UNIT I DEFINITIONS Terminology Related to Earthquake:
Magnitude: Measure of the amount of energy released during an earthquake. It is usually expressed using Richter scale. Professor Charles Richter noticed that at a constant distance, seismograms records of earthquake ground vibration of larger earthquake have bigger wave amplitude than those of smaller earthquakes, and for given earthquake, seismograms at farther distances have smaller wave amplitude than those at close distances. Now commonly used magnitude scale, the Richter scale. There are other magnitude scales viz, 1. Body wave magnitude 2. Surface wave magnitude and 3. Wave energy magnitude. It is defined as logarithm to the base 10 of the maximum trace amplitude, expressed in microns, which the standard short-period torsion seismometer would register due to the earthquake at an epicenter distance of 100 km. Earth quake are often classified into different groups based on their magnitude. Table is given by: GROUP
MAGNITUDE
Great
8 and Higher
Major
7-7.9
Strong
6-6.9
Moderate
5-5.9
Light
4-4.9
Minor
3-3.9
Very Minor
<3.0
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Intensity: Intensity is a qualitative measure of the actual shaking at a location during an earthquake, and is assigned in Roman Capital Numerical. It refers to the effects of earthquakes. Modified Mercalli scale is the standard measurement. There are many intensity scales. Two commonly used, ones are the Modified Mercalli Intensity (MMI) scale and MSK scale. Both are quite similar and range from I to XII . These intensity scale are based on the features of shaking- perception by people and animals, performance of buildings, and changes to natural surroundings. Table 2 for Ressi-Forrel scale of earthquake Intensity: Class 1. 2.
Name Imperceptible Feeble
3.
Very slight
4.
Slight
5. 6.
Weak Modessrate
7.
Strong
8. 9. 10.
Very strong Severe Destructive
Effects Recorded by sensitive seismograph Recorded by seismograph difference may be felt by number of person at rest. Felt by several persons at rest, is strong enough for the duration and direction to be recorded. Disturbs persons in motion movable objected distributed, creaking of doors and windows. Disturbances of furniture and ringing of bells. General awakening of those asleep, stopping of clocks, visible disturbances of trees. Overthrow of movable objects, fall of plaster, general panic with out serious damage to building. Fall of chimneys, cracks in the walls. Partial or total destruction of some buildings. All structures distributed.
Shaking intensity as per MSK scale: Intensity VIII- Destruction of buildings 1. Fright and panic. Also, persons driving motorcars are disturbed. Here and there branches of trees break off. Even heavy furniture moves and partly overturns. Hanging lamps are damaged in part. 2. Most buildings of type C suffer damage of Grade 2, and few of grade 3. Most buildings of Type B suffer damage of Grade 3, and most buildings of Type A suffer damage of Grade 4. Occasional breaking of pipe seams occurs. Memorials and monuments move and twist. Stone walls collapse. 3. Small landslips occur in hollows and on banked roads on steep slopes, cracks develop in ground up to widths of severals centimeters. Water in lakes becomes
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turbid. New reservoirs come into existances. Dry wells refill and existing wells become dry. In many cases, changes in flow and level of water are observed. Note: Type A - structures- rural constructions. Type B - Ordinary masonary constructions. Type C – Well-built structures Single Few- about 5% Many – about 50% Most – about 75% Grade 1 Damage – Slight damage Grade 2 moderate damage Grade 3 Heavy damage Grade 4 Destruction Grade 5 Total damage. Epicenter: The geographical point on the surface of earth vertically above the focus of the earthquake. Focus: The originating source of the elastic waves inside the earth which cause shakings of ground due to earthquake. The point of maximum shock/stress release during an earthquake. Deeper focus earthquakes are often less damaging because the rocks absorb more energy before the waves hit the surface. Shallow Focus Earthquake: Earthquake of focus less than 70 km deep from ground surface are called shallow focus earthquakess. Teleseism: A teleseism is an earthquake recorded by a seismograph at a distance. By international convention the distance is over 1000 Kilometers from the epicentre. Earthquake originating near the recording station are termed as near earthquake or local earthquake. Microseism: These are more or less continous seismographs.
disturbances in the ground recorded by
Micro earthquake: Very small earthquake having magnitude less than measurable than three on Richter scale are called Micro-earthquake. Highly sensitive seismographs are employed to monitor these for seismological and engineering applications. Accelerogram:
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The ground acccleration record produced by Accelerograph is called Accelerogram.
Accelerograph: This is an earthquake-recording device designed to measure the ground motion in terms of acceleration in the epicentral region of strong shaking. It writes the time wise history of ground acceleration at a particular site. Focal distance: The straight-line distance between the places of recording/observation to the hypocenter is called the focal distance. Intermediate Focus Eathquake: The focus is between 70 to 300 km deep. Epicentral Distance: Distance between epicentre and recording station in km. Fore Shocks: Smaller earthquake that precede the main earthquake. After shocks: Smaller earthquake that follow the main earthquake Asthenosphere: The layer of the upper mantle which is close to melting point and behaves in a semi-plastic way. Convection currents in this layer are believed to influence the movement of tectonic plates.
Benioff zone: 4
A region of earthquake activity inclined at an angle underneath a destructive boundary. Deeper earthquakes occur further from the boundary.
Constructive boundary: A part of the earth's crust where tectonic plates are moving away from each other, constructing new crustal material where they part. Associated with basic volcanism and frequent, shallow earthquakes. Debris avalanche: A sudden, large scale avalanche of rock. May be set off by heavy rain or by earthquake activity. Destructive boundary: A part of the earth's crust where tectonic plates move towards one another, resulting in the seduction of one below the other. Direct hazard: A threat to life or property arising from the direct action of a hazard (eg shaking in an earthquake or blast in a volcano).
Fault: A fracture in the rocks along which strain is occasionally released as an earthquake. By definition, only active faults are associated with earthquakes.
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Lithosphere: The rigid outer shell of the earth which normally comprises crust (oceanic or continental) and part of the upper mantle above the asthenosphere. Liquefaction: The process by which sediments and soil collapse, behaving like a thick liquid when shaken by earthquake waves. Magnitude/frequency relationship: The observed relationship (with most hazards) that bigger scale events occur less frequently while smaller scale events are relatively common. Richter scale: A measure of earthquake magnitude allowing an estimate of energy levels involved. Rossi-Forrel scale: An observational scale for measuring earthquake intensity. This was improved and expanded by Mercalli to produce the "Modified Mercalli Scale". Seismograph: A printout from a seismometer. Studies of seismograph traces can be used to pinpoint both the epicentre of an earthquake and the nature of the fault movement.
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Seismometer: An instrument for detecting and recording earthquake waves.
Seduction zone: A narrow region along a destructive plate boundary where one plate is consumed underneath another. Transform boundary: A plate boundary where the relative movement is sideways. The classic example of a transform boundary is in California where the San Andreas fault is a part of a transform plate boundary. Tsunami: An earthquake generated sea wave. Can travel thousands of miles and reach many metres in height when approaching shallow water.
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SEISMIC ZONES IN INDIA
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India being a large landmass is particularly prone to earthquakes. The Indian subcontinent is divided into five seismic zones with respect to the severity of the earthquakes. The classification of the zones has been done by the geologist and scientist as early as 1956 when a 3-zone (Severe, Light and Minor hazard) Seismic Zoning Map of India was produced. Since then the issue of seismic hazard has been addressed by different experts and agencies The aforementioned map was based on a broad concept of earthquake distribution and geotectonics. The severe hazard zones are roughly confined to plate boundary regions, ie, the Himalayan frontal arc in the North, the chaman fault region in the north west and the indo burma region in the north east. The lower hazard zone is confined to indian shield in the south and then moderate hazard zone confined to the transitional zone in between the two. The bureau of Indian standards is the official agency for publishing the seismic hazard maps and codes. It has brought out versions of seismic zoning map: a six zone map in 1962, a seven zone map in 1966, and a five zone map 1970/1984. The last of these maps is currently valid; this map was created based on the values of maximum MM intensities recorded in various parts of the country, in historic times. Zone V is the most vulnerable to earthquakes, where historically some of the country's most powerful shock have occured. This region included the Andaman & Nicobar Islands, all of North-Eastern India, parts of north-western Bihar, eastern sections of Uttaranchal, the Kangra Valley in Himachal Pradesh, near the Srinagar area in Jammu & Kashmir and the Rann of Kutchh in Gujarat. Earthquakes with magnitudes in excess of 7.0 have occured in these areas, and have had intensities higher than IX. Much of India lies in Zone III, where a maximum intensity of VII can be expected. Four of the major metropolitan areas lie in Zone IV, i.e. New Delhi, Mumbai and Calcutta. Only Chennai lies in Zone II. A large section of south-central India lies in Zone I along with a section stretching from eastern Rajasthan into northern Madhya Pradesh. Some areas of Orissa, Jharkhand and Chhatisgarh also lie in Zone I. In recent years india has been a host to many earthquakes of varying magnitude and intensity. The following table gives a detailed chronology. EPICENTER 33TE
Lat(Deg Long(Deg N) E)
LOCATION
MAGNITUDE
1819 June 16
23.6
68.6
KUTCH,GUJARAT 8.0
1869
25
93
NEAR
9
CACHAR, 7.5
JAN 10
ASSAM
1885 MAY 30
34.1
74.6
SOPOR, J&K
7.0
1897 JUN 12
26
91
SHILLONG PLATEAU
8.7
1905 APR 04
32.3
76.3
KANGRA, H.P
8.0
1918 JUL 08
24.5
91.0
SRIMANGAL, ASSAM
7.6
1930 JUL 02
25.8
90.2
DHUBRI, ASSAM
7.1
1934 JAN 15
26.6
86.8
BIHAR-NEPAL BORDER
8.3
1941 JUN 26
12.4
92.5
ANDAMAN ISLANDS
8.1
1943 OCT 23
26.8
94.0
ASSAM
7.4
1950 AUG 15
28.5
96.7
ARUNACHAL PRADESH-CHINA BORDER
8.5
1956 JUL 21
23.3
70.0
ANJAR, GUJARAT 7.0
1967 DEC 10
17.37
73.75
KOYNA, MAHARASHTRA
10
6.5
1975 JAN 19
32.38
78.49 KINNAUR, HP
6.2
1988 AUG 06
25.13
MANIPUR95.15 MYANMAR BORDER
6.6
1988 AUG 21
26.72
86.63
BIHAR-NEPAL BORDER
1991 OCT 20
30.75
78.86
UTTARKASHI, UP 6.6 HILLS
1993 SEP 30
18.07
LATUR76.62 OSMANABAD, MAHARASHTRA
6.3
1997 MAY 22
23.08
80.06 JABALPUR,MP
6.0
1999 MAR 29
30.41
79.42
CHAMOLI UP
11
DIST,
6.4
6.8
.
DEFINITION OF RICHTER SCALE : Seismic waves are the vibrations from earthquakes that travel through the Earth; they are recorded on instruments called seismographs. Seismographs record a zig-zag trace that shows the varying amplitude of ground oscillations beneath the instrument. Sensitive seismographs, which greatly magnify these ground motions, can detect strong earthquakes from sources anywhere in the world. The time, locations, and magnitude of an earthquake can be determined from the data recorded by seismograph stations. The Richter magnitude scale was developed in 1935 by Charles F. Richter of the California Institute of Technology as a mathematical device to compare the size of earthquakes. The magnitude of an earthquake is determined from the logarithm of the amplitude of waves recorded by seismographs. Adjustments are included for the variation in the distance between the various seismographs and the epicenter of the earthquakes. On the Richter Scale, magnitude is expressed in whole numbers and decimal fractions. For example, a magnitude 5.3 might be computed for a moderate earthquake, and a strong earthquake might be rated as magnitude 6.3. Because of the logarithmic basis of the scale, each whole number increase in magnitude represents a tenfold increase in measured amplitude; as an estimate of energy, each whole number step in the magnitude scale corresponds to the release of about 31 times more energy than the amount associated with the preceding whole number value Earthquakes with magnitude of about 2.0 or less are usually call micro earthquakes; they are not commonly felt by people and are generally recorded only on local seismographs. Events with magnitudes of about 4.5 or greater there are several thousand such shocks annually - are strong enough to be recorded by sensitive seismographs all over the world. Great earthquakes, such as the 1964 Good Friday earthquake in Alaska, have magnitudes of 8.0 or higher. On the average, one 12
earthquake of such size occurs somewhere in the world each year. Although the Richter Scale has no upper limit, the largest known shocks have had magnitudes in the 8.8 to 8.9 range. Recently, another scale called the moment magnitude scale has been devised for more precise study of great earthquakes. The Richter Scale is not used to express damage. An earthquake in a densely populated area which results in many deaths and considerable damage may have the same magnitude as a shock in a remote area that does nothing more than frighten the wildlife. Large-magnitude earthquakes that occur beneath the oceans may not even be felt by humans. SEISMIC ACTIVE ZONE: The design of a seismic resistant building involves the usage of seismic coefficients. For the purpose manipulating these coefficients the country is divided into FIVE zones ( as recommended in IS 1897 - 1984) ZONE 1 ZONE 2
ZONE 3 ZONE 4 ZONE 5
Area without any damage Area with major damage ( i.e., causing damages to structures with fundamentally periods greater than 1.0 second ) earthquakes corresponding to intensities V to VI of MM scale ( MM - Modified Mercalli Intensity scale ) Moderate damage corresponding to intensity VII of MM scale Major damage corresponding to intensity VII and higher of MM scale. Area determines by pro seismically of certain major fault systems.
UNIT II
EARTHQUAKE HISTORY The observations of structural performances of buildings during earthquakes provide volumes of information about the merits and demerits of the design and construction practices in a region since it is based on the actual test on prototype structures. The study helps in the elevation of strengthening measures of buildings and modifying the provisions of the modern code of practice with minimum additional expenditure. Numerical techniques have made great stride in Earthquake Engineering and it is important to critically evaluate the validity of these techniques by the experience of instrumented buildings during actual strong motion earthquakes, which are generally carried out experimentally using earthquake simulators. The numerous buildings suffered severe damage in Caracas during the Venezuela earthquake (1967) which were designed according to modern methods as reported by Borges et al.(1969) and degenkolb et al.(1969). Similar experiences were observed in many other earthquakes. This is the cause for great concern and there is a need for better
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understanding of the behaviour of buildings during some important earthquakes has been carried out. Finally, the important lessons from the damage behaviour of buildings during earthquakes are summarized. The indirect damages of buildings during earthquakes are some times far greater than the damages due to earthquake itself, such as, out break of fire, rock fall, landslide, avalanche and tsunamis. However, these damages are not due to inadequacies in the design and planning and therefore, not discussed here. Observations Of Behaviour Of Buildings During Past Earthquakes A description of behaviour of buildings during different earthquakes the world are summarized here for simple reason that they provide good engineering information about the behaviour of structures and helps in evolving its strengthening measures. In many cases, illustrates the effectiveness of earthquake resistant measures. Lisbon (Portugal) earthquake of nov.1, 1955: It has the maximum intensity of X on modified Mercalli (MM) scale of Lisbon. Nearly 15,000 buildings in the city collapsed and some 60,000 people were killed. The narrow streets largely aggravated the large-scale disaster where it was practically impossible to prevent the spread of fires and the pilling up of debris. There were three shocks in all, the first was the most severe shock and there was not a single stone building remained intact, thirty-to monasteries and 53 palaces were also destroyed;(Poliyakov, 1974). Rann of kutch earthquake of June 16th, 1819: This devastating earthquake occurred on 16th June 1819 between 6.45 and 6.50 pm resulting in nearly 1543 deaths and huge loss of property. It was felt in Ahmedabad, Porbondar, Jaisalmer, and Bhuj etc. In Bhuj alone more than 7000 houses were damaged. The houses built on low rocky ridges suffered less damage whereas houses founded on a slope leading to plain of spring and swamps were completely ruined. The Anjar earthquake of 21st July 1956 of magnitude 7 in this region also caused considerable property damage. There was total devastation for kutcha-pucca construction. Bihar-Nepal earthquake of August26, 1833: A violent earthquake of magnitude 7.0-7.5 struck on August 26, 1833 between 5.30 and 6.00 pm (IST) killing 414people in Nepal and several hundred in India with severe damage at Katmandu, Bhatgaon, Khokha and Patan in Nepal, and Monghyer and Purnea district in India. At Bhatgaon, a loss of 2000 houses (i.e.42%) was reported. The maximum intensity reported was IX. Assam (India) earthquake of June 12,1897: The magnitude was estimated to be greater than 8.5 and responsible for 1542 deaths. It occurred at 5.15 local time. The peak ground acceleration was estimated to have reached 50 of gravity. It is one of the greatest earthquakes of the world. All the stone and brick buildings were destroyed over an area of 3,70,000 sq.kms. (Tandon and Srivastava, 1974). Some of the buildings sank into the ground up to their roofs due to
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liquefaction of soil. The traditional lkra type of construction of building of Assam showed good performance. Great Kangra earthquake of April 4, 1905: This earthquake of magnitude greater than 8.0 occurred at 6.0 hrs20.0m (IST) with its epicenter at 32.25N, 76.25E.The maximum MM intensity X was observed in the epicentral region had taken a total 20,000 lives. The buildings were built of sun-dried bricks and some times with stone foundations raised about 15 cm above ground. Roofs were normally of slates but thatch was also used. The damage were severe, the houses became a heap of sun-dried bricks, slates and rafter. San Francisco (California, USA) earthquake of April 18, 1906: The earthquake had a magnitude of 8.3 and about 700 and 800 people died. Buildings on hard ground received comparatively minor damage such as collapsed chimneys, shattered windows. However load bearing structural elements were not seriously damaged. Structures erected on soft ground were severely damaged. Destruction of brick buildings was very severe with walls and entire sections collapsing. Damage to structures on filled up ground was especially severe due to differential settlements. The tall buildings resting on piles withstood the earthquake well and it provided the first test of multistorey steel frame buildings. Extensive nonstructural damage was common but none of these multistorey buildings so heavily damaged so as to be unsafe. Wood frame construction performed very well. Unreinforced sand-lime mortar brick bearing walls performed poorly. During the earthquake, most of the fire station buildings in the city were destroyed. The fires that were caused by the destruction of burning stoves and short circuits in electric wires lasted three days.
Messina (Sicily) earthquake of December 28,1908: It has the maximum intensity of x on MM scale. Peak ground acceleration was 208 of gravity. In the past this city had been repeatedly subjected to severe earthquakes. During this earthquake, 1,00,000 people (according to some data-1, 60,000) were killed, 98 percent of the buildings were completely. The reason for such disastrous consequences was primarily very poor quality of construction. The walls of the buildings were made of quarry stone laid in a weak lime mortar; no special earthquake proof measures had been taken. The ground conditions were not also suitable. The buildings were erected on loose alluvium and highly weathered crystalline rock. Kanto (Japan) earthquake of September 1, 1923: The peak ground acceleration was about 50% of gravity. It destroyed the Tokyo and Yokohama cities. The earthquake and the fires that followed caused the death of cover 1,40,000 people with just as many injured. The numbers of buildings destroyed were 12,86,261 and 4,47,128 buildings were destroyed by fire. Damage was especially
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severe in places where structures were built on loose alluvium and appreciably less on firm ground. This earthquake illustrates the great influence of ground on the intensity of earthquake. The advantages of structural frame systems and serious shortcoming of brick construction were clearly established. Thus, for example, out of 710 reinforced concrete frame buildings, which were carefully investigated by Japanese specialists, 69 buildings (9.7%) was damaged and 16 buildings (2.2%) were collapsed. Where as out of 485 brick buildings with load bearing brick walls 47 buildings (9.7%) were completely destroyed and 383 buildings (79%) were severely damaged. On the basis of these studies, the maximum height of brick buildings was limited to 9m in Japan. Great Bihar earthquake of January 15, 1934: This disastrous earthquake of magnitude 8.4 occurred at 2.00 pm with its epicenter at 26.5N, 86.5E in which nearly 11,000 lives were lost. The areas affected have been found scattered within a region of 48,60,000 sq.km. There was complete damage to all the masonry buildings. Landslides have occurred in the mountain areas near Katmandu, Udaipur, Garji and eastern Nepal. Large-scale liquefaction was also reported in purnea where houses have been tilted and sunk into the ground. At many places sand and water fountains erupted. Fukui (Japan) earthquake of June 28, 1948: The earthquake of magnitude 7.2 occurred at 4.00 am. The peak ground acceleration of 0.6 g was observed and the focal depth of 15 kms was estimated. During the earthquake 5268 people were killed and 35,437 structures were destroyed. Forty-six out of forty seven reinforced concrete frame (cast in-situ) buildings up to 9 stories high survived the earthquake well. One building, which was completely destroyed, was attributed to errors in calculations (Okamoto 1973).
Great Assam earthquake of 1950: The devastating earthquake of magnitude 8.5 on Richter scale occurred at 14hrs 09m 30s(GMT) with epicenter 28.5N,97.0E having a depth of focus of about 15km in area of nearly 46,000 square km suffered extensive damage. The epicenter of the shock was located on the uninhabited part just outside the northeast boundary of India. It caused great destruction to property in northeastern Assam. Chile (South America) earthquake of May1960: The series of shocks began on May 21 with the largest shock of magnitude 7.5. This was followed by several more shocks, four of the largest having magnitude from 6.5 to 7.8. On May 22, a larger shock occurred with magnitude 8.5. During the following month there were 50 shocks with magnitudes form 5 to 7. A total of 450,000 buildings were severely damaged of which 45,000 were completely destroyed and more than 1000 persons were killed. It was possible to study the performance of the modern buildings, which were designed according to country’s earthquake resistant construction regulations.
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The severe damages were due to old buildings with plain brick walls, which were apparently weakened by the previous earthquakes. Such wall construction in Chile is not permitted by current regulations. Buildings with reinforced brick and concrete walls behaved much better. Better earthquake resistance of reinforced concrete frame walls with brick cladding and wood frame walls were observed. The performance of steel framed three storeys building presented considerable interest. In longitudinal and transverse directions provision was made for diagonal bracing (on the first storey in both directions). During the May 22, tremor, the building was without bracing as a result of which its rigidity was sharply reduced (The fundamental time period changed from 0.8 to 1.06s). Despite the decrease in stiffness of the building in horizontal direction it did not receive any damage during another stronger earthquake. It was apparently the reduced rigidity of the building, which attract3ed less inertia forces, and consequently survived the earthquake. Nilgata (Japan) earthquake of 1964: The earthquake (M=7.5 h=40 km D=50 km) has caused considerable destruction in the city of Nilgata, which was primarily due to very poor ground conditions. The predominant time period of the soil layers of city of Nilgata varied from 0.25s to 0.5s. IT was observed that the damages to the buildings were heavy on soil having predominant time periods close to 0.5s and less otherwise, (Mawasumi, 1968). The main cause of damage was the liquefaction of soil underneath. The rigid reinforced concrete buildings under gone large settlement and tilting. One such building completely toppled over. Among the 1500 reinforced concrete buildings in Nilgata, 310 suffered damage, with two thirds of them settling or tilting without noticeable damage to above ground structural elements. Serious damage occurred to closely spaced building due to mutual pounding during seismic shocks, this should be taken into account in designing the expansion joints. In areas of well-consolidated ground, there was no damage. Examination of foundations showed destruction in many cases of reinforced concrete piles. Buildings erected on short piles drived to poorly compacted soils underwent considerable tilting and settlement. Above ground structural elements of buildings erected on piles driven on hard soils were not damaged. Buildings with basements suffered considerably less tilting then buildings on shallow strip footing foundations. Anchorage (Alaska) earthquake of March27, 1964: It was one of the greatest earthquake (M=8.4,h=20km, D=130km at anchorage) in the history. The damage to the structures was heaviest, and many of the buildings were completely demolished. The predominant period of the soil layer was estimated to be near 0.5s. This was possibly the reason that the tall buildings in the city with natural periods close to the predominant periods suffered more damage than lower buildings. Residential wood frame buildings exhibited fairly good earthquake resistance except in some cases when their foundations were destroyed. Least damage was sustained by wood structures built on firm ground (Kunze et al., 1965;Steinburge, 1965 and Wiegel, 1970). The Anchorage earthquake also provided a number of examples of the behaviour of Precast, prestressed reinforced concrete structural elements. The Precast elements were jointed by welding. A large number of the buildings collapsed. Other Precast reinforced
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concrete buildings also suffered serious damage. It was observed, that in all cases destruction and damage to Precast, prestressed structural elements were caused by poor behaviour of joints of supports. The Precast, prestressed elements as a rule were not destroyed. Tashkent (USSR) earthquake of April 26, 1966: The earthquake (M=5.4 h=8 km D=0) though small caused severe damages. The location of the epicenter was right under the city that accounted for the large vertical component of ground movement, which was the reason for devastation. The predominant period of ground was estimated to 0.1s, (Polyakov, 1974). Nearly all the brick buildings were damaged to some degree. But many old sun dried brick buildings in the center of the city were damaged so badly that they had to be demolished. Hindukush (India) earthquake of June 6, 1966: No accelerograph was located in the area; however, few response recorders were actuated, which have indicated a maximum acceleration of about 0.055 g, (Krishna and Arya, 1966). The old building construction of timber encased in masonry walls showed vertical cracks at the corners. In some cases separation of walls, cracking of jack arches over door opening, tilting of walls etc., were also observed. The timber joints were found to be deteriorated. Six stories r.c. Frame building, showed some shear cracks in the roof beams and longitudinal cracks in the slab between the beams. The main reason for these shear cracks in beams appears to be the earthquake forces applied at roof level on the mass of the roof as well as on the mass of some non structural elements standing on the roof for architectural regions. The two-storied hospital building constructed in 1:1:1 lime sand and surkhi mortar. The building has performed well except the crack where it widens in section. These cracks may be attributed to significant change in stiffness of the building. A similar two storey Medical college building in lime sand surkhi survived with very minor cracks in the walls.
Anantnag Earthquake of February20, 1967: This earthquake of Magnitude 5.3-5.7 with a depth of focus of 24 kn struck at nearly 8.49 pm (IST). A total of 786 houses were totally damaged and nearly 25,000 houses were partially damaged [Gosain and Arya (1960)] Kashmir valley has been shake by many severe earthquakes in the past. The earthquakes of 22.6.1969; June 6,1828,May 30, 1885 and September 2, 1963 were the severest. The earthquake of 30th May 1885 was one of the most disastrous earthquakes in Kashmir valley. During this earthquake about 6000 people were killed. Koyna earthquake of Dec. 11, 1967: The Magnitude of the earthquake was recorded as 6.5 and the depth of focus w as about 8 km with its epicenter at 1722.4N, 7344.8E. It occurred at 22 hrs 51m 19s (GMT).
