elastic and dynamic analysis of a multistorey frame

1. ELASTIC AND DYNAMIC ANALYSIS OF A MULTISTOREY FRAME By Nayan Kumar Dutta

2. What is an Earthquake ? Sudden movement of the earths crust 90% of all earthquakes result from movements on geological faults tectonic earthquakes Earthquakes are generally natural disasters of unpredictable nature. But due to human activity such as construction of large dams and reservoirs, mine blasts, nuclear tests, etc earthquake may be generated.

3. Causes of Earthquakes Plate Tectonics Elastic Rebound Theory

4. Theory of Plate Tectonics The lithosphere if fragmented into seven major tectonic plates and many smaller ones. Due to convection current in viscous mantle these plates move in different directions and at different speeds from those of the neighbouring ones.

5. Elastic Rebound Theory Most boundaries of the plates have irregularities and this leads to a form of stick-slip behaviour. Once the boundary has locked, continued relative motion between the plates leads to increasing stress and stored strain energy in the volume around the fault surface. This continues until the stress has risen sufficiently to overcome the strength of the rock, suddenly allowing sliding over the locked portion of the fault, releasing the stored energy that spreads out through seismic waves that causes earthquakes.

6. Focus and Epicentre The point within the earth from which the earthquake originates is the Focus or Hypocenter. The point on the earths surface lying vertically above the focus is the Epicenter. Distance from epicenter to any point of interest is called epicentral distance. The depth of focus from the epicenter, is the Focal Depth, shallow focus earthquakes with focal depths less than about 70km are the most damaging.

7. How are Earthquakes Located? P wave travels faster than S wave. The difference in arrival time between the two types of seismic waves can be used to calculate the distance of the earthquake's epicentre from the measuring station. DE = DeltaT x (VP VS) / (VP - VS) where DE = Distance to epicentre (km) DeltaT = Difference between P and S-wave arrival time (s) VP = P-wave velocity (km/s) VS = S-wave velocity (km/s)

8. A circle with a radius equal to the distance to the epicentre is plotted around the seismograph station. This is then repeated for the other two stations and the point where the three circles intersect is the location of the earthquakes epicentre.

9. Measerement of earthquake(Magnitude &Intensity) Magnitude is a quantitative measure of the size of an earthquake. There is only one magnitude per earthquake. Richter defined the magnitude of an earthquake as the logarithm to base 10 of the maximum seismic wave amplitude (in microns) recorded on a standard seismograph at a distance of 100 km from the epicentre An increase in magnitude (M) by 1.0 means that the amplitude of the earthquake waves increases 10 times. Earthquake magnitude is related to the amount of energy released in the earthquake. log10 E = 11.8 + 1.5M, where, energy, E, is in ergs Other magnitude scales are Surface wave magnitude, Body wave magnitude, Duration magnitude and Moment Magnitude (MW).

10. Intensity of an Earthquake Intensity is a qualtitative measure of the severity of shaking at a location during an earthquake. The severity of shaking is much higher near the epicenter than farther away. Intensity scales are - Rossi-Forel intensity scale (developed in the late 19th century) ten stages Mercalli intensity scale (1902) twelve stages Modified Mercalli Intensity (MMI) scale (1931) Medvedev-Spoonheuer-Karnik (MSK) intensity scale (1964) Both scales are quite similar and range from I (least perceptive) to XII (most severe).

11. Details of MSK Intensity Scale

12. Recently in Nepal Earthquake (of 7.8 magnitude) more than 18,000 people died.

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15. So the social consequences of earthquakes, in terms of human casualties and injuries and direct and indirect economic losses justify the need to be prepared for earthquakes. Earthquakes are still difficult to predict So,we should prepare for earthquake by making our buildings with proper structural design procedure.

16. Indian Codes relevant to Earthquake Engineering IS 1893 - 2002: Criteria for earthquake resistant design of structures. IS 13920 - 1993: Code of practice for ductility detailing of reinforced concrete structures subjected to Seismic forces. IS 4326 - 1993: Earthquake resistant design and construction of buildings code of practice. IS 13828 - 1993: Improving Earthquake resistance of low strength masonry buildings - Guidelines. IS 13827 - 1993: Guidelines for improving earthquake resistance - Earthen Buildings. Among these codes in our project we have used IS 1893- 2002,IS13920-1993 and IS 875.

