DCR-IS 1893 ppt

8/20/2019 DCR-IS 1893 ppt

1/55

1

1

Seismic FORCEESTIMATIONIS 1893-2002

Seismic FORCESeismic FORCEESTIMATIONESTIMATIONIS 1893IS 1893-- 2002 2002

Durgesh C. Rai

Department of Civil Engineering, IIT Kanpur

2

The material contained in this lecture handout is a pr operty ofProfessors 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 shortcourse on Seismic Design of RC Structures conducted at Ahmedabad duringNov 26-30, 2012. It is not to be s old, reproduced or generally distributed.

EQEQEQEQ BehaviourBehaviourBehaviourBehaviour

is different!!is different!!is different!!is different!!

EQEQEQEQ BehaviourBehaviourBehaviourBehaviour

is different!!is different!!is different!!is different!! 4

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

5

IS:1893-2002

IS:1893 first published in 1962.

Revised in 1966, 1970, 1975, 1984, and now in2002.

Beginning 2002, this code is being split intoseveral parts

So that revisions can take place more frequently!

Only Part 1 and 4 of the code has beenpublished.

6

What does IS:1893 Cover?

Specifies Seismic Design Force

Other seismic requirements for design, detailingand construction are covered in other codes

e.g., IS:4326, IS:13920, ...

For an earthquake-resistant structure, one hasto follow IS:1893 together with seismic designand detailing codes.

8/20/2019 DCR-IS 1893 ppt

2/55

2

7

Coverage of Part 1

General Provisions Applicable to all structures

Provisions on Buildings

To address the situation that other parts of thecode are not yet released, Note on page 2 ofthe code says in the interim period, provisions ofPart 1 will be read along with the relevantclauses of IS:1893-1984 for structures otherthan buildings This can be problematic.

For instance, what value of R to use for overheadwater tanks?

8

Major Changes

Since the code has been revised after a very

long time (~18 years), there are manysignificant changes.

Some of the philosophical changes are discussedin Foreword of the code.

9

Zone Map

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

In 1967, Koyna earthquake (M6.5, about 200killed) 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

10

Zone Map (contd…)

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

Revision of zone map in 2002 edition

Zone I has been merged upwards into zone II.

Now only four zones: II, II I, IV and V.

In the peninsular India, some parts of zone I

and zone II are now in zone III.

11

Zone Map (contd…)

Notice the location of Allahabad and Varanasi inthe new zone map.

There is an error and the locations of these twocities have been interchanged in the map.

Varanasi should be in zone III and Allahabad inzone II.

The Annex E of the code gives correct zones forthese two cities

12

Zone Map (contd…)

Also notice another error in the new zone map

Location of Calcutta has been shown incorrectlyin zone IV

Calcutta is in fact in zone III

Annex E of the code correctly lists Kolkata is inzone III.

8/20/2019 DCR-IS 1893 ppt

3/55

3

13

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 thespecialists.

14

Other Effects

Read second para, page 3

Earthquakes can cause damage in a number ofways. For instance:

Vibration of the structure: this induces inertiaforce on the structure

By inertia force, we mean mass t imes acceleration

Landslide triggered by earthquake

Liquefaction of the founding strata

Fire caused due to earthquake

Flood caused by earthquake

15

Other Effects (contd…)

The code generally addresses only the firstaspect: the inertia force on the structure.

The engineer may need to also address othereffects in certain cases.

16

Intensity versus Magnitude

It is important that you understand thedifference 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 soiland geology

Read more about magnitude and intensity at:

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

17

Seismic Hazard

Last para on page 3

The criterion for seismic zones remains same asbefore

IX V

VIIIIV

VIIIII

VI (and lower)II

Area liable to shaking intensityZone

18

Shaking Intensity

Shaking intensity is commonly measured interms 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.

8/20/2019 DCR-IS 1893 ppt

4/55

4

19

Zone Criterion

Our zone map is based on likely intensity.

It does not address the question: how often sucha 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 hashigher seismicity

Current trend world wide is to

Specify the zones in terms of groundacceleration that has a certain probability ofbeing exceeded in a given number of years.

20

Peak Ground Acceleration

Maximum acceleration response of a rigid

system (Zero Period Acceleration) is same asPeak 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 PGAfrom an acceleration spectrum.

