assesment of seismic methods

8/11/2019 Assesment of Seismic Methods

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ABSTRACT


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CONTENTS

I. Introduction

II.

Seismic Inputs for Structures

III. Linear Analysis

Static

Response Spectrum Analysis

Time history

IV.

Non-linear Analysis

Static: Pushover analysis

Dynamic: Non-linear Time history

PDelta analysis

Large displacement analysis

V.

Conclusion


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LIST OF TABLES

Table 1

LIST OF FIGURES:

Figure 1


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I. INTRODUCTION

An earthquake is a sudden and transient motion of the earths surface. The seismic

assessment and design of structures is required because of the occurrence of earthquakes.

Earthquakes are caused by differential movements of the earths crust. The result of these

movements is the well-known ground shaking that can lead to significant damage and/or

collapse of buildings, infrastructure systems (e.g. dams, roads, bridges, viaducts etc.),

landslides, when soil slopes loose their cohesion, liquefaction in sand and destructive waves

or tsunamis in the maritime environments.

Causes of Earthquakes:

Movement of the tectonic plates relative to each other, both in direction and magnitude,

leads to an accumulation of strain, both at the plate boundaries and inside the plates. This

strain energy is the elastic energy that is stored due to the straining of rocks, as for elastic

materials. When the strain reaches its limiting value along a weak region or at existing faults

or at plate boundaries, a sudden movement or slip occurs releasing the accumulated strain

energy. The action generates elastic waves within the rock mass, which propagate through the

elastic medium, and eventually reach the surface of the earth. Most earthquakes are produced

due to slips at the faults or at the plate boundaries. However, there are many instances where

new faults are created due to earthquakes.

The elastic rebound theory of earthquake generation attempts to explain the earthquakes

caused due to a slip along the fault lines. An earthquake caused by a fault typically proceeds

according to the following processes:

a. Owing to various slow processes involved in the tectonic activities of the earths

interior and the crust, strain accumulates in the fault for a long period of time. The large field

of strain at a certain point in time reaches its limiting value.

b. A slip occurs at the faults due to crushing of the rock mass. The strain is released and the

tearing strained layers of the rock mass bounces back to its unstrained condition.

c. The slip that occurs could be of any type, for example, dip slip or strike slip. In most

instances it is a combined slip giving rise to push and pull forces acting at the fault, as shown

in Figure. This situation is equivalent to two pairs of coupled forces suddenly acting.

d. The action causes movement of an irregular rock mass leading to radial wave propagation

in all directions.

e. The propagating wave is complex and is responsible for creating displacement and

acceleration of the soil/rock particles in the ground. The moment of each couple is referred to

as the seismic moment and is defined as the rigidity of rock multiplied by the area of faulting

multiplied by the amount of slip. Recently, it has been used as a measure of earthquake size.

The average slip velocity at an active fault varies and is of the order of 10100mm per year.


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Fig: Unstrained and Strained conditions of earth layers along fault line.

Fig: Elastic Rebound Theory

Seismic Waves:

The large strain energy released during an earthquake causes radial propagation of waves

within the earth (as it is an elastic mass) in all directions. These elastic waves, called seismic

waves, transmit energy from one point of earth to another through different layers and finally

carry the energy to the surface, which causes the destruction. Within the earth, the elastic

waves propagate through an almost unbounded, isotropic, and homogeneous media, and form


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what are known as body waves. On the surface, these waves propagate as surface waves.

Reflection and refraction of waves take place near the earths surface and at every layer

within the earth. The body waves are of two types, namely, P waves and S waves.

Surface waves propagate on the earths surface. They are better detected in shallow

earthquakes. They are classified as L-waves (Love waves) and R-waves (Rayleigh waves). In

L waves, particle motion takes place in the horizontal plane only and it is transverse to the

direction of propagation. The wave velocity depends on the wavelength, the thickness of the

upper layer, and the elastic properties of the two mediums of the stratified layers. L waves

travel faster than R waves and are the first to appear among the surface wave group. In R

waves, the particle motion is always in a vertical plane and traces an elliptical path, which is

retrograde to the direction of wave propagation.