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The maximum MM intensity of VIII was observed. The area was considered seismically inactive. Earthquake has damaged 40,000 houses and 177 persons lost their lives. The peak acceleration recorded was 0.67 g[Arya, Chandrasekaran and Srivastave(1968)]. The traditional construction in the area was non seismic and had little resistance against lateral forces. Most of the building structures in the area were single storied built in masonry. The Koynanagar experience very heavy shocks resulting in severe damages. The cladding wall timber framework buildings failed, whereas, modern random rubble masonry buildings suffered heavy damage. Stone masonry was also heavily damaged than the brick masonry. At Koyna a hundreds of failures was due to bulging out of wall that caused the fall of stone on one face while on the other face standing intact. The outside face many not be able to withstand the tension with the result that the stones would get loosened and fall down. The buildings were mostly founded on murum and there were hardly any failure of foundations. The epicenter of the earthquake was very close to the Koyna dam. The accelerograph installed within the dam provided the most valuable instrumental data. Off Tokachi(Japan) earthquake of May 16, 1968: The earthquake of magnitude 7.9 occurred under sea 170 kms east of the city of Hachinobe. The damage of reinforced concrete buildings was severe which consists of destruction of city Han, public library, technical high school at Hachinobe and Hakodate University. Broach Earthquake of March 23, 1970: A shallow earthquake of Magnitude6.0 occurred at Broach in the early hours of March 23, 1970. The epicenter was at 21.7N, 72.9E. Twenty-three persons were reported to have died and about 250 persons were injured. About 115 houses badly damaged or collapsed while 2500 houses were partially damaged [Bulsari and Thakkar (1970)] Kinnaur earthquake of Jan. 19,1975: The magnitude of the earthquake was estimated as 6.7 and the maximum observed intensity in the region was IX on MM scale. The earthquake caused death of sixty people and several hundred severely injured. The traditional construction in the area was non seismic and had little resistance against the lateral forces. Nearly 2,000 dwellings were heavily damaged, (Singhet. Al. 1975). The random rubble masonry and dressed stone masonry construction with heavy flat roofs suffered extensive damage. Buildings constructed in hollow concrete blocks or dressed stone masonry in cement mortar developed small cracks in walls. Light structures made of corrugated iron sheets nailed to tikber frames and arches did not suffer any damage. The temples, monasteries and monuments also suffered badly. Indo-Nepal earthquake of May 21, 1979: The magnitude of earthquake was 6.0 on Ritcher scale and the maximum intensity was VI on the MM scale, (ashwani et al., 1981). The quality of construction in the region was poor. The maximum damage occurred to the houses of random rubble stone masonry (RRsm) in mud mortar having
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foundation on loose soil. Partial or complete collapse of mud walls has been notice. Dressed stone masonry building with cement mortar developed wall cracks. Western Nepal –India earthquake of July 29, 1980: The main shock with estimated magnitude ranging from 6.2 to 6.5 caused considerable damage to buildings and loss of life. The maximum intensity estimated was VIII on MM scale, (Satyendra and Ashok, 1981). Due to remoteness of the region, almost all the village buildings are constructed of stacks of random rocks pieces (without any mortar) wet mud plaster on their interior sides and covered with a sloping roof of slabs resting on timber beams and rafters. The majority of new construction use mud mortar. However, few use cement mortar. The traditional construction as described offers little or no resistance to lateral forces during earthquakes and thus suffered severe damage. Random rubble stone masonry showed complete collapse. The gable end walls collapsed resulting in partial collapse of the adjacent structure. Failure of timber posts and rafters also resulted in collapse of some roofs. Dressed stone masonry in the absence of any mortar developed cracked in the cement plaster. Poor bonding at the junctions resulted in loss of contact between the cross walls. Reinforce concrete construction did not suffer any damage. Dry packed stone masonry walls w9th continuous lintel band over openings and cross walls did not suffer any damage. Jammu and Kashmir (India) earthquake of August 24, 1980: The earthquake has been assigned magnitude 5.2 on the Richter scale and the maximum intensity was recorded VIII on MM intensity scale. Eighty percent of the houses were either damaged or totally collapsed. The traditional construction is predominantly random rubble stone masonry with mud mortar. Mud houses in the Bhaddo area suffered heavy damage and so as the random rubble masonry. A large size bounding stone, known as Dasalu in local dialect, is used at some places particularly at corners made of two walls. Where Dasalu is not used properly, the corners of the walls opened out resulting in the collapse of building. Lightweight structure made of corrugated iron sheets mailed in limber trusses did not suffer any damage, [(Prakash and Mam, 1981)]. The bonding stone Dasalu is found to be effective in the walls constructed of random rubble masonry. For its effectiveness the spacing of these should be about 1.0 to 1.5 meters both horizontally and vertically. Great Nicobar (India) earthquake of Jan. 20,1982: The earthquake of Richter magnitude 6.3 occurred at the east coast of Great Nicobar Island. The focal depth was estimated to 28 kms,(Agarwal,1982). The houses of Nicobar founded on multiple deep piles of 10 to 15 cm dia separated from ground, have not damaged. The timber cum hollow block masonry construction also faired well with minor damages. Buildings on fills have shown damage. Assam earthquake of August 6th, 1988: The earthquake of magnitude of 7.2 occurred at 6.36 hours (IST) on August 6 th, 1988 with its epicenter at 25.14 N, 95.12 E. the focal depth was estimated to 96 KM. Guwahati, Jorhat , Sibsagar and Silchar were shaken. No deaths were reported because
20
the epicenter of the earthquake was in a remote area and possibly Assam houses (Ikra and bamboo houses) are able to resist earthquake much better. Bihar Nepal Earthquake of August 21, 1988: The earthquake of magnitude 6.6 struck at 4 hrs 39 m 11.25 sec (IST) with its epicenter in Nepal near the Bihar Nepal border (Lat 26.775 and long 86.609) in close proximity to 1934 earthquake epicenter. The focal depth is estimated to be 71 KM. The maximum intensity of VIII+ was observed at Darbhanga and Munghyer in Bihar and Dharan in Nepal. This earthquake has taken 281 lives in Bihar and nearly 650 lives in Nepal. The total number of injured persons in Bihar is 3767. It damaged / collapsed 1.5 lacks houses/ buildings in Bihar alone. At Darbhanga the high intensity was mainly attributed to the soft alluvial soil and liquefaction resulting in large-scale subsidence of soil while in Dharan the high intensity is attributed to amplification of ground acceleration due to hill and hill slope. The recent R.C.C constructions with codal; provision has shown better performance while old and poorly built load bearing unreinforced masonry brick buildings performed badly. Largescale liquefaction of ground was observed in the Gangetic plane resulting in ground subsidence. Mud houses and brick houses laid in mud mortar was affected most in the villages. Severe damage to old masonry buildings having jack arch construction was observed. Framed construction has shown better performance. Uttarkashi Earthquake of October 20, 1991: The earthquake of magnitude 6.6 rocked the Uttarkashi region at 2.53 hrs (IST) with its epicenter at village Agora (30.75 N, 78.68 E) and focal depth 12 Km. The maximum intensity in epicentral track was observed IX on Modified Mercalli scale. The earthquake caused enormous destruction of houses and loss of life, killing nearly 770 people and injured nearly 5000, mostly all due to collapse of random rubble residential houses. The affected region lies between seismic zone IV and V according to seismic zoning map of India. The maximum affected area was Uttarkashi, Tehri and Chamoli districts. Telecommunication and power supply were badly effected due to damaged telephone and electric poles. Rubble stone masonry houses in mud mortar close to the severely effected area were totally collapsed and others got severe damage. Many school and health buildings were also damaged. Many bridges were severely damaged / collapsed. Gawana steel lattice bridge located about 6 Km from Uttarkashi on road to Gangotri collapsed, severely affecting the relief and rescue operations immediately after the earthquake. Widespread rock falls landslides / rockslides were observed mostly along the road causing heavy damage to hilly roads and blocking it. The Latur (Killari) earthquake of sept 30, 1993: The moderate shallow focus earthquake of magnitude 6.4 occurred in peninsular India with its epicenter near Killari created Havoc. The peninsular India has been considered seismically stable. The earthquake caused strong ground shaking in the region of Latur, Osmanabad, Sholapur, Gulberga and Bidar. There was heavy damage in a localized area of 15 km close to Killari, which is on the northern side of river Terna. The maximum intensity in the epicentral track was VIII+ on Modified Mercalli scale. It
21
destroyed more than 28,700 houses damaging about 1,70,000 houses and killing about 9,000 people. The random rubble stone houses in mud mortar totally destroyed. The heavy roofs and thick walls with little shear and no tensile strength were the main reasons for the failure. The most common construction of random rubble stone walls laid in mud mortar are made thick (70 to 180 cm) with small openings for the doors and windows. The foundations of these houses are taken to a depth varying from 60 to 250 cm below the top cover of black cotton soil. The roof consists of timber rafters in two perpendicular directions over which wooden planks and a thick layer of mud is laid. The mud layer on roof varies between 30 to 80 cm making very heavy. The walls did not have the interlocking stones and the houses did not have any earthquake resistant features. The Jabalpur earthquake of May 21,1997: The earthquake of magnitude 6.1 occurred on May 21,1997 at 04hrs 22s in southern India with its epicenter near Jabalpur with its focus at 33.0 km. The earthquake lasted 20 secs. The maximum intensity on MM intensity scale is estimated to be VIII. The latitude and longitude were 23.18 N, 80.02 E. The southern India has been considered seismically stable. The earthquake caused strong ground shaking in the region of Jabalpur, Seoni, Mandla and other towns in the Narmada belt of Madhyapradesh. About 25 people were killed and more than 100 injured. Most deaths were due to collapse of houses. There was wide spread damage in Ragchi, Garha and Sarafa areas on the cities outskirts. In Jabal, some buildings in Khumeria cantonment, which was the countries oldest factory, developed cracks. Water supply was disrupted at many places in the city as pipelines burst. Telephone lines and electricity supply were also affected. Bhuj earthquake of January 26, 2001: The earthquake of magnitude 6.9 occurred on January 26, 2001 and has caused widespread damage to variety of buildings and many of them have collapsed. Total deaths reported were 19,500. For the first time in India large number of urban buildings including the multistorey buildings at Bhuj, Ahmedabad, Gandhidham and other places have damaged / collapsed. The mushrooming of multistorey buildings without any consideration of earthquake resistant design and construction practices has generated a countrywide debate about its seismic safety. It has caused damage to the common type of load bearing buildings and RCC framed buildings. Most of the rural construction of mud, adobe, burnt brick and stone masonry either in mud or cement mortar have shown severe damage or collapsed. The stone masonry buildings undergo severe damage resulting in complete collapse and pile up in a heap of stones. The inertia forces due to roof / floor is transmitted to the top of the walls and where the roofing material is improperly tied to the wall, it will be dislodged. The weak roof support connection is the cause of separation of roof from the support and leads to complete collapse. At many places the height of random rubble stone masonry walls in mud mortar / poor cement mortar was about 5 m. These were provided with earthquake band at only lintel level and therefore, damage was observed in the high walls between the lintel and the roof level. The failure of bottom chord of roof truss may also cause complete collapse of truss as well as the whole building. The Bhuj earthquake has
22
again showed that stone houses are most vulnerable to earthquakes as it was observed in Uttarkashi, Killari and Chamoli earthquakes. As the prosperity of Gujarat state flourished, multistorey buildings started mushrooming. In the last 10 years many four storey and ten storey multistorey buildings were constructed. The multistorey buildings with out a lift were constructed up to four storey and buildings with lift were constructed up to ten storey. Unscrupulous builders and architects unaware of any earthquake resistant provisions have been constructing buildings. The collapse of newly built apartments and office blocks prove this point. The modern RCC frame construction consist of bare RCC beam column frame and the masonry infill. The masonry infill varies from dressed stone in mud mortar, clay brick in cement mortar, cement concrete block masonry in mud/cement mortar. Most of the multistorey buildings in Ahmedabad and Ghandhinagar were of RCC frame constructions with bricks / cement concrete block masonry in cement mortar as infill material. Most of these type of construction was of Stilt type i.e., soft storey construction. In this type of construction either very few or no infill walls are provided in the ground floor and is left open for parking the vehicles of the residents. The damage to multistorey buildings in Bhuj is found to be wide spread. It is interesting to note that multi storey buildings have also damaged as far distances as Ahmedabad, Gandhidham and Surat. Whereas well designed and well constructed RCC framed buildings following the Indian standard code of practice have performed very well during the earthquake. Most of the buildings constructed by CPWD, Post and Telegraph and other government agencies have performed well. The damage in RC framed buildings is mostly due to failure of infill, or failure of columns or beams. The column may have damaged by cracking or buckling due to excessive bending combined with dead load. The buckling of columns is significant when the columns are slender and the spacing of the stirrup in the column is large. Severe crack occurs near the rigid joints of frame due to shearing action, which may lead to complete collapse. Most of the damage occurred at the beam column junction. Widespread damage was also observed at the inter face of stone or brick masonry infill and RCC frame. In most of the cases diagonal cracks appeared in the stone or brick infill. The buildings resisting on soft ground storey columns without or with very few infill walls have undergone severe damage and many have collapsed.
Performance Of Various Type Of Buildings Different types of buildings suffer different degrees of damage during earthquakes and the same has been studied here. 1.Mud and adobe houses: Unburnt sun dried bricks laid in mud mortar are called adobe construction. Mud houses are the traditional construction, for poor and most suitable in view of their initial cost, easy availability, low level skill for construction and excellent insulation against heat and cold. More than 100 million people in India live in these type of houses. There are numerous examples of complete collapse of such buildings in 1906 Assam, 1948 Ashkhabad, 1960 Agadir, 1966 Tashkent, 1967 Koyna, 1975 Kinnaur, 1979 Indo-Nepal, 1980 Jammu and Kashmir and 1982 Dhamar earthquakes. It is very weak in shear, tension and compression. Separation of walls at corner and junctions takes place easily
23
under ground shaking. The cracks pass through the poor joints. After the walls fail either due to bending or shearing in combination with the compressive loads, the whole house crashes down. Extensive damage was observed during earthquake especially if it occurs after a rainfall, (Krishna and Chandra, 1983). Better performance is obtained by mixing the mud with clay to provide the cohesive strength. The mixing of straw improves the tensile strength. Coating the outer wall with waterproof substance such as bitumen improves against weathering. The strength of mud walls can be improved significantly by spilt bamboo or timber reinforcement. Timber frame or horizontal timber runners at lintel level with vertical members at corners further improves its resistance to lateral forces which has been observed during the earthquakes. 2.Masonry buildings: Masonry buildings of brick and stone are superior with respect to durability, fire resistance, heat resistance and formative effects. Masonry buildings consist of various material and sizes (i) Large block (block size >50 cm)-concrete blocks, rock blocks or lime stones;(ii) concrete brick-solid and hollow; (iii) Natural stone masonry. Because of its easy availability, economic reasons and the merits mentioned above this type of construction are widely used. In very remote areas in Himalayas buildings are constructed of stacks of random rock pieces without any mortar. The majority of new construction use mud mortar, however, few use cement mortar also. Causes of failure of masonry buildings: These buildings are very heavy and attract large inertia forces. Unreinforced masonry walls are weak against tension (Horizontal forces) and shear, and therefore, perform rather poor during earthquakes. These buildings have large in plane rigidity and therefore have low time periods of vibration, which results in large seismic force. These buildings fall apart and collapsed because of lack of integrity. The lack of structural integrity could be due to lack of ‘through’ stones, absence of bonding between cross walls, absence of diaphragm action of roofs and lack of box light action. Common type of damage in masonry building: All of them undergo severe damage resulting in complete collapse and pileup ina heap of stones. The inertia forces due to roof or floor is transmitted to the top of the walls and if the roofing material is improperly tied to the wall, it will be dislodged. The weak roof support connection is the cause of separation of roof from the support and leads to complete collapse. The failure of bottom chord of roof truss may also cause complete collapse of truss as well as the whole building. If the roof/floor material is properly tied to the top walls causing it to shear of diagonally in the direction motion through the bedding joints. The cracks usually initiate at the corners of the openings. The failure of pier occurs due to combined action of flexure and shear. Near vertical cracks near corner wall joint occur indicating separations of walls. For motion perpendicular to the walls, the bending moment at the ends result in cracking and separation of the walls due to poor bonding. Generally gable end wall collapses. Due to large inertia forces acting on the walls, the Wythe of masonry is either bulge outward or inward. The falling away of half the wall thickness on the bulged side is common
24
feature. The bonding stone is found to be effective as in Jammu Kashmir earthquake of August 24, 1980. Unreinforced dressed rubble masonry (DRM) has shown slightly better performance than random rubble masonry. The most common damage is due to cracks in the walls. The masonry with lower unit mass and greater bond strength shows better performance. The unreinforced masonry as a rule should be avoided as a construction material as far as possible in seismic area. 3.Reinforced masonry buildings: Reinforced masonry buildings have withstood earthquakes well, without appreciable damage. For horizontal bending, a tough member capable of taking bending if found to perform better during earthquakes. If the corner sections or opening are reinforced with steel bars even greater strength is attained. Even dry packed stone masonry wall with continuous lintel band over openings and cross walls did not undergo any damage. 4.Brick-R.C. frame buildings: This type of building consists of RC frame structures and brick lay in cement mortar as infill. This type of construction is suitable in seismic areas. Causes of failure of RC frame buildings: The failures are due to mainly lack of good design of beams /columns frame action and foundation. Poor quality of construction inadequate detailing or laying of reinforcement in various components particularly at joints and in columns /beams for ductility. Inadequate diaphragm action of roof and floors. Inadequate treatment of masonry walls. Common type of damage in RC frame buildings: The damage is mostly due to failure of infill, or failure of columns or beams. Spalling of concrete in columns. Cracking or buckling due to excessive bending combined with dead load may damage the column. The buckling of columns are significant when the columns are slender and the spacing of stirrup in the column is large. Severe crack occurs near rigid joints of frame due to shearing action, which may lead to complete collapse. The differential settlement also causes excessive moments in the frame and may lead to failure. Design of frame should be such that the plastic hinge is confined to beam only, because beam failure is less damaging than the common failure. 5.Wooden buildings: This is also most common type of construction in areas of high seismicity. It is also most suitable material for earthquake resistant construction due to its light weight and shear strength across the grains as observed in 1933 Long beach, 1952 Kern country, 1963 Skopje, and 1964 Anchorage earthquake. However during off- Tokachi earthquake (1968), more than 4,000 wooden buildings were either totally pr partially damaged. In addition there were failure due to sliding and caving in due to softness of ground. The main reason of failure was its low rigidity joints, which acts as a hinge. Failure is also due to deterioration of wood with passage of time. Wood frames without walls have almost no resistants against horizontal forces. Resistant is highest for diagonal braced wall. Buildings with diagonal bracing in both vertical and horizontal plane perform much better. The traditional wood frame Ikra construction of Assam and houses of Nicobars
25
founded on wooden piles separated from ground have performed very well during earthquakes. Wood houses are generally suitable up to two storeys. 6. Reinforced Concrete Buildings: This type of construction consists of shear walls and frames of concrete. Substantial damage to reinforced concrete buildings was seen in the Kanto (1923) earthquake. Later in Niigata (1964), Off-Tokachi (1968) and Venezuela (1967) earthquake it suffered heavy damages. The damage to reinforced concrete buildings may be divided broadly into vibratory failure and tilting or uneven settlement. When a reinforced concrete building is constructed on comparatively hard ground vibratory failure is seen, while on soft ground tilting, uneven settlement or sinking is observed. In case of vibratory failure the causes of damage may be considered to be different for each case, but basically, the seismic forces, which acted on a building during the earthquake, exceeded the loads considered in the design, and the buildings did not have adequate resistance and ductility to withstand them. In general these buildings performed well as observed in Skopje (1963) and Kern country (1952) earthquakes. The shear walls are fond to be effective to provide adequate strength to the buildings. Severe damage to spandrel wall between the vertical openings is observed. Tilting and singing of reinforced concrete buildings during earthquakes were seen in the Kanto and Niigata earthquakes. Most failed because the dead weights could not be supported after the settling of the ground. Such damage is peculiar to buildings in soft ground, the damage becomes higher in the following order: pile foundation, mat foundation, continuous foundation and independent foundation. The hollow concrete block buildings with steel reinforcement in selected grout filled cells have shown good performance. The Precast and prestressed reinforced concrete buildings also suffered severe damage mostly because of poor behaviour of joints or supports. The Precast and prestressed element as a rule were not destroyed as observed in 1952 Kern country and 1964 Anchorage earthquakes. 6. Steel Skeleton Buildings: Buildings with steel skeleton construction differ greatly according to shapes of cross sections and method of connection. They many be broadly divided into two varieties, those employing braces as earthquake resistant elements and those which are rigid frame structures. The former is used in low building while the later is used in highrise buildings. When braces are used as earthquake resistant elements, it is normal to design so that all horizontal forces will be borne by the braces. This type of building is generally light and influence of wind loads are dominant in most cases. However, there are many cases in which the braces have shown breaking or buckling in which joints have failed (Wiegel, 1970). Steel skeleton construction, particularly the structural type in which frames are comprised of beams and columns consisting of single member H-beams, is often used in high-rise buildings. The non-structural damage is common but none of these building severely damages as observed in 1906 San Francisco earthquake
26
7.Steel and Reinforced Concrete Composite Structures: Steel and Reinforced Concrete Composite Structures are composed of steel skeleton and reinforced concrete and have the dynamic characteristics of both. It is better with respect to fire resistance and safety against buckling as compared to steel skeleton. Whereas compared to reinforced concrete structures it has better ductility after yielding. As these features are the properties, which are effective for making a building earthquake resistant and are, found to perform better during earthquakes (Wiegel, 1970).
ANALYSIS OF FRAMES SUBJECTED TO HORIZONTAL FORCES: A Building frame is subjected the horizontal forces due to wind pressure and seismic pressure and seismic effects. These horizontal forces cause axial forces in columns and bending moment in all members of the frame. As stated earlier, a building frame is all highly indeterminate structure. The degree of indeterminacy of the building bent (Fig1) is found by providing a cut near mid-span of each beam. Each cut beam will thus have three unknown reaction components: Moment (M), Shear (F) and Axial thrust (H). Each column with its cut beams will act as a cantilever, which is statically determinate structure. Thus, if n is the number of beams in a bent, the degree of indeterminacy will be 3n for the building bent shown in figure1, there are 8 beams and hence the bent is statically indeterminate up to 24 th degree. An ordinary 20 storey building with 20 storeys and 5 stacks of columns has 80 beams, thus having the degree of indeterminacy of 240.
27
H1
F1 Fig 1 Due to this reason, suitable assumptions are made so that the frame subjected to horizontal forces can be analysed by using simple principles of mechanics. Following approximate methods are commonly used for the analysis of building frames subjected to lateral forces: i. Portal method ii. Cantilever method.
