1 Zheng Ping Wu, Harrison Grierson Consultants Ltd, Christchurch. Email: z.wu@harrisongrierson.com

ADVANCED SEISMIC ANALYSIS METHODS AND APPLICATION TO

EARTHQUAKE DAMAGED BUILDINGS’ STRENGTHENING DESIGN

Zheng Ping Wu1

ABSTRACT: Using advanced modal response spectrum methods, the current practice of the New Zealand standards

and the guidelines/regulations of the national and regional authorities, this paper presents the investigations on the

buildings subjected to seismic damages and proposes respective strengthening methodologies. Two engineering cases

were investigated: one five story office building and one L-shaped two storey retail building. Detailed strength

capacities in terms of New Building Standard (NBS) as well as the overall behavior of the buildings were achieved

based on the detail modal response spectrum analysis. Strengthening was designed successfully based on the latest

engineering standards and regulations. It was found to be imperative to employ advanced modal response spectrum

analysis for all the horizontally and/or vertically irregular buildings. Further researches were recommended: (a) to

refine the formula for seismic shear distribution to roof in New Zealand standard, and; (b) to better understand the

energy dissipation mechanism in the connection details of the concentric braced frames.

KEYWORDS: Modal response spectrum analysis (RSA), concentric braced frame (CBF), New Zealand standards

1. INTRODUCTION

A comprehensive structural assessment for an existing

building is always a complex task, especially for an

earthquake damaged existing tall buildings. They were

constructed decades ago and normally only limited

engineering documents are available. For a structurally

irregular building, it requires the structural engineers even

more to utilize an advanced analysis tool such as

commercially available software ETABS or SAP 2000 to

carry out the full modal response spectrum analysis.

Indeed, the response of any building under the coarse

seismic actions is very complex. It is hard to understand

the overall structural response of the building without

detail computer analysis of the whole structure. It is

required to “collect” sufficient modal responses of the

structure before an almost “true” and “full” response of

the building could be achieved.

Using the advanced modal response spectrum analysis

methods, the current practice of the New Zealand

Standards and the guidelines/regulations of the national

and regional authorities, the purpose of this paper is

threefold:

• To study the structural layout of the building and its

necessity using advanced analysis tool when

carrying out structural seismic response assessment.

• To assess the building’s structural response under

the seismic actions and propose respective repair and

strengthening methodologies. This is to bring the

earthquake damaged building back to its intended

service while being able to sustain the code required

seismic actions.

• To investigate the earthquake resistance capacity of

the individual element and to carry out its

strengthening design if needed.

Engineering projects used are the comprehensive

structural assessments and strengthening methodologies

for two buildings in Christchurch damaged in the

September 2010 and February 2011 earthquakes and

aftershocks. One is a five storey reinforced concrete

office building and another is an L-shaped two storey

reinforced concrete commercial retail building. This paper

also outlines the criteria used in the modal analysis, and;

the guidelines/ regulations in relations to the seismic

modal analysis and the strengthening design.

For both engineering projects, it was aimed to establish:

a) the current condition of the building structures,

including its seismic resistance strength of the individual

structural elements and the building as whole, and; b) the

repair and strengthening methodologies. Based on the site

investigation and the detail modal analysis, the

comprehensive assessment for the building’s strength

capacity was achieved, from which repair and

strengthening methodologies were designed successfully.

Different strengthening concepts were adopted for these

two buildings. While individual column strengthening

was chosen for the five storey building and the upper

level of the two storey L-shaped building, the concentric

bracing frames were adopted for the ground floor of the

two storey building. Discussions were given to the

seismic load distribution to the roof level and the plastic

energy dissipation design of concentric braced frame,

whereby further researches were recommended.

2. STRUCTURAL SEISMIC ANALYSIS

In this paper, modal response spectrum analysis [1]

(RSA) was used. It is an approximate method of dynamic

analysis. For a single degree freedom system (SDOF)

with the same damping ratio and different natural

frequencies, it gives the maximum (peak) response

(acceleration, velocity or displacement) when responding

to a specific seismic excitation. For a structure with n-

degree of freedom, it is transformed to n single-degree

systems, whereby response spectra principles could be

applied to the systems with multiple degrees of freedom.