Fig: Seismic Waves

Measurement of an Earthquake:

The instrument that measures the ground motion is called a seismograph and has three

components, namely, the sensor, the recorder, and the timer. The principle of operation of the

instrument is simple. Right from the earliest seismograph to the most modern one, the


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principle of operation is based on the oscillation of a pendulum subjected to the motion of the

support. A pen attached to the tip of an oscillating pendulum. The support is in firm contact

with the ground. Any horizontal motion of the ground will cause the same motion of the

support and the drum. Because of the inertia of the bob in which the pen is attached, a relative

motion of the bob with respect to the support will take place. The relative motion of the bobcan be controlled by providing damping with the aid of a magnet around the string. The trace

of this relative motion can be plotted against time if the drum is rotated at a constant speed.

Fig: Schematic diagram of seismograph

From these instruments the magnitude and intensity of an earthquake are obtained which will

help while calculating the design earthquake forces for the earthquake resistant design of

structures.


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II. SEISMIC INPUTS FOR STRUCTURES

Seismic inputs are the earthquake data that are necessary to perform different types of

seismic analysis. In the context of seismic analysis and design of structures, variousearthquake data may be required depending upon the nature of analysis being carried out.

These data are presented in two different ways, namely, in deterministic and probabilistic

forms. Seismic inputs in deterministic form are used for deterministic analysis and design of

structures, while those in probabilistic form are used for random vibration analysis of

structures for earthquake forces, seismic risk analysis of structures, and damage estimation of

structures for future earthquakes. Seismic inputs for structural analysis are provided either in

the time domain or in the frequency domain, or in both time and frequency domains.

They

include magnitude, intensity, peak ground acceleration/velocity/displacement, duration,

predominant ground frequency, and so on. Further, certain types of analysis, such as, seismicrisk analysis, damage estimation of structures, and probabilistic seismic analysis, the

prediction of seismic input parameters for future earthquakes are essential.

Time History Records:

The most common way to describe a ground motion is with a time history record. The motion

parameters may be acceleration, velocity, or displacement, or all the three combined together.

Generally, the directly measured quantity is the acceleration and the other parameters are the

derived quantities. However, displacement and velocity can also be measured directly. The

measured time histories of records include errors resulting from many sources, such as noises

at high and low frequencies, base line error, and instrumental error. These errors are removedfrom the data before they are used. Further, measured data are in an analogue form, which are

digitized before they are used as seismic inputs. In recent years, digital seismographs are

more commonly used but the various errors mentioned above are equally present in the

analogue and digital forms. Time histories of ground motions are used directly for the time

domain analysis of structures subjected to deterministic seismic inputs. Time history analysis

is carried based on these records.

Frequency Contents of Ground Motion:

As the response of any structure depends on the ratio between the natural frequency of the

structure and the frequency of excitation, it is important to know the frequency contents of

the ground motion. For frequency domain analysis of structures, seismic input is required in

the form of frequency contents of the ground motion. The most convenient and useful way of

providing this information is by way of a Fourier synthesis of the time history of the ground

motion. At any measuring station, ground motions are recorded in three orthogonal

directions; two of them are in horizontal directions and the third is in the vertical direction.

Thus, three components of ground motions are available from any measuring station. For

structural analysis, these three components of ground motions are transformed into those

corresponding to the principal directions. It has been observed that the major direction of

ground motion lies in the direction of the line joining the measuring station and the epicenter.The other two components of the ground motion are decided accordingly.


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Power Spectral Density Function of Ground Motion:

Frequency contents of ground motion can also be represented by a power spectrum or power

spectral density function. The difference between the frequency contents represented by a

power spectrum and the Fourier amplitude spectrum is that the former is used to provide a

probabilistic estimate of the frequency contents of ground motions at a site, which areunknown.

Response Spectrum of Earthquake:

A third type of spectrum, which is used as seismic input is the response spectrum of an

earthquake. In fact, the response spectrum of an earthquake is the most favored seismic input

for earthquake engineers. There are a number of response spectra that are defined for

representing the ground motion, such as, displacement response spectrum, pseudo velocity

response spectrum, absolute acceleration response spectrum, and energy spectrum. These

spectra also show the frequency contents of the ground motion, but not as directly as the

Fourier spectrum does. The absolute acceleration response spectrum is commonly used as aninput for the response spectrum methods of analysis of structures. Another way of

characterizing the ground motion is to obtain the maximum energy response spectrum.


