Seismic FORCE ESTIMATION IS 18931893 - 2002 1893-2002
The material contained in this lecture handout is a pr operty of Professors Sudhir K. Jain, C.V.R.Murty and Durgesh C. Rai of IIT Kanpur, and is for the sole and exclusive use of the participants enrolled in the short course on Seismic Design of RC Structures conducted at Ahmedabad during Nov 26-30, 2012. It is not to be s old, reproduced or generally distributed.
Durgesh Durgesh C. Rai Department of Civil Engineering, IIT Kanpur 1
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Structure of Revised IS:1893 • Since 1984: – More information – More experience
Detailed Provisions
– Practical difficulties
• IS 1893: From 2002 onwards… Part 1 Part 2
EQ Behaviour is different!!
Part 3 Part 4 Part 5
:: General Provisions and Buildings :: Liquid Retaining Tanks – Elevated/ Elevated/Ground Ground Supported Supported :: Bridges and Retaining Walls :: Industrial and Stack-like Structures :: Dams and Embankments
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IS:1893-2002
IS:1893 first published in 1962.
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Revised in 1966, 1970, 1975, 19 84, and now in 2002. Beginning 2002, this code is being split into several parts
What does IS:1893 Cover?
Specifies Seismic Design Force Other seismic requirements for design, detailing and construction are covered in other codes
So that revisions can take place more frequently!
Only Part 1 and 4 of the code has been published.
e.g., IS:4326, IS:13920, ...
For an earthquake-resistant structure, one has to follow IS:1893 together with seismic design and detailing codes.
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Coverage of Part 1
General Provisions
Major Changes
Applicable to all structures
Provisions on Buildings To address the situation that other parts of the code are not yet released, Note on page 2 of the code says in the interim period, provisions of Part 1 will be read along with the relevant clauses of IS:1893-1984 for structures other than buildings
This can be problematic. For instance, what value of R to use for ov erhead water tanks?
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Zone Map
Zone Map (contd…)
1962 and 1966 maps had seven zones (0 to VI)
In 1967, Koyna Koyna earthquake (M6.5, (M6.5, about 200 killed) occurred in zone I of 1966 map In 1970 zone map revised:
Zones O and VI dropped; only fiv e zones
Latur (1993) earthquake (mag. 6.2, about about 8000 deaths) in zone I! Revision of zone map in 2002 edition Zone I has been merged upwards into zone II.
No change in map in 1975 and 1984 editions
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Now only four zones: II, II I, IV and V.
In the peninsular India, some parts of zone I and zone II are now in zone III.
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Zone Map (contd…)
Zone Map (contd…)
Notice the location of Allahabad and Varanasi in the new zone map. There is an error and the locations of these two cities have been interchanged in the map. Varanasi should be in zone III and Allahabad in zone II.
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Since the code has been revised after a very long time (~18 years), there are many significant changes. Some of the philosophical changes are discussed in Foreword of the code.
Also notice another error in the new zone map Location of Calcutta has been shown incorrectly in zone IV Calcutta is in fact in zone III
Annex E of the code correctly lists Kolkata is i n zone III.
The Annex E of the code giv es correct zones for these two cities
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Coverage of Part 1
General Provisions
Major Changes
Applicable to all structures
Provisions on Buildings To address the situation that other parts of the code are not yet released, Note on page 2 of the code says in the interim period, provisions of Part 1 will be read along with the relevant clauses of IS:1893-1984 for structures other than buildings
This can be problematic. For instance, what value of R to use for ov erhead water tanks?
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Zone Map
Zone Map (contd…)
1962 and 1966 maps had seven zones (0 to VI)
In 1967, Koyna Koyna earthquake (M6.5, (M6.5, about 200 killed) occurred in zone I of 1966 map In 1970 zone map revised:
Zones O and VI dropped; only fiv e zones
Latur (1993) earthquake (mag. 6.2, about about 8000 deaths) in zone I! Revision of zone map in 2002 edition Zone I has been merged upwards into zone II.
No change in map in 1975 and 1984 editions
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Now only four zones: II, II I, IV and V.
In the peninsular India, some parts of zone I and zone II are now in zone III.
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Zone Map (contd…)
Zone Map (contd…)
Notice the location of Allahabad and Varanasi in the new zone map. There is an error and the locations of these two cities have been interchanged in the map. Varanasi should be in zone III and Allahabad in zone II.
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Since the code has been revised after a very long time (~18 years), there are many significant changes. Some of the philosophical changes are discussed in Foreword of the code.
Also notice another error in the new zone map Location of Calcutta has been shown incorrectly in zone IV Calcutta is in fact in zone III
Annex E of the code correctly lists Kolkata is i n zone III.
The Annex E of the code giv es correct zones for these two cities
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Preface
Other Effects
It is clear that the code is meant for normal structures,, and structures
For special structures, site-specific seismic design criteria should be evolved by the specialists.
Read second para, page 3 Earthquakes can cause damage in a number of ways. For instance:
Vibration of the structure: this induces inertia force on the structure
Landslide triggered by earthquake
Liquefaction of the founding strata
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Fire caused due to earthquake Flood caused by earthquake
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Intensity versus Magnitude
Other Effects (contd…)
The code generally addresses only the first aspect: the inertia force on the structure. The engineer may need to also address other effects in certain cases.
It is important that you understand the difference between Intensity and Magnitude Magnitude tells
How strong was the vibration at a l ocation Depends on magnitude, distance, and local soil and geology
Read more about magnitude and intensity at:
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How big was the earthquake How much energy was released b y earthquake
Intensity tells
http://www.nicee.org/EQTips/EQTip03.pdf
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Seismic Hazard
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By inertia force, we mean mass t imes acceleration
Shaking Intensity
Last para para on page page 3
The criterion for seismic zones remains same as before Zone
Area liable to shaking intensity
II
VI (and lower)
III
VII
IV
VIII
V
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Shaking intensity is commonly measured in terms of Modifi Modified ed Mercalli Mercalli scale or MSK scale. scale.
See Annex. D of the code for M SK Intensity Scale
There is a subtle change: Modified Mercalli intensity is replaced by MSK intensity! In practical terms, both scales are same. Hence, it does not really matter.
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Zone Criterion
Peak Ground Acceleration
Our zone map is based on likely intensity.
It does not address the question: how often such a shaking may take place. For example, say Area A experiences max intensity VIII every 50 years, Area B experiences max intensity VIII every 300 years Both will be placed in zone IV, even though area A has higher seismicity
Maximum acceleration response of a rigid system (Zero (Zero Period Acceleration) Acceleration ) is same as Peak Ground Acceleration (PGA). Hence, for very low values of period, acceleration spectrum tends to be equal to PGA.
Current trend world wide is to
We should be able to read the value of PGA from an acceleration spectrum.
Specify the zones in terms of ground acceleration that has a certain probability of being exceeded in a given number of years.
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Typical shape of acceleration spectrum
Peak Ground Acceleration (contd…)
1.80
Average shape of acceleration response response spectrum for 5% damping (Fig. on next slide)
1.40
Ordinate at 0.1 to 0.3 sec ~ 2.5 ti mes the PGA
n1.20 o i t a r e l e c1.00 c A l a r t 0.80 c e p S
There can be a stray peak in the ground motion; i.e., unusually large peak.
1.60
) g (
Such a peak does not affect most of the response spectrum and needs to be i gnored.
Effective Peak Ground Acceleration (EPGA) defined as 0.40 times the spectral acceleration in 0.1 to 0.3 sec range (cl. 3.11)
0.60 0.40
PGA = 0.6g
0.00 0.0
1.0
1.5
2.0 2. 5 Period (sec)
3. 0
3. 5
4.0
4. 5
•Spectral acceleration at zero period (T=0) gives PGA •Value at 0.1-0.3 sec is ~ 2.5 times PGA value
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Earthquake Level
Earthquake Level (contd…)
Maximum Credible Earthquake (MCE):
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0.5
•Typical shape of acceleration response spectrum
There are also other definitions of EPGA, but we will not concern ourselves with those.
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0.20
Largest reasonably conceivable earthquake that appears possible along a recognized fault (or within a tectonic province). It is generally an upper bound of expected magnitude. Irrespective of return period of the earthquake which may range from say 100 years to 10,000 years. Usually evaluated based on geological evidence
Other terms used in literature which are somewhat similar to max credible EQ:
Max Possible Earthquake
Max Expectable Earthquake
Max Probable Earthquake Max Considered Earthquake
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Max Considered EQ (MCE)
Term also used in the International Building Code 2000 (USA)
IS:1893
Corresponds to 2% probability of being exceeded in 50 years (2,500 year return period) 10% probability of being exceeded in 100 years (1,000 year return period)
For the same tectonic province, MCE based on 2,500 year return period will be larger than the MCE based on 1,000 year return period
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Design Basis EQ (DBE)
Design Basis EQ (DBE) (contd...)
This is the earthquake motion for which structure is to be designed c onsidering inherent conservatism in the design process
Cl. 3.6 of the code (p. 8)
UBC1997 and IBC2000:
Earthquake that can reasonably be expected to occur once during the design life of the structure
Corresponds to 10% probability of being exceeded in 50 years (475 year return period)
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What is reasonable…not reasonable…not made clear in our code. code. Also, design life of different structures may be different.
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MCE versus DBE
IBC2000 provides for DBE as two-thirds of MCE
IS1893 provides for DBE as one-half of MCE
Modal Mass
The factor 2 in denominator denominator of eqn for Ah on p.14 accounts for this See definition of Z on p.14 of the code
It is that mass of the structure which is effective in one particular natural mode of vibration Can be obtained from the equation in Cl. 7.8.4.5 for simple lumped mass systems
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MCE motion as per Indian code does not correspond to any specific probability of occurrence or return period.
Uniform Building Code 1997 (USA)
Max Considered EQ (MCE) (contd...)
It requires one to know the mode shapes One must perform dynamic analysis to obtain mode shapes
Next slides to appreciate the physical significance of Modal Mass
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Example on Modal Mass
Example on Modal Mass (contd…)
Three degrees of freedom system Total mass of structure: 100,000kg 5% damping assumed in all modes To be analyzed for the ground motion for which acceleration response spectrum is given here.
First mode of vibration:
Period (T1)=0.6sec, Modal Mass= 90,000kg
Spectral acceleration = 0.87g
Max Base shear contributed by first mode =
g , n o i t a r e l e c c A
Obtained using first mode shape Read from Response Spectrum for T=0.6sec
= (90,000kg)x(0.87x9.81m/sec 2 ) = 768,000 N = 768 kN
m u m i x a M
Undamped Natural Period T (sec)
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Modal Participation Factor (Cl.3.21)
Example on Modal Mass (contd...)
Second mode of vibration:
Period (T2)=0.2sec Modal Mass=8,000kg
Spectral acceleration (for T1=0.2sec) = 0.80g
Max Base shear contributed by second mode =
A term used in dynamic analysis.
