Dcr is 1893

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Seismic FORCE ESTIMATION

IS 1893-2002

Seismic FORCE Seismic FORCE ESTIMATIONESTIMATION

IS 1893IS 1893--20022002

Durgesh C. Rai

Department of Civil Engineering, IIT Kanpur

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The material contained in this lecture handout is a property 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 sold, reproduced or generally distributed.

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Structure of Revised IS:1893Structure of Revised IS:1893

• Since 1984:– More information

– More experience

– Practical difficulties

• IS 1893: From 2002 onwards…

Part 1 :: General Provisions and Buildings

Part 2 :: Liquid Retaining Tanks – Elevated/Ground Supported

Part 3 :: Bridges and Retaining Walls

Part 4 :: Industrial and Stack-like Structures

Part 5 :: Dams and Embankments

Detailed Provisions

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IS:1893-2002

� IS:1893 first published in 1962.

� Revised in 1966, 1970, 1975, 1984, and now in 2002.

� Beginning 2002, this code is being split into several parts

� So that revisions can take place more frequently!

� Only Part 1 and 4 of the code has been published.

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What does IS:1893 Cover?

� Specifies Seismic Design Force

� Other seismic requirements for design, detailing and construction are covered in other codes

� 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� 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 overhead water tanks?

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Major Changes

� 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.

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Zone Map

� 1962 and 1966 maps had seven zones (0 to VI)

� In 1967, Koyna earthquake (M6.5, about 200 killed) occurred in zone I of 1966 map

� In 1970 zone map revised:

� Zones O and VI dropped; only five zones

� No change in map in 1975 and 1984 editions

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Zone Map (contd…)

� Latur (1993) earthquake (mag. 6.2, about 8000 deaths) in zone I!

� Revision of zone map in 2002 edition

� Zone I has been merged upwards into zone II.

� Now only four zones: II, III, 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…)

� 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.

� The Annex E of the code gives correct zones for

these two cities

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Zone Map (contd…)

� 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 in

zone III.

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Preface

� It is clear that the code is meant for normal structures, and

� For special structures, site-specific seismic design criteria should be evolved by the specialists.

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Other Effects

� 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

� By inertia force, we mean mass times acceleration

� Landslide triggered by earthquake

� Liquefaction of the founding strata

� Fire caused due to earthquake

� Flood caused by earthquake

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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.

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Intensity versus Magnitude

� It is important that you understand the difference between Intensity and Magnitude

� Magnitude tells

� How big was the earthquake

� How much energy was released by earthquake

� Intensity tells

� How strong was the vibration at a location

� Depends on magnitude, distance, and local soil

and geology

� Read more about magnitude and intensity at:

� http://www.nicee.org/EQTips/EQTip03.pdf

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Seismic Hazard

� Last para on page 3

� The criterion for seismic zones remains same as before

IXV

VIIIIV

VIIIII

VI (and lower)II

Area liable to shaking intensityZone

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Shaking Intensity

� Shaking intensity is commonly measured in terms of Modified Mercalli scale or MSK scale.

� See Annex. D of the code for MSK Intensity Scale

� There is a subtle change: Modified Mercalliintensity is replaced by MSK intensity!

� In practical terms, both scales are same. Hence, it does not really matter.

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Zone Criterion

� 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

� Current trend world wide is to

� 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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Peak Ground Acceleration

� Maximum acceleration response of a rigid system (Zero Period Acceleration) is same as Peak Ground Acceleration (PGA).

� Hence, for very low values of period, acceleration spectrum tends to be equal to PGA.

� We should be able to read the value of PGA

from an acceleration spectrum.

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Peak Ground Acceleration (contd…)

� Average shape of acceleration response spectrum for 5% damping (Fig. on next slide)� Ordinate at 0.1 to 0.3 sec ~ 2.5 times the PGA

� There can be a stray peak in the ground motion; i.e., unusually large peak. � Such a peak does not affect most of the response spectrum and needs to be ignored.

� Effective Peak Ground Acceleration (EPGA) defined as 0.40 times the spectral acceleration in 0.1 to 0.3 sec range (cl. 3.11)� There are also other definitions of EPGA, but we will not concern ourselves with those.

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Typical shape of acceleration spectrum

•Typical shape of acceleration response spectrum

•Spectral acceleration at zero period (T=0) gives PGA

•Value at 0.1-0.3 sec is ~ 2.5 times PGA value

PGA = 0.6g0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

Per iod (sec)

Spectr

al A

ccele

ratio

n (

g)

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Earthquake Level

� Maximum Credible Earthquake (MCE):

� 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

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Earthquake Level (contd…)

� 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)

� Corresponds to 2% probability of being

exceeded in 50 years (2,500 year return period)

� Uniform Building Code 1997 (USA)

� 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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Max Considered EQ (MCE) (contd...)

� IS:1893

� MCE motion as per Indian code does not

correspond to any specific probability of

occurrence or return period.

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Design Basis EQ (DBE)

� This is the earthquake motion for which structure is to be designed considering inherent conservatism in the design process

� UBC1997 and IBC2000:

� Corresponds to 10% probability of being

exceeded in 50 years (475 year return period)

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Design Basis EQ (DBE) (contd...)

� Cl. 3.6 of the code (p. 8)

� Earthquake that can reasonably be expected to

occur once during the design life of the structure

� What is reasonable…not made clear in our 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

� The factor 2 in denominator of eqn for Ah on p.14

accounts for this

� See definition of Z on p.14 of the code

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Modal Mass

� 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

� 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

� 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.

Undamped Natural Period T (sec)

Maximum Acceleration, g

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Example on Modal Mass (contd…)

� First mode of vibration:

� Period (T1)=0.6sec,

� Modal Mass= 90,000kg

� Obtained using first mode shape

� Spectral acceleration = 0.87g

� Read from Response Spectrum for T=0.6sec

� Max Base shear contributed by first mode =

= (90,000kg)x(0.87x9.81m/sec2) = 768,000 N = 768 kN

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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 =

= (8,000kg)x(0.80x9.81m/sec2) = 62,800 N = 62.8 kN

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Modal Participation Factor (Cl.3.21)

� A term used in dynamic analysis.

� More later

� Read the definition in Cl. 3.21

� There seems to be a typographical error.

� “amplitudes of 95% mode shapes” should be read as “amplitude of mode shapes”

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Seismic Weight (Cl.3.29)

� 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

� Buildings designed for storage purposes are likely to have larger percent of service load present at the time of shaking.

� Notice the values in Table 8

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Seismic Mass (Cl.3.28)

� 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.

� Mass times gravity is weight

� 1 kg mass is equal to 9.81N (=1x9.81) weight

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Section 4

Terminology on Buildings

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Centre of Stiffness

� 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:

� 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

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Centre of Rigidity

� 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!

� Experts will tell you that there are subtle

differences between these two terms. But that is

not important from our view point.

� It would have been better if the code had used either stiffness or rigidity throughout

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Eccentricity

� Cl. 4.21 defines Static Eccentricity. � 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.

� Hence, a dynamic amplification is to be applied

to the static eccentricity before it can be used in

design.

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Eccentricity (contd…)

� An accidental eccentricity is also considered because:

� The computation of eccentricity is only

approximate.

� During the service life of the building, there could

be changes in its use which may change centre

of mass.

