Seismic Analysis in Moderate and Maximum Loading

TITLE: SEISMIC ANALYSIS IN MODERATE AND MAXIMUM LOADING
1.ABSTRACT
In this paper seismic response of two buildings are analyzed. One of the building is located in Berkeley
which experiences enormous amount of seismic activity, while the other building is located in Hatta
region in the middle East where earthquakes are not a normal occurrence. In the calculations of the
seismic response of the two conditions the linear state of stress is frequently used. As specified by
Eurocode 8(EC 8), four methods can be used in this analysis but only equivalent lateral force(ELF) and
modal response spectrum analysis(MRA) are considered.
The choice of the two methods was appropriate since it was necessary to use a linear and a non-linear
method for analysis in order to obtain better behavioral representation of the building materials. For the
non- linear analysis ductility was the vital material property which was used to obtain accurate data. Since
a 12 stories building has a lot of complexity in its analysis, it was important to do various assumptions,
these assumptions made it easy to obtain shear lateral load, natural period and Eigen values used in the
calculations. In the ELF method horizontal force was used as the major seismic loading. With this factor
the higher frequencies which were obtained were limited in making decisive influence on the seismic
behavior of the building. For the modal response Analysis complete quadric combination method was
used(CQC), this is because the Eigen values which were obtained by the software were mutually
independent.
2.INTRODUCTION
SeismoArtif software was used in both the ELF and modal spectral analysis. There were a lot of finite
element Analysis calculations which were tiresome to do using hand calculations. This involved the use
of Eigen vectors and values which were important in obtaining the seismic response of the two buildings.
Also this software was used to get the material geometrical non-linearity. Since the building designs were
not constrained to certain parameters the appropriate Eigen values were used to simplify the analysis of
the building, this made it easy to get the correct columns, beams and slab dimension which were
recommended according to the seismic loading of the area.
For this simplification to work well the structural system were assumed to have only three degrees of
freedom, this minimizes the calculations complexity and also makes them reliable since only important
parameter are considered. In the stories level Eigen modes were normalized. The following were the
boundary conditions used.
ϕ1=0.6219 s
ϕ2=1.091 s
From the finite element modelling(FEM) analysis, the building material were considered to behave
linearly. Due to the difference in seismic loading a considerable difference in the deflection of the
material was experienced. When the building frame consisted of flexible beams the deflection was as
follows.
Hatta region=0.002002m
Berkeley region=0.002348m
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When rigid beams were considered in the analysis, there was a significant reduction in the overall
deflection.
Hatta region=0.00157214m
Berkeley region=0.00158098m
3.DECLARATION
I hereby declare that the work presented in this paper is entirely my own. There is no any academic fraud
presented in this thesis. Therefore, this paper has never been submitted in any level of learning institution.
For all the documentation used in this research appropriate credit has been given to the respective authors
by the referencing of the work. There is no plagiarism in this paper hence it is academically valid.
