earthquake resistant building civil
DESCRIPTION
civil engineeringTRANSCRIPT
EARTHQUAKE RESISTANT BUILDING
A report submitted in partial fulfilment of the requirement for the degree of
Bachelor of technology in civil engineering
Under the supervision of
Mr. Parag Agrawal
Assistant Professor
Submitted by:
Piyush Kumar Yadav (1209700077)
Praveen Jaiswal (1209700081)
Prateek Singh (1209700080)
Rajesh Ranjan (1209700086)
DEPARTMENT OF CIVIL ENGINEERING
GALGOTIAS COLLEGE OF ENGINEERING & TECHNOLOGY
Greater Noida - 201306,
Uttar Pradesh, India.
Affiliated to
Dr. APJ Abdul Kalam Technical University LUCKNOW
May, 2016
i
ABSTRACT
Earthen buildings are traditionally constructed since prehistoric times in all parts of the
world. Yet there is practically no standardization attempted so far. As usually constructed, they
are weak and most vulnerable to complete the collapse as observed during earthquakes in the
past. An attempt has been made here to identify the main defects and structural weakness in such
constructions. Then suggestions are given to improve their behavior under normal conditions and
to increase their resistance to earthquakes. It is recognized that no test results are yet available to
evaluate such recommendations. The need to carryout properly planned investigations is
therefore emphasized.
ii
DECLARATION
We hereby declare that the practical project report entitled Earthquake Resistant Building is
being submitted in the particle fulfilled of the requirement for the B.Tech Civil Engineering of
the Galgotias College of Engineering And Technology.
Certified that the above statement made by the students is correct to the best of
our knowledge and belief.
Under Guidance
Mr. Parag Aggrawal Prof. Maya Rai
(Asst. Professor) Head of Department
Greater Noida Dept. of Civil Engineering
Galgotias College of Engineering Galgotias College of Engineering
And Technology And Technology
iii
ACKNOWLEDGMENT
The satisfaction that accompanies the successful completion of any task would be in
complete without the mention of people whose ceaseless cooperation made it possible, whose
constant guidance and incouragement crown all efforts with success.
We are greatful to our project coordinator and our project guide Mr. Parag Agrawal for his
guidance, inspiration and constructive suggestions that helped us in the preparation of this
project.
We also thank Dr. Maya(Head of Department Civil Engineering, GCET) for her
knowledgeable insight and guidance.
I am obliged to all the staff members, for the valuable information provided by them. Last but
not the least, we thank our fellow students who have helped in successful completion of this
project.
Piyush Kumar Yadav
Praveen Jaiswal
Prateek Singh
Rajesh Ranjan
iv
Table of Contents
ABSTRACT .............................................................................................................. I
DECLARATION .................................................................................................... II
ACKNOWLEDGMENT ...................................................................................... III
CHAPTER-1 ............................................................................................................. 1
INTRODUCTION ................................................................................................ 1
CHAPTER-2 ……………………………………………………………………...7
LITERATURE REVIEW GENERAL .................................................................. 7
CHAPTER-3 ............................................................................................................. 9
OBJECTIVE ......................................................................................................... 9
CHAPTER-4 ...........................................................................................................10
METHODOLOGY .............................................................................................10
4.1 Base Isolation System ..............................................................................10
4.1.1 Basic idea of how base isolation works ................................................10
4.1.2 Base isolation technique in India .........................................................11
4.2 Seismic Analysis by Response Spectra ....................................................12
4.2.1 Response Spectrum Concept .................................................................12
4.2.2 Response Spectrum Analysis Applied to MDOF Systems ....................14
4.2.3 Ductile Behavior Consideration ...........................................................15
4.3 Seismic Response by Time-History Analysis ...........................................17
4.3.1 Response of a SDOF System to General Dynamic Loading; Duhamel’s
Integral...........................................................................................................17
4.3.2 Linear Time History Analysis for MDOF Systems ...............................19
4.3.3 Time History Analysis for Earthquakes ................................................19
4.4 Equivalent Static Method .........................................................................20
CHAPTER-5 ...........................................................................................................22
MAKING OF BUILDINGS & STRUCTURES EARTHQUAKE PROOF .......22
5.1 What is an earthquake? ...........................................................................22
5.2 What makes a building or structure fail in earthquakes? .......................24
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5.3 How can we make buildings resistant to earthquakes with earthquake
engineering? ..................................................................................................25
5.4 When looking at design and construction, how do we build earthquake
proof buildings? .............................................................................................27
5.6 Ground Motion ........................................................................................32
CHAPTER-6 ...........................................................................................................34
DESIGN CONSIDERATION AND CALCULATION ......................................34
6.1 Calculation ..............................................................................................35
CHAPTER-7 ...........................................................................................................49
IMPORTANCE OF CONSTRUCTION & MAINTENANCE...........................49
7.1 Need for a comprehensive approach to earthquake-resistant
construction. ..................................................................................................49
7.2 Importance of conceptual design .............................................................50
7.3 Control or decrease of demands ..............................................................50
CHAPTER-8 ...........................................................................................................51
CONCLUSION ...................................................................................................51
REFERENCES .......................................................................................................52
vi
List of Figure
FIGURE 1 SATELLITE VIEW .............................................................................................. 1
FIGURE 2 GRAPH REPRESENTATION ................................................................................. 2
FIGURE 3 COLUMN VIEW .............................................................................................. 3
FIGURE 4 DIFFERENCE IN COLUMN .................................................................................. 4
FIGURE 5 BUILDING CRACK ........................................................................................... 5
FIGURE 6 RESTRAIN VIEW ............................................................................................. 6
FIGURE 7 ISOLATION BEARING ..................................................................................... 10
FIGURE 8 ISOLATION BEARING ON MOVEMENT ............................................................... 10
FIGURE 9 REPRESENTATION OF SPECTRUM ..................................................................... 12
FIGURE 10 MOMENT VIEW ......................................................................................... 13
FIGURE 11 DISTANT VIEW IN MOMENT ......................................................................... 13
FIGURE 12 S-W GRAPH ............................................................................................. 14
FIGURE 13 BUILDING DESIGN ...................................................................................... 23
FIGURE 14 FOUNDATION DESIGN ................................................................................. 26
FIGURE 15 STEEL BEAM ............................................................................................. 28
FIGURE 16 EARTH QUAKE PROVE BUILDING .................................................................... 29
FIGURE 17 HAITI EARTH QUAKE 2010 .......................................................................... 31
FIGURE 18 NIIGATA EARTHQUAKE 1964 ........................................................................ 32
FIGURE 19 JAPAN EARTHQUAKE 2011 .......................................................................... 33
FIGURE 20 EARTHQUAKE PROVE BUILDING DESIGN ........................................................... 34
1
CHAPTER-1
INTRODUCTION
An earthquake-proof building is a building that has been built to survive an earthquake. The
building is built with technology made to help the building survive an earthquake. Buildings falls
in earthquakes because joints and connections cannot resist the tremendous stresses imposed by
many tones of pressure concentrated on bolts, welds and other fixings.
Seismology is the study of vibrations of earth mainly caused by earthquakes. The study of
these vibrations by various techniques, understanding the nature and various physical processes
that generate them from the major part of the seismology.
Elastic rebound theory is one such theory, which was able to describe the phenomenon of
earthquake occurring along the fault lines. Seismology as such is still a very unknown field of
study where a lot of things are yet to be discovered.
Figure 1 satellite view
2
The above Picture is showing the fault lines and we can see that epicenters are all concentrated
all along the fault lines. The reason for seismic activities occurring at places other than the fault
lines are still a big question mark. Also the forecasting of earthquake has not been done yet and
would be a landmark if done so.
There is general saying that it’s not the earthquake which kills people but its the bad engineering
which kills people. With industrialization came the demand of high rise building and came
dangers with that.
Figure 2 Graph Representation
A seismic design of high rise buildings has assumed considerable importance in recent times.
In traditional methods adopted based on fundamental mode of the structure and distribution of
earthquake forces as static forces at various stories may be adequate for structures of small
height subjected to earthquake of very low intensity but as the number of stories increases the
seismic design demands more rigorous.
3
During past earthquakes, reinforced concrete (RC) frame buildings that have columns of
different heights within one storey, suffered more damage in the shorter columns as compared to
taller columns in the same storey. Two examples of buildings with short columns in buildings on
a sloping ground and buildings with a mezzanine floor can be seen in the figure given below.
Figure 3 Column View
4
Poor behavior of short columns is due to the fact that in an earthquake, a tall column and a short
column of same cross section move horizontally by same amount which can be seen from the
given figure below.
Figure 4 Difference in Column
5
However, the short column is stiffer as compared to the tall column, and it attracts larger
earthquake force. Stiffness of a column means resistance to deformation- the larger is the
stiffness, larger is the force required to deform it.