� Design eccentricity (cl.4.6) is obtained from static eccentricity by accounting for (cl.7.9.2)

� Dynamic amplification, and

� Accidental eccentricity

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Dual System

� Consider buildings with shear walls and moment 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 total design seismic loads.

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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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� Conditions of Cl. 4.9 are not met. Here, two

possibilities exist (see Footnote 4 in Table 7, p. 23):

� 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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� Clearly, the dual systems are better and are

designed for lower value of design force.

� See Table 7 (p. 23) of the code. There is different

value of response reduction factor (R) for the

dual systems.

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Moment Resisting Frame

� Cl. 4.15 defines Ordinary and Special Moment Resisting Frames.

� Ductile structures perform much better during earthquakes.

� 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)

� 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.

� This is because in that event, the seismic loads

from upper parts of the building get transferred

to the basement walls and then to the

foundation. That is,

� Columns in the basement storey will have insignificant seismic loads, and

� Basement walls act as part of the foundation.

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Number of Storeys (contd…)

� Definition of number of storeys

� Was relevant in 1984 version of the code wherein

natural period (T) was calculated as 0.1n.

� In the current code, it is not relevant

� In new code, Cl. 7.6 requires height of building.

� See the definition of h (building 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

� 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.

� Hence, the term Extreme Soft Storey and cl. 7.10

(Buildings with Soft Storey) were added hurriedly

after the earthquake.

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Soft Storey (contd…)

� 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.� 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.

� 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

� Note that the stiffness and strength are two different things.

� Stiffness: Force needed to cause a unit

displacement. It is given by slope of the force-

displacement relationship.

� Strength: Maximum force that the system can

take

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Weak Storey (contd…)

� 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

� Storey Drift defined in cl. 4.23 of the Code.

� Storey drift not to exceed 0.004 times the storey

height.

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Definition of Vroof

� On p. 11, it is defined as peak storey shear force at the roof due to all modes considered.� It is better to define it as peak storey shear in the

top storey due to all modes considered.

10

55

Section 6.1: General Principles IS:1893-2002(Part I)

56

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

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Ground Motion (cl. 6.1.1)

� Usually, the vertical motion is weaker than the horizontal motion

� On average, peak vertical acceleration is one-half to two-thirds of the peak horizontal acceleration.

� Cl. 6.4.5 of 2002 code specifies it as two-thirds

58

Ground Motion Contd…

� All structures experience a constant vertical acceleration (downward) equal to gravity (g) at all times.

� 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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� Example: A roof accelerating up and down by 0.20g.

� Implies that it is experiencing acceleration in the

range 1.20g to 0.80g (in place of 1.0g that it

would experience without earthquake.)

� Factor of safety for gravity loads (e.g., dead and live loads) is usually sufficient to cover the earthquake induced vertical acceleration

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� 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.,

� Large span structures

� Cantilever members

� Prestressed horizontal members

� Structures where stability is an issue

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Effects other than shaking

� Ground shaking can affect the safety of structure in a number of ways:

� Shaking induces inertia force

� Soil may liquefy

� Sliding failure of founding strata may take place

� Fire or flood may be caused as secondary effect

of the earthquake.

� 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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Design Lateral ForceDesign Lateral Force

• Philosophy of Earthquake-Resistant Design

– First calculate maximum elastic seismic forces

– Then reduce to account for ductility and overstrength

Lateral Force

Elastic Force reduced by R

Design Force

Actual

MaximumElastic Force

Elastic

0

H, ∆∆∆∆

Lateral Deflection

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Earthquake Design Principle

� 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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Clause 6.1.3

� 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

� A well designed structure can withstand a horizontal force several times the design force due to:

� Overstrength

� Redundancy

� Ductility

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Overstrength

� The structure yields at load higher than the design load due to:� Partial Safety Factors

� Partial safety factor on seismic loads

� Partial safety factor on gravity loads

� Partial safety factor on materials

� Material Properties � 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

12

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Redundancy

� Yielding at one location in the structure does not imply yielding of the structure as a whole.

� 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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Ductility

� As the structure yields, two things happen:

� 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)

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)(F Force Design

)(F Force Elastic MaximumFactor Reduction Response

des

el=

Design force

MaximumLoad Capacity

To

tal H

ori

zo

nta

l L

oa

d

Roof Displacement (∆)

Non linear Response

First

Significant

Yield

Linear Elastic Response

∆max

Fy

Fs

Fdes

∆y∆w

Fel

Load at First Yield

Due to

Overstrength

Due to Redundancy

Due to Ductility

Maximum force if structure remains elastic

0

Total Horizontal

Load

∆

Figure: Courtesy Dr. C V R Murty

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Para 2 and 3 of Cl. 6.1.3.

� 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.

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Para 2 and 3 of Cl. 6.1.3 Contd…

� 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.

� The connections between different parts have

been problem areas.

� Connections in precast structures in high seismic

regions require special attention.

13

73

Past Performance

� 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 lateral

loads are serious concern.

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Para 4 of Cl. 6.1.3

� This is an important clause for moderate seismic regions.

� 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.

75

Soil Structure Interaction (Cl. 6.1.4)

� 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.

� This is valid for structures located on rock sites.

� For soft soil sites, this may not always be a good

assumption.

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Soil Structure Interaction (Cl. 6.1.4) Contd…

� Presence of structure modifies the free field motion since the soil and the structure interact.� 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 given earthquake depends on the properties and geological features of the subsurface soils also.

77

SSI Contd…

� Consideration of SSI generally

� Decreases lateral seismic forces on the structure

� Increases lateral displacements

� Increases secondary forces associated with P-

delta effect.

� For ordinary buildings, one usually ignores SSI.

� NEHRP Provisions provide a simple procedure to

account for soil-structure interaction in buildings

78

Direction of Ground Motion (Cl. 6.1.5)

� During earthquake shaking, ground shakes in all possible directions.

� Direction of resultant shaking changes from

instant to instant.

� Basic requirement is that the structure should be able to withstand maximum ground motion occurring in any direction.

� For most structures, main concern is for horizontal

vibrations rather than vertical vibrations.

14

79

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:� 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.

80

Building Plans with Orthogonal Systems

81

Building Plans with Non-Orthogonal Systems

walls

82

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:� 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.

83

Sections 6.2 and 6.3

IS:1893-2002(Part I)

84








� This lecture covers sub-sections: Cl. 6.2 and Cl. 6.3

15

85

Cl.6.2 Assumptions

� 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.

86

Mexico Earthquake of 1985

� Earthquake occurred 400 km from Mexico City

� Great variation in damages in Mexico City� Some parts had very strong shaking

� In some parts of city, motion was hardly felt

� Ground motion records from two sites:� UNAM site: Foothill Zone with 3-5m of basaltic rock underlain by softer strata

� SCT site: soft soils of the Lake Zone

87

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

Time (sec)

Figure from Kramer, 1996

88

Mexico Earthquake of 1985 (contd…)

� 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.

89

Assumption b)

� 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.

� Same with strong earthquake shaking and

maximum flood.

90

Assumption c) on Modulus of Elasticity

� 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

16

91

Loads and StressesLoads 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

92

Cl.6.3 Load Combinations and Increase in


� Cl.6.3.1.1 gives load combinations for Plastic Design of Steel Structures

� Same as in IS:800-1978

� More load combinations in IS:800-2007

� Cl.6.3.1.2 gives load combinations for Limit State Design for RC and Prestressed Concrete Structures

� Same as in IS:456-2000 (RC structures) and

IS:1343-1980 (Prestressed structures) with one

difference

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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 IS:456, the

footnote creates an impression that it is not

always needed.