(i) Portal method: For the purpose of analysis, it is assumed that the horizontal forces are acting on the joints. The portal method is based on the following two important assumptions: a) The point of contra flexure in al the members lie at their mid points. b) The horizontal shear taken by each interior column is double the horizontal shear taken by each exterior column. A1 B1 C1 D1 Top storey A2
B2
C2
D2
2nd storey A3
Fig .2 B3
C3
1st storey
28
D3
A4
B4
C4
D4
Figure 2 shows a three storey-building frame with three spans. Let P1, P2 and P3 be the external horizontal forces acting on the joints of the wall columns. Under the action of horizontal forces, the frame will deflect. The point of contra flexure will lie at the middle of each member. Only horizontal shears will act at these points of contra flexure, since bending moment will be zero at these points. Consider the top story having vertical members A1 A2, B1 B2, C1 C2 and D1 D2. the horizontal shear for the outer columns A1 A2 and D1 D2 will be P each while that for the inner columns B1 B2 and C1 C2 will be 2P each, as marked. The value of P is given by P1 = P + 2P + 2P + P P = (1/6) P1 Similarly consider the second story, where the exterior columns A2 A3 and D2 D3 have shear Q. the value of shear Q is found by P1 + P2 = Q + 2Q + 2Q + Q Q = (1/6) (P1 + P2) Similarly for the bottom story, the shear R is given by P1 + P2 + P3 = R + 2R + 2R + R R = (1/6) (P1 + P2 + P3) Knowing the horizontal shear at the point of contra flexure, the bending moment in the column can be easily found. A1 B1 C1 D1 P P 2P 2P h/2 A2 m m B2 m, m C2 m m D2+ h/2 Q 2Q 2Q Q A3
L
B3
L
C3
L
D3
Fig.3 Let us consider the floor A2 B2 C2 D2 between 3rd and 2nd story. The shear acting at the point of contra flexure is as shown in figure 3. The joint A2 is subjected to clockwise moment of Ph/2 at A2 in the column A2 A3. The beam A2 B2 is thus required to resist a clockwise
29
moment of m = (P + Q)*h/2 at A2. Similarly at the joint B, there will be a clockwise moment equal to (2P + 2Q)*h/2. But there are two beams to resist this. Hence clockwise moment in each beam will be (P + Q)*h/2.Thus the ends of the beam receive the same clockwise moment of (P + Q)*h/2, with the result that the points of contra flexure will lie in the middle of the beams. The moment m acting at each end of the beam A2 B2, B2 C2, C2 D2 give rise to vertical reactions in columns, if L is the span of these beams, each beam will impose an upward pull of 2m/L on wind ward column and a push of 2m/L n leeward column connected to the beam, for each span. The vertical reactions will neutralize for any intermediate column, provided span of beams on either side are equal. Only the end columns will experience vertical reactions. The windward columns will have an upward pull of 2m/L and the leeward column will have a downward push of 2m/L. (ii)Cantilever Method: The cantilever method is based on the following assumptions: 1) The point of contra flexure in each member lies at its mid span or mid height. 2) The direct stresses (Axial stresses) in the columns, due to horizontal forces, are directly to their distance from the centroidal vertical axis of the frame. P A B C D P’ E
F
G
H
I
J
K
L
M
N
O
P
Fig 4a P’’
Figure 4a shows a building frame subjected to horizontal forces. Figure 4b shows the top story up to the points of contra flexure of the columns. The reactions at the point of contraflexure will be direct and shear forces only. Let V1, V2, V3 and V4 be the axial forces in the columns AE, BF, CG and DF, having areas of cross sections a1, a2, a3 and a4 respectively. P L1 H1
L2
L3
H2
H3
H4
Fig 4b V1
V2
V3 x2
x1
x3 x4 Centroidal axis
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V4 Plane of section
From statics we have P = H1 + H2 + H3 + H4 From assumption 2, we have V1/a1 V2/a2 ------ = ------ = X1 X2
V3/a3 ------ = X3
(1) V4/a4 -----X4
(2)
Where X1, X2, X3, X4 are the centroidal distances of the columns from vertical centroidal axes of the frame. By taking moments about the mid point of intersection of the vertical centroidal axes and top beam, we get (H1 + H2 + H3 + H4)*h/2 = V1.X1 + V2.X2 + V3.X3 + V4.X4 or V1.X1 + V2.X2 + V3.X3 + V4.X4 = P h/2 (3) from 2 and 3, the axial forces V1, V2, V3 and V4 can be determined. P
A
M1 B
h /2
P
A
B
M2
L1
L2/2
H1
H2
C
L1/2
Fig 5
V1
V1
V2
In order to determine H1, take the moments about point of contraflexure M1 in the beam AB. (Figure 5) H1 * h/2 = V1 * L1/2 H1 = V1.L1/h (a) Similarly, taking moments about point of contra flexure M2 in the beam BC H1 * h/2 + H2 *h/2 = V1 (L1 + (L2/2)) + V2 (L2/2) H1 + H2 = 2[V1.L1 + (V1 + V2) L2/2] / h (b) Since H1 is known from a, H2 can be determined. In the similar manner H3 and H4 can be determined. Example 1: Analyse the building frame, subjected to horizontal forces, as shown in fig. Use portal method. 120kN A 180 KN
E
I
B
C
D
F
G
H
J
K
7m
3.5m
Solution
31
L 5m
1. Horizontal shear Let the horizontal shears in the exterior columns be P and in the interior columns be 2P for the top storey. Similarly, for the bottom storey, let the shears be R and 2R for the exterior and interior columns. For the top storey, we have P+2P+2P+P=120 ∴ P = 120 / 6 = 20 kN. For the bottom storey, we have R+ 2R + 2R + R = 120 + 180 ∴
R= 300 / 6 = 50 kN
2. Moments at the ends of columns For the top storey, MEA=MAE=MHD=MDH = PX h/2 = 20X3.5/2=35 kN-m MFB=MBF=MGC=MCG} =2PXh/2=20X3.5=70 kN-m. For the bottom storey, MIE=MEI=MLH=MHL =RXh/2=50X3.5/2=87.5 kN-m MJF=MFJ=MKG=MGK=2R.h/2 +=50X3.5=175 kN-m. 3. Moments at the ends of the beams First floor beams MEF=MEI=35+87.5=122.5 kN-m Simi1arly, MFE =MFG=MGF=MHG=122.5, Since the point of contraflexure lies at the middle of each span. In general, m= (P+R) h/2=(20+50) X3.5/2=122.5 Roof beams MAB= MBA= MBC= MCB=MCD=MDC= P.h/2 =20X3.5/2=35 kN-m. 4. Shear in beams Since no external vertical force is acting on the beam, shear F’ is given by F=m1+m2/L Where m1 and m3 are the moments at ends of the beam of span L. Thus, FEF=122.5+122.5/7=35 KN↑
32
FFE=35 KN↓ FFG =FGF =122.5+122.5/3.5=70kN FGH=FHG=122.5+122.5/5=49 kN FAB=FBA=35+35/7=10kN FBC=FCB=35+35/3.5=20kN FCD=FDC=35+35/5=14kN 5. Axial force in columns The axial forces in the columns will be as under: Column AE= shear in beam AB= 10kN↑ Column EI=axial force in AE+ shear in EF = 10+35=45 kN↑ Column DH==shear in beam DC= l4kN↑ Column HL=axial force in DH+ shear in HG =14+49=63 kN↑ Since the spans are not equal, interior columns will also have axial forces, Column BF=FBA—FBC=10-2=-10 KN (i.e.↑) Column FJ= (—10) + (FFE-FFG)=(—l0)+(35—70)=-45 kN (i.e. ↑) Alternatively, axial force in BF =2m’/L1- 2m’/L2= 2x35/7- 2x35/3.5=-10 Kn and axial force in column FJ=(-1)+(2m/L1-2m/L2) =(—10)+(2*122.5/7-2*122.5/3.5) =—45 kN (i.e. ↑) Axial force in CG=3m’/L2-2m’/L3 =2*35/3.5-2*35/5=6(↑) Axial force in column GK
33
=6+(2m/L2-2m/L3) =6+(2*122.5/3.6-2*122.5/5) =27↑ Check: Total axial force at the base =-45(↑)-45(↑)+27(↑)+63(↑) =zero. Example 2. Re-analyze the frame of example 1 by cantilever method, assuming that all the columns have the same area of cross-section. 120kN A
B
C
X1= 8.25m 180 KN
D X4=7.25m
M E
x2
X3
F
M H
G
N
N
I
J
K
7m
3.5m
L 5m
Solution 1. Location of centroidal axis of the columns Let the centroidal axis be at a distance x from the windward column AEI. Taking moment of areas of the columns about AEI, we get X=(2X0)+(2X7)+(2X 10.5)+(2 X 15.5)/8= 8.25 m X1=8.25(=X);X2=8.25-7=1.25 m X3=3.5-1.25=2.25 m X4=(7+3.5+5)-8.25=7.25 m 2. Axial forces in columns of first storey Let the axial force in column EI=V1=V Since the areas are equal, The axial forces in other columns
34
will be in proportion to their distances from the centroidal axis. V/X1=V2/X2=V3=X3=V4/X4 V2=V.X2/X1=1.25/8.25 V=0.1515V(↑) V3=V.X3/X1=2.25/8.25 V=0.2727 V (↑) V4=V.X4/X1=7.25/8.25 120kN A
B
V=0.8788 V(↑)
C D X1= 8.25m
X4=7.25m x2
180 KN
E
X3
F
G
H1
H2
V1
H3
V2 J
I
H H4
V3
V4 L
K
7m
3.5m
5m
Taking moments of all forces about the point of contraflexure N of the leeward column, we get (120x 5.25)+(180X1.75)-(VX15.5)—(0.1515 VX8.5)+(0.2727 VX5)=0 which gives V—V1=61.267 kN (↓) V2=0.1515X61.267=9.282 (↓) V3=0.2727X61.267=16.707 (↑) V4=0.8788X61.267=53.842 (↑) Check: ∑V=61.267+9.282-16.707-53.842=0. 2. Axial forces in the columns of second storey 120kN A
B
C
X1= 8.25m x2 H1’ V1’
D X4=7.25m
X3 H2’
V2’ 7m
V3’ 3.5m
35
H3’
H4’ V4’
5m
Let V1=V’=axial force in column AF V2=0.1515 V’;V3’=0.2727 V’ and V4=0.8788 V’ Taking moments about point of contraflexure M, we get (120Xl.75) —(V’X15.5)-(0.1515 V’X8.5)+(0.2727 V’X5)=0 From which V’=V’1=13.615 (↓) V2’=0.1515 X13.615=2.063 (↓) V3’=0.2727X13.615=3.713 (↑) V4’=0.8788X13.615=11.965 (↑) Check: ∑V=13.615+2.063-3.713-11.965=0. 4. Shears at ends of beams The shears at the ends of beams can be determined from the axial forces in the columns at various joints. Let us assume downward force as negative. Joint E: FEE=V’1-V1=13.615-61.267=-47.652 Joint F: FFG=-47.652+2.063-9.282=-54.871 Joint G : FGH=-54.871-3.713+16.707=-41.877 Joint A: FAB=-13.615 Joint B: FBC=-13.615-2.063=-15.678 Joint C: FCD=-15.678+3.713=-11.965. 5. Moments at the ends of beams The shears at he ends of beams can be determined from the axial forces in the columns at various joints. Let us assume downward force as negative. (a) First floor MEF=MFE=FFEXL1/2=47.652X7/2=166.8 kN-m MFG=MGF=54.871X3.5/2=96.0 MGH=MHG=41.879X5/2=104.7
(b) Second floor MAB=MBA=13.615X7/2=47.6 kN-m 36
BBC==MCB=15.678X3.5/2=27.4 MCD=MDC=11.965X5/2=29.9 6. Moments at the ends of columns (a) Top storey MAB = MAB=47.6 kN-m Since there is point of contraflexure at the middle of column, AE, MEA=47.6 kN-m MBF==MBA+MBC=47.6+27.4=75 kN-m MCG=MCD=27.4 +29.9=57.3 MGC=57.5 MDH=MDC=29.9 kN-m MHD=29.9kN.m. (b) Bottom storey MEI+MEA =MEF ∴
MEI= MEF-MEA=166.8-47.6=119’2 kN-m
MIE=119.2 Kn-m MFJ+MFB=MFE+MFG MFJ=166.8+96-75=187.8kN-m Hence MJF=187.8 kN-m MGK=96+10.47-57.5=143.2 MKG=143.2 kN-m MHL+MHD=MGH MHL=104.7-29.9=74.8 MLH=74.8 Alternatively, the moment at the column ends at the can be found by first determining horizontal shears (H) at the point of contraflexure and multiplying there by half the height of the column. Thus, MAE =H1’Xh/2;MBF=H1’Xh/2etc. Similarly, MEI =Xh/2;Mfj=H2Xh/2etc.
37
The method - of determining horizontal shears have been explained in 27.7. For example, H1’=V1’L1/h =l3.6l5X7/3.5=27’23 H2’=2[V1’.L1+(V1’+V2’)L2/2/h-H1’ =2[13.615X7+(13.615+2.063)+3.5/2]/3.5-27.23 =42.908 ∴
MAE=H1’Xh/2=27.23X3.5/2X47.65 MBF=H2’Xh/2=42.908X3.5/2=75 Which is the same as found earlier.
MONOLITHIC BEAM TO COLUMN JOINTS In the earlier chapters, considerably emphasis has been placed on the design of structural members for compression, bending, shear, development of reinforcement and torsion. A beam-column joint is a very critical element in reinforced concrete construction where the elements intersect in all the three directions. Floor slab has been removed for convenience. Quite often in design the details of joint are simply ignored. Joints are most critical because they ensure continuity of a structure and transfer forces that are present at the ends of the members into and through the joint. Frequently joints are points of weakness due to lack of adequate anchorage for bars entering the joint from the columns and beams. The code is silent regarding the design of beam – column joints. A joint should maintain its integrity and should be designed so that it is stronger than the members framing into it. Failure should not occur within the joint. In fact, failure due to over
38
loading should occur in beams through large flexural cracking and plastic hinging and not in columns. The forces acting on an exterior beam – column joint are shown in Figs. 1a and 1b during reversal of the seismic force. The nature of stress in steel will change with the change in the direction of the seismic force. The points of inflection are assumed at the mid-height of the columns. The shear in the joint is equal to: Vj = σ yAs – Vcol Where,Vj = shear in the joint As = area of tension steel in the beam Vcol = shear in the column The joint shear causes diagonal tension and compression in the joint. With each reversal of seismic loading, the joint shear changes sign causing cracks due to diagonal tension in both directions. Moreover, the nature of bond stress also changes in the joint around the beam and column reinforcement. It causes splitting stresses in the concrete around the bar. It is essential to maintain integrity of the concrete core within the joint for a smoother transfer of forces, and that ultimate moment capacities of the members meeting at the joint may be developed. The forces acting on an interior beam – column joint are shown in Fig. 1c. The shear in the joint is equal to Vj = σ yAt1 + σ sAt2 + C’ - Vcol Where,At1 = area of tension steel in beam At2 = area of compression steel in beam C’ = compression in concrete = k σ ckbx σs = stress in the compression steel b = breadth of the beam k, x = stress block parameters The main factors to be considered in the design of joint include: (a) Shear, (b) Anchorage of reinforcement, and (c) Transfer of axial load. The transverse reinforcement is provided for confinement of concrete and shear resistance. The transverse reinforcement required in the column or in the joint (whichever is more) must be extended through the joint as well. If, however, the concrete is confirmed by beams framing into all four sides of the column, and their dimensions conform to those shown in Fig. 2a, b and c, the required transverse reinforcement within the joint may be reduced upto nil. In addition, it must be ensured that the beam reinforcement is adequately anchored. Quite often the beam – column joint is under a severe congestion of reinforcement due to too many bars converging within a limited space of the joint. The proportioning of beam and column sizes must be done carefully. In case the sizes of beam and column are same, it will be very difficult to place the reinforcement within the joint. The bars will have to be cranked as shown in Figs. 3a and b, which is not a very desirable arrangement.
39
By selecting little larger concrete area and lower reinforcement percentage, it is possible to avoid congestion of steel. Corner joints In planar frames, industrial bents, retaining walls or other similar structures, corner joints pose a specific problem. The corner may be subjected to opening or closing forces. Diagonal tension cracking may be the cause of failure in opening corners, whereas, in closing corners, the anchorage of reinforcement may cause a serious problem. The detailing of reinforcement in corner joints may be done as shown in Figs. 4a and b.
DESIGN FOR DUCTILITY Selection of cross-sections that will have adequate strength is rather easy. But it is much more difficult to achieve the desired strength as well as ductility. To ensure sufficient ductility, the designer should pay attention to detailing of reinforcement, bar cut-offs, splicing and joint details. Sufficient amount of ductility can be ensured by following certain simple design details such as : 1. 2. 3.
The structural layout should be simple and regular avoiding offsets of beams to columns, or offsets of columns from floor to floor. Changes in stiffness should be gradual from floor to floor. The amount of tensile reinforcement in beams should be restricted and more compression reinforcement should be provided. Stirrups to prevent it from buckling should enclose the latter. Beams and columns in a reinforced concrete frame should be designed in such a manner that inelasticity is confined to beams only and the columns should remain elastic. To ensure this, sum of the moment capacity of the columns for the design axial loads at a beam-column joint should be greater than the moment capacities of the beams along each principal plane Σ Mcolumn > 1.2 Σ Mbeam
4.
The shear reinforcement should be adequate to ensure that the strength in shear exceeds the strength in flexure and thus, prevent a non-ductile shear failure before the fully reversible flexural strength of a member has been developed. Clause 6.3.3. of IS : 13920-1993 requires that the shear resistance shall be the maximum of the : a. Calculated factored shear force as per analysis, and b. Shear force due to formation of plastic hinges at both ends plus the factored gravity loads on the span. i. For sway to right (Fig. A)
40
Va = Vb =
M pl + M p2 Lc M pl + M p2 Lc
+ 0.5wL
c
− 0.5wL
c
− 0.5wL
c
+ 0.5wL
c
ii. For sway to left Va = Vb =
M pl + M p2 Lc M pl + M p2 Lc
Where, Mpl
=
Mp2
=
w Lc
= =
hogging or sagging probable moment capacity at the left end of the beam = 1.4 times the yield moment capacity at each end of the beam sagging or hogging probable moment capacity at the right end of the beam factored gravity load = 1.2 (DL + LL) clear span of beam
The resistance Mp corresponds roughly to the probable moment of resistance of the beam section of either side of the joint. It is the assumed that the ratio of the actual ultimate tensile stress to the actual tensile yield strength of the steel is not less than 1.25. Use of longitudinal reinforcement with yield strength substantially higher than that assumed in the design will lead to higher shear and bond stresses at the time of development of yield moment. This may lead to unexpected brittle failures and should be avoided. It is known that the length of the yield region is related to the relative magnitudes of the ultimate and yield strengths. The larger is the ratio of the ultimate to yield moment, the longer is the yield region. The factor is equal to 1.25 times the yield strength of steel divided by 0.87 (that is 1.25 / 0.87= 1.43 = 1.40). The design shear at each and A and B shall be the absolute maximum of the corresponding two values of Va and Vb. 5.
6. 7. 8.
Closed stirrups or spirals should be used to confine the concrete at sections of maximum moment to increase the ductility of members. Such sections include upper and lower ends of columns, and within beam-column joints, which do not have beams on all sides. If axial load exceeds 0.4 times the balanced axial load, a spiral column is preferred. Splices and bar anchorages must be adequate to prevent bond failures. The reversal of stresses in beams and columns due to reversal of direction of earthquake force must be taken into account in the design by appropriate reinforcement. Beam-column connections should be made monolithic.
41
Detailing for Ductility The following recommendations are based on the provisions of IS: 4326 – 1993, IS : 13920 – 1933 and ACI 318 and lessons learnt from the failure of concrete structures during past earthquakes. A. Girders (1) At any section of a flexural member and for the top as well as for the bottom reinforcement: 1. The reinforcement ratio p should each be greater than 0.24 σck IS: 13920 – 1993 p> σy 1.4
ACI 318-1999
As for flanged sections bw d As = area of steel on either face 2. the reinforcement ratio p should not exceed 0.025. At least two bars should be provided continuously both at top and bottom. The positive moment resistance at the face of a joint should not be less than one-half of the negative moment resistance provided at that face of the joint. Design Tables 20.2 and 20.3 similar to Tables 5.4 and 6.2 have been generated using the above recommendations and may be used for the design of beam sections for ductility. Neither the negative nor the positive moment resistance at any section along the member length should be less than one-fourth of the maximum moment resistance provided at the face of either joint. When a beam frames into a column, both the top and bottom bars of the beam should be anchored into the column so as to develop their fully strength in bond beyond the section of the beam at the face of the column. Where beams exist on both sides of the column, both face bars of beams must be taken continuously through the column as shown in Fig. 5. To avoid congestion of steel in a column in which the beam frames on one side only, the use of hair pin type of bars spliced outside the column instead of anchoring the bars in the column is suggested. The spacing of the vertical stirrups should not exceed 0.25 d in a length equal to 2nd near each end of the beam and 0.5 d in the remaining length of the beam as shown in Fig.6.
Where, p
(2) (3)
(4) (5)
(6)
p> σ y =
B. Columns 1. If average axial stress P/A on a column under earthquake condition is less than 0.1 σ ck, the column reinforcement will be designed according to the requirement of girders discussed earlier. But, if P/A > 0.1 σ ck, special confining reinforcement is required at the column ends:
42
i. The cross-sectional area of bars forming circular hoops or spirals used for confinement of concrete is given by: Ag σ −1 ck asp = 0.09 p Dc . Ac σsp ii. In the case of rectangular closed stirrups used in rectangular sections the area of bars is given by: Ag σ −1 ck asp = 0.18 p h Ac σsp Where, h = longer dimension of the rectangular confining stirrup as shown in Fig. 7 2. The special confining steel where required must be provided above and below the beam connections, as shown in Fig. 8, in a length of the column at each end which is largest of the following: i. 1/6 of the clear height of the column, ii. Larger lateral dimension of the column, and iii. 450 mm. The pitch of lateral ties should not exceed 1/4th of the minimum member dimension nor 100 mm. 3. Shear reinforcement must be provided in columns to resist the nominal sheet resulting from the lateral and vertical loads at limit state of collapse of the frame. Shear strength of columns increases in the presence of compressive axial loads. Clause 40.2.2. Of IS: 456 requires that for members subjected to axial compression Pu the shear strength of concrete τ c’ is given by: τ c’ = δ τ c 3P u
δ =1+ A σ g ck Pu = axial load in N Ag = gross area of the concrete section in mm2 τ c = shear strength of concrete as given in I.S 456 The spacing of shear reinforcement should not exceed 0.5 d, where d is the effective depth of column measured from compression fibre to the tension steel. 4. Spiral columns should be used wherever possible especially if Pu > 0.4 Pb Where, Pb = balance axial load Figure 20.13 shows that spiral columns are much more ductile as compared with columns with lateral ties. C. Beam – Column Connections The beam-column joints are generally the weakest links in a structure. To avoid frame failure due to inadequate joints, the joint details must be carefully considered as discussed in section above. The following points need special attention: Where,
43
1. Anchorage of beam reinforcement in the joint. 2. The ties as required at the end of the column must be provided through the connection as well as, provided that if the connection is confined by beams from all the four sides, the amount of this reinforcement will be reduced to half of this value. This reinforcement known as joint hoops is shown in Fig. 6. Example: Consider an inner beam-column joint in the ground floor roof of an eight storey building in Noida, UP. The data are as follows: Grade of concrete
= M25
Clear span of beam to the left side of the joint
4.5 m
Clear span of beam to the right side of the = 4m joint Slab thickness
= 125 mm, finish or slab = 50 mm thick
Live load on floor
= 2 kN/m2
Wall thickness on beams
115 mm
The axial load in column at the joint
= 900 kN
Beam size
= 230 mm x 550 mm with 1.5% steel at top (3-25 mm and 2-16 mm) and 0.8% steel at bottom on either side of the joint
Column size
= 230 m x 650 mm with 3.46% steel (8-25 mm and 4-20 mm bars)
Check if the joint satisfies weak girder-strong column proportion. Also check the shear in beam and column. Solution a. Let us first examine the beam-column joint in bending Bending of column about weak axis From SP-16, chart for doubly reinforced sections, for a given amount of reinforcement, Mu Hogging moment capacity of beam = = 4.45 bd 2 Or, Mu = 4.45 x 230 x 500 x 500 = 255.87 kNm
44
From SP-16 chart for singly reinforced sections, for a given amount of reinforcement, Mu Sagging moment capacity of the beam = = 2.50 bd 2 Or, Mu = 2.50 x 230 x 500 x 500 = 143.75 kNm From SP-16 chart Pu 1.2 x 900 x 1000 = = 0.29 σ ck bD 25 x 650 x 230 pσ ck = 3.46 / 25 = 0.138 Mu Therefore, = 0.225 or, Mu = 193.4 kNm σ ck bD 2 Σ Mg = 255.87 + 143.75 = 399.60 kNm Σ Mc = 2 x 193.4 = 386.8 kNm Σ Mc = < 1.2 Σ Mg Hence, the beam column joint is not based on weak girder-strong column proportions. There is a need to increase width of column. (b) Let us now examine the shear capacity of beam on left side of the joint. Dead load intensity on beam = 28.5 kN/m Live load intensity on beam = 7 kN/m Factored shear due to gravity = 1.2 (28.5 + 7) x 4.5/2 = 95.85 kN Shear due to formation of plastic hinge in beam =1.4x 399/6/4.5=124.32 kN Total Vu = 220 kN Nominal shear stress τ v = 220 x 1000/230 x 500 = 1.91 Mpa Shear strength of concrete τ c= 0.72 Mpa for 1.5% tension steel Provide 10 mm – 2 legged stirrups @ 150 mm c/c OK (c) Let us now examine the shear capacity of column Storey height = 3.25 m Factored shear in column = 1.4 x 399.6/3.25 = 172 kN Nominal shear stress τ v = 172 x 1000/230 x 650 = 1.15 Mpa Shear strength of concrete τ c= 0.77 Mpa for 1.7% tension steel on one face Increase in shear strength as per IS: 456-2000, 3P u
3 x 1.2 x 900 x 1000
δ = 1 + A σ =1 + 230 x 650 x 25 =1.87 g ck Increased shear strength of concrete = 1.87 x 0.77 = 1.43 Mpa > 1.15 Mpa OK
DESIGN OF SHEAR WALLS INTRODUCTION
45
Shear walls are specially designed structural walls incorporated in buildings to resist lateral forces that are produced in the plane of the wall due to wind, earthquake and other forces. Shear walls are usually provided in tall buildings and have been found of immense use to avoid total collapse of buildings under seismic forces. It is always advisable to incorporate them in buildings built in regions likely to experience earthquake of large intensity or high winds. Shear walls for wind are designed as simple concrete walls. The design of these walls for seismic forces required special considerations, as they should be saf3e under repeated loads. Shear walls for wind or earthquakes are generally made of concrete or masonry. They are usually provided between columns, in stairwells, Toilets, utility shafts, etc. Initially shear walls were used in RCC buildings to resist wind forces. These came into general practice only as slate as 1940. With the introduction of shear walls, concrete construction can be used for tall buildings. Earlier tall buildings were made only of steel, as bracings to take lateral load could be easily provided in steel constructions. However, since recent observations as shown consistently the excellent performance of buildings with shear walls even under seismic forces, such walls is now extensively used for all earthquake resistant design. 1.CLASSIFICATION OF SHEAR WALLS: 1. Simple rectangular types and the flanged walls (called the bar bell type walls with boundary elements) 2. Coupled shear walls 3. Rigid frame shear walls 4. Framed walls with in filled frames 5. Column supported shear walls 6. Core type shear walls 2.DESIGN OF RECTANGULAR AND FLANGED SHEAR WALLS: IS 13920-1993 clause 9(7) deals with requirements and design of simple free standings shear walls. 2.1General Dimensions: The following factors determine the general dimensions of the wall. 1. The thickness of the wall (t) should not be less than 150mm 2. If it is flanged wall, the effective extension of the flange width beyond the face of web to be considered in design, is to be lee of the following (a) ½ distance to an adjacent shear wall web (b) 1/10th of the total wall height (c) Actual width 3. Where the extreme fiber compressive stresses in the wall due to all loads (the gravity loads and the lateral forces) exceed 0.2 fck boundary elements are to be provided along the vertical boundaries of the walls. Boundary elements are portions along the wall edges specially enlarged and strengthened by longitudinal and transverse steel as in columns. These elements can be discontinued when the compressive stresses are less than 0.15 fck. Boundary elements are also not
46
required if the entire wall section is provided with special confirming steel reinforcements. 2.2 Reinforcements The following rules are to be observed for detailing of steel: 1. Walls are to be provided with reinforcement in two orthogonal directions in the plane of the wall. The minimum steel ratios for each of the vertical and horizontal directions should be 0.0025. [As/Ac (gross)]=ρ ≥ 0.0025 This reinforcement is distributed uniformly in the wall. 2. If the factored shear stress (v) exceeds 0.25√ fck or if the thickness of the wall exceeds 200mm the bars should be provided as two mats in the plane of the wall one on each face. (This adds to ductility of wall by reducing the fragmentation and premature deterioration on reversal of loading). 3. The diameter of the bars should not exceed 1/10th of the thickness of the part of the wall. 4. The maximum spacing should not exceed, L/5, 3t or 450mm, where L is the length of the wall. 2.3 Reinforcements for shear The nominal shear is calculated by the formula V=Vu/td Where D = effective width (= 0.8 for rectangular sections) Vu = the factored shear The nominal shear should not exceed the maximum allowable beam shear given in IS 456-2000 Table 20. Table 62 of SP 16 can be used for determining the diameter of shear steel and its spacing. The vertical steel provided in the wall for shear should not be less than the horizontal shear. PROBLEM 1. (Design of simple shear wall with enlarged ends) Design a shear wall of length 4.16m and thickness 250mm is subjected to the following forces. Assume fck = 25 and fy =415N/mm2 and the wall is a high wall with the following loadings: Loading Axial force (KN) Moment (KN-m) Shear (KN) 1. DL+LL 1950 600 20 2. Seismic load 250 4800 700 Step 1. Determine design loads P1(Case1)=(0.8*1950)+(1.2*250)=1860KN P2(Case2)=1.2(1950+250)=2640KN Moment =1.2(4800+600)=6480KN Shear =1.2(700+20)=864KN
47
Step 2. Check whether boundary elements are required (Extreme stresses are more than 4N/mm2 boundary elements are to be provided) Assuming uniform thickness L=4160mm; t=250mm I=1.5x1012 mm4 A= 4160x250=1.04x106mm2 fc=[P/A]± [My/I] =[(2.64)106/(1.04)106]± [(6.48)109*4160/2(1.5)1012] 0.2fck=0.2*25=5N/mm2 As extreme stresses are high, boundary elements are needed. Also there is tension in one end due to bending moment. Step3. Adopt the dimensions of boundary elements. Adopt a bar bell type wall with a central 3400mm portion and two ends 380X760mm giving a total length of (3400+380)=4160mm. Step 4. Check whether two layers of steel are required. Two layers are required if (a) Shear stress is more than 0.25√ fck. (b) The thickness of section is more than 200mm. a) Depth of section= center to center boundary elements=3400+380=3780mm V=V/bd=864x103/(250x3780)=0.92N/mm2 0.25√ fck =0.25√20=1.11N/mm2 b) Thickness of 250 is more than 200mm Use two layers of steel with suitable cover. Step 5.Determine steel required Let us put min-required steel and check the safety of wall (p=0.0025) As (min)=0.0025*250*1000 per meter length=625mm2 is two layers Provide 10φ @250mm,provide the same vertical and horizontal steel. Step 6. Calculate Vs to be taken by steel V=0.92N/mm2 τ c (for 0.25% steel and fck=20)=0.36 N/mm2 Maximum shear allowed=3.1 N/mm2 Designed steel is necessary for Vs Vs=(0.92-0.36) bd=0.56*250*3780=529.2KN Step7. Calculate steel necessary to take Vs As the wall is high, horizontal steel is more effective. Therefore Vs/d =0.87fy(Asv/Sv), d=3780mm Required Asv/Sv = [(529.2*103)/(0.87*415*3780)] = 0.3888 Consider 1m height = Sv Horizontal steel area = 628mm2 = Asv Available Asv/Sv = 628/1000=0.628 The nominal steel provided will satisfy shear requirements. Step 7(a). Find flexural strength of web part of wall Vertical load on wall (case 1 load) P=1860KN 48
Assuming it as a UDL over the area the axial load for the central part beams =Pw Pw= 1860{3400*250/[(3400*250)+2(380*760)]}=1860*0.595=1107KN -------------(1) Step8. Calculate the parameters λ ,φ ,β , x/L (As per code IS 13920) λ = Pw/( fck*t*L)= 1107*103/(20*250*3400)=0.065 φ = 0.87 fy p/ fck = 0.87*415*0.0025/20=0.045, β =0.516 x/L=(λ +φ )/(0.36+2φ )=0.24< 0.5 Mu/( fck*t*L2)= φ (1+λ /φ )(0.5-0.42 x/L)= 0.041 Mu= 2370kN-m< 6480(required) Step 9. Calculate compression and tension in the boundary elements due to M1=6480M1=6480-2370=4110KN Step 10. Calculate compression and tension in the boundary elements due to M1 Distance between boundary elements=3480+380=3.86m=c Axial load=M1/c=4110/3.86=1065KN This load acts as tension at one end and compression at the other end. Step 11. Calculate compression due to the load at these ends Fraction of area at each end= (1-0.595)/2 = 0.2025 (from step 7a point 1) P2 = 0.2025*2640=535KN Factored compression at tension end (taking P1)= 0.2025*1860=377KN Compression at compression end= 1065+535=1600KN Tension at the tension end=-1065+377=-688KN Step 12. Design the boundary elements compression (a) Design one end as column with details (b) Check laterals for confinement (c) Check for anchorage and splice length Step 13. Design the reinforcement around openings, if any, of the wall Openings are provided in the main body of the wall. Assume opening size as 1200x1200 Area of reinforcement cut off by the opening =1200 (thickness)% of steel/100=1200*250*0.0025=750mm2 4no’s of 16mm bar area=804mm2 Provide 2no’s of 16mm dia one each face of the wall, on all the sides of the hole to compensate for the steel cut off by the hole.