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4.TABLE OF CONTENT
1.ABSTRACT…………………………………………………………………………………….………..1
2.INTRODUCTION…………………….………………………………………………………… ......…2
3.TABLE OF CONTENT……………………………………………………………………….…..….….3
4.DECLARATION ………………………………………….………………………..........…… .….…..4
5.LITRATURE REVIEW……………………………….…………………………….. ….………….…..5
Section 1………………………………..…………………………… ………………...…….…..5
6.DATA ANALYSIS……………………………………………………………………………… ….…12
Section 2……………………………………………………………………… …….…..…....….12
Section 3……………..…………………………………………………………….… ……….…15
7.DISCUSSION………………….………………… ………………………………………...…………16
Section 4………………………………………………………………………………………….19
8.RECOMMENDATION…………..…………………………………………………………………….23
9.CONCLUSION……………………....…………………………………………………………..……..23
10.REFERENCES……………………………………..……………………………………...………….24
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5.LIST OF FIGURES
Figure 1 seismic zones…………………………………………………………………….………5
Figure 2 lateral load resisting system………………………………………….……….………….5
Figure 3 effect of stiffness…………………………………………………………...…………….6
Figure 4 dimensions of structural members…………………………………………..…..……….8
Figure 5 equivalent lateral force (in x direction) ………………………………………..…….…..8
Figure 6 application of lateral force in (y-direction) ……………………….…… ……... ….…....9
Figure 7 equivalent lateral drift(Hatta)……………………………………….…………..… …....9
Figure 8 equivalent lateral drift(Berkeley)…………………………………….…………… ……10
Figure 9 site coefficients……………………………………………………………..……… ……11
Figure 10 approximate mass of individual levels………………………………………..… ……..12
Figure 11 graph showing the computed drifts………………………………………….…… ……13
Figure 12 table of p-delta effects……………………………………………… ……...…… ……13
Figure 13 development of elastic response spectrum…………………………………...…… …..14
Figure 14 table of computed values of natural period (extreme loading)………………………….15
Figure15 table of computed values of natural period (mild loading) ………………………… …16
Figure 16 computed stories shear………………………………………………… ………..……..19
Figure 17 comparison table for ELF and modal response spectrum………………………………19
6.LITERATURE REVIEW
Section 1
(i)Adherence to the building design codes.
It is vital that the building design engineer follows a specified procedure which will allow, that the
building is safely design. This ensures its stability in hazardous cases such as occurrence of an earthquake
with high magnitude. For the building to withstand collapse the engineer is required to do a requisite post
performance test on the building. For this to be successful adherence to the following procedure is
compulsory(EeroCode8,1998).
(i)It is important to maintain the building with a simple geometry. The two buildings situated in Berkeley
and Hatta region will follow this design code. The building floor plan is rectangular. Designing the
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building with the appropriate proportions such as the proper aspect ratio and correct slenderness is also
important.
(ii)Adoption of a structural system, this system will be used to resist lateral loads made to the building
columns and beams. Structural walls in RC buildings are mostly preferred than the other types since they
have an efficient performance in areas where seismic activity is experienced.
(iii)Determination of individual sizing element of the building, this should be based by using appropriate
ratio and cross section which require minimal structural members to be reinforced.
(iv)The identification of the building collapse mechanisms. In case of disaster the engineer should have a
hint on how the building columns and beams will behave on failure. Usually in the frame structure
presence of plastic moment hinges ensure that the beams have good rotational ductility which is required.
(v)Preparation of structural analysis model this will be done by obtaining the building dimensions and
details from the available design strategies. The inter stories drift, horizontal deformation and the
elasticity of the building member are to be considered. For this step it is vital to apply design using lateral
forces, this can be done by performing structural analysis and measuring the stress results from the
structural elements (Bisch, Caralo et al ,2012).
(vi)In this last step, final touches in the design process will be done. Minor flaws will be rectified this will
then be followed by the following sequence of activities.
a) Conducting soil analysis underneath the building, the soil should be able to resist any major
shaking of the ground and should always remain intact or minimally deform.
b) The design foundation layout
c)Calculation of building joints such as wall to beam, beam to column and slab to wall distance.
d)Beams should be strong enough to withstand flexure, shear and have the adopting capacity to
resist deformation.
As per the Indian seismic code the earthquake is always a random event and it always have a time
constraint in its occurrence. But according to most earthquakes design codes, the vibration cause by
occurrence of earthquake causes an induced inertial forces which directly act at the building foundation.
This induced force is called the seismic design Base shear and it is this quantity which is always involved
in the force-base earthquake-resistance of story buildings. Furthermore, shaking of most building is
attributed to the frequency of the vibrations and its natural periods (Kalkam, A.K Chopra,2010).
There are also other types of codes that reflect the structural flexibility factor of the building, this code is
used to ensure that the building constructed are economical and they can also allow the building to
undergo damage so as to be able to reduce the overall cost of construction.