� It has been noticed that many designers do not routinely consider this combination because of the way it is written.

94

Load Combination 0.9DL ±±±±1.5EL

� Horizontal loads are reversible in direction.

� In many situations, design is governed by effect of horizontal load minus effect of gravity loads.

� 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.

95

Direction of Earthquake Loading

� 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� 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

Direction of Earthquake Loading (contd…)

� 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.

17

97

Direction of Horizontal Ground Motion in Design

(Cl.6.3.2.1)

� 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.

� 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

98

Cl.6.3.2.1 (contd…)

� 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”

99

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) ELx = Design EQ load in X-direction

� 1.2 (DL+LL-ELx)

� 1.2 (DL+LL+ELy) ELy = Design EQ load in Y-direction

� 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

100

Non-Orthogonal Systems (Cl.6.3.2.2)

� 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 unconservativefor elements not oriented along X- and Y-directions.

101

• Lateral force resisting system non-parallel in two plan directions

– Consider design based on one direction at a time

ELx

y

y

x

x

ELy

Load CombinationsLoad Combinations……

102

– Problem

Elements at 450 orientation designed only for 70%of lateral force

0

0.2

0.4

0.6

0.8

1

0 15 30 45 60 75 90

ELx

ELyV

Force effective along

direction of inclined

element

Orientation of inclined element with respect to x-axis


θ

18

103

Non-Orthogonal Systems (Cl.6.3.2.2) (contd…)

� 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:� 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

104

– Solution :: Try (100%+30%) together

ELx

y

x

x

ELy

0.3ELx

0.3ELy


Note that directions of earthquake forces are reversible. Hence, all

combinations of directions are to be considered.

105


� Thus, EL now implies eight possibilities:+(Elx + 0.3ELy)

+(Elx - 0.3ELy)

-(Elx + 0.3ELy)

-(Elx - 0.3ELy)

+(0.3ELx + Ely)

+(0.3ELx - ELy)

-(0.3ELx + ELy)

-(0.3ELx - ELy)

106

– Justification :: Say ELx = ELy = V

V

0.3Vsinθ

V*=Vcosθ + 0.3Vsinθ

θ

0

0.5

1

1.5

0 15 30 45 60 75 90

ELx+0.3ELy

0.3ELx+ELy

Vcosθ

0.3V

y

x

V*

θ


107


1.5 (DL+LL)

1.2[DL+LL+(ELx+0.3ELy)]

1.2[DL+LL+(ELx-0.3ELy)]

1.2[DL+LL-(ELx+0.3ELy)]

1.2[DL+LL-(ELx-0.3ELy)]

1.2[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+(ELx+0.3ELy)]

1.5[DL+(ELx-0.3ELy)]

1.5[DL-(ELx+0.3ELy)]

1.5[DL-(ELx-0.3ELy)]

1.5[DL+(0.3ELx+ELy)]

1.5[DL+(0.3ELx-ELy)]

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)]

�Therefore, one must consider 25 load cases:

108


� 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%.

19

109

Cl.6.3.4.1

� 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.� Now, EQ load means the following 24 combinations:

� ± Elx ± 0.3ELy ± 0.3ELz

� ± Ely ± 0.3ELx ± 0.3ELz

� ± Elz ± 0.3ELx ± 0.3ELy

� Hence, EL now means 24 combinations

� A total of 73 load cases for RC structures!

110

Cl.6.3.4.2

� 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

2)(2)(2)( ELzELyELxEL ++=

111

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.

112

Typographical Errors in Table 1

� The Table within Table 1, giving values of desirable minimum values of N.� 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”

� Note 1 is also repeated within Note 4. � Hence, Note 1 should be dropped.

113

Second Para of Cl.6.3.5.2

� It points out that in case of loose or medium dense saturated soils, liquefaction may take place.

� Sites vulnerable to liquefaction require

� Liquefaction potential analysis.

� Remedial measures to prevent liquefaction.

� Else, deep piles are designed assuming that soil

layers liable to liquefy will not provide lateral

support to the pile during ground shaking.

114

Liquefaction Potential

� Information given in cl.6.3.5.2 and Table 1 on Liquefaction Potential is very primitive:

� Note to Cl.6.3.5.2 encourages the engineer to refer to specialist literature for determining liquefaction potential analysis.

� It is common these days to use SPT or CPT results for detailed calculations on liquefaction potential analysis.

20

115

Sections 6.4

IS:1893-2002(Part I)

Lecture 2

116








� This lecture covers sub-section 6.4.

117

Response Spectrum versus Design Spectrum

� 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

Undamped Natural Period T (sec)

Spectral Acceleration, g

118

Response Spectrum versus Design Spectrum (contd…)

� 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 averageshape without local peaks and valleys you see in the response spectrum

119

Design Spectrum

� 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.

� See Fig. next slide.

120

Design Spectrum (contd…)

Natural vibration period Tn, sec

Spec

tral

Acc

eler

atio

n, g

Fig. from Dynamics of Structures by Chopra, 2001

21

121


� Design Spectrum is a design specification

� It must take into account any issues that have bearing on seismic safety.

122


� Design Spectrum must be accompanied by:

� Load factors or permissible stresses that must be

used

� Different choice of load factors will give different seismic safety to the structure

� Damping to be used in design

� Variation in the value of damping used will affect the design force.

� Method of calculation of natural period

� Depending on modeling assumptions, one can get different values of natural period.

� Type of detailing for ductility

� Design force can be lowered if structure has higher ductility.

123

• Two methods of estimation of design seismic lateral force

– Seismic Coefficient Method

– Response Spectrum Method

– In both methods

•Seismic Design Force Fd = Fe /R = A W� A = Design acceleration value

�W = Seismic weight of structure

Design SPECTRUMDesign SPECTRUM……

124

• Design Horizontal Acceleration Spectrum

( )( )

R

ITg

SZ

TA

a

h2

=

Maximum Elastic Acceleration

Reduction to account for ductility and overstrength

Design Lateral ForceDesign Lateral Force……

125

• Seismic Zone Factor

– Reflects Peak Ground Acceleration (PGA) of the region duringMaximum Credible Earthquake (MCE)

0.360.240.160.10Z

VIVIIIIISeismic Zone

Acceleration

PGA

Time

Spectral Acceleration

Natural Period

PGA

0

(ZPA::Zero Period Acceleration)

Seismic zone factorSeismic zone factor

126

– Relative Values Consistent

– Factor of 2 in Ah for reducing

PGA for MCEto PGA for Design Basis Earthquake (DBE)

0.360.240.160.10Z


1.6

1.5

1.5

(Earthquake which can be reasonably expected to occur

at least once during the lifetime of structures)

Design SPECTRUMDesign SPECTRUM……

22

127

• Importance factor I– Degree of conservatism– Willing to pay more for assuring essential services– Domino effect of disaster– Important & community buildings

• 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

1.0All Others2

1.5Important, Community & Lifeline Buildings1

IBuildingS.No.

Importance factorImportance factor

128

Soil Effect

� Recorded earthquake motions show that response spectrum shape differs for different type of soil profile at the site

Period (sec)

Fig. from Geotechnical

Earthquake Engineering, by

Kramer, 1996

129

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.

