sections (AISC 2005b) with high strength Steel (fy=345Mpa) have been use for

this study.

1.4 Outline of the Project:

The project outline is shown on the next page in the form of flowchart

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Chapter 1 deals with Introduction, advantages of Steel CBF, limitations of code based

design provisions for Steel CBF, objectives, scope of project and outline of report.

Chapter 2 deals with literature review of force/strength based and displacement-based

approach of seismic design for Steel CBF.

Chapter 3 deals with design of a four storey Steel CBF for high seismicity by using

force/strength based approach of current Indian design standard IS: 1893-2002 (BIS:

2002).

Comparison of strength based & displacement

based seismic design of steel concentrically braced

frames

Chapter 1: Introduction

Chapter 2: Literature Review

Chapter 3: Strength Based Design

Chapter 4: Displacement Based

Design

Chapter 5: Comparison between

strength and displacement based

design

Chapter 6 : Findings of study &

Conclusions

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Chapter 4 deals with design of a four storey Steel CBF for high seismicity by using

displacement base approach of recent PBPD method proposed by Chao and Goel

(2001).

Chapter 5 deals with comparing with design as well as their seismic performance

through nonlinear static push over analysis (NSPA).

Chapter 6 deals with findings of study, conclusions, thrust areas and recommendations

derived from this study.

(a)

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(b)

Figure 1.1: Steel CBF used as a structural system

Concentric Braced Frame

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CHAPTER 2

A Review of Seismic Design of Steel Concentrically Braced Frames

And Related Research

2.1 Introduction

The design procedures for regular structures specified in the current seismic codes,

such as IS 1893 PART 1 :2000, are mainly based on elastic analyses under seismic

horizontal forces (Equivalent Lateral Force Procedure), without attempting to predict the

inelastic response. These procedures offer considerable simplification and do not require

the designer to use the understanding of structural dynamics. The structures designed by

these procedures may possess sufficient strength and stiffness to satisfy the requirements

of serviceability limit state. However, the design procedures do not always lead to the

intended failure mode and the expected ductility under severe ground motions. The

energy dissipation capacity of the structure designed by these procedures can be less than

that required to prevent collapse under severe ground motions. Therefore, alternative

design procedure based on inelastic structural analysis and the plastic design should be

adopted for the ultimate limit state.

This chapter begins with reviewing and discussing the current seismic design

codes and provisions for steel concentrically braced frames. After that, related past studies

that addressed the problems of current code procedures or proposed new design methods

based on inelastic analysis and plastic design concepts are also reviewed and discussed.

2.2 EQUIVALENT LATERAL BASE SHEAR FORCE PROCEDURE

The characteristics parameters like intensity, duration etc. of seismic ground

vibrations depend upon the magnitude of the earthquake ,its depth of focus , distance from

the epicenter, properties of soil of medium through which the seismic waves travel and

the soil strata where the structure stands. The random earthquake motions can be resolved

in any directions. Vertical acceleration is considered in large span structures.

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The response of a structure to ground vibrations depends on the nature of

foundation soil, form, material, size and mode of constructions of structures and the

duration and characteristics of ground motion.

2.2.1 Assumptions

The following are the assumptions in the earthquake resistant design of structures:

1. Impulsive ground motions of earthquake are complex, irregular in character,

changing in period and time and of short durations, they, therefore, may not cause

resonance as visualized under steady state sinusoidal excitations, except in tall

structures founded on deep soft soils.

2. Wind, maximum flood or maximum sea waves will not occur simultaneously with

the earthquake.

3. For static analysis, elastic modulus of materials shall be taken unless otherwise

mentioned.

2.2.2 DESIGN LATERAL FORCES

Design Horizontal seismic coefficient

The design horizontal seismic coefficients Ah (cl.6.4.2 of IS 1893 (Part 1): 2000) for

structure is determined from

Ah = .. (2.1)

Where;

Z = the zone factor as given Table 2 of IS 1893 (Part 1):2002, based on classifying the

country in four seismic zones,

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I= Importance factor, depending upon functional use of the structures as given in Table 6

of IS 1893 (part 1) :2002,

R= Response reductions factor, depending on the perceived seismic damage, performance

of the structures, characterized by ductile or brittle deformations, as given in Table 7 of IS

1893 (Part 1):2002.However, the value of (I/R) shall not be greater than 1.0, and

S/g= Average response acceleration coefficient for rock or soil sites as given Fig.2 and

Table 3 of IS 1893 (part 1) :2002.

It is further stipulated in cl.6.4.2 of IS 1893 (part 1) :2002, that for any structure with

undamped natural period of vibrations of the structure (in seconds) T 0.1 second, the

value of Ah will not be taken less than Z/2 whatever be the value of I/R.

2.2.3 DESIGN SEISMIC BASE SHEAR

The total design lateral force or design seismic base shear VB along any principal

direction (cl.7.5.3 of IS 1893 (part 1):2002) shall be determined from the following

equations:

VB = Ah W (2.2)

Where;

W is the seismic weight of the building as given in cl.7.4.2 of IS 1893 (Part 1):2002.