In general, for a multi-degree freedom (MDOF) system

subjected to ground seismic action, its equation of motion

is expressed as

[ ]{ } [ ]{ } [ ]{ } [ ]{ }g

uBMuKuCuM ɺɺɺɺɺ −=++ (1)

Where [ ]M is the mass matrix. By neglecting the mass

coupling effect, it is a diagonal or uncoupled mass matrix

in the form of tributary lump masses to the corresponding

displacement degree of freedoms. [ ]K is the stiffness

matrix. [ ]C is the damping matrix accounting for all the

energy dissipating mechanism in the structure. { }B is the

displacement transformation vector defining the degrees

of freedoms that the seismic action applies. In general

term, the displacement { }u , velocities { }uɺ acceleration

{ }uɺɺ of the structure and the ground motion g

uɺɺ are all

function of time. In explicit matrix form, the mass,

damping and stiffness are expressed as the follows.

[ ]

=

nnm

m

m

M

⋯

⋮⋮⋮⋮

⋯

⋯

00

00

00

22

11

(2)

[ ]

=

nnnn

n

n

ccc

ccc

ccc

C

⋯

⋮⋮⋮⋮

⋯

⋯

21

22221

11211

(3)

[ ]

=

nnnn

n

n

kkk

kkk

kkk

K

⋯

⋮⋮⋮⋮

⋯

⋯

21

22221

11211

(4)

For a multi-degree of freedom (MDOF) system, it is often

accurate enough for a general structural engineering

application not to carry out a response history analysis.

These structures are often excited by a single component

of the ground motion at one time (e.g. acceleration in

either x-x or y-y direction), where multiple support

excitation is not considered. In other words, the

simultaneous action of other two components is not

considered. Also, all the supports of the building structure

are assumed to be excited simultaneously by the same

excitation. Based on these assumptions, the response

spectrum analysis procedure calculates the peak response

values of forces and deformations over the duration of the

earthquake-induced excitation directly from the

earthquake response spectrum without undertaking

response history analysis of the structure. By doing so, the

dynamic analysis is reduced to a series of static analyses.

For each mode, the static analysis for a structure subjected

to forces, fn, produces the respective modal response, n

φ .

It is then multiplied by the spectral ordinate, n

A , to

obtained the peak modal response rno, i.e.

{ }nnno

Ar φ= (5)

In order to find out the modal response n

φ of the

structure, [ ]C and g

uɺɺ are set to be zero in Equation (1), it

then becomes

[ ]{ } [ ]{ } 0=+ uKuM ɺɺ (6) It is further rearranged to

[ ] [ ] { } 02 =

n

MK φω (7)

Where { }

nφ is the deflected shape matrix, i.e.

dimensionless natural mode shapes. Solution to this

equation is obtained using its corresponding natural

frequencies i

ω by setting

[ ] [ ] 02 =

MK ω (8)

Having achieved the mode shapes { }n

φ , the maximum

(peak) response can be established using the method

shown in Equation (5) or graphically shown in Figure 1

below.

Figure 1: Resultant response and modal components Mode shapes of low-order mathematical expression tend

to provide the greatest contribution to structural response.

As orders increase, mode shapes contribute less, and are

predicted less reliably. It is reasonable to truncate analysis

when the number of mode shapes is sufficient.

In the above procedure, one fact is worthwhile to be noted

that, although the response spectrum analysis solves a

series of static analyses, it is still a dynamic analysis

procedure due to that it adopts the vibration properties in

its procedure development. These properties are natural

frequencies, natural modes and damping ratio. These are

the dynamic related nature of the structure. It also uses the

dynamic characteristics of the ground motion through its

response (design) spectrum. One of the main advantages

of RSA is that these dynamic features have been done in

developing earthquake response spectrum, whereby the

earthquake excitation has been characterized by the

smooth design spectrum.