Read the definition in Cl. 3.21
“amplitudes of 95% mode shapes” should be read as “amplitude of mode shapes”
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Seismic Weight (Cl.3.29)
Seismic Mass (Cl.3.28)
It is the total weight of the building plus that part of the service load which may reasonably be expected to be attached to the building at the time of earthquake shaking.
It includes permanent and movable partitions, permanent equipment, etc. It includes a part of the live load
It is seismic weight divided by acceleration due to gravity That is, it is in units of mass (kg) rather than in the units of weight (N, or kN) In working on dynamics related problems, one should be careful between mass and weight.
Buildings designed for storage purposes are likely to have larger percent of service load present at the time of shaking.
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There seems to be a typographical error.
= (8,000kg)x(0.80x9.81m/sec 2 ) = 62,800 N = 62.8 kN
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More later
Mass times gravity is weight 1 kg mass is equal to 9.81N (=1x9.81) weight
Notice the values in Table 8 36
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Centre of Stiffness
Section 4 Terminology on Buildings
Cl. 4.5 defines Centre of Stiffness as The point through which the resultant of the restoring forces of a system acts. It should be defined as:
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Centre of Rigidity
Eccentricity
In cl. 4.21, while defining static eccentricity, Centre of Rigidity is used. Both Centre of Stiffness (CS) and Centre of Rigidity (CR) are the same terms for our purposes!
Cl. 4.21 defines Static Eccentricity.
Experts will tell you that there are subtle differences between these two terms. But that is not important from our view point.
This is the calculated distance between the Centre of Mass and the Centre of Stiffness.
Under dynamic condition, the effect of eccentricity is higher than that under static eccentricity.
It would have been better if the code had used either stiffness or rigidity throughout
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Hence, a dynamic amplification is to be applied to the static eccentricity before it can be used in design.
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Dual System
Eccentricity (contd…)
An accidental eccentricity is also considered because:
The computation of eccentricity is onl y approximate. During the service life of the bui lding, there could be changes in its use which may change centre of mass.
Consider buildings with shear walls and m oment resisting frames. In 1984 version of the code, Table 5 (p. 24) implied that the frame should be designed to take at least 25% of the t otal design seismic loads.
Design eccentricity (cl.4.6) is obtained from static eccentricity by accounting for (cl.7.9.2)
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If the building undergoes pure translation in the horizontal direction (that is, no rotation or twist or torsion about vertical axis), the point through which the resultant of the restoring forces acts is the Centre of Stiffness
Dynamic amplification, and Accidental eccentricity 42
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Dual System (contd…)
Dual System (contd…)
In the new code several choices are available to the designer:
When conditions of Cl. 4.9 are met: dual system.
Example 1: Analysis indicates that frames are taking 30% of total seismic load while 70% loads go to shear walls. Frames and walls will be designed for these forces and the system will be termed as dual system. Example 2: Analysis indicates that frames are taking 10% and walls take 90% of the total seismic load. To qualify for dual system, design the walls for 90% of total load, but design the frames to resist 25% of total seismic load
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Frames are not designed to resist seismic loads. The entire load is assumed to be carried by the shear walls. In Example 2 above, the shear walls will be designed for 100% of total seismic loads, and the frames will be treated as gravity frames (i.e., it is assumed that frames carry no seismic loads) Frames and walls are designed for the forces obtained from analysis, and the frames happen to carry less than 25% of total load. In Example 2 above, the frames will be designed for 10% while walls will be designed for 90% of total seismic loads.
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Moment Resisting Frame
Dual System (contd…)
Clearly, the dual systems are better and are designed for lower value of desig n force.
See Table 7 (p. 23) of the code. There i s different value of response reduction factor (R) for the dual systems.
Cl. 4.15 defines Ordinary and Special Moment Resisting Frames. Ductile structures perform much better during earthquakes.
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Hence, ductile structures are designed for lower seismic forces than non-ductile structures. For example, compare the R values in Table 7
IS:13920-1993 provides provisions on ductile detailing of RC structures. IS: 800-2007 does have seismic design provisions for some framing systems.
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Number of Storeys (Cl.4.16)
Number of Storeys (contd…)
When basement walls are connected with the floor deck or fitted between the building columns, the basement storeys are not included in number of storeys.
Definition of number of storeys
This is because in that event, the seismi c loads from upper parts of the building get transferred to the basement walls and then to the foundation. That is,
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Conditions of Cl. 4.9 are not met. Here, t wo possibilities exist (see Footnote 4 in Table 7, p. 23):
In the current code, it is not relevant
In new code, Cl. 7.6 requires height of building.
Columns in the basement storey will have insignificant seismic loads, and Basement walls act as part of the foundation.
Was relevant in 1984 version of the code wherein natural period (T) was calculated as 0.1n.
See the definition of h (buil ding height) in Cl. 7.6 Compare it with definition in Cl. 4.11. Clearly, the definition of Cl. 7.6 is more appropriate.
The definition of Cl. 4.11 needs revision
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Soft Story
Soft Storey (contd…)
Cl. 4.20 defines Soft Storey Sl. No. 1 in Table 5 (p. 18) defines Soft Storey and Extreme Soft Storey In Bhuj earthquake of January 2001, numerous soft storey buildings collapsed.
There is not much of a difference between soft storey and extreme soft storey buildings as defined in the code, and the latter definition is not warranted.
Hence, the term Extreme Soft Storey and cl. 7.10 (Buildings with Soft Storey) were added hurriedly after the earthquake.
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Hence, the definition of soft storey needs a review. We should allow more variation between stiffness of adjacent storeys before terming a building as a “soft storey building”
The code does not have enough specifications on computation of lateral stiffness and this undermines the definition of soft storey and extreme soft storey.
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Weak Storey
Weak Storey (contd…)
Note that the stiffness and strength are two different things.
Stiffness: Force needed to cause a unit displacement. It is giv en by slope of the forcedisplacement relationship. Strength: Maximum force that the system can take
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Soft storey refers to stiffness Weak storey refers to strength Usually, a soft storey may also be a weak storey
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Storey Drift
Definition of Vroof
Storey Drift defined in cl. 4.23 of the Code.
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Most Indian buildings will be soft storey as per this definition simply because the ground storey height is usually different from that in the upper storeys.
Storey drift not to exceed 0.004 times the storey height.
On p. 11, it is defined as peak storey shear force at the roof due to all m odes considered.
It is better to define it as peak storey shear in the top storey due to all modes considered.
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General Principles and Design Criteria (Section 6)
Four main sub-sections
Cl. 6.1: General Principles Cl. 6.2: Assumptions Cl. 6.3: Load Combination and Increase in Permissible Stresses Cl. 6.4: Design Spectrum
Section 6.1: General Principles IS:1893-2002(Part I)
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Ground Motion (cl. 6.1.1)
Ground Motion Contd…
Usually, the vertical motion is weaker than the horizontal motion On average, peak vertical acceleration is onehalf to two-thirds of the peak horizontal acceleration.
Cl. 6.4.5 of 2002 code specifies it as two-thirds
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Hence, the vertical acceleration during ground shaking can be just added or subtracted to the gravity (depending on the direction at that instant).
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Ground Motion Contd…
Ground Motion Contd…
Example: A roof accelerating up and down by 0.20g.
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All structures experience a constant vertical acceleration (downward) equal to gravity (g) at all times.
Implies that it is experiencing acceleration in the range 1.20g to 0.80g (in place of 1.0g that it would experience wi thout earthquake.)
Main concern is safety for horizontal acceleration. Para 2 in cl. 6.1.1 (p. 12) lists certain cases where vertical motion can be important, e.g.,
Factor of safety for gravity loads (e.g., dead and live loads) is usually sufficient to cover the earthquake induced vertical acceleration
Large span structures Cantilever members Prestressed horizontal members Structures where stability is an issue
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Design Lateral Force
Effects other than shaking
Ground shaking can affect the safety of structure in a number of ways:
• Philosophy of Earthquake-Resistant Design – First calculate maximum elastic seismic forces – Then reduce to account for ductility and overstrength
Shaking induces inertia force
Lateral Force
Soil may liquefy Sliding failure of founding strata may take place Fire or flood may be caused as secondary effect of the earthquake.
H , ∆ Maximum Elastic Force
Elastic
Elastic Force reduced by R
Cl. 6.1.2 cautions against situations where founding soil may liquefy or settle: such cases are not covered by the code and engineer has to deal with these separately.
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Actual
Design Force
0
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Earthquake Design Principle
Clause 6.1.3
The criteria is:
Minor (and frequent) earthquakes should not cause damage Moderate earthquakes should not cause significant structural damage (but could have some non-structural damage) Major (and infrequent) earthquakes should not cause collapse
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Para 1 of this clause implies that Design Basis Earthquake (DBE) relates to the “moderate shaking” and Maximum Considered Earthquake (MCE) relates to the “strong shaking”. Indian code is quite empirical on the issue of DBE and MCE levels. Hence, this clause is to be taken only as an indicator of the concept.
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Seismic Design Principle
Overstrength
A well designed structure can withstand a horizontal force several times the design force due to:
The structure yields at load higher than the design load due to:
Partial Safety Factors
Overstrength
Redundancy Ductility
Partial safety factor on seismic loads Partial safety factor on gravity loads Partial safety factor on materials
Material Properties
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Lateral Deflection
Member size or reinforcement larger than required Strain hardening in materials Confinement of concrete improves its strength Higher material strength under cyclic loads
Strength contribution of non-structural elements Special ductile detailing adds to strength also
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Redundancy
Ductility
Yielding at one location in the structure does not imply yielding of the structure as a whole.
As the structure yields, two things happen:
Load distribution in redundant structures provides additional safety margin. Sometimes, the additional margin due to redundancy is considered within the “overstrength” term.
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There is more energy dissipation in the structure due to hysteresis The structure becomes softer and its natural period increases: implies lower seismic force to be resisted by the structure
Higher ductility implies that the structure can withstand stronger shaking without collapse
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Response Reduction Factor
∆
Overstrength, redundancy, and ductility together lead to the fact that an earthquake resistant structure can be designed for much lower force than is implied by a strong shaking. The combined effect of overstrength, redundancy and ductility is expressed in terms of Response Reduction Factor (R)
Total Horizontal Load
Maximum force if structure remains elastic F el Linear Elastic Response
d a o L l a t n o z i r o H l a t o T
Maximum Load Capacity F y Load at First Yield F s
Due to Ductility Non linear Response Due to Redundancy
First Significant Yield
Due to Overstrength
Design force F des
0
∆w
Figure: Courtesy Dr. C V R Murty
∆max
∆y
Roof Displacement (∆)
Response Reduction Factor 69
Maximum Elastic Force (Fel ) Design Force (Fdes )
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Para 2 and 3 of Cl. 6.1.3.
Para 2 and 3 of Cl. 6.1.3 Contd…
Imply that the earthquake resistant structures should generally be ductile. IS:13920-1993 gives ductile detailing requirements for RC structures. Ductile detailing provisions for some steel framing systems are available in IS:800-2007.
However, it is advisable to refer to international codes/literature for ductile detailing of steel structures.