2.2.3.1 Distribution of design force

The design base shear VB shall be distributed along the height of the building as per the

following equation (cl.7.7 of IS 1893 (Part 1):2002)

Qi = (2.3)

Where;

Qi = design lateral force at floor i,

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Wi = Seismic weight of floor i,

Hi = Height of floor I measured from base, and

n = Number of storeys in the building at which the masses are located

2.3 REVIEW OF RELATED RESEARCH ON CONCENTRICALLY BRACED

FRAMES

The design of concentrically bracings may be found in Becker (1995), Becker and

Ishler (1996), Bruneau et al. (1997), Bozorgnia and Bertero (2004), and Williams (2004).

Thus, many studies have been carried out to investigate and revise the design procedures

currently used in seismic codes or to develop new design procedures for the

concentrically braced frames.

Concentrically Braced Frames (CBFs) are very efficient steel structures that are

commonly used to resist forces due to wind or earthquakes because they provide complete

truss action.

Based on research performed during last the last twenty years or so (for example,

Goel, 1992a), current seismic codes such as (ANSI, 2005a) now include provisions to

design ductile concentrically braced frames called Special Concentrically Braced Frames

(SCBFs). Since the seismic forces are assumed to be entirely resisted by means of truss

action , the columns are designed based on axial load demand only, and simple shear

connections are used to join the beams and columns (Tremblay and Robert,2000; Mac

Rae et al., 2004; ANSI, 2005c). It has been estimated that CBFs comprise about 40

percent of the newly built commercial constructions in the last decade in California

(Uriz,2005).This is attributed to the simpler design and high efficiency of CBFs compared

to other systems such as moment frames, especially after the 1994 Northridge earthquake.

Mac Rae has proposed the Steel concentrically braced frames are generally

designed to resist lateral force by means of truss action. Design considerations for

columns in these frames are therefore governed by the column axial force while column

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bending moment demands are generally ignored. However, if the columns cannot carry

moments, then dynamic inelastic time-historey analyses show that a soft-storey

mechanism is likely to occur causing large concentrated deformations in only one storey.

Such large concentrations of damage are not generally seen in real frames since columns

are generally continuous and they possess some flexural stiffness and strength. This paper

develops relationships for column stiffness and drift concentration within a frame based

on pushover and dynamic analyses. It is shown that continuous seismic and gravity

columns in a structure significantly decrease the possibility of large drift concentrations.

An assessment method and example to determine the required column stiffness necessary

to limit the concentration of storey drift is provided.

R.G. Redwood, V.S. Channagiri studied that new provisions of the CSA standard

for steel structures (CAN/CSA-S16.1-M89) dealing with detailing of concentrically

braced frames for seismic design are described and related to requirements of the National

Building Code of Canada. The basis of the new requirements is outlined, and an example

eight-storey frame is used to outline a methodology for the design process for a ductile

braced frame and to illustrate the impact of the provisions.

Tremblay, R. And N.Robert.2000 suggested that Single-storey buildings typically

incorporate a steel roof deck diaphragm that is relied on to transfer lateral loads to the

vertical bracing bents. Modern building codes allow engineers to use reduced seismic

loads in design provided that the seismic load resisting system (SLRS) of the structure is

adequately designed and detailed to withstand strong ground shaking through ductile

response. This approach has been adopted by the North American model codes which

typically include special provisions to achieve satisfactory inelastic seismic performance.

The vertical braces of steel buildings are usually selected as the energy dissipating fuse

element, while the diaphragm and other elements in the SLRS should be designed to have

a capacity that exceeds the nominal resistance of the braces. Steel bracing members

designed for compression inherently possess significant reserve strength when loaded in

tension, which means that large brace tension loads must be considered in the design of

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the surrounding protected structural components. Capacity design seismic provisions have

led to the need for much thicker roof deck panels and more closely spaced diaphragm

connection patterns compared with past practice. This paper provides a description of the

current US seismic design approach and an example as it is applied to a single-storey

building and its diaphragm. An overview of the related aspects of an on-going research

project on the flexibility and ductility of the roof diaphragm in low-rise steel buildings is

also included.

Shaback, B and T.Brown.2003 deduced that the hysteretic behavior of nine square

hollow structural steel (HSS) sections with gusset plate end connections subject to

inelastic cyclic loading has been examined by an experimental investigation.

2.3.1NHRP Seismic Design Salient Feature On CBFs

The configuration of braces also affects system performance. Multiple

configurations of bracing are used, and these configurations are identified in Figure 2.1.

Braces buckle in compression and yield in tension. The initial compressive buckling

capacity is smaller than the tensile yield force, and for subsequent buckling cycles, the

buckling capacity is further reduced by the prior inelastic excursion. Therefore, bracing

systems must be balanced so that the lateral resistance in tension and compression is

similar in both directions. This means that diagonal bracing (Figure 2.1) must be used in

matched tensile and compressive pairs. As a result, diagonal

Fig: 2.1 Various Braced Frames Systems

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bracing (Figure 2.1) must be used in opposing pairs to achieve this required balance.