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III. LINEAR ANALYSIS

Static Analysis:

SEISMICCOEFFICIENT ANALYSIS OF BUILDINGS USING IS 1893 (PART 1)-2002As per IS 1893 (part1)-2002, Seismic Coefficient analysis Procedure is summarized in

following steps (6).

a) Design Seismic Base Shear- The total design lateral force or design seismic base shear

(VB) along any principal direction of the building shall be determined by the following

expression

VB= AhW

Where

Ah= Design horizontal seismic coefficient

W = Seismic weight of the building.

b) Seismic Weight of Building- The seismic weight of each floor is its full dead load plus

appropriate amount of imposed load as specified. While computing the seismic weight of

each floor, the weight of columns and walls in any storey shall be equally distributed to

the floors above and below the storey. The seismic weight of the whole building is the

sum of the seismic weights of all the floors. Any weight supported in between the storey

shall be distributed to the floors above and below in inverse proportion to its distancefrom the floors.

c) Fundamental Natural Time Period- The fundamental natural time period (Ta)

calculates from the expression

Ta= 0.075h0.75for RC frame building

Ta= 0.085h0.75 for steel frame building

If there is brick filling, then the fundamental natural period of vibration, may be taken as

Ta= 0.09hd) Distribution of Design Force- The design base shear, VBcomputed above shall be

distributed along the height of the building as per the following expression

Qi


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Response Spectrum Analysis:

The word spectrum in seismic engineering conveys the idea that the response of buildings

having a broad range of period is summarized in a single graph. For a given earthquake

motion and a percentage of critical damping, a typical response spectrum gives a plot of

earthquake-related responses such as acceleration, velocity, and deflection for a complete

range, or spectrum, of building periods. Thus, a response spectrum may be visualized as a

graphical representation of the dynamic response of a series of progressively longer

cantilever pendulums with increasing natural periods subjected to a common lateral seismic

motion of the base. The response spectrum method of analysis is not an exact method of

analysis in the sense that its results are not identical with those of the time history analysis.

However, for most of the cases, the results are accurate enough for structural design

applications. Apart from this drawback, there are other limitations to the method, namely:

(i) It is strictly applicable for linear analysis

(ii)

It cannot be applied as such for the case of multi-support excitations.

However, the method has been extended for the latter with additional approximations.

The response spectrum technique is really a simplified special case of modal analysis. The

modes of vibration are determined in period and shape in the usual way and the maximum

response magnitudes corresponding to each mode are found by reference to a response

spectrum. The response spectrum method has the great virtues of speed and cheapness. The

basic mode superposition method, which is restricted to linearly elastic analysis, produces the

complete time history response of joint displacements and member forces due to a specific

ground motion loading.


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Response spectrum methodology:

1. This method produces a large amount of output information that can require an

enormous amount of computational effort to conduct all possible design checks as a

function of time.

2.

The analysis must be repeated for several different earthquake motions in order toassure that all the significant modes are excited, since a response spectrum for one

earthquake, in a specified direction, is not a smooth function.

3.

There are significant computational advantages in using the response spectra method

of seismic analysis for prediction of displacements and member forces in structural

systems.

4.

The method involves the calculation of only the maximum values of the

displacements and member forces in each mode using smooth design spectra that are

the average of several earthquake motions.

5. In this analysis, the CQC method to combine these maximum modal response values

to obtain the most probable peak value of displacement or force is used. In addition, it

will be shown that the SRSS and CQC methods of combining results from orthogonal

earthquake motions will allow one dynamic analysis to produce design forces for all

members of the structure.

6. It is apparent that use of the response spectrum method has limitations, some of which

can be removed by additional development. However, it will never be accurate for

nonlinear analysis of multi degree of freedom structures.

7.

All displacements produced by the response spectrum method are positive numbers.

Therefore, a plot of a dynamic displaced shape has very little meaning because each

displacement is an estimation of the maximum value.8.

Inter-story displacements are used to estimate damage to non-structural elements and

cannot be calculated directly from the probable peak values of displacement.

Concept of Equivalent Lateral Force and Response Spectrum Method of Analysis:

The equivalent lateral force for an earthquake is a unique concept used in earthquake

engineering. The concept is attractive because it converts a dynamic analysis into partly

dynamic and partly static analyses for finding the maximum displacement (or stresses)

induced in the structure due to earthquake excitation. For seismic resistant design of

structures, these maximum stresses are of interest only, not the time history of stresses. The

equivalent lateral force for an earthquake is defined as a set of lateral static forces which will

produce the same peak response of the structure as that obtained by the dynamic analysis of

the structure under the same earthquake. This equivalence is restricted only to a single mode

of vibration of the structure, that is, there a set of lateral force exist for each mode of

vibration. The equivalent (static) lateral force for an earthquake is obtained by carrying out a

modal analysis of structures, and then a static analysis of the structure with equivalent (static)

lateral force in each mode of vibration is performed to obtain the desired responses.