Another code used by structural engineers is the deterministic upper bound value. Because parameters
such as base shear and importance factor are obtained by uncertainties it is important to use this code to
ensure the design method objective is to create an earthquake-resistance design and not an earthquake
proof design which can be uneconomical (FeilFar & Fichinger,1998). As per the Indian design code the
design base shear force is given by;
Seismic Zone V IV III II
Z 0.36 0.24 0.16 0.10
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Fig1.
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Fig2
(ii)Structural Configurations
In order to do correct structural analysis, it is important to note the building dynamic characteristics which
are affected by the oscillation of the building due to inertia forces. For the building located in Hatta this
rule can be exempted but for the building in Berkeley it is important to analyze the Natural period of
earthquakes that occurs at the area. The natural period of the building can be calculated using the
following equation (Feisher & Goel,2006).
Tn=2 π √ m
k
Considering that both building have equal weights the difference of natural period will be minimal
considering they encounter same instance of seismic activity. Building usually oscillate in The X, Y or Z
direction or by rotating.
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0
1
2
3
2 3 40 1
Design Acceleration Spectrum( S a /g)
Fundamental Translational Natural PeriodT (s)
Soil Type II
Soil Type III
Soil Type I

Factors influencing natural period
(i)The building structural element size this includes the beam, columns and slab dimensions
(ii)Loading
Unit weight of infill wall=density of the wall x total wall volume.
Wall openings
Window =2x1.5m3
Doors=3 x1.5 m3
Floor load=10kN load
Infill wall height=2.2m
Beam dead load=1.2kN
The effect of stiffness
To understand the effect of natural period on the stiffness of the building we will use details of 12 stories
buildings for analysis. The table below shows the range of the appropriate column dimensions.
Building Descriptions No of stories X-direction
bays
Y-direction
bays
Column
dimensions(mm)
Location
1(Hatta)
Moderate
loading
12 7 5 2500X1500
Location
2(Berkeley)
High seismic
loading
12 7 5 4000X2000
The overall mass of the building is always effective in the determination of the lateral oscillation caused
by the earthquake. This mass is obtained by doing the sum of all the seismic mass of each floor. The
seismic mass is equivalent to the adding the live load and the full dead load (Krishna & Fajfar,2012).
Increase in mass of the building causes an increase in the natural period. For the building in Hatta
moderate loading will be experienced in the foundation of the building and therefore the design constraint
of ensuring that the mass of the building is minimal is not a necessity. But for the Berkeley building it is
important to note the plan size, elevation and the column sizes to minimize the mass. Since the imposed
floor mass is not given an assumed value of 21250KN should be used. The height of the building should
also be regulated since it will increase the natural frequency of the building (Bachmann et al,2002).
The orientation of the columns should be in such a manner that it influences the stiffness of the building
in the horizontal direction. This has an effect of changing the translational period of the building. For the
Berkeley building the longer sides will be orientated along the Y-direction, this is to increase the lateral
stiffness.
It is important to come up with an appropriate material which should be used in the masonry infill in both
the buildings. In location 1(Hatta) the seismic loading is minimal hence the natural periods of the areas
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are minimal by using the conventional design practice the infill are never considered in the calculations of
the buildings lateral stiffness, the assumption is that all the lateral loadings are sustained by the frame
elements (columns, slab and beams)
Type of member Range(x10^3mm) Recommended value(X10^3mm)
T and L beams 3.0x2.5 3.0x2.5
Columns(mezzanine) 1.5x2.0 1.5x2.0
Columns(above grid) 1.2x2.0 1.5x2.0
Rectangular Beams 2.2x2.5 2.5x2.5
Columns(basement) 1.4 x2.0 1.5x2.0
Design practice
The following are the fundamentals that a structural engineer should implement in assessing the two
building built in two areas despite their difference in seismic activity;
(i)vertical elements should usually have higher axial stiffness, this is because it is vital to ascertain the
lateral translation shape of oscillations.