21

Peak Ground Acceleration (contd…)

Average shape of acceleration responsespectrum 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 spectralacceleration 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.

22

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

Period (sec)

S p e c t r a l A c c e l e r a t i o n ( g )

23

Earthquake Level

Maximum Credible Earthquake (MCE):

Largest reasonably conceivable earthquakethat 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 10,000years.

Usually evaluated based on geological

evidence

24

Earthquake Level (contd…)

Other terms used in literature which aresomewhat similar to max credible EQ:

Max Possible Earthquake

Max Expectable Earthquake

Max Probable Earthquake

Max Considered Earthquake

8/20/2019 DCR-IS 1893 ppt

5/55

5

25

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 on2,500 year return period will be larger than theMCE based on 1,000 year return period

26

Max Considered EQ (MCE) (contd...)

IS:1893

MCE motion as per Indian code does notcorrespond to any specific probability of

occurrence or return period.

27

Design Basis EQ (DBE)

This is the earthquake motion for whichstructure is to be designed considering inherentconservatism in the design process

UBC1997 and IBC2000:

Corresponds to 10% probability of beingexceeded in 50 years (475 year return period)

28

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

Cl. 3.6 of the code (p. 8)

Earthquake that can reasonably be expected tooccur 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.

29

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.14accounts for this

See definition of Z on p.14 of the code

30

Modal Mass

It is that mass of the structure which is effectivein one particular natural mode of vibration

Can be obtained from the equation in Cl. 7.8.4.5for simple lumped mass systems

It requires one to know the mode shapes

One must perform dynamic analysis to obtainmode shapes

Next slides to appreciate the physical

significance of Modal Mass

8/20/2019 DCR-IS 1893 ppt

6/55

6

31

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 accelerationresponse spectrum is given here.

Undamped Natural Period T (sec)

M a x i m u m A

c c e l e r a t i o n , g

32

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/sec 2 ) = 768,000 N = 768 kN

33

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/sec 2 ) = 62,800 N = 62.8 kN

34

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”

35

Seismic Weight (Cl.3.29)

It is the total weight of the building plus thatpart of the service load which may reasonablybe expected to be attached to the building atthe 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 arelikely to have larger percent of service loadpresent at the time of shaking.

Notice the values in Table 8

36

Seismic Mass (Cl.3.28)

It is seismic weight divided by acceleration dueto gravity

That is, it is in units of mass (kg) rather than inthe units of weight (N, or kN)

In working on dynamics related problems, oneshould be careful between mass and weight.

Mass times gravity is weight

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

8/20/2019 DCR-IS 1893 ppt

7/55

7

37

Section 4

Terminology on Buildings

38

Centre of Stiffness

Cl. 4.5 defines Centre of Stiffness as The point

through which the resultant of the restoringforces of a system acts.

It should be defined as:

If the building undergoes pure translation in thehorizontal direction (that is, no rotation or twist ortorsion about vertical axis), the point through

which the resultant of the restoring forces acts isthe Centre of Stiffness

39

Centre of Rigidity

In cl. 4.21, while defining static eccentricity,Centre of Rigidity is used.

Both Centre of Stiffness (CS) and Centre ofRigidity (CR) are the same terms for ourpurposes!

Experts will tell you that there are subtledifferences between these two terms. But that isnot important from our view point.

It would have been better if the code had usedeither stiffness or rigidity throughout

40

Eccentricity

Cl. 4.21 defines Static Eccentricity.

This is the calculated distance between theCentre of Mass and the Centre of Stiffness.

Under dynamic condition, the effect ofeccentricity is higher than that under staticeccentricity.

Hence, a dynamic amplification is to be appliedto the static eccentricity before it can be used indesign.

41

Eccentricity (contd…)

An accidental eccentricity is also consideredbecause:

The computation of eccentricity is only

approximate.

During the service life of the bui lding, there could

be changes in its use which may change centreof mass.

Design eccentricity (cl.4.6) is obtained fromstatic eccentricity by accounting for (cl.7.9.2)

Dynamic amplification, and

Accidental eccentricity

42

Dual System

Consider buildings with shear walls and momentresisting frames.

In 1984 version of the code, Table 5 (p. 24)implied that the frame should be designed totake at least 25% of the total design seismic

loads.