If a short column is not adequately designed for such a large force, it can suffer significant
damage during an earthquake. This behavior is called Short Column Effect. The damage in these
short columns is often in the form of X-shaped cracking - this type of damage of columns is due
to shear failure.
Figure 5 Building Crack
.
Many situations with short column effect arise in buildings. When a building is rested on
sloped ground, during earthquake shaking all columns move horizontally by the same amount
along with the floor slab at a particular level (this is called rigid floor diaphragm action). If
short and tall columns exist within the same storey level, then the short columns attract several
6
times larger earthquake force and suffer more damage as compared to taller ones. The short
column effect also occurs in columns that support mezzanine floors or loft slabs that are added in
between two regular floors.
Figure 6 Restrain View
There is another special situation in buildings when short-column effect occurs. Consider a wall
(masonry or RC) of partial height built to fit a window over the remaining height. The adjacent
columns behave as short columns due to presence of these walls. In many cases, other columns
in the same storey are of regular height, as there are no walls adjoining them. When the floor slab
moves horizontally during an earthquake, the upper ends of these columns undergo the same
displacement. However, the stiff walls restrict horizontal movement of the lower portion of a
short column, and it deforms by the full amount over the short height adjacent to the window
opening. On the other hand, regular columns deform over the full height. Since the effective
height over which a short column can freely bend is small, it offers more resistance to horizontal
motion and thereby attracts a larger force as compared to the regular column. As a result, short
column sustains more damage. X-cracking in a column adjacent to the walls of partial height. In
new buildings, short column effect should be avoided to the extent possible during architectural
design stage itself. When it is not possible to avoid short columns, this effect must be addressed
in structural design. The Indian Standard IS:13920-1993 for ductile detailing of RC structures
requires special confining reinforcement to be provided over the full height of columns that are
likely to sustain short column effect. The special confining reinforcement (i.e., closely spaced
closed ties) must extend beyond the short column into the columns vertically above and below
by a certain distance. In existing buildings with short columns, different retrofit solutions can be
employed to avoid damage in future earthquakes. Where walls of partial height are present, this
will eliminate the short column effect.
7
CHAPTER-2
LITERATURE REVIEW GENERAL
Performance evaluation of structures should be conducted considering post-elastic
behavior. Therefore, a nonlinear structures are expected to deform inelastically when subjected
to severe earthquakes, so seismic analysis procedure must be used for evaluation purpose as
post-elastic behavior cannot be determined directly by an elastic analysis. Moreover, maximum
inelastic displacement demand of structures should be determined to adequately estimate the
seismically induced demands on structures that exhibit inelastic behavior. Various simplified
nonlinear analysis procedures and approximate methods to estimate maximum inelastic
displacement demand of structures are proposed in literature. The widely used simplified
nonlinear analysis procedure, pushover analysis is discussed in detail.
The published reports ATC 40 (1996) and FEMA 273 (1997) highlighted the non-linear static
pushover analysis. It is an efficient method for the performance evaluation of a structure
subjected to seismic loads. The step by step procedure of the pushover analysis is to determine
the capacity curve, demand curve and performance point. These reports deal with modeling
aspects of the hinge behavior, acceptance criteria and procedures to locate the performance
point.Sudhir K. Jain and Rahul Navin (2000) studied the seismic strengthening of multistorey
reinforced concrete frames which were assessed by means of non-linear pseudo static analysis of
four bays, three, six and nine storey frames were designed for seismic zones I to V as per Indian
codes. The over strength increases as the number of storeys decreases; over strength of the three
storey frame was higher than the nine storey frame. Further, interior frames have higher over
strength as compared to exterior frames of the same building. These observations were
significant for seismic design codes which, at present do not take into account the variation in
over strength.
A modal pushover analysis procedure for estimating seismic demands for buildings was
developed by Chopra and Goel (2002). The modal pushover analysis was applied to a nine-
storey steel building to determine the peak inelastic response and it was compared with rigorous
non-linear response history analysis. It was concluded that the modal pushover analysis was
accurate enough for practical application in building evaluation and design. Santosh Kumar et al.
(2003) studied the evaluation of multistorey buildings with and without considering the stiffness
of infill located in zone III. The study compromised of seismic loads, gravity load analysis and
lateral load analysis as per the seismic code for the bare and infill structure by considering
different analytical models, and their evaluation was carried out using pushover analysis. The
results in terms of natural periods, lateral deformation and ductility ratio were compared for the
different building models. It was concluded that the performance point of all the building models
considered for the study falls before the life safety point. Hence the buildings need not be
8
retrofitted. Base shear capacity was observed to be 20 greater than the design base shear;
therefore the building has safe under design basis earthquake.
Anil Babu et al. (2008) conducted vulnerability analysis on two existing multistorey buildings.
Gravity load analysis, response spectrum analysis and pushover analysis were performed. The
capacity of each member was obtained and compared with the demand. The result showed the
level of vulnerability of the buildings. The first building, which was in zone III, was able to
sustain the gravity load. The second building, located in zone IV, however was adequate under
gravity load. But, under earthquake load, demands on some of the members crossed their
capacities.
Shahrin Hossain (2011) followed the procedures of ATC 40 in evaluating the seismic
performance of residential buildings in Dhaka. The present study investigated as well as
compared the performances of bare frame, full infilled and soft ground storey buildings. For
different loading conditions resembling the practical situations of Dhaka city, the performances
of these structures were analysed with the help of capacity curve, capacity spectrum, deflection,
drift and seismic performance level. The performance of an in filled frame was found to be much
better than a bare frame structure. It is found that, consideration of effect of the infill leads to
significant change in the capacity. Investigation of buildings with soft storey showed that soft
storey mechanism reduced the performance of the structure significantly and makes them most
vulnerable type of construction in earthquake prone areas.
Ramaraju et al. (2012) carried out the nonlinear analysis (pushover analysis) for a typical six
storey office building designed for four load cases, considered three revisions of Indian (IS: 1893
and IS: 456) codes. In that study, nonlinear stress–strain curves for confined concrete and user-
defined hinge properties as per Eurocode 8 were used. A significant variation was observed in
base shear capacities and hinge formation mechanisms for four design cases with default and
user-defined hinges at yield and ultimate. This may be due to the fact that, the orientation and the
axial load level of the columns cannot be taken into account properly by the default-hinge
properties. Based on the observations in the hinging patterns, it was apparent that the user-
defined hinge model was more successful in capturing the hinging mechanism compared to the
model with the default hinge.
9
CHAPTER-3
OBJECTIVE
Most of the loss of life in past earthquakes has occurred due to the collapse of buildings,
constructed in traditional materials like stone, brick, adobe and wood,which were not perticularly
engineered to be earthquake resistant.While theoretically , if appropiate resoures and building
materials are made available, it may be possible to construct buildings which can withstand the
effects of earthquake without any appriciable damage, but practically it is not feasible to do so
due to very high costs involved.From the safety view point, the safety of human life is the
primary concern and the functioning of the buildings has lower priority.
If a building is designed and constructed in such a way that even in the event of the probable
maximum earthquake intensity in the region,
1-An ordinary building should not suffer total or partial collapse,
2-it should not suffer such irreparable damage which would require demolishing and
rebuilding,
3-It may sustain such damage which could be repair quickly and the put back to its usual
functioning,
4-The damage to an important building should even be less so that the functioning of the
activities during post-emergency period may continue unhampered and the community buildings
may be used as temprory shelters for the adversly affected people.
The present state of research indicates that fortunately the above structural safety can be
achieved by adopting appropriate design and construction details involving only small extra
expenditure which would be within the economic means.
The object of this project is to deal with the basic concepts involved in achieving
appropriate earthquake resistance of such buildings as stated above, which may be collectively
called as Non-Engineered Buildings.In this project we are designing a G+4 office cum residential
building with respect to several dead and live loads or vertical loads as well as eathquake loads
or horizontal loads.
10
CHAPTER-4
METHODOLOGY
4.1 Base Isolation System
A base isolated structure is supported by a series of bearing pads which are placed between the
building and the building’s foundation.The bearing is very stiff and strong in the vertical
direction but flexible in the horizontal direction.
Figure 7 Isolation Bearing
4.1.1 Basic idea of how base isolation works
Figure 8 Isolation Bearing On Movement
11
The figure shows an earthquake acting on both, a base isolated building and a conventional
fixed base building. Due to earthquake, the ground beneath each building begins to move to the
left. Each building responds with movement, the building undergoes displacement towards the
right. The building’s displacement in the direction opposite to the ground motion is due to the
inertia. The inertial force acting on a building are the most important of all those forces
generated during earthquake. The inertial forces which the building undergoes are proportional
to the building’s acceleration of the ground motion. Actually buildings do not shift in only one
direction. Due to the complex nature of earthquake ground motion, the building tends to vibrate
back and forth in varying directions.