Other bracing configurations, such as the X-brace, multi-storey X-brace and chevron

brace directly achieve this balance. X-bracing is most commonly used with light bracing

on shorter structures. Research shows that the buckling capacity of X-bracing is best

estimated by using one half the brace length when the braces intersect and connect at mid

section (Palmer 2012). However, the inelastic deformation capacity of the X-braced

system is somewhat reduced from that achievable with many other braced frame systems

because the inelastic deformation is concentrated in one-half the brace length because the

other half of the brace cannot fully develop its capacity as the more damaged half

deteriorates. The compressive buckling resistance of most other brace configurations is

best estimated by considering true end-to-end length of the brace with an effective length

factor, K, of 1.0 (i.e., neglecting rotation stiffness of the brace-to-gusset connection.)

Concentration of inelastic deformation in a limited number of stories occurs with

braced frames. Experiments suggest that multi-storey X-bracing offers a slight advantage

in that it provides a somewhat more robust path for transferring storey shear to adjacent

stories even after brace buckling and fracture because the remaining tension brace may

directly transfer its force to the next storey. Chevron or inverted-chevron bracing

(inverted V- or V-bracing) has intersecting brace connections at mid span of the beam

(Figure 2.1). Large unbalanced forces and bending moments on the beam occur because

the buckling load is smaller than the tensile yield resistance and decreases with increasing

damage. The bending moment increases as the compressive resistance deteriorates and

AISC 341 requires that the beam be designed for these bending moments. Research shows

that the beam deformation associated with the unbalanced forces in chevron bracing

increases the axial compressive deformation of the brace and reduces the inelastic

deformation capacity prior to brace fracture (Okazaki et al. 2012). However, flexural

yielding of the beam increases the damping of dynamic response.

Other bracing configurations are possible, and some are expressly prohibited in

AISC 341. K-braces intersect at mid-height of the column. They have the same

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unbalanced force problem as noted with chevron bracing, but bending moments and

inelastic deformation will occur in the column and may fail, triggering collapse. As a

result, K-bracing is not permitted for the SCBF system. In addition, tension-only bracing

has had relatively poor performance during past earthquakes because the lack of

compressive brace resistance leads to inelastic behavior with slack braces that have no

stiffness until the slack is taken up. The slack braces may lead to progressively increasing

drift and impact loading on the brace, and early brace fracture may occur. Consequently,

tension-only bracing is also prohibited for the SCBF system.

2.4 Performance Based Plastic Design (PBPD) Method

In order to achieve more predictable structural performance under strong

earthquake ground motions, knowledge of the ultimate structural behavior such as

nonlinear relationship between force and deformation and the yield mechanism of the

structure are essential. Consequently, design factor such as determination of appropriate

design lateral forces and member strength hierarchy, selection of desirable yield

mechanism, and structure strength & drift for a given hazard levels should become part of

the design process from the beginning .

The PBPD method uses pre-selected target drift and yield mechanisms as key

performance limit states. These two limit states are directly related to the degree and

distribution of structural damage, respectively. The design base shear for a specified

hazard level is calculated by equating the work needed to push the structure

monotonically up to the target drift to the energy required by an equivalent elastic -

Plastic Single Degree of Freedom (EP-SDOF) system to achieve the same state (Fig

2.2). Also, a new distribution of lateral design forces is used (Chao et al, 2007), which is

based on relative distribution of maximum storey shears consistent with inelastic dynamic

response result. Plastic design is then performed to detail the frame members and

connections in order to achieve the intended yield mechanism & behavior.

.

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Fig. 2.2: PBPD Design Lateral Force

In this design approach the designer selects the target displacements & yield

mechanism & determines the design forces and members sizes for a given a earthquake.

There is no need factor such as R, I & Cd as are required in the current design course and

over which debate already exists. The PBPD design procedures is not to different from

what is done in current practices, yet it can be readily incorporated within the context of

border Performance Bases Earthquake Engineering (PBEE) frame work. It does differ

from the way PBEE is practiced currently which usually starts with an initial design

according to conventional elastic design procedures using applicable design codes,

allowed by a cumbersome and time consuming iterative assessment process by using

inelastic static or dynamic analyses until the desired performance objectives are met. The

iteration are carried out in a purely trail & error manner. No guidance is provided to the

designer as to how to achieve the desired goals such as controlling drifts or the

distributions and extent of inelastic deformation. In contrast, the PBPD method is a direct

design method, which required no evaluation after the initial design because the nonlinear

behavior and key performance criteria are built into the design process from the start. The

design procedure is easy to follow it can be easily programmed as well. Al though not

necessary, structures designed by PBPD could be evaluated by other evaluation methods

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if desired. In cases where significant structural irregularities are present, the method will

provide a good initial design, which may require some refinement through nonlinear static

or dynamic analysis.