8/20/2019 DCR-IS 1893 ppt

8/55

8

43

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% oftotal seismic load while 70% loads go to shear walls. Framesand 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 fordual system, design the walls for 90% of total load, but

design the frames to resist 25% of total seismic load

44


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 Example2 above, the shear walls will be designed for 100% of totalseismic loads, and the frames will be treated as gravity

frames (i.e., it is assumed that frames carry no seismicloads)

Frames and walls are designed for the forces obtained from

analysis, and the frames happen to carry less than 25% oftotal load. In Example 2 above, the frames will be designedfor 10% while walls will be designed for 90% of total seismic

loads.

45


Clearly, the dual systems are better and aredesigned for lower value of design force.

See Table 7 (p. 23) of the code. There i s differentvalue of response reduction factor (R) for thedual systems.

46

Moment Resisting Frame

Cl. 4.15 defines Ordinary and Special MomentResisting Frames.

Ductile structures perform much better duringearthquakes.

Hence, ductile structures are designed for lowerseismic forces than non-ductile structures. Forexample, 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.

47

Number of Storeys (Cl.4.16)

When basement walls are connected with thefloor deck or fitted between the buildingcolumns, the basement storeys are not includedin number of storeys.

This is because in that event, the seismic loads

from upper parts of the building get transferredto the basement walls and then to thefoundation. That is,

Columns in the basement storey will have insignificantseismic loads, and

Basement walls act as part of the foundation.

48

Number of Storeys (contd…)

Definition of number of storeys

Was relevant in 1984 version of the code whereinnatural 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

8/20/2019 DCR-IS 1893 ppt

9/55

9

49

Soft Story

Cl. 4.20 defines Soft Storey

Sl. No. 1 in Table 5 (p. 18) defines Soft Storeyand Extreme Soft Storey

In Bhuj earthquake of January 2001, numeroussoft storey buildings collapsed.

Hence, the term Extreme Soft Storey and cl. 7.10(Buildings with Soft Storey) were added hurriedlyafter the earthquake.

50

Soft Storey (contd…)

There is not much of a difference between soft

storey and extreme soft storey buildings asdefined in the code, and the latter definition isnot 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 thedefinition of soft storey and extreme soft storey.

51

Weak Storey

Note that the stiffness and strength are twodifferent 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 cantake

52

Weak Storey (contd…)

Soft storey refers to stiffness

Weak storey refers to strength

Usually, a soft storey may also be a weakstorey

53

Storey Drift

Storey Drift defined in cl. 4.23 of the Code.

Storey drift not to exceed 0.004 times the storeyheight.

54

Definition of Vroof

On p. 11, it is defined as peak storey shearforce 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.

8/20/2019 DCR-IS 1893 ppt

10/55

10

55

Section 6.1: General PrinciplesIS: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 inPermissible Stresses

Cl. 6.4: Design Spectrum

57

Ground Motion (cl. 6.1.1)

Usually, the vertical motion is weaker than thehorizontal motion

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

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

58

Ground Motion Contd…

All structures experience a constant verticalacceleration (downward) equal to gravity (g) atall times.

Hence, the vertical acceleration during groundshaking can be just added or subtracted to thegravity (depending on the direction at thatinstant).

59


Example: A roof accelerating up and down by0.20g.

Implies that it is experiencing acceleration in the

range 1.20g to 0.80g (in place of 1.0g that itwould experience without earthquake.)

Factor of safety for gravity loads (e.g., dead andlive loads) is usually sufficient to cover theearthquake induced vertical acceleration

60


Main concern is safety for horizontalacceleration.

Para 2 in cl. 6.1.1 (p. 12) lists certain caseswhere vertical motion can be important, e.g.,

Large span structures

Cantilever members

Prestressed horizontal members

Structures where stability is an issue

8/20/2019 DCR-IS 1893 ppt

11/55

11

61

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 effectof the earthquake.

Cl. 6.1.2 cautions against situations wherefounding soil may liquefy or settle: such cases

are not covered by the code and engineer hasto deal with these separately.