3. ANALYSIS CRITERIA FROM THE

CODES AND STANDARDS

In order to ensure the reliability of the structural seismic

analysis, especially the commonly used modal response

spectrum methods, the structural design codes and

standards of every country/region provide a full set of

criteria that governs and verifies the results of the

computer analysis. In New Zealand codes, these are

mainly given in AS/NZS 1770.5: 2004 [2]. They are a)

the mass participation ratio; b) the base shear ratio, and;

c) methods of the modal combination. In addition, NZS

3101 [4] requires: d) reduction factor for the reinforced

concrete structural members: beams, columns, walls and

floor slabs.

3.1 MASS PARTICIPATION RATIO

For the modal response spectrum analysis, it is required

by AS/NZS 1170.5:2004, that sufficient number of modes

shall be included to ensure the minimum 90% of the total

mass participated in the dynamic calculation. It is

particularly important for each of the structure’s

orthogonal principal directions.

3.2 BASE SHEAR RATIO

Theoretically, the design spectrum used in the modal

response analysis consists of pairs of values: period

versus acceleration or period versus displacement. These

acceleration or displacement values obtained from the

geological data for the particular site have often been

normalized. It means that the values of acceleration or

displacement have been divided by a number (i.e.

normalization factor) which represents some reference

value. One of the commonly used normalization factors is

'g', the gravity acceleration. In order to reinstate the actual

seismic magnitude, a scale factor is required in the

computer analysis. It can be initially calculated as the

follows for the units of kN-m.

µk

SfactorScale

p×= 81.9 (6)

Where p

S is the structural performance factor. In

accordance with AS/NZS1770.5:2004, µk is given as the

follows. For soil classes A, B, C and D

µk µ= For sT 7.0

1≥ (7a)

1

7.0

)1(1 +

−=

Tµ For sTs 7.04.0

1<≤ (7b)

For soil class E

µk µ= For sTs 5.10.1

1<≤ (7c)

1

7.0

)1(1 +

−=

Tµ

For sTs 0.14.01

<≤

and sT 5.11

≥ (7d)

If kip-in units are used in the computer analysis, 9.81

shall be replaced by 386.4 (in/sec2) in Equation (6).

After initial analysis, this initial calculated scale factor

should be reviewed based on the resulted base shear due

to all modes (i.e. the sufficient number of modes that

achieves 90% mass participation). The scale factor shall

then be adjusted to a value such that the dynamic base

shear reaches more than 80% of the base shear calculated

using static equivalent method.

3.3 MODAL COMBINATION

To achieve the maximum (peak) response of the structure

under the ground seismic actions, various modal

combination methods are available, namely: i) square root

of the sum of the square (SRSS); ii) root mean square

method; iii) complete quadratic combination (CQC)

method, and; iv) absolute sum (ABSSUM) method.

Research had shown that ABSSUM gives always an

overestimate the response. Commonly adopted ones are

hence CQC and SRSS methods.

In AS/NZS 1170.5:2004, it is recommended that: a) When

the modal responses for different modes are not coupled,

SRSS shall be used; and b) When the modal responses for

different modes are coupled, CQC combination method

shall be used. In practice, due to the complex of the

structure layout, CQC shall be used in most situations.

In engineering application, the seismic actions in two or

more orthogonal horizontal directions are often analyzed

and combined for design. To combine the effects of these

orthogonal directions, either SRSS combination method

or by using the load combinations could be used.

3.4 MEMBER REDUCTION FACTOR

For the concrete structural members, cracking shall be

taken into account in the seismic response analysis to

obtain the reliable computer results. This can be

facilitated by using the effective section properties for the

respective forces, for which the guidelines could be found

in Section 6 of NZS3101: Part2:2006.

For the applications presented in this paper, the following

reduction factors were adopted: For wall: a) 1.0 (i.e. no

reduction) for the horizontal axial forces, shear forces of

both in-plane and out-of plane; b) 0.33 for vertical axial

forces; and c) 0.25 for the in-plane and out-of-plane

moment forces. Reduction factor of 0.8 and 0.4 were used

for the concrete columns and beams, respectively.

4. EARTHQUAKE DAMAGED

BUILGINGS’ ASSESSMENT

Two cases were analyzed using the modal response

spectrum method based engineering software ETABS:

one two storey L-shaped commercial retail building and

one 5 storey office building. Both buildings were

damaged in September 2010 and February 2011

earthquakes and aftershocks. The purpose was to carry

out structural assessment and propose strengthening

methodologies to bring the buildings back to service

while meeting current statutory requirements of the

structural strength capacity, i.e. minimum 67% strength of

New Building Standard (NBS).