Coupled Shear Wall: 49
A coupled shear wall consists of two solid wall elements jointed together by deep floor beams, giving openings for corridors in buildings. The vertical load (p) is shared equally by the two solid elements if equal; otherwise each wall element will have its own vertical load like P1 and P2. The overturning moment M causes a compression C in one wall and a tension in other wall, C = T = M/a a = (L + l’)/2 The reversal of overturning moment will interchange these actions. The solid wall elements can be designed as columns. The connecting beam is to be designed for a shear equal in magnitude to C and T and moment equal to T.l’/2. Design a coupled shear wall with following data:Length of the wall Moment on the wall Load on the wall Thickness of wall
= = = = =
10.00 m 2000.00 kN.m 2000.00 kN 3.00 m 0.30 m
= = =
(L + l’)/2 (10 + 3)/2 6.50 m
C/T = = =
M/a 2000/6.5 307.70 kN
l’ t a
(L - l’)/2
= =
(10 - 3)/2 3.50 m
For solid element, length Thickness of wall
= =
3.50 m 0.30 m
Max.Compression
= = =
P/2 + C 2000/2 + 307.7 1307.70 kN
Minimum eccentricity moment
= = =
0.02 P 0.02 x 1307.7 26.20 kN.m
Slenderness Moment
= =
0.031 P 0.031x 1307.7
50
Total moment
Mu
=
40.54 kN.m
= =
26.20 + 40.54 66.74 kN.m
For P = 1307.70kN, Mu = 66.74kN.m Pu/(fckbD)
= = =
(1.2x1307.7x1000)/(15x3500x300) 0.0996 0.1
Mu/(fckbD2)
= = =
(1.2x66.74x1000)/(15x3500x3002) 0.017 0.2
with d’/D
= = = =
50/300 0.167 0.2 0
P/fck
Provide minimum reinforcement. Provide 6# 32mm Ф bars at each outer end. Steel area Steel to be provided at each Inner edge
= =
7.54 x 2 x 3.0 4524.00 mm2
= =
4524.00/2 x1.25 2830.00 mm2
Provide 4# 32 mm Ф bars at each inner end giving Ast 3217.00 mm2 In tension side, Maximum load
= =
1000.00 – 310.00 610.00 kN
Therefore provide the same reinforcement for the tension side also. Provide 6# 32mm Ф bars at each outer end. Provide 4# 32mm Ф bars at each inner end giving Ast 3217.00mm2 For connecting beam, Shear Moment Vertical load w
= = = = =
310.00 kN 310.00 x 3.0 / 2 465.00 kN 7.0+15.0 22.00 kN/m
51
= = = =
22 x 3.02 /12 16.50 kN.m 22 x 3.0 /2 33.00 kN
Total design shear
= =
310.00+33.00 343.00 kN
Total design moment
= =
465.00 + 16.50 481.50 kN.m
Moment M Shear S
With b = 300mm, D = 900mm, d = 900-50 = 850mm k
= =
(1.2x482x106)/(300x8502) 2.7 N/mm2
d’/d
= = = =
50/850 0.05 0.9 x 300 x 850 /100 2295.00 mm2
Ast Provide 3# 32mm Ф bars at top. Ast provided is 2413.00mm2
For reversal of earthquake, 3# 32mm Ф bars provided at top and bottom. Check for shear: Tv Pt Tc Vu/d
= = = = =
(1.2 x 343.00 x 103)/ (300 x 850) 1.61N/mm2 (2412.00 x 100)/(300 x 850) 0.95 0.6 N/mm2
= =
(1.60-0.6) x 300 30.3kN/mm
Provide 2 legged stirrups 10mm Ф bars @ 150mm c/c. Provide 4# 10mm Ф bars. Drift: A 13 storied building has four-bay frames at a spacing of 6m c/c. calculate the drift at the top under a wind pressure of 1.5 N/mm2. With the following data: L Number of storey n
= =
52
6.00 m 13
Number of bay m Height of each storey h Wind pressure P B Column of size Beam of size Drift Δf Where
= = = =
4 3.65 m 1.50 N/mm2 6.00 m
= =
0.3 m x 0.6 m 0.3 m x 0.725 m
=
___ Wh ____ x ( n + β (1 + 2n.n-1) (24 (m+1)E I1) 3
2
m - Number of bay n - Number of storey W - Storey horizontal load on frame β = l x I1 / (h x I2) I1 – moment of inertia of column I2 – moment of inertia of beam l - span of beam h - storey height E - modulus of elasticity of material of frame W
= = =
Pxbxh 1.5 x 6000 x 3650 32850 kN
Moment of inertia of column, I1
= =
300 x 6003 / 12 5400 x 106 mm4
Moment of inertia of column, I2
= =
300 x 7253 x 1.66/ 12 8964 x 106 mm4
= = = = =
l x I1 / (h x I2) (6000 x 5400x106)/(3650x8964x106) 0.99 1.00 2 x 105 N/mm2
β
E Drift
Δf `
=
___ Wh3____ x ( n2 + β (1 + 2n.n-1) (24 (m+1)E I1)
___ = (32850x10 x 3650 ) (13 + 1(1+2 x 13 x 13-1) 24 (4+1)(2x105)x 5400x106 = 5941mm 3
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3
2
UNIT III EARTHQUAKE RESPONSE OF STRUCTURES INTRODUCTION •Earthquakes response of the structures is based on the advanced structural dynamics analysis techniques. •Motion of the structures are due to earthquakes is considered as “single degree of freedom system (SDOF) of body or mass is moving with base” type of problem. This earthquake motion cause structural damages is called strong motion earthquake •Richter scale provides a convenient means of classifying earthquake according to size. •Earthquake of magnitude 5 or grater make ground motions that are severe enough damaging the structures. (E.g.: San Francisco earthquake’1906- 8.2) •Fundamental difficulty in assessing earthquake response is due to 1) Random nature of excitation 2) Non-linear nature of the response. Application of response spectrum: Prescribing an appropriate earthquake response input is problematic, because it is very difficult to accurately predict future seismic ground motions that may occur at a given site during the useful life of a structure. Therefore seismic design of building is generally based on analysis reflecting a range of pssible earthquake ground motions. The Response spectrum method is the most in dynamic analysis and is generally considered as “state-ofthe-art” among building design engineers. The method employs superposition of a limited number of modal maximum responses as determined from a spectral curve for a prescribed dynamic excitation. Linear elastic structural behavior is a basic assumption of the response spectrum approach. The Response spectrum method is computationally more efficient than the exact time history technique and with appropriate modal combination schemes; can yield results that show excellent comparison with the time history analysis. Development of earthquake response spectrum: There are several approaches, which can be used for developing response spectra to represent earthquake ground motions for design purposes. Normally three main approaches followed. 1.The use of actual earthquake response spectra based on recorded ground motions. 2.The use of recommended procedures for the development of smoothed design spectra. 3.Performance of site-specific study resulting in unique design spectra reflecting the actual site conditions. These three approaches are discussed as follows,
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Development of response spectrum from earthquake records: The generation of a response spectrum curve can be idealized by subjecting a series damped SDOF mass spring system with continuously varying natural periods to a given ground excitation. The absolute value of the peak displacement response (relative to the ground) occurring during the excitation for each system is represented by a point on the relative-displacement spectrum curve. In fig 2.1 the generation of the response spectrum for El Centro 1940 earthquake is illustrated. Using the ground acceleration records as input, (fig 2.1(a)) a family of response spectrum curves can be generated for various levels of damping (fig 2.1(b)) where higher damping values generally resulting lower spectral response. The response spectrum curves may also be represented in terms of pseudo-velocity or pseudo acceleration where these pseudo-values are based on the relative displacements as follows. Sd = spectral relative displacement. Sv = ω . Sd = spectral pseudo-velocity Sa = ω . Sv = ω2 . Sd = spectral pseudo-accelerations Where ω = natural frequency (rad/sec). The pseudo velocity and pseudo acceleration spectra do not reflect true maximum values of velocity and accelerations but rather provide a direct means of evaluating the true relative displacement. The pseudo velocity and pseudo accelerations may be viewed as approximations to the true maxima for relative velocity and absolute accelerations. Spectra for the true maxima for relative velocity and absolute acceleration can be calculated in addition to the true displacement curve. However For the purpose of structural design, spectra based on true relative displacement are of most interest because these spectral displacements control the force levels induced in the structure. Response spectra are often represented showing Sv , Sd, and Sa ordinates on a single tripartite logarithmic plot. In fig 2.2 a tripartite plot of the El Centro 1940 response spectrum for 5% critical damping is shown. Spectra curves developed from actual earthquake records are quite jagged, being characterized by sharp peaks and troughs (fig 2.1(b)). Because the magnitude and locations of these peaks and troughs can vary significantly for different earth quake records and because of the uncertainties inherent in predicting future seismic ground motions, it is wise to consider several possible earth quake spectra in the evaluation of structural response for design purposes. Thus, if response to actual recorded earthquakes is to serve as a design basis, analysis should be performed using several selected spectra that are believed to be representative of critical ground motions that may occur at the site. Development of smoothed design response spectra: To provide an alternative to the use of several earthquake spectra for design, much work has been done to develop smoothed design spectra that represent approximate upper bound response envelopes based on expected critical levels of ground motion (Newmark (26,27), Blume (9), seed (37), trifunac (45). Some code writing bodies such as
55
the American Petroleum Institute (API), the veterans Administration (VA), the Applied Technology Council (ATC), and the Nuclear Regulatory Commission (NRC) have incorporated recommendations for the development of design response spectra in their respective regulation (2,48,5,46) for construction and design practices. (Note that ATC guidelines have not yet been adopted by actual building codes.) To illustrate this general approach for developing response spectra, refer again to Figure 2.2, where the values of maximum ground acceleration, velocity and displacement for the E1 Centro 1940 record are plotted along with the spectrum curve. Comparison of the spectrum profile with the lines of ground motion maxiama reflect the following important characteristics, 1.In the very low period range, the spectrum curve approaches the line of maximum ground acceleration, becoming virtually coincident for periods less than about 0.03 secs. 2.In the low period range between 0.10 and 0.50 seconds, the variations of the spectrum curve tends to show correlation with the line of maximum ground accelerations. 3.In the medium period range between 0.50 and 3.0 seconds, the variation of the spectrum curve tends to show correlation with the line of maximum ground velocity. 4.In the higher period range between 3.0 and 10.0 seconds, the variation of the spectrum curve tends to show correlation with the line of maximum ground displacement. 5.In the very high period range (>10 secs), the spectrum curve gradually approaches the line of maximum ground displacement.( not shown in fig . 2.2). However, reasonable smoothed design spectra based on enveloping the spectral response of several earthquakes records of similar intensity and site conditions can be constructed from a limited number of “ base line” parameters that reflect the influences of expected ground motions maxima as well as other ground motions characteristics .In recent codified recommendations other development of response spectra (5.48), these base line parameters have been termed “effective” ground motion maxima. For example, the ATC recommendations (5) incorporate the use of the seismicity parameters “effective peak accelerations” (EPA) and “effective peak velocity”(EPV) in the development of response spectrum curves. The following interpretations of EPA and EPV is given in the commentary of the ATC provisions: To best understand the meaning of EPA & EPV, they should be considered as normalizing factors for construction of smoothed elastic response spectra for ground motion of normal duration. The EPA & EPV thus obtained are related to beak acceleration and peak ground velocity but are not necessarily the same as or even proportional to peak accelerations and velocity.
56
Thus EPA & EPV for a motion may be either greater or smaller than peak acceleration and velocity, although generally the EPA will be smaller than the peak acceleration while the EPV will be larger than the peak velocity. Despite the lack of precise, the EPA &EPV are valuable tools for taking into consideration the important factors relating ground shaking to the performance of a building. Since smoothed design spectra are generally normalized to peak ground motion values, the engineer may be misled to believe that there is a direct theoretical correspondence between peak ground motions and overall spectral magnitude. Response spectra may be viewed as being composed of four parts spanning different period ranges shown as zones A,B,C,D in figures 2.3 & 2.4 .Most design spectra use the following general relationship to represent the variation of spectral acceleration with period , Sa = (1/T) p Where the value of p will vary depending upon the design spectrum used when the various zones of the curve .In general, the characteristics of the spectral acceleration curves (fig 2.3) for the various zones as follows, Zone A: Very low period range ,peak acceleration related . Spectral accelerations start from the peak ground acceleration value at T = 0,and rise to the maximum spectral acceleration values in zone B. The periods in this range are generally smaller than the periods corresponding to the maximum frequency content of the ground motion. Values of p in the neighborhood of –1.0 are often used in this zone. A p value –1.0 results in spectral acceleration varying linearly with period. Zone B : Low period range, peak acceleration related. In this zone, the maximum spectral accelerations result because the predominant periods of the ground acceleration lie in this period range. Many recommended design spectra (including Newmark’s) specify a line of constant acceleration, p=0, t0 represent this zone. Zone C: Medium period range, peak velocity related. Spectral accelerations being to decrease rapidly with the increasing period and taper off to a more gradual decrease .For this zone, p values ranging between 0.5 and 1.0 are recommended by various design spectra. Newmark’s recommend p = 1.0. Zone D : Long period range ,peak displacement related . In this zone, the periods are several times greater than the predominant periods of the ground accelerations and the resulting dynamic amplifications are relatively small. In this zone, the rate of descent of acceleration spectrum is greater than that in zone C, Newmark recommends a value of p = 2.0 for this zone.
57
In figure 2.5, the Newmark (26), Blume (9), API (9), VA (48), ATC (5) and NRC (46) recommended smoothed design spectra are plotted for 0,4g peak acceleration and 5% critical damping. In table 2.1, p values used in the various spectrum zones are shown for these spectra. Local soil characteristics can have an important influence on the relative spectral amplifications in these zones by influencing the surface ground motions that result from a given base rock excitation. For this reason, many recommended design spectra make allowance for the influence of soil type on the shape of the spectrum curve. The general tendency of overlying soil is to push the spectra response curve further out along the period scale, causing greater in the greater amplification in the longer period range as in figure 2.6. Greater effective peak ground velocity and displacement are expected for sites with softer soil conditions. For the Newmark spectrum, estimates of these peak values can be directly used to modify the spectrum for various soil conditions. For other recommended spectra, such as ATC &API, local soil conditions are accounted for by classifying the site in to one of a limited number of soil type categories and by applying different spectrum modifications for each category. DEVELOPMENT OF SITE SPECIFIC RESPONSE SPECTRA: The development of site-specific ground motions is generally responsibility of geo-technical engineering consultants working within the structural engineer’s design criteria. The structural engineer’s association of California (SEAOC) has published guidelines (42) for developing the site-specific seismic ground motions in which the following general steps are recommended: 1.Geological and seismology study. 2.Establish average recurrence rates and probabilistic description of earthquake events for each source. 3. Determine ground motions characteristics. EXPLANATION OF RESPONSE SPECTRUM: Response spectrum may be plotted for any two independent variables with respect to other variables. (E.g.. Time Vs wavelength with respect to different frequencies) •In this topics we are discussing about response spectrum for ground motion (earthquake), such as acceleration, velocity, displacement. •Response spectrum is a plot of maximum response (e.g.: acceleration, velocity, displacement) of SDOF system to a given input Vs some system parameter, generally the undamped natural frequency. Simply say that it is a function of dynamic input and period of vibration of system. •It also defined as representation of the maximum response of a idealized SDOF systems having certain period and damping during earthquake ground motion. •The maximum response is plotted against undamped natural period and for various damping values, and it can be expressed in terms of maximum relative acceleration, maximum relative velocity and displacement.
58
•The response spectrum may also be plotted for soil mass, which is below the superstructure (e.g.: multistory building, dam structures etc…). CLASSIFICATION OF RESPONSE SPECTRUM BASED ON DYNAMIC PROPERTY: 1.Acceleration response spectrum (Sa) 2.Velocity response spectrum (Sv) 3.Displacement response spectrum (Sd) BASED ON ELASTIC PROPERTY OF STRUCTURAL SYSTEM: 1.Elastic response spectrum 2.Inelastic response spectrum. ACCELERATION RESPONSE SPECTRUM •Acceleration response spectrum (Sa) is plotted against natural period of vibration (T) Vs acceleration (a) with respect to different damping ratios. •This spectrum is most commonly used for describe the seismic event. (E.g. El Centro earthquake California May 18 1940.) VELOCITY RESPONSE SPECTRUM •Velocity response spectrum (Sv) is plotted against natural period of vibration (T) Vs velocity (V) with respect to different damping ratios. •This spectrum is also used for describe the seismic event next to the acceleration response spectrum (Sa). (E.g. El Centro earthquake California May 18 1940).
DISPLACEMENT RESPONSE SPECTRUM •Displacement response spectrum (Sd) is plotted against natural period of vibration (T) Vs displacement (d) with respect to different damping ratios. • •This spectrum is also used for describe the seismic event next to the Velocity response spectrum (Sv). (E.g. El Centro earthquake California May 18 1940.) ELASTIC RESPONSE SPECTRUM
59
•In this type response spectrum the structure is considered as elastic and it has constant viscous damping is assumed. •The solution of equation of motion of a linear elastic SDOF system can be written by assuming the difference between damped and undamped period of vibration. d(t) =1/ ów a g (t ) -wz(t-t)sinw (t- t)dt Where d(t) system relative displacement w - Angular frequency. a g - Ground acceleration z - Damping ratio, t- time
INELASTIC RESPONSE SPECTRUM •In this spectrum structural system subjected to earthquake excitation is behave as nonlinear fashion. •The initial period of vibration and elastic equivalent viscous damping of the system are not sufficient to obtain maximum response, which will depend on the actual shape of the force-displacement curve of the system. •To overcome this difficulty the structure is assumed as linear elastic-perfectly plastic response being equal to the actual response of the system. But need to incorporate the some significant parameters. FORMULATION OF RESPONSE SPECTRUM: SDOF SYSTEM SUBJECTED TO BASE MOTION. •Base is considered as and has translational motion •The equation of motion of SDOF system subjected to support excitation is expressed as, m ǜ + c ů +ku = cż + kz Or m w’’ + c w‘+k w = -mz “ (- ve sign due to reversing sense of Z(t))
SDOF SYSTEM
60
•By using Duhamel’s integral, we can obtain maximum relative displacement and maximum absolute acceleration. ω (t, ωn, ξ) = (1/ωn) W(t) Where W (t) = Z (τ) exp (– ξ ωn (t- τ)) sin ωn (t- τ) d •The maximum value of relative displacement occurs at time ‘tm’. This is customarily given the symbol ‘Sd’ and is called spectral displacement. Sd (T, ξ) = ωmax = (1/ ωn) W(tm) • A plot of ‘Sd’ Vs natural period vibration (T = 2 P/ ωn) is called displacement response spectrum. •The above equation has the dimension of velocity .The maximum value of this integral is called spectral pseudo velocity ‘Sv’. The plot of ‘Sv’ vs. ‘T’ is called the pseudo velocity spectrum. Sv (T, ξ) = W(Tm) = ωn. Sd Similarly pseudo -velocity & acceleration spectrum we can formulate. u(t)=p0/k{sinωn.t[sinωn.t-(t/td) sinωn.t-(cos ωn.t/ ωn.td)+(1/ ωn.td)] - cos ωn.t[cos ωn.t+1+(t/td) cos ωn.t – (1/ωn.td)(sinωn.t)t]} For undamped system maximum absolute acceleration is given by ü(max)= (ωn**2)* ωmax 1.The maximum absolute acceleration of a lightly damped system can be approximated by spectral pseudo -acceleration “Sa” where Sa (T, ξ) = (ωn**2) . Sd = Sv * ωn 2.A plot of Sa Vs P is called pseudo- acceleration response spectrum from that maximum spring force KSd is given by (fs) max=KSd=(K*Sa)/ ωn**2=mSa i.e. spring force KSd=Sa*mass 3.It is plotted to linear scale. It gives maximum pseudo velocity as a function of the natural period of the structure for several value of damping. 4.The sharp peaks and valleys in figures are the result of local resonance and anti resonance of the ground motion. 5. For design purpose these irregularities can smoothened out and a number of different response spectrum averaged after normalizing them to a standard intensity. 6. So it possible to plot all the three response spectra simultaneously on a tripartite log-log graph as shown. SEISMOGRAPHIC INSTRUMENTS Accelerograph/ accelerograms: These instruments can provide continuous record of earthquake acceleration of the ground (or) of a building, in the region of greatest shaking. Understanding of seismically
61
induced forces or deformations in structure has developed to a considerable extent, as a consequence of earthquake ground motions / structural response recorded in the form of accelerograms by strong-motion accelerographs. The time-history record of acceleration is recorded in optical/digital form. Integration of acceleration records enables velocities and displacement to be estimated. NATURE OF ACCELEROGRAMS:Nature of accelerograms depends on a number of factors: 1. Magnitude of earthquake. 2. Distance from the source of energy released. 3. Geological characteristics of the rocks along the wave 4. Source mechanism. 5. Local soil conditions
transmission.
TYPES OF EARTHQUAKE MOTION RECORDED IN ACCELEROGRAMS 1.Single shock motions (e.g.. Port Huechem, 1957;Libya 1963;Skopje 1963;San Salvador 1986). 2.Moderately long & extremely irregular motions (e.g. El Centro 1940; Chile 1945;Loma pieta 1989;North ridge 1994). 3.Long ground motions exhibiting pronounced prevailing periods of vibration (e.g. Mexico 1964;Bucharest 1947; Mexico 1985). 4.Ground motions involving large-scale permanent deformations of ground (e.g. Anchorage 1964;Niigata 1964. CAUSES: Type 3: Effects of soft layers filtering the waves. Type 4: Result of particular soil conditions, such as presence of Type 1&2: Registered on hard soil, due to their motions. ENERGY RELEASED DURING EARTHQUAKE •Kinetic energy (Ek) •Damping energy (Ed) •Elastic energy (Es) •Hysteretic energy (Eh) During the earthquake motion, the energy balance is expressed as Ek+Ed+Es+Eh = Ei Where Ei ---- is the input energy. VIBRATION MEASURING INSTRUMENTS SYSTEM These system consist of, •A motion detector – Transducer (Accelerometer)
62
saturated sand.