62

Design Lateral ForceDesign Lateral Force

• Philosophy of Earthquake-Resistant Design

– First calculate maximum elastic seismic forces

– Then reduce to account for ductility and overstrengthLateral Force

Elastic Forcereduced by R

Design Force

Actual

MaximumElastic Force

Elastic

0

H , ∆∆∆∆

LateralDeflection

63

Earthquake Design Principle

The criteria is:

Minor (and frequent) earthquakes should notcause damage

Moderate earthquakes should not causesignificant structural damage (but could havesome non-structural damage)

Major (and infrequent) earthquakes should notcause collapse

64

Clause 6.1.3

Para 1 of this clause implies that Design BasisEarthquake (DBE) relates to the “moderateshaking” and Maximum Considered Earthquake(MCE) relates to the “strong shaking”.

Indian code is quite empirical on the issue ofDBE and MCE levels.

Hence, this clause is to be taken only as anindicator of the concept.

65

Seismic Design Principle

A well designed structure can withstand ahorizontal force several times the design forcedue to:

Overstrength

Redundancy

Ductility

66

Overstrength

The structure yields at load higher than thedesign 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

8/20/2019 DCR-IS 1893 ppt

12/55

12

67

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 toredundancy is considered within the

“overstrength” term.

68

Ductility

As the structure yields, two things happen:

There is more energy dissipation in the structuredue to hysteresis

The structure becomes softer and its naturalperiod increases: implies lower seismic force tobe resisted by the structure

Higher ductility implies that the structure canwithstand stronger shaking without collapse

69

Response Reduction Factor

Overstrength, redundancy, and ductilitytogether lead to the fact that an earthquakeresistant structure can be designed for muchlower force than is implied by a strong shaking.

The combined effect of overstrength,redundancy and ductility is expressed in termsof Response Reduction Factor (R)

70

)(FForceDesign

)(FForceElasticMaximumFactorReductionResponse

des

el=

Design force

Maximum Load Capacity

T o t a l H o r i z o n t a l L o a d

Roof Displacement (∆)

Non linearResponse

FirstSignificant

Yield

Linear ElasticResponse

∆max

F y

F s

F des

∆y∆w

F el

Load atFirst Yield

Due toOverstrength

Due toRedundancy

Due toDuctility

Maximum forceif structure remains elastic

0

TotalHorizontal

Load

∆

Figure: CourtesyDr. C V R Murty

71

Para 2 and 3 of Cl. 6.1.3.

Imply that the earthquake resistant structuresshould generally be ductile.

IS:13920-1993 gives ductile detailingrequirements 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 steelstructures.

72

Para 2 and 3 of Cl. 6.1.3 Contd…

As of now, ductile detailing provisions forprecast structures and for prestressed concretestructures are not available in Indian codes.

In the past earthquakes, precast structures haveshown very poor performance during

earthquakes. The connections between different parts have

been problem areas.

Connections in precast structures in high seismicregions require special attention.

8/20/2019 DCR-IS 1893 ppt

13/55

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 lateralloads are serious concern.

74

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 exceedsdesign seismic force, one needs to comply withthe seismic requirements on design, detailingand construction.

75

Soil Structure Interaction (Cl. 6.1.4)

If there is no structure, motion of the groundsurface is termed as Free Field Ground Motion

Normal practice is to apply the free field motionto the structure base assuming that the base isfixed.

This is valid for structures located on rock sites.

For soft soil si tes, this may not always be a goodassumption.

76

Soil Structure Interaction (Cl. 6.1.4) Contd…

Presence of structure modifies the free fieldmotion since the soil and the structure interact. Hence, foundation of the structure experiences

a motion different from the free field groundmotion.

The difference between the two motions isaccounted 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 onthe properties and geological features of thesubsurface 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 allpossible directions.

Direction of resultant shaking changes from

instant to instant.

Basic requirement is that the structure should

be able to withstand maximum ground motionoccurring in any direction.

For most structures, main concern is for horizontalvibrations rather than vertical vibrations.

8/20/2019 DCR-IS 1893 ppt

14/55

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 twoperpendicular horizontal directions.

Hence for design, maximum seismic force is notapplied in the two horizontal directionssimultaneously.

If the walls or frames are oriented in twoorthogonal (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 bedesigned for the motion experienced by thefloor.

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 withthe 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

8/20/2019 DCR-IS 1893 ppt

15/55

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 necessitatedthis 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 UNAMsite

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 weaklong-period waves Natural period of soft clay layers happened to

be close to the dominant period of incidentseismic waves

This lead to resonance-like conditions

Buildings between 7 and 18 storeys sufferedextensive 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 strongground shaking taking place simultaneously isvery very low.