17. Method of seismic Analysis 1. Linear static analysis (or equivalent static analysis) : Applicable for regular structures and low rise buildings. 2. Linear dynamic analysis :- can be performed either by response spectrum method (mode superposition method like SRSS,CQC) or by elastic time history method. 3. Non-linear static analysis:- 4. Non-linear dynamic analysis:- Describe the actual behaviour of the structure during an earthquake.

18. Slabs forces the beam to bend with it when horizontal forces act.

19. The philosophy of earthquake design for structures is: In frequent, minor ground shaking - Main structural members should not be damaged, other building parts may have repairable damage In occasional, moderate ground shaking - Main structural members may sustain reparable damage, other building parts may have to be replaced In rare, major ground shaking Structural members may be irreparably damaged but the structure should not collapse General Goals in Seismic-Resistant Design and Construction Courtesy: IITK-BMTPC EQ. Tips

20. After minor shaking, the building will be fully operational within a short time and the repair costs will be small. After moderate shaking, the building will be operational once the repair and strengthening of the damaged main members are completed. After a strong earthquake, the building may become unsuitable for further use, but will stand so that inhabitants can be evacuated. Important buildings, like hospitals and fire stations, play a critical role in post- earthquake activities and must remain functional immediately after the earthquake. Collapse of dams during earthquakes can cause flooding. Damage to sensitive facilities like nuclear power plant, chemical plants, etc. can cause a further disaster. These structures must sustain very little damage and should be designed for a higher level of earthquake protection.

21. Seismic Zoning Map of India In 1935, GSI prepared a seismic hazard map of three zones depicting likely damage scenario (severe, moderate, light). By evaluating peak horizontal ground acceleration based on earthquake data from 1904-1950, Jai Krishna developed a 4-zone seismic map in 1958. The Indian peninsular regions were not given any seismic consideration as it was considered to be a stable plateau. BIS provided a seismic zone map in IS: 1893-1962 with seven zones based on isoseismals of major earthquakes and average intensity attenuation relationship. Past smaller earthquakes, trend of principal tectonic features and local ground conditions were also considered. For Zone 0 (intensity less than V) seismic loading on the structure need not be considered.

22. Koyna earthquake of 1967 (magn. 6.5) in Peninsular India caused the revision of the seismic zone map in IS: 1893-1970. Number of zones was reduced to five (based on five seismo-tectonic units of the country). Due to the Latur earthquake (magn. 6.2) in 1993, the seismic status of the Indian peninsular shield was again reviewed. The IS 1893-2002 map has only four zones. Zone I has been enhanced to Zone II. Enhanced extent of Zone III (Chennai is now in Zone III, previously in Zone II). This 2002 seismic zone map is not the final word on the seismic hazard of the country, and hence there can be no sense of complacency in this regard! The decision of the BIS is to have a new revised zoning map using probabilistic framework. To account for new available information, the shapes of some of the isoseismals were changed and the extent of Zone 0 in the southern part of the Indian Peninsula was reduced in the seismic zone map of IS: 1893-1966

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25. EARTHQUKE LOAD DESIGN (STATIC EQUIVALENT METHOD) Z = zone factor = 0.16 (zone-3) I = importance factor = 1.5 The structure is a special RC moment resisting frame (SMRF) R = Response reduction factor = 5 Factored dead load on each floor = 3.725 kN/m2 Live load on each floor = 4 kN/m2 EQ in X direction, Ta = 0.508. For type 3 Soil, Sa/g = 2.5. Dead Load from beam on each floor = 434.49 kN Dead Load from column on each floor = 205.8 kN Dead load from column on ground level = 176.4 kN Dead load from wall (2nd from 6th floor) = 1556.526 kN Dead load from wall (ground floor) = 778.31 kN Dead load from wall (roof level) = 862.31 kN

26. DEAD LOAD ON ROOF Dead Load from Slab = 3.445 kN/m2 Dead Load from column = 102.9 kN Total Load, On Ground Level = 3040.40 kN On Floor level (2nd to 6th) = 3846.20 kN On Roof level (7th) = 2393.90 kN Horizontal Acceleration (Ah) = (1.5/5) x (0.16/2) x (2.5) = 0.06 Total weight of ll the floor = 28510.9 kN DESIGN BASE SHEAR V b = Ah x W = (0.06 x 28510.9) kN = 1710.65 kN EQ in Z direction, d = 14.5, Ta = 0.638, Horizontal Acceleration (Ah) = (1.5/5) x (0.16/2) x (2.13) = 0.05112 DESIGN BASE SHEAR V b = Ah x W = (0.05112 x 28510.9) KN = 1457.47 kN