•Intermediate signal modification system (Amplifier). •Display system (Oscilloscope). •Vibrometers & Accelerometers are called seismic transducers. PURPOSE: To detect the desired motion quantity and in most cases. To produce an output that is proportional to the input motion but of different form. •Most widely used transducer is accelerometer&Vibrometer. ACCELEROMETER •It is a device that senses acceleration and produce output voltage proportional to the input acceleration. •This relative motion instrument (RMI) measures, as a function of time, the relative motion between the moving mass (a) and the base point ‘b’. •It provides an electrical signal as its output, the signal being proportional to the relative displacement of ‘a’. VIBROMETER •It is the seismic instrument whose output is to be proportional to the displacement of the base •This instrument is not widely used because of its low natural frequency. MODAL COMBINATION RULES: •Peak modal responses cannot be directly to find the peak value of total response, because modal responses attain their peaks at different time instants. •So, some approximations for combining the peak modal responses are given by scientists with some restrictions, these approximation rules are called modal combination rules. •Most commonly used rules SRSS (Square-Root-of –Sum –of –Squares) CQC (Complete Quadratic Combination) ABSSUM (Absolute Sum) SRSS •This rule is given by Dr E.Rosenblueth (1951). r0 » (Srn02 )½ Where r0 ------ Peak value of ‘n’th mode contribution. •The peak response in each mode is squared •Squared modal peaks are summed. •Square root of the sum provides estimates of the peak modal response. •This combination rule provides excellent response estimates of structures with wellseparated natural frequencies. •It cannot be used unsymmetrical plan buildings have pairs (triplets) of closely spaced natural frequencies. 63
NATURE OF DYNAMIC LOADING IN STRUCTURES DUE TO EARTHQUAKES Important considerations in earth quake resistant design: Earth quake excitations are highly random and erratic Analysis is to be made for the displaced position of the structure rather than the forces acting on the structure. Normal analysis involving equivalent lateral static forces is based on the peak acceleration only, where as the preceding undulating accelerations of lower amplitudes may cause structures’ failure, as the behavior of the structure during the action of the undulating excitations become softer.
Irregular structures and structures involving more than 40 stories has to be dynamically analysed. Reversal of stresses that occur during the earthquake motions also requires a dynamic analysis to be done on the structure. Objectives of earth quake resistant design: To resist minor levels of earth quake ground motion without any damage. To resist moderate levels of earth quake ground motion without structural damage, but possibly with some non-structural damage. To resist major levels of earth quake ground motion having an intensity equal to the strongest either experienced or forecast at the site without collapse, but possibly with some structural as well as some non-structural damage. Hence the design codes specify for the design of the structure only for a reduced earthquake excitation so that the first two requirements are satisfied in a linear range, after which in the non linear range the required deformation are provided by means of providing proper strength and ductility. The excitations at the base of the soil layer is transferred to the top layers where the structure rests, which is based on the soil mass, soil damping and soil stiffness characteristics. 64
Model for simulating soil characteristics:
From the topsoil layer the excitations are transferred to the structure based on the time period of the structure. Calculation of response components: The response components include displacements, rotations, forces etc and the excitations include accelerations, velocity, Sa/g etc or any other components. These components are plotted with respect to time periods which forms the design spectrum from which the component to be considered for the structure is to be obtained from the time period of the structure. The ground excitations that are recorded with respect to time are converted as variations with respect to the time period by means of Fourier transformation, which breaks up the given excitation into harmonic frequencies and plots the peak response for each frequency. Analyzing single degree of freedom structures of different frequencies for the given excitation and plotting the peak response of each frequency with respect to the frequency of the structure can also establish the above. The design spectrum is obtained from the response spectrum by smoothening the response spectrum curve and combining spectra of two or three earthquakes that may affect the structure.
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Apart from the structural components, in actual case the non-structural components play a vital role in deciding on the fundamental period of the structure. The presence of the non-structural components reduces the time period of the structure and hence the assumption of a longer period based on the lateral force resisting systems alone will result in a non-conservative estimation of the earthquake forces. But in the range of larger amplitudes of displacements that cause non-linearities in the structure, most of the non-structural components fail and the period is increased. Hence it would be judicial to select certain components alone, like rigid stair walls, bending interaction of slab and girder etc apart from the lateral force resisting components and omit other trivial components like plumbing, piping etc in the calculation of natural period to be considered for the analysis. The other reasons for the incremental increase in the time period would be due to the softening effects in the structure due to reduction in effective section properties in case of cracked concrete, residual stress development in case of steel structures and loosening up of foundation due to non linear soil behavior. The mode shapes would not undergo considerable changes in the non-linear region and the same mode shapes are considered even in the non-linear region for the calculation of lateral forces. The natural periods and the mode shapes which are the primary properties governing the structural response are related to the mass and stiffness matrices of the structure and the designer, by varying the mass and stiffness properties and by selecting appropriate design spectrum for the region may design a optimal structure. RESPONSE OF SINGLE DEGREE OF FREEDOM LINEAR STRUCTURES: Single degree of freedom systems involves simple structures like water tanks, pergolas etc that can be easily idealized as a single mass concentrated at the top of a mass less stiffness system (column).
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The response involves determination of displacements in the structure and then the member forces and moments from the displaced configuration of the structure. In case of single storey systems, it is considered as a single DOF system by taking in to account, only the horizontal DOF and eliminating the other DOFs by condensation methods in which the rotational and the vertical components are condensed out.
Generalized Single Degree Of System (Idealization And Equilibrium formulation):
Idealisation:
Mathematical equilibrium formulation: Forming the dynamic equilibrium of the structure shown above, acted by force P(t), spring force F(s) and damping force F(d), the equation can be given as: Mǘ + Ců + Ku = P(t) Where ǘ is represents the acceleration and ů represents velocity. Equation formulation for earthquake excitation: In case of earthquake excitation, the external force acting on the structure is not considered, but the ground motions during the earthquake are considered as base motions and are converted to equivalent excitations as shown below:
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Here the total displacement (ut) of the structure can be given as the sum of relative (ur) and the base displacement (ub). i.e. ut = ur + ub -------- 1 The equilibrium equation can be given as: Mut’’ + Cur’ + kur = 0 --------2 Substituting 1 in 2 gives M (ur’’ + ub’’) + Cu’ + Ku = 0 => Mur’’ + Cur’ + kur = - Mub’’ ---------3 (u’’ and u’ represents the time based differentials of the time function) Equation 3 is similar to normal dynamic equilibrium equation based on D’Alembert’s principle in which the excitation component P(t) is replaced by the component - Mub’’. Hence the earthquake excited SDOF system can be analysed by solving the dynamic equilibrium equation obtained after the above said replacement of the excitation function. Solution Of Equation For Single DOF System: The dynamic differential equation for SDOF system subjected to earthquake (Given by equation 3) can be solved by any of the following methods based on the nature of the equation: 1) Classical method 2) Duhamel’s integral 3) Transform methods & 4) Numerical methods In case of linear systems the response of the system is separately determined for the dynamic excitations and for the forces acting before the commencement of the dynamic excitations (static forces) and the results are added, where as such a separation of the problem is not possible in case of non-linear systems. The classical method of solution comprises of determining the complementary function and the particular integral and is used in case of such simple linear differential equations that can be easily solved by this method. The solution of a freely vibrating system can be given as: A SIN (שt) + B COS (שt) = 0, which gives the complementary function. Te particular integral depends on the excitation force. The boundary conditions are used to determine the constants A and B. 68
If the function is of a sort that can be integrated easily, the Duhamel’s integral can be used in which the function is assumed to act a sequence of infinitesimally small impulses. The displacement solution using Duhamel’s integral method can be given as: U(t) = 1/(m ( ∫ )שp(τ) sin [( שt – τ)] dτ) (limits 0 to τ) Where שrepresents the natural frequency, and τ, the time instant considered. In case of transform methods either the Fourier or Laplace transform is used, in which the given differential equation in terms of variable t is converted into an algebraic function in terms of i שso that the operations on the equation can be performed easily, after which inverse transformation is performed to get the solution. The solution of the Fourier transform, F[P(t)] = ∫ e –i שt p(t) dt, can be given as, U = (ao) / (2k) + Σ (an cos (nωt) + bn sin (nωt)) / (k) (0 to n) Where, ao = (2/τ) ∫ f(t) dt (limits 0 to τ) an = (2/τ) ∫ f(t) cos (nωt) dt (limits 0 to τ) bn = (2/τ) ∫ f(t) sin (nωt) dt (limits 0 to τ) Where τ is a time instant considered. The numerical methods are involved if the excitations are too complex to be integrated or in case of non linear systems which can be performed either as numerical solution for duhamel’s integral or using finite difference or finite element approach. Displacement Solution For Nonlinear Systems: In case of code based design for earthquakes the structure is allowed to deform in the inelastic range and provisions are given for required ductility in the structure. Thus the study of the structure in inelastic range is important in case of earthquake excitation. The force deformation behavior can be as such taken as variations given by hysteresis curves or can be idealized as elasto-plastic systems. Here up to linear range the initial stiffness value has to be used after which the a trace has to made on the history of loading at each time instant and based on the load deformation curve the stiffness at each infinitesimal time instant is determined as the tangent modulus of the curve at that instant. Hence the stiffness can be given as a function of force and velocity.
Various numerical time stepping procedures can be used for the solution of the above problem. The different procedures are: 1) Those based on interpolation of excitation 2) Based on finite difference expressions and
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3) Based on assumed variation of acceleration In these methods, the time domain is divided in to a lot of infinitesimal time instants Δt, and for each variation the variation in response Δu is determined and is added to the displacement u up to the time considered for getting the response at time t + Δt. The force value is linearly interpolated between the times t and t + Δt, the stiffness values are taken as per the load deformation variation and a constant damping value as per the linear system is considered. Determination of other response components – Forces and Rotations. After determination of displacement component, the other responses can be determined by either finding the equivalent static force to bring about the given deformed shape and then analyzing the structure for the lateral forces acting, or, by calculating the forces directly from the deformation knowing the stiffness of the system. The former method is usually adopted. Example:
For the above system the deflection at the top end of the two columns is the same, and equal to U which is obtained from the normal procedures of SDOF analysis by considering the mass of the system to be lumped at the center of the beam and considering only the horizontal Degree of Freedom. Knowing the end displacement of both the columns, the story shears of the columns are determined as (k1*U) & (k2*U) respectively. After determination of story shear the story moment is calculated at the end of each column by multiplying the story shear of the column with corresponding length of the column. Thus the story moments at the column ends would be (k1*U*L1) and (k2*U*L2) respectively. Solution For Multi Degree Of Freedom System: Problem Formulation: In the same way as that of a SDOF system the equilibrium equation of a multi DOF system can be given as M u’’ + C u’ + K u = 0 And for earthquake excitation, the equation can be given as M ur’’ + C ur’ + K ur = - ι Mb’’
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Where M is the mass matrix of the structure elements of which are obtained as the mass required at each i th DOF to counteract an unit acceleration at the j th DOF, K is the stiffness matrix and C is the damping coefficient matrix obtained as the damping required at each i th DOF to counteract an unit velocity at the j th DOF. The total deformation response can be given as a sum of the rigid body deformation of the structure to the earthquake excitation and the deformation of the structure due to its flexibility. ‘ι’ represents the rigid body deformation matrix of each DOF and will be unity if all the DOFS of the structure undergoes the same rigid body deformation.
The general solution can be given as [ K – Mω]Φ = 0 where Φ represents the modal matrix of the structure and from the above equation the mode shapes and natural frequencies are determined. Orthogonality of the modes and its implications: The orthogonality conditions of the modes can be given as, ΦnT k Φr = 0 and ΦnT m Φr = 0. This implies that, if a modal mass or a modal stiffness matrix M = ΦT m Φ or K = ΦT k Φ respectively are formed, they would be diagonal matrices. Further it can be implied that [(fI)nT ur = 0] ((fI)n = inertia force in nth DOF, ur = rth mode displacement) and [(fs)nT ur = 0] where fs represents the static force, thus proving that work done by nth mode forces in going through rth mode displacements (where r not = n) is zero. Thus it implies that the forces due to displacements in any mode will not affect the displacements in any other mode. Solution Of Differential Equation: The solution can be obtained either by classical methods or by modal methods, the former being used very rarely. In case of modal methods, due to the modal orthogonality, the solution is determined separately for each mode and then the solutions obtained for different modes are combined together based on the modal contribution factors using one of different combination rules such as SRSS, CQC or Absolute sum rules.
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Modal analysis for MDOF systems: The classical solution for the linear differential equation Mu’’ + Ku = p(t) (1) for MDOF system will not be efficient for systems with more DOFS, nor is it feasible for systems excited by other types of forces. Consequently, it is advantageous to transform these equations to modal coordinates. The system displacement can be expanded in terms of modal contributions and the dynamic response of a system can be expressed as U(t) = Σ Φr qr (t) (r = 1 to n) = Φ.q(t) (2) Substituting 2 in 1 and pre multiplying each term by ΦT and applying orthogonal relation, thereby eliminating all terms of the summation except when r = n, the relation reduces to Mnq’’(t) + K qn(t) = pn(t) Where M, K and pn are the modal matrices formed by pre and post multiplication by the modal matrix. From the above equation ‘q’ is determined knowing the mass, stiffness matrices, time periods and the modal matrix from which the solution is determined as explained in the model problem. Model problem for Modal analysis of MDOF system: Prob: A three-story frame shown in the figure is subjected to an excitation F cosωt at the top story level. Determine the response at the top level on the consideration of 1. First mode only 2. First two modes 3. All the three modes
Given Data: Ω = 0, 0.5 ω1 & 1.3 ω2 k1 = k2 = 160 kN / mm, k3 = 240 kN / mm m = 20000 kg Solution: [k] = 8 X 107
(Taking 80 outside)
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[m] = 2 X 104
(from the figure)
From the given mass and stiffness matrices the natural periods and frequencies can be determined as: ω2 = (1924.733, 14437.2, 27889)T, => ω = (43.87, 120.15, 167)T
Φ=
Modal mass matrix Mr = ΦT m Φ =
Modal force matrix Fr = ΦT f(t) = F cosωt (11
1)T
Displacement at the top story level = u(t) = 1.0 * F cosωt / ((20000 * 1.6896) (1924.733 - Ω2)) + 1.0 * F cosωt / ((20000 * 2.9667) (14437.2 - Ω2)) + 1.0 * F cosωt / ((20000 *13.2) (27889 - Ω2)).
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Consideration of 1st term alone implies 1st mode shape alone, and as per the number of mode shapes to be used corresponding number of terms are utilized and solution is attained for different Ω values. From the results it can be implied that the initial fewer modes will have more effect than the higher modes on the result and hence, it would be sufficient to consider only few initial modes in case of multi story buildings. The forces and moments, from the displacement result, can be obtained either by equivalent static method or by determining the storey shears of each story from the corresponding inter story drifts in case of shear frames, by multiplying them with the corresponding story stiffness values and for moment frames, from the condensation equations or by reverse engineering.
BASE SHEAR CALCULATION USING RESPONSE SPECTRUM METHOD BASIC DEFINITIONS: 1. Importance factor(I): It is a factor used to obtain the design seismic force depending on the functional uses of the structures, characterized by hazards consequences of its failure, its postearthquake functional needs historic value, or economic importance. 2. 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 these standards are reasonable estimate of effective peak ground acceleration given in Annex E of IS-1893 (part1)-2002 3. Structural response factor (Sa/g): It is a factor denoting the acceleration response spectrum of the structures subjected to earthquake ground vibrations, and depends on natural period of vibration and damping of the structures. 4. Response reduction factor(R): It is the factor by which the actual base shear force, that would be generated if the structures were to remain elastic during its response to the Design Basis Earthquake (DBE) shaking, shall be reduced to obtain design lateral forces. SEISMIC WEIGHT( W ): 1. Seismic weight of floors: The Seismic weight of each floor is its full DL + Appropriate amount of imposed loads as specified below. 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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Imposed uniformity distributed floor loads( kN/m2)
Percentage of imposed load
Up to & including 3 Above 3
25 50
The seismic weight of the whole building is the sum of the seismic weights of the all the floors. FUNDAMENTAL NATURAL PERIOD (Ta): The approximate fundamental natural period of vibration Ta in sec. Type of building Moment resisting frame without brick in fill panels
Ta
1- for RC Frame building
0.075 h 0.75
2- for Steel Frame building
0.085 h 0.75
All other buildings moment resisting frame with brick infill Panels
0.09h / d0.5
Where h = Height of the building in m. This excludes the basement storeys, where basement walls are connected with the ground floor deck or fitted between building columns. But, it includes the basement storeys, when they are not so connected. d=Base dimension of the building at the plinth level in m. along the considered direction of lateral forces DESIGN ACCELERATION SPECTRUM(Ah): It shall be determined by the following expression Ah= (Z*I*Sa) / 2*R*g Where Z= Zone factor (given on table.2 of IS 1893-part1-2002) I=Importance factor (given in table 6 of IS 1893-part1-2002) R= Response reduction factor (given in table 7 of IS 1893-part1-2002) however the ratio (I/R) shall not be greater than 1. Sa/g = average response acceleration coefficient from fig( given for 5% damping) For other values of damping Sa/g value shall be multiplied with the factors given in table. Damping %
0
2
5
7
10
15
20
25
30
Factors
3.2
1.4
1
0.9
0.8
0.7
0.6
0.55
0.5
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DESIGN SEISMIC BASE SHEAR: The total design lateral force or design seismic base shear( VB )along any principal directions shall be determined by the following expression. VB =Ah*W Where, Ah =Design horizontal acceleration spectrum W = Seismic weight of the buildings Example: A Four story RC office building shown in figure is located in shillong. The foundation soil is medium stiff and the entire building is supported on raft foundation. The lumped weight due to dead load is 12 kN / m 2 on floors and 10 kN/m2 on roof. The floors carry a live load of 4 kN/m2 and the roof is designed for 1.5 kN/m2. Determine the design seismic on the structure. PLAN
6m
4.5m 4.5m 3.2m 3.2m 3.2m 4.2m
4@5m Solution:
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ELEVATION
VB = Ah*W Ah = (Z/2)*(I/R)*(Sa/g) Shillong is in the zone V, Hence Zone factor = 0.36 For office building Importance factor is 1 Reduction factor in X direction is 3 Reduction factor in X direction is 3 I/R=1/3<1 Calculation of time period Ta: The frame is Moment Resisting frame with brick infill Ta=. 0.09h/d0.5 H=13.8 D=20 in X direction D=15 in Y direction Ta in X direction Ta = 0.09*13.8/200.5 = 0.28 sec Ta in Y Direction Ta= 0.09*13.8/150.5 = 0.32sec For Ta =. 28sec and Ta=0.32sec Sa/g=2.5(From graph in IS 1893-part1-2002) Calculation of seismic weight: Floor area = 15 * 20 = 300 m2 Since the Imposed load is greater than 3 kN/m2, Percentage of Imposed load is 50 Lumped wt. @ Floor levels = W1=W2=W3 = 300.( 12+0.5*4 )= 4200 kN. Roof level W4 = 300* 10 = 3000 kN Total seismic weight of the structure W = (3*4200)+3000 = 15600 kN. Calculation of horizontal acceleration spectrum (Ah): In this problem the values of Ah will be same in X & Y directions. Ah= (0.36/2)*(1/3)*2.5 = 0.15 Therefore, VB= Ah * W = 0.15 * 15600 = 2340 KN.
Distribution of total base shear at floor levels:
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Storey level
Wi kN
hi m.
Wi * hi2 x 103
4 3 2 1
3000 4200 4200 4200
13.8 10.6 7.4 4.2
571.3 471.9 230 74.1
(Wi * hi2) Lateral force @ ----------------floor level, kN Σ Wi * hi2 0.424 992 0.350 819 0.171 400 0.055 129 Total = 2340
RESISTANCE OF STRUCTURES AND STRUCTURAL ELEMENTS TO DYNAMIC LOADS The term dynamic refers to loads, which suddenly change in time, with variations in magnitude, direction, and point of application taking place either jointly or separately. Dynamic loads imparts accelerations to the bodies on which they are imposed, thereby giving rise to inertia forces and causing the system to vibrate TYPES OF DYNAMIC LOADS CYCLIC LOADS When speaking of cyclic loads, we generally mean vibration loads whose variations in time follow a harmonic law. Such loads may arise in say, unbalanced mass rotating machinery. IMPACT LOADS The term impact refers to loads that are applied suddenly and act for a short time. Impact load may be either single or multiple. MOVING LOADS By moving loads we customarily mean live loads caused by traffic, moving cranes, etc. In reality, the loads discussed above may form various combinations often accompanied by other types of dynamic load, such as wind loads, sea-wave loads, and the like. In terms of confidence in their values, dynamic loads may be classified into deterministic and stochastic or random. A deterministic dynamic load is always a prescribed function of time. In contrast, the variations of a stochastic or random force in time may be affected by quite a number of random factors, so its determination always implies a certain probabilistic element.
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Seismic loads are of kinematic origin. They owe their existence to vibrations caused in structures by the movement of the earth’s surface during an earthquake. Seismic forces or loads are random in character, though they are usually regarded as deterministic in practical calculations to simplify the design model. VIBRATION In the study of resistance of structural elements to dynamic loads the other to terms to be known are Free vibration. Forced vibration. If we apply an external force to upset the stable equilibrium of a mechanical system and then remove that force, the system will vibrate about its original position. The vibration experienced by the system upon removal of the disturbing force is called free vibration. They depend on the systems properties and the initial conditions at the instant when the force is removed. Since the initial conditions may vary from case to case, the free vibrations of the same system may follow different patterns, with the dynamic deflection line changing its configuration in time. The vibration pattern, which is determined by the relative dynamic deflection at different points on the system, can be prevented from varying in time by properly choosing the initial conditions. In this situation, we speak of the natural mode of vibrations. The name natural implies that the modes of these vibrations and the respective frequencies depend solely on the parameters of the system itself, namely on the magnitude and distribution of its masses and stiffness and the type of supports. A system with n degrees of freedom has n natural frequencies and n modes of vibrations. Under real conditions, the free vibrations of a system are damped more are less quickly, because a good deal of energy is spent to overcome various internal and external resistances. Each mode of natural vibrations has a damping velocity of its own. Accordingly, as free vibrations are damped, the compound motions combining several natural modes gradually reduce to a single mode having the least pronounced damping. The free vibrations of an SDOF system always occur at the natural frequency of that system. If a vibrating system is subjected to exciting forces, as is the case with a cantilever pole supporting an unbalanced rotating mechanism, what we have are forced vibrations. These depend on both the systems parameters and the characteristics of the disturbing force. GENERAL Seismic loads make up a special group of dynamic loads whose exact magnitudes and character cannot be evaluated in advance. We have also found out that the instrumental records, which represent the time-variation patterns of individual earthquakes, never repeat themselves even though the seismic events may occur at the same place, so their classification may be given in general outline only. The acceleration caused due to earthquake is measured using accelogram. The common features of it are given below.
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All accelograms reflect non-periodic vibrations of varying amplitude and period. Here the term period refers to twice the time interval between two adjacent accelerations of zero amplitude. The accelerations within the initial portion of the record have relatively low amplitudes. The duration of the initial portion depends on the epicentral distance, ranging from 1s to 4s when the epicentral distance is small. The accelerations within the middle portion characterizing the effect of transverse waves have the largest amplitudes, the respective periods being slightly longer than are equal to those within the initial portion. The accelerations within the end portion have long periods and gradually decreasing amplitudes, which, however, do not follow any steady pattern as they die down. There is no well-defined boundary between the middle and the end portions. The total duration of vibration varies from event to event, increasing with increasing intensity and epicentral distance. Approximately, vibrations continue for 10 to 40s, often giving more than hundred peaks per record. The vertical acceleration is usually 60% to 70% of the horizontal component. Unfortunately, no other data for classification have yet been obtained. What complicates the situation further is the absence of a single theory of strength of materials under static and, which is of particular importance in earthquake-resistant design, dynamic loads. As long as we do not for sure what actually causes structural material to fail, we cannot decide which techniques would be comprehensively reliable in experimental investigations. By the same token, the amount of experimental work to be done appreciably increases. In fact, instead of solving a general strength problem once, the investigator has to tackle its numerous particular cases, which happen to present themselves in the course of analysis and design. As a result, only after a sufficiently large number of alternatives have been investigated is he able to establish empirical relationships of more or less common character. Also, in solving experimental problems, the investigator has to make too much effort to represent the actual loading system, which can never be achieved in full measure, thereby further distorting the picture. RESISTANCE OFFERED BY VARIOUS STRUCTURAL ELEMENTS METALS Extensive work has been carried out on steel and aluminum-alloy specimens under cyclic loading to determine the dynamic strength of these metals. Work has been done to find how the fatigue strength of a material is affected by what are called as stress raisers (sudden changes in cross-section in a structural member such as notches, holes, or screw threads). It has been proved by way of experiments that stress raisers reduce the endurance limit (ultimate dynamic strength of material after number of cycles) of a material, the effect being most pronounced at holes and at the points where members 80
change in section at a sharp angle. As regards dynamic strength, stress concentration is especially undesirable in members made of brittle materials. Tests on metals suggest that the dynamic behaviour of members markedly depends on the type of joint and weld. The best results have been obtained with lap joints formed by front fillet welds at a leg ratio of 1:2 for which the endurance limit is same as for a solid member. It has also been observed that the endurance limit rises when both front and side fillet welds are used to form a lap joint. Based on the tests on welded joints some suggestions are given for method of connection to resist dynamic loads. They are as follows: Horizontal bars should be joined by semiautomatic submerged arc welding in a pool of molten metal contained in a reusable copper mould or, where no such mould is available, copper backing plates. As an alternative, they may be joined by manual multielectrode welding in a pool of molten metal contained in a reusable copper mould. Vertical bars should be joined by semiautomatic submerged arc welding in a pool of molten metal contained within a copper or a graphite mould, or, where no such mould is available, by manual multiple-blead arc welding against a steel-backing strip. The skill of welders, which generally has little effect on the load bearing capacity of the structural members under static loading, becomes a matter of primary importance where the dynamic strength is a factor. The thing is that poor workmanship may entail additional stress raisers because of lack of penetration, non-uniform throat thickness, and other defects inevitable where unskilled welders are allowed to do the job. In another test a cantilever beam was subjected to cyclic loading. In the course of loading, with the displacements maintained at a sufficiently high level, the steel was found to grow softer, as it were. In fact, as the number of cycles increased, the same displacements were produced by ever decreasing imposed loads. The Hysteresis loop obtained seems that it gets wider as the maximum stress developed during the cyclic loading increases. Based on various test over steel, an empirical formula for dynamic strength was formulated α = 1.045 – 0.0218 log n Where, α = dynamic strength/ static strength. n= number of cycles. CONCRETE
81
Many experiments were carried out in the TsNIISK institute to find the dynamic strength of heavy concrete in compression. Experiments show that long-time compression, in which structures are believed to work before earthquakes, make mortar and concrete stiffer and limit their ductility. It is, therefore, assumed that long-time compression prior to seismic loading may adversely affect the dynamic strength of materials. Earthquakes make mortar and concrete stiffer and limit their ductility. It is, therefore, assumed that long-time compression prior to seismic loading may adversely affect the dynamic strength of materials. Based on experimental work by Yu. Kotov an empirical formula was given for the dynamic strength of heavy cement concrete of compressive strength 20mPa and 30 mPa. It is given by α = 1.08 – 0.09 log n Expression for dynamic modulus of elasticity is also given by the research conducted in the same institute. It is given by E (dynamic) = E (static) * (1.445- 0.356 T) Where, T is the time period. As can be seen from the above table, the dynamic moduli are larger than the static moduli, although the difference is insignificant. During the tensile test of concrete it was found that the ultimate tensile strength of concrete depends on the duration of loading. REINFORCED CONCRETE In the earth quake resistant design of reinforced concrete structures, it is extremely important to ensure the composite behaviour of the concrete and the reinforcing steel under alternating loads. A concrete beam of size 120mm * 380mm with the following arrangement was tested under cyclic loading.
