A Study on Uncertainty in Seismic
design and Method of analysis

 

Devbrat bose (author)

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prof. Suhail qureshi (author)

 

 

ABSTRACT

An
earthquake is a natural inevitable unpredictable phenomena which takes place
when high stresses built in the earth crust, are suddenly released as the crust
breaks with a few  kilometers from the
earth’s surface. The destruction caused on the structure is not only the
shaking of structure , but also due to the action of lateral forces on the
structure which tend to bend the structure against the ground motion in order
to maintain the inertia of rest. The input shaking causes the foundation of
a building to oscillate back and forth in a more or less horizontal plane. The
building mass has inertia and wants to remain where it is and therefore,
lateral forces are exerted on the mass in order to bring it along with the
foundation. For analysis purposes, this dynamic action is simplified as a group
of horizontal forces that are applied to the structure in proportion to its
mass and to the height of the mass above the ground.

 

 

INTRODUCTION

Structures of
civil engineering  are mainly considered
to resist static loads.  In General, the
effects of dynamic loads acting on the structure are not measured. This feature
of neglecting the dynamic loads sometimes becomes the cause of disaster,
particularly in case of seismic forces due to earthquake.  Recently an example of this category is
earthquake occurred on Jan.26, 2001 in Bhuj (Gujarat). This has produced a
growing interest for earthquake resistant design of structures. Other
earthquakes in asia are Indian ocean earthquake (2004) , Kashmir and regions of
Pakistan (2005) , bihar and Nepal earthquake (1934) , assam (1950) etc

 

Earthquakes are catastrophic events
that occur mostly at the boundaries of portions of the earth’s

crust called tectonic plates. When
movement occurs in these regions, along faults, waves are generated at the
earth’s surface that can produce very destructive effects.

 

 Aftershocks are smaller quakes that occur
after all large earthquakes. They are usually most intense in size and number
within the first week of the original quake. They can cause very significant
re-shaking of damaged structures, which makes earthquake-induced disasters more
hazardous. A number of moderate quakes (6+ magnitude on the Richter scale) have
had aftershocks that were very similar in size to the original quake.
Aftershocks diminish in intensity and number with time. They generally follow a
pattern of being at least 1 large (within magnitude 1 on the Richter scale)
aftershock, at least 10 lesser (within magnitude 2 on the Richter scale)
aftershocks, 100 within magnitude 3 on the Richter scale, and so on. The Loma
Prieta earthquake had many aftershocks, but the largest was only magnitude 5.0,
with the original quake being magnitude 7.1.

 

In multistory buildings with floors
of equal weight, the loading is further simplified as a group of loads, each
being applied at a floor line, and each being greater than the one below in a
triangular distribution .Seismically resistant structures are designed to
resist these lateral forces through inelastic action and must, therefore, be
detailed accordingly. These loads are often expressed in terms of a percent of
gravity weight of the building and can vary from a few percent to near 50% of
gravity weight. Increased compression may exceed the axial compressive capacity
of columns while decreased compression may reduce the bending strength of
columns.

 

Literature
review:

 

Earthquake
engineering Research institute  (EERI)  has conducted the full survey of Bhuj
earthquake or also known as Kutch earthquake. This earthquake is considered in
one of the most destructive and disastrous earthquake in the last fifty years
history  of india . The important cities
affected by the earthquake are Bhuj , Anjar, rajnagar , Gandhidham , Morbi etc.
where the maximum amount of damage and casualties has take place. It reveals
the structural weakness or inefficient in the form of design and planning ,
improper analysis of calculation of dynamic loads which results in design deficiency
and inadequate  constructions.

In earthquake engineering, we deal with random variables and therefore
the design must be

treated differently from the orthodox design. The orthodox viewpoint
maintains that the objective of design is to prevent failure; it idealizes
variables as deterministic. This simple approach is still valid and applied to
design under only mild uncertainty. But when confronted with the effects of
earthquakes, this orthodox viewpoint seems so over trustful as to be worthless.
In dealing with earthquakes, we must contend with appreciable
probabilities that failure will occur in the near future. Otherwise, all the
wealth of this world would prove insufficient to fill our needs: the most
modest structures would be fortresses. We must also face uncertainty on a large
scale while designing engineering systems—whose pertinent properties are still
debated to resist future earthquakes about whose characteristics we know even