Spec

tral

Acc

eler

atio

n C

oef

fici

ent

(Sa

/g)

Period(s)

Fig. from

IS:1893-2002

130


� 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.

131


� The International Building Code (IBC2000) classifies the soil type based on weightedaverage (in top 30m) of:

� 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.

132

Shape of Design Spectrum

� 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 motion characteristics expected.

23

133

Response Reduction Factor

� As discussed earlier, the structure is allowed to 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

� 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.

134

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

135

Response Reduction Factor (R) (contd…)

� Study Table 7 very carefully including all the footnotes. We have already discussed terms: Dual systems, OMRF, and SMRF� Notes 4 and 8 were covered earlier when we discussed

Dual systems.

� The values of R were decided based on engineering judgment.� 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.

136


� Note 6 prohibits ordinary RC shear walls in zones IV and V.

� Such a note is not there for OMRF.

� 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.

� This needs to be corrected in the code.

137


� Moreover, there are a number of other systems that are prohibited in high zones and those are not listed in this table. For instance,

� 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.

� It would be better for this table to drop Note 6.

� In its place, there could be a general note that

some of the above systems are not allowed in

high seismic zones as per IS:4326 or IS:13920.

138

Response Reduction Factor (contd…)

� 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)

� This statement should not be there.

� For buildings, I never exceeds 1.5 and the lowest

value of R is 1.5 in Table 7

� 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.

24

139

– R values can be taken as for Dual Systems, only if both conditions below are satisfied

•Shear walls and MRFs are designed to resist VB in proportion to their stiffness considering their interaction at all floor levels

•MRFs are designed to independently resist at least 25% of VB

Shear Wall MRF

Response Reduction Factor Response Reduction Factor ……

140

Design Spectrum for Stiff Structures

� For very stiff structures (T < 0.1sec), ductility is not

helpful in reducing the design force.

� Codes tend to disallow the reduction in force in

the period range of T < 0.1sec

Actual shape of response spectrum(may be used for higher modes only)

T(seconds)

Sp

ectr

al a

ccel

erat

ion

Design spectrum assumes peakextends to T=0

Concept sometimes used by the codes for response spectrum in low period range.

141

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.

142

Underground Structures Cl.6.4.4

� 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 one-half if the structure is at depth of 30m or below.

� Linear interpolation for structures and

foundations if depth is less than 30m.

143

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 above-ground structure) with foundation going deeper than 30m: � 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

Equations for Design Spectrum

� 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.

25

145

Equations for Design Spectrum

� 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)

146

Site Specific Design Criteria Cl.6.4.6

� 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.

147

Sections 7.1 to 7.7 on Buildings

IS:1893-2002(Part I)

148

Buildings (Section 7)

� Sub-sections� 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

149

Regular and Irregular Configuration (Cl. 7.1)

� 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.

150

Importance of Configuration

� To quote Late Henry Degenkolb, the well-known earthquake engineer in California:

If we have a poor configuration to start with,

all the engineer can do is to 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 its

ultimate performance too much.

26

151

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).

152

Regular versus Irregular Configuration

� Tables 4 and 5 list out the irregularities in the building configuration

� Table 4 and Fig. 3 for Irregularities in Plan

� Table 5 and Fig. 4 for Irregularities in Elevation

153

A Remark on IS:13920

� 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.

154

Design Imposed Load…(Cl. 7.3)

� 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:

� 1.2 DL + 0.3LL + 1.2LL

� The Cl. 7.3.3 should be dropped.

155

Design Lateral Force (Cl. 7.5)

� Note that the code no longer talks of two methods: seismic coefficient method and response spectrum method.

� There have been instances of designer calculating seismic design force for each 2-D frame separately based on tributary mass shared by that frame.

� This is erroneous since only a fraction of the

building mass is considered in the seismic load

calculations.

156

EQx

Mass being considered for calculation of inertia force due to earthquake

EQx

Mass that causesEarthquake Force

in X-Direction

Plan of building

Calculation of design seismic force on the basis of

tributary mass on 2-D frames leads to significant under-design.

27

157

• Seismic Weight of Building W

– Dead load

– Part of imposed loads

50Above 3.0

25Up to and including 3.0

% of Imposed Load

to be considered

Imposed Uniformly Distributed Floor Loads

(kN/m2)

Design Lateral Force (Cl. 7.5)Design Lateral Force (Cl. 7.5) ……

158

Design Lateral Force (Cl. 7.5) (contd…)

� Now, Cl. 7.5.2 makes it clear that one has to evaluate seismic design force for the entire building first and then distribute it to different frames/ walls.

� Cl. 7.5.2 does not mean that one has to necessarily carry out a 3-D analysis.

� One could still work with 2-D frame systems.

159

Fundamental Natural Period (Cl. 7.6)

� For frame buildings without brick infills

� For all other buildings, including frame buildings

with brick infill panels:

where h is in meters

..aT h= 0 750 075

a

. hT

d=

0 09

d

d

160

Fundamental Natural Period (Cl. 7.6) (contd…)

� 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.

161

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

� 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.

162

Observations on Steel Frame Buildings During San Fernando EQ

Fig. from NEHRP Commentary

28

163

Observations on RC Frame Buildings During San Fernando EQ


164

Observations on RC Shear Wall Buildings During San Fernando EQ


165

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

� In low and medium rise buildings, � Fundamental period dominates the response, and

� Fundamental mode shape is close to a straight line (with regular distribution of mass and stiffness)

� For tall buildings, contribution of higher modes can be significant even though the first mode may still contribute the maximum response.

166

Vertical Distribution of Seismic Load (Cl. 7.7.1) (contd…)

� Hence, NEHRP provides the following expression for vertical distribution of seismic load

� Where k = 1 for T ≤ 0.5sec, and k = 2 for T ≥ 2.5 sec. Value of k varies linearly for T in 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.

∑=

=n

j

k

jj

k

ii

Bi

hW

hWVQ

1

167

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.

168

Concept of Floor Diaphragm Action

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

29

169

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 stiffness.

170


Lateral Load Distribution Due to Rigid Floor Diaphragm: Symmetric Case – No Torsion

171

� When building is not symmetrical, the floor undergoes rigid body translation and rotation.

172


Analysis of Forces Induced by Twisting Moment (Rigid Floor Diaphragm)

173

Rigid 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.

� Rotation of columns is governed by out-of-plane behavior of slab and beams.

(a) In-plane floor deformation, (b) Out-

of-plane floor deformation.


174

Buildings without Diaphragm Action

� When the floor diaphragm does not exist, or when the diaphragm is extremely flexible as compared to the vertical elements

� The load can be distributed to the vertical

elements in proportion to the tributary mass

30

175

Flexible Floor Diaphragms� There are instances where floor is not rigid.

� “Not rigid” does not mean it is completely 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.

(Plan View of Floor)

In-plane flexibility of diaphragm to be considered when

∆2>1.5{0.5(∆

1+ ∆

2)}

Definition of Flexible Floor

Diaphragm (Cl. 7.7.2.2)


176

Analysis for Flexible Floor Diaphragm Buildings

� 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

177


Lateral Load Distribution

Considering Floor Diaphragm Deformation: Vertical Analogy Method

178

Analysis for Flexible Floor Diaphragm Buildings (contd…)

� Alternatively, one can take the design force as envelop of (that is, the higher of) the two extreme assumptions, i.e.,

� Rigid diaphragm action

� No diaphragm action (load distribution in

proportion to tributary mass)

179

Section 7.8: Dynamic Analysis

IS:1893-2002(Part I)

180


� Sub-sections

� Cl. 7.1: Regular and Irregular Configurations












� This lecture covers sub-section 7.8

31

181

About This Lecture

� 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.