PBPD application to concentrically braced frames with degrading hysteretic

behavior due to brace buckling is currently being developed. The results thus far have

been most encouraging

Fig. 2.3: Typical Hysteretic responses for CBF

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CHAPTER 3

Design of a Four Storey Steel CBF for High Seismicity by using Force/Strength

Based

Approach of Current Indian Design Standard IS: 1893-2002 (BIS, 2002)

3.1 Introduction

Seismic designs of structure are based on force/strength based approach used

today and the IS: 1893 (Part I), 2002 code is based on this approach. Seismic designs of

most of the structure are on the basis of lateral force assumed to be equivalent to the

actual loading. It is based on providing the structure with a minimum lateral strength to

resist seismic loads, assuming that the structure will behave adequately in the non-linear

range. The base shear which is the total horizontal force on the structure is calculated on

the basis of structure mass and fundamental period of vibration and corresponding mode

shape. The base shear is distributed along the height of structure in terms of lateral forces

according to code formula. Only some simple constructional detail rules are to be satisfied

as material ductility, member slenderness, etc. This method is usually conservative for

low to medium height buildings with a regular conformation.

Steel CBF is designed as per the IS 800:2007 along with IS 1893 (Part 1):2002 for

site and geometric configurations. In this chapter we formulate the problem and design it

as per the strength based method and obtain the section. For analysis we use ABAQUS

finite element software.

3.2 Case Study

A design case study of 4-storey frames in a study building located in high seismic

zone (Zone V as per IS: 1893-Part-I 2000) for soft soil condition with Maximum

Considered Earthquake (MCE) is considered for the following geometric configurations.

The plan and elevation of this CBF is shown in Figure 3.1.

Figure 3.1: Plan and elevation of four

Given Data:

Elastic response spectra

Damping factor

Site condition

Material property

Selected study frame for code

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Figure 3.1: Plan and elevation of four-storey CBF study building

Elastic response spectra : IS: 1893 (Part 1) 2002.

Damping factor : 5%

: Soft soil

Material property : Fe 345 steel with elastic perfectly plastic

stress strain relationship

Selected study frame for code-based and displacement-based seismic design

storey CBF study building

IS: 1893 (Part 1) 2002.

Fe 345 steel with elastic perfectly plastic

stress strain relationship

based seismic design

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Hot rolled steel section : From AISC standard. (AISC, 2005b)

Table 3.1 Floor wise seismic weight for study building

Floor Level i Floor Height (m) Seismic Weight (kN)

4th

4.0 5000

3rd

4.0 5000

2nd

4.0 5000

1st 4.0 5000

Design:

Design of steel concentrically braced frame along X-X direction,

There are two set of steel CBF in X-X direction as lateral load resisting systems for

earthquake in X-direction.

Thus, seismic weight is distributed equally on each set and floor wise seismic weight

on each set of steel CBF is as per Table 3.2

Total seismic weight, W = 2

Fundamental time period

Total height of building = 16 m

Calculation of Design base shear,

Zone factor Z, is not considered for

Importance factor,

Response reduction factor,

Spectral acceleration,

Figure 3.2: Calculation of

Therefore,

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Total seismic weight, W = 20000 kN

Fundamental time period for Steel CBF and for soft soil condition is,

Total height of building = 16 m

s

Calculation of Design base shear,

Ah =

is not considered for Maximum Considered Earthquake (MCE

Importance factor,

ion factor,

Spectral acceleration,

= 2.50

Figure 3.2: Calculation of Sa/g from elastic response spectra of IS: 1893

condition is,

Maximum Considered Earthquake (MCE ),

from elastic response spectra of IS: 1893-PartI-2002

Design base shear,

Table 3.2 Storey

Floor Level

4th

3rd

2nd

1st

3.3 Design of frame components

Code based design method is an iterative procedure which do not provide design

equation for individual components of Steel CBF. Initial section for column and beam of

CBF are selected from AISC stee

sections, CBF is modeled using B31 (3 dimensional beam element) in ABAQUS 6.9

(ABAQUS, 2009) which is general purpose Finite Element Software. The design is

optimized by elastic analysis of this fram

in Table 3.2), such that demand to capacity ratio is near to unity.

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Table 3.2 Storey-wise Lateral Distribution of Design Base Shear

(kN) (m)

5000 16 1280000 0.534

5000 12 720000 0.30

5000 8 320000 0.133

5000 4 80000 0.033

=2400000 =1.0

3.3 Design of frame components



CBF are selected from AISC steel sections by trial and error method. With these initial



optimized by elastic analysis of this frame under equivalent static lateral load (as obtained

in Table 3.2), such that demand to capacity ratio is near to unity.

(cl. 9.3.1.1, IS 800:2007)

gn Base Shear

(kN)

6675

3750

1662.5

412.5

=12500



l sections by trial and error method. With these initial



e under equivalent static lateral load (as obtained

(cl. 9.3.1.1, IS 800:2007)

Fig: 3.2 Details of beam, column and brace analyzed by code

Table 3.3: Cross Sections of Beam, Column & Brace

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Fig: 3.2 Details of beam, column and brace analyzed by code


Fig: 3.2 Details of beam, column and brace analyzed by code-based method.


