seismic analysis of multi storey reinforced concrete buildings frame”

“COMPUTER AIDED seismic ANALYSIS of MULTI-STOREY REINFORCED CONCRETE

BUILDINGS FRAME”

(2010-2014)Department of Civil Engineering

A Project Submitted For the Degree of Bachelor of Technology In Civil Engineering

By : Ms. Dimpy Khurana (08820703410) Ms. Ankita Sinha (04620703410)Mr. Alok Rathore (01620703410)Mr. Rahul Kr Neeraj (07320703410)Mr. Prem Pal (07220703410)

DATE:_________________

CERTIFICATE

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This is to certify that the Minor Project Report entitled “COMPUTER AIDED SEISMIC ANALYSIS OF MULTI-STOREY REINFORCED CONCRETE BUILDINGS FRAME” is being submitted by

Ms. Dimpy Khurana (08820703410) Ms. Ankita Sinha (04620703410)Mr. Alok Rathore (01620703410)Mr. Rahul Kr Neeraj (07320703410)Mr. Prem Pal (07220703410)

in partial fulfilment requirement for the degree in Bachelor of technology (B. Tech.) in Civil Engineering as prescribed by Guru Gobind Singh Indraprastha University, Delhi is record of bonafide work done by them.

( supervisor ) Head of Department & supervisor( Civil Engineering )

This is to certify that the candidate was examined by us in the minor project examination held at C.B.P. Govt. Engineering College on 11-12-2013

( Internal Examiner ) ( External Examiner )

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ACKNOWLEDGEMENT

We wish to convey our sincere gratitude to our respected principal Prof. V.K Minocha for providing us opportunity to work on this project our Head of Department Mr. S.K Tiwari. We would like to express our profound sense of deepest gratitude to our guide and motivator Mr. Rajesh Pradhan, Civil Engineering Department, CBPGEC, New Delhi for his valuable guidance, sympathy and co-operation for providing necessary facilities and sources during the entire period of this project. We would also like to thank the technical staff of Civil Engineering Department for the facilities and co-operation received from them.

We wish to thank Mr. Ajay Kumar Verma, Government contractor and civil material distributor and his colleagues who have provided us the data of a real building in Delhi.

Last, but not least, we would like to thank the authors of various research articles and books that were referred to.

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INDEXS.No. TOPIC Page No.

CHAPTER 1 1.1 Introduction 5-81.2 Scope Of Project 9-111.3 Objective Of Project 12

CHAPTER 2 2.1 Measurement Of Earthquake 14-172.2 Types Of Earthquake Measurement Scales 18-192.3 Types Of Earthquake Waves 20-212.4 Effect Of Earthquake On Buildings 22-242.5 How to protect structures from earthquake damage 25-272.6 Selection of software 282.7 Summary 29

CHAPTER 3 Problem Undertaken & Software Analysis 30-143

CHAPTER 4 Conclusions And Recommendations 144-147

CHAPTER 5 Summary & Future Scope 148-149

ANNEXURE 1 Codes Related to Earthquake 151-1712 Multi-degree freedom System & Earthquake analysis 172-177

REFERENCES

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Chapter 1

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1.1 Introduction

The opinion that designing new buildings to be Earthquake resistant will cause substantial additional costs is still among the constructional professionals. In a country of moderate seismicity adequate seismic resistance of new buildings may be achieved at no or no significant additional cost however the expenditure needed to ensure adequate seismic resistance may depend strongly on the approach selected during the conceptual design phase and the relevant design method. Regarding the conceptual design phase early collaboration between the architect and civil engineering is crucial. Concerning the design method it should be stated that significant progress has been made recently. Intensive research has improved the understanding of the behaviour of a building or structure during an earthquake and resulted in the development of more efficient and modern design methods.

The Advantages Of The Modern Method:• Drastic reduction in the seismic design Forces at ultimate limit state.• Better resistance against collapse.• Good deformation control• Prevention of damage for earthquake up to a chosen intensity (damage limit state earthquake)• Larger flexibility in case of changes in building use.• Practically equal costs.• The last three advantages are particularly important to the building owner.

The 2001 Gujarat earthquake is a recent example of catastrophe. It was the first major earthquake to hit an urban area of India in the last 50 years. It Killed 13,800 people, Injured 167,000 and a large number of reinforced concrete multi-storeyed frame buildings were heavily damaged and many of them were collapsed completely in the towns of Kachchh district. Destruction total estimated to be about US$ 5billion.It is tempting to think that this risk concentrated only in areas of high seismicity but this reasoning does not hold. In regions of low to moderate seismicity can be predominant risk as well. Buildings that are very vulnerable and at risk from even a relatively weak earthquake continue to built today. Still for new buildings the basic principles of earthquake resistant design and also the basic earthquake specifications of building codes are not followed. The reason is unawareness, convenience or intentional ignorance. As a result the earthquake risk continues to increase unnecessarily. The opinion that designing new buildings to be earthquake resistant will cause substantial additional costs is still common among construction professionals. Moreover appropriate official controls and checks are lacking.The recent earthquakes in the past have indicated the need of awareness that we need to incorporate for a new construction, retrofitting of existing structures and general safety.

Over the centuries, many researchers have come to a conclusion that earthquakes don’t kill people; buildings do. Earthquake does cause buildings, bridges and other structures to experience sudden lateral acceleration but this solely is not responsible for their collapse. Many experts now believe we can get rid of this fearsome temblor through earthquake-resistant buildings which can prevent the total collapse and preserve life. Today, the sciences of building earthquake-resistant structures have advanced tremendously and many developed countries have been practicing this approach .There are tremendous techniques from base isolation and damping process to resistant design techniques. In a developing country, expensive technology is quite difficult to incorporate whereas simple techniques which deal with the basic principles can be followed without any harsh investment.

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Before approaching these techniques it’s also equally essential to understand earthquakes. Earthquakes do occur when tectonic plates move and rub against each other. The case becomes extreme when large earthquakes may hit sometimes as a result of this movement. They snap and rebound to their original position which is also coined as Elastic Rebound Theory. When this earthquake’s ground motion occurs beneath a building and it is strong enough, it sets the building in motion, starting with the building foundation, and transfers the motion throughout the rest of building in a very complex way. These motions in turn induce forces which can produce damage.

Our concern is to make our structure withstand such forces. Every building must withstand significant lateral force. We need to give our attention while designing the plan, section of a building, selecting the construction material and while implementing the ideas in the construction phase. There are tremendous techniques that can be embraced by a normal building. When dispatching the forces toward the footing from the structure, columns play a vital role than that of the beams so designing a structure with strong columns than beams is appreciated.

Structure might be of various shapes but for earthquake-resistant design, a simple and regular shape such as rectangular can be beneficial. Shear wall is a best walling system for earthquake-resistant buildings but it can be a bit expensive. In such cases, cross-bracing can be provided which also helps in dispatching the forces with great efficiency. While considering height of the building, the floor area and the overall width of the area must be in a decreasing form as stories increase. As all the load will be transferred to a base column, so the width of base column should also be properly reinforced. Proper spacing must be maintained between two buildings. Simple but good plans are always appreciated and are good to resist earthquake.

When stirrups are being bent for beams and columns, proper locking at the edge with at least 45 degree must be maintained as they form good bonding and resist the buckling phenomenon. Proper space between the bars to facilitate during concrete compaction, the interlocking of two beams with

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proper development length and mix design of concrete are also major considering point during the construction phase. Footing as per the soil condition must be identified and proper placing of footing must be done. Horizontal truss for the roofing system can be best choice in normal building. Identifying the safe region of a building can be beneficial at the time of emergency. Moreover obeying a country building code and getting assistance of experts can have a great advantage.

Proper selection of material for construction also plays a vital role. More economical material which is locally available, extracted from renewable resources can be eco-friendly in the construction and also add up tremendous aesthetical benefits. Light material can be used which makes the structure more strong in a non-load bearing structure. Retrofitting for existing structure in accordance with code can make the pre-existing structure safe. Being aware about the catastrophe well in advance is one of the means to get rid of the problems and implementing the safety in need and save lives.

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1.2 Scope of project

Study area: New Delhi

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The Indian subcontinent has a history of devastating earthquakes with 59% of the land being vulnerable to earthquakes. The Indian plate is driving Asia at a rate of approximately 47 mm/year. Intra plate earthquakes from Himalayan region and inter plate earthquakes of local origin are the major reasons for seismic design of buildings. And due to earthquake:

Structures in to and fro motion develop stresses due to inertial force(NFL)

Vertical shaking adds or subtracts to weight of structure.

These lateral inertia forces are transferred by the floor slab to the walls or columns, to the

foundations, and finally to the soil system underneath. This sometimes leads to settlement

of foundation due to soil liquefaction.

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Thus, there is an enormous need to establish a Seismic Disaster management plan for India which can only be done through analysis and modelling of structures. Modelling and simulation of structural components and complex structures through software's is the most sophisticated way of analysis.

Computers can perform complicated computations at a high speed therefore computer programs are used for analysis and design of structural member. Hand computations are applicable for small problem and tedious for even for medium sized calculations and 3-D analysis is almost impossible. On the other hand in computer analysis 3-D analysis can be easily performed with a high degree of accuracy. STAAD Pro V8i is a very powerful which can be used for 3-D analysis and is useful for

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analysis and design of multi-storied buildings. Full range of analysis including static, P-delta, response spectrum, time-history, cable etc. and steel design, concrete design and timber design is available in STAAD Pro.

1.3 Objective of project

Seismic analysis of different prototype of RCC building was selected. Prototypes were having various dimensions of beams and columns. These were analysed through STAAD pro V8i for same load combinations.

Buildings were analysed for:

o Rayleigh frequencyo Modal frequency method

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o Response spectrum base shear calculationo Time history Base shear calculation

And 10 mode shapes were generated and various reactions and forces were calculated.

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Chapter 2

2.1 Measuring the size of an earthquakeEarthquakes range broadly in size. A rock-burst in an Idaho silver mine may involve the fracture

of 1 meter of rock; the 1965 Rat Island earthquake in the Aleutian arc involved a 650 kilometre length of the Earth's crust. Earthquakes can be even smaller and even larger. If an earthquake is felt or causes perceptible surface damage, then its intensity of shaking can be subjectively estimated. But ma ny large earthquakes occur in oceanic areas or at great focal depths and are either simply not felt or their felt pattern does not really indicate their true size.

Today, state of the art seismic systems transmit data from the seismograph via telephone line and satellite directly to a central digital computer. A preliminary location, depth-of-focus, and

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magnitude can now be obtained within minutes of the onset of an earthquake. The only limiting factor is how long the seismic waves take to travel from the epicentre to the stations - usually less than 10 minutes.