182

Requirement of Dynamic Anal. Cl. 7.8.1

Ht > 12 m Ht > 40 mIV and V

Ht > 40 mHt > 90 mII and III

Irregular

Buildings

Regular

Building

Seismic

Zone

� Notice wordings of section b) in Cl. 7.8.1

� All framed buildings higher than 12m….

183

Why Dynamic Analysis?

� 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

184

Why Dynamic Analysis? (contd…)

� 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:

� These too will require dynamic analysis.

185

Lower Bound on Seismic Force (Cl. 7.8.2)

� 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.

� Implies that empirical T is more reliable than T

computed by dynamic analysis

186

Lower Bound on Seismic Force (Cl. 7.8.2) (contd…)

� There are considerable uncertainties in modeling a building for dynamic analysis, e.g.,� 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

32

187

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

� Even when the results of dynamic analysis are scaled up to design force based on empirical T:

� The load distribution with building height and to

different elements is based on dynamics.

188

Value of Damping Cl. 7.8.2.1

� Damping to be used

� Steel buildings: 2% of critical

� RC buildings: 5% of critical

� For masonry buildings? Not specified.

� Recommended value is 5%

� 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.

189

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.

190

Value of Damping Cl. 7.8.2.1 (contd…)

� 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.

191

A Note on Static Procedure

� The procedure of Cl.7.5 to 7.7 does not 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

� Even though its applicability is limited to simple

buildings

192

Number of Modes Cl. 7.8.4.2

� The code requires sufficient number of modes so that at least 90% of the total seismic mass is excited in each of the principal directions.

� There is a problem in wordings of this clause. First sentence reads as:

� The number of modes to be used in the analysis

should be such that the sum total of modal

masses in all modes considered is at least 90

percent of the total seismic mass and missing

mass correction beyond 33 percent.

� The portion highlighted in red should be deleted.

33

193

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….

194

Modal Combination Cl. 7.8.4.4

� 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.

195

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.,

� Moment in a beam at a given location, Axial force in column, etc.

� Deflection at a given location

196

Alternate Method to CQC

� Use SRSS (Square Root of Sum of Squares) if the natural modes are not closely-spaced.

� Use Absolute Sum for closely-spaced modes

� To appreciate the alternative method, consider two examples.

....2

4

2

3

2

2

2

1++++= λλλλλ

...4321 ++++= λλλλλ

197

Example 1 on Modal Combination:

� For first five modes of vibration, natural period/ natural frequency and maximum response are given. Estimate the maximum response for the structure.

1201502303501100Response Quantity

9.097.145.002.861.05Natural

Frequency

0.110.140.200.350.95Natural Period

5 4321Mode

198

Example 1 on Modal Combination (contd…)

� All natural frequencies differ from each other by more than 10%.

� As per Cl. 3.2, none of the modes are closely-

spaced 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

1193)120()150()230()350()1100( 22222 =++++=

34

199

Example 2 on Modal Combination

� For first six modes of vibration, natural period/ natural frequency and maximum response are given. Estimate the maximum response for the structure.

8090200190230850Response Quantity

4.003.852.941.351.281.06Natural frequency

(Hz)

0.250.260.340.740.780.94Natural period (sec)

654321Mode

200

Example 2 on Modal Combination (contd…)

� 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)

984)170()200()420()850(2222 =+++=

201

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 the procedure of Cl. 7.8.4.5 is not valid.

202

Lumped Mass Model for Cl. 7.8.4.5

X3(t)

X2(t)

X1(t)

203

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.

� It is not uncommon to confuse between the units of mass and weight when performing dynamic analysis.� Leads to huge errors.

204

Lecture 3

This lecture covers

Sections 7.9 to 7.11

IS:1893-2002(Part I)

35

205


� Sub-sections

� Cl. 7.1: Regular and Irregular Configurations












� This lecture covers sub-sections 7.9 to 7.11

206

TorsionTorsion

• Uncertainties

– Location of imposed load

– Contributions to structural stiffness

• Accidental Eccentricity

– Torsion to be considered in Symmetric Buildings

• Design Eccentricity

−

+=

isi

isidi b050e

b050e51ofWorste

.

..

ib

207

Design eccentricity� Now the equation for design eccentricity is:

� Notice:� First equation has 1.5 times the computed eccentricity, plus additional term due to accidental eccentricity

� 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 accidental eccentricity.

edi =

1.5esi+0.05bi

esi-0.05bi

208

First Equation for Design Eccentricity

� The intention is to add the effect of accidental 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:

1.5esi ± 0.05biedi =

209

– Two cases of Design Eccentricity

CM CSCM*

ib05.0

isibe 05.0−isi

be 05.05.1 +

sie5.0

sie ib05.0

sie

CM CSCM*

TorsionTorsion……

210

ith floor

esi

CR CM

bi

1.5esi+0.05 bi

CR CM CM*

Calculated locations of

CM and CR

Location CM* to be used

in analysis for first eqn. of

cl. 7.9.2

Considering EQ in Y-Direction

First Equation for Design Eccentricity (contd…)

36

211

Second Equation for Design Eccentricity

� In second equation, it is expected that there is accidental eccentricity in the opposite sense, i.e., it tends to oppose the computed eccentricity.

� 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:

edi =esi ± 0.05bi

212

ith floor

esi

CR CM

bi

esi

CR CM

Calculated locations of

CM and CR

Location CM* to be used

in analysis for first eqn. of

cl. 7.9.2

Considering EQ in Y-Direction

Second Equation for Design Eccentricity (contd…)

CM*

0.05 bi

213

• Incorporating the provision in practice


si i

di

si i

. e . be

e . b

+= −

1 5 0 05

0 05

CMCS

214

• Incorporating the provision in practice…

– Effect of shear and torsion (esi)

•Analysis A


CMCS

215


– Effect of shear only

•Analysis B


CMCS

216


– Effect of shear, torsion esi and 0.05bi•Analysis C


CMCSCM*

0.05bi

37

217


– Solution

•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


218

Definition of Centre of Rigidity

� Earlier we defined Centre of Rigidity as:� 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.

� 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.

219

CR for Multi-Storey Buildings

� It can be defined in two ways:

� All Floor Centre of Rigidity, and

� Single Floor Centre of Rigidity

220

All Floor CR Definition

� 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.

� As per this definition, location of CR is

dependent on building stiffness properties as

well as on the applied lateral load profile.

221

All Floor Definition of CR

Figure 1: ‘All floor’ definition of center of rigidity

Fjy

CR

CR

CR

CR

CR

CRF(j+1)y

F1y

F2y

F(j-1)y

Fny

No rotation in any floor

Fig. Dhiman Basu

222

Single Floor CR Definition

� 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.

38

223

Single Floor Definition of CR

CRjth floor does not rotate (other floors may rotate)

Fig. Dhiman Basu

224

Choice of Definition

� 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.� Use any definition that you find convenient to use.

� For computer-aided analysis, the all-floor definition is more convenient.