It is common to assume that strong earthquakeshaking and strong wind will not occur

simultaneously.

Same with strong earthquake shaking andmaximum flood.

90

Assumption c) on Modulus of Elasticity

Modulus of elasticity of materials such asconcrete, masonry and soil is difficult to specify

Its value depends on

Stress level

Loading condition (static versus dynamic)

Material strength

Age of material, etc

8/20/2019 DCR-IS 1893 ppt

16/55

16

91

Loads and StressesLoads and Stresses

• Loads

– EQ forces not to occur simultaneously withmaximum flood, wind or wave loads

– Direction of forces

• One horizontal + Vertical

• Two horizontal + Vertical

92

Cl.6.3 Load Combinations and Increase in

Permissible Stresses

Cl.6.3.1.1 gives load combinations for Plastic

Design of Steel Structures Same as in I S:800-1978

More load combinations in I S:800-2007

Cl.6.3.1.2 gives load combinations for LimitState Design for RC and Prestressed ConcreteStructures

Same as in I S:456-2000 (RC structures) andIS:1343-1980 (Prestressed structures) with one

difference

93

Load Combinations in Cl.6.3.1.2

Compare combinations of this clause with thosein Table 18 (p.68) of IS:456-2000

Combination 0.9DL ±±±± 1.5EL The way this combination is written in I S:456, the

footnote creates an impression that it is notalways needed.

It has been noticed that many designers do not routinelyconsider 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 effectof horizontal load minus effect of gravity loads.

In such situations, a load factor higher than 1.0on gravity loads will be unconservative.

Hence, a load factor of 0.9 specified on gravityloads in the combination 4)

Many designs of footings, columns, and positivesteel in beams at the ends in frame structuresare governed by this load combination

Hence, this combination has been made veryspecific in IS:1893-2002.

95

Direction of Earthquake Loading

During earthquake, ground moves in alldirections; the resultant direction changes everyinstant.

Ground motion can resolved in two horizontaland one vertical direction.

Structure should be able to withstand groundmotion in any direction

Two horizontal components of ground motiontend to be comparable Say, the epicentre is to the north of a site.

Ground motion at site in the north-south andeast-west directions will still be comparable.

96

Direction of Earthquake Loading (contd…)

Vertical component is usually smaller than thehorizontal motion

Except in the epicentral region where vertical

motion can be comparable (or even stronger) tothe horizontal motion

As discussed earlier, generally, most ordinarystructures do not require analysis for verticalground motion.

8/20/2019 DCR-IS 1893 ppt

17/55

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 orwalls oriented in two perpendicular directions,say X and Y.

One must consider design ground motion to actin X-direction, and in Y-direction, separately

That is, one does not assume that the designmotion in X is acting simultaneously with thedesign 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 safeif 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 thereforeneeds 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 areNOT oriented along two perpendicular directions

In such a case, design for X- and Y-directionloads acting separately will be unconservativefor elements not oriented along X- and Y-directions.

101

• Lateral force resisting systemnon-parallel in two plan directions

– Consider design based on one direction at a time

EL x

y

y

x

x

EL y

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 6 0 7 5 90

ELx

ELyV

Force effective along

direction of inclined

element

Orientation of inclined element with respect to x-axis


θ

8/20/2019 DCR-IS 1893 ppt

18/55

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 theelement.

It may be too tedious to apply lateral loads ineach of the directions in which the elements areoriented.

For such cases, the building may be designedfor: 100% design load in X-direction and 30% design

load in Y-direction, acting simultaneously

100% design load in Y-direction and 30% designload in X-direction, acting simultaneously

104

– Solution :: Try (100%+30%) together

EL x

y

x

x

EL y

0.3EL x

0.3EL y


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 inthe X-direction may be different from that in the

Y-direction

Some codes use 40% in place of 30%.

8/20/2019 DCR-IS 1893 ppt

19/55

19

109

Cl.6.3.4.1

In complex structures such as a nuclear reactor

building, one may have very complex structuralsystems.

Need for considering earthquake motion in allthree 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 ofsum of squares in the two (or, three) directionsof ground motion

2)(2)(2)( ELz ELy ELx EL ++=

111

Increase in Permissible Stresses: Cl.6.3.5.1

Applicable for Working Stress Design

Permits the designer to increase allowablestresses in materials by 33% for seismic loadcases.