Magnitude:

Modern seismographic systems precisely amplify and record ground motion (typically at periods of between 0.1 and 100 seconds) as a function of time. This amplification and recording as a function of time is the source of instrumental amplitude and arrival-time data on near and distant earthquakes. Although similar seismographs have existed since the 1890's, it was only in the 1930's that Charles F. Richter, a California seismologist, introduced the concept of earthquake magnitude. His original definition held only for California earthquakes occurring within 600 km of a particular type of seismograph (the Woods-Anderson torsion instrument). His basic idea was quite simple: by knowing the distance from a seismograph to an earthquake and observing the maximum signal amplitude recorded on the seismograph, an empirical quantitative ranking of the earthquake's inherent size or strength could be made. Most California earthquakes occur within the top 16 km of the crust; to a first approximation, corrections for variations in earthquake focal depth were, therefore, unnecessary.

Richter's original magnitude scale (ML) was then extended to observations of earthquakes of any distance and of focal depths ranging between 0 and 700 km. Because earthquakes excite both body waves, which travel into and through the Earth, and surface waves, which are constrained to follow the natural wave guide of the Earth's uppermost layers, two magnitude scales evolved - the mb and MSscales.

The standard body-wave magnitude formula is

mb = log10(A/T) + Q(D,h) ,

Where A is the amplitude of ground motion (in microns); T is the corresponding period (in seconds); and Q(D,h) is a correction factor that is a function of distance, D (degrees), between epicentre and station and focal depth, h (in kilometres), of the earthquake. The standard surface-wave formula is

MS = log10 (A/T) + 1.66 log10 (D) + 3.30.

There are many variations of these formulas that take into account effects of specific geographic regions, so that the final computed magnitude is reasonably consistent with Richter's original definition of ML. Negative magnitude values are permissible.

A rough idea of frequency of occurrence of large earthquakes is given by the following table:

MS Earthquakes Per year ---------- ----------- 8.5 - 8.9 0.3 8.0 - 8.4 1.1 7.5 - 7.9 3.1 7.0 - 7.4 15 6.5 - 6.9 56 6.0 - 6.4 210

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This table is based on data for a recent 47 year period. Perhaps the rates of earthquake occurrence are highly variable and some other 47 year period could give quite different results.

The original mb scale utilized compression body P-wave amplitudes with periods of 4-5 s, but recent observations are generally of 1 s-period P waves. The MS scale has consistently used Rayleigh surface waves in the period range from 18 to 22 s.

When initially developed, these magnitude scales were considered to be equivalent; in other words, earthquakes of all sizes were thought to radiate fixed proportions of energy at different periods. But it turns out that larger earthquakes, which have larger rupture surfaces, systematically radiate more long-period energy. Thus, for very large earthquakes, body-wave magnitudes badly underestimate true earthquake size; the maximum body-wave magnitudes are about 6.5 - 6.8. In fact, the surface-wave magnitudes underestimate the size of very large earthquakes; the maximum observed values are about 8.3 - 8.7. The mostly damage to structure is caused by the energy for shorter period.

Energy, E

The amount of energy radiated by an earthquake is a measure of the potential for damage to man-made structures. Theoretically, its computation requires summing the energy flux over a broad suite of frequencies generated by an earthquake as it ruptures a fault. Because of instrumental limitations, most estimates of energy have historically relied on the empirical relationship developed by Beno Gutenberg and Charles Richter:

log10E = 11.8 + 1.5MS

Where energy, E, is expressed in ergs. The drawback of this method is that MS is computed from a bandwidth between approximately 18 to 22 s. It is now known that the energy radiated by an earthquake is concentrated over a different bandwidth and at higher frequencies. With the worldwide deployment of modern digitally recording seismograph with broad bandwidth response, computerized methods are now able to make accurate and explicit estimates of energy on a routine basis for all major earthquakes. A magnitude based on energy radiated by an earthquake, Me, can now be defined,

Me = 2/3 log10E - 2.9.

For every increase in magnitude by 1 unit, the associated seismic energy increases by about 32 times.

Although Mw and Me are both magnitudes, they describe different physical properties of the earthquake. Mw, computed from low-frequency seismic data, is a measure of the area ruptured by an earthquake. Me, computed from high frequency seismic data, is a measure of seismic potential for damage. Consequently, Mw and Me often do not have the same numerical value.

Intensity

The increase in the degree of surface shaking (intensity) for each unit increase of magnitude of a shallow crustal earthquake is unknown. Intensity is based on an earthquake's local accelerations and how long these persist. Intensity and magnitude thus both depend on many variables that include exactly how rock breaks and how energy travels from an earthquake to a receiver. These factors make it difficult for engineers and others who use earthquake intensity and magnitude data to evaluate the error bounds that may exist for their particular applications.

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An example of how local soil conditions can greatly influence local intensity is given by catastrophic damage in Mexico City from the 1985, MS 8.1 Mexico earthquake cantered some 300 km away. Resonances of the soil-filled basin under parts of Mexico City amplified ground motions for periods of 2 seconds by a factor of 75 times. This shaking led to selective damage to buildings 15 - 25 stories high (same resonant period), resulting in losses to buildings of about $4.0 billion and at least 8,000 fatalities.

The occurrence of an earthquake is a complex physical process. When an earthquake occurs, much of the available local stress is used to power the earthquake fracture growth to produce heat rather that to generate seismic waves. Of an earthquake systems total energy, perhaps 10 percent to less that 1 percent is ultimately radiated as seismic energy. So the degree to which an earthquake lowers the Earth's available potential energy is only fractionally observed as radiated seismic energy.

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2.2 Types of Earthquake Measurement Scales:

The Mercalli intensity scale is a seismic scale used for measuring the intensity of an earthquake. It measures the effects of an earthquake, and is distinct from the moment magnitude usually reported for an earthquake (sometimes misreported as the Richter magnitude), which is a measure of the energy released. The intensity of an earthquake is not totally determined by its magnitude.

The scale quantifies the effects of an earthquake on the Earth's surface, humans, objects of nature, and man-made structures on a scale from I (not felt) to XII (total destruction).[1][2] Values depend upon the distance to the earthquake, with the highest intensities being around the epicentral area.

The Richter magnitude scale (often shortened to Richter scale) was developed to assign a single number to quantify the energy released during an earthquake.

Magnitude DescriptionMercalli intensity Average earthquake effects

Average frequency of occurrence (estimated)

Less than 2.0 Micro I Micro earthquakes, not felt, or felt rarely by sensitive people. Recorded by seismographs

Continual/several million per year

2.0–2.9

Minor

I to II Felt slightly by some people. No damage to buildings. Over one million per year

3.0–3.9 II to IV Often felt by people, but very rarely causes damage. Shaking of indoor objects can be noticeable.

Over 100,000 per year

4.0–4.9 Light IV to VI

Noticeable shaking of indoor objects and rattling noises. Felt by most people in the affected area. Slightly felt outside. Generally causes none to minimal damage. Moderate to significant damage very unlikely. Some objects may fall off shelves or be knocked over.

10,000 to 15,000 per year

5.0–5.9 Moderate VI to VIII

Can cause damage of varying severity to poorly constructed buildings. At most, none to slight damage to all other buildings. Felt by everyone. Casualties range from none to a few.

1,000 to 1,500 per year

6.0–6.9 Strong VII to XDamage to a moderate number of well built structures in populated areas. Earthquake-resistant structures survive with slight to moderate damage. Poorly-designed

100 to 150 per year

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structures receive moderate to severe damage. Felt in wider areas; up to hundreds of miles/kilometres from the epicentre. Strong to violent shaking in epicentral area. Death toll ranges from none to 25,000.

7.0–7.9 Major

VIII or greater[

Causes damage to most buildings, some to partially or completely collapse or receive severe damage. Well-designed structures are likely to receive damage. Felt across great distances with major damage mostly limited to 250 km from epicentre. Death toll ranges from none to 250,000.

10 to 20 per year

8.0–8.9

Great

Major damage to buildings, structures likely to be destroyed. Will cause moderate to heavy damage to sturdy or earthquake-resistant buildings. Damaging in large areas. Felt in extremely large regions. Death toll ranges from 1,000 to 1 million.

One per year

9.0 and greater

Near or at total destruction - severe damage or collapse to all buildings. Heavy damage and shaking extends to distant locations. Permanent changes in ground topography. Death toll usually over 50,000.

One per 10 to 50 years

The scale is a base-10 logarithmic scale. The magnitude is defined as the logarithm of the ratio of the amplitude of waves measured by a seismograph to arbitrary small amplitude.

The moment magnitude scale (abbreviated as MMS; denoted as MW or M) is used by seismologists to measure the size of earthquakes in terms of the energy released.[1] The magnitude is based on the seismic moment of the earthquake, which is equal to the rigidity of the Earth multiplied by the average amount of slip on the fault and the size of the area that slipped.[ The symbol for the moment magnitude scale is , with the subscript meaning mechanical work accomplished. The moment magnitude is a dimensionless number defined by

Where is the seismic moment in N⋅m (107 dyne⋅cm)

2.3 Types of Seismic Waves

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There are many types of seismic waves, body wave, surface waves:

Body waves consist of:Primary waves (P waves) (or "longitudinal waves") travel through fluids, and solids. They are compression waves and rely on the compression strength and elasticity of the materials to propagate. They are known as body waves because they travel though the body of a material in all directions and not just at the surface, as water waves do. For P waves, the motion of the material particles that transmit the energy move parallel to the direction of propagation. P waves travel the same way as sound waves in air. The transmission of compression waves is due to the strong electronic between atoms that get squeezed together too tightly. P waves are the fastest seismic waves and travel at roughly 6.0 km/s in the crust (more than seven times the speed of sound).

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Main types of seismic waves.wave type particle motion namebody waves Longitudinal P wave

Transverse S wave

surface waves horizontal transverse Love wavevertical elliptical Rayleigh wave

Secondary waves(S waves) depend on the shear strength of the material. The strength of atomic bonds in solids allows them to transmit transverse motions. S waves do not travel as fast as P waves and have a velocity of about 3.5 km/s in the crust.

Surface waves are very similar to ocean waves as they only occur at the surface of the earth and do not penetrate into the interior deeply. There are two types of surface waves: Love waves and Rayleigh waves. Love waves cause surface motions similar to that by S-waves, but with no vertical component. Typically, it the surface waves that does the most damage during an earthquake, especially at distances far from the epicentre. The velocity of surface waves varies with their wavelength but always travel slower than P and S waves.

Unlike body waves, surface waves move along the surface of the Earth. Surface waves are to blame for most of an earthquake's carnage. They move up and down the surface of the Earth, rocking the foundations of man-made structures. Surface waves are the slowest moving of all waves, which means they arrives the last. So the most intense shaking usually comes at the end of an earthquake.