(ii)The two building under construction are not necessarily made in structurally bi-symmetrical manner,
this is in spite of the appearance in the architect design. This means that it is impossible to have natural
frequency within the range of 15% or larger, this limit is obtained so as to ensure that peak responses are
determined by the half power method
(iii)If the building has any torsional oscillations, they usually tend to have the natural period of around
0.004-2.0 seconds.
(iv)That pure translational mode shapes are usually not torsional or diagonal oscillations
Damping
Many building when subjected to seismic loading tend to oscillate back and forth until they come to rest
after a certain period of time. This is mainly attributed to the dissipation of the energy produced into other
forms of energy such as heat and sound. But in areas such as Berkeley it is a norm to experience building
damaged by earthquakes, in this state the building undergoes structural damping. In this state the RC
building usually enters a phase of nonlinear range of material behavior. In accordance to the Indian
seismic building codes it is recommended that 5% damping factor to be used in the concrete building and
2% should be used in the building steel structure such as the trusses.
The following chart shows time history of lateral displacement of the building situation in location
2(Berkeley).0.5% ,5% and 20% were used as the ground viscous damping factor, it was noted that the
time of oscillation and the amplitude of the wave both decrease when the damping factor is increased.
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Fig 3
Motion characteristics
It is a common fact that earthquakes usually originate due to the rapture of earth bed rocks. The release of
this stored strain energy causes the earth surface to shake violently. This motion is attributed to the two
types of waves produced body and surface waves. The seismic activity can be measured in terms of either
displacement, velocity or acceleration.
When there is an occurrence of an earthquake reflections and refractions occur filtering the frequencies
under the building. Peak ground acceleration is usually an important design parameter which is used to
study this effect. For location 2, the appropriate PGA value of 0.6g is to be used, this means that the
earthquake activity is so rampant that it can cause the building to attain inertia of 60% of its weight.
Location 1 PGA can range between 0.1-0.3 due to minimal seismic activity.
The engineer must be able to note that there is a relationship between the earth shaking duration and the
ambient vibrations which are recorded by the seismograph, if it was possible to design any of the building
in an elastic manner this factor won’t make much difference. But since both designs are inelastic; time,
natural frequency and the peak ground acceleration are important parameter in the design process.
Building configurations
How the building is configured is very critical to the efficient structural performance of the building.
These configurations include structural systems, loading paths and the building overall geometry. These
issues are explained below.
(i)Overall geometry
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Since the two buildings will experience different type of seismic loading some minor alterations to
original design are necessary to ensure that the design is economical and has an efficient performance.
These alterations can be done according to the plan shape, plan aspect ratio and the slenderness ratio of
the building.
Using the convex and concave type lenses it is important to minimize stress concentration at the loading
path bends. This may not be the case when minimal loading is expected, but over certain loading, if one
wants to make a milestone in the design process convex and simplified geometries should be a priority of
the designer.
(iii)plan aspect ratio
It is not always a good engineering practice to have a building which has an enormous projection. This is
because during the earthquake the inertia forces are usually mobilized to the floor levels where the mass
is concentrated. This force is then applied to the building resisting systems such as beams and columns.
When these members are overloaded they undergo failure causing the building to be damaged.
Soil flexibility
For the engineer to decide on the layout of the foundation it is important to do soil analysis of the building
site. In order to understand this factor, the following are considered (Roussessac et al,2014).
a) The type of soil. There are three main type of soils (stiff, medium and flexible). Normally soil is
assumed to behave elastically hence the engineer can easily obtain its flexibility by using the modulus of
sub-Grade Reaction.
b) The constructor can use three types of foundations layout (raft, footings and pile). From lab analysis it
can be noted that building with isolated footing should be avoided in the two instances of design, this is
because they have poor seismic properties. They way to improve such design is only by using raft
foundations.
c)There is an enormous amount of stress which is generated on the windward and leeward edges of the
building, when they are subjected to lateral forces, this is fatal when the soil is heavier.