In addition to displacing towards right, the un-isolated building is also shown to be changing
its shape from a rectangular to a parallelogram, this is deformation of the building. The primary
cause of earthquake damage to buildings is the deformation which the building undergoes as a
result of the inertial forces acting upon it.
Even though the base-isolated building is too displacing but it retains its original rectangular
shape. Deformation undergoes only in the rubber-lead bearings supporting the building. The base
isolated building itself escapes the deformation and damage which implies that the inertial force
acting on it has been reduced. Experiments and observation of base isolated buildings in
earthquake has been shown to reduce building acceleration to as little as 1/4 of the acceleration
of comparable fixed-base buildings.
Acceleration is decreased because the base isolation system increases a building’s period of
vibration, the time it takes for the building to roll back and forth and then back again. In general,
structures with longer periods of vibration tend to reduce acceleration, while those with shorter
periods tend to increase or amplify acceleration.
Finally, the rubber isolation bearings are highly elastic so they don’t suffer any damage and the
lead plug reduces the energy of motion (that is Kinetic Energy) by converting it into heat. By
reducing the heat entering the building, it helps to slow down and eventually stop the building’s
vibration sooner than would otherwise be the case, it damps the building’s vibration.
4.1.2 Base isolation technique in India
In India, base isolation technique was first applied after the 1993 Killari (Maharastra)
earthquake. Two single storey buildings in newly relocated Killari town were built with rubber
base isolators resting on hard ground.
After the 2001 Bhuj (Gujarat) earthquake, the four-storey Bhuj Hospital building was built with
base isolation technique. All of these are brick masonry buildings with concrete roof.
12
4.2 Seismic Analysis by Response Spectra
Response spectrum analysis is perhaps the most common method used in design to
evaluate the maximum structural response due to the seismic action. This is a linear approximate
method based on modal analysis and on a response spectrum definition. According to the
analogy between SDOF and MDOF systems, the maximum modal response of the nth mode, Y ,
is the same as for a SDOF system havin ω =ωn and ξ =ξn.
It should be emphasized that this procedure only leads to the maximum response, instead
of fully describing the response. This saves up a lot of calculation effort with evident
consequences in the time consumed and CPU requirements. The maximum response is
established for each mode by means of the adequate response spectrum. Therefore the response
spectrum analysis is often considered to be the most attractive method for the seismic design of a
given structural system.
4.2.1 Response Spectrum Concept
To explain the response spectrum concept, one considers a SDOF system submitted to an
external action that may be either an applied force or a support displacement. The procedures
used to formulate and solve the equation of motion, q(t ), and therefore to achieve the time
dependent response of the referred SDOF system, were already discussed in paragraphs 2.1 to
2.5. For the response spectrum definition, it is necessary to evaluate the value of the maximum
response, which may be easily determined once its equation of motion, q(t ), is fully known.
Figure 9 Representation Of Spectrum
If the procedure of determining the maximum response is repeated for a
sufficient range of SDOF systems, with a specified critical damping ratio, ξ , and for different
natural vibration frequencies, ω , submitted to the same external action, it is possible to define a
function and represent it in a diagram similar to the one shown in figure 8. This diagram is
13
generally known as a response spectrum, S(ω,ξ ). Usually it is represented with the x-axis being
the natural vibration frequencies or periods of vibration of the SDOF and the y-axis being the
corresponding maximum response values. Generally, in the same graph different response
spectra, corresponding to the same action and to different damping ratios usually found in
common structures (2%, 5% and 10%) are shown as in figure 8.
Figure 8 represents a typical relative displacement response spectrum, Sd (ω ,ξ ), for values of
critical damping ratio, ξ , usually found in common structural systems. The meaning of the
relative displacement, q*. It is worth to analyse the evolution of the response spectrum function:
1) For low values of frequency, close to zero, one may see that the maximum value for the
relative displacement tends to a certain value, which is the support displacement, qs. This is
easily explained if one remembers the concept of the natural vibration frequency, ω , in a SDOF
system. In fact a SDOF with a low value of ω is very flexible and behaves as shown in figure 9
when submitted to a support displacement.
Figure 10 Moment View
2) After a certain value of frequency, the relative displacement tends to zero. In fact high values
of frequency correspond to a very stiff system. The response motion will then be as shown in
figure 10 – the relative displacements, q*, tend to zero.
Figure 11 Distant View in Moment
14
It should be noted that the maximum responses, S(ω,ξ ) may be presented in every desired
form, i.e. for displacements, Sd (ω ,ξ ), velocities, Sv (ω,ξ , and accelerations, Sa (ω,ξ ) , or even
in the form of internal forces or bending moments in a given point of the SDOF system. The
available response spectra used for design purpose, in most of the Seismic Design codes, are
defined by means of an accelerogram representing a typical earthquake in the region of the
structure.
4.2.2 Response Spectrum Analysis Applied to MDOF Systems
The equation of motion for the nth degree of freedom under a support excitation in direction J
for a given MDOF system may be written as:
(1)
For direction J, the maximum value for the modal coordinate in terms of displacements, Yn′,max
, may be easily achieved if the displacement response spectrum, Sd (ω ,ξ ), is available. Instead
of solving mathematically an expression in the form of (2.80), Yn,max is established from the
response spectrum, ′ (n Sd ωn ,ξ ), for the SDOF system with both the same natural vibration
frequency, ωn and critical damping ratio, ξ n . The procedure is illustrated in figure.
Figure 12 S-W Graph
After establishing the maximum value for the modal coordinate, Y = Sd, the modal participation
factor is recovered as:
(2)
15
In the same way one may calculate the maximum response in terms of accelerations, Yn,max , or
velocities, Y , if the corresponding spectra, Sa (ω ) or Sv (ω )are accessible.
(3)
We now discuss the problem of establishing a reasonable value for the global maximum response
of the system. The assumption behind the reasoning expressed in (1), i.e. to sum the maximum
values of each modal coordinate, Y n,max, certainly will correspond to an upper limit of the
global response with a low probability of occurrence, since is very unlikely for the maximum
modal responses to happen simultaneously. In fact this is the main disadvantage of the response
spectra analyses: The result provided is a set of extreme values that don’t take place at the same
time and therefore do not correspond to an equilibrium state. Thus this method can’t provide
information on the failure mode of the structure, which is an important information from the
engineering point of view.
To minimize these disadvantages it is necessary to combine the modal responses. There are
several ways of carrying out this and it is out of the purpose of the present text to discuss them.
Therefore only two methods are presented. It should be mentioned that there is some controversy
about which method leads to better results. In the design codes, usually the first method to be
discussed below is suggested. However is up to the designer to choose more accurate procedures
of combining the modal response if the SRSS method can’t be applied.
4.2.3 Ductile Behavior Consideration
As may be understood by the discussion so far, earthquake analysis by response spectra is based
on the assumption that the system behaves linearly. This means that even for the maximum
response situation the internal forces on the different structural elements of the system are
assumed to be proportional to the displacements achieved.
16
However this hypothesis is far from reality for structural materials as reinforced concrete or
steel. For instance, a sketch of the stress-strain curve for steel, in figure, shows that this material
will roughly behave linearly until yielding and thereafter non-linearly until failure. The symbols
εy and εu stand for yielding and ultimate strains, respectively. The capacity of the material to
absorb deformations in a stabilized way is called ductility. One way of measuring ductility is the
ratio of ultimate deformation to the yielding deformation. The larger this value the more ability
of the material to dissipate energy after yielding, and therefore the more ductile. The seismic
design criteria consider that a structure submitted to an extreme earthquake should be prevented
from collapse but significant damage is expected. Therefore this type of action must be included
among the design load conditions for the Ultimate Limit State design. Under these conditions,
yielding is expected which will lead to inelastic response of the structure.
Assuming that the deflections, δ , produced by a given earthquake are essentially
the same whether the structure behaves linearly or yields significantly, one can utilize the non-
linear behaviour and design structures for less values of stresses, σ, or internal forces, F. This
idea is illustrated in figure.
Therefore if the response spectra method is used to design a structural system, the stresses
/internal forces corresponding to the maximum deformations previously achieved may be
reduced to take into account the yielding of the material. This is done by means of the
coefficient, η , called the reduction factor or behavior coefficient the physical meaning of which
is shown in figure above.
The determination of this coefficient is also a matter of controversy. Usually, the value given for
the behaviour coefficient is much less than the real one as the elastic response is reduced using
further reduction coefficients. However, it is accepted that in order to maximize the non-linear
behaviour of the system and thus its behaviour coefficient, it is desirable to design it in a
redundant way i.e. with a sufficient number of plastic hinges allowed before collapse.It should be
stated that ductility does not depend only on the material characteristics but also on the system
and the direction of loading. Consider, for instance, the MDOF system. The horizontal motion of
the mass will induce bending moments on the column whereas the vertical motion of the mass
will lead to a compression tension. For the first situation the moment-rotation curve will show
17
that the element has capacity to absorb deformations after yielding and so ductile behaviour may
be assumed. On the other hand, the axial force – axial deformation diagram often show brittle
behaviour and so η = 1 is usually adopted. This is the reason why in most of the analyses, for
vertical seismic action, the reduction factor is taken as unity.