An earthquake will generate all of these types of waves and they will propagate over the surface of the earth and through the body of the earth. The waves can be distinguished by the differing velocities and particle motions. Seismometers measure the particle motion produced by these waves. P-waves are fastest, followed in sequence by S-wave, Love and Rayleigh waves.

Real earthquake ground motion at a particular building site is vastly more complicated than the simple wave form. Here it's useful to compare the surface of the ground under an earthquake to the surface of a small body of water, like a pond. You can set the surface of a pond in motion--by throwing stones into it.

The first few stones create a series of circular waves, which soon begin to collide with one another. After a while, the collisions, which we term interference patterns begin to predominate over the pattern of circular waves. Soon, the entire surface of the water is covered by ripples, and you can no longer make out the original wave forms. During an earthquake, the ground vibrates in a similarly complex manner, as waves of different frequencies and amplitude interact with one another.

The complexity of earthquake ground motion is due to three factors:

The seismic waves generated at the time of earthquake fault movement were not all of a uniform character.

As these waves pass through the earth on their way from the fault to the building site, they are modified by the soil and rock media through which they pass

Once the seismic waves reach the building site they undergo further modifications that are dependent upon the characteristics of the ground and soil beneath the building. We refer to these three factors as source effects, path effects, and local site effects.

2.4 Effect of earthquake on buildings

Systematic study of earthquakes has also one very practical aspect. Strong earthquakes often cause great damage to houses and other buildings, and occasionally they level to the ground large and rich cities, and bury thousands of people under the ruins. Therefore, one of the most important goals of seismology is to theoretically study how the movement of the earth affects buildings, and to apply

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http://science.howstuffworks.com/nature/natural-disasters/12-of-the-most-destructive-earthquakes.htm

these results as well as the experience gained in catastrophic earthquakes to show the ways of constructing buildings resistant as much as possible against earthquakes. Investigation of earthquakes with modern instruments has given the following results on the ways how the earth shakes:1. An earthquake consists of a series of periodic displacements of the earth, after which every point of the surface either returns to its initial position, or acquires a new position, corresponding to some linear displacement. 2. A sizeable linear displacement can be detected after an earthquake only by means of a very precise triangulation, but is often easily seen during large earthquakes, either as cracks appearing on the earth surface, or as a larger or smaller denivelation of the ground.3. The periodic motion can be described as a sum of waves or oscillations in the three mutually perpendicular directions: one vertical and two horizontal directions, e.g. NS (north-south) and EW (east-west). If one combines the two horizontal directions into one resultant, one can talk about only one horizontal and one vertical component of the wave motion or oscillation of the earth. Since the linear movements of the earth are either harmless or induce damage which can be neither predicted nor calculated, here we consider only the oscillatory or the wave motions. A point performs a vibration when it first moves in some positive direction, for example towards the right hand side, and then reaches a certain largest distance with respect to its initial position. From there it returns, going in the negative direction, passing through its initial position down to the same maximal distance on the other side; after that it returns again and comes back to the initial point. The point “A” is moved first to a, goes back to “A”, continues until “a1”, and returns to “A”. If there were no obstacles, this process would be continued endlessly.

If a certain point in the earth or on the surface of the earth acquires from the earthquake some velocity in the direction “Aa”, it shall be able to move in this direction only to the point where the elasticity of the earth absorbs the whole energy of its motion. Thus the motion from “A” to “a” is retarded, or in other words: in each position of the point “A”, which is not its initial position, a force is acting on the point oriented towards the initial position, and the acceleration of this point increases as the distance from the initial position grows. For very small displacements “Aa” one can assume that the acceleration is proportional to the distance “Aa”. The largest distance reached by the point, with respect to its initial position, is called the amplitude of the oscillation. The time needed for the point to perform the complete motion from “A” to “a” and back, passing through “A” to “a1” and then back to”A”, is called the period of oscillation. If some point on the surface of the earth rises, it pulls with it all the surrounding points, so that they move in the same manner as the original point, but with a certain delay. From these points the movement is conveyed to further neighboring points, etc. After some time the surface of the earth looks just like a surface of the water a short time after a stone has fallen in it, i.e. the waves are formed which, starting from the point at which the motion began, spread in all directions. Therefore this kind of oscillatory motion is also called the wave motion.

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Permanent ground deformations can tear a structure apart. Some foundation types are better able to resist these permanent ground deformations than others. For example, the use of pile foundations, with the piles extending beneath the anticipated zone of soil liquefaction, can be effective in mitigating the hazard’s effects. The use of heavily reinforced mats can also be effective in resisting moderate ground deformation due to fault rupture or lateral spreading. Most earthquake-induced building damage, however, is a result of ground shaking. When the ground shakes at a building site, the building’s foundations vibrate in a manner that’s similar to the surrounding ground. Brittle elements tend to break and lose strength. (Examples of brittle elements include unreinforced masonry walls that crack when overstressed in shear, and unconfined concrete elements that crush under compressive overloads.) Ductile elements are able to deform beyond their elastic strength limit and continue to carry load. (Examples of ductile elements include tension braces and adequately braced beams in moment frames).

For economic reasons, building codes permit buildings to be damaged by the infrequent severe earthquakes that may affect them, but prevent collapse and endangerment of life safety. For buildings that house important functions essential to post-earthquake recovery, including hospitals, fire stations, emergency communications centres, etc., codes adopt more conservative criteria that’s intended to minimize the risk that the buildings would be so severely damaged they could not be used for their intended function.

Throughout the 20 th century, the intent of seismic design in building codes was to avoid earthquake-induced damage that would pose a significant risk to safety while still permitting economical designs. Thus, building code provisions were developed that would permit some damage to occur, but protect against damage likely to lead to either local or partial collapse, or the generation of dangerous falling debris. When these building codes were first developed, the technical community didn’t have a good understanding of ground shaking, its magnitude, the dynamic response characteristics of structures, or nonlinear behaviour. Today’s codes still seek to protect life safety vs. minimize damage, but do so through a variety of prescriptive criteria based on observation, as well as laboratory and analytical research. Research has spawned numerous innovations now common in earthquake engineering, including ductile detailing of concrete structures, improved connections for moment frames, base isolation technology, energy dissipation technology, and computing tools. Current research activities are focused on three areas: 1) performance-based design, 2) development of damage-resistant systems, and 3) improvement in the ability to predict the occurrence and intensity of earthquakes. The concept of performance-based design is that a designer can be inventive in terms of the combinations of structural framing systems and detailing chosen vs. adhering to prescriptive criteria contained in building code. But this approach presumes that the designer can demonstrate, typically through simulation that the structure is capable of performing acceptably. The ability to actually implement performance-based design is becoming more practical. As this trend continues, designers will find that they’re no longer constrained to certain structural systems and configurations, or have to adhere to minimum design base shears, drift, or detailing criteria, which provides more freedom in the design of structures of the future. The Most Important Aspects of Seismic Design

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Continuity: The pieces that comprise a structure must be connected with sufficient strength so that, when the structure responds to shaking, the pieces don’t pull apart and the structure responds as an integral unit. Stiffness and Strength: Structures must have sufficient lateral and vertical strength so the forces induced by relatively frequent, low-intensity earthquakes don’t cause damage, and rare, high-intensity earthquakes don’t strain elements so far beyond yield points that they lose strength. Regularity: A structure is “regular” if its configuration has a pattern of lateral deformation during response to shaking that’s relatively uniform throughout its height – without twisting or large concentrations of deformation in small areas of the structure. Redundancy: Redundancy is important because of the basic design strategy behind the building codes. If a structure only has a few elements to resist earthquake-induced forces, the structure may lose its ability to resist further shaking when those elements become damaged; however, if a large number of seismic-load-resisting elements are present and some become damaged, others may still provide stability. Defined Yield Mechanisms: In this approach, which is often called as “capacity design,” it must be decided which elements will yield under a strong earthquake. These elements are detailed so they can sustain yielding without undesirable strength loss. At the same time, all other elements of the structure, such as gravity load-carrying beams, columns, and connections, are proportioned so they’re strong enough to withstand the maximum forces and deformations that can be delivered by an earthquake once the intended yield mechanism has been engaged.

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2.5 How to protect structures from earthquake damage

In recent times, reinforced concrete buildings have become common in India, particularly in towns and cities. Reinforced concrete (or simply RC) consists of two primary materials, namely concrete with reinforcing steel bars. Concrete is made of sand, crushed stone (called aggregates) and cement, all mixed with pre-determined amount of water. Concrete can be molded into any desired shape, and steel bars can be bent into many shapes. Thus, structures of complex shapes are possible with RC. A typical RC building is made of horizontal members (beams and slabs) and vertical members (columns and walls), and supported by foundations that rest on ground. The system comprising of RC columns and connecting beams is called a RC Frame. The RC frame participates in resisting the earthquake forces. Earthquake shaking generates inertia forces in the building, which are proportional to the building mass. Since most of the building mass is present at floor levels, earthquake-induced inertia forces primarily develop at the floor levels. These forces travel ownwards through slab and beams to columns and walls, and then to the foundations from where they are dispersed to the ground. As inertia forces accumulate downwards from the top of the building, the columns and walls at lower storey’s experience higher earthquake-induced forces and are therefore designed to be stronger than those in storeys above. Stirrups in RC beams help in three ways, namely:

i. They carry the vertical shear force and thereby resist diagonal shear cracks (Figure 2b),ii. They protect the concrete from bulging outwards due to flexure, andiii. They prevent the buckling of the compressed longitudinal bars due to flexure.

In moderate to severe seismic zones, the Indian Standard IS13920-1993 prescribes the following requirements related to stirrups in reinforced concrete beams:

(a) The diameter of stirrup must be at least 6mm; in beams more than 5m long, it must be at least 8mm.

(b) Both ends of the vertical stirrups should be bent into a 135° hook and extended sufficiently beyond this hook to ensure that the stirrup does not open out in an earthquake. The spacing of vertical stirrups in any portion of the beam should be determined from calculations

(c) The maximum spacing of stirrups is less than half the depth of the beam.(d) For a length of twice the depth of the beam from the face of the column, an even more

stringent spacing of stirrups as specified in (c).