 

 

Factors affecting analysis and design of
structure due to various behavior of structures under seismic forces:

 

 

Building
behavior :-

                                 The building
is subjected to various types of forces , mostly due to vibration caused on
account of earthquake forces. The foundation of structure or structural members
are not damaged due to impact forces or external pressure due to winds, but due
to action of inertial forces caused by various vibrations and shakening of
structure of the building. The increased weight of structure has adverse
effects on design of building against seismic forces. It increases the inertial
forces on the structure as mass of structure get increased and secondly it
results in  buckling and crushing of
structural members such as walls and columns when the earthquake forces tends
to bend the structural members or moved out the members from its initial
position .

 

Fig :- showing behavior of building under seismic forces

 

 

Influence
of soil :-

                            Due to vibration
of  structure, which is associated with
the ground motions , the amplification of acceleration and its frequency of
vibration coincides with the vibrations transferred to soil . This phenomena of
coinciding of frequency is called resonance. Thus it is possible for the
building and the ground which it rest on it have same fundamental time period
and frequency of vibrations which wake the situation more adverse during
occurrence of such conditions . Thus , it is concluded from the fact that, to
avoid such conditions the structure must ensures that it has different
frequency and time period of vibrations to that of ground on which it rest
upon. 

 

Fig :- showing action of seismic waves  on foundation soil

 

 

Damping :-

                 when the vibrational characteristics of structure coincides with
the vibrational characteristics of seismic waves , results in resonance which
is responsible for heavy destruction of structure. but, considering the fact
that resonance in building is not same as in ideal cases which we have studied,
rather they are damped resononating in nature. Their damping behavior depends
on the constructional material , connection type and other influence due to
presence non structural members , which are only used to serve for
architectural purposes and thus have no stiffness characteristics on the
building. Damping of structure is measured with reference to critical damping
in some percentage.

 

Fig
:- showing concept of damping

 

 

Building motions and separations :-

                 Earthquake-induced motions,
even when they are more violent than those induced by wind, evoke a totally
different human response—first, because earthquakes occur much less frequently
than windstorms, and second, because the duration of motion caused by an
earthquake is generally short. People who experience earthquakes are grateful
that they have survived the trauma and are less inclined to be critical of the
building motion. Earthquake-induced motions are, therefore, a safety rather
than a human discomfort issue. Lateral deflections that occur during
earthquakes should be limited to prevent distress in structural members and
architectural components. Non load-bearing in-fills, external wall panels, and
window glazing should be designed with sufficient clearance or with flexible
supports to accommodate the anticipated movements.

 

METHODS OF SEISMIC DESIGN:-

Based on
the three criteria strength, stiffness and ductility the methods for seismic
design are described below

 

 

LATERAL STRENGTH BASED DESIGN:

                It is one
of the commonly used design method used nowadays. The concept of this method is
based on providing the structure with sufficient lateral strength to
resist  various impacts on structure due
to seismic forces, assuming the condition of structure that it will behave
adequately in non-linear range . To achieve this , only simple construction
details are needed to satisfied for safe structural characteristics against
uneven failure

 

DISPLACEMENT BASED DESIGN :

              
 In this
method the structure is designed in such away that , to possess sufficient
strength an ductility so that it can transfer the vibrational energy by
yielding and should bear the shock and shaking of structure effectively. This
method operates directly with deformation quantities hence gives better insight
on the expected performance of the structures. This method of design has been
adopted by many countries in the form of their own design codes.

 

 

CAPACITY BASED DESIGN:

             Capacity based
design is one of such techniques which is new to field of seismic design
of  various structures . It is based on
the positioning of plastic hinges which is in predetermined positions and
predetermined sequences . The main objective of this method is to avoid the
brittle failure of   structural member , which is achieved by
transforming brittle failure members into ductile modes

 

ENERGY BASED DESIGN:

                This is the most capable and
innovative approach of earthquake resistant design. this method is based on the
concept of total energy is dissipated by the kinetic energy , the elastic
strain energy and energy resisted through deformations and damping of the
structural members associated with it.