For the two storey L-shape building, its L-shape layout

produces the horizontal torsion deformations under

seismic actions. On the first floor level, there are

terminations of the masonry walls for the stair wells at the

both ends of the L-shape and the terminations of the

centre core walls. All these together produce both

horizontal and vertical structural irregularity of the

building.

For the five storey office building, its core walls were

arranged on one side of the building, which makes the

structure subjecting to large stiffness eccentricity in

horizontal plan, hence producing torsion deformation

under seismic actions. In vertical elevation, the irregular

window openings and the reinforced concrete wall filled

external wall have all accumulated up the vertical

irregularity.

Hence, in accordance with Section C4.5 of NZS1170.5

Supp 1:2004, both buildings shall be analyzed using a

rigorous method for its seismic response.

For both cases, accidental eccentricity considered was

± 0.1 times the plan dimension of the structure

perpendicular to the action of the seismic acceleration.

Based on AS/NZS1170.0:2002 [3], following load

combinations were analyzed for the earthquake effects to

the building structures.

1) G +ΨE Q + Ex-direction + 0.3 Ey-direction

2) G +ΨE Q + 0.3 Ex-direction + Ey-direction Where ΨE is the earthquake combination factor for the

live loads.

4.1 APPLICATION I: FIVE STOREY OFFICE

BUILDING

As shown in Figure 2, the five storey building,

approximately 20 m x 30 m in plan, was constructed in

1952 as an extension from its two storey existing factory

building next. It was the main building of the

entertainment complex called “Sol Square” in the centre

Figure 2: Five storey reinforced concrete framed office

building (Typical floor plan layout) of Christchurch before the major earthquakes. It had a

reinforced concrete beam and column frame system to

resist vertical and horizontal loads with reinforced

concrete floor slabs throughout all floors providing

diaphragm actions. Core-wells were arranged on one side

of the building at the front and rear for the access stairs

and the lifts. External wall were of brick infill to the

frames, except the rear walls were of reinforced concrete

wall on 3rd

and 4th

floor. The front wall was of brick

veneer wall supported on the frame beams. The

foundations were separate footings for the internal

columns and strip footings on the perimeters. The internal

footings were tied in both directions by the gird beams in

both directions. The building had gone through the

alterations on the ground floor and the top floor in around

1995 and 2000.

4.1.1 Summary of the Earthquake Damages Site inspections were carried out in July and August 2013

to identify the damage extents to the building. It was

found that the damage was of substantially structural to

the reinforced concrete walls and the columns throughout.

Typical damage cracks are shown in Figure 3.

a) Horizontal cracks in column at the beam’s soffit

b) Cracks in reinforced concrete stair well wall Figure 3: Typical earthquake damage

4.1.2 Structural Assessment and Strengthening

Design Based on the existing drawings and the site inspection,

ETABS models was set up to analysis the structural

response under the seismic actions, as shown in Figure 4.

To achieve 95% mass participation ratio, 20 modes were

included in the calculation. The first five modes are

shown in Figure 5 to Figure 9. It was seen that the

building undergoes substantial twisting in the primary

responses. The transverse direction of the core wall (i.e.

x-direction) subjects to large deformation as a result of

the twisting. It was also shown that the external reinforced

concrete parapet wall on each floor level was weak in its

out-of plane direction during response to the earthquake.

Based on the ETABS results, the beams and columns

were all checked. The results were expressed as the

strength capacity over the force demands in terms of

percentage of the New Building Standard (%NBS). Figure

10 shows the results for the frame at the front wall. It was

Figure 4: ETABS analysis model

Figure 5: Mode 1

Figure 6: Mode 2

Figure 7: Mode 3

Figure 8: Mode 4

Figure 9: Mode 5 found that the building was weak in resisting lateral

seismic loads. This is quite common for the old buildings

in Christchurch. Historically, the old buildings were

designed based on much smaller seismic resistance

requirements than it is in the current practice. The

engineer at old time found that the building design was

actually governed by the vertical gravity load other than

the seismic lateral loads.