225

To Calculate Eccentricity

� Need to locate

� Centre of Mass, and

� Centre of Rigidity

� Centre of Mass is easy to locate.

� Unless there is a significant variation in mass

distribution, we take it at geometric centre of the

floor.

� Locating CR is not so simple for a multi-storey building.

226

To Locate CR

� The way we defined it, one needs to apply lateral loads at the CR.

� But, we do not know CR in the first place.

� Notice the condition that the floor should not rotate.

� 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

227

To Locate All-Floor CR

(b) Free body diagram of a particular floor

(a) Lateral loads are applied at all floors of the constrained model

Central nodes of both ends of the diaphragm are constrained to ensure equal horizontal displacement

Column shear

Resultant of column shears passes through the center of rigidity of the floor


Lateral load proportional to the mass distribution distributed along the floor length

Fig. Dhiman Basu

228

To Locate Single-Floor CR

(b) Free body diagram of a particular floor

Column shear

Resultant of column shears passes through the center of rigidity of the floor

(a) Lateral load is applied at the constrained floor

Lateral load proportional to the mass distribution distributed along the floor length


Fig. Dhiman Basu

39

229

Alternative to Locating CR

� 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 All-Floor Definition.

� This method is based on superpositionconcept and was first published by Goel and Chopra (ASCE, Vol 119, No. 10).

230

Superposition Method

� Apply lateral load profile at the CM’s and analysethe building; say the solution is F1� 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 F2� This amounts to solving the problem as if 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.

231

Superposition Method (contd…)

Loads applied at CMs

Floors can translate and rotate

Loads applied at CMs

Floors can only translate

Solution F2Solution F1Fig. CVR Murty

232


� Hence, solution for loads applied at 1.5 times computed eccentricity

= solution F1 + 0.5(solution F1 – solution F2)

� To this, add solution due to accidental torsion:

� Apply on every floor a moment profile equal to

load profile times accidental eccentricity; say

solution F3

233


� Following solution for

� F1 + 0.5 (F1 – F2) ± F3

� Following solution for

� F1 ± F3

isd bee 5.05.1 +=

isd bee 5.0−=

234

Suggestions on Cl.7.9

� 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!� Indeed, 7.8.4.5 is not applicable to buildings highly irregular in plan.

40

235

Bldgs with Soft Storeys Cl. 7.10

� Most of the time, soft storey building is also the weak storey building.

� 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 storey.

236

• Need to increase Stiffness and Strength of Open or Soft Storeys

• Inverted

pendulum !!

Buildings with Soft StoreysBuildings with Soft Storeys……

237

Bldgs with Soft Storeys Cl. 7.10 (contd…)

Open ground story Bare frame

Notice that the soft-storey is subject to severe deformation

demands during seismic shaking.

Fig from Murty et al,

2002

238

• Dynamic Analysis– Include strength and stiffness of infills

– Inelastic deformations in members

OR

Static Design– 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

Buildings with Soft StoreysBuildings with Soft Storeys……

239

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� 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.

240


� There are reservations on the way entire Cl. 7.10 has been included in the code.

� First approach is too open ended and does not

enable the designer to implement it.

� Second approach is too empirical 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!

41

241


� We need considerable amount of research on Indian buildings with soft storey features in order to develop robust design methodology.

242

Deformations Cl. 7.11

� For a good seismic performance, a building needs to have adequate lateral stiffness.

� Low lateral stiffness leads to:

� 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 vibrations.

� Large deformations may lead to pounding with

adjacent structures.

243

• Inter-storey Drift

– Storey drift under design lateral load with partial load factor 1.0

ih0040.<δ

δ

ih

Deformations C.7.11Deformations C.7.11……

244

Deformations Cl. 7.11 (contd…)

� Note that real displacement in a strong shaking will be much larger than the displacement calculated for design seismic loads

� Because design seismic force is a reduced force.

� 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.

245

Computation of Drift

� Note that higher the stiffness, lower the drift but higher the lateral loads. Hence,

� 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 flexibility

(even if unreliable) should be incorporated.

246

Computation of Drift (contd…)

� Thus, in computation of drift:

� Stiffness contribution of non-structural elements

and non-seismic elements (i.e., elements not

designed to share the seismic loads) should not

be included.

� 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.

42

247

Para 2 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.

248

Para 3 of Cl. 7.11.1

� This para allows larger than the specified drift for single-storey building provided it is duly accounted for in the analysis and design.

249

Compatibility of Non-Seismic Elements (Cl. 7.11.2)

� 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.

250

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 to safeguard against this kind of collapse.

251


Shear WallGravity columns

Floor slab

n

i i i jj

P F h=

∆ +

∑ ∑

1

i iP∆F1

F2

F3

F4

P1

P2

P3

P4

h1

h2

h3

h4

∆ ∆

Shear Wall

Floor slab

Gravity column

Imposed displ. at all floors

252


� 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.

� For safety against Maximum Considered

Earthquake, multiplier should be (2R).

43

253

Separation Between Adjacent …Cl. 7.11.3

� 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).

� 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.

254

Separation Between Adjacent …Cl. 7.11.3 (contd…)

� 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.

255


Potential pounding

location

Building 1 Building 2

Potential pounding

location

Building 1 Building 2

a b

Pounding in situation (b) is far more damaging.

256

� Two adjacent buildings

� Two adjacent units of same building

� Amount of separation

•Floors levels are at same elevation

•Floors levels are at different elevations

( )design2design1

2

Rδδ +⋅>∆

( )design2design1R δδ +⋅>∆

11 δ⋅R22 δ⋅R

Separation Between Adjacent Separation Between Adjacent ……Cl. 7.11.3Cl. 7.11.3

257


� To handle pounding by roof of one unit to the middle of columns of the other unit:

Soft Timber

Structural

Grade Steel

Fig. From Arnold and Reitherman

258

Section 7.12: Miscellaneous, and

Section 7.1: Regular and Irregular Configuration

IS:1893-2002(Part I)

44

259

Foundations Cl. 7.12.1

� This clause is to prevent use of foundation types vulnerable to differential settlement.

� In zones IV and V, ties to be provided for isolated spread footings and for pile caps

� Except when footings directly supported on rock

260

Foundations Cl. 7.12.1 (contd…)

� Recall newly-introduced Note 7 inside Table 1 of the code which states:

Isolated R.C.C. footing without tie beams, or

unreinforced strip foundation shall not be

permitted in soft soils with N<10.

� This note is applicable for all seismic zones.

� It would be better to bring this note inside Cl. 7.12.1.

261

Foundations Cl. 7.12.1 (contd…)

� Ties to be designed for an axial load (in tension and in compression) equal to Ah/4 times the larger of the column or pile cap load.

� 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 pile cap load.

� Any other alternative design approaches?

262

• Towers, Parapets, Stacks, Balconies (Small)

– Design of these attachments

– Design of their connections to main structure

• Design force

– 5× vertical seismic coefficient for horizontal projections

– 5× horizontal seismic coefficient for vertical projections

Cantilevers and ProjectionsCantilevers and Projections

5Ah

5Av

263

Compound Walls Cl. 7.12.3

� To be designed for design horizontal coefficient Ah and importance factor = 1

264

Cl. 7.1

Regular and Irregular Configuration

45

265

Building ConfigurationBuilding Configuration

• Configuration emphasised

– Comprehensive section on identifying irregularities

– Qualitative definitions of irregular buildings

• Two types

– Plan Irregularities

– Vertical Irregularities

266

• Plan Irregularities

– Torsion Irregularity

∆+∆>∆

22.1 21

2

Heavy Mass

Irregular Orientation of Lateral Force Resisting System

1∆ Floor 2∆

Building ConfigurationBuilding Configuration……

267

Torsional Irregularity

� Look at the top two figures of page. 19 (Fig. 3)� Can you make out anything what this figure is trying to show?