As of now, ductile detailing provisions for precast structures and for prestressed concrete structures are not available in Indian codes. In the past earthquakes, precast structures have shown very poor performance during earthquakes.
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=
The connections between different parts have been problem areas. Connections in precast structures in high seismic regions require special attention.
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Past Performance
Para 4 of Cl. 6.1.3
The performance of flat plate structures also has been very poor in the past earthquakes.
For example, in the Northridge (California) earthquake of 1994. Additional punching shear stress due to l ateral loads are serious concern.
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The design seismic force provided in the code is a reduced force considering the overstrength, redundancy, and ductility.
Hence, even when design wind force exceeds design seismic force, one needs to comply with the seismic requirements on design, detailing and construction.
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Soil Structure Interaction (Cl. 6.1.4)
Soil Structure Interaction (Cl. 6.1.4) Contd…
If there is no structure, motion of the ground surface is termed as Free Field Ground Motion Normal practice is to apply the free field motion to the structure base assuming that the base is fixed.
Presence of structure modifies the free field motion since the soil and the structure interact.
This is valid for structures located on rock sites. For soft soil si tes, this may not always be a good assumption.
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Hence, foundation of the structure experiences a motion different from the free field ground motion. The difference between the two motions is accounted for by Soil Structure Interaction (SSI)
SSI is not the same as Site Effects
Site Effect refers to the fact that free field motion at a site due to a giv en earthquake depends on the properties and geological features of the subsurface soils also.
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Direction of Ground Motion (Cl. 6.1.5)
SSI Contd…
Consideration of SSI generally
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This is an important clause for moderate seismic regions.
Decreases lateral seismic forces on the structure Increases lateral displacements
During earthquake shaking, ground shakes in all possible directions.
Increases secondary forces associated with Pdelta effect.
For ordinary buildings, one usually ignores SSI. NEHRP Provisions provide a simple procedure to account for soil-structure interaction in buildings
Direction of resultant shaking changes from instant to instant.
Basic requirement is that the structure should be able to withstand maxi mum ground motion occurring in any direction.
For most structures, main concern is for horizontal vibrations rather than vertical vibrations.
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Direction of Ground Motion (Cl. 6.1.5) (contd…)
One does not expect the peak ground acceleration to occur at the same instant in two perpendicular horizontal directions. Hence for design, maximum seismic force is not applied in the two horizontal directions simultaneously. If the walls or frames are oriented in two orthogonal (perpendicular) directions:
Building Plans with Orthogonal Systems
It is sufficient to consider ground motion in the two directions one at a time. Else, Cl. 6.3.2: will come back to this later.
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Floor Response Spectrum (Cl. 6.1.6)
Equipment located on a floor needs to be designed for the motion experienced by the floor. Hence, the procedure for equipment will be:
walls
Analyze the building for the ground motion. Obtain response of the floor. Express the floor response in terms of spectrum (termed as Floor Response Spectrum) Design the equipment and its connections with the floor as per Floor Response Spectrum.
Building Plans with Non-Orthogonal Systems 81
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General Principles and Design Criteria (Section 6)
Four main sub-sections
Sections 6.2 and 6.3
IS:1893-2002(Part I)
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Cl. 6.1: General Principles Cl. 6.2: Assumptions Cl. 6.3: Load Combination and Inc rease in Permissible Stresses Cl. 6.4: Design Spectrum
This lecture covers sub-sections: Cl. 6.2 and Cl. 6.3
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Cl.6.2 Assumptions
Mexico Earthquake of 1985
Same as in the 1984 edition, except the Note after Assumption a)
There have been instances such as the Mexico earthquake of 1985 which have necessitated this note.
Earthquake occurred 400 km from Mexico City Great variation in damages in Mexico City
Ground motion records from two sites:
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Some parts had very strong shaking In some parts of city, motion was hardly felt UNAM site: Foothill Zone wi th 3-5m of basaltic rock underlain by softer strata SCT site: soft soils of the Lake Zone
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Mexico Earthquake of 1985 (contd…)
Mexico Earthquake of 1985 (contd…)
PGA at SCT site about 5 times higher than that at UNAM site
Epicentral distance is same at both locations
Extremely soft soils in Lake Zone amplified weak long-period waves
Natural period of soft clay layers happened to be close to the dominant period of incident seismic waves This lead to resonance-like conditions
Buildings between 7 and 18 storeys suffered extensive damage
Natural period of such buildings close to the period of seismic waves.
Time (sec) Figure from Kramer, 1996
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Assumption b)
Assumption c) on Modulus o f Elasticity
A strong earthquake takes place infrequently.
A strong wind also takes place infrequently. Hence, the possibility of strong wind and strong ground shaking taking place simultaneously is very very low. It is common to assume that strong earthquake shaking and strong wind will not occur simultaneously.
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Modulus of elasticity of materials such as concrete, masonry and soil is difficult to specify Its value depends on
Stress level Loading condition (static versus dynamic) Material strength Age of material, etc
Same with strong earthquake shaking and maximum flood.
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Cl.6.3 Load Combinations and Increase in Permissible Stresses
Loads and Stresses • Loads – EQ forces not to occur simultaneously with maximum flood, wind or wave loads – Direction of forces • One horizontal + Vertical • Two horizontal + Vertical
Cl.6.3.1.1 gives load combinations for Plastic Design of Steel Structures
Same as in I S:800-1978
More load combinations in I S:800-2007
Cl.6.3.1.2 gives load combinations for Limit State Design for RC and Prestressed Concrete Structures
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Load Combination 0.9DL ±1.5EL
Load Combinations in Cl.6.3.1.2
Compare combinations of this clause with those in Table 18 (p.68) of IS:456-2000 Combination 0.9DL ± 1.5EL
The way this combination is written in I S:456, the footnote creates an impression that it is not always needed.
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Direction of Earthquake Loading
In such situations, a load factor higher than 1.0 on gravity loads will be unconservative. Hence, a load factor of 0.9 specified on gravity loads in the combination 4)
Many designs of footings, columns, and positive steel in beams at the ends in frame structures are governed by this load combination Hence, this combination has been made very specific in IS:1893-2002.
Direction of Earthquake Loading (contd…)
During earthquake, ground moves in all directions; the resultant direction changes every instant. Ground motion can resolved in two horizontal and one vertical direction. Structure should be able to withstand ground motion in any direction Two horizontal components of ground motion tend to be comparable
In many situations, design is governed by effect of horizontal load minus effect of gravity loads.
It has been noticed that many designers do not routinely consider this combination because of the way it is written.
93
Horizontal loads are reversible in direction.
95
Same as in I S:456-2000 (RC structures) and IS:1343-1980 (Prestressed structures) with one difference
Vertical component is usually smaller than the horizontal motion
Except in the epicentral region where vertical motion can be comparable (or even stronger) to the horizontal motion
As discussed earlier, generally, most ordinary structures do not require analysis for vertical ground motion.
Say, the epicentre is to the north of a site. Ground motion at site in the north-south and east-west directions will still be comparable. 96
16
Direction of Horizontal Ground Motion in Design (Cl.6.3.2.1)
Cl.6.3.2.1 (contd…)
Consider a building in which horizontal (also termed as lateral) load is resisted by frames or walls oriented in two perpendicular directions, say X and Y.
If at a given instant, motion is in any direction other than X or Y, one can resolve it into X- and Y-components, and the building will still be safe if it is designed for X- and Y- motions, separately. Minor typo in this clause: “direction at time” should be replaced by “direction at a time”
One must consider design ground motion to act in X-direction, and in Y-direction, separately That is, one does not assume that the design motion in X is acting simultaneously with the design motion in the Y-direction
97
98
Non-Orthogonal Systems (Cl.6.3.2.2)
Load Combinations for Orthogonal System
Load EL implies Earthquake Load in +X, -X, +Y, and –Y, directions. Thus, an RC building with orthogonal system therefore needs to be designed for the following 13 load cases:
1.5 (DL+LL) 1.2 (DL+LL+ELx) 1.2 (DL+LL-ELx) 1.2 (DL+LL+ELy) 1.2 (DL+LL-ELy) 1.5 (DL+ELx) 1.5 (DL-ELx) 1.5 (DL+ELy) 1.5 (DL-ELy) 0.9DL +1.5ELx 0.9DL-1.5ELx 0.9DL+1.5ELy 0.9DL-1.5ELy
ELx = Design EQ load in X-direction ELy = Design EQ load in Y-direction
99
When the lateral load resisting elements are NOT oriented along two perpendicular directions In such a case, design for X- and Y-direction loads acting separately will be unconservative for elements not oriented along X- and Ydirections.
100
Load Combinations… Combinations…
Load Combinations… Combinations…
– Problem
• Lateral force resisting system non-parallel in two plan directions
1
– Consider design based on one direction at a time
ELx
0.8
y
V Force effective along direction of inclined element
EL x x
ELy
0.6 0.4 0.2 0 0
15
30 45 6 0 7 5 90
θ
y
Orientation of inclined element with respect to x-axis
x
101
EL y
Elements at 450 orientation designed only for 70% of lateral force 102
17
Load Combinations… Combinations…
Non-Orthogonal Systems (Cl.6.3.2.2) (contd…)
– Solution :: Try (100%+30%) together
A lateral load resisting element (frame or wall) is most critical when loading is in direction of the element. It may be too tedious to apply lateral loads in each of the directions in which the elements are oriented. For such cases, the building may be designed for:
EL x x
0.3EL y y
0.3EL x x
100% design load in X-direction and 30% design load in Y-direction, acting simultaneously 100% design load in Y-direction and 30% design load in X-direction, acting simultaneously
103
EL y 104
Note that directions of earthquake forces are reversible. Hence, all combinations of directions are to be considered.
Load Combinations… Combinations…
Non-Orthogonal Systems (Cl.6.3.2.2) (contd…)
– Justification :: Say ELx = EL y = V
y
Thus, EL now implies eight possibilities: +(Elx + 0.3ELy) +(Elx - 0.3ELy) -(Elx + 0.3ELy)
Vcos θ
θ x
V
-(Elx - 0.3ELy) +(0.3ELx + Ely)
V*=Vcosθ + 0.3Vsinθ 0.3Vsinθ
+(0.3ELx - ELy) -(0.3ELx + ELy) -(0.3ELx - ELy)
0.3V
1.5 V*
ELx+0.3ELy
1
0.3ELx+ELy
0.5 0 0 105
15
30
45
60
75
90
θ
106
Non-Orthogonal Systems (Cl.6.3.2.2) (contd…)
Non-Orthogonal Systems (Cl.6.3.2.2) (contd…)
Therefore, one must consider 25 load cases:
1.5 (DL+LL)
1.5[DL+(ELx+0.3ELy)] 1.5[DL+(ELx-0.3ELy)]
1.2[DL+LL+(ELx+0.3ELy)] 1.2[DL+LL+(ELx-0.3ELy)] 1.2[DL+LL-(ELx+0.3ELy)]
1.5[DL-(ELx+0.3ELy)] 1.5[DL-(ELx-0.3ELy)]
1.2[DL+LL-(ELx-0.3ELy)] 1.2[DL+LL+(0.3ELx+ELy)] 1.2[DL+LL+(0.3ELx-ELy)] 1.2[DL+LL-(0.3ELx+ELy)] 1.2[DL+LL-(0.3ELx-ELy)]
1.5[DL+(0.3ELx+ELy)] 1.5[DL+(0.3ELx-ELy)]
Note that the design lateral load for a building in the X-direction may be different from that in the Y-direction Some codes use 40% in place of 30%.