4.3 Seismic Response by Time-History Analysis
Time-History analysis is a step-by-step procedure where the loading and the response history are
evaluated at successive time increments, Δt – steps. During each step the response is evaluated
from the initial conditions existing at the beginning of the step (displacements and velocities) and
the loading history in the interval. With this method the non-linear behaviour may be easily
considered by changing the structural properties (e.g. stiffness, k) from one step to the next.
Therefore this method is one of the most effective for the solution of non-linear response, among
the many methods available. Nevertheless, in the present text, a linear time history analysis is
adopted i.e. the structural properties are assumed to remain constant during the entire loading
history and further it is assumed that the structure behaves linearly. As a consequence the mode
superposition method, already discussed in chapter 2, may be applied.
4.3.1 Response of a SDOF System to General Dynamic Loading;
Duhamel’s Integral
The equilibrium equation for a given general dynamic loading, p(t), may be expressed in the
same form as (4) for a damped SDOF system, i.e.:
(4)
It should be noted that both the response, q(t), and the dynamical loading, p(t), depend on time.
The purpose of Duhamel’s integral is to achieve the response at any time, t, due to load applied
at another time τ.
The response to general dynamic loading of a SDOF system subjected to initial conditions q0
and q is deduced considering first the corresponding free vibration response.
(5)
If the starting time is different from 0, the above expression may be written in a general form
introducing τ as the time corresponding to the initial conditions:
18
(6)
Now we consider the same SDOF system acted upon by a load p(τ). This load induces into the
system a velocity variation, Δq& , in the interval Δτ given by the impulse-momentum
relationship:
(7)
The second term in this equation represents the area of the plot p(τ) in the time interval Δτ. For a
differential time interval, dτ, this area is simply p(τ)dτ, which allows to re-write equation:
(8)
Using the previous relation and noticing that the response after the termination of the short
duration impulse, p(τ ) dτ , is a free vibration motion subjected to an initial velocity, dq&(τ), one
may write the differential response, dq(t), as follows, for t>τ:
(9)
The entire loading history may be considered to consist of a succession of such short impulses,
each producing its own differential response according to the expression above. Because the
system is assumed to be linear, the total response may be established by summing all the
differential responses developed during the loading history. This is the same as saying that the
response at time t is given by the integral of the differential displacements since time t=0 until
time t., i.e.:
(10)
This result is known as Duhamel’s Integral and is one of the most important results in Structural
Dynamics as it may be used to express the response of any damped SDOF system subjected to
any form of dynamical loading, p(τ). There are several procedures to evaluate this integral and it
is out of the purpose of this text to discuss them here.
To take into account initial conditions, the free damped vibration response must be
added to the solution, which leads to the result:
19
(11)
As one may notice the general response for damped SDOF systems is composed by two terms
with the same nature as discussed. The first term reflects only the influence of the initial
conditions and the second term corresponds to the loading effect on the structural response
4.3.2 Linear Time History Analysis for MDOF Systems
The determination of the modal coordinates of a given MDOF systems, Yn(t), is accomplished
in which the vector {p(t )} represents the general dynamic loading applied in the corresponding
degrees of freedom. in which the vector {p(t )} represents the general dynamic loading applied in
the corresponding degrees of freedom.
(12)
assuming that the systemstarts from rest, with ξ =ξn and ω =ωn , i.e.:
(13)
4.3.3 Time History Analysis for Earthquakes
As mentioned before, an earthquake action is considered as a base motion computed on the basis
of the support acceleration. The equation of motion for the nth mode under direction J is the
following:
(14)
Remembering the expression of the modal participation factor, PnJ, it is obvious that the second
term may be written as:
20
(15)
the load vector {p(t)} as:
(16)
By substituting the value of p(t):
(17)
The problem now consists in solving this expression above for each modal coordinate. One of
the most common techniques is to assume the load subdivided into a sequence of time intervals,
steps, in which the modal coordinates, Yn(t), are calculated. This procedure is called the step-by-
step integration method and next we shall briefly describe one of the many different ways to
solve it.
4.4 Equivalent Static Method
This method is perhaps the simplest procedure at disposal for a structural engineer to perform an
earthquake analysis and achieve reasonable results. It is prescribed in any relevant code for
earthquake analysis and is widely used especially for buildings and other common structures
meeting certain regularity conditions.
The method is also called The Lateral Forces Method as the effects of an earthquake
are assumed to be the same as the ones resulting from the statical transverse loadings. As
discussed before, in the Rayleigh method, an inertia loading provides a good approximation to
the natural vibration shape of the structure. If the structural response is not significantly affected
by contributions from higher modes of vibration it is reasonable to assume that with an
appropriate set of inertia forces one may achieve a good approximation for the response. This is
the basic concept of the Equivalent Static Method. Each code presents its own procedure to
compute and to distribute the static equivalent forces in order to achieve the earthquake effects
on the structure11.
Usually an expression is defined to prescribe the minimum lateral seismic force, also
designated the base shear force. One usual requirement for the structure regarding the
application of this method is that the natural vibration period of the structure should be limited
by a maximum value, which leads to a certain minimum value of frequency/stiffness. This is due
to the fact that often the response is mainly controlled by the first mode of vibration. Thus,
imposing a minimum value of frequency the higher modes contribution may be neglected.
21
The structure to be analysed by the equivalent static method should respect certain
regarding its geometrical regularity and stiffness distribution such as:
� All lateral load resisting elements (such as columns or walls) should run from
the base to the top without any interruption:
� Mass and lateral stiffness should not change abruptly from the base to the top;
� Geometrical asymmetries in height or in plan due to setbacks should not
exceed certain values;
22
CHAPTER-5
MAKING OF BUILDINGS & STRUCTURES
EARTHQUAKE PROOF
What is an earthquake?
What makes a building or structure fail in earthquakes?
How can we make buildings resistant to earthquakes?
When looking at design and construction, how do we earthquake proof buildings?
How can existing buildings be strengthened to resist earthquakes?
Chinese Version
There are a wide variety of earthquake effects - these might include a chasm opening up or a
drop of many metres across a fault line. Therefore, it is not possible to design an earthquake
proof building which is guaranteed to resist all possible earthquakes. However, it is possible
during your design and construction process to build in a number of earthquake resistant features
by applying earthquake engineering techniques, which would increase enormously the chances
of survival of both buildings and their occupants.
5.1 What is an earthquake?
Both the sea bed and the land that we inhabit are formed of a crusty skin of light rocks floating
on the soft centre of the earth, which is made of heavier molten rock and molten iron. This crusty
skin is not one solid piece but is made up of lumps, separated by faults and trenches, or pressed
together into mountains. These separate lumps and plates are not static but are moved in slow
motion by convection forces in the molten core, gravitational forces from the Sun and Moon and
centrifugal forces from the Earth's rotation. Some plates are moving apart, particularly in the Mid
Ocean Trenches, where molten material pushes up and shoves the plates apart, whilst others are
bumping into each other head on, these form mountains like the Himalayas (the whole of the
Indian Sub-Continent is moving northwards and hitting Asia, for example). Some are sliding one
over another, like the west coast of the Americas, where the land plates are sliding over the
denser ocean bed plates, causing the Andes and the Rockies to be thrust upwards. Some plates
are moving along past each other, sticking together a while at a fault line, often in combination
with bumping or sliding under/over (As in San Francisco).
All of these movements cause earthquakes (and usually volcanoes as well). If the movement was
steady, about a millimeter or so a year, no one would notice. But the plates tend to jam; the
movement carries on, but the material where they touch is stretched, or compressed, or bent
sideways. The material deforms (like stretching or compressing or twisting a bit of plastic). At
some stage it reaches the breaking point along all or part of the joint, then it breaks, and there is a
sudden movement. The movement may be tiny or may be several feet; but enormous amounts of
energy are released, far more than the biggest Nuclear Bombs. The shock waves from this
release of energy shoot out in all directions, like the ripples
23
Figure 13 Building Design
24
When you throw a stone in a pond: except that they travel faster through the land. They can
be measured all around the whole world. This is an Earthquake.
Prior to the Earthquake there are often little warning shakes, where highly stressed bits break
and the plate joints readjust themselves a little, but allow the main join to become more stressed.
After the primary Earthquake when the main join has failed and moved, there is another
readjustment, and further bits around the fault become overstressed too, and they fail. These
aftershocks can themselves be highly energetic Earthquakes. After the Earthquake, the area
settles down again. But the movement carries on and the next Earthquake is already building up,
remorselessly. People forget and build buildings and structures that are going to kill their
children next time when they could ensure that during the design and construction phase some
earthquake proof measures have been incorporated.