Columns, the vertical members in RC buildings, contain two types of steel reinforcement, namely:(a) long straight bars (called longitudinal bars) placed vertically along the length, and (b) Closed loops of smaller diameter steel bars (called transverse ties) placed horizontally at

regular intervals along its full length.Columns can sustain two types of damage, namely axial-flexural (or combined compression bending) failure and shear failure. Shear damage is brittle and must be avoided in columns by providing transverse ties at close spacing. Design Strategy Designing a column involves selection of materials to be used (i.e., grades of concrete and steel bars), choosing shape and size of the cross-section, and calculating amount and distribution of steel reinforcement. The first two aspects are part of the overall design strategy of the whole building. The Indian Ductile Detailing Code IS: 13920-1993 requires columns to be at least 300mm wide. A column width of up to 200mm is allowed if unsupported length is less than 4m and beam length is less than 5m. Columns that are required to resist earthquake forces must be designed to prevent shear failure by a skillful selection of reinforcement.Vertical Bars tied together with Closed Ties Closely spaced horizontal closed ties help in threeWays, namely

(i) they carry the horizontal shear forces induced by earthquakes, and thereby resist diagonal shear cracks,

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(ii) they hold together the vertical bars and prevent them from excessively bending outwards (in technical terms, this bending phenomenon is called buckling), and

(iii) They contain the concrete in the column within the closed loops. The ends of the ties must be bent as 135° hooks. Such hook ends prevent opening of loops and consequently bulging of concrete and buckling of vertical bars.

The Indian Standard IS13920-1993 prescribes following details for earthquake-resistant columns: (a) Closely spaced ties must be provided at the two ends of the column over a length not less

than larger dimension of the column, one-sixth the column height or 450mm. (b)Over the distance specified in item (a) above and below a beam-column junction, the

vertical spacing of ties in columns should not exceed D/4 for where D is the smallest dimension of the column (e.g., in a rectangular column, D is the length of the small side). This spacing need not be less than 75mm nor more than 100mm. At other locations, ties are spaced as per calculations but not more than D/2.

(c) The length of tie beyond the 135° bends must be at least 10 times diameter of steel bar used to make the closed tie; this extension beyond the bend should not be less than 75mm. Construction drawings with clear details of closer ties are helpful in the effective implementation at construction site. In columns where the spacing between the corner bars exceeds 300mm, the Indian Standard prescribes additional links with 180° hook ends for ties to be effective in holding the concrete in its place and to prevent the buckling of vertical bars. These links need to go around both vertical bars and horizontal closed ties; special care is required to implement this properly at site.

Lapping Vertical BarsIn the construction of RC buildings, due to the limitations in available length of bars and due to constraints in construction, there are numerous occasions when column bars have to be joined. ASimple way of achieving this is by overlapping the two bars over at least a minimum specified length, called lap length. The lap length depends on types of reinforcement and concrete. For ordinary situations, it is about 50 times bar diameter. Further, IS: 13920-1993 prescribes that the lap length be provided ONLY in the middle half of column and not near its top or bottom ends. Also, only half the vertical bars in the column are to be lapped at a time in any storey. Further, when laps are provided, ties must be provided along the length of the lap at a spacing not more than 150mm.

Reinforcing the Beam-Column JointDiagonal cracking & crushing of concrete in joint region should be prevented to ensure good earthquake performance of RC frame buildings. Using large column sizes is the most effective way of achieving this. In addition, closely spaced closed-loop steel ties are required around column bars to hold together concrete in joint region and to resist shear forces. Intermediate column bars also are effective in confining the joint concrete and resisting horizontal shear forces providing closed-loop ties in the joint requires some extra effort. Indian Standard IS: 13920-1993 recommends continuing the transverse loops around the column bars through the joint region. In practice, this is achieved by preparing the cage of the reinforcement (both longitudinal bars and stirrups) of all beams at a floor level to be prepared on top of the beam formwork of that level and lowered into the cage. However, this may not always be possible particularly when the beams are long and the entire reinforcement cage becomes heavy.

Strong column weak beam combination makes a better seismic performance.

Steel Structures that Provide Earthquake ResistanceBraced-frame systems rely on the stiffness and strength of vertical truss systems for lateral resistance. Braced frames are categorized as concentric or eccentric, depending on whether the connections of braces to beams, columns, and beam-to-column joints are concentric or not. Concentrically braced frames can have many alternative patterns, including a single diagonal brace in

26

a bay, intersecting X-pattern braces in a bay, and inverted-V-pattern and V-pattern braces in a bay. The latter case is also known as “chevron-pattern bracing.” Buckling-restrained braced frames are a special type of concentrically braced frame with braces specially designed to withstand yield level compressive forces without buckling. Eccentrically braced frames are arranged as modifications of the single-diagonal pattern or chevron-pattern bracing. AISC 341 places strict limits on the eccentricities and detailing that can be used. Shear-wall systems rely on vertical plates, reinforced by bounding structural members, to provide lateral resistance. Moment-frame systems rely on the rigidity of beams and columns interconnected to resist relative rotation. There are frames in which conventional rolled shapes are used as the beams in the frames, and frames in which trusses form the horizontal members of the frames.

Dual systems utilize a combination of moment frames and braced frames or shear walls. The moment frame, acting alone, must be capable of providing at least 25 percent of the structure’s required lateral seismic resistance; the braced frames or shear walls that the moment frames are paired with must be proportioned, based on their stiffness, to resist that portion of the total required design lateral forces (determined considering their interaction with the moment frame, which may be more or less than 75 percent of the total required resistance, and may vary with height). Cantilevered columns systems rely on the cantilever strength and stiffness of columns restrained against rotation at their bases. Each of these elements can be coupled with different horizontal elements, including wood-sheathed floors and roofs, steel deck roofs, concrete-filled steel deck floors and roofs, formed concrete slabs, precast concrete floors and roofs, and horizontal bracing systems.

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2.6 Selection of software

It is a user friendly package and graphical user interface of STAAD pro V8i is very wonderful.Numerous benefits are associated with this software. Some of which include;

It supports several steel, concrete and timber design codes. Generation of loads Cleanup capability Wide Application in Structural Engineering Concrete and steel design have been included into STAAD.pro to help us optimize our

design with full control of parameters such as deflection, reinforcement for your concrete columns, beams, slabs and shear walls and as a result of this, the stress of using one software to do modelling, another software for steel design and another one to design your concrete beams, slabs and foundations is wept out.

we can customize it to fit any design you need because of it in-built parametric library. With it, we don't need to use multiple software programs to check the integrity of our

structure under different conditions; we can also subject your structure to linear, dynamic, and even non-linear conditions.

It is the best and most professional software for steel, concrete, timber, aluminium and cold-formed steel design. Some of the things we can do using the software:

Used in the design of culverts. Used in the design of petrochemical plants, Used in the design of tunnels, Used in the design of bridges, etc. It is a user friendly package and graphical user interface of STAAD is very wonderful.

The principle objective of this project is to analyse and design a earthquake resistant multi-storeyed building (3 dimensional frame) using STAAD Pro V8i. The design involves load calculations manually and analyzing the whole structure by STAAD Pro. The design methods used in STAAD Pro V8i analysis are Limit State Design conforming to Indian Standard Code of Practice. STAAD Pro V8i features a state-of-the-art user interface, visualization tools, powerful analysis and design engines with advanced finite element and dynamic analysis capabilities. From model generation, analysis and design to visualization and result verification, STAAD Pro V8i is the professional’s choice.STAAD Pro V8i has a very interactive user interface which allows the users to draw the frame and input the load values and dimensions. Then according to the specified criteria assigned it analyses the structure and designs the members with reinforcement details for RCC frames. We continued with our work with some more multi-storeyed under various load combinations.

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2.7 Summary

During earthquake analysis, we can study dynamic properties of building in terms of natural frequency and base shear.

Natural Frequency can be calculated by

1. Rayleigh Frequency2. Modal / Eigen Calculation Method

Base Shear can be calculated by :

1. Time history Analysis 2. Response Spectrum Method

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Chapter 3: Problems undertaken and software analysis

30

Assumed Preliminary data required for analysisType of Structure – Multi-storey rigid jointed plane frame (Ordinary RC moment resisting frame)

Seismic Zone – IV (table 2, IS 1893(Part 1):2002)

Number of stories – Four (G+3)

Materials – Concrete (M20) and Reinforcement (Fe 415)

Size of column – 250mm*450mm

Size of beams – 250mm*400mm in longitudinal and 250mm*350mm in transverse direction

Specific weight of RCC – 25kN/m^3

Rock/Soil type – Soft Rock (variable)

Response spectra – As per IS 1893 (part 1):2002

Time history – Compatible to IS 1893(part 1): 2002 spectra rocky site for 5% damping

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Open STAAD Pro V8i

32

Click on new project

Specify name, location & Dimensional Units (Taking Length unit as meter and Force unit as kilo Newton)

33

Add beam and Finish

`

34

Grid Appears

Go to GEOMETRY RUN STRUCTURAL WIZARD Or we can select OPEN STRUCTUAL WIZARD in the new project only

35

In StWizard In MODEL TYPE Select FRAME MODEL.

36

Select BAY FRAME

Set BAY FRAME length, width and height and number of bays in respective direction.

37

Check preview and close and Add.

Structure appears in the main window Remove Grid

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Final structure:

Go to GENERAL Tab In PROPERTY Tab Define Section PropertiesClick on Definein Property Dialogue box Click on rectangleGive dimensionsAdd

Three different sections defined for respective column (ref section 1), beams in longitudinal (ref section 2) and transverse (ref section 3) direction.

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Go to Select beams parallel to Y select ref 1 section assign to selected beamin the dialogue box click YES.

Repeat the step same as above

Select ref section 2

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Select beam parallel to X assign to selected beams assign yes

Select ref section 3

Select beam parallel to Z assign to selected beams assign yes

Final structure:

Go to SUPPORT tab the dialogue box appears of support Create Fixed add

Fixed support defined

41

Take front view

Select Support 2 Select nodes assign to selected beams yes

For three dimensional view

42

In general tab Loads & Definition

43

CALCULATING NATURAL FREQUENCY OF A BUILDING-MODAL SHAPE

In load and definition dialogue box select seismic definition add

In the new window appeared

In Type IS 1893-2002 Generate

44

Set the Parameters:

45

Modified definitions Add

In the new dialoged box put self weight factor as 1 Add

46

Set Load definitions as follows:

Assign Self weight to view.Assign UDL with force in all beams.

Then go to Command menu Miscellaneous Cut off Mode shapes, enter value 10 and press OK

Command Pre print analysis Print all

Analysis & Print in the dialogue box Print All

Analysis run analysis (Control +F5)

Click on the Output view file and done.

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Result:

48

Loading 1 is “seismic” (seismic effect in X, Y & Z direction)

Loading 2 is “dead” (Dead Load)

Loading 3 is “live” (Live Load)

49

PROTOTYPE A:

DIMENSIONS:

100*300mm (Y direction)

100*250mm (X direction)

100*200mm (Z direction)

Modal frequency:

50

PROTOTYPE B:

Dimensions:




Modal frequency:

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PROTOTYPE C:

DIMENSION:

150*350 (Y direction)



Modal frequency:

54

PROTOTYPE D:

DIMENSION:




Modal frequency:

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CALCULATING NATURAL FREQUENCY OF A BUILDING – RAYLEIGH METHOD

In load and definition dialogue box select seismic definition add

In the new window appeared

In Type IS 1893-2002 Generate

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Set the Parameters:

59

Modified definitions Add

In the new dialoged box self weight self weight factor as 1 Add

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In Loads and definition Load Case detailsLoad type Define Give name Add loads

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Select load case details Select LoadAddSelf weightself weight load X Factor 1Add

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Go to Frequency Rayleigh Frequency Add

Similarly, add other loads.