1.5[DL-(0.3ELx+ELy)] 1.5[DL-(0.3ELx-ELy)] 0.9DL+1.5(ELx+0.3ELy)] 0.9DL+1.5(ELx-0.3ELy)] 0.9DL-1.5(ELx+0.3ELy)] 0.9DL-1.5(ELx-0.3ELy)] 0.9DL+1.5(0.3ELx+ELy)] 0.9DL+1.5(0.3ELx-ELy)] 0.9DL-1.5(0.3ELx+ELy)] 0.9DL-1.5(0.3ELx-ELy)]
107
108
18
Cl.6.3.4.1
Cl.6.3.4.2
In complex structures such as a nuclear reactor building, one may have very complex structural systems. Need for considering earthquake motion in all three directions as per 100%+30% rule.
In place of 100%+30% rule, one may take for design force resultants as per square root of sum of squares in the two (or, three) directions of ground motion EL = ( ELx)2 + ( ELy)2 + (ELz )2
Now, EQ load means the following 24 combinations:
± Elx ±
± Ely ± 0.3ELx ± 0.3ELz
0.3ELy ± 0.3ELz
± Elz ±
0.3ELx
± 0.3ELy
Hence, EL now means 24 combinations A total of 73 load cases for RC structures!
109
110
Typographical Errors in Table 1
Increase in Permissible Stresses: Cl.6.3.5.1
Applicable for Working Stress Design
Permits the designer to increase allowable stresses in materials by 33% for seismic load cases. Some constraints on 33% increase for steel and for tensile stress in prestressed concrete beams.
The Table within Table 1, giving values of desirable minimum values of N.
Note 1 is also repeated within Note 4.
111
Hence, Note 1 should be dropped.
112
Second Para of Cl.6.3.5.2
Liquefaction Potential
It points out that in case of loose or medium dense saturated soils, liquefaction may take place.
Sites vulnerable to liquefaction require
113
This Table pertains to Note 3 and hence should be placed between Notes 3 and 4 (and not between Notes 4 and 5 as printed currently) Caption of first column in this sub-table should read “Seismic Zone” and not “Seismic Zone level (in metres)” Caption of second column in this sub-table should read “Depth Below Ground Level (in metres)” and not “Depth Below Ground”
Liquefaction potential analysis. Remedial measures to prevent li quefaction.
Else, deep piles are designed assuming that soil layers liable to liquefy will not provide lateral support to the pile during ground shaking.
Information given in cl.6.3.5.2 and T able 1 on Liquefaction Potential is very primitive: Note to Cl.6.3.5.2 encourages the engineer to refer to specialist literature f or determining liquefaction potential analysis. It is common these days to use SPT or CPT results for detailed calculations on liquefaction potential analysis.
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19
General Principles and Design Criteria (Section 6)
Four main sub-sections
Lecture 2
Cl. 6.1: General Principles Cl. 6.2: Assumptions Cl. 6.3: Load Combination and Increase in Permissible Stresses Cl. 6.4: Design Spectrum
This lecture covers sub-section 6.4.
Sections 6.4 IS:1893-2002(Part I)
115
116
Response Spectrum versus Design Spectrum
Response Spectrum versus Design Spectrum (contd…)
Consider the Acceleration Response Spectrum
Notice the region of red circle marked: a slight change in natural period can lead to large variation in maximum acceleration
g , n o i t a r e l e c c A l a r t c e p S
Natural period of a civil engineering structure cannot be calculated precisely Design specification should not very sensitive to a small change in natural period. Hence, design spectrum is a smooth or average shape without local peaks and valleys you see in the response spectrum
Undamped Natural Period T (sec)
117
118
Design Spectrum
Design Spectrum (contd…)
Since some damage is expected and accepted in the structure during strong shaking, design spectrum is developed considering the overstrength, redundancy, and ductility in the structure. The site may be prone to shaking from large but distant earthquakes as well as from medium but nearby earthquakes: design spectrum may account for these as well.
g , n o i t a r e l e c c A l a r t c e p S
Natural vibration period Tn , sec
See Fig. next slide.
Fig. from Dynamics of Structures by Chopra, 2001
119
120
20
Design Spectrum (contd…)
Design Spectrum (contd…)
Design Spectrum is a design specification It must take into account any issues that have bearing on seismic safety.
Design Spectrum must be accompanied by:
Load factors or permissible stresses that must be used
Damping to be used in design
Depending on modeling assumptions, one can get different values of natural period.
Type of detailing for ductility
121
Variation in the value of damping used will affect the design force.
Method of calculation of natural period
Different choice of load factors will give different seismic safety to the structure
Design force can be lowered if structure has higher ductility.
122
Design SPECTRUM …
Design Lateral Force… Force…
• Design Horizontal Acceleration Spectrum
• Two methods of estimation of design seismic lateral force
Maximum Elastic Acceleration
– Seismic Coefficient Method – Response Spectrum Method
S a
Z
– In both methods
Ah (T ) =
• Seismic Design Force F d = F e /R = A W
g
A
= Design acceleration value W = Seismic weight of structure
123
2 R
Reduction to account for ductility and overstrength
124
Seismic zone factor
Design SPECTRUM… SPECTRUM…
• Seismic Zone Factor Seismic Zone Z
II 0.10
– Relative Values Consistent III
IV
0.16 0.24 0.36
II
III
Z
0.10
IV
V
0.16 0.24 0.36 1.5
– Factor of 2 in A h for reducing PGA for MCE to PGA for Design Basis Earthquake (DBE)
PGA
Time
PGA (ZPA:: Zero Period Acceleration)0
Seismic Zone
1.6
Spectral Acceleration
Acceleration
1.5
V
– Reflects Peak Ground Acceleration (PGA) of the region during Maximum Credible Earthquake (MCE)
125
(T ) I
Natural Period
126
(Earthquake which can be reasonably expected to occur at least once during the lifetime of structures)
21
Importance factor • Importance factor I – – – –
Soil Effect
Degree of conservatism Willing to pay more for assuring essential services Domino effect of disaster Important & community buildings
S.No. Building 1 Important, Community & Lifeline Buildings 2 All Others
Recorded earthquake motions show that response spectrum shape differs for different type of soil profile at the site
I 1.5 1.0
• Can use higher value of I • Buildings not mentioned can be designed for higher value of I depending on economy and strategic considerations • Temporary (short term) structures exempted from I
Fig. from Geotechnical Earthquake Engineering, by Kramer, 1996
Period (sec)
127
128
Soil Effect (contd…)
Soil Effect (contd…)
This variation in ground motion characteristic for different sites is now accounted for through different shapes of response spectrum for three types of sites.
) g / a S ( t n e i c i f f e o C n o i t a r e l e c c A l a r t c e p S
Fig. from IS:1893-2002
Design Spectrum depends on Type I, II, and III soils Type I, II, III soils are indirectly defined in Table 1 of the code. See Note 4 of Table 1: The value of N is to be taken at the founding level. What is the founding level of a pile or a well foundation?
This is left open in the code.
Period(s)
129
130
Shape of Design Spectrum
Soil Effect (contd…)
The International Building Code (IBC2000) classifies the soil type based on weighted average (in top 30m) of:
131
Soil Shear Wave Velocity, or
Standard Penetration Resistance, or Soil Undrained Shear Strength
I feel our criteria should also use the average properties in the top 30m rather than just at the founding level.
The three curves in Fig. 2 have been drawn based on general trends of average response spectra shapes. In recent years, the US codes (UBC, NEHRP and IBC) have provided more sophistication wherein the shape of design spectrum varies from area to area depending on the ground mo tion characteristics expected.
132
22
Response Reduction Factor
As discussed earlier, the structure is allowed t o be damaged in case of severe shaking.
Hence, structure is designed for seismic force much less than what is expected under strong shaking if the structure were to remain linear elastic Earlier code just provided the required design force
Response Reduction Factor (contd…)
For buildings, Table 7 gives values of R For other structures, value of R is to be given in the respective parts of code
It gave no direct indication that the real force may be much larger
Now, the code provides for realistic force for elastic structure and then divides that force by (2R)
This gives the designer a more realistic picture of the design philosophy.
133
134
Response Reduction Factor (R) (contd…)
Study Table 7 very carefully including all the footnotes. We have already discussed terms: Dual systems, OMRF, and SMRF
Response Reduction Factor (R) (contd…)
Notes 4 and 8 were covered earlier when we discussed Dual systems.
The values of R were decided based on engineering judgment.
Note 6 prohibits ordinary RC shear walls in zones IV and V.
The effort was that design force on SMRF as per new provisions should be about the same as that in the old code. For other building systems, lower values of R were specified. It is hoped that with time, these values will be refined based on detailed research.
This needs to be corrected in the code.
136
Response Reduction Factor (R) (contd…)
Response Reduction Factor (contd…)
Moreover, there are a number of other systems that are prohibited in high zones and those are not listed in this table. For instance,
Note the definition of R on page 14 contains the statement: However, the ratio (I/R) shall not be greater than 1.0 (Table 7)
OMRF’s are also not allowed in zones III, IV and V as per IS:13920. Load bearing masonry buildings are required to have seismic strengthening (lintel bands, vertical bars) in high zones as per IS:4326.
This statement should not be there.
It would be better for this table to drop Note 6.
137
This confuses people and they take it to mean that the code allows Ordinary Moment Resisting Frames in zones IV and V.
As per IS:13920, all structures in zones III, IV and V should comply with ductile detailing (as per IS:13920). Hence, Ord. RC shear walls prohibited in zones III also.
135
Such a note is not there for OM RF.
For buildings, I never exceeds 1.5 and the lowest value of R is 1.5 in Table 7
In its place, there could be a general note that some of the above systems are not allowed in high seismic zones as per I S:4326 or IS:13920.
Thus, this statement does not kick in for buildings
For other structures, there are situations where (I/R) will need to exceed 1.0
For instance, for bearings of important bridges.
138
23
Design Spectrum for Stiff Structures
Response Reduction Factor …
– R values can be taken as for Dual Systems , only if both conditions below are satisfied
• Shear walls and MRFs are designed to resist V B in proportion to their stiffness considering their interaction at all floor levels • MRFs are designed to independently resist at least 25% of V B Shear Wall
For very stiff structures (T < 0.1sec), ductili ty is not helpful in reducing the design force. Codes tend to disallow the reduction in force in the period range of T < 0.1sec Design spectrum assumes peak extends to T=0 Actual shape of response spectrum (may be used for higher modes o nly) n o i t a r e l e c c a l a r t c e p S
MRF
T(seconds)
139
140
Underground Structures Cl.6.4.4
Design Spectrum for Stiff Structures (contd…)
Statement in Cl.6.4.2
Provided that for any structure with T ≤ 0.1s, the value of Ah will not be taken less than Z/2 whatever be the value of I/R This statement attempts to ensure a minimal design force for stiff structures. Note that this statement is valid only when the first (fundamental) mode period T ≤ 0.1sec even though the code does not specify so.