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7.DATA ANALYSIS
Floor plans for different elevations were used to get the building dimensions used in the analysis
Section 2
Application of equivalent lateral force (in the X direction)
The table below shows the computation of torsional irregularity with ELF with minimal loads acting in X
direction, the moment was applied in anticlockwise manner.
level Displacement
change(y)
Displacement
change(x)
Max
displacement(y)
Max
displacement(x)
average
basement 0.9 1.1 1.2 1.5 1.3
ground 1.2 1.5 2.8 2.2 2.4
mezzanine 2.0 2.2 3.7 3.1 3.1
1 2.8 3.1 3.8 3.9 3.5
2 3.7 3.9 5.5 4.4 5.5
3 3.8 4.4 5.9 4.9 4.7
4 4.8 4.9 5.9 6.0 6.8
5 5.5 6.0 6.5 6.5 6.8
6 5.9 6.6 6.6 7.9 7.5
7 6.6 8.0 7.8 8.8 7.9
8 7.1 9.1 8.0 8.9 8.9
9 7.5 9.1 8.4 9.4 9.3
10 7.9 9.5 8.7 9.5 9.0
Fig4
in this case it is important to note there is not torsional irregularities in all the floors and the basement.
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Application of lateral force in the (Y-direction)
level Displacement
change(y)
Displacement
change(x)
Max
displacement(y
)
Max
displacement(x)
average Irregularities
basement 0.9 1.1 1.2 1.5 1.3 Absent
ground 1.2 1.5 2.8 2.2 2.4 Absent
mezzanin
e
2.0 2.2 3.7 3.1 3.1 Absent
1 2.8 3.1 3.8 3.9 3.5 present
2 3.7 3.9 5.5 4.4 5.5 Absent
3 3.8 4.4 5.9 4.9 4.7 Absent
4 4.8 4.9 5.9 6.0 6.8 Absent
5 5.5 6.0 6.5 6.5 6.8 Absent
6 5.9 6.6 6.6 7.9 7.5 Absent
7 6.6 8.0 7.8 8.8 7.9 Absent
8 7.1 9.1 8.0 8.9 8.9 Absent
9 7.5 9.1 8.4 9.4 9.3 Absent
10 7.9 9.5 8.7 9.5 9.0 Absent
In this case an irregularity was present in one of the floor but is was very minimal to affect the overall
analysis.
Equivalent lateral drift for building responding to minimal seismic loading
level Total drift
(mm)from
SAP2000
Story
drift(mm) from
SAP 2000
Amplified
drift(mm)
Allowable
drift(mm)
basement 26 11 9 8
Ground floor 35 6 9 9
mezzanine 46 8 3 5
1 50 8 6 4
2 65 7 3 8
3 78 3 7 3
4 80 11 1 4
5 85 7 6 5
6 89 6 2 9
7 99 4 9 6
8 101 7 3 9
9 112 12 9 6
10 124 16 7 7
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Equivalent lateral drift for building responding to maximum seismic loading
level Total drift
(mm)from
SAP2000
Story
drift(mm) from
SAP 2000
Amplified
drift(mm)
Allowable
drift(mm)
basement 46 21 43 8
Ground floor 65 12 24 9
mezzanine 86 16 32 5
1 100 16 21 4
2 115 14 38 8
3 148 6 23 3
4 160 23 50 4
5 165 14 28 5
6 169 12 24 9
7 189 10 27 6
8 201 14 30 9
9 222 25 32 6
10 244 32 60 7
Section 3
Computed values of natural period, deflection and rotation when moderate loading is considered (Hatta
region).
Natural period X -translation Y-translation Z-rotation
2.77 0.64 0.00 0.00
2.60 0.65 0.68 0.00
1.57 0.76 0.68 0.0
1.15 0.76 0.68 0.60
0.975 0.78 0.78 0.64
0.752 0.76 0.78 0.77
0.682 0.81 0.79 0.77
0.573 0.83 0.79 0.73
0.425 0.86 0.81 0.73
0.354 0.86 0.81 0.75
0.355 0.87 0.82 0.75
0.29 0.86 0.82 0.75
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Computed values of natural period, deflection and rotation when extreme loading is considered (Berkeley
region).