W36X441

(BEAM)

W36X800

(COLUMN)

HSS 16X16X0.625

(RECTANGULAR

BRACE)

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Table 3.4: Sectional Properties of Beam, Column & Brace

AISC

SECTION

Ax

(in2)

D

(in)

Bf

(in)

Tf

(in)

Tw

(in)

Iz

(in4)

Ix

(in4)

Iy

(in4)

Zx

(in3)

Zy

(in3)

W36X441 130 38.90 17 2.44 1.36 32100 194 1990 1990 368

W36X800 236 42.60 18 4.29 2.38 64700 1060 4200 3650 743

HSS

16X16X0.625

35 16 - 0.58 - 1370 2170 1370 200 200

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CHAPTER 4

Design of a four storey Steel CBF for high seismicity by using displacement based

approach of PBPD method

4.1 Introduction

It is desirable to design structures so that they behave in a predictable manner.

This can be achieved by allowing for the formation of a preselected desirable yield

mechanism so that the structure has adequate strength and ductility during design level

ground motions. The preselected yield mechanism can be defined as a strong column

weak beam mechanism to prevent formation of collapse mechanisms with poor energy

dissipation capacity for the structure. However, elastic design procedures used in current

seismic code cannot guarantee to design the structure with a desirable mechanism and to

predict the predominantly inelastic nature of the structure response during severe

earthquakes. Therefore, use of plastic theory in seismic design procedure, especially in

performance-based design, is necessary to avoid undesired collapse mechanisms.

Many experimental and analytical studies have been carried out in the past to

investigate the validity of the distribution of lateral forces prescribed by various seismic

design codes, particularly the IS 1893-Part1 Criteria for Earthquake Resistant Design of

Structures, Part 1: General Provisions and Buildings (BIS,2002). For simplicity of the

design procedure, a linear distribution of the equivalent lateral forces has been generally

used in code. However, many studies have shown that this distribution may not be valid in

the inelastic state and may underestimate the storey shears.

Since the performance-based plastic design procedure is primarily based on

inelastic state is used.

Fig 4.1: Target Yield Mechanism of CBF with Chevron Bracing

A design case study of 4

condition and maximum selected earthquake is considered.

4.2 Case Study

For target ductility ratio,

Using elastic response spectra in IS: 1893 (Part 1) 2002.

Damping factor = 5%

Site condition = Soft soil

Material property Fe 3

Hot rolled steel section used from AISC standard.

Fundamental Time Period:

Equivalent fundamental time period of inelastic structure

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A design case study of 4-storey frames as same as in chapter 3, under the soft so

condition and maximum selected earthquake is considered.

For target ductility ratio, t = 4.0

Using elastic response spectra in IS: 1893 (Part 1) 2002.

= 5%

Site condition = Soft soil

Fe 345 steel with elastic perfectly plastic stress strain relationship

Hot rolled steel section used from AISC standard.

Fundamental Time Period:

Equivalent fundamental time period of inelastic structure ,


frames as same as in chapter 3, under the soft soil

45 steel with elastic perfectly plastic stress strain relationship

Where,

= Fundamental time period of linear elastic structure = 0.1 X No of storey = 0.4 sec

t = Displacement ductility ratio

= Strain hardening ratio = 0

The average response acceleration coefficient

Ductility reduction factor

Ductility reduction factor

Energy modification factor

Yield drift and Plastic drift

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Fundamental time period of linear elastic structure = 0.1 X No of storey = 0.4 sec

= Displacement ductility ratio

= Strain hardening ratio = 0

The average response acceleration coefficient Sa/g for and

Sa/g = 1.25

Ductility reduction factor , Energy modification factor

Ductility reduction factor ,

Energy modification factor ,

2 1 0.44

Plastic drift

Fundamental time period of linear elastic structure = 0.1 X No of storey = 0.4 sec

= 5%

For steel moment resisting frames, the yield drift

Assume, = 0.09% = 0.0

Evaluation of Seismic Lateral Force Distr

Table 4.1 Evaluation of Seismic Lateral Force Distribution

Floor Level

4th

3rd

2nd

1st

28

For steel moment resisting frames, the yield drift assumed to be between

% = 0.009

4 1 $%0.009 $% 0.027 Evaluation of Seismic Lateral Force Distribution


(KN)

5000 16 1280000 0.534

5000 12 720000 0.30

5000 8 320000 0.133

5000 4 80000 0.033

=2400000 =1.0

assumed to be between 0.6% to 1%


8.544

3.600

1.064

0.132

=13.34

Calculation of yield base shear

Shear Proportioning Factor

A PBPD method based on inelastic state uses a new term named shear

proportioning factor derived from the concept of the relative distributions is defi

Where, i is the static storey

Vn is the static

distribution shape of the first mode of vibration

Assuming an inve

to derive the static storey

Where, is the lateral force distribution factor,

Where,

wi is the weight of the structure at level

hi is the height of beam level

29

Calculation of yield base shear Vby

=

Shear Proportioning Factor


proportioning factor derived from the concept of the relative distributions is defi

storey shears at level i,

is the static storey shears at the top level computed from the linear lateral force

distribution shape of the first mode of vibration and the exponent b

Assuming an inverted triangular force distribution along the height of the structure

storey shears, the lateral force at level i can be expressed as:

is the lateral force distribution factor, is the total base shea

the weight of the structure at level i

the height of beam level i from the ground,


proportioning factor derived from the concept of the relative distributions is defined as:

shears at the top level computed from the linear lateral force

b is a numerical factor.

rted triangular force distribution along the height of the structure

can be expressed as:

is the total base shear.