5.2 What makes a building or structure fail in earthquakes?
An Earthquake moves the ground. It can be one sudden movement, but more often it is a
series of shock waves at short intervals, like our ripples from the pebble in the pond analogy
above. It can move the land up and down, and it can move it from side to side.
All buildings can carry their own weight (or they would fall down anyway by themselves).
They can usually carry a bit of snow and a few other floor loads and suspended loads as well,
vertically; so even badly built buildings and structures can resist some up-and-down loads. But
buildings and structures are not necessarily resistant to side-to-side loads, unless this has been
taken into account during the structural engineering design and construction phase with some
earthquake proof measures taken into consideration. This weakness would only be found out
when the Earthquake strikes, and this is a bad time to find out. It is this side-to-side load which
causes the worst damage, often collapsing poor buildings on the first shake. The side-to-side load
can be worse if the shocks come in waves, and some bigger buildings can vibrate like a huge
tuning fork, each new sway bigger than the last, until failure. This series of waves is more likely
to happen where the building is built on deep soft ground, like Mexico City. A taller or shorter
building nearby may not oscillate much at the same frequency.
Often more weight has been added to a building or structure at most frequently at greater heights;
say another floor and another over that; walls built round open balconies and inside partitions to
make more, smaller, rooms; rocks piled on roofs to stop them blowing away; storage inside. This
extra weight produces great forces on the structure and helps it collapse. The more weight there
is, and the higher this weight is in the building, the stronger the building and its foundations must
be to be resistant to side earthquakes; many buildings have not been strengthened when the extra
weight was added. Often, any resistance to the sway loading of the building is provided by walls
and partitions; but these are sometimes damaged and weakened in the Main Earthquake. The
building or structure is then more vulnerable, and even a weak aftershock, perhaps from a
slightly different direction, or at a different frequency, can cause collapse. In a lot of multi storey
buildings, the floors and roofs are just resting on the walls, held there by their own weight; and if
there is any structural framing it is too often inadequate. This can result in a floor or roof falling
off its support and crashing down, crushing anything below.
25
Often more weight has been added to building or structure at a higher level, for example
another floor, extra walls and partitions, extra storage or even rocks piled on roofs to stop them
blowing away. Small cracks appear in the concrete. The bonding of the 'stirrups' (the small steel
bars which bind the main reinforcement together) to the concrete weakens, the outer concrete
crumbles (spalling), the main reinforcing bars can bend outwards away from the column and all
strength disappears. This was beautifully demonstrated under the Oakland Freeway, where huge
round concrete columns crumbled and crumpled. They have now been reinforced with massive
belts around them as a result of an earthquake engineering review and to improve structural
dynamics.
In a lot of multi storey buildings the lower floor has more headroom (so taller columns); and
it often has more openings (so less walls); and it is usually stood on 'pinned' feet with no
continuity. So the ground-to-first floor columns, which carry the biggest loads from the weight
and the biggest cumulative sideways loads from the earthquake, are the longest and the least
restrained and have the least end fixity. They are often the first to fail. It only takes one to fail for
the worst sort of disaster, the pancake collapse so familiar to anyone who has seen the results in
Armenia, Mexico, Turkey, Iran, Peru, and now Pakistan and Kashmir. Sometimes buildings are
built on soft soil; this can turn into quicksand when shaken about, leading to complete slumping
of buildings into the soil. Some tall buildings can stay almost intact but fall over in their entirety.
The taller the building, the more likely this is to happen, particularly if the building can oscillate
at the frequency of the shock waves, and particularly if some liquefaction of soft soil underneath
has allowed the building to tilt.
5.3 How can we make buildings resistant to earthquakes with
earthquake engineering?
To be earthquake proof, buildings, structures and their foundations need to be built to be resistant
to sideways loads. The lighter the building is, the less the loads. This is particularly so when the
weight is higher up. Where possible the roof should be of light-weight material. If there are
floors and walls and partitions, the lighter these are the better, too. If the sideways resistance is to
be obtained from walls, these walls must go equally in both directions. They must be strong
enough to take the loads. They must be tied in to any framing, and reinforced to take load in their
weakest direction. They must not fall apart and must remain in place after the worst shock waves
so as to retain strength for the aftershocks.
If the sideways resistance comes from diagonal bracing then it must also go equally all round
in both directions. Where possible, it should be strong enough to accept load in tension as well as
compression: the bolted or welded connections should resist more tension than the ultimate
tension value of the brace (or well more than the design load) and it should not buckle with loads
well above the design load. And the loads have got to go down to ground in a robust way. If the
sideways load is to be resisted with moment resisting framing then great care has to be taken to
ensure that the joints are stronger than the beams, and that the beams will fail before the
columns, and that the columns cannot fail by spalling if in concrete. Again the rigid framing
should go all around, and in both directions.
26
Figure 14 Foundation Design
If the building earthquake resistance is to come from moment resisting frames, then special
care should be taken with the foundation-to-first floor level. If the requirement is to have a taller
clear height, and to have open holes in the walls, then the columns at this level may have to be
much stronger than at higher levels; and the beams at the first floor, and the columns from
27
ground to second floor, have to be able to resist the turning loads these columns deliver to the
frame. Alternatively, and preferably, the columns can be given continuity at the feet. This can be
done with 'fixed feet' with many bolts into large foundations, or by having a grillage of steel
beams at the foundation level able to resist the column moments. Such steel grillage can also
keep the foundations in place.
If the beams in the frame can bend and yield a little at their highest stressed points, without
losing resistance, while the joints and the columns remain full strength, then a curious thing
happens: the resonant frequency of the whole frame changes. If the building was vibrating in
time with shock waves, this vibration will tend to be damped out. This phenomenon is known as
'plastic hinging' and is easily demonstrated in steel beams, though a similar thing can happen
with reinforced concrete beams as long as spalling is avoided.
All floors have to be connected to the framing in a robust and resilient way. They should
never be able to shake loose and fall. Again all floors should be as light as possible. They should
go all round each column and fix to every supporting beam or wall, in a way that cannot be
shaken off. One way of reducing the vulnerability of big buildings is to isolate them from the
floor using bearings or dampers, but this is a difficult and expensive process not suitable for low
and medium rise buildings and low cost buildings (though it may be a good technique for
Downtown Tokyo). Generally it is wise to build buildings that are not too high compared to their
width in Earthquake areas, unless special precautions are taken.
5.4 When looking at design and construction, how do we build
earthquake proof buildings?
When designing earthquake safe structures the first consideration is to make the highest bit, the
roof, as light as possible. This is best done with profiled steel cladding on light gauge steel Zed
purlins. This can also have double skin with spacers and insulation. It can have a roof slope
between 3 and 15 degrees. If it is required to have a 'flat' roof, this could be made with a
galvanized steel decking and solid insulation boards, and topped with a special membrane. Even
a 'flat' roof should have a slope of about 2 degrees. If it is required to have a 'flat' concrete roof,
then the best solution is to have steel joists at about 2m, 6", centers, and over these to have
composite style roof decking. Then an RC slab can be poured over the roof, with no propping;
the slab will only be say 110mm, 4 1/2", and will weigh only about 180 kg/sqm. Such a slab will
be completely bonded to the frame and will not be able to slip off, or collapse.
If the building or structure is a normal single storey, then any normal portal frame or other steel
framed building, if the design and construction is competently done, will be resistant to
Earthquake loads. If it is to have 2 or more stories, more needs to be done to ensure its survival
in an earthquake. As with the roof, the floors should be made as light as possible. The first way
to do this is to use traditional timber joists and timber or chipboard or plywood flooring. If this is
done it is vital that the timber joists are firmly through bolted on the frames to avoid them
slipping or being torn off. The frame needs them for stability and the floor must never fall down.
A better alternative is to substitute light gauge steel Zeds for the timber joists. These can span
further and are easier to bolt firmly to the framework. Then, floor-boards or tongue-and-groove
28
chipboard can easily be screwed to the Zeds. However in Hotels, Apartment buildings, Offices
and the like, concrete floors may be needed. In such cases we should reduce the spans to the
spanning capacity of composite decking flooring, and pour reinforced concrete slabs onto our
decking. The decking is fixed to the joists, the joists into the main beams, the main beams into
the columns and the concrete is poured around all the columns. There is simply no way that such
floors can fall off the frame.
Figure 15 Steel Beam
Once the floors are robustly fitted to the frames, the frames themselves must be correctly
designed. Please look at the diagram above.
29
Figure 16 Earth Quake Prove Building
30
The frame should not be built on simple pinned feet at ground level. Outside earthquake
zones it is normal to build a 'nominally pinned footing' under each column. This actually gives
some fixity to the base as well as horizontal and vertical support. But in an earthquake, this
footing may be moving and rotating, so rather than provide a bit of fixity, it can push to left or
right, or up and down, and rotate the column base, helping the building to collapse prematurely.