In Live load Member loadUniform forceassign valueAdd

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Again, go to floor loadFloorAssign value in respective direction with specific rangeadd

Similarly, define other loads.

And load final definition will be

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ASSIGN THE LOADS.

Assign dead loads to the view.

Assign UDL to all beams (in X & Z direction)

Analyzing the main result:

65

Tab Analyze run analysis save the file

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Results:

here CPS is cycles per second.

Loading 1 is “seismic” (seismic effect in X direction)

Loading 2 is “seismic Y ” (seismic effect in Y direction)

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Loading 3 is “seismic Z” (seismic effect in Z direction)

Loading 4 is “dead” (Dead Load)

Loading 5 is “live” (Live Load)

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PROTOTYPE A

DIMENSION:



100*200 (Z direction)

Rayleigh frequency:

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PROTOTYPE B:

Dimensions:




Rayleigh frequency:

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PROTOTYPE C:

DIMENSION:




Rayleigh frequency:

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PROTOTYPE D:

DIMENSION:




Rayleigh frequency:

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Response Spectrum analysis of base shear

In General tab Load & Definition tab Load definition Seismic definition

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Click on seismic parameter select IS 1893:2002GenerateGenerate to the given parameters of problemGenerate Add

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Click on self weight Self weight factor =1 add Member load select type UNI Assign weightAdd

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Floor weight tab Select range Assign pressure Define Y range Add

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Final seismic definition as:

Assign self weight to view.

Assign UDL in all the beams (in X & Z direction)

Load Case Details Define Load type in seismic Add Title Add

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Assign to the various loads in dead, live, Seismic Primary loads.

In response spectrum primary load,

Assign Self weight ( X, Y & Z with factor 1) UDL (member load) 13kN/m in GX, GY &GZ. Floor load (in Y range) of 2.5kN/m^2 in GX, GY & GZ.

Add response spectrum in the same load case as follows:

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Assign the loads.

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Open STAAD Editor.

In Floor weight add the following statement as highlighted in the green box.

Control +S (Save the file)

Command Pre print analysis Print all

Analysis & Print in the dialogue box Print All

Analysis run analysis (Control +F5)

Click on the Output view file and done.

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Result:

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PROTOTYPE A

DIMENSION:




Time history:

89

PROTOTYPE B:

Dimensions:




Response spectrum:

91

PROTOTYPE C:

DIMENSION:




Response spectrum:

93

PROTOTYPE D:

DIMENSION:




Response spectrum:

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Base Shear By Time History Method

In Load & Definition tab Load & Definition Time history definition Add type 1 Acceleration Define time and acceleration

Add time and acceleration valuesAdd

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Final load case definition:

Assign primary Loads details as:

Dead load Live load Time history load

98

Assign time history as:

Final Loads will be as follows:

Assign the respective loads as:

Assign self weight to the view Assign UDL to beams (in X & Z direction)

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Command miscellaneous cut off mode shape10Ok

Go to CommandPre print analysisPrint all

Go to Analysis/Print tab All

AnalysisRun Analysis

View Output fileDone

Result

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0 5 10 15 20 25 30 35

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4TIME HIS-

TORY

Time in sec

ON Y – AXIS ACCELERATION IN m/sec2

ON X – AXIS TIME IN sec

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How To Generate Mode Shapes:

After post processing Go to Post processing

Go to dynamics tabSelect the Mode number View the respective mode.

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MASS PARTICIPATION FOR RESPECTIVE MODES

MAXIMUM & MINIMUM REACTION FORCE AND MOMENTS IN BEAM & NODES (IN X , Y & Z DIRECTION )

Beam L/C Node Fx kN Fy kN Fz kNMx kNm My kNm Mz kNm

Max Fx 30 1 DEAD 17 626.319 0 0 0 0 0

Min Fx 293 TIME HISTORY 16 -16.093 -6.487 0 0 0 14.638

Max Fy 28 1 DEAD 29 14.653 53.781 0 0 0 48.909Min Fy 27 1 DED 29 14.653 -53.781 0 0 0 48.909Max Fz 19 1 DEAD 11 128.541 0 5.136 0 -7.374 0Min Fz 59 1 DEAD 41 128.541 0 -5.136 0 7.374 0Max Mx 70 2 LIVE 13 0.717 2.36 0.03 0.597 -0.03 1.414Min Mx 82 2 LIVE 28 0.717 1.546 -0.03 -0.597 0.044 0.396Max My 19 1 DEAD 14 119.264 0 5.136 0 10.602 0Min My 59 1 DEAD 44 119.264 0 -5.136 0 -10.602 0Max Mz 27 1 DEAD 29 14.653 -53.781 0 0 0 48.909Min Mz 40 1 DEAD 30 86.37 14.713 0 0 0 -29.358

SUPPORT REACTIONS

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Analyzing A Single Beam In Longitudinal Direction:

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MEMBER 41 SHEAR BENDING AND ITS VALUE ( Distance , Fy kN & Mz kNm )

distance m Fy Kn Mz kNm0 42.177 30.5960.41666667 35.561 14.3860.83333333 28.512 1.0221.25 21.028 -9.3141.66666667 13.328 -16.4712.08333333 5.627 -20.422.5 -2.073 -21.1612.91666667 -9.774 -18.6933.33333333 -17.474 -13.0163.75 -25.175 -4.1314.16666667 -32.658 7.9334.58333333 -39.708 23.0245 -46.323 40.962

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MEMBER 41 DEFLECTION AND ITS VALUE ( DISTANCE & DISPLACEMENT )

distance m displacement mm0 -0.0110.41666667 -0.010.83333333 -0.0091.25 -0.0081.66666667 -0.0072.08333333 -0.0062.5 -0.0052.91666667 -0.0043.33333333 -0.0043.75 -0.0034.16666667 -0.0024.58333333 -0.0015 0

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Analyzing A Single Column In Vertical Direction:

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MEMBER 49 SHEAR BENDING AND ITS VALUE ( Distance , Fy kN & Mz kNm )

distance m Fy kN Mz kNm0 -5.504 -6.3980.29166667 -5.504 -4.7930.58333333 -5.504 -3.1870.875 -5.504 -1.5821.16666667 -5.504 0.0231.45833333 -5.504 1.6281.75 -5.504 3.2342.04166667 -5.504 4.8392.33333333 -5.504 6.4442.625 -5.504 8.0492.91666667 -5.504 9.6553.20833333 -5.504 11.263.5 -5.504 12.865

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MEMBER 49 DEFLECTION AND ITS VALUE ( DISTANCE & DISPLACEMENT )

Distance m displacement mm0 00.29166667 -0.0210.58333333 -0.0750.875 -0.151.16666667 -0.2351.45833333 -0.321.75 -0.3942.04166667 -0.4472.33333333 -0.4672.625 -0.4452.91666667 -0.3683.20833333 -0.2273.5 -0.011

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MAXIMUM NODAL DISPLACEMENT

TIME HISTORY BENDING EFFECT IN Z DIRECTION

116

TIME HISTORY Torsion: Axial Force: Shear EFFECT IN Z DIRECTION

117

NODE 13

118

TIME VS DISPLACEMENT GRAPH IN DIRECTION OF X, Y & Z RESPECTIVELY

119

TIME VS ACCELERATION GRAPH IN DIRECTION OF X, Y & Z RESPECTIVELY

120

NODE 10

121


122


123

NODE 7

124


125


126

NODE 4

127


128


129

NODE 14

130


131


132

NODE 15

133


134


135

PROTOTYPE A

DIMENSION:




Time history:

136

PROTOTYPE B:

Dimensions:




Time history:

138

PROTOTYPE C:

DIMENSION:




Time history:

140

PROTOTYPE D:

DIMENSION:




Time history:

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Chapter 4: Conclusions And Recommendation

1. For final deflection which includes the effect of creep, temperature, shrinkage and measured from as cast level of support (SPAN/250) final.

Considering all the safety parameters Prototype MAIN is considered to be best and economical design. As per the Indian ductile detailing code is 13920-1993 required column to be atleast 300mm

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wide. A column width of upto 200mm is allowed if unsupported length is less then 4m & beam length is less then 5m.

Prototype A Prototype B Prototype C Prototype D MAIN X- Direction 100*250 mm 200*350mm 150*300mm 300*450mm 250*400mmY- Direction 100*300mm 200*400mm 150*300mm 300*500mm 250*450mmZ- Direction 100*200mm 200*300mm 150*250mm 300*400mm 250*350mm

By Rayleigh Method

Direction Prototype A Prototype B Prototype C Prototype D MAINX Displacement

cm89.5613 22.8501 40.2264 10.5997 14.7663

Frequency 0.5932 1.1740 0.8849 1.7235 1.4604Y Displacement

cm0.0336 0.0350 .0345 0.0364 0.0354

Frequency 41.4040 35.3542 37.2552 33.3293 34.3453Z Displacement

cm31.0928 10.1299 16.1672 5.0773 7.0768

Frequency 1.0335 1.7910 1.4228 2.5205 2.13924

Prototype A and B fails in X- direction.Prototype A fails in Z- direction.Prototype C, D and main is safe in all directions.Considering all the safety parameters Prototype MAIN is considered to be best and economical design.

2. Modal / Eigen Solution Method

MODE NO. PROTOTYPE A PROTOTYPE B PROTOTYPE C PROTOTYPE D MAIN Mode 1 0.149 0.48 0.291 0.989 0.713Mode 2 0.236 0.683 0.435 1.305 0.974Mode 3 0.263 0.769 0.488 1.485 1.103Mode 4 0.472 1.552 0.94 3.189 2.302Mode 5 0.868 2.318 1.523 4.304 3.248Mode 6 0.876 2.556 1.658 4.836 3.618Mode 7 0.935 2.84 1.725 5.409 4.13Mode 8 1.235 3.009 2.05 5.823 4.208Mode 9 1.254 3.722 2.448 6.773 5.144Mode 10 1.514 3.872 2.511 7.044 5.355

Graph show below as per value or result:

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1 2 3 4 50

1

2

3

4

5

6

7

8

Mode 1Mode 2Mode 3Mode 4Mode 5Mode 6Mode 7Mode 8Mode 9Mode 10

NUMBER ON X - AXIS REPRESENTATION1 PROTOTYPE A2 PROTOTYPE C3 PROTOTYPE B4 MAIN5 PROTOTYPE D

3. For the mode with lesser frequency has greater value of mass participation factor in the respective direction i.e., greater time period, greater is the mass participation of respective mode.