To strengthen the building, two schemes were proposed

for the upper structure: 1) to strengthen all weak columns;

and 2) to strengthen the selected columns in combination

of adding several shear walls. The first scheme maintains

the current seismic resistant frame system; whilst in the

second scheme, the shear walls would be added and

become more effective in reducing the twisting of the

building. Figure 11 shows the typical strengthening

design for the columns. Both schemes require the

foundation strengthening.

For the foundation strengthening, a raft foundation was

proposed. It aimed to reduce the bearing pressure as the

geotechnical investigation found that the bearing capacity

of the ground was actually much lower than the required

capacity, especially for the service limit state. By using

the raft foundation, it would also improve the building

behavior during seismic induced liquefaction events by

bridging over the liquefied zone in the instance of strong

earthquake.

Figure 10: Strength %NBS for the front frame

Figure 11: Front and rear frame column strengthening

These proposed strengthening designs were carried out

successfully and presented to the client in time. However,

due the significant cost of the strengthening, the decision

was made to demolish the building for the redevelopment

by its new owner.

4.2 APPLICATION II: L-SHAPED TWO STOREY

RETAIL COMMERCIAL BUILDING

As shown in Figure 12, the L-shaped two storey

commercial retail building located in the north of

Christchurch was constructed in 1987 with the ground

floor being un-reinforced concrete slab-on-grade. The

first floor was constructed of 75 mm reinforced concrete

topping on 75 mm thick precast planks spanned on

reinforced concrete beams. The north and west ends of the

building have precast concrete and reinforced masonry

concrete walls surrounding stair wells for accessing to the

upper floor. The central lift core located on one side of the

“L” shape corner was constructed using reinforced

concrete masonry. The lateral load resisting system for

the lower floor consists of the concrete shear walls

located in the middle and two building ends, whilst the

upper floor’s lateral resistance is dependent on the

cantilever capacity of the individual columns due to the

fact that there was no roof bracing constructed. The

building is founded on 150mm square by 9.5 m long

precast reinforced concrete driven piles.

Figure 12: L-shaped two storey retail commercial

building (Ground floor plan layout)

a) Cracks in reinforced concrete column at first floor

beams’ soffit

b) Vertical cracks in ground masonry wall Figure 13: Typical earthquake damage

4.2.1 Summary of the Earthquake Damages Series of site inspections were carried out since the major

earthquake in September 2010 and the interim detail

engineering evaluation (DEE) reports were produced for

the client to monitor the status of the building and to

assess the building’s suitability for its service continuity.

The latest site inspections were conducted in May and

June 2013. Structural damages are: a) substantial

subsidence of the un-reinforced concrete ground slab; b)

horizontal cracks in the columns at the soffit of the first

floor beams, and; c) cracks in the ground masonry walls.

Figure 13 shows the typical damages.

4.2.2 Structural Assessment and Strengthening

Design Based on the existing drawings obtained from the

Christchurch City Council and the site inspection, ETABS

model as shown in Figure 14 was set up to analysis the

structural response under the seismic actions so as to

establish the strength status of the building.

Figure 14: ETABS analysis model At the beginning of computer analysis, 15 modes were

included in the calculation. However, this could only

achieve around 75% mass participation. After few trials,

90 modes were included in calculation. It achieved more

than 97% mass participation for the lateral translational

actions and more than 95% mass participation for the

rotational action in all x-x, y-y and z-z direction. To

include so many modes in achieving the required mass

participation shows that the structure’s seismic response

was mathematically highly loosely ‘scattered”, or

structurally extremely “irregular”. It proves again that the

modal response spectrum analysis was imperative in such

Figure 15: Mode 1

Figure 16: Mode 2

Figure 17: Mode 3

Figure 18: Mode 4

Figure 19: Mode 5

Figure 20: Mode 6

structural layout. Figure 15 to Figure 20 show the first six

modes. It was seen that the primary modes exhibited

substantial twisting and “open-up/close-down” of the “L”

shape.

With regards to the base shear and the share distribution

to the storey levels, Table 1 and Table 2 show the seismic

load distribution to the roof and the first floor calculated

based on the ETABS calculation and the static equivalent

methods.