.8m
1.5m
.8m
The experiment showed that The manner of cracking and the shearing force V that caused the cracking were practically independent of the amount of lateral reinforcement and the number of load cycles applied.
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For beams with no stirrups, the shearing force at which failure occurred was practically the same as the shearing force at the onset of cracking. For laterally reinforced beams, shearing force was much greater, being 1.5 to 2 times or 2 to 3 times as large as that for beams with no stirrups. The repeated manner of loading had little effect on the shearing force. In an investigation conducted jointly by the TsNIISK and the NIIZhB research institutes, the following equations were derived which would hold good for 100
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Wood is one of the most attractive materials as regards its earthquake resistance. As compared with concrete and masonry, it offers a far greater resistance to tension and spalling, while having a much smaller weight. Also, it is a good deal lighter than, although not as strong as, steel. Nevertheless, wood has been finding few applications in earthquake-proof load-bearing structures, because it cannot serve for a long time and has to be protected against fire. Based on experiments conducted on wood the following inference were found: The dynamic ultimate strength of the test pieces subjected to single dynamic loading is, on the average, by 25% higher than the static ultimate strength. The maximum sag under dynamic loads approaching the breaking value, on the average, by 13% to 20% smaller than under static loads, and the dynamic modulus of elasticity is by 10% greater than its static counterpart. Under repeated dynamic loading, the ultimate strength of wood decreases with increasing number of cycles sustained.
DUCTILITY & ENERGY ABSORPTION Conceptual Design Design objectives Nothing within the power of structural engineer can make a badly conceived building into a good earthquake resistant structure. Decisions made at the conceptual stage are extremely important. Anatomy of building The vertical division of the building primarily poses problems, making it difficult to avoid irregularities in mass or stiffness. However, the service cores and exterior cladding provide an opportunity to incorporate shear walls and braced panels. One of the main objectives in early planning is to establish the optimum location for service core and stiff structural elements that will be continuous to the foundation It is not unusual to find that structural and architectural requirements are in conflict at the concept planning stage but it is essential that a satisfactory compromise is reached at this time.
Overall form
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The desirable aspects of building form are simplicity, regularity and symmetry in both plan and elevation. These properties all contribute to a more even and more predictable distribution of earthquake forces in the structural system. Any irregularity in the distribution of stiffness or mass is likely to increase d dynamic response. Torsional forces from ground motion are not commonly of great concern unless the building has an inherently low torsional strength. However, the torsion also arises from eccentricity in the building layout. The effective force exerted by lateral ground movement acts at the center of gravity of each floor creating a torsional moment about the center of structural resistance and this will have to be dealt with in addition to torsional component of ground motion. Buildings, which are tall in relation to their base width, will generate high forces at the base due to the overturning moment. Buildings with a height to width ratios of about 4 are common, whereas those with a height to width ratio of 6 are rare. It is probably within range 4-6 that the problems arising from overturning forces become critical. The high problems arising from overturning forces become critical. The high forces may lead to foundation uplift or to unduly high tensile or compressive forces I columns. The effect of out of step vibration also occurs in any building founded on subsoil where there is a marked discontinuity. As an extreme example, a structure founded partly on rock and partly on alluvium would be severely stressed at the interface between the two, each material tending to vibrate differently. The solution to many of the problems arising form buildings of irregular form is to divide them into regular shapes by means of joints. Such joints are required to be sufficiently wide to avoid damage by impact during earthquakes. Buildings on sloping ground tend to pose torsional problems as shown in fig. 1. The solution to this is to provide additional stiffening elements at the low end of the site to bring center of resistance as close to center of mass.
Sloping site (M Center of mass; R, Center of resistance) Framing systems
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Consideration of the overall concept and of the detailed framing system are not independent, and at the planning stage some consideration will need to be given to the framing layout Bi-directional egg crate system is suitable for tall buildings but unsuited to office buildings, which need large unobstructed areas. The structural core and frame can be used for buildings up to about 40 storeys and above this height the single framed tube should be used with the tube in tube system being used for highest buildings. The shear walls are much stiffer than frame elements. Within the basic category of frame shear wall systems, many hybrid systems can be produced to suit the particular needs of a project. In planning the framed structure the relationship between members at beam column junctions become critical. Fig shows possible failure modes under lateral loads and it is clear from this that yielding in the major earthquake must occur in the beams and not in the columns
Local failure by column yielding
Local failure by beam yielding
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Considering single beam column connection such as that in Fig. It follows that Mb1+Mb2=Mc1+Mc2 The problem posed by the above equation increases as beam spans increase leading to a need for greater continuity reinforcement at the support and consequently a greater ultimate moment. Another case posing difficulty is the spandrel beam, which is oversized for architectural reason and may have an unnecessarily high yield moment. So in the planning stage itself due consideration has to be given to all these aspects. DESIGN PHILOSOPHY The following philosophy is widely accepted in national and state building codes. Structures should be able to a) Resist minor earthquake without damage b) Resist moderate earthquakes without structural damage c) Resist major earthquakes of severity equal to the strongest that could be experienced in the area without collapse but with some structural and nonstructural damage. Elastic design Ductile design Xy = displacement at yield Xu = Ultimate displacement Xu
Xy
From the above philosophy we can understand that the earthquake design does permits substantial damage whereas it is not acceptable for other environmental loadings. The fundamental reason for this lies in the costs of seismic design provisions, which would be excessive if the maximum design earthquake were to be resisted without damage. Hence the acceptance of survival as the aim in a major earthquake means that design objective becomes that of preserving the lives of the building occupants. Calculation of lateral forces 87
a) b) c) d) e) f)
The factors that are taken into account for assessing lateral loads are as follows Zoning factor Importance factor Subsoil factor Structural type factor Natural period of vibration The applicable building mass
Zoning factor: Seismic zoning assesses the maximum severity of shaking that is expected in a region. For E.g. UBC uses Z values of 1,0.75,0.375,0.188. Normally zoning will be laid down by the code. In a nutshell zoning status will be based on the assessment of seismic hazard. Importance factor: It is customary to recognize that certain categories of building used should be designed for greater levels of safety and this is achieved by specifying higher design lateral forces. Such categories are a) Buildings that are essential after an earthquake –hospitals, fireplaces, power stations etc b) Places of assembly-schools, theatres c) Structures whose collapse would endanger the population-nuclear plant, dangerous chemical storage vessels, large dams etc Typically the value of I varies from 1.0 to1.5 but values 2.0 and 4.0 are used in U.S.S.R. Structures in category c) are designed on a different design basis, concentrating on reducing the risk of serious accident to an acceptable level. Subsoil Factor: The effect of subsoil may be both to magnify ground motion and to lengthen he characteristic period of motion. The soil factor takes into account of both the magnification and the interaction between building response and soil response. If the natural period of vibration of the building and soil are close, resonance will occur. The soil factor is typically in the range of 1.5-2 for soft soil compared with the value of 1 for rock. An interesting development is that the Structural Engineers Association of California (1985) omits any resonance between buildings and soil from its recommended S values and proposes three values. a) S=1, for rock like material having a shear wave velocity greater than 2500 ft/sec or a stiff/dense soil condition where the soil depth is less than 200 ft b) S=1.2, for dense/soil where soil depth exceeds 200 ft d) S=1.5, for soft to firm clays or loose sands 30 ft or more in depth. e) Structural Type Factor (K): The inherent ductile nature, redundancy and damping of a building structure are of great importance to its good performance in an earthquake. Factors contributing to this are material and member ductility, a high degree of redundancy with respect to all failure modes, regular form, low eccentricity, good construction quality control and high damping.
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Customarily K factors for buildings as a whole vary so that the highest value is twice the lowest, but parts of buildings such as parapets, towers, tanks, chimneys and other appendages may be assigned much higher values. Weight W: The weight is normally the total dead load plus an estimate of the possible live load that could be reasonably be expected. Period T: Because the design loading depends on the building period and the period cannot be calculated until a design has been prepared, most codes provide formulae from which T may be calculated. The International Conference of Building Officials (1985) gives the building period T in seconds for moment frames as T=0.1N And for stiff buildings (shear wall, braced frame) as T=0.5h/√D (feet units) or T=0.9h/√D (metric units) Distribution Of Lateral Forces Qi=VB Wihi2 ∑W h 2 j j Qi = Design lateral force at floor i Wi = Seismic Weight of floor i hi = height of floor i measured from base VB= AhWi Ah =Design horizontal spectrum=Z I Sa 2Rg Applied technology council (1982) introduced a factor “K” K=1, when T<0.5 s K=2, when T>2.5 s New mark & Hall (1982) introduced a method for checking whether the lateral force distribution is in agreement with the structure as designed. The procedure is as follows. a) Calculate lateral forces as per the codal recommendation b) Select member sizes for the structure c) Compute lateral displacements x, for the structure under the action of lateral forces d) Calculate new lateral forces from equation replacing the values of hi with the computed values of x e) Compare the recomputed storey shears with the values derived from step a). If any of these differ by more than 30% a dynamics analysis has to be undertaken. Designing for Ductility
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The use of reinforced concrete as a ductile material began in the early 1960s with the publication of Blume, New mark & Corning (1961) which established that properly detailed reinforced concrete beams and columns would respond to dynamic forces in a ductile manner and would sustain a number of cycles of stress reversal. The same conclusion was drawn for shear walls, principally the work of Prof R.Park and Paulay at the university of Canterbury in New Zealand during the 1970s Design codes for reinforced concrete in seismic zones are well established and when properly applied provide a sound basis for design and detailing. Principles Ductility is achieved in structural members firstly by designing elements within known limits where they can deform in a ductile manner and by avoiding the possibility of brittle failure. Avoiding the possibility of brittle failure means that at ultimate load conditions there is still an adequate safety of margin between the actual stress ad brittle failure stress. For example a tension bolt in a steel beam connection should be at a safe stress level when the beam has reached the ultimate moment. Designing whole structural systems for ductility requires a) Any mode of failure should involve the maximum possible redundancy. b) Brittle type failure modes such as overturning should be adequately safeguarded so that ductile failure will occur first. Table.1 Types of brittle failure Structure Overturning Foundation Rotational shear failure Structural steel Bolt shear or tension failure Member buckling Member shear failure Reinforced concrete Bond or anchorage failure Member tension failure Masonry Member shear failure Out of plane bending failure Toppling Thus ductility can be defined as the ratio of displacement at maximum load to displacement at yield. Two values of ductility are of prime concern. Firstly the ductile capacity is the value at ultimate member load, and secondly the ductility requirement is the value at the ultimate design load. For practical values of section size and reinforcement, section ductile capacity is increased for a) An increase in compression steel content. b) An increase in concrete compressive strength. c) An increase in ultimate concrete strain. Similarly section ductile capacity is decreased for
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a) An increase in tension steel content. b) An increase in steel yield strength. c) An increase in axial load. The effect of confining concrete with stirrups or spiral reinforcement is to increase the ultimate concrete strain, thereby increasing the ductile capacity. There is a further advantage in practice as shear resistance is increased and additional lateral support is given to the main reinforcement. Practical values of stirrups or spiral reinforcement, which will provide effective containment are substantially larger than those customarily used for reinforced concrete design in non-seismic conditions. Fig illustrates the effect of axial load and confinement on rotational ductile capacity. Effect Of Axial Load And Confinement On Rotational Capacity Confined Section Unconfined section
Ductile detailing for typical R.C members: Flexural members 1. The factored axial stress on the member under earthquake loading shall not exceed 0.1fck. 2. The member shall preferably have a width to depth ratio of more than 0.3. 3. The width of the member shall not be less than 200 mm. 4. The depth D shall preferably not more than ¼ of the clear span. Longitudinal reinforcement: 1. The top as well as bottom reinforcement shall consist of at least two bars through out the member length. 2. The tension steel ratio on any face at any section shall not be less than ρ min=0.24√(fck/fy); 3. The max steel ratio on any face at any section shall not exceed ρ max=0.025. 4. In external joint anchorage length should be provided (fig)
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Anchorage Of Beam Bars In An External Joint Splicing: The longitudinal bars shall be spliced, only if hoops are provided over the entire splice length, at spacing not exceeding 150-mm. The lap length shall not be less than the bar development length in tension.
Lap splices shall not be provided within a distance of 2d from joint face and within quarter length of the member where flexural yielding is likely under the effect of earthquake forces. Use of welded splice and mechanical connections may also be made as per IS 456 2000. However, not more than half the reinforcement shall be spliced at a section where flexural yielding may take place. Web reinforcement Web reinforcement shall consist of vertical hoops. A vertical hoop is a closed stirrup having a 135° hoop with a 10-diameter extension (but not < 75 mm) at each end that is embedded in the confined core. The min diameter of the bar forming a hoop shall be 6 mm. However, in beams with a clear span exceeding 5 m, the minimum bar diameter shall be 8-mm.
The shear force to be resisted by the vertical hoops shall be the maximum of
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a) Calculated factored shear force as per analysis b) Shear force due to formation of plastic hinged at both the ends of the beam plus the factored gravity load on the span. The contribution of bent up bars and inclined hoops to shear resistance of the section shall not be considered. The spacing of the bars shall not exceed d/4 or 8 times the diameter of smallest longitudinal bar. However it need not be less than 100 –mm. The first hoop shall be at a distance not exceeding 50 –mm from the joint face. Vertical hoops at the same spacing as above shall be provided over a length equal to 2d on either side of a section where flexural yielding is likely under the effect of an earthquake. Columns Dimension The minimum dimension of the member shall not be less than 2. However in frames, which have beams with center-to-center span exceeding 5 m or columns of unsupported length exceeding 4, the shortest dimension of the column shall not be less than 300 mm & limiting ratio of column face dimension 0.4 Longitudinal Reinforcement Lap splices shall be provided only in the central half of the member length. It should be proportioned as a tension splice. Hoops shall be provided over the entire splice length at spacing not exceeding 150 mm center to center. Not more than 50% of the bars shall be spliced at one section.
Transverse reinforcement in columns
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Transverse Reinforcement Spiral or circular hoops or rectangular hoops 1. Spacing of parallel legs shall not exceed 300mm 2. Else provide cross ties (fig) 3. If more transverse reinforcement is needed to take care of shear, Special confining reinforcement is necessary Ash = 0.09 SDk fck Ag - 1.0 fyAk Ak Ash = Area of bar cross section S = pitch of spiral or spacing of hoops Dk=diameter of core Ag=gross area Ak=area of concrete bar Beam column joints Damage studies have shown that considerable distress may be suffered in this area, the principal failure mechanism being Shear within joint Anchorage failure of beam bars anchored in the joint Bond failure Effects of loading It should be emphasized that these effects exists under non-seismic loading but are of much insignificance under seismic conditions and the effects are much aggravated by cyclic loading. Design practice is based on the fundamental concept that failure should not occur within the joint, so that it should be strong enough to withstand the yielding of connecting beams (usually) or columns. Anchoring Unless special measures are taken to remove the plastic hinge region away from the face of column, the onset of yielding is likely in the beam will penetrate the column area. For this reason the anchorage length of the beam bars anchored within the column area on external joints is reduced by the lesser of half the column depth or 10 times the bar diameter as illustrated in fig. One solution to this difficult problem of anchoring beam bars is the use of beam stubs as shown.
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Shear walls For Years shear walls were regarded as brittle elements. It was assumed that they would behave elastically only for moderate earthquakes. In order to resist major earthquakes, they were combined with frame that was intended to survive after major damage has been inflicted on frames.
a) Bending
b) Rocking
c) Diagonal tension
d) Sliding
General Requirements for shear walls 1. Thickness not less than 150 mm 2. Min reinforcement ratio 0.25% 3. If factored shear stress exceeds 0.25√fck or thickness exceeds 200 mm reinforcement in two curtains. Spacing …l/5 or 3t or 450 mm 4. The diameter of the bars used shall not exceed 1/10th of the thickness of that part. The wall must be designed to maintain the elastic integrity at all levels other than in the intended ductile zone. Slabs The designs of slabs in seismic resistant structure are as same as for non-seismic conditions except in the following particulars Slabs function as diaphragms in transmitting forces laterally, especially between vertical elements of varying stiffness. Horizontal shears are thus induced in the slab. For full depth R.C slabs, the shear will be generally being insignificant. Energy Absorption: It is important for buildings in a seismic zone to be resilient, i.e., absorb the shock from the ground and dissipate this energy uniformly through out the structure In MRFs, the dissipation of the input seismic energy takes place in the form of flexural yielding, and resulting in the formation of plastic hinges. Due to the cyclic nature of flexural yielding both negative and positive moment hinges may be formed. The energy dissipated by the MRFs is reflected in the lateral load Vs Lateral displacement.
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The area enclosed by the loops is a measure of the energy dissipated through the plasticity. Since concrete is brittle, the plasticity is due to the reinforcing steel .
Some of the common sense lessons 1. All frame elements must be detailed so that they can respond to strong earthquakes in a ductile manner 2. Non-ductile modes such as shear and bond failures must be avoided. This implies that anchorage and splicing of bars should not be done in areas of high concrete stress. And a high resistance to shear should be provided. 3. Rigid elements must be attached to the structure with ductile or flexible fixings 4. A high degree of structural redundancy should be provided so that as many zones of energy-absorbing ductility as possible are developed before a failure mechanism is created. For framed structures this means that a yielding should first occur in beams and columns should remain elastic at the maximum design earthquake 5. Joints should be provided at discontinuities, with adequate provision for movement so that pounding of the two faces against each other is avoided. 6. In shaking a building, an earthquake ground motion will search for every structural weakness. These weaknesses are usually created by sharp changes in stiffness, strength and/or ductility, and the effects of these weaknesses are accentuated by poor distribution of reactive masses. Damage studies reveal the importance of avoiding sudden changes in lateral stiffness and strength.
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UNIT IV CHARACTERISTICS OF EARTQUAKE INTRODUCTION: India has a huge earthquake problem. More than 50% of the country is prone to disastrous earthquake. During 1897 to 1950, the country witnessed four great earthquakes of magnitude 8.4 to 8.7; fortunately, no earthquakes of comparable size have been taken place since 1950. However, the experience in moderate earthquakes (Magnitude 6– 6.5)of Bihar(1988),Uttarkashi(1991), Latur(1993), Jabalpur(1997),and Chamoli (1999) and in the more recent M7.7 Bhuj (2001) earthquake clearly underline the human misery associated with disasters. EARTH & ITS INTERIOR:
A large collection of materials and masses were coalesced to form the earth. Large amount of heat was generated by this fusion, and slowly as the Earth cooled down,
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the heavier and denser materials sank to the center and the lighter ones rose to the top. The differentiated earth consist of the following • Inner core ( Radius 1290 km.) – Solid, Heavy metals. • Outer core ( Thick 2200 km.) – Liquid • Mantle ( Thick 2900 km.) – ability to flow • Crust ( Thick 5 to 42 km.) – Light materials. At the Core: Temperature – 25000C, Pressure – 4 million atmospheres. Density- 13.5 g/cc. & reduces to Temp 250C, Density 1.5 g/cc. & pressure 1 atm.@ surface. SEISMIC WAVES: Large strain energy released during earthquake travel as seismic waves in all directions through the earth’s layers, reflecting at each interface. These waves are two types - Body waves (P-wave & S-wave) and Surface waves (Love wave& Rayleigh wave) BODY WAVES: Primary waves ( P Wave): Material particles undergo extensional & compressional strains along the direction of energy transmission. It is a fastest wave; for example, in granites its speed is 4.8km/sec. The velocity at which a P wave propagates in an elastic medium may be found as VP = [ E(1-µ) / ρ(1+µ)(1-2µ) ] 0.5 Where, V P - Velocity of P wave E - Modulus of elasticity µ - Poison’s ratio ρ - Density of the medium Secondary waves ( S wave ): It will oscillate at right angle, does not travel through liquid, material particle oscillate with right angle to the wave and in association with love waves it cause maximum damage to structures. The velocity at which an S wave propagates in an elastic medium may be found as VS =[E/ 2 ρ (1+µ)] 0.5 Where, V S - Velocity of S wave E - Modulus of elasticity µ - Poison’s ratio ρ - Density of the medium
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Surface waves: Love waves: It will cause surface motions similar to S-wave but no vertical moment. Rayleigh waves: Makes a material particle oscillate in an elliptic path in the vertical plane. The velocity at which a Rayleigh wave propagates in a elastic medium may be found as VR = 0.914 VS or 0.547VP
STRONG GROUND MOTIONS: Shaking due to ground motions on the earth’s surface is a net consequence of motions caused by seismic waves generated by energy release at each materials point within the three-dimensional volume that ruptures at the fault. These waves arrive at various instants of time, have different amplitude and any carry different levels of energy. Thus, the motion at any site on ground is random in nature with its amplitude and direction varying randomly with time. Large earthquake at great depth or at great distances can produce weak motions that may not damage structures or even be felt by humans. This makes it possible to locate distant earthquakes. However, from engineering viewpoint, strong motions that can possibly damage structures are of interest. This can happen with earthquakes in the vicinity or even earthquakes at reasonable medium to large distances. Characteristics: The motion of the ground can be described in terms of displacement, velocity or acceleration. The variation of ground acceleration with time recorded at a point on ground during an earthquake is called an accelerogram. The nature of accelerograms may vary depending on energy released at source, type of slip at fault rupture, geology along the travel path from rupture to the Earth’s surface, and local soil. The carry distinct information regarding; Peak amplitude, duration of strong shaking, frequency content and energy content which are often used to distinguish them. DAMAGES DUE TO EARTHQUAKE: First-degree damage: Small cracks in walls, Flaking of Plaster and stucco. Second -degree damage: Small cracks in walls and joints between panels, Flaking of large pieces of plaster and stucco, fall of roof tiles, cracks in chimney. Third-degree damage: Large deep and through cracks in walls and joints between panels, fall of chimney are the symptoms of third degree damage. Fourth-degree damage: Fall of interior walls, filler wall panels thrown out of frames, breaks in walls, partial walls of buildings, and destruction of braces between individual parts of buildings. Fifth-degree damage: ( Collapse) Total destruction of buildings.
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Table(1) shows the degree of damage Actual Degree of damage, d, to buildings designed to resist earthquakes earthquake of intensities intensity Up to 7 7 8 9 6 ≤1.3 ≤ 1.2 ≤1.1 ≤1 7
1.8 - 2.2
1.5 – 1.8
1.3 - 1.5
1.1 - 1.3
8
2.2 - 3.2
1.8 - 2.2
1.5 - 1.8
1.3 - 1.5
9
3.2 - 4.5
2.2 - 3.2
1.8 - 2.2
1.5 - 1.8
d = (1/n) Σ di di - Degree of damage of individual buildings. If
d=1 Small damage d=2 Moderate damage d=3 Severe damage d=4 Destruction d=5 Collapse
EFFECT OF SOIL CONDITIONS: Destructive effect of earthquake also depend on the local geology, because closely located structures similar in design and erected on different soils were found to suffer different damage during the same earthquake. Basic reasons: (i) Varying dynamic characteristics of soil layers (ii) Varying breaking strength of the soil, which affects the bearing capacity of the foundation. Following table (2) shows categories of soil. Sl.no. Soil categories Vn , km/s 1
Granites
5.6
2
Lime stones and sand stones
4.5 – 2.5
3
Half- stones (gypsum and marls)
3.0 – 1.7
4
Fragmental rocks (rock debris, gravel, pepple)
2.1 – 0.9
5
Sands
1.6 – 0.6
6
Clay, soils (clays, loams, sandy loams)
1.5 – 0.6
7
Loose fill-up soils
0.6 – 0.2
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Where no local seismic risk maps are available, the site seismicity should be assessed on the basis of general engineering geological conditions and approximate recommendations. The effect that the reduced bearing capacity and considerable deformity of the soil foundation may have on the stability of buildings can be well illustrated by extensive settlement and tilting of buildings. Ex - Nigata earthquake in Japan Buildings with shallow foundation not only tilted but also experienced some overturning
EARTQUAKE RESPONSE OF THE STRUCTURES Earthquake causes shaking of ground. So a building resisting on it will experience motion at its base. From Newton’s 1st of motion (Every body continues in a state of rest or of uniform motion in a straight line unless it is compelled to change that state by a force imposed on the body), the base of the building moves with the ground, and the roof has a tendency to stay in its original position. But since the walls and columns are connected to it, they drag the roof along with them. This tendency to continue to remain in the previous position is known as inertia. In the building, since the walls or columns are fixed are flexible, the motion of the roof is different from that of the ground. Consider a building whose roof is supported on columns, when the ground moves, even the building is thrown backwards, and the roof experience a force, called inertia force. If the roof has a mass M and the experiences an acceleration a, then from Newton 2nd law of motion (the acceleration of given particle is proportional to the impressed force and takes place in the direction of straight line in which the force is impressed), the inertia force F1 is mass M times acceleration a, and its direction is opposite to that of the acceleration. Clearly, more mass means higher inertia force. Therefore, lighter buildings sustain the earthquake shaking better. EFFECT OF DEFORMATIONS IN STRUCTURES: The inertia force experienced by the roof is transferred to the ground via the columns. These forces generated in the columns can also be understood in another way. During earthquake shaking, the columns undergo relative movement between their ends. In the straight vertical position, the columns carry no horizontal earthquake force through them. But, when forced to bend, they develop internal forces. The more is the relative horizontal displacement between top and bottom. HORIZONTAL AND VERTICAL SHAKING: Earthquake causes shaking of the ground in all three directions-along the two horizontal directions (x,y), and the vertical direction(z). During earthquake, the ground
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shakes randomly back and forth (-,+) along each of these x,y and z directions. All structures are primarily designed to carry the gravity loads,i.e.,they are designed for the force equal to the mass(this includes mass due to self weight and imposed loads) times the acceleration due to gravity g acting in the downward direction(-z). This downward force Mg is called the gravity load. The vertical acceleration during ground shaking either adds to or subtracts from the acceleration due to gravity. Since factors of safety are used in the design of structures to resist the gravity loads, usually most structures tend to be adequate against vertical shaking. However, horizontal shaking along x and y directions remains a concern. Structures designed for gravity loads, in general, may not be able to safely sustain the effect of horizontal earthquake shaking. Hence it is necessary to ensure adequacy of the structures against horizontal earthquake effects.