27. 40 A plot of the peak value of a response quantity to a ground motion time history, as a function of the natural vibration period, Tn, or natural frequency, wn, of the system is called the response spectrum for that quantity. Each such plot is for SDOF systems having a fixed damping ratio, z, and several such plots for different values of z are included together in one graph to cover the range of z values for real structures. What is Response Spectrum ? zz zz zz ,,max, ,,max, ,,max, nno nno nno TtuTu TtuTu TtuTuD

28. 41 Deformation Response Spectrum El Centro ground motion

29. 42 Response Spectra (z = 2%) for El Centro ground motion Deformation Response Spectrum Pseudo-velocity Response Spectrum Pseudo-acceleration Response Spectrum

30. 43 Why do we need three spectra when each of them contains the same information ? Each spectrum provides a physically meaningful quantity. Deformation spectrum provides peak deformation Pseudo-velocity spectrum directly related to peak strain energy of the system Pseudo-acceleration spectrum directly related to the peak equivalent static force and base shear

31. 44 Tripartite Response Spectrum for El Centro ground motion

32. 45 Mean and mean +1s spectra. Dashed lines show an idealized design spectrum.

33. 46 As per IS 1893(Part 1) : 2002

34. Masses are connected to each other and to a supporting point by linear springs and viscous dashpots.

35. 48 Each characteristic deflected shape Mode Shape So for a N-DOF system there exist N mode shapes and N natural frequencies. Note: Any ith mode shape has (i-1) nodes (points of zero displacement). NODE

36. 49 Modal Combination Rules The maximum or peak of the desired response quantity is first obtained for each mode and then these modal maxima are combined according to a modal combination rule. 1.Square Root of Sum of Squares (SRSS) Method:- Assumed that the modes achieve peak responses at randomly distributed time instants. It provides a very good approximation of the peak response for modes with well-separated natural frequencies but fails for closely spaced modes 2.Complete Quadratic Combination (CQC) Method:- Based on the use of cross-modal coefficients, it is an improvement over the SRSS method and applicable to a wide class of structures. In this method all possible quadratic combinations are incorporated.

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38. All forces are in kN

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40. 56 SRSS

41. 57 SRSS

42. 58 CQC

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44. 60 Ductility is the ability of a member to deform beyond its elastic limit without failure. Ductility Concrete and masonry are brittle. Steel is ductile. Courtesy: IITK-BMTPC EQ. Tips

45. 61 Ductile and Brittle Failure Courtesy: IITK-BMTPC EQ. Tips

46. 62 Ductile Chain design As more and more force is applied, the chain will eventually break when the weakest link in it breaks. If the ductile link is the weak one (i.e., its capacity to take load is less), then the chain will show large final elongation. Instead, if the brittle link is the weak one, then the chain will fail suddenly and show small final elongation. Thus, to design a ductile chain, the ductile link has to be made the weakest link. Courtesy: IITK-BMTPC EQ. Tips

47. 63 Strong-Column Weak-Beam Design The beams should be made the ductile weak link in the chain and not the columns because the failure of a column affects the stability of the whole building while the failure of a beam has a localized effect. Strong-Column Weak-Beam Design Method Courtesy: IITK-BMTPC EQ. Tips

48. 64 Design Provisions for Ductility IS codes (such as IS 13920 : 1993) enforce ductility specifications with the following objectives: Provide large capacity for inelastic deformations. Prescribe relative strengths of different members to control failure mechanism at joints. Permit structure to undergo large inelastic deformations before collapse fail-safe design philosophy.

49. Clause 7.4.5 :-Special confining reinforcement shall be provided over the full height of column which has significant variation in stiffness along its height. This clause deals with short column effect.

50. Ductile detailing of beam

51. Ductile detailing of column

52. 6 d ( ! 65 mm ) 6 d ( ! 65 mm )

53. Earthquake resisting materials1.Masonry Masonry is made up of burnt clay bricks and cement or mud mortar. Masonry can carry loads that cause compression (i.e. pressing together) but can hardly take load that causes tension (i.e. pulling apart). Masonry is a brittle material, these walls develop cracks once their ability to carry horizontal load is exceeded. 2.Concrete Concrete is another material that has been popularly used in building construction particularly over the last four decades. Cement concrete is made of crushed stone pieces (called aggregate), sand, cement and water mixed in appropriate proportions. Concrete is much stronger than masonry under compressive loads, but again its behavior in tension is poor. 3. Steel Steel is used in masonry and concrete buildings as reinforcement bars of diameter ranging from 6mm to 40mm. reinforcing steel can carry both tensile and compressive loads. Moreover steel is a ductile material.

