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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14. 16
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
23. 27
24. 28
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.
37. (s)
38. All forces are in kN
39. 55
40. 56 SRSS
41. 57 SRSS
42. 58 CQC
43. 59
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