SEISMIC ANALYSIS METHODS

 Main features of seismic method of
analysis based on Indian Standard 1893(part 1): 2002 are described as follows

 

Equivalent lateral force method:

                The approach of equivalent lateral force procedure , uses a simple
technique of the structures fundamental period and anticipated maximum ground
acceleration , or velocity , together with relevant factors , to determine the
maximum base shear. The loads acting on the structure specifically horizontal
loads are then distributed to the full height of the structure .Then the
structure is analyzed  for static loads .
Then the design forces are calculated in this static load analysis are
generally less than the forces which are actually acting on the structure corresponding
to the seismic forces. .                                                                              The
design lateral forces or the design force for base shear are imposed on the
structure as per the  clauses stated in
IS 1893

Response Spectrum analysis:

                Earthquake
acceleration show the irregularity of the ground motions, such as acceleration
and velocity as a function of time . these ground motion characteristics
provide information related to the nature of ground motions. Thus it is
necessary, to have such a meaningful data which describes the criteria of
design purposes. This meaningful data is provided by the method called  response spectrum method. this method can be
more efficiently defined as a graphic representation of maximum responses of
damped  single degree of freedom (SDOF),
in which the mass spring system is continuously varying with natural
frequencies as well as natural periods to a given ground motion characteristics

.

Objectives:

The
main objectives are as follows

·        
To
understand the fundamentals as well as the basic terminology of the earthquake
forces.

·        
To
understand the behavior of ground motions with respect to the structural
behavior on the basis of characteristics such as frequencies and time period of
vibrations.

·        
To
familiarize with the design procedure and codes adapted, according to the
nature of earthquake forces .

·        
Discuss
the various aspects and their proper evaluation of various risks occur due to
earthquake.

·        
To
adopt the method which can able to analyze , and helps in managing destruction
caused due to earthquake.

 

PROBLEM FORMULATION

 

Uncertainty or
randomness in seismic design
:-

The
largest uncertainty involved in the seismic design of structure are associated
with the prediction of the potential of the earthquake , that may affect a
specific location on earth, any time with 
fixed period and their characteristics.

·        
Duration of earthquake

·        
Frequency of p-waves and
s-waves

·        
Magnitude and intensity of
earthquake

·        
Maximum acceleration and
ground motion characteristics

·        
Types and nature of waves

·        
Location of epicenter and its
focus

 

 

RANDOMNESS
IN CAPACITY AND DEMAND
UNCERTAINITY
IN DEMAND :- There are various unavoidable
sources of uncertainty occurs in the expected demands on a structure. These
sources of uncertainty include:

Seismology .
Ground motion characteristics
Structural characteristics
Modeling
Structural Analysis Method

UNCERTAINITY
IN CAPACITY :- In recent years , strength of structure is
calibrated in terms of capacity . However , the previous studies and research
has proved that , capacity of a structure is not only a function of
strength  of bearing loads and forces
but also to proper dissipation of energy to nearby  members without failure. Thus it is however
difficult to finalize or calculate the overall capacity of a building or
structure against these types of forces , which overall affects the design
strength and load calculation , which is going to imposed on the structure.
Thus uncertainty in capacity of structure include following difficulties :
·        
composite
action of joints
·        
connection
between various structural members
·        
proportioning
of ductile elements in structure
·        
 Members to serve for structural behavior as
well as architectural importance.

CONCLUSION

The
structure should be well analyzed for properly resisting those forces due to
earthquake without failure. There are various techniques available and
documented in various design standards. But the most effective technique should
be one which effectively detects the various characteristics of seismic forces
associated with the ground motion characteristics and the nature of those
forces when imposed on the structure. Also unconditionally they have easy
constructability and feasible in cost of construction

 

REFRENCES

1.       Kumar, S.
L., Research Paper published  at the PEC,
1933.

 

 2. ”
Study on Seismic Capabilities of Dhajji-Dewari Frames” M A Dar, J Raju, A.R Dar
and A H Shah, (AARCV) 2012 at  India
(Proceedings of International Conference on Advances in Architecture and Civil
Engineering (AARCV 2012, 21st -23rd June 2012, Paper ID SAM206, vol
1)) (ISBN 978-93-82338-01-7)

 

3. Coull , Alex
, Smith , Bryan trafford., Analysis and design , Design of tall structures.

 

4.Taranath,S.B
, CRC press , Taylor and francis group,  design of tall structures

 

5. Jain ,
S. K. , paper published on CURRENT SCIENCE, VOL. 89, NO. 9, IIT Kanpur , Department of Civil
Engineering