54. Approaches for Earthquake-Resistant Design of Structures First Approach : Design the structure with sufficient strength, stiffness and inelastic deformation capacity. Second Approach : Use of control devices to reduce the forces acting on the structure. Control devices may be defined as external structural protective systems that reduce the energy dissipation demand on primary structural members when the structure is subjected to external input energy.

55. Classification of Control Systems

56. 1.Passive Control Systems:- These do not require power to operate hence termed passive Systems in this category are very reliable since they are unaffected by power outrages, which are common during earthquakes. 2.Active Control System:- These require considerable amount of external power, in the order of tens of kilowatts They are more effective than passive devices because of their ability to adapt to different loading conditions and to control different modes of vibration Since the large amount of power required for their operation may not always be available during seismic events, they are not very reliable. 3. Semi-Active Control Systems:- cannot inject energy into the controlled system, but their mechanical properties can be adjusted to improve these performance. These are often viewed as controllable passive devices. 4. Hybrid Control Systems:- Combined passive and active control systems less power and resources are required than active control systems

57. COMPARISION OF DIFFERENT CATEGORIES OF CONTROL SYSTEMS

58. Types of Passive Control Systems Base Isolation Systems Metallic Dampers Friction Dampers Viscoelastic Dampers Fluid Viscous Dampers Tuned Mass Dampers Tuned Liquid Dampers Shape Memory Alloy Dampers

59. Base Isolation Systems One of the most powerful tools of earthquake engineering, applicable for new structures as well as for the retrofit of existing structures. It is the only practical way of reducing simultaneously inter-story drift and floor acceleration

60. 84 Structural Response with and without Base Isolation Model of a one story building without base isolation SDOF system Model of a one story building with base isolation 2-DOF system c1 c2

61. Base isolation drastically reduces the fundamental frequency of the system Fixed Base Base Isolated Period

62. 86 Base Isolation Systems Elastomeric-type Lead Rubber Bearing Sliding-type Elastomeric Bearing with steel shims (Laminated Rubber Bearing) High Damping Rubber Bearing Super- high Damping Rubber Bearing Friction Pendulum System

63. 87 Elastomeric Rubber Bearing Made from natural rubber or neoprene. Improved by vulcanization bonding of sheets of rubber and thin steel reinforcing plates or steel shims laminated rubber bearing. The steel shims reduce the vertical deformation of the bearing and lateral bulging of the rubber layer. Critical damping is of the order of 2% -3% low damping bearing Easily manufactured at comparatively low cost, are unaffected by time and resistant to environmental degradation. .

64. 88 Used as bridge bearing and vibration isolator for buildings Elastomeric Rubber Bearing.contd.

65. 89 Lead Plug Bearing Disadvantage of elastomeric bearings low damping property can be overcome by plugging a lead core into the bearing. A hole is introduced in the center of the elastomeric bearing and a lead plug is tightly fitted into that hole. The bearing is designed so that it is very stiff and strong in the vertical direction but flexible enough in the horizontal direction. Top and bottom of the bearing are fitted with steel plates which are used to attach the bearing to building through its foundation. Critical damping 15% - 35%

66. 90 Lead Plug Bearing.contd.

67. 91 High Damping Rubber Bearing (HDRB) Another way to increase the damping is to modify the rubber compounds. The modification is to add carbon black or other types of filler material with rubber. Damping obtained 10% - 15% of critical. Super high damping rubber bearing (HDRB-S) has damping 20% higher than that of conventional HDRB and very stable against cyclic deformation during a large-scale earthquake.

68. 92 Sliding Systems This works by limiting the transfer of shear across the isolation interface. In China there are at least three buildings on sliding systems that use a specially selected sand at the sliding interface. A type of isolation containing a lead-bronze plate sliding on stainless steel with an elastomeric bearing has been used for a nuclear power plant in South Africa.

69. CONCLUSION Earthquake is still unpredictable. So we should design our structures with proper Earthquake Codal provisions.Strict laws should be enforced by the Government for following the codes. Codes should be revised on the basis of probabilistic approaches. So, by using these we can cope up with earthquake effects. 93

70. References 1. IS: 1893-2002 2. IS:13920-1993 3. IS: 875(Part I,Part II) 94