� There is a problem with these two figures!

268

Torsional Irregularity (contd…)

� These figures were taken from NEHRP Commentary where it appears as follows:

� The figures have not been traced correctly for IS:1893!

Heavy

Mass

Vertical Components of Seismic Resisting System

269

– Re-entrant Corners

L

L

A A

A

A

A

20.015.0 −>L

A


270

– Diaphragm DiscontinuityFlexible

Opening

Opening


46

271

OutOut--ofof--Plane OffsetsPlane 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.

272

– Out of Plane Offsets

Shear Wall Shear Wall

Shear Wall


273

– Non-Parallel System

x

y


274

• Vertical Irregularities

– Stiffness Irregularity (Soft Storey)

kiki-1

ki+1

17.0 +<ii

kk

++< +++

38.0 321 iii

i

kkkk


275

– Mass Irregularity

• induced by the presence of a heavy mass on a floor, say a swimming pool.

WiWi-1

Wi+1

1 2 +>ii

WW

1 2 −> ii WW


276

Mass and Stiffness IrregularityMass and Stiffness Irregularity

• 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.

47

277

– Vertical Geometric Irregularities

L

A

A A

L

L

A A

20.015.0 −>L

A


278

L2

L1

L2

L1

12 5.1 LL >


279

– In-plane Discontinuity in Lateral Load Resisting Elements

Upper Floor Plan

Lower Floor Plan


280

– Strength Irregularity (Weak Storey)

SiSi-1

Si+1

18.0 +< ii SS


281

Building Configuration…

� Geometrically building may appear to be regular and symmetrical, but may have irregularity due to distribution of mass and stiffness.

� 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.

282

Arrangement of shear walls and braced frames-not recommended.Note that the heavy lines indicate shear walls and/or braced frames

(b)

(b)

(a)

(a)

Arrangement of shear walls and braced frames- recommended.Note that the heavy lines indicate shear walls and/or braced frames

Fig. From NEHRP Commentary

48

283

Diaphragm Discontinuity

� 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.

� Again, these are from NEHRP Commentary and not traced correctly in our code.

284

Diaphragm Discontinuity (contd…)

Discontinuity in Diaphragm Stiffness

FLEXIBLE

DIAPHRAGM

R I G I D

D I A P H R A G M O P E N

Vertical Components of Seismic Resisting System

Notice the words “mass resistance

eccentricity” do not make sense.

Fig in Code

Fig in NEHRP

285

Problems with Irregularities

� In buildings with vertical irregularity, load distribution with building height is different from that in Cl. 7.7.1.

� Dynamic analysis is required.

� In buildings with plan irregularity, load distribution to different vertical elements is complex.

� Floor diaphragm plays an important role and

needs to be modelled carefully.

� A good 3-D analysis is needed.

286

Problems with Irregularities (contd…)

� 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.

287

Code on Irregularity� Our code has simplistic method of treating the irregularities.� For irregular buildings, it just encourages dynamic analysis.

� Compare Tables of NEHRP shown earlier in this lecture.� 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

Seismic Force Seismic Force Seismic Force Seismic Force EstimationEstimationEstimationEstimationSeismic Force Seismic Force Seismic Force Seismic Force EstimationEstimationEstimationEstimation

49

289

Design Seismic Lateral ForceDesign Seismic Lateral Force

• Two ways of calculating

– Equivalent Static Method

•Seismic Coefficient Method

� Single mode dynamics

� Simple and regular structures

– Dynamic Analysis Method

•Response Spectrum Method�Multi-mode dynamics

� Irregular structures

•Time History Method� Special structures

290

Origin ofOrigin ofOrigin ofOrigin ofEquivalent Static Equivalent Static Equivalent Static Equivalent Static

MethodMethodMethodMethod

Origin ofOrigin ofOrigin ofOrigin ofEquivalent Static Equivalent Static Equivalent Static Equivalent Static

MethodMethodMethodMethod

291

• Dynamic Characteristics

PropertyProperty Mode 1Mode 1 Mode 2Mode 2

m2

m1k1

k2

Equivalent SDOFs K1

M1

K2

M2

Natural Frequency

1

11

M

K=ω

2

22

M

K=ω

Natural Period11 /2T ωπ= 22 /2T ωπ=

Dynamics of 2 DOF SystemDynamics of 2 DOF System

292

• Lateral Force


m2

m1k1

k2

PSA

Dynamics of 2 DOF SystemDynamics of 2 DOF System……

T

PSA1

T

PSA (g) PSA (g)

PSA2

T1 T2

SD 21

11

PSASD

ω=

22

22

PSASD

ω=

293

• Lateral Force…


m2

m1k1

k2

Lateral Displacement


Mode Participation Factor

{ } [ ]{ }

1

T1

1M

1mϕ=Γ

{ } [ ]{ }

2

T2

2M

1mϕ=Γ

{ } { }

=

Γϕ=

22

21

2222

u

u

SDu{ } { }

=

Γϕ=

12

11

1111

u

u

SDu

294

• Lateral Force…


m2

m1k1

k2

Lateral Force


{ } [ ]{ }

==12

1111 F

FuF k { } [ ]{ }

==22

2122 F

FuF k

F11

F12

F21

F22

Base Shear ∑=

=2

1ii11B FV ∑

=

=2

1ii22B FV

50

295

• Lateral Force



m2

m1k1

k2F11

F12

F21

F22

Resultant Base Shear ( ) ( )22B21BB VVV +=

>

B

2B

B

1B

V

V

V

V

Usually, for regular buildings

296

• Equivalent Static Force– Since mode 1 is dominant


BuildingBuilding Mode 1Mode 1

F11

F12

F11

F12

1BB VV ≈

VB VB1

297

MDOF SystemMDOF System

• Vibration modes

[ ]

=

3

2

1

m00

0m0

00m

m

[ ]

=

3332

232221

1211

kk0

kkk

0kk

k

{ }

11

11

K,M

, ϕω

PropertyProperty

m3

m1k1

k3m2

k2

Mode 1Mode 1 Mode 2Mode 2 Mode 3Mode 3

[ ] [ ]( ){ } { }0: ProblemValue Eigen 2 =ϕω− mk

{ }

22

22

K,M

, ϕω { }

33

33

K,M

, ϕω

298

• Lateral Force

PropertyProperty

m3

m1k1

k3m2

k2

Mode 1Mode 1 Mode 2Mode 2 Mode 3Mode 3

MDOF SystemMDOF System……

VB1 VB2 VB3Base Shears

Response of the whole building is usually that of its dominant first mode.

Response of the whole building is usually that of its dominant first mode.