The entire procedure is known as the response spectrum method of analysis and is developed

using the following steps.


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1. A modal analysis of the structure is carried out to obtain the mode shapes, frequencies, and

mode participation factors for the structure.

2. An equivalent static load is derived to get the same response as the maximum response

obtained in each mode vibration, using the acceleration response spectrum of the earthquake.

3. The maximum modal responses are combined to find the total maximum response of thestructure.

There are no approximations involved in the first two steps. Only the third one involves

approximations.

As a result, the response spectrum method of analysis is called an approximate method of

analysis. The approximation introduces some errors into the computed response. The

magnitude of the error depends upon the problem (both the type of structure and the nature of

earthquake excitation). However, seismic response analysis of a number of structures have

shown that for most practical problems, the response spectrum method of analysis estimates

reasonably good responses for use in design. The method is primarily developed for single-

point excitation with a single-component earthquake. However, the method could be

extended to multi-point-multi-component earthquake excitations with certain additional

assumptions. Furthermore, response spectrum method of analysis is derived for classically

damped structures. Therefore, its application to non-classically damped structural systems is

not strictly valid. However, with some other simplifying assumptions, the method has been

used for non-classically damped systems.

RESPONSE SPECTRUM MODAL ANALYSIS OF BUILDINGS USING IS 1893 (PART

1)-2002

As per IS 1893 (part1)-2002, Dynamic analysis shall be performed to obtain the design

seismic force, and its distribution to different levels along the height of the building and to

the various lateral load resisting elements, for the following buildings:

a) Regular buildings -Those greater than 40 m in height in Zones IV and V, and those greater

than 90 m in height in Zones II and III.

b) Irregular buildings - All framed buildings higher than 12 m in Zones IV and V, and those

greater than 40 m in height in Zones II and III.

Dynamic analysis may be performed by The Response Spectrum Method. Procedure is

summarized in following steps (6).

a) Modal mass (Mk)Modal mass of the structure subjected to horizontal or vertical as

the case may be, ground motion is a part of the total seismic mass of the Structure that

is effective in mode k of vibration. The modal mass for a given mode has a unique

value, irrespective of scaling of the mode shape.

Mk=


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Where

g = acceleration due to gravity

ik = mode shape coefficient at floor i in mode k

Wi= Seismic weight of floor i.

b) Modal Participation factor (Pk)Modal participation factor of mode k of vibration is the

amount by which mode k contributes to the overall vibration of the structure under horizontal

or vertical earthquake ground motions. Since the amplitudes of 95% mode shape can be

scaled arbitrarily, the value of this factor depends on the scaling used for the mode shape.

Pk =

c) Design lateral force at each floor in each mode The peak lateral force (Qik) at floor i in

Mode k is given by

Qik= AhkikPkWi

Where,

Ahk= Design horizontal spectrum value using natural period of vibration (Tk) of mode k.

Ahk =

Z = zone factor for the maximum considered earthquake

I= Importance factor depending upon the functional use of the structures

R= Response Reduction factor = Average response acceleration coefficient for rock or soil sites as given by responsespectra and based on appropriate natural periods and damping of the structure.

d) Storey shear forces in each modeThe peak shear force (Vik) acting in storey i in mode k

is given by

e) Storey shear force due to all modes consideredThe peak storey shear force (Vi) in storeyi due to all modes considered is obtained by combining those due to each mode as per SRSS.

If the building does not have closely spaced modes, than the peak response quantity due to all

modes considered shall be obtained as per Square Root of Sum of Square method

Dynamic analysis may be performed either by time history method or by the response

spectrum method. However in either method, the design base shear VB shall be compared

with a base shear (VB) calculated using a fundamental period Ta. When VBis less than all the

response quantities shall be multiplied by VB/VB.


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Linear Time History Analysis:

The acceleration values, in this alternative, shall not be taken from a general spectrum curve

representing all the earthquakes like in the response spectrum, but from the actual recorded

earthquake acceleration data; and the response given to these accelerations by the structure

and the seismic isolation system shall be calculated step by step.