For higher modes, this restrictions should not be imposed.
141
When seismic waves hit the ground surface, these are reflected back into ground The reflection mechanics is such that the amplitude of vibration at the free surface is much higher (almost double) than that under the ground Cl.6.4.4 allows the design spectrum to be onehalf if the structure is at depth of 30m or below.
Linear interpolation for structures and foundations if depth is less than 30m.
142
Equations for Design Spectrum
Underground Structures (contd…)
The clause is also applicable for calculation of seismic inertia force on foundation under the ground, say a well foundation for a bridge. Hence, the wording Underground structures and foundations Note that in case of a bridge (or any aboveground structure) with foundation going deeper than 30m:
143
Concept sometimes used by the codes for response spectrum in low period range.
Second para of Cl.6.4.5 and the equations
This should not be a part of C.6.4 .5 and should have had an independent clause number Note the word “proposed” in this para is misleading and should not be there.
This clause (Cl. 6.4.4) can be used to calculate seismic inertia force due to mass of foundation under the ground, and not for calculation of inertia force of the superstructure. 144
24
Equations for Design Spectrum
Site Specific Design Criteria Cl.6.4.6
Response spectrum shapes in Fig. 2 are for 5% damping.
These shapes are also given in the form of equations Table 3 gives multiplying factors to obtain design spectrum for other values of damping Note that the multiplication is not to be done for zero period acceleration (ZPA)
145
Seismic design codes meant for ordinary projects For important projects, such as nuclear power plants, dams and major bridges site-specific seismic design criteria are developed
These take into account geology, seismicity, geotechnical conditions and nature of project
Site specific criteria are developed by experts and usually reviewed by independent peers A good reference to read on this:
Housner and Jennings, “Seismic Design Criteria”, Earthquake Engineering Research Institute, USA, 1982.
146
Buildings (Section 7)
Sub-sections
Sections 7.1 to 7.7 on Buildings IS:1893-2002(Part I)
147
148
Importance of Configuration
Regular and Irregular Configuration (Cl. 7.1)
149
Cl. 7.1: Regular and Irregular Configurations Cl. 7.2: Importance Factor I and Response Reduction Factor R Cl. 7.3: Design Imposed Loads for Earthquake Force Calculation Cl. 7.4: Seismic Weight Cl. 7.5: Design Lateral Force Cl. 7.6: Fundamental Natural Period Cl. 7.7: Distribution of Design Force Cl. 7.8: Dynamic Analysis Cl. 7.9: Torsion Cl. 7.10: Buildings with Soft Storey Cl. 7.11 Deformations Cl. 7.12 Miscellaneous
The statement of Cl. 7.1 is an attempt to emphasize the importance of structural configuration for ensuring good seismic performance. Good structural configuration has implications for both safety and economy of the building.
To quote Late Henry Degenkolb, the wellknown earthquake engineer in California: If we have a poor configuration to start with, all the engineer can do is t o provide band-aid – improve a basically poor solution as best as he can. Conversely, if we start off with a good configuration and a reasonable framing system, even a poor engineer can’t harm it s ultimate performance too much.
150
25
Regular versus Irregular Configuration
Importance of Configuration (contd…)
Quote from NEHRP Commentary:
The major factors influencing the cost of complying with the provisions are: 1. The complexity of the shape and structural framing system for the building. (It is much easier to provide seismic resistance in a building with a simple shape and framing plan.) 2. The cost of the structural system (plus other items subject to special seismic design requirements) in relation to the total cost of the building. (In many buildings, the cost of providing the structural system may be only 25 percent of the total cost of the project.) 3. The stage in design at which the provision of seismic resistance is first considered. (The cost can be inflated greatly if no attention is given to seismic resistance until after the configuration of the building, the structural framing plan, and the materials of construction have already been chosen). 151
Tables 4 and 5 list out the irregularities in the building configuration
Table 4 and Fig. 3 for I rregularities in Plan
Table 5 and Fig. 4 for I rregularities in Elevation
152
A Remark on IS:13920
Design Imposed Load…(Cl. 7.3)
Recently, BIS has issued some amendments to IS:13920-1993 (see next slide). In the context of Table 7, note that provisions of IS:13920 are now mandatory for all RC structures in zones III, IV and V.
There could be differences of opinion about Cl. 7.3.3.
Say the imposed load is 3 kN/sq.m This clause implies that we take only 25% of imposed load for calculation of seismic weight, and also for load combinations. This amounts to:
153
1.2 DL + 0.3LL + 1.2LL
The Cl. 7.3.3 should be dropped.
154
Design Lateral Force (Cl. 7.5)
Note that the code no longer talks of two methods: seismic coefficient method and response spectrum method.
Mass that causes Earthquake Force in X-Direction
EQx
There have been instances of designer calculating seismic design force for each 2-D frame separately based on tributary mass shared by that frame.
Mass being considered for calculation of inertia force due to earthquake
This is erroneous since only a fraction of the building mass is considered in the seismic load calculations.
EQx
Plan of building 155
Calculation of design seismic force on the basis of tributary mass on 2-D frames leads to significant underdesign.
156
26
Design Lateral Force (Cl. 7.5)
…
Design Lateral Force (Cl. 7.5) (contd…)
• Seismic Weight of Building W – Dead load – Part of imposed loads
% of Imposed Load Imposed Uniformly Distributed Floor Loads to be considered (kN/m2 )
Now, Cl. 7.5.2 makes it clear that one has to evaluate seismic design force f or the entire building first and then distribute it to different frames/ walls. Cl. 7.5.2 does not mean that one ha s to necessarily carry out a 3-D analysis.
Up to and including 3.0
25
Above 3.0
50
157
One could still work wi th 2-D frame systems.
158
Fundamental Natural Period (Cl. 7.6)
Fundamental Natural Period (Cl. 7.6) (contd…)
For frame buildings without brick infills
Ta = 0.075h0.75
For all other buildings, including frame buildings with brick infill panels:
T a =
Needless to say, brick infill in Cl. 7.6 really implies masonry infills These need not just be bricks: could be stone masonry or concrete block masonry.
0.09h d d
where h is in meters d
159
160
Rationale for new equations for T
Experimental observations on Indian RC buildings with masonry infills clearly showed that T = 0.1n significantly over-estimates the period. For instance, see
Observations on Steel Frame Buildings During San Fernando EQ
Jain S K, Saraf V K, and Mehrotra B, “Period of RC Frame Buildings with Brick Infills,” J. of Struct. Engg, Madras, Vol. 23, No 4, pp 189-196. Arlekar, J N, and Murty, C V R, “Ambient Vibration Survey of RC MRF Buildings with URM Infill Walls,” The Indian Concrete Journal , Vol.74, No.10, Oct. 2000, pp 581-586.
For frame buildings with masonry infills, T = 0.09h/( √d) was found to give a much better estimate.
Fig. from NEHRP Commentary
161
162
27
Observations on RC Frame Buildings During San Fernando EQ
Observations on RC Shear Wall Buildings During San Fernando EQ
Fig. from NEHRP Commentary
163
Fig. from NEHRP Commentary
164
Vertical Distribution of Seismic Load (Cl. 7.7.1) Lateral load distribution with building height depends on
Natural periods and mode shapes of the building Shape of design spectrum
j
Fundamental period dominates the response, and Fundamental mode shape is close to a straight line (with regular distribution of mass and stiffness)
k j
j 1
For tall buildings, contribution of higher modes can be significant even though the first mode may still contribute the maximum response.
165
Hence, NEHRP provides the following expression for vertical distribution of seismic load W h k Qi = V B n i i
∑= W h
In low and medium rise buildings,
Vertical Distribution of Seismic Load (Cl. 7.7.1) (contd…)
Where k = 1 for T ≤ 0.5sec, and k = 2 for T ≥ 2.5 sec. Value of k varies linearly for T i n the range 0.5 sec to 2.5 sec.
In IS:1893 over the years, k = 2 has been taken regardless of natural period
This is conservative value and has been retained in the code.
166
Horizontal Distribution... (Cl. 7.7.2)
Floor diaphragm plays an important role in seismic load distribution in a building. Consider a RC slab
For horizontal loads, it acts as a deep beam with depth equal to building width, and the beam width equal to slab thickness. Being a very deep beam, it does not deform in its own plane, and it forces the frames/walls to fulfil the deformation compatibility of no in- plane deformation of floor. This is rigid floor diaphragm action.
Concept of Floor Diaphragm Action
Fig. from Jain S K, “A Proposed Draft for IS:1893…Part II: Commentary and Examples,” J. of StructEngg, Vol. 22, No. 2, July 1995, pp 73-90
167
168
28
Horizontal Distribution... (Cl. 7.7.2) (contd…)
Implications of rigid floor diaphragm action:
In case of symmetrical building and loading, the seismic forces are shared by different frames or walls in proportion to their own lateral sti ffness.
Lateral Load Distribution Due to Rigid Floor Diaphragm: Symmetric Case – No Torsion
Fig. from Jain S K, “A Proposed Draft for IS:1893…Part II: Commentary and Examples,” J. of StructEngg, Vol. 22, No. 2, July 1995, pp 73-90
169
170
When building is not symmetrical, the floor undergoes rigid body translation and rotation.
Analysis of Forces Induced by Twisting Moment (Rigid Floor Diaphragm)
Fig. from Jain S K, “A Proposed Draft for IS:1893…Part II: Commentary and Examples,” J. of StructEngg, Vol. 22, No. 2, July 1995, pp 73-90
171
172
Rigid Diaphragm Action
Buildings without Diaphragm Action
In-plane rigidity of floors is sometimes misunderstood to mean that
The beams are infinitely rigid, and
The columns are not free to rotate at their ends.
When the floor diaphragm does not exist, or when the diaphragm is extremely flexible as compared to the vertical elements
Rotation of columns is governed by out-of-plane behavior of slab and beams.
The load can be distributed to the vertical elements in proportion to the tributary mass
(a) In-plane floor deformation, (b) Outof-plane floor deformation. Fig. from Jain S K, “A Proposed Draft for IS:1893…Part II: Commentary and Examples,” J. of Struct Engg, Vol. 22, No. 2, July 1995, pp 73-90
173
174
29
Flexible Floor Diaphragms
Analysis for Flexible Floor Diaphragm Bu ildings
There are instances where floor is not rigid. “Not rigid” does not mean it is compl etely flexible!
Hence, buildings with flexible floors should be carefully analyzed considering in-plane floor flexibility.
Note 1 of Cl. 7.7.2.2 gives the criterion on when the floor diaphragm is not to be treated as rigid.