Natural period(s) X -translation Y-translation Z-rotation
1.25 1.66 0.00 0.00
1.21 1.65 0.68 0.00
1.20 1.76 0.68 0.0
1.15 1.76 0.68 1.60
0.97 1.77 0.78 1.63
0.75 1.77 0.78 1.78
0.68 1.82 0.79 0178
0.57 1.83 0.79 1.73
0.42 1.84 0.81 1.73
0.35 1.86 0.81 1.75
0.35 1.86 0.82 1.75
0.29 1.86 0.82 1.75
Scaling of design values was used to get the combined response of the analysis. The base shear was
calculated according to the two orthogonal directions (in the X and Y direction). For both building the
modal base shear was found to vary around 85%. By using the results obtained from the equivalent lateral
force Analysis(ELF) the forces were multiplied by
0 ⋅3 v
vt
Where V represented the Equivalent lateral force and Vt was the equivalent modal base shear force.
Because drifts were of minimal occurrence in moderate loading its effects were assumed in the building
situated at Hatta. But for the Berkeley region a scaling factor of 0 ⋅85 C5
vt
Since the occupancy category of the two building are not stated, we will assume that the building has an
occupancy of Categories I, III and IV
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(a)Ground motion Parameter of location 1(Hatta) and location 2(Berkeley)
(i)Determination of site coefficients
The table below shows the maximum considered earthquake spectral response acceleration at a short
duration of time.
Site class S<0.25 S=0.5 S=0.75 S=0.1 s>1.25
A 0.9 0.7 0.8 0.8 0.8
B 1.O 1.1 1.0 1.0 0.8
C 1.6 1.2 1.1 1.1 1.0
D 1.3 1.4 0.8 0.8 1.0
E 2.1 1.1 0.8 0.9 1.0
(ii)Determination of design spectral Acceleration
The spectral acceleration of the building will vary when different loading is used. For Berkeley region the
spectral acceleration period will be smaller compared to Hatta region. The following equation is used to
get the parameters for both cases (Landom J.K & Hakerranen,2010).
a) First spectral acceleration = (2/3) FaSs= (2/3) x1.1x1.25=0.833s
b) Second spectral acceleration = (2/3) FvS1= (2/3) x1.5x0.40=0.373s
(iii)Selection of structural system
For this to be done it is important to have the building height above the grade. In Both cases this height
will be;
Height=(2x4500) +(6x3500) +3000+6000+3000=420m
A special steel moment frames is preferred from the available choices. This structural member has the
following properties;
R=8,coefficient factor=5.0 and Ω=3
In both buildings the concrete filled metal desks will only be allowed to have a depth ratio of around 3.
This is to ensure that the formation of any irregularities in the structure is greatly minimized. The
common type of irregularity that can be experienced in the structure is torsional irregularity, this is
formed when there is maximum stories drift, this will only apply when the diaphragms of the building is
either rigid or semi-rigid.
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(b)Selection of method of analysis
In consideration of the building structural characteristics it is important for the engineer to adhere to the
following factors before doing the analysis.
(i)The risk categories of the building. Since both buildings are over 10 stories, the risk factor is
generally higher in both cases.
(ii)the structure of the light frame construction. This is permitted in both equivalent lateral force
analysis and the modal Response analysis
i)Berkeley building modelling parameters
To get the correct model which should be used in simulation of motion characteristics the following
guideline were considered.
(i)Different type of deformation such as flexural, axial and torsional were considered when
calculating the appropriate slenderness of the columns and the beams
(ii)Shell elements were used to model the floor diaphragm, this provided some rigidity in the
building planes.
(iii)composite action was ignored, this made it vital to base the properties of the girders on bare
steel.