IV. NON-LINEAR ANALYSIS

Pushover Analysis:

The non-linear static pushover analysis is becoming a popular tool for seismic

performance evaluation of existing and new structures. The expectation is that the pushover

analysis will provide adequate information on seismic demands imposed by the design

ground motion on the structural system and its components. Summarize the basic concepts on

which the pushover analysis can be based, assess the accuracy of pushover predictions,

identify conditions under which the pushover will provide adequate information and, perhaps

more importantly, identify cases in which the pushover predictions will be inadequate or evenmisleading. The pushover analysis of a structure is a static non-linear analysis under

permanent vertical loads and gradually increasing lateral loads. The equivalent static lateral

loads approximately represent earthquake induced forces. A plot of the total base shear versus

top displacement in a structure is obtained by this analysis that would indicate any premature

failure or weakness. The analysis is carried out up to failure, thus it enables determination of

collapse load and ductility capacity. On a building frame, and plastic rotation is monitored,

and lateral inelastic forces versus displacement response for the complete structure is

analytically computed. This type of analysis enables weakness in the structure to be

identified. The decision to retrofit can be taken in such studies. The seismic design can be

viewed as a two-step process. The first, and usually most important one, is the conception of

an effective structural system that needs to be configured with due regard to all importantseismic performance objectives, ranging from serviceability considerations. The second step


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consists of the design process that involves demand/capacity evaluation at all important

capacity parameters, as well as the prediction of demands imposed by ground motions.

Suitable capacity parameters and their acceptable values, as well as suitable methods for

demand prediction will depend on the performance level to be evaluated.

Necessity of nonlinear static pushover analysis:-1) The existing building can become seismically deficient since seismic design code

requirements are constantly upgraded and advancement in engineering knowledge. Further,

Indian buildings built over past two decades are seismically deficient because of lack of

awareness regarding seismic behaviour of structures. The widespread damage especially to

RC buildings during earthquakes exposed the construction practices being adopted around the

world, and generated a great demand for seismic evaluation and retrofitting of existing

building stocks. Limitation of pushover is Incorporation of torsional effects (due to mass,

stiffness and strength irregularities).

2) 3-D problems (orthogonality effects, direction of loading, semi-rigid diaphragms, etc)

3) Use of site specific spectra.

4) Cumulative damage issues.5) Most importantly, the consideration of higher mode effects once a local mechanism has

formed.

Since the pushover analysis is approximate in nature and is based on static loading, as such it

cannot represent dynamic phenomena with a large degree of accuracy. It may not detect some

important deformation modes that occur in a structure subjected to severe earthquakes, and it

may significantly from predictions based on invariant or adaptive static load patterns,

particularly if higher mode effects become important.

Although pushover analysis is advantageous in having a sense on nonlinear behaviour of

structures, the method includes some limitations that restrict its use. Therefore, following

statements are considered before and/or during pushover analysis:

Pushover analysis is valid for low to mid-rise structures that have a fundamental vibration

mode dominant on the structural behaviour. That means the method can be applied on

structures whose higher modes can be neglected. Higher modes are important in nonlinear

analysis results of high-rise and special structures.

The structural system of the building must be simple and regular. Results of pushover

analysis are not reliable for structures that have torsional effects caused by mass, stiffness and

strength irregularities.

Selected lateral load pattern that is applied to structure is important in displacement profile.

An invariant load pattern assumes that the inertia forces are constant during the analysis. As a

result, the structure displaces in accordance with the pattern the invariant load dictates. Sincecapacity curve is a summary of loads and global displacements, selection of invariant load

pattern affects the shape of this curve and the target displacement consequently.

Pushover analysis gives an envelope behaviour which is an idealized case of real structural

behaviour. Real behaviour of the structure can be totally different due to chaotic nature of

earthquake ground motions.

Target displacement can differ significantly than the value obtained by dynamic analysis.

This is because of modes different than fundamental modes are ignored and the capacity

curve is idealized by linear lines.

If the structural system shows excessive stiffness degradation, strength deterioration or

pinching, these properties must be incorporated well into the system so as to estimate

inelastic displacement demand better.


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If P-delta effect is important for the structural system, it may affect significantly the inter-

storey drift and the target displacement. Therefore, it must be considered in the analysis.

If the effective viscous damping of the system is much more different than 5%, inelastic

displacement demand can be affected considerably.

Target displacement is affected by foundation uplift, torsional effects and semi-rigid floor

diaphragms.

V. CONCLUSION

assesment of seismic methods

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