One can actually model the floor slab in the computer analysis. Fig. on next slide shows the vertical analogy method to consider diaphragm flexibility in lateral load distribution
Definition of Flexible Floor Diaphragm (Cl. 7.7.2.2)
Fig. from Jain S K, “A Proposed Draft for IS:1893…Part II: Commentary and Examples,” J. of Struct Engg, Vol. 22, No. 2, July 1995, pp 73-90
(Plan View of Floor) In-plane flexibility of diaphragm to be considered when ∆2 >1.5{0.5(∆1+ ∆2 )}
175
176
Analysis for Flexible Floor Diaphragm Buildings (contd…)
Alternatively, one can take the design force as envelop of (that is, the higher of) the tw o extreme assumptions, i.e.,
Lateral Load Distribution Considering Floor Diaphragm Deformation: Vertical Analogy Method
Rigid diaphragm action No diaphragm action (load distribution in proportion to tributary mass)
Fig. from Jain S K, “A Proposed Draft for IS:1893…Part II: Commentary and Examples,” J. of Struct Engg, Vol. 22, No. 2, July 1995, pp 73-90
177
178
Buildings (Section 7)
Sub-sections
Cl. 7.3: Design Imposed Loads for Earthquake Force Calculation Cl. 7.4: Seismic Weight Cl. 7.5: Design Lateral Force
Cl. 7.6: Fundamental Natural Period
Section 7.8: Dynamic Analysis
IS:1893-2002(Part I)
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Cl. 7.7: Distribution of Design Force Cl. 7.8: Dynamic Analysis Cl. 7.9: Torsion
Cl. 7.10: Buildings with Soft Storey Cl. 7.11 Deformations
Cl. 7.12 M iscellaneous
Cl. 7.1: Regular and I rregular Configurations Cl. 7.2: Importance Factor I and Response Reduction Factor R
This lecture covers sub-section 7.8
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About This Lecture
Requirement of Dynamic Anal. Cl. 7.8.1
The intent is not to teach Structural Dynamics or to teach how to carry out dynamic analysis of a building.
Interested persons may learn Structural Dynamics from numerous excellent text books available on this subject.
Irregular Buildings
II and III
Ht > 90 m
Ht > 40 m
IV and V
Ht > 40 m
Ht > 12 m
All framed buildings higher than 12m….
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Why Dynamic Analysis?
Why Dynamic Analysis? (contd…)
Expressions for design load calculation (cl. 7.5.3) and load distribution with height based on assumptions
Fundamental mode dominates the response Mass and stiffness distribution are evenly distributed with building height
Thus, giving regular mode shape
In tall buildings, higher modes can be quite significant. In irregular buildings, mode shapes may be quite irregular Hence, for tall and irregular buildings, dynamic analysis is recommended. Note that industrial buildings may have large spans, large heights, and considerable irregularities:
183
These too will require dynamic analysis.
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Lower Bound on Seismic Force (Cl. 7.8.2)
Lower Bound on Seismic Force (Cl. 7.8.2) (contd…)
This clause requires that in case dynamic analysis gives lower design forces, these be scaled up to the level of forces obtained based on empirical T .
There are considerable uncertainties in modeling a building for dynamic analysis, e.g.,
Implies that empirical T is more reliable than T computed by dynamic analysis
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Regular Building
Notice wordings of section b) in Cl. 7.8.1
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Seismic Zone
Stiffness contribution of non-structural elements Stiffness contribution of masonry infills Modulus of elasticity of concrete, masonry and soil Moment of inertia of RC members
Depending on how one models a building, there can be a large variation in natural period. Ignoring the stiffness contribution of infill walls itself can result in a natural period several times higher
186
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Value of Damping Cl. 7.8.2.1
Lower Bound on Seismic Force (Cl. 7.8.2) (contd…)
Empirical expressions for period
Based on observations of actual as-built buildings, and hence Are far more reliable than period from dynamic analysis based on questionable assumptions
Steel buildings: 2% of critical RC buildings: 5% of critical
For masonry buildings? Not specified.
The load distribution with building height and to different elements is based on dynamics.
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Even when the results of dynamic analysis are scaled up to design force based on empirical T:
Damping to be used
Implies that a steel building will be designed for about 40% higher seismic force than a similar RC building. The code should specify 5% damping for both steel and RC buildings.
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Value of Damping Cl. 7.8.2.1 (contd…)
Value of Damping Cl. 7.8.2.1 (contd…)
Damping value depends on the material and the level of vibrations
Higher damping for stronger shaking
Means that during the same earthquake, damping will increase as the level of shaking increases. We are performing a simple linear analysis, while the real behaviour is non-linear. Hence, one fixed value of damping is used in our analysis.
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Choice of damping has implications on seismic safety. Hence, damping value and design spectrum level go together. Most codes tend to specify 5% damping for buildings. What value of damping to be used in “static procedure” of Cl. 7.5?
Not specified. I recommend 5% be mentioned in the code.
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A Note on Static Procedure
Number of Modes Cl. 7.8.4.2
The procedure of Cl.7.5 to 7.7 does n ot require dynamic analysis.
Hence, this procedure is often termed as static procedure or equivalent static procedure or seismic coefficient method.
However, notice that this procedure does account for dynamics of the building in an approximate manner
The code requires sufficient number of modes so that at least 90% of the t otal seismic mass is excited in each of the principal directions. There is a problem in wordings of this clause. First sentence reads as:
Even though its applicability is limited to simple buildings
The number of modes to be used in the analysis should be such that the sum total of modal masses in all modes considered i s at least 90 percent of the total seismic mass and missing mass correction beyond 33 percent.
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Recommended value is 5%
The portion highlighted in red should be deleted.
192
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Modal Combination Cl. 7.8.4.4
Number of Modes Cl. 7.8.4.2 (contd…)
Last sentence reads as:
The effect of higher modes shall be included by considering missing mass correction using well established procedures
It should read as:
The effect of modes with natural frequency beyond 33 Hz shall be included by….
193
This clause gives CQC method first and then simpler method as an alternate. CQC is a fairly sophisticated method for modal combination. It is applicable both when the modes are well-separated and when the modes are closely-spaced. Many computer programs have CQC method built in for modal combination.
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Alternate Method to CQC
Modal Combination Cl. 7.8.4.4 (contd…)
Response Quantity could be any response quantity of interest:
Base shear, base moment, …
Force resultant in a member, e.g.,
Use SRSS (Square Root of Sum of Squares) if the natural modes are not c losely-spaced. λ =
Moment in a beam at a given location, Axial force in column, etc.
Deflection at a given location
195
+ λ 2 + λ 3 + λ 4 + ...
To appreciate the alternative meth od, consider two examples.
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Example 1 on Modal Combination:
Example 1 on Modal Combination (contd…)
For first five modes of vibration, natural period/ natural frequency and maximum response are given. Estimate the maximum response for the structure.
Mode
1
2
3
4
5
Natural Period
0.95
0.35
0.20
0.14
0.11
Natural Frequency
1.05
2.86
5.00 7.14 9.09
Response Quantity
1100
350
230
150
All natural frequencies differ from each other by more than 10%.
197
+ λ 22 + λ 23 + λ 24 + ....
Use Absolute Sum for closely-spaced m odes λ = λ 1
2
λ 1
As per Cl. 3.2, none of the modes are closelyspaced modes.
As per section a) in Cl. 7.8.4.4, we can use Square Root of Sum of Squares (SRSS) method to obtain resultant response as
= (1100 ) 2 + (350) 2 + (230) 2 + (150) 2 + (120) 2 = 1193
120
198
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Example 2 on Modal Combination
Example 2 on Modal Combination (contd…)
For first six modes of vibration, natural period/ natural frequency and maximum response are given. Estimate the maximum response for the structure.
Mode
1
2
3
4
5
6
Natural period (sec)
0.94
0.78
0.74
0.34
0.26
0.25
Natural frequency (Hz)
1.06
1.28
1.35
2.94
3.85
4.00
Response Quantity
850
230
190
200
90
80
199
As per Cl. 3.2, modes 2 and 3 are closed spaced since their natural frequencies are within 10% of the lower frequency. Similarly, modes 5 and 6 are closely spaced. Combined response of modes 2 and 3 as per section b) in Cl.7.8.4.4 = 230+190=420 Combined response of modes 5 and 6 = 90 + 80 = 170 Combined response of all the modes as per section a)
=
(850) 2
+ (420) 2 + (200) 2 + (170) 2 = 984
200
Lumped Mass Model for Cl. 7.8.4.5
Dynamic Analysis as per Cl. 7.8.4.5
The analysis procedure is valid when a building can be modeled as a lumped mass model with one degree of freedom per floor (see fig. next slide) If the building has significant plan irregularity, it requires three degrees of freedom per floor and t he procedure of Cl. 7.8.4.5 is not valid.
X3(t) X2(t) X1(t)
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Summary
Dynamic analysis requires considerable skills. Just because the computer program can perform dynamic analysis: it is not sufficient. One needs to develop in-depth understanding of dynamic analysis.
There are approximate methods (such as Rayleigh’s method, Dunkerley’s method) that one should use to evaluate if the computer results are right.
This lecture covers Sections 7.9 to 7.11 IS:1893-2002(Part I)
It is not uncommon to confuse between the units of mass and weight when performing dynamic analysis.
203
Lecture 3
Leads to huge errors. 204
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Torsion
Buildings (Section 7) • Uncertainties
Sub-sections
Cl. 7.1: Regular and I rregular Configurations
Cl. 7.2: Importance Factor I and Response Reduction Factor R
Cl. 7.3: Design Imposed Loads for Earthquake Force Calculation Cl. 7.4: Seismic Weight
Cl. 7.5: Design Lateral Force
– Location of imposed load – Contributions to structural stiffness
• Accidental Eccentricity – Torsion to be considered in Symmetric Buildings
Cl. 7.6: Fundamental Natural Period Cl. 7.7: Distribution of Design Force
• Design Eccentricity 1.5 esi + 0.05 bi e di = Worst of esi − 0.05bi
Cl. 7.8: Dynamic Analysis Cl. 7.9: Torsion Cl. 7.10: Buildings with Soft Storey Cl. 7.11 Deformations Cl. 7.12 M iscellaneous
This lecture covers sub-sections 7.9 to 7.11
bi 205
206
Design eccentricity
First Equation for Design Eccentricity
Now the equation for design eccentricity is:
1.5esi+0.05bi edi =
esi-0.05bi
Notice:
First equation has 1.5 times the computed eccentricity, plus additional term due to accidental eccentricity
The intention is to add the effect of ac cidental eccentricity to 1.5 times calculated eccentricity. Hence, the first equation should be taken to mean having + and - sign for the second term, whichever is critical: edi = 1.5esi ± 0.05bi
Accidental eccentricity is specified as 5% of plan dimension.
Second equation does not have factor of 1.5, and sign of accidental eccentricity is different. In lecture 2, we discussed dynamic amplification of 1.5 and the acci dental eccentricity.