Any pinned footing may actually be moving differently from other footings on the same
building, and so not even be giving horizontal or vertical support, but actually helping to tear the
building apart. So to earthquake proof the building REIDsteel would start with steel ground
beams joining the feet together, and these should have moment resistance to prevent the bottoms
of the columns from rotating. These ground beams may well go outside the line of the building,
thus effectively reducing the height-to-width ratio as well, helping to reduce total over-turning.
This ground beam may be built on pads or piles or rafts as appropriate. On loose soils, the
bearing pressure should be very conservatively chosen, to minimise effect of liquefaction.
By applying earthquake engineering techniques, REIDsteel would then fit the columns to
these ground beams with strong moment connections. Either the connections should be strong in
both directions, or some columns designed to resist loads in one direction and others in the other
direction. The columns should not be the item that fails first: the ground beam should be able to
rotate and form plastic hinges before either the connection or the column fails. The reason is that
a column failing could instigate a collapse; the connection failing could instigate the column
failure. In comparison, the plastic hinging of the ground beam takes time, absorbs energy, and
changes the resonant frequency of the frame while leaving the frame nearly full strength.
Next, REIDsteel would fix the main beams to the outer columns with full capacity joints. This
will almost always mean haunched connections. Great care would be taken to consider the shear
within the column at these connections. The connections should be equally strong in both up or
down directions, and the bolt arrangement should never fail before the beam or the column. In
extreme earthquake sway, the beams should always be able to form hinges somewhere, in one or
two places, without the column with its axial load failing elastically. In this way the frame can
deflect, the plastic hinges can absorb energy; the resonant frequency of the structure is altered,
all without collapse or major loss of strength. All this takes a little time until the tremor passes.
The inner columns do not give a lot of sway resistance, but even so, should have connections
which do not fail before the beam or the column. Then, the floors are fitted, Light-weight or
conventional cladding is fitted to the frames, light-weight or thin concrete roofs are fitted as
described above. You have a building that will behave very well in an earthquake with
significant resistance to damage.
Nothing can be guaranteed to be fully resistant to any possible earthquake, but buildings
and structures like the ones proposed here by REIDsteel would have the best possible chance of
survival; and would save many lives and livelihoods, providing greater safety from an
earthquake.
Earthquakes are a major geological phenomena. Man has been terrified of this phenomena for
ages, as little has been known about the causes of earthquakes, but it leaves behind a trail of
destruction. There are hundreds of small earthquakes around the world every day. Some of them
are so minor that humans cannot feel them, but seismographs and other sensitive machines can
31
record them. Earthquakes occur when tectonic plates move and rub against each other.
Sometimes, due to this movement, they snap and rebound to their original position. This might
cause a large earthquakes as the tectonic plates try to settle down. This is known as the Elastic
Rebound Theory.
Figure 17 Haiti Earth Quake 2010
Every year, earthquakes take the lives of thousands of people, and destroy property worth
billions. The 2010 Haiti Earthquake killed over 1,50,000 people and destroyed entire cities and
villages. Designing Earthquake Resistant Structures is indispensable. It is imperative that
structures are designed to resist earthquake forces, in order to reduce the loss of life. The science
of Earthquake Engineering and Structural Design has improved tremendously, and thus, today,
we can design safe structures which can safely withstand earthquakes of reasonable magnitude.
Earthquakes cause massive vibrations in the Earth’s crust. This can cause a number of
problems in the ground, which in turn becomes a hazard to all life and property. The effect
depends on the geology of soil and topography of the land.
32
Figure 18 Niigata Earthquake 1964
5.6 Ground Motion
The most destructive of all earthquake hazards is caused by seismic waves reaching the ground
surface at places where human-built structures, such as buildings and bridges, are located. When
seismic waves reach the surface of the earth at such places, they give rise to what is known as
strong ground motion. Strong ground motions cause’s buildings and other structures to move and
shake in a variety of complex ways. Many buildings cannot withstand this movement and suffer
damages of various kinds and degrees.
33
Figure 19 Japan Earthquake 2011
34
CHAPTER-6
DESIGN CONSIDERATION AND CALCULATION
A detailed earthquake resistant design of a four storey public cum office building according to
IS 13920: 1993 following with IS 456: 2000 and SP 16: 1980
Figure 20 Earthquake Prove Building design
35
6.1 Calculation
Preliminary data
1. Type of structure Multi-storey rigid joint frame
2. Zone IV
3. Layout As shown in fig
4. Number of stories Four(G+3)
5. Ground storey height 4.0 m
6. Floor-to-floor height 3.35 m
7. External walls 250 mm thick including plaster
8. Internal walls 150 mm thick including plaster
9. Live load 3.5 kN/m2
10. Materials M 20 and Fe 415
11. Seismic analysis Equivalent static method(IS 1893(Part
1):2002)
12. Design philosophy Limit state method conforming to IS
456: 1978
13. Ductility design IS 13920: 1993
14. Size of exterior column 300*530 mm
15. Size of interior column 300*300 mm
16. Size of beams in longitudinal 300*450 mm
and transverse direction
17. Total depth of slab 120 mm
36
LOADING DATA
Dead Load (DL)
Terrace water proofing (TWF) = 1.5kN/m2
Floor Finish (FF) = 0.5kN/m2
Weight of slab = 25D kN/m2, where D is total depth of slab
(Assuming total depth of slab = 120 mm)
Weight of walls
37
External walls (250 mm thick) = 5 kN/m/meter height (20 @ 0.25)
Internal walls (150 mm thick) = 3 kN/m/meter height (20 @ 0.25)
Live Load (LL)
Roof = 1.5 kN/m2
Live load on floor = 3.5 kN/m2
Earthquake Load (EQ)
Ah = (Z/2) (Sa/g)(I/R)
Sa/g = 2.5* , I = 1.0,m
R = 5.0 (SMRF)
Ah = (0.24/2) * (2.5) * (1.0/5.0) = 0.06
T = 0.09 h/d1/2 = 0.09 * (14.05)/(11.50)1/2 = 0.372
For T = 0.372 , Sa/g = 2.5 (from IS 1893 (Part 1): 2002)
Dead Load Analysis
DL at roof level
Weight of slab = 25D = 25 * 0.12 = 3.0 kN/m2
Weight of finishes = F.F. + T.W.F. = 0.5 + 1.5 = 2.0 kN/m2
Total weight = 5.0 kN/m2
Total weight on beam C1-C5
Tributary floor area on beam C1-C5 = 0.5 * (0.9 + 4.6) * 1.85 * 2 = 10.175 m2
Slab weight on beam C1-C5 = 5 * 10.175 = 50.875 m2
Weight on beam C1-C5 per meter = 50.875/4.6 = 11.05 kN/m
Self-weight of beam = 25 * 0.30 * (0.45-0.10) = 2.625 kN/m
Total weight on beam C1-C5 = 11.05 + 2.625 = 13.684 kN/m
Total weight on beam C5-C5
38
Tributary floor area on beam C5-C5 = 0.5 * 2.3 *1.15 * 2 = 2.645 m2
Total weight on beam C5-C5 = 5 * 2.645 = 13.225 kN/m
Weight on beam C5-C5 = 13.225/2.3 = 5.75 kN/m
Self weight of beam = 25 * 0.30 * (0.45-0.10) = 2.625 kN/m
Total weight on beam C5-C5 = 5.75 + 2.625 = 8.375 kN/m
DL at floor level
Weight of slab = 25D = 25 * 0.12 = 3.0 kN/m2
Weight of finishes (F.F) = 0.5 kN/m2
Total weight = 3.5 kN/m2
Total weight on beam C1-C5
Tributary floor area on beam C1-C5 = 0.5 * (0.9+4.6) * 1.85 * 2 = 10.175 m2