VB is the design base shear.

The equation of Vi and

The shear proportioning factor

based plastic design procedure. The factor is directly related to the

and stiffness along the height of the structure. It also represents the variation of

drifts along the height. Therefore, the factor can be

distribution based on inelastic state and to design beams of the structure.

Using the shear proportioning factor, the lateral forces,

the top level n can be written as

Where and i+1 are the shear proportioning factors at level

30

is the design base shear.

Vn put in equation of i

The shear proportioning factor i, plays an important role in

based plastic design procedure. The factor is directly related to the

and stiffness along the height of the structure. It also represents the variation of

drifts along the height. Therefore, the factor can be used to derive a lateral force


Using the shear proportioning factor, the lateral forces,fi and fn, applied at level

can be written as

are the shear proportioning factors at level i and

, plays an important role in the performance-

based plastic design procedure. The factor is directly related to the storey lateral strength

and stiffness along the height of the structure. It also represents the variation of storey

used to derive a lateral force


, applied at level i and at

and i+1, respectively.

Evaluation of Storey-

Table 4.2 Evaluation of Storey

Floor

Level

(m)

(kN)

4th

16 0.53 4140

3rd

12 0.30 2330.4

2nd

8 0.13 1

1st 4 0.03 256.344

Design of Bracing Memb

It is based on following 3 criterias:

Strength Criterion

Fracture Criterion

Compactness Criterion

Strength Criterion:

The braces are designed based on their ultimate state, i.e., tension yielding and

post-buckling, to resist total design storey she

columns. Thus,31

-wise Lateral Force Distribution

Table 4.2 Evaluation of Storey-wise Lateral Force Distribution

(kN)

(kN)

=

4140 4140 1.0 16.00

2330.4 6470.4 1.5628 6.7536

1033.14 7503.54 1.8124 1.9968

256.344 7768 1.8763 0.2556

=6.25 =25.006

Design of Bracing Members:

It is based on following 3 criterias:

Strength Criterion

Fracture Criterion

Compactness Criterion


buckling, to resist total design storey shear, neglecting contribution from

columns. Thus,

wise Lateral Force Distribution

66240

27964.8

8265.12

1025.376

=25.006 =103495.

3


ar, neglecting contribution from

32

()*+,-.*-/,)1 (3. 0.535,)1 cos(:) Table 4.3: Required Brace Strength

Floor Level Vi

(kN)

Vi (for 1 CBF )

(kN)

)1cos (kN)

4 41 4140 1035 1385 2 41 6470.4 1617.5 2164.15 2 41 7503.54 1875.75 2510 1 41 7768

2598.30 2598.30

Designing the braces for the maximum storey shear, i.e., 2598.30 kN, we get the

section HSS 12 X 12 X 0.25 having strength of 2675 kN, thus satisfying the

strength criterion.

Design of Beams:

The post-buckling strength of a brace is taken as 0.5 Pcr for in-plane buckling.

Beams intersected by the braces should be designed assuming that no gravity loads are

resisted by the braces. Those beams should also be designed to support vertical and

horizontal unbalanced loads resulting from the force difference in the tension and

compression braces. The design of beams should follow the beam-column design

requirements due to presence of high axial forces. The unbalanced loads resulting from

the braces are as follows:

= ( .3. 0.535,) cos => ? .3. 0.535,@ sin

Where,

33

Fh is the horizontal unbalanced force

Fv is the vertical unbalanced force

Ry is the ratio of the expected yield strength to the specified minimum yield

strength, taken equal to 1

Py is the nominal yield strength = FyAg , and

Pcr is the nominal compressive strength = Fcr Ag

Table 4.4: Design Parameters for Beams of 4-storey CBF

Floor

Level

RyPy

(kN)

0.5 Pcr

(kN)

Fh

(kN)

Fv

(kN)

Pu

(kN)

Mu

(kNm)

4th 2403.96 270.445 2017.67 1400 3000 9600

The section corresponding to the moment of 9600 kNm is W36X395.