4. Time history calculation for base shear is considerably less by the calculated base shear by response spectrum method. This would need scaling. Hence it is justified why time history analysis method is discouraged by current codes.

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Chapter-5: Summary and Future scope

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5.1 Summary

Our final work was the proper analysis of an earthquake resistant Four (G+3) storey 3-D RCC frame under various load combinations.The structure was subjected to various combinations of dead load, live load, seismic load, and time history load. Seismic load calculations were done following IS 1893-2000. The materials were specified and cross-sections of the beam and column members were assigned. The supports at the base of the structure were also specified as fixed. The codes of practice to be followed were also specified for design purpose with other important details. Then STAAD Pro V8i was used to analyze the structure and design the members. In the post-processing mode, after completion of the design, we can work on the structure and study the bending moment and shear force values with the generated diagrams.

The building is made keeping in mind. Strong column and weak beam design. The failure of column can affect the stability of the whole building, but the failure of beam cause a localized effect.

The design of the building is dependent upon the minimum requirements as prescribed in the Indian Standard Codes. The minimum requirements pertaining to the structural safety of buildings are being covered by way of laying down minimum design loads which have to be assumed for dead loads, imposed loads, and other external loads, the structure would be required to bear. Strict conformity to loading standards recommended in this code, it is hoped, will ensure the structural safety of the buildings which are being designed. Structure and structural elements were normally designed by Limit State Method.

Complicated and high-rise structures need very time taking and cumbersome calculations using conventional manual methods. STAAD Pro V8i provides us a fast, efficient, easy to use and accurate platform for analyzing and designing structures.

5.2 Future ScopeThere is much to explore in this flourishing field of seismic isolation. Especially in our country

a lot of research work can be done & needed to be done. In this particular dissertation work the study is being carried out only for 1st mode of vibration, the effect of higher modes on torsional coupling of superstructure can be a stuff to be explored. Further the superstructure was assumed to be perfectly rigid for this study, so the effect of superstructure flexibility can also be investigated. Further the parametric studies can be conducted might be based on extent of eccentricity or superstructure stiffness variation etc.

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Annexure:

Annexure 1: Code usedCODE OF EARTHQUAKE USED FOR EXPERIMENTS AND TABLES USED

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The first formal seismic code in India, namely IS 1893, was published in 1962. Today, the Bureau of Indian Standards (BIS) has the following seismic codes:

IS 1893 (Part I), 2002 IS 13920, 1993

TERMINOLOGY FOR EARTHQUAKE ENGINEERING

[ For the purpose of this standard, the following definitions shall apply which are applicable generally to all structures.]

{NOTE — For the definitions of terms pertaining to soil mechanics and soil dynamics references may be made to IS 2809 and IS 2810}.

Closely-Spaced Modes

Closely-spaced modes of a structure are those of its natural modes of vibration whose natural frequencies differ from each other by 10 percent or less of the lower frequency.

Critical Damping

The damping beyond which the free vibration motion will not be oscillatory.

Damping

The effect of internal friction, imperfect elasticity of material, slipping, sliding, etc in reducing the amplitude of vibration and is expressed as a percentage of critical damping.

Design Acceleration Spectrum

Design acceleration spectrum refers to an average smoothened plot of maximum acceleration as a function of frequency or time period of vibration for a specified damping ratio for earthquake excitations at thebase of a single degree of freedom system.

Design Basis Earthquake ( DBE )

It is the earthquake which can reasonably be expected to occur at least once during the design life of the structure.

Design Horizontal Acceleration Coefficient (Ah )

It is a horizontal acceleration coefficient that shall be used for design of structures.

Design Lateral Force

It is the horizontal seismic force prescribed by this standard, that shall be used to design a structure.

Ductility

Ductility of a structure, or its members, is the capacity to undergo large inelastic deformations without significant loss of strength or stiffness.

EpicenterThe geographical point on the surface of earth vertically above the focus of the earthquake.

Effective Peak Ground Acceleration ( EPGA )

It is 0.4 times the 5 percent damped average spectral acceleration between period 0.1 to 0.3 s. This shall be taken as Zero Period Acceleration ( ZPA ).

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Floor Response Spectra

Floor response spectra is the response spectra for a time history motion of a floor. This floor motion time history is obtained by an analysis of mu13ti7storey building for appropriate material damping values subjected to a specified earthquake motion at the base of structure.

Focus

The originating earthquake source of the elastic waves inside the earth which cause shaking of ground due to earthquake.

Importance Factor (I)

It is a factor used to obtain the design seismic force depending on the functional use of the structure, characterised by hazardous consequences of its failure, its post-earthquake functional need, historic value, or economic importance.

Intensity of Earthquake

The intensity of an earthquake at a place is a measure of the strength of shaking during the earthquake, and is indicated by a number according to the modified Morcalli Scale or M.S.K. Scale of seismic intensities (see Annex D ).

Liquefaction

Liquefaction is a state in saturated cohesion less soil wherein the effective shear strength is reduced to negligible value for all engineering purpose due to pore pressure caused by vibrations during an earthquake when they approach the total confining pressure. In this condition the soil tends to behave like a fluid mass.

Litho logical Features

The nature of the geological formation of the earths crust above bed rock on the basis of such characteristics as colour, structure, mineralogical composition and grain size.

Magnitude at' Earthquake ( Richter's Magnitude )

The magnitude of earthquake is a number, which is a measure of energy released in an earthquake. It is defined as logarithm to the base 10 of the maximum trace amplitude, expressed in microns, which the standard short-period torsion seismometer ( with a period of 0.8 s, magnification 2 800 and clamping nearly critical ) would register due to the earthquake at an epicentral distance of 100 km.

Maximum Considered Earthquake ( MCE )

The most severe earthquake effects considered by this standard.

Modal Mass (Mk )

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Modal mass of a 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.

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 and vertical earthquake ground motions. Since the amplitudes of 95 percent mode shapes can be scaled arbitrarily, the value of this factor depends on the scaling used for mode shapes.

Modes of Vibration ( see Normal Mode) Mode Shape Coefficient (Pik )

When a system is vibrating in normal mode k, at any particular instant of time, the amplitude of mass i expressed as a ratio of the amplitude of one of the masses of the system, is known as mode shape coefficient ( ).

Natural Period ( T)

Natural period of a structure is its time period of undamped free vibration.

Fundamental Natural Period ( T1)

It is the first ( longest ) modal time period of vibration.

Modal Natural Period ( Tk)

The modal natural period of mode k is the time period of vibration in mode k.

Normal Mode

A system is said to be vibrating in a normal mode when all its masses attain maximum values of displacements and rotations simultaneously, and pass through equilibrium positions simultaneously.

Response Reduction Factor (`R)

It is the factor by which the actual base shear force, that would be generated if the structure were to remain elastic during its response to the Design Basis Earthquake (DBE) shaking, shall be reduced to obtain the design lateral force.

Response Spectrum

The representation of the maximum response of idealized single degree freedom systems having certain period and damping, during earthquake ground motion. The maximum response is plotted against the undamped natural period and for various damping values, and can be expressed in terms of maximum absolute acceleration, maximum relative velocity, or maximum relative displacement.

Seismic Mass

It is the seismic weight divided by acceleration due to gravity.

Seismic Weight ( W)

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It is the total dead load plus appropriate amounts of specified imposed load.

Structural Response Factors ( Sa/g)

It is a factor denoting the acceleration response spectrum of the structure subjected to earthquake ground vibrations, and depends on natural period of vibration and damping of the structure.

Tectonic Features

The nature of geological formation of the bed rock in the earth's crust revealing regions characterized by structural features, such as dislocation, distortion, faults, folding, thrusts, volcanoes with their age of formation, which are directly involved in the earth movement or quake resulting in the above consequences.

Time History Analysis

It is an analysis of the dynamic response of the structure at each increment of time, when its base is subjected to a specific ground motion time history.

Zone Factor ( Z )

It is a factor to obtain the design spectrum depending on the perceived maximum seismic risk characterized by Maximum Considered Earthquake ( MCE ) in the zone in which the structure is located. The basic zone factors included in this standard arereasonable estimate of effective peak ground acceleration.

Zero Period Acceleration ( ZPA )

It is the value of acceleration response spectrum for period below 0.03 s ( frequencies above 33 Hz ).

TERMINOLOY FOR EARTHQUAKE ENGINEERING OF BUILDINGS[ For the purpose of earthquake resistant design of buildings in this standard, the following definitions shall apply.]

Base

It is the level at which inertia forces generated in the structure are transferred to the foundation, which then transfers these forces to the ground. Base Dimensions ( d)

Base dimension of the building along a direction isthe dimension at its base, in metre, along that direction.

Centre of Mass

The point through which the resultant of the masses of a system acts. This paint corresponds to the centre of gravity of masses of system.

Centre of Stiffness

The point through which the resultant of the restoring forces of a system acts.

Design Eccentricity ( edi )

It is the value of eccentricity to be used at floor i in torsion calculations for design.

Design Seismic Base Shear ( Vb)

It is the total design lateral force at the base of a structure.

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Diaphragm

It is a horizontal, or neatly horizontal system, which transmits lateral forces to the vertical resisting elemeMs, for example, reinforced qoncrete floors and horizontal bracing systems.

Dual System

Buildings with dual system consist of shear walls (or braced frames) and moment resisting frames such that:

a) The two systems are designed to resist the total design lateral force in proportion to their lateral stiffness considering the interaction of the dual system at all floor levels; and

b) The moment resisting frames are designed to independently resist at least 25 percent of the design base shear.

Height of Floor ( hi )

It is the difference in levels between the base of the building and that of floor I.

Height of Structure ( h )

It is the difference in levels, in metres, between its base and its highest level.

Horizontal Bracing System

It is a horizontal truss system that serves the same function as a diaphragm.

Joint

It is the portion of the column that is common to other members, for example, beams, framing into it.

Lateral Force Resisting Element

It is part of the structural system assigned to resist lateral forces.

Moment-Resisting Frame

It is a frame in which members and joints are capable of resisting forces primarily by flexure.

Ordinary Moment-Resisting Frame

It is a moment-resisting frame not meeting special detailing requirements for ductile behaviour.

Special Moment-Resisting Frame

It is a moment-resisting frame specially detailed to provide ductile behaviour and comply with the requirements given in IS 4326 or IS 13920 or SP 6(6).

Number of Storeys ( n )

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Number of storeys of a building is the number of levels above the base. This excludes the basement storeys, where basement walls are connected with the ground floor deck or fitted between the building columns. But, it includes the basement storeys, when they are not so connected.

Principal Axes

Principal axes of a building are generally two mutually perpendicular horizontal directions in plan of a building along which the geometry of the building is oriented.