Table 1: Seismic Loads Based on ETABS (kN)

DL SDL LL Mass: DL

+ SDL +

0.3 LL

Seismic

force for

ETABS

Total

seismic

force

Roof 831.1 274.8 0.0 1105.9 694.4 6315.5

First

Storey

7258.9 955.8 2723.9 9031.8 5621.2

Table 2: Seismic Loads Distribution: static equivalent (kN)

Height

(m)

Mass x

Height

0.08 x

Base

shear

0.92 *

Contribution

ratio

Storey

seismic

force

Based on

Cd(T1) x

mass

Roof 2.55 2820.0 505.2 482.2 987.4 688.9

First

Storey

3.45 31159.9 5328.1 5328.1 5626.6

Based on the ETABS calculation, the primary period T1 =

0.536 second and the total mass ( G + ΨE Q ) for seismic

action is 10137.7 kN. The resulted Cd (T1) = 0.696, and

the base shear = 7055.9 kN, respectively. The base shear

from ETABES is 6315.6 kN. Hence the ratio of ETABS

calculated base shear to that of the static equivalent

method was 89.5%. It is greater than the code required

80%, hence satisfactory.

With regards to the seismic shear distributed to the roof, it

was seen that the static calculation was 43.3% greater

than that of the ETABS calculation. However, the ETABS

result agrees very well with the results of the roof mass

multiplies )(1

TCd

.

Based on the ETABS results, the strength checks were

carried out. It is found that the existing columns had

approximately 60% of the current New Zealand Standard

required strength, i.e. 60% New Building Standard,

(NBS). It would explain very well why the upper columns

and walls did not crack during the two major Christchurch

earthquakes in 2010 and 2011. Based on the static

equivalent calculation, the strength would be around

40%NBS. If that were the case, the upper columns should

have been failed. There should be at least some hairline

cracks on the surface of the upper columns, which was

not the case based on the detailed series of site

inspections. To strengthen the upper columns and wall to

100%NBS, box jacketing to the half height of the upper

columns and steel member (PFC) strengthening to the full

height of the upper wall were adopted.

Based on the detailed site inspections and comprehensive

structural analyses, concentric braced frames (CBF) on

the ground floor were selected together with the ground

tie beams system.

Figure 21 shows the strengthening plan layout, where the

CBFs were designed to enhance the lateral seismic load

resistance from the upper level to the ground. The tie

beams were designed as the collectors to ensure the

diaphragm actions of the first floor being transferred to

the CBFs. They were to be fixed to the transverse

reinforced concrete frame beams and the first floor slabs.

These collector beams also worked as perimeter ties of

the building.

Figure 22 shows the typical layout of the CBFs. The

connection details to the base were given in Figure 23,

where clear space of 40 mm (i.e. two times of the

connection plate thickness) was given to facilitate the

plastic deformation of the connection during seismic

events.

Figure 21: Strengthening layout plan Based on the geotechnical investigation, the site is

subjected to liquefaction in the layers from 1.8 m to 2.6 m

and 7.0 m to 8.2 m. Both layers are well within the depth

of the piles. It was hence imperative to ensure the

robustness of the critical columns in the strong earthquake

events. As such, ground tie beams were designed to

bridge these critical columns to the adjacent pile

foundations. Figure 24 shows the details of the ground

beams at the location of these critical columns, which in

this case was defined as the columns located close to the

location of the CBFs.

Figure 22: Conccentric bracing frame (CBF)

Figure 23: Strengthening layout plan

Figure 24: Ground tie beam details considering

liquefaction

5. DISCUSSION AND FURTHER

RESEARCH RECOMMENDATION

5.1 VERTICAL DISTRIBUTION OF THE BASE

SHEAR

The total base shear is distributed to each storey in

according to the contribution of the storey mass

production with its height from the base. For a building

with the uniform floor mass and uniform storey heights,

the distribution shape is an inverted triangle. Furthermore,

AS/NZS code for seismic action recognizes that the first

mode distribution fails to account for the effect of the

higher modes. It tends to increase the shear in the upper

storeys. It defines the shear distribution as given in

Equation below.