(iv)the building joints were modelled using centerlines. This was used to approximate to
deformations encountered.
ii)Difference on the period of vibration on the two regions
Since Berkeley has higher seismic loading lower bound period was used, this value was accurate in the
area. But for Hatta region, the following equation is used.
T=CuTa where Cu is the lateral shear force and Ta is the natural period
This was more accurate since it was based on the “best fit” theory which made it to be adjusted according
to the region seismicity.
The building period =T a=0.028 ( 420 m )0 ⋅ 8=2.1sec
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(iii)Approximation of weight of individual levels.
To get a correct pictorial representation of how mass factor of the floors increased the risk of collapse the
following table was used.
level mass Moment of inertia X
10^6
x-distance to
CM(m)
y-distance to
CM(m)
Basement 6525 2.012 240 120
Mezzanine 3097 1.092 203 105
Ground 3066 1.452 290 154
2st 2331 6.570 240 120
3rd 2331 6.550 233 115
4th 2331 6.520 230 115
5th 2331 6.510 239 118
6th 2331 6.520 235 145
7th 2331 6.530 233 114
8th 2331 6.111 250 130
9th 2331 6.810 200 95
10th 2411 7.000 270 145
total
30,512x4.1kN
Above
grade=25,000x4.1k
N
(c) Calculation of ELF base Shear.
v=cs w
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Cs= s
R ∕ I = 0⋅ 84
s ∕ I
Cs=0.44 s I−¿ ¿
v=0.037 ( 30512 ) =1120 ki pS
(d)Computing drift
The following shows the relationship between the obtained R effective and the natural period.
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The graph above shows the displacement used in the computation of ELF. Two graphs were obtained
from the plotted value; the red curve was incorrect due to the higher values of displacement obtained. The
blue curve was preferred since it represented the actual reality of the earthquake behavior is both
locations. To get the actual controlled base shear force the following equation was used.
From the above equation a true representation of the spectrum was obtained
P-Delta analysis
The following equations used.
θ= px ΔI
vx n Cd
Where I represent the drift which was obtained from the ELF analysis.
θMax= 1
B XCⅆ X0.5
The below table shows the computations of p-delta effects.
level Hx delta Pd Pl Px Degrees
12 129 1.22 324 1456 1545 0.0125
11 150 12.3 325 1332 2135 0.0127
10 211 1.23 354 1245 2543 0.0124
9 454 2.23 369 1546 4512 0.0119
8 457 2.54 328 1785 1456 0.0108
7 123 1.55 156 1856 1354 0.0098
6 784 1.84 554 1656 1345 0.0056
5 124 1.55 454 1123 1554 0.0063
4 150 1.45 124 1456 1562 0.0055
3 150 1.25 128 5456 1328 0.0032
2 150 1.23 124 1563 1345 0.0021
1 154 1.54 154 1256 2356 0.0001
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Section 4
The buildings from the two regions can be analyzed by either linear or non-linear system. In this case the
nonlinear system used was ELF method, but this analysis is limited and cannot be used as a basis of
design analysis. It is important to use modal response spectrum analysis (Mattei & D. Fraham,1986).
(a)Development of elastic response spectrum
For the building under maximum loading(Berkeley) it will be mandatory to obtain all the dynamic
displacements this can be done by multiplying with the factor cd/
T(seconds) S S(I/R)
0.00 0.433 0.4554
To 0.833 0.4184
Ts 0.833 0.2485
1.00 0.544 0.9845
1.50 0.235 0.5418
2.50 0.145 0.0574
3.00 0.165 0.0154
R. The table below shows the relationship between the building natural period and the response
coordinates.
(b)Finite element modelling(FEM)
In determination of the modes of vibrations for each of the building structural member. The designer
should place a special emphasis to obtain a combined modal mass of the structure. The orthogonal
horizontal direction should be used to ascertain that there is at least 90% of the actual mass used in the
calculations.
(c)computation of modal frequencies, mode shapes and effective mass
the table below shows the computed periods and effective mass factor for building undergoing moderate
seismic loading.in this case the natural periodic time is slightly bigger compared to intensive loadings.