Slab weight on beam C1-C5 = 3.5 * 10.175 = 35.62 kN
Weight on beam C1-C5 per meter = 35.62/4.6 = 7.74 kN/m
Self-weight of beam = 25 * 0.30 *(0.45-0.10) = 2.625 kN/m
Weight of walls = 20 * 0.15 * (3.35 – 0.45) = 14.50 kN/m
Total weight on beam C1-C5 = 7.74 + 14.50 + 2.625 = 24.86 kN/m
Total weight on beam C5-C5
Tributary floor area on beam C5-C5 = 0.5 *2.3 *1.15 * 2 = 2.645 m2
Total weight on beam C5-C5 = 3.5 * 2.645 = 9.2575 kN
Weight on beam C5-C5 = 9.2575/2.3 = 4.025 kN/m
Self-weight of beam = 25 * 0.30 * (0.45 – 0.10) = 2.625 kN/m
Weight of walls = 20 * 0.15 * (3.35 – 0.45) = 14.50 kN/m
Total weight on beam C5-C5 = 4.025 + 2.625 +14.50 = 21.15 kN/m
39
Live Load Analysis
LL at roof level
Weight of live load = 1.5 kN/m2
Total weight on beam C1-C5
Tributary floor area on beam C1-C5 = 0.5 * (0.9+4.6) * 1.85 * 2 = 10.175 m2
Total weight on beam C1-C5 = 1.5 * 10.175 = 15.265 kN
Weight on beam C1-C5 = 15.625/4.6 = 3.32 kN/m
Total weight on beam C5-C5
Tributary floor area on beam C5-C5 = 0.5 * 2.3 * 1.15 * 2 = 2.645 m2
Total weight on beam C5-C5 = 1.5 * 2.645 = 3.9675kN
Weight on beam C5-C5 = 3.9675/2.3 = 1.725 kN/m
LL at floor level
Weight of live load = 3.5 kN/m2
Total weight on beam C1-C5
Tributary floor area on beam C1-C5 = 0.5 * (0.9 +4.6) * 1.85 * 2 = 10.175 m2
40
Total weight on beam C1-C5 = 3.5 * 10.175 = 35.62 kN
Weight on beam C1-C5 = 35.62/4.6 = 7.74 kN/m
Total weight on beam C5-C5
Tributary floor area on beam C5-C5 = 0.5 * 2.3 * 1.15 * 2 = 2.645 m2
Total weight on beam C5-C5 = 3.5 * 2.645 = 9.2575 kN
Weight on beam C5-C5 = 9.2575/2.3 = 4.025 kN/m
Earthquake Load Analysis
Determination of total base shear
Dead load
(a) Weight of floor i.e. (Ws + FF) = 40.70 *11.50 * (3.0+0.5) = 1638.175 kN
(b) Weight of roof i.e. (Ws + TWF + FF) = 40.70 * 11.50 * (3.0+1.5+0.) = 2340.25 kN
(c) Weight of peripheral beams (Transverse) = (2(4.6-0.45/2-0.3/2)*2.625)*2 + (1(2.3-
0.30/2-0.3/2) * 2.625) * 2 = 54.86 kN
41
(d) Weight of peripheral beams (Longitudinal) = (11(3.7-0.3/2-0.3/2)*2.625)*2 = 196.35 kN
(e) Weight of parapet wall (1.0m height, 150 mm thick) = 2 * (40.70 + 11.50) * 1.0 * 3 =
313.20 kN
(f) Weight of external wall (thickness of wall 250 mm ) = 20 *0.25 * (20.9 + 74.8) * (3.35 –
0.45) = 1387.65 kN
(g) Interior beams (Transverse) = ((2 * 4.225 + 2.0) * 2.625 ) * 11 = 274.32 kN
(h) Interior beams (Longitudinal) = ((3.7-0.3) * 2.625 * 11) * 2 = 196.35 kN
(i) Weight of interior walls (thickness = 150 mm),
Length (Transverse) = ((4.6 – 0.45/2 – 0.3/2) * 2 + (2.3-0.3)) * 10 = 104.5 m
Length (Longitudinal) = ((3.7 -0.3) * 11 * 2) = 74.8 m
Height = 3.35-0.45 = 2.90 m
Weight = 20 * 0.15 * (104.5 + 74.8) * 2.90 = 1559.91 kN
(j) Weight of exterior column/height = 2 * 12 *0.30 * 0.53 * 25 = 95.4 kN/m
(k) Weight of interior column/height = 2 * 12 * 0.30 * 0.30 * 25 = 54 kN/m
Live Load
Live load on roof = Zero
Live load on floors = 50% of 3.5 kN/m2 = 1.75 kN/m2
Total live load on each floor = 40.70 * 11.50 * 1.75 = 819.08 kN
Concentrated mass
At roof = (b + c + d + e + f/2 + g + h + i/2 + j * 3.35/2 + k * 3.35/2) + 0.0 = 5074.98 kN
At 2nd and 3rd floor = (a + c + d + f + g + h + i + (j + k) 3.35) + 819.08 = 6578.95 kN
At 1st floor = (a+ c + d + f + g + h+ i + (j + k)(3.35 + 4.0)0.5) + 819.08 = 6622.82 kN
Total weight = 5074.98 + 2 * 6578.95 + 6622.80 = 24855.69 kN
Total base shear = Ah * W= 0.06 * 24855.69 = 1491.34 kN
Base shear in each frame = 1491.34/12 = 125 kN
Determination of design lateral loads at each floor
Level Wi (MN) hi (meter) Wi hi2 Wihi
2/ Wi hi2 Qi(kN)
(1) (2) (3) (4) (5) (6)
Roof (level 5) 5.074 14.05 1001.62 0.452 56.50
Third floor 6.578 10.70 753.16 0.34 42.50
42
Second floor 6.578 7.35 355.36 0.16 20.00
First floor 6.622 4.00 105.95 0.048 6.00
Ground floor - 0.00
∑ = 2216.04 ∑ = 1.0 ∑ = 125
LOAD COMBINATION
Load case Details of load cases
1 1.5 (DL + IL)
2 1.2 (DL+IL+EL)
3 1.2 (DL + IL –EL)
4 1.5 (DL + EL)
5 1.5 (DL – EL)
6 0.9 DL + 1.5 EL
7 0.9 DL + 1.5 EL
Design of flexure member
43
Factored axial stress less than 0.1 fck
The member shall preferably have a width-to-depth ratio of more 0.3 Width/Depth = 300/450 =
0.67 > 0.3 OK
Width less than 200 mm = 300 mm OK
Depth not greater than ¼( clear span) i.e. ¼(4600-300) = 1075 mm OK
Longitudinal reinforcement
Reinforcement at section 2 due to hogging moment 219.1 kN-m
Assuming 25 mm dia bars with 25 mm clear cover
Effective depth (d) = 450-25-25/2 = 412.5 mm
From Table D, SP 16: 1980
Mu,lim/bd2 = 2.76 (For M 20 and Fe = 415)
Mu,lim = 2.76 * 300 * 412.52 = 140.88kN-m
Actual moment 219.1 kN-m is greater than Mu,lim. So section is doubly reinforced.
From Table 50, SP 16: 1980
Mu/bd2 = (219.1 * 106)/(300 * 412.52) = 4.29 =4.30
d’/d = (25 + 12.5)/41.25 = 0.091 = .01
Referring to table 50, SP 16:1980
P1(top)= 1.429 and P1(bottom)= 0.498 (1)
Corresponding to Mu/bd2 = 4.30 and d’/d = 0.10
Reinforcement at section 2 due to sagging moment
Mu,lim = 2.76 * 300 * 412.52 = 140.88 kN-m
Actual moment 112.3 kN-m is smaller than Mu,lim, so section is singly reinforced.
Reinforcement from table 2, SP 16:1980
Mu/bd2 = (112.3 * 106)/(300 * 412.52) = 2.54
P2(bottom) = 0.857 (2)
44
Required reinforcement maximum of equation (1) and (2),
P(top) = 1.429 and P(bottom) = 0.857
Reinforcement at top (At) = 1.429 * 300 * 412.52 = 1768.38 mm2 (2 @ 16 mm of diameter + 4 @
22 mm of diameter = 1922 mm2)
Reinforcement at bottom (Ab) = 0.857 * 300 * 412.52 = 1060.54 mm2 (2 @ 16 mm of diameter
+2 @ 22 mm of diameter = 1162 mm2)
Top and bottom reinforcement shall consist at least 2 bars throughout the member length OK
Tension steel ratio should be less than 0.24 fck1/2/fy , i.e. 0.258 given 0.857 OK
Shear reinforcement
Details of web reinforcement
Minimum diameter of hoop 6 mm and in case of beam with clear span greater than 5 m hoop
diameter 8 mm OK
At section 2
Pt = 1922/(300 * 412.5) = 0.0155 = 1.5% at top
Pb = 1162/(300 * 412.5) = 0.00938 = 0.938% at bottom
Referring Table 50, SP 16: 1980
Mu,lim/bd2 = 4.7 (Pt = 1.55 and d’/d = 0.10)
Mu,lim (Hogging moment capacity) = 4.70 * 300 * 412.52 = 239.92 kN-m
Table 2, SP 16 : 1980
Mu,lim (Sagging moment capacity) = 2.72 * 300 * 412.52 = 138.84 kN-m
At section 7
Pt = 1162/(300 * 412.5) = 0.00938 = 0.938% at top
Pb = 515/(300 * 412.5) = 0.00416 = 0.416% at bottom
Referring Table 2, SP 16: 1980
Mu,lim/bd2 = 2.72 (Pt = 0.938 and fck 20)
Mu,lim (Hogging moment capacity) = 2.72 * 300 * 412.52 = 138.84 kN-m
45
Mu,lim(Sagging moment capacity) = 1.35 * 300 * 412.52 = 68.91 kN-m
Design of Exterior Column
Size of column 300 mm * 530 mm
Concrete mix M 20
Vertical reinforcement Fe 415
Axial load from load case 5 475.6 kN
Moment from load case 5 203.3 kN
Column subjected to bending and axial load
IS 13920:1993 specification will be applicable if axial stress greater than 0.1 fck i.e. 475.6 *
1000/300 * 530 = 2.99 N/mm2 greater than 0.1 * 20 = 2 N/mm2 OK
Minimum dimension of member should not less than 250 mm (300 mm) OK
Shortest cross –section dimension/perpendicular dimension should not less than 0.4 i.e. 300/530
= 0.56 OK
Vertical (longitudinal reinforcement)
Assume 20 mm diameter with 40 mm cover (d’ = 40 + 10 = 50 mm, d’/D = 50/530 = 0.094=
0.10
From chart 45 , SP 16 : 1980
Pu/fckbD = 475.6 * 103/(20 * 300 * 530) = 0.15
Mu/fckbD2 = 203.30 * 106/ (20 * 300 * 5302) = 0.12
Reinforcement on four sides from Chart 45, SP 16 : 1980
P/fck = 0.08, reinforcement in % = 0.08 * 20 = 1.6%
As = pbd/100 = 1.6 * 300 * 530/100 = 2544 mm2
Using 8 bars @ 20 diameter
Transverse reinforcement
Hoop requirement is as per IS 13920
If the length of hoop is greater than 300 mm a cross tie shall be provided
46
Hoop spacing shall not be exceeded half the least lateral dimension of column i.e. 300/2 = 150
mm.