Table 4.5: Sectional Properties of Beam, Column & Brace

AISC

SECTION

Ax

(in2)

D

(in)

Bf

(in)

Tf

(in)

Tw

(in)

Iz

(in4)

Ix

(in4)

Iy

(in4)

Zx

(in3)

Zy

(in3)

W36X395 116 38.40 16.8 2.20 1.22 28500 142 1750 1710 325

W36X441 130 38.90 17 2.44 1.36 32100 194 1990 1990 368

HSS

12X12X0.25

10.80 12 - 0.23 - 248 384 248 47.6 47.6


34



W36X441

(COLUMN)

W36X395

(BEAM)

HSS

12X12X0.25

(RECTANGUL

AR BRACE)

35

CHAPTER 5

Comparison of Code-Based and PBPD Designs

5.1 General

This Chapter deals with comparison of Code-Based and PBPD designs so as to

arrive at more realistic and reasonable design.

The code-based and PBPD designs are compared on the basis of

1) Lighter design.

2) Achieving the assumed fundamental time period in design procedure.

3) Performance in nonlinear static pushover analysis (NSPA).

Following analysis techniques are used for comparison purpose

1) Eigen value analysis:

This analysis evaluate fundamental mode of vibration which is an important dynamic

characteristic of structural system as the base shear demands is entirely dependent on the

fundamental time period.

2) Nonlinear static pushover analysis (NSPA):

Pushover analysis is an approximate analysis method in which the structure is subjected to

monotonically increasing lateral forces with an invariant height-wise distribution until a

structural system undergoes inelastic state. Figure 5.1 shows a typical pushover plot of a

structural system with base shear as ordinate and roof displacement as abscissa.

The various steps involved in carrying out the Nonlinear Static Pushover analysis are as

follows.

1) Determine the gravity loading and the vertical distribution of the lateral loads.

2) Determine the desired building performance level.

36

3) Calculate the status of the structures based on its performance level.

4) Compute the maximum target Displacement, t.

Figure 5.1: Typical pushover curve

5.2 Modeling of steel CBF in ABAQUS 6.9

Both steel CBF design are modeled using B31 element in general purpose FE software

ABAQUS 6.9 (Abaqus, 2009). Typical model of code-based CBF is shown in Figure 5.2.

This figure also shows the boundary conditions of steel CBF.

Figure 5.2: Typical model of code

5.3 Eigen value analysis

Eigen value analysis has been conducted on both designs by Frequency step with

Lanczos eigen solver of ABAQUS 6.9 (Aba

between assumed and obtained fundamental time period of both design. Figure 5.3 present

a typical fundamental mode of code

Table 5.1: Comparison between assumed and obtained fundame

Design

Code-based design

PBPD

37

Figure 5.2: Typical model of code-based CBF in ABAQUS 6.9

5.3 Eigen value analysis


Lanczos eigen solver of ABAQUS 6.9 (Abaqus, 2009).Table 5.1 shows the comparison


a typical fundamental mode of code-based design of four-storey CBF.

Table 5.1: Comparison between assumed and obtained fundamental time period of both

design

T1 (assumed)

(s)

based design 0.68

0.80

based CBF in ABAQUS 6.9


qus, 2009).Table 5.1 shows the comparison


storey CBF.

ntal time period of both

T1 (obtained)

(s)

0.62

1.05

Figure 5.3: Typical fundamental mode of code

5.4 Nonlinear static pushover

NSPA is used to evaluate the expected performance of a structural system by estimating

its strength and deformation demands in design earthquakes. This evaluation is based on

an assessment of important performance parameters, including global drift, inter

drift, and inelastic element deformations. The IS: 1893

recommended lateral force d

model of design is subjected to the unidirectional monotonic push till the respective target

displacement so as to induce significant inelastic deformations in the system. Thereof

displacement versus base shear plot is bilinearized by equating the areas under the actual

pushover curve and the approximate one and yield point

for each design.

38

Figure 5.3: Typical fundamental mode of code-based design of four

Nonlinear static pushover analysis (NSPA):

used to evaluate the expected performance of a structural system by estimating


an assessment of important performance parameters, including global drift, inter

rift, and inelastic element deformations. The IS: 1893-Part I

recommended lateral force distribution is used for NSPA of both design model. Each


isplacement so as to induce significant inelastic deformations in the system. Thereof


pushover curve and the approximate one and yield point and yield base shear is

based design of four-storey CBF

used to evaluate the expected performance of a structural system by estimating


an assessment of important performance parameters, including global drift, inter-storey

Part I-2002 (BIS, 2002)

both design model. Each


isplacement so as to induce significant inelastic deformations in the system. Thereof


yield base shear is obtained

39

Figure 5.4 shows the unidirectional monotonic pushover load on finite element model of

code-based steel CBF

Figure 5.4: Typical pushover load on code-based design of four-storey CBF

Figure 5.5 shows typical deformed shape of code-based design of four-storey CBF obtained

from NSPA. From this deformed shape a soft-storey formation is observed at second

storey indicating that code-based design fails at higher lateral load.

Monotonic uni-directional pushover load

till plastic collapse mechanism

Figure 5.4: Typical deformed shape of

Figure 5.5 shows typical base shear versus roof displacement plot for code

four-storey CBF obtained from NSPA.