P-∆ Effect

It is the secondary effect on shears and moments of frame members due to action of the vertical loads, interacting with the lateral displacement of building resulting from seismic forces.

Shear Wall

It is a wall designed to resist lateral forces acting in its own plane.

Soft Storey

It is one in which the lateral stiffness is less than 70 percent of that in the storey above or less than 80 percent of the average lateral stiffness of the three storeys above.

Static Eccentricity ( ea )

It is the distance between centre of mass and centre of rigidity of floor 1.

Storey

It is the space between two adjacent floors.

Storey Drift

It is the displacement of one level relative to the other level above or below.

Storey ShearIt is the sum of design lateral forces at all levels above the storey under consideration.

Weak Storey

It is the one in which the storey lateral strength is less than 80 percent of that in the storey above. The storey lateral strength is the total strength of all seismic force resisting elements sharing the storey shear in the considered direction.

Load Combination and Increase in Permissible Stresses

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1. Load Combinations

When earthquake forces are considered on a structure , these shall be combined as per 6.3.1.1 and 6.3.1.2 where the terms DL, IL and EL stand for the response quantities due to dead load, imposed load and designated earthquake load respectively.

Load factors for plastic design of steel structures

In the plastic design of steel structures, the following load combinations shall be accounted for:

1) 1.7 (DL + IL)

2) 1.7 (DL*EL)

3) 1.3(DL+1L*EL)

Partial safety factors for limit state design of reinforced concrete and prestressed concrete structures

In the limit state design of reinforced and prestressed concrete structures, the following load combinations shall be accounted for:

1) 1.5(DL+ IL)

2) 1.2 (DL ± LEL)

3) 1.5(DL ± EL)

4) 0.9 DL ± 1.5 EL

2. Design Horizontal Earthquake Load

When the lateral load resisting elements are oriented along orthogonal horizontal direction, the structure shall be designed for the effects due to full design earthquake load in one horizontal direction at time.

When the lateral load resisting elements are not oriented along the orthogonal horizontal directions, the structure shall be designed for the effects due to full design earthquake load in one horizontal direction plus 30 percent of the design earthquake load in the other direction.

[NOTE — For instance, the building should be designed for ( F.Lx 0.3 ELy ) wen as ( 0.3 ELx ELy ), where x and y are two orthogonal horizontal directions. EL in 6.3.1.1 and 6.3.1.2 shall be replaced by ( ELx 0.3 ELy ) or ( * 0.3 ELx ).]

3. Design Vertical Earthquake Load

When effects due to vertical earthquake loads are to be considered, the design vertical force shall be calculated in accordance with 6.4.5.

4. Combination for Two or Three Component Motion

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When responses from the three earthquakecomponents are to be considered, the responses dueto each component may be combined using theassumption that when the maximum response from one component occurs, the responses from the other two component are 30 percent of their maximum. All possible combinations of the three components ( ELx, ELy and ELz) including variations in sign ( plus or minus ) shall be considered. Thus, the response due earthquake force ( EL ) is the maximum of the following three cases:

1) ± ELx±0.3 ELy±0.3 ELz

2) ±ELy±0.3 ELx ±0.3 ELz

3) ± ELz ± 0.3 ELx+ 0.3 ELy

where x and y are two orthogonal directions and z is vertical direction.

As an alternative to the procedure in 6.3.4.1, the response ( EL ) due to the combined effect of the three components can be obtained on the basis of 'square root of the sum of the square ( SRSS )' that is

EL = √( (ELx )2 +(ELy )2 +(ELz )2)

[NOTE — The combination procedure of 6.3.4.1 and 6.3.4.2 apply to the same response quantity (say, moment in a column about its major axis, or storey shear in a frame) due to different components ofthe ground motion.]

When two component motions ( say one horizontal and one vertical, or only two horizontal ) are combined, the equations in 6.3.4.1 and 6.3.4.2 should be modified by deleting the term representing the response due to the component of motion not being considered.

5. Increase in Permissible Stresses Increase in permissible stresses in materials

When earthquake forces are considered along with other normal design forces, the permissible stresses in material, in the elastic method of design, may be increased by one-third. However, for steels having a definite yield stress, the stress be limited to the yield stress; for steels without a definite yield point, the stress will be limited to 80 percent of the ultimate strength or 0.2 percent proof stress, whichever is smaller; and that in prestressed concrete members, the tensile stress in the extreme fibers of the concrete may be permitted so as not to exceed two-thirds of the modulus of rupture of concrete.

Increase in allowable pressure in soils

When earthquake forces are included, the allowable bearing pressure in soils shall be increased as per Table I, depending upon type of foundation of the structure and the type of soil.

In soil deposits consisting of submerged loose sand soils falling under classification SP with standard penetration N-values less than 15 in seismic Zones III, IV, V and less than 10 in seismic Zone II, the vibration caused by earthquake may cause liquefaction or excessive total and differential settlements. Such sites should preferably be avoided while locating new settlements or important projects. Otherwise, this aspect of the problem needs to be investigated and appropriate methods of

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compaction or stabilization adopted to achieve suitable N-values as indicated in Note 3 under Table 1. Alternatively, deep pile foundation may be provided and taken to depths well into the layer which is not likely to liquefy. Marine clays and other sensitive clays are also known to liquefy due to collapse of soil structure and will need special treatment according to site condition.

Design Spectrum

For the purpose of determining seismic forces, the country is classified into four seismic zones as shown in Fig. 1.

The design horizontal seismic coefficient Ah for a structure shall be determined by the following expression:

Provided that for any structure with T ≤ 0.1 s, the value of Ah will not be taken less than Z/2 whatever be the value of I/R

where

Z = Zone factor given in Table 2, is for the Maximum Considered Earthquake ( MCE ) and service life of structure in a zone. The factor 2 in the denominator of Z is used so as to reduce the Maximum Considered Earthquake ( MCE ) zone factor to the factor for Design Basis Earthquake ( DBE ).

I = Importance factor, depending upon the functional use of the structures, characterised by hazardous consequences of its failure, post-earthquake functional needs, historical value, or economic importance( Table 6).

R = Response reduction factor, depending on the perceived seismic damage performance of the structure, characterised by ductile or brittle deformations. However, the ratio (I/R) shall not be greater than 1.0 ( Table 7). The values ofR for buildings are given in Table 7.

Sa/g= Average response acceleration coefficient

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The design acceleration spectrum

The design acceleration spectrum for vertical motions, when required, may be taken as two-thirds of the design horizontal acceleration spectrum specified in 6.4.2.

Figure 2 shows the proposed 5 percent spectra for rocky and soils sites and Table 3 gives the multiplying factors for obtaining spectral values for various other dampings.

Seismic Weight

Seismic weight of floors

The seismic weight of each floor is its full dead load plus appropriate amount of imposed load, as specified in 7.3.1 and 7.3.2. 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.

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Seismic Weight of BuildingThe seismic weight of the whole building is the sum of the seismic weights of all the floors. Any weight supported in between storeys shall be distributed to the floors

above and below in inverse proportion to its distance from the floors.

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Design Lateral Force

Buildings and portions thereof shall be designed and constructed, to resist the effects of design lateral force specified in 7.5.3 as a minimum.

The design lateral force shall first be computed for the building as a whole. This design lateral force shall then be distributed to the various floor levels. The overall design seismic force thus obtained at each floor level, shall then be distributed to individual lateral load resisting elements depending on the floor diaphragm action.

Design Seismic Base Shear

The total design lateral farce or design seismic base shear (178) along any principal direction shall be determined by the following expression:

VB =AhW

where

Ah = Design horizontal acceleration spectrum value as per 6.4.2, using the fundamental natural period T as per 7.6 in the considered direction of vibration; and

W = Seismic weight of the building as per 7.4.2. 7.6 Fundamental Natural Period

Fundamental Natural Period

The approximate fundamental natural period of vibration ( T.), in seconds, of a moment-resisting frame building without brick in panels may be estimated by the empirical expression:

T = 0.075 h0.75 for RC frame building

= 0.085 h0.75 for steel frame building

where

h = Height of building, in m. This excludes the basement storeys, where basement walls are connected with the ground floor deck or fitted between the building columns. But it includes the basement storeys, when they are not so connected.

The approximate fundamental natural period of vibration ), in seconds, of all other buildings, including moment-resisting frame buildings with brick infill panels, may be estimated by the empirical expression:

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where

h = Height of building, in m, as dermal in 7.6.1; and

d = Base dimension of the building at the plinth level, in m, along the considered direction of the lateral force.

Distribution of Design Force

Vertical Distribution of Base Shear to Different Floor Levels

The design base shear(VB) computed in 7.5.3 shall be distributed along the height of the building as per the following expression:

where

Qi = Design lateral force at floor i,

Wi= Seismic weight of floor 1,

Hi = Height of floor i measured from base, and

n = Number of storeys in the building is the number of levels at which the masses are located.

Dynamic Analysis

Dynamic analysis shall be performed to obtain the design seismic force, and its distribution to different levels along the height of thebuilding 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. Modelling as per 7.8.4.5 can be used.

b) Irregular buildings (as defined in 7.1) –

All framed buildings higher than 12m in Zones IV and V, and those greater than 40 m in height in zones II and III.

The analytical model for dynamic analysis of buildings with unusual configuration should be such that it adequately models the types of irregularities present in the building configuration. Buildings with plan irregularities, as defined in Table 4 (as per 7.1),cannot be modelled for dynamic analysis by the method given in 7.8.4.5.

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[NOTE — for irregular buildings, lesser than 40 m in height in Zones It and III, dynamic analysis, even though not mandatory, is recommended.]

Dynamic analysis may be performed either by the 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, where Ta is as per 7.6. Where VB is less than ( VB) , all the response quantities ( for example member forces, displacements, storey forces, storey shears and base reactions) shall be multiplied by VB / VB.

o The value of damping for buildings may be taken as 2 and 5 percent of the critical, for the purposes of dynamic analysis of steel and reinforced concrete buildings, respectively.

Time History MethodTime history method of analysis, when used, shall be based on an appropriate ground motion and shall be performed using accepted principles of dynamics.