207
208
Torsion… Torsion…
First Equation for Design Eccentricity (contd…)
– Two cases of Design Eccentricity
bi esi
CM*
CM
CS
CM CM* CS
Calculated locations of CM and CR
CR
CM
CR
CM CM
ith floor
0.05bi
esi
0.05bi
0.5esi
1.5esi
+ 0.05bi
*
esi
esi
1.5esi+0.05 bi
− 0.05bi
Location CM* to be used in analysis for first eqn. of cl. 7.9.2
Considering EQ in Y -Direction 209
210
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Second Equation for Design Eccentricity
Second Equation for Design Eccentricity (contd…)
bi
In second equation, it is expected that there is accidental eccentricity in the opposite sense, i.e., it tends to oppose the computed eccentricity.
esi
Calculated locations of CM and CR
CM
CR
ith floor
Hence, factor 1.5 is not applied to the computed eccentricity. Again, this equation also should be understood to mean having + and - sign for second term, whichever is critical:
*
CM CR
CM
0.05 bi
edi = esi ± 0.05bi
Location CM* to be used in analysis for first eqn. of cl. 7.9.2
esi
Considering EQ in Y -Direction 211
212
Torsion… Torsion…
Torsion… Torsion…
• Incorporating the provision in practice 1.5 esi + 0.05bi edi = esi − 0.05bi
CS
• Incorporating the provision in practice… – Effect of shear and torsion (e si ) • Analysis A
CM
213
CS
CM
214
Torsion… Torsion…
Torsion… Torsion…
• Incorporating the provision in practice…
• Incorporating the provision in practice…
– Effect of shear only
– Effect of shear, torsion e si and 0.05bi
• Analysis B
• Analysis C
CS
CM
CS
CM
CM*
0.05b i 215
216
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Definition of Centre of Rigidity
Torsion… Torsion…
• Incorporating the provision in practice…
– Solution
Earlier we defined Centre of Rigidity as:
• Effect of esi only A-B
• Effect of 0.05bi only
C-A
• Effect of 1.5esi+0.05bi along with shear
B+1.5(A-B)+(C-A) = 0.5(A-B)+C
217
This definition was for single-storey building. How do we extend it to multi-storey buildings? Recall that I mentioned in Lecture 2 that we will not distinguish between the terms Centre of Rigidity and Centre of Stiffness.
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CR for Multi-Storey Buildings
All Floor CR Definition
It can be defined in two ways:
All Floor Centre of Rigidity, and Single Floor Centre of Rigidity
Centre of rigidities are the set of points located one on each floor, through which application of lateral load profile would cause no rotation in any floor.
219
As per this definition, location of CR is dependent on building stiffness properties as well as on the applied lateral load profile.
220
All Floor Definition of CR
Single Floor CR Definition
CR
Fny F(j+1)y F jy F(j-1)y F2y F1y
221
If the building undergoes pure translation in the horizontal direction (that is, no rotation or twist or torsion about vertical axis), the point through which the resultant of the restoring forces acts is the Centre of Rigidity.
CR CR CR CR
Centre of rigidity of a floor is defined as the point on the floor such that application of lateral load passing through that point does not cause any rotation of that particular floor, while the other floors may rotate.
This definition is independent of applied lateral load.
No rotation in any floor
CR
Figure 1: ‘All floor’ definition of center of rigidity
Fig. DhimanBasu
222
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Single Floor Definition of CR
Choice of Definition
CR
j th floor does not rotate (other floors may rotate)
Question is: which definition of CR to choose for multi-storey buildings? In fact, some people also use the concept of Shear Center in place of CR. But, we need not concern ourselves about it. Results could be somewhat different depending on which definition is used. But, the difference is not substantial for most buildings.
Fig. DhimanBasu
223
Use any definition that you find convenient to use.
For computer-aided analysis, the all-floor definition is more convenient.
224
To Calculate Eccentricity
Need to locate
Centre of Mass, and Centre of Rigidity
The way we defined it, one needs to apply lateral loads at the CR.
Centre of Mass is easy to locate.
To Locate CR
Unless there is a significant variation in mass distribution, we take it at geometric centre of the floor.
225
Notice the condition that the floor should not rotate.
Locating CR is not so simple for a multi-storey building.
But, we do not know CR i n the first place.
Hence, we could apply the load at CM, and restrain the floor from rotation by providing rollers The resultant of the applied load and reactions at the rollers will pass through CR
226
To Locate All-Floor CR
To Locate Single-Floor CR
Central nodes of both ends of the diaphragm are constrained to ensure equal horizontal displacement Column shear
Central nodes of both ends of the diaphragm are constrained to ensure equal horizontal displacement
Lateral load proportional to the mass distribution distributed along the floor length
(a) Lateral loads are applied at all floors of the constrained model 227
Column shear
Resultant of column shears passes through the center of rigidity of the floor
Central nodes of both ends of the diaphragm are constrained to ensure equal horizontal displacement
(b) Free body diagram of a particular floor
(a) Lateral load is applied at the constrained floor
Fig. Dhiman Basu
Lateral load proportional to the mass distribution distributed along the floor length
Resultant of column shears passes through the center of rigidity of the floor
(b) Free body diagram of a particular floor
Fig. Dhiman Basu
228
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Alternative to Locating CR
Superposition Method
It is tedious to locate CR’s first and then calculate eccentricity.
One could follow an alternate route using computer analysis, provided one is using AllFloor Definition. This method is based on superposition concept and was first published by Goel and Chopra (ASCE, Vol 119, No. 10).
This incorporates the effect of computed eccentricity (without dynamic amplification or accidental ecc.)
Apply lateral load profile at CM’s but restrain the floors from rotating; say this solution is F 2
229
Apply lateral load profile at the CM’s and analyse the building; say the solution is F 1
This amounts to solving the problem as i f the lateral loads were applied at the CRs since the floors did not rotate.
The difference of F1 and F2 gives the solution due to torsion caused by computed eccentricity.
230
Superposition Method (contd…)
Superposition Method (contd…)
Hence, solution for loads applied at 1.5 times computed eccentricity = solution F 1 + 0.5(solution F1 – solution F2) To this, add solution due to accidental torsion:
Loads applied at CMs Floors can translate and rotate
Solution F1
Loads applied at CMs Floors can only translate
Apply on every floor a moment profile equal to load profile times accidental eccentricity; say solution F3
Solution F2 Fig. CVR Murty
231
232
Suggestions on Cl.7.9
Superposition Method (contd…)
Following solution for ed = 1.5es + 0.5b i F1 + 0.5 (F1 – F2) ± F3 Following solution for ed = e s − 0.5b i F1 ± F3
In Cl.7.9.1, the following statement should be deleted: However, negative torsional shear shall be neglected
This statement is needed only when second equation of design eccentricity is not specified. Notice that Cl.7.8.4.5 says if highly irregular buildings are analyzed as per 7.8.4.5, while 7.8.4.5 says that it is applicable only for regular or nominally irregular buildings!
233
Indeed, 7.8.4.5 is not applicable to buildings highly irregular in plan.
234
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Bldgs with Soft Storeys Cl. 7.10
Most of the time, soft storey building is also the weak storey building.
Buildings with Soft Storeys… Storeys…
• Need to increase Stiffness and Strength of Open or Soft Storeys
In the code, distinction between soft storey and weak storey has not been made. Soft/weak storey buildings are well-known for poor performance during earthquakes. In Bhuj earthquake of 2001, most multistorey buildings that collapsed had soft ground st orey. • Inverted pendulum !!
235
236
Buildings with Soft Storeys… Storeys…
Bldgs with Soft Storeys Cl. 7.10 (contd…)
• Dynamic Analysis – Include strength and stiffness of infills – Inelastic deformations in members OR
Static Design
Fig from Murtyet al, 2002
Open ground story
– Design columns and beams in soft storey for 2.5 times the Storey Shears and Moments calculated under seismic loads – Design shear walls for 1.5 times the Storey Shears calculated under seismic loads
Bare frame
Notice that the soft-storey is subject to severe deformation demands during seismic shaking. 237
238
Buildings with Soft Storeys Cl. 7.10 (contd…)
This clause gives two approaches for treatment of soft storey buildings. First approach is as per 7.10.2
239
Buildings with Soft Storeys Cl. 7.10 (contd…)
There are reservations on the way entire Cl. 7.10 has been included in the code.
It is a very sophisticated approach. Based on non-linear analysis. Code has no specifications for applying this approach. Cannot be applied in routine design applications with current state of the practice in India.
Second approach as per 7.10.3 is an empirical provision.
First approach is too open ended and does not enable the designer to implement it. Second approach is too empi rical and may be impractical in some buildings.
Also note that Table 5 defines Soft Storey and Extreme Soft Storey
And yet, nowhere the treatment is different for these two!
240
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Deformations Cl. 7.11
Buildings with Soft Storeys Cl. 7.10 (contd…)
We need considerable amount of research on Indian buildings with soft storey features in order to develop robust design m ethodology.
For a good seismic performance, a building needs to have adequate lateral stiffness. Low lateral stiffness leads to:
241
Large deformations and strains, and hence more damage in the event of strong shaking Significant P-∆ effect Damage to non-structural elements due to large deformations Discomfort to the occupants during vi brations. Large deformations may lead to pounding with adjacent structures.
242
Deformations C.7.11… C.7.11…
Deformations Cl. 7.11 (contd…)
• Inter-storey Drift – Storey drift under design lateral load with partial load factor 1.0 δ < 0.004hi
δ
hi
243
Note that real displacement in a strong shaking will be much larger than the displacement calculated for design seismic loads As a rule of thumb, the maximum displacement during the MCE shaking (e.g., PGA of 0.36g in zone V) will be about 2R times the computed displacement due to design forces.
244
Computation of Drift
Computation of Drift (contd…)
Note that higher the stiffness, lower the drift but higher the lateral loads. Hence,
Thus, in computation of drift:
For computation of T for seismic design load assessment, all sources of stiffness (even if unreliable) should be included. For computation of drift, all sources of flexi bility (even if unreli able) should be incorporated.
Stiffness contribution of non-structural elements and non-seismic elements (i.e., elements not designed to share the seismic loads) should not be included.
245
Because design seismic force is a reduced force.
This is because such elements cannot be relied upon to provide lateral stiffness at large displacements
All possible sources of flexibility should be incorporated, e.g., effect of joint rotation, bending and axial deformations of columns and shear walls, etc.
246
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Para 2 of Cl. 7.11.1
Para 3 of Cl. 7.11.1
Cl. 7.8.2 required scaling up of seismic design forces from dynamic analysis, in case these were lower than those from empirical T. This para allows drift check to be performed as per the dynamic analysis which may have given lower seismic forces, i.e., no scaling-up of forces needed for drift check.