FLOW OF INERTIA FORCES TO FOUNDATIONS: The lateral inertia forces are transferred by the floor slabs to the walls or columns, to the foundations and finally to the soil system underneath. IMPORTANCE OF ARCHITECTURAL FEATURES: The behaviors of the building during earthquake depend critically on its overall shape, size and geometry. If we have a poor configuration to start with, all the engineer can do is to provide a band-aid – improve a basically poor solution as best as he can. Conversely, if we start-off with a good configuration and reasonable framing system, even a poor engineer cannot harm its ultimate performance too much. ARCHITECTURAL FEATURES: Both shape and structural system work together to make the structure a marvel. 1. Size of the building: In tall buildings with large height – base size ratio, the horizontal moments of the floor during a ground shaking is large. In short but very long buildings, the damaging effects during earthquake shaking are many. And, in buildings with large plan area like warehouses, the horizontal seismic forces can be excessive to be carried by columns and walls. 2. Horizontal layout of buildings: In general, buildings with simple geometry in plan have performed well during strong earthquake. Buildings with re-entrant corners, like U,V,H,+ shaped in plan, have sustained significant damage. The bad effects of these interior corners in the plan of buildings are avoided by making the buildings two parts (For example, an L shaped plan can be broken up in to two rectangular plan shapes). 3. Vertical layout of buildings: The earthquake forces developed at different floor level in a building need to be brought down along the height to be ground by the shorter part, any deviation and discontinuity in this load transfer path results in poor performance of the buildings.
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Buildings that are fewer columns or walls in a particular storey or with unusually tall storey tend to damage or collapse which is initiated in that storey. Many buildings with an open ground storey intended for parking collapsed or were severely damaged. Buildings on sloppy ground having unequal height of columns along the slope, which causes ill effects like twisting and damage in shorter columns. 4. Adjacency of buildings: When two buildings are too close to each other, they may pound on each other during strong shaking. With increase in building height, the collision can be a greater problem. When the building height does not match the roof of shorter building may found at the mid height of the column of the taller one, this can be very dangerous.
TWISTING OF BUILDING: The walls and columns are like ropes, and the floor is like cradle. Building vibrates back and forth during earthquake. Buildings with more than one storey are like rope swing with more than one cradle. If the mass on the floor on the building is more on one side, then that side of the building moves more under ground movement. This building moves such that its floors displace horizontally as well as rotate. Buildings with unequal vertical members also the floors twist about a vertical axis, and displace horizontally. IMPROVING THE DUCTILITY OF THE BUILDINGS: In India, most non-urban buildings are made in masonry. In the plains, masonry is generally made of burnt clay bricks and cement mortar. However in hilly areas, stone masonry with mud mortar is more prevalent; but in recent times it is being replaced with cement mortar. Masonry can carry loads that cause compression (pressing together), but can hardly take load that causes tension (Pulling apart). Steel is used in masonry and concrete buildings as reinforcement bars of diameter ranging from 6mm to 40mm.Reinforcing steel can carry tensile and compressive loads. Moreover, steel is a ductile material. This important property of ductility enables steel bars to undergo large elongation before breaking. CAPACITY DESIGN CONCEPT: The ductile bar elongates by a large amount before if breaks, while the brittle bar break suddenly on reaching its maximum strength at a relatively small elongation. We want to have such ductile failure. EARTHQUAKE- RESISTANT DESIGN OF BUILDINGS: The failure of a column can affect the stability of the whole building, but the failure of a beam causes localized effects. Therefore, it is better to make beams to be the ductile weak links than columns. The method of designing R.C buildings is called the strong column weak beam design method. QUALITY CONTROL IN CONSTRUCTION:
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The capacity design concept in earthquake –resistant design of buildings will fail if the strength of the brittle links fall below their minimum assured values. The strength of brittle construction materials, workmanship, supervision and construction methods. Similarly, special care is needed in construction to ensure that the elements meant to be ductile are indeed provided with features that give adequate ductility. Thus, strict adherents to prescribed standards of construction materials and construction processes is essential in assuring an earthquake-resistant buildings. Regular testing of construction materials at qualified laboratories, periodic training of workman at professional training houses and on-site evaluation of technical work or elements of good quality control.
CONCEPT OF EARTHQUAKE RESISTANT DESIGN OF STRUCTURES INTRODUCTION The earthquake hazard to life and is almost entirely with man made structures. A study of structural performance of buildings during the past earthquakes has clearly indicated that the commonly employed constructions are not earthquake resistant and therefore requires improvement in earthquake resistant design and construction techniques. There is a great need that the earthquake resistance features are well understood and implemented in the new constructions. It is usually not possible to achieve earthquake proof construction due to constraints of availability of materials, techniques of construction, prohibitive cost and uncertainties of earthquake forces. But it is possible to achieve their earthquake resistance through simple principles of planning, design and construction detail so as to make them collapse proof and the damage to an acceptable limit of repair. Since, the most severe probable earthquake motion characteristics at a site can only be estimated approximately and its chances of occurring during the useful life time of a structure is very uncertain therefore, an elastic design for such uncertain forces will lead to very uneconomical design. In such situations, elastic design is neither possible nor justifiable. It is obvious that where large ground movements occur, it may not be possible to save structures from destruction or damage. Here, the basic philosophy and principle of earthquake resistant design irrespective of any specific type of structure are discussed. Although, some passing references have been made to building for better explanation. PHILOSOPHY OF EARTHQUAKE RESISTANT DESIGN
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Earthquake prediction is uncertain and can only be possible partially for certain faults. Successful earthquake prediction cannot eliminate earthquake event. As earthquakes cannot be predicted accurately, magnitude, intensity and duration of earthquake must be estimated on the basis of available seismic history and geological information. Assuming successful prediction, even if all the population is evacuated safely, the structures cannot be saved from earthquakes. Therefore, earthquake resistant design of a structure is the only answer in minimizing the damaging effects of earthquakes on structures. For ordinary structures it is not feasible to undertake a special development of earthquake criteria for each structure, instead, general design criteria are presented in the code which are applicable to regular structures of more or less uniform configurations. The design philosophy is developed on the basis of lessons learnt from the past earthquakes and analytical studies. Structure based special design criteria are also used besides the use of basic design criteria such as dams, nuclear power plants etc. In addition to taking into account the probability of occurrence of earthquakes and expected severity of shaking, these criteria are also based on considerations of allowable stresses, permissible inelastic strain, desired factor of safety against collapse, acceptable dam etc. Basically, the earthquake resistant design and construction is based on (i) the philosophy of estimation of earthquake loading on a structure and (ii) the philosophy for earthquake resistant design. Estimation of Earthquake Loading Earthquake forces in a structure is generated depending upon the intensity of the vibratory ground motion, and the mass and stiffness distribution, damping property of structure, and the manner in which it is supported on foundation. Design basis earthquake loading for less important structures for less important structures, only elastic design is carried out either (i) by seismic coefficient method or (ii) by response spectrum method. Design basis earthquake loading for important structures For design both seismic response spectrum method and time history analysis are used. For important structures earthquake forces are worked out considering the type of structure and expected earthquake intensity at the site based on estimated earthquake parameters (Magnitude of earthquake, depth of focus, epicentral distance) in order to derive Peak Ground Acceleration (PGA). Estimation of Earthquake Parameters Detailed seismo-tectonic studies around a site help in arriving at the design earthquake parameters. These include data on past earthquakes in the region (location of their epicenters, magnitude and focal depths), seismicity map (showing the magnitude rated epicenters, seismotectonic lineaments in the region, return period of earthquakes for
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a given magnitude) and regional geology and seismotectonic maps (showing stratigraphy and structural trends, and faults and evidences of movement along faults in recent geological times, data on soil properties at the site, depth of water-table. The regional area around the site is sub-divided into tectonic provinces. A tectonic province is a continuous geological region characterized by relative consistency of geological structure and seismo-tectonic characteristics. All the seismogenic faults and tectonic structures should be identified. As many earthquakes as possible will be associated with the seismogenic faults and tectonic structures. Occurrence rates (in time and space) of earthquakes of different magnitudes associated with each tectonic structure and fault will be estimated. A maximum earthquake potential will be assigned to each known fault and tectonic structure. Earthquakes, which cannot be associated with, know faults and. structures should be identified. These earthquakes will be known as Floating earthquake Maximum earthquake potential associated with each tectonic unit/fault or tectonic province is assigned. The maximum earthquake potential associated with a tectonic unit should be moved to a point on the tectonic structure closest to the site. For the tectonic province adjacent to that in which the site lies, the maximum earthquake potential should be moved to a point nearest to the site on the boundary of the tectonic province. Estimation of earthquake density Earthquakes release suddenly large energy in a very short time and makes the ground to vibrate caused by several waves originating from a source of disturbance inside the earth. The intensity of vibration normally decreases with the increase in distance from the epicenter. The earthquake parameters, which influence the earthquake intensity at a site, are the magnitude of earthquake, epicentral distance and focal depth. The source mechanism also affects the intensity. For design purpose the intensity of ground motion is estimated in terms of peak ground acceleration and its frequency contents. The frequency contents are estimated based on the predominant periods of ground motion expected at the site. The estimation of earthquake intensity in the form of peak ground acceleration (PGA) is worked out from the estimated earthquake parameters for the design earthquake magnitude, focal depth and epicentral distance using a empirical relationship. The PGA is also defined as zero period acceleration (ZPA). Finally, forces are evaluated from dynamic analysis of a structure subjected to earthquake loading either in the form of spectra or acceleration time history of the ground motion. Earthquake resistant design The basic philosophy of earthquake resistant design is the provision of adequate strength and ductility against future expected severe earthquake. It is based on design for following two levels of earthquake.
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i.
Structures are designed to remain elastic during more frequent moderate size earthquakes by permitting the increase in permissible stresses, then check
ii.
Structures are designed to resist infrequent most severe earthquake allowing limited damage without collapse, which may occur once in its useful lifetime.
If the following measures are taken to increase the resistance, a structure will withstand earthquakes more effectively. i.
Integrity of structure: The whole structure should be tied together by earthquake bands, earthquake framing etc. so as to act as one unit. Proper distribution and continuity of load bearing structural elements are essential for an integral action of a structure. The most vulnerable places in various type of construction are its joints where due to shear and tension, the joints fails. Designing the connections and details of a structure to be earthquake resistant is almost as important as checking the overall behaviour of structure. If the strength and ductility of the connections are not adequate and if the details are not properly made, the structure as a whole is not likely to display effective seismic performance.
ii.
Seismic lateral force-strength ratio: A structure should have a minimum level of strength and stiffness, smoothly increasing from top to bottom of a structure and evenly distributed in plan. This distribution is such that the seismic lateral force to strength ratio is everywhere approximately constant.
iii.
Safe construction (no collapse or failure of structure): Brittle structures without any reinforcement or structures having no seismic resistance provisions fail suddenly when the seismic force exceeds the strength of the structure. On the other hand, the steel structure or the reinforced structures do not fail on reaching the yield level but undergo plastic deformation. Ductile behaviour of structure should therefore be ensured so that the structure is able to absorb the damaging earthquake energy without resulting in complete or partial collapse. In weak column-strong beam structure will result collapse of entire structure because hinges will form in the columns, which also carry large axial loads. See Fig. I. Failure of structure may also result from foundation failure and poor structural design. In general safe construction can be achieved by using •
Strong column-weak girder/beam design.
•
The walls must be tied together effectively to avoid separation at the vertical joints. The roof and trusses must be firmly fixed to the perimeter walls.
•
Lateral resisting elements should be present along both the principal axes of the structure.
•
Introducing ductility by providing reinforcements at critical locations / junctions.
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Fig.1 Failure modes of different beam column arrangement PRINCIPLES OF EARTHQUAKE RESISTANT DESIGN The principles of earthquake resistance design is ‘to evolve safe and economical design of structures to withstand possible future earthquakes. (a) Reducing the earthquake forces and (b) withstanding it by increasing the resistance of the structure can achieve this. (a) Reducing the earthquake forces The structures can be safe guarded from damaging earthquake forces acting on a structure either by reducing earthquake forces or partially deflecting the earthquake energy from the structure by adopting any or a combination of the following procedures. i.
Use of light weight construction: Since, the earthquake force generated is proportional to the mass, a decrease in the mass of the structure by using the light weight materials, reduces the magnitude of seismic forces and hence increases the seismic safety of structures.
ii.
Avoid quasi-resonance: Earthquake forces generated’ can be reduced by suitable design such that by keeping the fundamental time period of the structure away from the predominant ground motion time period range.
Therefore construction of a tall flexible structure at a soft soil site where expected ground motion is of predominantly low frequency is not advisable since a quasiresonance situation may arise. At such a site construction of small stiff structure is advisable. However, cons of tall flexible structures are advisable on rocky sites where high frequency ground motion is expected. An important feature of earthquake resistant design is that the intensity of earthquake forces on a structure is dependent on the mass and stiffness distribution of
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structure itself (i.e. natural frequency of the structure) unlike the forces due to wind, gravity etc. and therefore the forces generated can be reduced by proper arrangement of mass and stiffness. iii.
Diverting or absorbing the earthquake energy: Non-conventional design methods have been evolved to either deflect part of the earthquake force from the structure or to absorb a part of the earthquake energy in specially designed devices introduced in the structure so as the remaining earthquake force can be withstood by the structure without any damage. These are achieved by a) Base isolation technique, or b) Introducing energy dissipating devices in a structure or c) Introducing a combined isol2tion and energy absorbing devices.
This concept of reducing the earthquake forces is based on the above theory of avoiding quasi resonance where the time period of structure is elongated by introducing a base isolation system between a structure and foundation. This deflects the earthquake energy from the structure and only part of it is transmitted to the structure, which can be resisted by the structure without or with minimum earthquake resistant provisions. iv.
Neutralizing the earthquake forces: In this the building itself respond actively against earthquakes and tries to control the vibrations. Such buildings are also known as Dynamic Intelligent Building (DIB). This is achieved by Active Control System, which consists of sensors to measure structural response, computer hardware and software to compute control forces on the basis of observed response and actuators to provide the necessary control forces.
(b) Increasing the capacity of structure to resist earthquakes A structure can be safe guarded from earthquakes by increasing its resistance capacity by introducing earthquake resistant features. Intelligent framing system, careful design and construction detail can vastly improve the performance of a structure to resist earthquakes. Great improvements in earthquake codes for design and construction have been made worldwide and this will certainly reduce loss of life and property damage in future earthquakes. Earthquake resistance of a structure can be increased with better understanding of earthquake behaviour of structures and by careful planning, design and construction. For an improved conventional method of design following are some of the important points, which should be considered. Planning considerations In the very early stage of planning the type of structure the configuration, basic materials, and the framing of the structure have to be carefully chosen. These selections 109
result in greatly improved and economical design of a structure and increase the seismic safety. Following should he taken care as far as possible at the planning stage of a structure [Code 4326(1976)]. •
Proper selection of site : Considerable advantage can be gained by choosing the best site/spot from the earthquake hazard point of view or the best type of structure for that site. The local geological structures, active faults and the soil characteristics together with the economic and social consequences of destructive earthquakes determine the suitable location. Building located on soft soil and near the steep vertical slope is liable to more damage and such sites should therefore be avoided.
•
Use of proper material properties: Structural materials have their own performance characteristics and should be selected according to the location and functions of structure. The earthquake force is proportional to mass and therefore the building should be as light as possible consistent with structural safety and fundamental requirements. Roof and upper stories of buildings should be designed as light as possible. The material selected should have high strength to weight ratio, high deformability, and high strength in compression, high tension and shear strength and reasonable cost. The mortar used should have sufficient strength. Good quality of construction is insurance for good performance of building during earthquake.
•
Configuration of structure: Irregular configured buildings usually develop torsion due to seismic forces. Hence, the structural configuration should be as simple as possible and symmetrical with respect to mass and rigidity so that the centers of mass and center of rigidity of the structure coincide with each other. Due to functional change etc. some accidental eccentricity should be considered. If functional requirements dictate adoption of geometrical asymmetry in the plan of building, then adjust moments of inertia of shear walls so that the center of mass and center of stiffness of building coincides. If not, provision should be made for extra shear due to torsion.
Irregular shaped buildings in plan such as T, L, U, H and other similar shapes undergo damages of one block or the other under strong motion earthquakes. These may be designed as a combination of few regular shaped blocks (i.e square or rectangular) with suitable construction joints. There should be enough clearance at the seismic, construction joints so that two adjacent blocks do not pound each other. It is also desirable to avoid drastic changes in vertical configuration of building. Also joints may separate parts of different rigidities. Between the seismic joint, the length to width ratio of a structure should not normally exceed three. •
Stiffness distribution:
Strength in various directions
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The structure should be capable of resisting earthquake forces about both the principal directions. This can be achieved by providing shear wall system and/or bracings to complement the frame’s strength and stiffness along both the axes of the building.
Fig. 2 shows inadequate and adequate stiffness distribution Shear walls should be well distributed over plan along both principal axes, which result in. symmetrical stiffness distribution. Avoid concentration of shear walls. Architects have liberty to locate these resisting elements and comply with structural considerations. The structure should be able to resist the reversible nature of earthquake forces. Continuity of construction All the elements of building should be suitably tied so that all the resisting elements counter the ear forces as one unit without separating from each other. Integrity of structures are obtained by providing reinforced concrete bands at appropriate locations in the buildings. Plinth, lintel and roof bands are used to tie up the brick masonry and stone masonry buildings. Roof and floor systems should be firmly tied or integrally cast to the perimeter walls. The floor slabs should be continuous throughout the structure as far, as possible. Concrete slabs arid support beam should be cast together. The roof trusses should be held down to walls by bolts. The r.c.c. Rigid slabs should be made continuous with the perimeter walls. Sudden change of stiffness Arbitrary position of infill walls, arbitrary introduction of bracing walls, or stepped elevation cause sudden change of stiffness. Avoid use of stiff walls between flexible frames. Short column and short beam attract lot of forces due to its high stiffness and therefore liable to undergo damages and therefore should be avoided. It is desirable to provide sliding joint on end of the flight of a staircase so as to permit relative movement and avoid strut action. Avoid planes of weakness by avoiding continuous rows of openings in load bearing walls. •
Safe space between adjacent buildings
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Separation of adjoining structures is required to avoid damage during an earthquake due to collision when they have different total heights or storey height at intermediate levels and different dynamic characteristics. Separation or gap should be more than the sum of dynamic deflection of the two buildings. •
Ductility provision
To avoid sudden collapse of the structures during earthquake and enable them to absorb energy beyond yield point, the main structural elements and their connections should be so designed such that the failure is of ductile nature. Ductility enables them to absorb energy by deformation. •
Damage to nonstructural elements
The nonstructural elements such as partitions, staircase, cladding, door-window frames etc., which are generally ignored in the analysis, provide much strength to the structure. Because of damage to these elements lot of energy is absorbed and is the reason of survival of many structures during earthquakes. Suitable details have to be planned out for connecting the nonstructural parts with the structural framing so that the deformation of the structural frame leads to minimum damage of the non-structural elements. Infill structure makes the structure rigid, and therefore attracts large force. This may cause damage in the brittle infill. If it is desired that panel or infill wall should not act as bracing element, it should be connected to main structure in such a manner so as to minimize their damage during an earthquake since the repair of these parts is quite costly. The above arrangements of infill wall will permit considerable deflection of frame .yet it will be held by the top beam from overturning. •
Projecting parts
Projecting parts such as parapets, cornices, balconies, canopies and chajjas be avoided as far as possible. Ceiling plaster should not be thicker than 6.0 mm for reinforced concrete and 12 mm for reinforced brickwork. •
Foundation
Avoid damage to the structure due to foundation failure for buildings founded on soils liable to liquefy by suitable design considerations. Sandy sand with high water table has high liquefaction potential. Liquefaction may result tilting, overturning and even sinking of structures unless they are founded properly taking such an eventualities into account. Loose fine sand, silt and expansive clays may give rise to large differential settlements causing damage to the structures, which they support and should generally be avoided. Raft foundation in such soil is less vulnerable. The hard ground is suitable to all types of structures. The entire building should be founded on same type of soil in order to avoid differential settlement. Avoid construction of buildings on filled in soil or weak soil, which will consolidate during earthquake resulting in large differential settlements.
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To avoid large differential settlement of building, ties to the cap/columns should connect all the individual footings or pile caps in soft soil. The ties and cap should be designed to take up these forces. While analyzing for earthquake forces, the structure-soil-foundation interaction should be considered which might influence significantly the response of structure due to the deformation of soil-foundation system. The transfer of overturning moments and forces to foundations requires special attention. •
Other planning considerations
Fire generally follows an earthquake and therefore, buildings shall be constructed to make them fire resistant in accordance with the provisions of relevant Codes for fire safety. Equipments should be properly anchored to the floor. Design considerations Earthquake load is an occasional load unlike the permanent loads due to selfweight of (including the fixtures, furniture etc.) and live loads. A fraction of live load is taken for design depending upon the probability of its presence at the time of earthquake. For design purposes, it is assumed that the maximum earthquake will not simultaneously occur with maximum of other occasional forces like wind, floods etc. The design of less important structure is therefore carried out for self weight etc. and then the design is checked for infrequent earthquake loads by permitting the increase in permissible stresses. The code specifies the use of elastic design (working stress method) permitting an increase of 33- %% in the normal working stresses in material (concrete, steel, wood etc.) when effects of earthquake load are combined with other normal dead and live loads. Allowable bearing pressure in soil is increased whenever the earthquake forces are considered along with normal design forces. In the ultimate load method of analysis, the factor for reinforced concrete and steel structures for earthquake condition is taken 1.4 instead of 1.85 under normal condition. A seismic design of a structure to remain elastic during a future maximum earthquake, which may or may not occur within the useful life of a structure would be highly uneconomical. A limited damage due to such an event is therefore allowed without permitting the collapse of the structure thus ensuring safety against loss of live and property. It may turnout to be less expensive to repair while allowing limited damage when hit by an earthquake rather than making the structure earthquake damage proof. The design shall be safe considering the reversible nature of earthquake forces. For preliminary design of important structures and for routine structures, empirical coefficients are used to evaluate the earthquake forces. The computed eccentricity should be increased by some percentage of the dimension of structure to take into account the accidental eccentricity. Overturning effect of horizontal load causing tension and compression at the extreme ends should be adequately considered. Nonlinear dynamic analysis in time domain is carried to establish the inelastic deformation.
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Emergency structures such as hospitals, fire stations, water supply, military Stations and other services such as power houses, broadcasting stations, telephone and telegraph buildings, cultural treasures, museums and monuments must be designed for higher safety. Special attention is needed for nursery schools, kinder gardens, primary schools and lunatic asylums. The community hails, assembly hails, places of worship and cinema halls should be adequately designed. Other important structures need special attention are nuclear power plants, gas and oil tanks, chemical factories, gasoline stations etc. and detailed dynamic analysis should be carried out. For detailed dynamic analysis the following procedure is adopted. i.
Estimate the design response spectra and its compatible ground motion.
ii.
Establish a mathematical model of structure representing its dynamic behaviour under the earthquake excitations. Interaction between the structure, foundation and the supporting soil should be considered in the model. Generally spring-massdashpot system is used to represent a structure. Model should be as simple as possible. Finite element modeling of structures is found to be suitable for many problems. In deriving a mathematical model, masses are generally lumped at convenient locations. Stiffness properties are worked out from the effective length of members, moment f inertia, area of cross section, modulus of elasticity. The damping values are selected based on experimental values and judgment. The damping is assumed to be viscous. This assumption is due to the convenience in tile solution of differential equations.
iii.
Determine the first few natural frequencies and mode shapes of vibration.
iv.
Determine the time history response either by direct integration or time wise mode superposition of first few modes. A detailed design criterion for multistorey building is presented elsewhere [6].
Construction detail In construction all those features as discussed in planning considerations have to be taken care as far as possible for improved performance. Strict supervision during construction should be made •
To ensure use of good quality material, good construction, improved workmanship and proper curing;
•
To ensure certain details particularly at critical sections and junctions in seismic areas;
•
To ensure the ties in the column should be properly hooked. Beam reinforcement is taken well inside the columns and the beam-column reinforcement is laid carefully since the detail is very critical;
•
To take care that the concrete is well compacted so that there is no honey combing;
•
To see that the end of reinforcement should not be left in any joint and the overlapping of rein is made at the point of maximum shear;
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•
To ensure that adequate gap is provided at the crumple section;
•
To see that the plinth beams or foundation beams are provided;
•
To ensure that the tiles or other loose roofing unit are tied properly.
•
To ensure that the bricks should be thoroughly wet before laying in good quality of mortar (not less than 1:6) and the vertical joints in brick masonry are properly filled up.
•
It is desirable to provide sliding joint at one end of the flight of a stair case so as to permit relative movement and avoid strut action.