Response Spectrum MethodResponse spectrum method of analysis shall be performed using the design spectrum specified in 6A.2, or by a site-specific design spectrum mentioned in 6.4.6.

o Free Vibration Analysis

Undamped free vibration analysis of the entire building shall be performed as per established methods of mechanics using the appropriate masses and elastic stiffness of the structural system, to obtain natural periods( T) and mode shapes {Φ} of those of its modes of vibration that need to be considered as per 7.8.4.2.

o Modes to he considered

The number of modes to be used in the analysis should be such that the sum total of modal masses of all modes considered is at least 90 percent of the total seismic mass and missing mass correction beyond 33 percent. If modes with natural frequency beyond 33 Hz are to be considered, modal combination shall be carried out only for modes upto 33 Hz. The effect of higher modes shall be included by considering missing mass correction following well established procedures.

o Analysis of building subjected to design forces

The building may be analyzed by accepted principles of' mechanics for the design forces considered as static forces.

o Modal combination

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The peak response quantities ( for example, member forces, displacements, storey forces, storey shears and base reactions) shall be combined as per Complete Quadratic Combination( CQC ) method.

where

r= Number of modes being considered

ρij = Cross-modal coefficient,

λi= Response quantity in mode i ( including sign ),

λj= Response quantity in mode j ( including sign),

ζ= Modal damping ratio (infraction) as specified in 7.8.2.1,

β= Frequency ratio

ωi= Circular frequency in ith mode, and

ωj= Circular frequency in jth mode.

Alternatively, the peak response quantities may be combined as follows:

If the building does not have closely-spaced modes, then the peak response quantity

( λ ) due to all modes considered shall be obtained as

where

λk = Absolute value of quantity in mode k. and

r = Number of modes being considered.

If the building has a few closely-spaced modes (see 3.2 ), then the peak response quantity ( λ* ) due to these modes shall be obtained as

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Where the summation is for the closely-spaced modes only. This peak response quantity due to the closely spaced modes (X,' ) is then combined with those of the remaining well-separated modes by the method described in 7.8.4.4 (a).

Buildings with regular, or nominally irregular.; plan configurations may be modelled as a system of masses lumped at the floor levels with each mass having one degree of freedom, that of lateral displacement in the direction under consideration. In such a case, the following expressions shall hold in the computation of the various quantities :

a) Modal Mass— The modal mass (Mk) of mode k is given by

where

g = Acceleration due to gravity,

Φik = Mode shape coefficient at floor i in mode k, and

Wi= Seismic weight of floor i

Modal Participation Factors

The modal participation factor ( Pk ) of mode k is given by:

Design Lateral Force at Each Floor in Each Mode

The peak lateral force ( Qik ) at floor i in mode k is given by

where

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Ak = Design horizontal acceleration spectrum value as per 6.4.2 using the natural period of vibration ( Tk ) of mode k.

Storey Shear Forces in Each Mode

The peak shear force (Vik) acting in storey i in mode k is given by

Storey Shear Forces due to All Modes Considered —

The peak storey shear force (Vik) in storey i due to all modes considered is obtained by combining those due to each mode in accordance with 7.8.4.4

Lateral Parces at Each Storey Due to All Modes Considered —

The design lateral forces, Froof and Fi , at roof and at floor i:

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Annexure 2: Multi-degree of freedom systems

Modeling of continuous systems as multidegree of freedom systems Eigen value problem Multidegree of freedom systems As stated before, most engineering systems are continuous and have an infinite number of

degrees of freedom. The vibration analysis of continuous systems requires the solution of partial differential equations, which is quite difficult.

In fact, analytical solutions do not exist for many partial differential equations. The analysis of a multidegree of freedom system on the other hand, requires the solution of a set of ordinary differential equations, which is relatively simple. Hence, for simplicity of analysis, continuous systems are often approximated as multidegree of freedom systems.

For a system having n degrees of freedom, there are n associated natural frequencies, each associated with its own mode shape.

Different methods can be used to approximate a continuous system as a multidegree of freedom system. A simple method involves replacing the distributed mass or inertia of the system by a finite number of lumped masses or rigid bodies.

The lumped masses are assumed to be connected by mass less elastic and damping members.

Linear coordinates are used to describe the motion of the lumped masses. Such models are called lumped parameter of lumped mass or discrete mass systems.

The minimum number of coordinates necessary to describe the motion of the lumped masses and rigid bodies defines the number of degrees of freedom of the system. Naturally, the larger the number of lumped masses used in the model, the higher the accuracy of the resulting analysis.

Some problems automatically indicate the type of lumped parameter model to be used. For example, the three storey building shown in the figure automatically suggests using a

three lumped mass model as indicated in the figure. In this model, the inertia of the system is assumed to be concentrated as three point masses

located at the floor levels, and the elasticities of the columns are replaced by the springs. Another popular method of approximating a continuous system as a multidegree of freedom

system involves replacing the geometry of the system by a large number of small elements. By assuming a simple solution within each element, the principles of compatibility and

equilibrium are used to find an approximate solution to the original system. This method is known as the finite element method.

Using Newton’s second law to derive equations of motion

The following procedure can be adopted to derive the equations of motion of a multidegree of freedom system using Newton’s second law of motion

Set up suitable coordinates to describe the positions of the various point masses and rigid bodies in the system. Assume suitable positive directions for the displacements, velocities and accelerations of the masses and rigid bodies.

Determine the static equilibrium configuration of the system and measure the displacements of the masses and rigid bodies from their respective static equilibrium positions.

Draw the free body diagram of each mass or rigid body in the system. Indicate the spring, damping and external forces acting on each mass or rigid body when positive displacement or velocity are given to that mass or rigid body.

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Apply Newton’s second law of motion to each mass or rigid body shown by the free body diagram as:

Example: Derive the equations of motion of the spring mass damper system‐ ‐shown in the figure.

Draw free body diagrams of masses and apply Newton’s second law of motion. The‐ coordinates describing the positions of the masses, xi(t), are measured from their respective static equilibrium positions, as indicated in the figure. The application of the Newton’s second law of motion to mass mi gives:

The equations of motion of the masses m1 and m2 can be derived from the above equations by setting i=1 along with xo=0 and i=n along with xn+1=0, respectively.

Equations of motion in matrix form

The equations of motion in matrix form in the above example can be expressed as:

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For an undamped system, the equations of motion reduce to:

The differential equations of the spring mass system considered in the example, can be seen‐

to be coupled. Each equation involves more than one coordinate. This means that the equations can not be solved individually one at a time; they can only be solved simultaneously.

In addition, the system can be seen to be statically coupled since stiffness’s are coupled‐ that is the stiffness matrix has at least one nonzero off diagonal term. On the other hand, if‐

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the mass matrix has at least one off diagonal term nonzero, the system is said to be‐ dynamically coupled. Further, if both the stiffness and the mass matrices have nonzero off‐diagonal terms, the system is said to be coupled both statically and dynamically.

Types of Modal combination:

a) Sum of the absolute values:

• Leads to very conservative results• Assumes that maximum modal values occur at the same time• Response of any given degree of freedom of the system is estimated as

b) Square root of the sum of the squares (SRSS or RMS):

• Assumes that the individual modal maxima are statistically independent.• SRSS method generally leads to values that are closer to the “exact” ones than those obtained using the sum of the absolute values.• Results can be conservative or unconservative.• Results from an SRSS analysis can be significantly unconservative if modal periods are closely spaced.• The response is estimated as:

c) Complete quadratic combination (CQC):

•The method is based on random vibration theory•It has been incorporated in several commercial analysis programs•A double summation is used to estimate maximum responses.

In which, ρ is a cross-modal coefficient (always positive), which for constant damping is evaluated by

where r = ρn / ρm and must be equal to or less than 1.0.

NOTE: Response spectrum method of dynamic analysis must be used carefully. The CQC method should be used to combine modal maxima in order to minimize the introduction of avoidable errors.

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The increase in computational effort, as compared to the SRSS method, is small compared to the total computer time for a seismic analysis. The CQC method has a sound theoretical basis and has been accepted by most experts in earthquake engineering. The use of the absolute sum or the SRSS method for modal combination cannot be justified. In order for a structure to have equal resistance to earthquake motions from all directions, the CQC3 method should be used to combine the effects of earthquake spectra applied in three dimensions. The percentage rule methods have no theoretical basis and are not invariant with respect to the reference system. Engineers, however, should clearly understand that the response spectrum method is an approximate method used to estimate maximum peak values of displacements and forces and that it has significant limitations. It is restricted to linear elastic analysis in which the damping properties can only be estimated with a low degree of confidence. The use of nonlinear spectra, which are commonly used, has very little theoretical background and should not be used for the analysis of complex three dimensional structures. For such structures, true nonlinear time-history response should be used.

RESPONSE SPECTRUM

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.For three dimensional seismic motions, the typical modal Equation is

where the three Mode Participation Factors are defined by

which i is equal to x, y or z.First, for each direction of ground motion maximum peak forces and displacements must be estimated. Second, after the response for the three orthogonal directions is solved it is necessary to estimate the maximum response due to the three components of earthquake motion acting at the same time.For input in one direction only

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LIMITATIONS OF THE RESPONSE SPECTRUM METHOD

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. In future time history method may be preferred more.

Storey drift displacements are positive number only. Therefore, a plot of a dynamic displaced shape has very little meaning since each displacement is an estimation of the maximum value. Inter-story displacements are used to estimate damage to non-structural elements and cannot be calculated directly from the probable peak values of displacement.

Estimation of Spectra Stresses in Beams: The fundamental equation for the calculation of the stresses within the cross section of a beam is

This equation can be evaluated for a specified x and y point in the cross section and for the calculated maximum spectral axial force and moments which are all positive values. It is apparent that the resulting stress may be conservative since all forces will probably not obtain their peak values at the same time.

BUILDING HEIGHT AND NATURAL FREQUENCY

RESONANT FREQUENCIES

When the frequency contents of the ground motion are centred on the building's natural frequency, we say that the building and the ground motion are in resonance with one another. Resonance tends to increase or amplify the building's response. Because of this, buildings suffer the greatest damage from ground motion at a frequency close or equal to their own natural frequency.

BUILDING FREQUENCY AND PERIODBuilding's response can be in terms of another important quantity, the building's natural period. The building period is simply the inverse of the frequency: Whereas the frequency is the number of times per second that the building will vibrate back and forth, the period is the time it takes for the building to make one complete vibration. The relationship between frequency f and period T is thus very simple math.

Some MCEER data is:

Building Heights & Natural FrequencyBuilding Height Typical Natural Period2 story .2 seconds5 story .5 seconds10 story 1.0 second20 story 2.0 second30 story 3.0 second50 story 5.0 seconds

In this we have introduced building to earthquake loads. We have learned to analyse structures through STAAD Pro.V8i We have explained two important terms related to building reaction to earthquakes i.e. base shear and fundamental period of vibration for various prototypes.

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References: CODE :

IS 456-2000 - BUREAU OF INDIAN STANDARDS. IS 1893-2002 - BUREAU OF INDIAN STANDARDS.

MANUAL :STAAD pro V8i technical reference manual.

WEBSITE : National Information Centre of Earthquake Engineering (www.nicee.org)

www.communities.bentley.com WWW.ddma.delhigovt.nic.in

BOOK :

Earthquake engineering by Pankaj Aggarwal.Earthquake Engineering by Halil Sezen

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http://www.communities.bentley.com/

http://www.nicee.org/