40

Figure 5.4: Typical deformed shape of code-based design of four

obtained from NSPA

typical base shear versus roof displacement plot for code

storey CBF obtained from NSPA.

based design of four-storey CBF

typical base shear versus roof displacement plot for code-based design of

41

Figure 5.5: Typical base shear versus roof displacement plot for code-based design of

four-storey CBF obtained from NSPA.

Table 5.2 shows the comparison between design and obtained yield base shear for both

designs from NSPA. From this table it is observed that code-based design is too

conservative as compare to PBPD design. The justification for the same is that PBPD

provides plastic design equations for individual component of steel CBF whereas in code-

based design the elements need to be optimized by an iterative procedure such that

capacity is more than demand.

Table 5.2: Comparison between design and obtained yield base shear for both designs

from NSPA.

Design Vby (Design)

(kN)

Vby (From NSPA)

(kN)

Code-based design 12500 13750

PBPD 7768 7684

42

CHAPTER 6

Concluding Summary and Scope for Future Work

6.1 Summary

Aim of this study is to compare the traditional code-based and recent performance-based plastic

design method for steel CBF. This comparison is based on lighter section for components of CBF

(light weight design), performance in nonlinear static pushover analysis (NSPA). Following points

from design and analysis can be summarized for the comparison

1. Code-based design is more conservative and heavy weight design as it follows strength-

based approach

2. In displacement-based approach significant inelastic deformation capacity of system is

fully utilized hence PBPD design result in light weight system

3. When fundamental time periods of both design as assumed in respective seismic force

calculations are compared with those obtained from eigen value analysis it is observed

that PBPD design is more accurate with less difference in assumed and obtained value.

4. Nonlinear static pushover analysis of these design shows that code-based design is more

prone to have soft-storey which is undesirable collapse mechanism where as PBPD design

achieves a pre-selected yield mechanism and hence effective in utilizing significant

inelastic deformation capacity. Hence it is suggested that existing design standard should

follow the displacement-based approach rather than elastic force/strength-based approach.

6.2 Scope for future work

This study is only limited to low rise CBF system. Following can be considered as scope for

future work

1. Design comparison for medium to high rise CBF.

2. Comparison of seismic performance of design can be evaluated by using nonlinear

dynamic analysis

43

References:

1) N. Subramanian (2008), Design of steel structures, OXFORD UNIVERSITY

PRESS Publication.

2) BIS, IS 1893 (Part 1): (2002), Criteria for Earthquake Resistant Design of structures

Part 1 General Provisions and Buildings, Bureau of Indian Standards, Fifth Revision.

3) BIS, IS 800:2007, General Construction in Steel Code of practice,Bureau of Indian

Standards, Fifth Revision.

4) Subhash C. Goel and Shin Ho Chao (2008), PERFORMANCE BASED PLASTIC

DESIGN EARTHQUAKE RESISTANT STEEL STRUCTURES,

INTERNATIONAL CODE OF COUNCIL Publication.

5) Soon Sik Lee and Subhash C. Goel (2001), PERFORMANCE BASED OF STEEL

MOMENT RESISTING FRAMES USING TARGET DRIFT AND YIELD

MECHANISM, Research Report UMCEE 01-17,.

6) Shin Ho Chao and Subhash C. Goel (2006), A SEISMIC DESIGN METHOD FOR

STEEL CONCETRIC BRACED FRAMES FOR ENHANCED PERFORMANCE,

4th

International Conference on Earthquake Engineering Taipei, Taiwan, Paper No,

227.

7) Swapnil B. Kharmale and Siddhath Ghosh (2012), SEISMIC LATERAL FORCE

DISTRIBUTION FOR DUCTILITY BASED DESIGN OF STEEL PLATE SHEAR

WALLS, Journal of Earthquake and Tsunami, Vol.6, No.1 (2012) 1250004 (24

pages).

8) Macrae, G.A., Y.Kimura, and C.Roeder. (2004) Effect of Column Stiffness on

Braced Frame Seismic Behaviour. Journal of Structural Engineering 130 (3): 381-

391.

9) Miranda, E.and V.V.Bertero. (1994). Evaluation of Strength Reduction Factors for

Earthquake Resistant Design.Earthquake Spectra 10, no.2:357-379.

10) Redwood, R.G and V.S Channagiri. (1991). Earthquake Resistant Design of

Concentrically Braced Steel Frames. Canadian Journal of Civil Engineering 18:839-

850.

44

11) Shaback, B.and T.Brown. (2003). Behaviour of Square Hollow Structural Steel

Braces with End Connections under Reversed Cyclic Axial Loading. Canadian

Journal of Civil Engineering 30:745-753.

12) Tremblay, R. M Bruneau, M. Nakashima, H. G. L. Prion, A.Filiatrault, and R.Devall.

(1996). Seismic Design of Steel Buildings: Lessons from the 1995 Hyogo Ken

Nanbu Earthquake.Canadian Journal of Civil Engineering 23: 727-756.

13) Tremblay, R, and N.Robert. (2000). Seismic design of Low and Medium Rise

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comparison of displacement based and force based method for seismic analysis of concentrically...

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