299

First Mode AnalysisFirst Mode Analysis

• Typical first mode shapes

Low-to-Medium Period Buildings (T<1s)

Low-to-Medium Period Buildings (T<1s)

Long Period Buildings (T>2s)

Long Period Buildings (T>2s)

Linear Parabolic

{ }

⋅ϕ=ϕ

⋮

⋮

⋮

⋮

H

hii011

{ }

⋅ϕ=ϕ

⋮

⋮

⋮

⋮

2i

i011 H

h

300

• Base Shear VB using T1

• Distribution of force along height

First Mode AnalysisFirst Mode Analysis……

1B PSAMV ⋅=

Fi

∑=

⋅=N

1k

2kk

2ii

Bi

hW

hWVF

51

301

Equivalent lateral Force MethodEquivalent lateral Force Method

• IS:1893 (Part1) - 2002

Fi

VB

Perform the usual static elastic structural analysis with these forces.

No dynamic analysis is done.(But, it is hidden in concept of Response Spectrum used in assumed vertical distribution of Base Shear VB.)

302

ExampleExampleExampleExampleExampleExampleExampleExample

303

• Seismic Zone V

– OMF and SMF

3.5m

3m

3.5m 5.0m

5.0m

4.0m

3.0m

3.0m

Three Storey Frame BuildingThree Storey Frame Building

304

Step 1Step 1

• Decide a structural system

5m

5m

Plan Elevation

3.5m 3.0m 3.5m

3m

3m

4m

3.5m 3.0m 3.5m

305

STEP 2STEP 2

• Estimate Seismic Weight W

– Clause 7.4 of IS:1893(1)-2002

•W = Full DL + Part LL

– Unit weights of dead loads from IS:875(1)

•Steel sections : 78.5 kN/m3

•Reinforced concrete : 25 kN/m3

•Masonry infill : 19.0 kN/m3

•Mortar plaster : 20.0 kN/m3

•Floor finish on floors : 1 kN/m2

•Weathering course on roof : 2.25 kN/m2

– Imposed loads from IS 875(2)

•On floors : 3.0 kN/m2

•On roof : 0.75 kN/m2 306

• Estimate Seismic Weight W…

– Imposed load as per Clause 7.3

•% of Imposed Load to be considered from Table 8

•No imposed load on roof

Step 2Step 2……

50> 3.0

25≤ 3.0

% of Load to be consideredImposed Load (kN/m2)

52

307

• Estimate Seismic Weight W…

– Total Seismic Weight W

W = 4900 kN

Step 2Step 2……

DL=1340 kN; LL=0

DL=1620 kN; LL=75 kN

DL=1800 kN; LL=75 kN

3.5m 3.0m 3.5m

3m

3m

4m

308

Step 3Step 3

• Estimate Design Horizontal Acceleration Spectrum Value Ah– Clause 6.4 of IS:1893(1)-2002

( )( )

R

ITg

SZ

TA

a

h2

=

Maximum Elastic Acceleration

Reduction to account for ductility and overstrength

309

• Estimate Ah…

– Seismic Zone Factor Z

– Importance factor I

Step 3Step 3……

0.360.240.160.10Z


1.0All Others2

1.5Important, Community & Lifeline Buildings1

IBuildingS.No.

310

• Estimate Ah…

– Response Reduction Factor R from Draft IS:800

Step 3Step 3……

=SMF5

OMF4R

311

• Estimate Ah…

– Empirical Natural Period Ta

Step 3Step 3……

=×

=

=×=

=

Frame Infilled sec...

Frame Baresec... ..

28010

10090

d

h090

480100850h0850

T

750750

a

NoteThe first expression is independent of

the base dimension of the building!!

312

• Estimate Ah…

– Structure Flexibility Factor Sa/g

•Structure on Type I (Rock or Hard Soil)

•5% damping

Step 3Step 3……

Sa /g

0

1.0Rock/ Hard Soil

Natural Period Ta

2.5

2.08

0.28 0.48

53

313

• Estimate Ah…

– OMF

– SMF

Step 3Step 3……

=×

××

=×

××

=Frame Bare.

...

Frame Infilled....

075052

08201360

090052

5201360

Ah

=×

××

=×

××

=Frame Bare.

...

Frame Infilled....

125032

08201360

15032

5201360

Ah

314

Step 4Step 4

• Calculate Design Base Shear Vb– Clause 7.5.3 of IS:1893(1)-2002

( ) WTAV ahB ×=

=×

=×=

OMF .

SMF .

kN7354900150

kN4414900090VB

315

Step 5Step 5

• Distribute Design Base Shear Vbalong height

– Clause 7.7.1 of IS:1893(1)-2002

∑=

=N

1j

2jj

2ii

Bi

hW

hWVQ

238.4 kN

148.9 kN

53.7 kN

397.4 kN

248.1 kN

89.5 kN

SMFSMF OMFOMF

316

Step 5Step 5

• Locate point of application of Qiat each floor

– At each floor level at design eccentricity

•Clause 7.9.1 of IS:1893(1)-2002

isi

isi

dibe

bee

05.0

or,05.05.1

−

+

=EQEQ

EQEQ

b

esi b

317

• Locate point of Qi…

– Two cases of Design Eccentricity

CM CSCM*

ib05.0

isibe 05.0−isi

be 05.05.1 +

sie5.0

sie ib05.0

sie

CM CSCM*

Step 5Step 5……

318


– Incorporating the provision in practice

Step 5Step 5……

si i

di

si i

. e . be

e . b

+= −

1 5 0 05

0 05

CMCS

54

319


– Incorporating the provision in practice…

•Effect of shear and torsion: esi� Analysis A

Step 5Step 5……

CMCS

320



•Effect of shear only

� Analysis B

Step 5Step 5……

CMCS

321



•Effect of shear, torsion esi and 0.05bi� Analysis C

Step 5Step 5……

CMCSCM*

0.05bi322



•Solution

� 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

Step 5Step 5……

CMCS

0.05bi

CMCS

CMCS CM*

AA

BB

CC

323

Step 6Step 6

• Load Combinations

– Lateral force resisting system orthogonal in two plan directions

•9 load cases for unsymmetrical buildings� Can reduce to 5 for beams

1.7 (DL + LL)

1.3 (DL + LL ± ELx)1.3 (DL + LL ± ELy) 1.7 (DL ± ELx)1.7 (DL ± ELy)

x

324

• Load Combinations…

– Lateral force resisting system non-parallel in two plan directions

•Consider design based on one direction at a time

ELx

y

y

x

x

ELy

Step 6Step 6……

55

325

• Load Combinations…

– Non-parallel system

•Consider design based on one direction at a time

• Replace

� ELx by (ELx ± 0.3ELy) and ELy by (ELy±0.3ELx)in the combinations for orthogonal systems

� Thus, 17 load cases for unsymmetrical buildings

1.7 (DL + LL)1.3 (DL + LL ± (ELx± 0.3ELy))1.3 (DL + LL ± (ELy±0.3ELx)) 1.7 (DL ± (ELx ± 0.3ELy))1.7 (DL ± (ELy±0.3ELx))

Step 6Step 6……

326

• Load Combinations…– Two/Three Component Motion

•Response (EL) due to earthquake force is maximum of ::

•Alternately, SRSS Method may be employed as ::

• If any one component is not being considered, the corresponding response quantity is dropped.

±±±

±±±

±±±

=

yxz

xzy

zyx

EL30EL30EL

EL30EL30EL

EL30EL30EL

EL

..

..

..

( ) ( ) ( )2z2

y2

x ELELELEL ++=

Step 6Step 6……

Education

Dcr is 1893