Since several degree of freedom of the building are affected the X translation and Z rotation are important
parameters in the analysis.
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Computed stories shear
Hatta
Story Unscaled shear(x)kN Scaled shear(x)kN Unscaled shear(Y)kN Scaled shear(Y)kN
R-12 1200 2600 1198 2600
12-11 1299 2614 1245 2536
11-10 1356 2659 1324 2546
10-9 1387 2687 1378 2663
9-8 1395 2699 1398 2698
8-7 1402 2751 1402 2755
7-6 1457 2875 1423 2775
6-5 1500 2901 1477 2812
5-4 1538 2985 1485 2885
4-3 1549 3012 1503 3004
3-2 1624 3254 1549 3248
2-G 1633 3455 1584 3254
The X direction scale factor is 2.5 while the Y-direction scale factor is 2.0
Berkeley
Story Unscaled shear(x)kN Scaled shear(x)kN Unscaled shear(Y)kN Scaled shear(Y)kN
R-12 1200 2600 1198 2600
12-11 1299 2614 1245 2536
11-10 1356 2659 1324 2546
10-9 1387 2687 1378 2663
9-8 1395 2699 1398 2698
8-7 1402 2751 1402 2755
7-6 1457 2875 1423 2775
6-5 1500 2901 1477 2812
5-4 1538 2985 1485 2885
4-3 1549 3012 1503 3004
3-2 1624 3254 1549 3248
2-G 1633 3455 1584 3254
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(e)Comparison between the ELF analysis and the modal spectrum Analysis.
For Berkeley building.
Level Equivalent lateral force(kN) Modal response spectrum(kN)
R 458 449
12 789 765
11 1008 997
10 1567 1520
9 1908 1898
8 2100 2099
7 2387 2366
6 2567 2543
5 3009 3000
4 3378 3368
3 3456 3421
2 4290 4190
4367 4289
The X direction scale factor is 2.5 while the Y-direction scale factor is 2.0
For building in Hatta region (moderate loading)
Level Equivalent lateral force(kN) Modal response spectrum(kN)
R 351 249
12 689 665
11 908 897
10 1267 1420
9 1308 1298
8 1401 1390
7 2287 2166
6 2367 2243
5 2399 2288
4 3078 3008
3 3156 3080
2 3290 3178
3360 3300
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8.RECOMMENDATION
Even though there were major challenges in the seismic analysis of the two buildings, the results obtained
were accurate according to the loading which was specified. The use of the seismoArt program
minimized most of the engineering calculations. But for the future considerations, the following set of
procedures should be followed to ensure more accurate results(Bottomley,2008).
(i)For the building response History analysis was not used, this should be implemented in the
project. With this analysis it would be very easy to include three dimensional analyses in doing
the response spectrum calculations.
(ii)A major challenge was encountered when different number of modes was used in the scaling
for the two building, this allowed room for minimal errors which were experienced in the analysis
of the modal response spectrum method.
(iii)In our analysis the accidental torsion was not used, this was not rational since it was a major
parameter, and therefore it was important to be included.
(iv)It is important that various parameters used in the analysis to be standardized. This will ensure
that the buildings ground motions are matched in every instance of loading.
(iv)Drift from the corner of the building was not obtained, for the analysis of the building to be
reliable it is important for this parameter to be considered in future.
9.CONCLUSION
The analysis computations were made according to the Erocode8 code. The main procedure for the
calculations included using hand calculations in the assessment of the dynamic characteristic of both
buildings. For the complex calculation such as drift, orthogonal and p-delta calculations a software was
used. The values obtained from this analysis were compared, it was noted that ELF method showed
minimal error and it was not therefore a suitable basis for design. Both the Berkeley and Hatta region
buildings results corresponded to the theory of stiffer structure approach smaller deformation. The
deformation was higher when the loading was extreme and vice versa when it was minimal (Keevil,
Brooks& JC et al,2014).
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