A factored shear force is given by
Vu = 1.4(Mu,limbL + Mu,lim
bR)/hst
Where Mu,limbL and Mu,lim
bR are moment of resistance, of opposite sign, of beams and hst is the
storey of height.
Moment of resistance of beam at section 2 is
Pt = 1922/(300 * 412.5) = 0.0155 = 1.55% at top
Pb = 1162/(300 * 412.5) = 0.00938 = 0.938% at bottom
Referring Table 50 , SP 16 : 1980
Mu,lim(Hogging moment capacity) = 4.70 * 300 * 412.52 = 239.92 kN-m
Mu,lim (Sagging moment capacity) = 2.72 * 300 * 412.52 = 138.84 kN-m
Nominal shear reinforcement shall be provided in accordance with IS 456 : 2000
Use 8 mm diameter two-legged stirrups Asv = 2 * 50.26 = 100.52 mm2
Design of Interior Column
Size of column 300 mm * 300 mm
Concrete mix M 20
Vertical reinforcement Fe 415
Axial load from load case 4 428.9 kN
Bending moment from load case 4 56 kN-m
Vertical reinforcement
Assume 20 mm diameter with 40 mm cover (d’ = 40+10 = 50 mm , d’/D = 50/300 = 0.16)
From Chart SP 16 : 1980
Pu/fckbD = 428.9 * 103/(20 * 300 * 300) = 0.238
Mu/fckbD2 = 56 * 106/(20 * 300 * 3002) = 0.104
47
As = pbd/100 = 1710 mm2
Providing 6 @ 20 mm diameter.
Transverse reinforcement
A factored shear force is given by
Vu = 1.4(Mu,limbL + Mu,lim
bR)/hst
Where Mu,limbL and Mu,lim
bR are moment of resistance, of opposite sign, of beams and hst is the
storey of height.
Moment of resistance of beam at section 7 is
Pt = 1162/(300 * 412.5) = 0.938 % at top
Pb = 515/(300 * 412.5) = 0.416% at bottom
Referring Table 2 , SP 16 : 1980
Mu,lim(Hogging moment capacity) = 2.72 *300 * 412.52 = 138.84 kN –m
Mu,lim (Sagging moment capacity) = 1.35 * 300 * 412.52 = 68.91 kN-m
Nominal shear reinforcement shall be provided in accordance with IS 456 : 2000
Use 8 mm diameter two-legged stirrups
As = 2 * 50.26 = 100.52 mm2
Spacing will be 187.5 mm c/c but hoop spacing is 150 mm c/c.
48
Detailing of Reinforcement
49
CHAPTER-7
IMPORTANCE OF CONSTRUCTION &
MAINTENANCE
Design and construction of a structure are intimately related and the achievement of good
workmanship depends, to a large degree, on the simplicity of detailing of the members and of
their connections and supports. For example, in the case of a reinforced concrete structure,
although it is possible to detail complex reinforcement on paper and even to realize it in
laboratory specimens so that seismic behavior is improved, in the field such design details may
not be economically feasible. A design is only effective if it can be constructed and maintained.
7.1 Need for a comprehensive approach to earthquake-resistant
construction.
The need for a more comprehensive approach to the earthquake-resistant construction
problem than that covered by existing seismic code procedures has been discussed by the author
in several publications and has been summarized in Reference 13. In a comprehensive approach
to the design of a structure it is first necessary to establish the design criteria, that is, behavior of
the structure - serviceability, damageability, and safety against collapse. Once the design criteria
are established,the limit state controlling the design, the selection of the design earthquake(s)
should be done according to the comprehensive approaches summarized. In this comprehensive
attempt to overcome the uncertainties involved in modeling the real three-dimensional soil-
foundation-superstructure system and in the estimation of the demands and supplies, usually
derived from numerical analysis, the design cannot be based on a single deterministic analysis of
a single selected model. The designer should consider several models, based on possible ranges
over which the parameters governing the behavior of the real system can vary.
50
7.2 Importance of conceptual design
As discussed in several publications, the author believes that in order to overcome or
decrease the uncertainties to which the values of most of the parameters in the estimation of the
demands and supplies are subjected in any current seismic-resistant design procedure, it is
necessary to pay more attention to conceptual design [12, 13]. Conceptual design is defined as
the avoidance or minimization of problems created by the effects of seismic excitation by
applying an understanding of the behavior rather than using numerical computations. Examples
of conceptual design are given in Reference 13. From the analysis of the basic design equations
and the general equation for predicting response [12, 13], it becomes clear that to overcome
detrimental effects of the uncertainties in many of the factors in these equations the following
philosophy can be applied: (1) control or decrease the demands as much as possible, and (2) be
generous in the supply, particularly by providing large ductility with stable hysteretic behavior
(toughness).
7.3 Control or decrease of demands
Because of the uncertainties regarding the dynamic characteristics of future earthquake
ground motions and their modifications as a result of the interaction of the soil with the
foundation-superstructure system response, the conceptual idea would be to control the input to
the structure foundation. One promising method is through the use of base isolation techniques
including energy absorbing devices in the system [16]. In the case of buildings, a decrease in
demand can be achieved by a proper selection of the configuration of the building and its
structural layout and by the proper proportioning and detailing of the structural and non-
structural components, that is, by following the basic principles or guideline for achieving
efficient seismic-resistant construction.
51
CHAPTER-8
CONCLUSION
The tasks of providing full seismic safety for the residents inhabiting the most earthquake-prone
regions are far from being solved. However in present time we have new regulations in place for
construction that greatly contribute to earthquake disaster mitigation and are being in applied in
accordance with world practice.
In the regulations adopted for implementation in India the following factors have been found to
be critically important in the design and construction of seismic resistant buildings:
occurrence and the likely severity of ground shaking and ground failure;
893 , IS
13920 to ensure good performance during future earthquakes.
analysis .i.e. ductility design should be done.
-spatial solutions should be applied that provide symmetry and regularity in the
distribution of mass and stiffness in plan and in elevation.
away with the harmful effects like that of “SHORT COLUMN EFFECT” .
Researchers indicate that compliance with the above-mentioned requirements will contribute
significantly to disaster mitigation, regardless of the intensity of the seismic loads and specific
features of the earthquakes. These modifications in construction and design can be introduced
which as a result has increase seismic reliability of the buildings and seismic safety for human
life.
52
REFERENCES
1. Chopra.R, Kumar.R, Chawla.K.S, T.P.Singh, “Traditional Earthquake Resistant Houses”, Honey
Bee, Vol 11&Vol 12,Oct 2000-Nov 2001.
2. Deodhar.S.V, Dubey.S.K, “Remedial Measures Against Earthquake disaster”, National Building
Material and Construction World, Vol 2, Jan 2003, Pg 52-56.
3. Earthquake Tip 8, “What is seismic design philosophy?”, Indian Concrete Journal, Jan 2004, Vol
2.
4. Earthquake Tip 17, “How do earthquakes affect reinforced concrete buildings?” Indian Concrete
Journal, April 2004, Vol 1.
5. IS 456: 2000, Plain and Reinforced code of practice.
6. IS 1893(Part-1): 2002, Criteria for earthquake resistant design of structure.
7. IS 13920: 1993, Ductile detailing of RCC structure subjected to earthquake force.
8. SP: 16, Design aid for reinforced concrete to IS 456: 2000.
9. Ramamurtham, Theory of structures.