247
248
Compatibility of Non-Seismic Elements (Cl. 7.11.2)
Compatibility of Non-Seismic Elements (Cl. 7.11.2) (contd…)
During shaking, gravity columns do not carry much lateral loads, but deform laterally with the shear walls due to compatibility imposed by floor diaphragm Moments and shears induced in gravity columns due to the lateral deformations may cause collapse if adequate provision not made. ACI Code for RC design has a separate section on detailing of gravity columns t o safeguard against this kind of collapse.
Important when not all structural elements are expected to participate in lateral load resistance.
Examples include flat-plate buildings or buildings with pre-fabricated elements where seismic load is resisted by shear walls, and columns carry only gravity loads.
During 1994 Northridge (Calif.) earthquake, many collapses due to failure of gravity columns.
249
250
Compatibility of Non-Seismic Elements (Cl. 7.11.2) (contd…)
Gravity columns
Shear Wall
F2
F3
∆
Floor slab
P2
h1
h 2 P4
F4
Shear Wall
P1
P3
Floor slab
∆
Compatibility of Non-Seismic Elements (Cl. 7.11.2) (contd…)
Pi ∆i
F1
Imposed displ. at all floors Gravity column
251
This para allows larger than the specified drift for single-storey building provided it is duly accounted for in the analysis and design.
Since deflections are calculated using design seismic force (which is a reduced force), the deflection is to be multiplied by R. Multiplier R could be debated since it will only ensure safety against Design Basis Earthquake.
h3
For safety against Maximum Considered Earthquake, multiplier should be (2R).
h 4
n Pi ∆i + ∑ Fi ∑ hj j = 1 252
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Separation Between Adjacent …Cl. 7.11.3
Separation Between Adjacent …Cl. 7.11.3 (contd…)
During seismic shaking, two adjacent units of the same building, or two adjacent buildings may hit each other due to lateral displacements (pounding or hammering).
Pounding effect is much more serious if floors of one building hit at the mid height of columns in the other building. Hence, when two units have same floor elevations, the multiplier is reduced from R to R/2.
This clause is meant to safeguard against pounding. Multiplication with R is as explained earlier: since deflection is calculated using design seismic force which are reduced forces.
253
254
Separation Between Adjacent …Cl. 7.11.3
Separation Between Adjacent …Cl. 7.11.3 (contd…)
Potential pounding location
Two adjacent buildings Two adjacent units of same building Amount of separation
Potential pounding location
• Floors levels are at same elevation
R ⋅ 2
(δ
∆ > R⋅
δ 1
∆> Building 1
Building 2
Building 1
Building 2
1 design
+ δ 2 design )
• Floors levels are at different elevations
a
b
design
+ δ 2 design
R1 ⋅ δ 1
R2 ⋅ δ 2
Pounding in situation (b) is far more damaging. 255
256
Separation Between Adjacent …Cl. 7.11.3 (contd…)
To handle pounding by roof of one unit to the middle of columns of the other unit: Soft Timber Structural Grade Steel
Section 7.12: Miscellaneous, and Section 7.1: Regular and Irregular Configuration Fig. From Arnold and Reitherman
257
IS:1893-2002(Part I)
258
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Foundations Cl. 7.12.1
Foundations Cl. 7.12.1 (contd…)
This clause is to prevent use of foundation types vulnerable to differential settlement.
Isolated R.C.C. footing without tie beams, or unreinforced strip foundation shall not be permitted in soft soils with N<10.
In zones IV and V, ties to be provided for isolated spread footings and for pile caps
Except when footings di rectly supported on rock
259
Recall newly-introduced Note 7 inside Table 1 of the code which states:
This note is applicable for all seismic zones. It would be better to bring this note inside Cl. 7.12.1.
260
Cantilevers and Projections
Foundations Cl. 7.12.1 (contd…)
Ties to be designed for an axial load (in tension and in compression) equal to A h /4 times the larger of the column or pile cap load.
• Towers, Parapets, Stacks, Balconies (Small) – Design of these attachments – Design of their connections to main structure
This is fairly empirical, and the specification appears on the low side. Many structural engineers design the ties for 5% of the larger of the column or pi le cap load.
• Design force – 5× vertical seismic coefficient for horizontal projections – 5× horizontal seismic coefficient for vertical projections
Any other alternative design approaches?
5Ah
5Av 261
262
Compound Walls Cl. 7.12.3
To be designed for design horizontal coefficient A h and importance factor = 1
Cl. 7.1 Regular and Irregular Configuration
263
264
44
Building Configuration
Building Configuration… Configuration…
• Plan Irregularities
• Configuration emphasised
– Torsion Irregularity
– Comprehensive section on identifying irregularities – Qualitative definitions of irregular buildings
Heavy Mass
• Two types Irregular Orientation of Lateral Force Resisting System
– Plan Irregularities – Vertical Irregularities
∆1 265
Floor
∆2
∆1 + ∆ 2 2
∆ 2 > 1.2
266
Torsional Irregularity
Torsional Irregularity (contd…)
Look at the top two figures of page. 19 (Fig. 3)
Can you make out anything what this figure is trying to show?
These figures were taken from NEHRP Commentary where it appears as follows:
Heavy Mass
Vertical Components of Seismic Resisting System
There is a problem with these two figures!
267
The figures have not been traced correctly for IS:1893!
268
Building Configuration… Configuration…
Building Configuration… Configuration…
– Re-entrant Corners
– Diaphragm Discontinuity Flexible A
L
A
Opening A
A L
269
A
A L
Opening
> 0.15 − 0.20
270
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OutOut-ofof-Plane Offsets
Building Configuration… Configuration…
– Out of Plane Offsets
• This is a very serious irregularity wherein there is an out-of-plane offset of the vertical element that carries the lateral loads. • Such an offset imposes vertical and lateral load effects on horizontal elements, which are difficult to design for adequately. • Again, there is a problem in figure for this in the code – Shear walls are not obvious.
271
Shear Wall
Shear Wall
Shear Wall
272
Building Configuration… Configuration…
Building Configuration… Configuration…
– Non-Parallel System
• Vertical Irregularities – Stiffness Irregularity (Soft Storey) y
x
ki+1 ki ki-1 273
< 0.7k i +1
k i
< 0.8
k i +1 + k i + 2 + k i + 3 3
274
Mass and Stiffness Irregularity
Building Configuration… Configuration…
– Mass Irregularity • induced by the presence of a heavy mass on a floor, say a swimming pool.
W i+1 W i W i-1
275
k i
• It is really the ratio of mass to stiffness of a storey that is important. • Our code should provide a waiver from mass and stiffness irregularities if the ratio of mass to stiffness of two adjacent storeys is similar.
W i > 2 W i −1 W i > 2 W i +1
276
46
Building Configuration… Configuration…
Building Configuration… Configuration…
– Vertical Geometric Irregularities
L1
A
A A
A
L
> 0.15 − 0.20
L2
L1
L2
L
> 1.5L1
L A
A L
L2 277
278
Building Configuration… Configuration…
Building Configuration… Configuration…
– Strength Irregularity (Weak Storey)
– In-plane Discontinuity in Lateral Load Resisting Elements
S i
Upper Floor Plan
< 0.8S i +1
Si+1 Si Si-1
Lower Floor Plan
279
280
Building Configuration…
Geometrically building may appear to be regular and symmetrical, but may have irregularity due to distribution of mass and stiffness. (a) (b) Arrangement of shear walls and braced frames-not recommended. Note that the heavy lines indicate shear walls and/or braced frames
It is better to distribute the lateral load resisting elements near the perimeter of the building rather than concentrate these near centre of the building.
Fig. From NEHRP Commentary
(a) (b) Arrangement of shear walls and braced frames- recommended. Note that the heavy lines indicate shear walls and/or braced frames
281
282
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Diaphragm Discontinuity
Diaphragm Discontinuity (contd…)
Diaphragm discontinuity changes the lateral load distribution to different elements as compared to what it would be with rigid floor diaphragm. Also, it could induce torsional effects which may not be there if the floor diaphragm is rigid . Observe the top two figures of page 20.
Notice the words “mass resistance eccentricity” do not make sense.
Fig in Code
Again, these are from NEHRP Com mentary and not traced correctly in our code.
RIGID
FLEXIBLE
O
DIAPHRAGM
P
E
N
DIAPHRAGM
Fig in NEHRP Vertical Components of Seismic Resisting System
Discontinuity in Diaphragm Stiffness 283
284
Problems with Irregularities
In buildings with vertical irregularity, load distribution with building height is different from that in Cl. 7.7.1.
Problems with Irregularities (contd…)
Dynamic analysis is required.
In buildings with plan i rregularity, load distribution to different vertical elements is complex.
In irregular building, there may be concentration of ductility demand in a few locations. Special care needed in detailing. Just dynamic analysis may not solve the problem.
Floor diaphragm plays an important role and needs to be modelled carefully. A good 3-D analysis is needed.
285
286
Code on Irregularity
Our code has simplistic method of treating the irregularities.
Compare Tables of NEHRP shown earlier in this lecture.
287
For irregular buildings, it just encourages dynamic analysis.
Seismic Force Estimation
For each type of irregularity and for each seismic performance category, different requirements are imposed.
Dynamic analysis is not always sufficient for irregular buildings, and Dynamic analysis is not always needed for irregularities. 288
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Design Seismic Lateral Force • Two ways of calculating – Equivalent Static Method • Seismic Coefficient Method
Single mode dynamics Simple and regular structures
– Dynamic Analysis Method
Origin of Equivalent Static Method
• Response Spectrum Method Multi-mode
dynamics Irregular structures
• Time History Method
Special structures
289
290
Dynamics of 2 DOF System
Dynamics of 2 DOF System… System…
• Lateral Force
• Dynamic Characteristics
m2
m2 k2
k2
m1
m1
k1
k1 Property Property
Equivalent SDOFs
Mode Mode11
Mode Mode22
M 1
M 2
K1
Property Property
Mode Mode11 PSA (g)
PSA2
K 2 M 2 T 2 = 2π / ω2
K 1 M 1 T 1 = 2π / ω1
Natural Period
T 1
292
Dynamics of 2 DOF System… System…
SD1 =
SD
m2 k2
m1
k1
293
T
SD2 =
ω12
PSA2
ω22
m1
F 12
F 22
F 11
F 21
k1
Property Property
Lateral Displacement
PSA1
• Lateral Force…
m2
Mode Participation Factor
T 2
T
Dynamics of 2 DOF System… System…
• Lateral Force… k2
PSA1
ω2 =
ω1 =
291
PSA (g)
K 2
PSA Natural Frequency
Mode Mode22
Mode Mode11
Γ 1 = {u}1
{ϕ}T 1 [m ]{1} M 1
= SD1{ϕ}1 Γ 1
u = 11 u12
Mode Mode22
Γ 2 = {u}2
Property Property
{ϕ}T 2 [m ]{1} M 2
Lateral Force
= SD2 {ϕ}2 Γ 2 u21 u22
=
Base Shear
Mode Mode11
F 11 {F }1 = [k]{u}1 = F 12 2
V B1 = ∑ F 1i i =1
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Mode Mode22
F 21 {F }2 = [k ]{u}2 = F 22 2
V B2 = ∑ F 2i i =1
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