+= ∑

=

n

iiiiiti

hWhWVFF1

)(/92.0 (8)

Where VF

t08.0= at the top level and zero elsewhere.

V is the total base shear. i

W and i

h are the storey mass

and its height from the base.

Similar consideration has been given in the Uniform

Building Code (UBC) [5] and in the National Building

Code of Canada (NBCC) [6, 7].

In addition, NBCC and UBC recognize the influence of

the building’s primary period， which reflects the overall

stiffness of the building structure. The distribution of

shear is given as

−+= ∑

=

n

iiiiitti

hWhWFVFF1

)(/)( (9)

Where t

F is defined as follows.

0=t

F 7.01

≤T (10a)

VTFt 1

07.0= 6.37.01

<< T (10b)

VFt

25.0= 6.31

≥T (10c)

It is seen that, in NBCC and UBC, extra distribution to

the roof level increases with the increases of the primary

period or the decrease of the overall building stiffness.

Furthermore, it is worthwhile to note that UBC has been

replaced by the new International Building Code (IBC).

Its Section 1613 uses the earthquake forces calculation of

ASCE 7 [8]. It defines the vertical distribution of the base

shear as below.

VW

WF

i

i

i

∑= (11)

This distribution refers to the effective mass only.

By comparing these four codes, it is found that the static

equivalent method formula given in NZS1170.5:2004

gives the greatest forces for the lower period building and

the lowest force for the higher period building. In the

second case study of this paper, it shows the

overestimation was substantially around 45%. As this

formula is a primary base for the daily seismic

engineering design. It would be of greatly worthwhile to

investigate further on this issue to avoid both under

estimate and over estimate of the base shear distribution

to the roof level.

5.2 CONCENTRIC BRACED FRAMES

In order to resist the seismic lateral forces, concentrically

braced frames (CBFs) [9, 10] or eccentrically braced

frames (EBFs) are the commonly used. Historically EBFs

have been developed to accommodate the architectural

requirements for openings, where its bracing members are

required to be offsite from the column or avoid the

intersecting with the floor beams. In design, both frames

need the appropriate selection of its local (e.g. plate/wall

thickness) and global (i.e. member itself) slenderness of

the bracing members such that adequate post-buckling

inelastic deformation could be facilitated. Apart from this,

the difference lies in their connection details. Figure 25

and Figure 26 are the different connection configurations

for EBFs and CBFs. While the EBFs use the “link

element”, the CBFs use the linear or elliptical clearance to

establish a plastic hinge zone to dissipate the energy when

subject to seismic actions.

(a) EBF’s connection I (b) EBF’s connection II Figure 25: Different connection configurations of EBFs

(a) CBF’s connection I (b) CBF’s connection II

(c) CBF’s connection III Figure 26: Different connection configurations of CBFs From these connections layout, it is found that the

connections for CBFs are simplest and most cost

effective. It hence becomes a practical and economical

structural solution for many applications. In HERA

Report R4-76, Figure 26 (a) is recommended as the

connection detail for the CBFs. However, if the complete

understanding could be established for the connection

shown in Figure 26 (b), it would made the CBFs much

more preferred seismic resistant bracing frame.

6. CONCLUSION AND REMARKS

Using advanced modal response spectrum analysis, the

current practice of the New Zealand standards and the

guidelines/regulations of the national and regional

authorities, this paper presents the investigations on the

structural response subject to the seismic actions and

proposes respective repair and strengthening

methodologies. Two engineering cases were investigated:

one five story reinforced concrete office building and one

L-shaped two storey reinforced concrete commercial

retail building. Detailed member capacities in terms of

New Building Standard (NBS) as well as the overall

behavior of the buildings were achieved based on the

detail modal response spectrum analysis results.

Strengthening of the building’s overall capacity as well as

the individual member were designed successfully based

on the latest engineering standards, guidelines and

regulations. It was found to be imperative to employ

modal response spectrum analysis for all the buildings

with vertical and/or horizontal irregularities so as to

establish its reliable structural response under seismic

actions. This is true even for the two storey irregular

buildings. In addition, discussion was given to the seismic

shear distribution to the roof level and the plastic energy

dissipation design of the concentric bracing frame

connections, from which recommendations for further

research were given.

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