DISCUSSION ON THE CODAL PROVISIONS GIVEN IN IS1893-2002 AND IS4326-1993 This Indian standard (part 1)(Fifth revision) was adopted by the Bureau of Indian standards, after the draft finalized by the Earthquake Engineering Sectional Committee had been approved by the civil Engineering Division council. IS-1893-2002 has 5 parts Part 1: General provisions and buildings Part II: Liquid retaining tanks-elevated and ground supported Part III: Bridges and retaining walls Part IV: Industrial structures including stack like structures Part V: Dams and embankments. Our scope of the discussion is about the part-1 only The following are the major and important modifications made in the fifth revision.. a) The seismic zone map is revised with only four zones, instead of five, zone I has been merged to zone II b) The factor s of seismic zone factors have been changed; these now reflect more realistic values of effective peak ground acceleration considering maximum considered earthquake and service life of structure in each zone. c) Response spectra are now specified for three types of founding strata namely rock and hard soil, medium soil, soft soil. d) Empirical expression for estimating the fundamental natural period Ta of multistoried buildings with regular moment resisting has been revised. Ta=0.07h0.75 for RCC buildings =0.085h0.75 for steel buildings =0.09h/sqrt (d)
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e) The concept of response reduction due to ductile deformation, or frictional energy dissipation in the cracks is brought in to the code explicitly by introducing the response reductions factor in place of the earlier performance factor. f) Lower bound is specified for the design base shear of buildings based on empirical estimate of the fundamental natural period Ta. g) The soil foundation factor is dropped instead a clause introduced to restrict the one of foundation vulnerable to differential settlements in severe seismic zone. h) Tensional eccentricity values have been revised upwards in a view of serious damages observed in building with irregular plan. i) Modal combination rule in dynamic analysis of building has been revised. j) Other clauses have been redrafted where necessary for more effective implementation. This standard (part 1) deals with the assessment of seismic loads on various structures and earthquake resistant design of buildings. Its basic provisions are applicable to buildings; elevated structures; bridges concrete masonry and earth dams; embankments and retaining wall and other structures General principles and design criteria is given by the clause 6 of page 12 of the code 1893 6.1.1 Ground motion: The characteristics (intensity duration, etc) of seismic ground vibrations expected at any location depends upon the magnitude of earthquake, its depth of focus, distance from epicenter, characteristics of the path through which the waves travel, and the soil strata on which cause the structure to vibrate, can be resolved in any three mutually perpendicular directions. Earthquake –generated vertical inertia forces are to be considered in design unless checked and proven by specimen calculations to be significant. Vertical acceleration should be considered in structures with large spans, those in which stability is a criterion for design, or for over all stability analysis of the structures. 6.1.2 The response of the structures to ground vibrations is a function of the nature of foundation soil; materials form size and mode of construction of structures and the durations and the characteristics of ground motion. This standard specifies design forces for structures standing on rocks soils, which do not settle, liquefy or slide due to loss of strength during ground vibrations. 6.1.3
The design approaches adopted in this standard is to ensure that the structure posses at least a maximum strength
1. To with stand minor earthquakes which occur frequently, with out damage; 2. To resist moderate earthquake without significant structural damage though some non structural damage may occur; and 3. Aim that structures withstand major earthquakes without collapse of the structures 6.1.4 Soil structure interaction: The soil-structure interaction refers to the effects of the supporting foundation medium on the motion of structure. The soil
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structures interaction may not be considered in the seismic analysis for the structures supported on rock or rock -like material. 6.1.5 The design lateral force specified in this standard shall be considered in each of the two orthogonal horizontal directions of the structures. 6.1.7 Addition to existing structure: Addition shall be made to existing structures only as follows An addition that is structurally independent from existing structures shall be designed and constructed in accordance with the seismic requirement for new structures. 6.1.8
Change in occupancy: When a change of occupancy results in a structure is being reclassified to a higher importance factor (I) , the structure shall confirm to the seismic requirement for a new with the higher importance factor 6.3. Load combinations: Load combination and increase in permissible stresses are given by the clause no 6.3 of IS code 1893 6.3.1.1 Load factors for plastic design of steel structures the following load combination can be accounted for 1) 1.7(DL+LL) 2) 1.7(DL+EL) 3) 1.3(DL+LL+EL) 6.3.1.2 Partial safety factors for limit state design of prestressed concrete and RCC structures 1) 1.5(DL+LL) 2) 1.2(DL+LL+EL) 3) 1.5(DL+EL) 4) 0.9DL+1.5EL 6.3.5 INCREASE IN PERMISSIBLE STRESSES 6.3.5.1 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. 6.3.5.2 Allowable pressure in soils is given in table 1 of IS code 1893 6.4 Design spectrum: For the purpose of determining seismic forces the country is classified into four Zones The design horizontal seismic coefficient Ah for the structure shall be determined from the following: Ah=(Z/2) x (I/R) x (Sa/g) 7.5.3 Design base shear: The total design lateral force or design seismic base shear (Vb) along any principal direction shall be determined from the following expression Vb = Ah x W 7.8 Dynamic analysis: Dynamic analysis shall be performed to obtain the design seismic force, and its distribution to different levels along the height of the building and to the various lateral load-resisting elements, for the following buildings:
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a) Regular buildings: Those greater than 40m in height in zones IV and V, and those greater than 90m in height in zone II and III. b) Irregular buildings: All framed buildings higher than 12m in zone IV and V, and those greater than 40m in height in zones II and III. 7.8.2 the dynamic analysis can be carried out in the following methods 7.8.3 Time history method: Time history method of analysis, when used, shall be based on an appropriate ground motion and shall be performed using accepted principles of dynamics. 7.8.4 Response spectrum method: Response spectrum method of analysis shall be performed using the design spectrum or by site- specific design spectrum. 7.8.4.1 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 systems, to obtain natural periods (T) and mode shapes (φ) of those of its modes of vibration that need to be considered.
IS4326 – 1993 – E.Q. Resistant design and construction of building 1. Scope: 1.1 This standard is deals with the selection of materials, special features of design and construction for EQ buildings including masonry constructions using rectangular masonry units, timber construction and buildings with pre fabricated flooring / roofing elements. 4. GENERAL PRINCIPLES: 4.1 Lightness: Since EQ force is a function of a mass; the building shall be as light as possible. 4.2 Continuity of construction: 4.2.1 As far as possible, the parts of the building should be tied together in such a manner that the building acts as one unit. 4.2.2 For parts of the building, the floor slab shall be continuous except at the expansion joints, floor slab should be integrally cast with beams. 4.2.3 Additions and alterations to the structures shall be accompanied by the provision of separation or crumple sections between the new and existing structures as for as possible. 4.3 Projecting and suspended parts: 4.4 Building configuration Building configuration is to minimize the torsion and stress concentration. 4.4.1 Simple rectangular plan and symmetrical 4.4.2 If the structure is not as per in 4.4.1 then the torsion and stresses should be considered in the structural design. 4.4.3 Building with other configuration should be provided with separations at suitable place. 118
4.5 Strength in various directions: The structure shall be designed to have a adequate strength against EQ effects along both the horizontal axes. 4.6 Foundations: The structure shall not be founded on such loose soils, which will subside or liquefy during an EQ, resulting in a large differential settlement. 4.7 Ductility: The main structure elements and their connection shall be designed to have a ductile failure. 4.8 Damage to nonstructural parts: Suitable details shall be worked out to connect the non-structural parts with structural framing. 4.9 Fire safety: Fire frequently follows an EQ and therefore, building shall be constructed to make them fire resistant in accordance with provisions of the following Indian standards for the fire safety , as relevant: IS 1641; 1988, IS1642;1989, IS 1643;1988, IS 1644:1988, and IS 1646:1986. 5 SPECIAL CONSTRUCTION FEATURES: 5.1 Separation of adjoining structures: Minimum width of separation gaps shall be Sl.no Gap width/Storey, in mm for Type of construction Design seismic coefficient=0.12 1 Box system or frames with shear walls 15.0 2 Moment resistant reinforced concreter frame 20.0 3 Moment resistant steel frame 30.0 NOTE: minimum total gap shall be 25mm. 5.3 FOUNDATIONS: 5.3.2 The sub grade below the entire area of the building shall preferable be of the same type of soil. 5.3.3 loose fine sand, soft silt and expansive clays should be avoided. Or raft foundation, pile taken to the hard stratum can be used. Sand piling, soil stabilization 5.3.4 Isolated footings for columns 5.4 Roofs and floors: Corrugated iron or asbestos sheets shall be preferable 5.4.2 Pent roofs: all roof trusses shall be supported on RCC or reinforced brick works band. 5.5 Stair cases: (Fig are given in IS code 4326 page 8) (1) Separated stair cases, (2) built in stair cases (3) stair cases with sliding .
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TYPES OF CONSTRUCTIONS 6.1 The types of construction usually adopted in buildings are as follows • Framed construction, • Box type constructions. 6.2 Framed construction: 6.2.1 Vertical load carrying frame constructions: 6.2.1.1 Moment resistant frames with shear wall Box type construction: This type of construction consists of prefabricated or in situ masonry, concreter or RCC wall along both the axes of the building. The wall support vertical loads and also act as shear walls for horizontal loads acting in any directions. All traditional masonry constructions fall under this category. 8 MASONRY CONSTRUCTIONS WITH RECTANGULAR MASONRY UNITS: 8.2 WALLS 8.3 Openings in bearing walls :(Table 4 and figure 7) 8.4 Seismic strengthening arrangements: 8.4.1 All masonry buildings shall be strengthened by the methods, as specified for various categories of buildings, as listed in table 5, and detailed in subsequent clauses. 8.5 Framing of thin load bearing walls: Load bearing walls can be made thinner than 200 mm say 150 mm inclusive of plastering on both sides. 8.6 Reinforcing Details for Hollow Block Masonry 8.6.1 Horizontal Band: U- shaped blocks may be used for construction of horizontal bands at various levels of the stories as shown in IS code, where the amount of horizontal reinforcement shall be taken 25 % more than that given table and provided by using four bars and 6mm dia stirrups. Other continuity details shall be followed, as shown in figure 11. 9 Floors / roofs with small precast components: 9.1 Precast RCC roof/floor: The nominal width varies from 300mm to 600mm, its height from 100mm to 200mm 9.1.1 Precast RCC cored unit roof or floor: the unit is a RCC component having a nominal width of 300mm to 600mm and thickness of 130mm to 150mm having to circular core of 90mm dia throughout the length of the unit. 9.1.2 Precast RC plank and joint scheme for roof/floor: max 1.5m and 300mm width.
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9.1.5 Precast RCC waffle unit roof/floor: lateral dimension up to 1.25m and depth depending upon the span of the roof / floor to be covered, the min thickness shall be 35mm 10 Timber constructions: 10.1 Timber has a higher strength per unit weight and is therefore very suitable for E.Q. resistant construction. 10.2 Timber construction shall be restricted to two storeys 10.3 Safety against fire should be considered mainly. 10.5 Foundations: 10.5.1 Timber construction preferably starts above the plinth level, the portion below being in masonry. It can be connected to foundation in two ways. (As shown in Fig 31) 10.6 Types of framing The types of construction usually adopted in timber buildings are as follows: (1) STUD WALL CONSTRUCTION The stud wall construction consists of timber studs and corner post framed into sills, to p plates and wall plates. (Fig 32) (2) BRICK NOGGED TIMBER FRAME CONSTRUCTION The brick nogged timber frame consists of intermediate vertical columns, sills, wall plates, horizontal noggin members and its diagonal braces framed into each other and the space between framing members filled with tight fitting brick masonry in stretcher bond. (Fig 33)
DYNAMIC PROPERTIES OF SOIL This chapter deals with problems of studying various dynamic effects on soil caused by dynamic loads. The various dynamic loads are 1. Dynamic loads from unbalanced machines 2. Seismic effects 3. Earth vibrations caused by transport vehicles and 4. Explosions The nature of the loads may be 1. Slow repetitive 2. Fast repetitive (or) 3. Transient
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Loading in nature is not truly periodic.Also,the magnitude of the loads in subsequent cycles may not be the same. Further, purely dynamic loads do not occur in nature, only combinations of static and dynamic loads occur. Some soils increase in strength under rapid cyclic loading while saturated sands or sensitive clays may lose strength with vibration. The behavior of soils in earthquake will discussed under the following 3 sub-headings 1. Settlement of dry sands 2. Liquefaction of saturated cohesionless soils 3. Dynamic design parameters of soil (shear modulus damping coefficient) 1. Settlement of dry sands:It is well known that loose sand can be compacted by vibration. In earthquake such compaction causes settlements, which may have serious effects on all types of constructions. It is therefore important to be able to assess the degree of vulnerability to compaction of a given sand deposit. Unfortunately this is difficult to do with accuracy, but it appears that sand with relative density less than 60% or with standard penetration resistance less than 15% are susceptible to significant settlement. The amount of compaction achieved by any given earthquake will obviously depend on the magnitude and direction of shaking as well as on relative density. Attempts have been made to predict the settlement of sands during earthquake and a simple method is presented below. It should be noted that this ignores the effect of important factors such as confining pressure and no. Of cycles but no fully satisfactory methods of settlement prediction as yet exists. There is a critical void ratio ecr above, which a granular deposit will compact when vibrated. If the void ratio of the stratum is e>ecr the max amount of possible settlement can be shown to be ΔH =( ecr - e )*H / (1- e ); Where, H =depth of the stratum ecr = e min+( e max- e min)* e [-0.75a/g] e min = minimum possible void ratio as determined by testing e max = maximum possible void ratio. a = amplitude of applied acceleration g = acceleration due to gravity 2. Liquefaction of saturated cohesionless soils:Under earthquake loading some soils may compact, increasing the pore water pressure, and causing a loss in shear strength. This phenomenon is generally referred to as liquefaction. Gravel or clay soils are not susceptible to liquefaction. Dense sands are less likely to liquefy than loose sands, while hydraulically deposited sands are particularly vulnerable due to their uniformity. Liquefaction can occur at some depth causing an upward flow of water. Although this flow may not cause liquefaction in the upper layers it is possible that the hydrodynamic pressure may reduce the allowable bearing pressure at the surface. Extensive liquefaction at Niigata (Japan) during the 1964 earthquake led to increased attempts to quantify liquefaction potential. As yet no generally accepted unified criterion
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has been developed for liquefaction potential. If liquefaction is likely to be a hazard the use of deep foundations or piling may be necessary in order to avoid unacceptable settlement or foundation failure during an earthquake. In most cases specialist advice on liquefaction should be taken. 3. Dynamic design parameters of soils:Dynamic properties of soils are strain dependent, according to the strain amplitude, it is divided into two categories: a) Large strain amplitudes (order of 0.01% to 0.1%) caused by earthquakes, blasts, and nuclear explosions. b) Small strain amplitudes (order of 0.0001% to 0.001%) caused by machines. The soils properties, which are needed in analysis and design of a structure, subjected to dynamic loading are (i) Dynamic moduli, such as young’s modulus E, shear modulus G, and bulk modulus K. (ii) Poisson’s ratio (iii) Dynamic elastic constants, such as co-efficient of elastic uniform compression cu, coefficient of elastic uniform shear cτ , coefficient of elastic non-uniform compression cΦ and coefficient of elastic nonuniform shear cΨ . (iv) Damping ratio ζ. (v) Liquefaction parameters, such as cyclic stress ratio, cyclic deformation and pore pressure response (vi) Strength-deformation characteristics in terms of strain rate effects. Various laboratory and field techniques have been developed to measure these properties over a wide range of strain amplitudes. Laboratory techniques:i. Resonant column test ii. Ultrasonic pulse test iii. Cyclic simple shear test iv. Cyclic torsional simple shear test, and v. Cyclic triaxial compression test. (i) Resonant column test:It is used to obtain the elastic modulus E, shear modulus G and damping characteristics of soils at low strain amplitudes. This test is based on the theory of wave propagation in prismatic rods. Either a cyclically varying axial load or torsional load is applied to one end of the prismatic or cylindrical specimen of soil. This is turn will propagate either a compression wave or a shear wave in the specimen. In this technique the excitation frequency generating the wave is adjusted until the specimen experiences resonance. The value of the resonant frequency is used in getting the value of E and G depending on the type of the excitation (axial or torsional). Several versions of torsional resonant columns device using different and conditions to constraint the test specimen are available. Some common and conditions used in developing the equipment are:
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a) Fixed – free: b) Free– free: c) Fixed –partially restrained: (ii) Ultra sonic pulse test: The theory of ultrasound is similar to that of audiable sound. Sound is the result of mechanical disturbance of a material that is a vibration. Ultrasonic pulsars of either compression or shear waves can be generated and received by suitable piezoelectric crystals. Using elastic theory, a relationship between the speed of propagation and wave amplitude of these waves and certain properties of the media through which they are traveling can be determined as follows. E=ρ v2c (1+ μ)(1-2 μ)/(1- μ); G= ρv2s; μ=(1-0.5(vc / vs)2) / (1-(vc / vs)2); δ=(2.302/n) * log10(A0/An); Where E = young’s modulus; ρ =mass density; vc =velocity of compression wave; μ =Poisson’s ratio; G =shear modulus; vs =velocity of shear wave; δ = logarithmic decrement A0= initial value of amplitude; An= amplitude after n oscillations; (iii) Cyclic simple shear-test: During an earthquake or other source of ground vibrations, a soils element below a foundation or in an embankment is subjected to an initial sustained stress together with a superimposed serious of repeated and reversals of shear stresses. The magnitude of induced shear stresses depends on the magnitude of acceleration of the dynamic force. In a direct shear box test, uniform state of shear strain occurs only on either side of failure plane. The simple shear device was designed to overcome this limitation of direct shear box by enabling a uniform state of shear strain throughout the specimen. This simulates the field conditions in a much better way. (iv) Cyclic torsional simple shear test:In cyclic simple shear apparatus, it is not possible to measure the confining pressure and the test is performed under consolidation conditions. A torsional simple shear device has been developed to overcome these difficulties. (v) Cyclic triaxial compression test:In one directional loading only compression of the sample is done while in two directional loading both compression and extension is done. In general the stressdeformation and strength characteristics of a soil depend on the following factors. Type of soil
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Relative density in case of cohesion less soils; consistency limits, water content and state of disturbance in cohesive soils. Initial static stress level i.e sustained stress Magnitude of dynamic stress No. of pulses of dynamic load Frequency of loading Shape of wave and form of loading One directional or two directional loading All the factors listed above can be studied lucidly on a triaxial setup. FIELD TESTS:Field methods generally depend on the measurement of velocity of waves propagating through the soil or on the response of soil structure systems to dynamic excitation. The following methods are in use for determining dynamic properties of soil. i. Seismic cross-borehole survey ii. Seismic up-hole survey iii. Seismic down-hole survey iv. Vertical block resonance test v. Horizontal block resonance test vi. Cyclic plate load test vii. Standard penetration test Seismic cross-borehole survey:This method is based on the measurement of velocity of wave propagation from one borehole to another. A source of seismic energy is generated at the bottom of one bore hole, and the time of travel of the shear wave from this bore hole to another at known distance is measured. Shear wave velocity is then computed by dividing the distances between the boreholes by the travel time. As discussed above, seismic cross borehole survey can be done using two boreholes one having the source for causing wave generation and another having geophone for recording travel time.
)
Seismic up-hole survey:In this method, the receiver is placed at the surface, and shear waves are generated at different depths within the borehole. The major disadvantage in seismic up-hole survey is that it is more difficult to generate waves of the desired type.
(ii)
Seismic down-hole survey:In this method , seismic waves are generated at the surface of the ground near the top of the borehole , and travel times of the body waves between the source and the receivers which have been clamped to the bore hole wall at predetermined depths are obtained. The main advantage of this method is that low velocity layers can be detected 125
even if trapped between the layers of greater velocity provided geophone spacing are close enough. (iii)
Vertical block resonance test:This test is used for the determining the values of coefficient of elastic uniform compression, young’s modulus and damping ratio of the soil. According to IS-5249: 1984, a test block size 1.50 x 0.75 x 0.70 m is cast in M15 concrete in a pit of plan dimensions 4.50 x 2.75 m and depth equal to the proposed depth of foundation. Foundation bolts should be embedded in to the concrete block at the time of casting for fixing the oscillator assembly. The line of action of the vibrating force should pass through the center of gravity of the block. Two acceleration displacement pickups are mounted on the top of the block such that they sense the vertical motion of the block. (v)Horizontal block resonance test:This test setup is similar to that of Vertical block resonance test, only change is Three acceleration displacement pickups are mounted on the side of the block such that they sense the horizontal motion of the block. (vi)Cyclic plate load test:The cyclic plate load test is performed in a test pit dug up to the proposed base level of foundation. The equipment is same as used in static plate load test. Circular or square bearing plates of mild steel not less than 25mm thickness and varying in size from 300 to 750mm with chequred or grooved bottom are used. The test pit should be at least five times the width of the plate. To commence the test , a seating pressure of about 7Kpa is first applied to the plate. It is then removed and dial gauges are set to read zero. Load is then applied in equal cumulative increments of not more than 100Kpa or of not more than one fifth of the estimated allowable bearing pressure. In cyclic plate load test ,each incremental load is maintained constant till the settlement of the plate is completed .The load is then released to zero and the plate is allowed to rebound . The reading of final settlement is taken . The load is increased to next higher magnitude of loading and maintained constant till the settlement is complete , which again is recorded . The load is then reduced to zero and the settlement reading is taken . The next increment of load is then applied . The cycles of unloading and reloading are continued till the required final load is reached. From these data ,the load intensity versus elastic rebound is plotted ,and the slope of the line is coefficient of elastic uniform compression. Cu = P / Se
(in KN/m3)
Where, P = Load intensity ,(KN/m2) Se = Elastic rebound corresponding to P. (in m) (vii) Standard Penetration Test :
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The SPT is the most extensively used in-situ test in India and many other countries. These test is carried in a bore hole using a split spoon sampler as per IS :21311981. DYNAMIC EARTH PRESSURE ON RETAINING WALLS In the seismic zones, the retaining walls are subjected to dynamic earth pressure, the magnitude of which is more than the static earth pressure due to ground motion. Since a dynamic load is repetitive in nature there is a need to determine the displacement of the walls due to earthquakes and their damage potential. This becomes essential if the frequency of dynamic load is likely to be closed to the natural frequency of the wall –backfill-foundations- base soil systems. This essentially consists in writing down the equation, motion of the system under free and forced vibrations. This requires the information on the distribution of back fill soil mass and base soil mass participating in vibrations .It is often difficult to assess these. Therefore, more often, pseudo-static analysis is carried out for getting dynamic earth pressure. In this method, an equivalent static force replaces the dynamic force. PSEUDO-STATIC METHOD: Mononobe-okabe theory:- Mononobe-okabe (1929) modified classical coulomb’s theory for evaluating dynamic earth pressure by incorporating the effect of inertia force .
Figure shows a wall of height (H) and inclined vertically at an angle α retaining cohessionless soil with unit weight γ and angle of shearing resistance Φ . BC1 is the trial failure plane, which is inclined to vertically by an angle θ. The backfill is inclined and making an angle (i) with horizontal. During an earthquake the inertia force may act an assumed failure wedge ABC1 both horizontally and vertically. If ah and av are the horizontal and vertical accelerations
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caused by the earthquake in the wedge ABC1 .The corresponding inertial forces are W1.ah/g horizontally and W1.av/g vertically , W1 being the weight of wedge . During the worst condition W1.ah/g acts towards the fill and W1.av/g acts vertically over either in the downward or upward directions. Therefore the direction that gives the maximum increasing earth pressure is adopted in practice. Weight W1 and the inertia forces W1 .αh and ± W1 . αv can be combined to give a resultant W ,where W = W1 {(1± αv)2 + αh2}1/2 The resultant W is inclined with vertical at angle Ψ, such that Ψ = tan-1 (αh/1± αv) The direction of all the three forces W, P & R are known at the magnitude of only one force W is known .The magnitude of the other forces can be obtained by considering the force polygon. Mononobe & okabe (1929) gave the following relation for the computation of dynamic active earth pressure. (PA) dyn = 1/2 γH2 (KA) dyn Where - (KA) dyn is co-efficient of dynamic active earth pressure and given by (KA) dyn = {(1± αv) cos2 (Φ-Ψ –α)/(cosΨ. Cos2α.cos (δ + α +Ψ)} X [1/{1+(sin (Φ+δ). sin (Φ-i-Ψ)/(cos(α- i).cos(δ+α+Ψ)}1/2]2 Mononobe & Okabe (1929) gave the following relation for the computation of dynamic Passive earth pressure . (PP) dyn = 1/2 γH2 (KP) dyn Where - (KP) dyn is co-efficient of dynamic passive earth pressure and given by (KP) dyn = {(1± αv) cos2 (Φ-Ψ +α)/(cosΨ. cos2α.cos (δ - α +Ψ)}X [1/{1-(sin (Φ+δ). sin (Φ+ i-Ψ)/(cos(α- i).cos(δ-α+Ψ)}1/2]2 Stability of retaining walls: Factor of safety Case In an earthquake conditions Sliding ≥ 1.2 Overturning ≥1.5
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In static conditions ≥1.5 ≥2.0
Bearing failure Slip failure
≥2.0 ≥1.3
≥3.0 ≥1.5
Problem: A 6m height retaining wall with back face inclined 20o with vertical retains cohessionless backfill (Φ = 33o,γ=18 kN/m3,δ = 20o).The backfill surface is sloping at an angle 10o to the horizontal ,if the retaining wall is located in a seismic region(αh=0.1) determine the total static and dynamic active earth pressure. Solution: Static active earth pressure: PA=0.5 γH2 {cos2 (Φ-α)/(Cos2α.cos (δ + α)}* [1/{1+(sin (Φ+δ). sin (Φ-i)/(cos(α- i).cos(δ+α)}1/2]2 =168.42KN/m Dynamic active earth pressure: Assuming αv= (αh/2) =0.1/2=0.05 Ψ = tan-1 (αh/1± αv) Ψ = tan-1 (0.1/1± .05); =5.440(+αv) or
60 (-αv)
(PA) dyn = 0.5 γ H2 {(1± αv) cos2 (Φ-Ψ –α)/(cosΨ. Cos2α.cos (δ + α +Ψ)}* [1/{1+(sin (Φ+δ). sin (Φ-i-Ψ)/(cos(α- i).cos(δ+α+Ψ)}1/2]2 For Ψ=5.440 (PA) dyn = 214.26 KN/m For Ψ=60 (PA) dyn = 198.05 KN/m Therefore + αv case governs the value of dynamic active earth pressure.
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