Some constraints on 33% increase for steel andfor tensile stress in prestressed concrete beams.

112

Typographical Errors in Table 1

The Table within Table 1, giving values ofdesirable minimum values of N. This Table pertains to Note 3 and hence should

be placed between Notes 3 and 4 (and notbetween Notes 4 and 5 as printed currently)

Caption of first column in this sub-table shouldread “Seismic Zone” and not “Seismic Zone level(in metres)”

Caption of second column in this sub-tableshould read “Depth Below Ground Level (inmetres)” 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 mediumdense saturated soils, liquefaction may takeplace.

Sites vulnerable to liquefaction require

Liquefaction potential analysis.

Remedial measures to prevent liquefaction.

Else, deep piles are designed assuming that soillayers liable to liquefy will not provide lateralsupport to the pile during ground shaking.

114

Liquefaction Potential

Information given in cl.6.3.5.2 and Table 1 onLiquefaction Potential is very primitive:

Note to Cl.6.3.5.2 encourages the engineer torefer to specialist literature for determiningliquefaction potential analysis.

It is common these days to use SPT or CPTresults for detailed calculations on liquefactionpotential analysis.

8/20/2019 DCR-IS 1893 ppt

20/55

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 slightchange in natural period can lead to largevariation in maximum acceleration

Undamped Natural Period T (sec) S p e c t r a l A c c e l e r a t i o n , g

118

Response Spectrum versus Design Spectrum (contd…)

Natural period of a civil engineering structurecannot be calculated precisely

Design specification should not very sensitive toa small change in natural period.

Hence, design spectrum is a smooth or averageshape without local peaks and valleys you see inthe response spectrum

119

Design Spectrum

Since some damage is expected and accepted inthe structure during strong shaking, designspectrum is developed considering theoverstrength, redundancy, and ductility in the

structure.

The site may be prone to shaking from large butdistant earthquakes as well as from medium butnearby earthquakes: design spectrum mayaccount for these as well.

See Fig. next slide.

120

Design Spectrum (contd…)

Natural vibration period Tn, sec

S p e c t r a l A c

c e l e r a t i o n , g

Fig. from Dynamics of Structures by Chopra, 2001

8/20/2019 DCR-IS 1893 ppt

21/55

21

121


Design Spectrum is a design specification

It must take into account any issues that havebearing on seismic safety.

122


Design Spectrum must be accompanied by:

Load factors or permissible stresses that must beused

Different choice of load factors will give different seismicsafety 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 differentvalues of natural period.

Type of detailing for ductility

Design force can be lowered if structure has higher ductility.

123

• Two methods of estimation ofdesign seismic lateral force

– Seismic Coefficient Method

– Response Spectrum Method

– In both methods

• Seismic Design Force F d = F e /R = A W A = Design acceleration value

W = Seismic weight of structure

Design SPECTRUMDesign SPECTRUM……

124

• Design Horizontal Acceleration Spectrum

( )

( )

R

I T g

S Z

T A

a

h2

=

MaximumElastic

Acceleration

Reduction to account for ductility andoverstrength

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

V IV III II Seismic

Zone

Acceleration

PGA

Time

Spectral Acceleration

NaturalPeriod

PGA

0

(ZPA::Zero Period Acceleration)

Seismic zone factor Seismic zone factor

126

– Relative Values Consistent

– Factor of 2 in Ah for reducing

PGA for MCEtoPGA for Design Basis Earthquake (DBE)

0.360.240.160.10Z

V IV III II Seismic Zone

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……

8/20/2019 DCR-IS 1893 ppt

22/55

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 Idepending on economy and strategic considerations

• Temporary (short term) structures exempted from I

1.0 All Others2

1.5Important, Community & Lifeline Buildings1

IBuilding S.No.

Importance factor Importance factor

128

Soil Effect

Recorded earthquake motions show that

response spectrum shape differs for differenttype of soil profile at the site

Period (sec)

Fig. fromGeotechnicalEarthquakeEngineering, byKramer, 1996

129

Soil Effect (contd…)

This variation in ground motion characteristic fordifferent sites is now accounted for through differentshapes of response spectrum for three types of sites.

S p e c t r a l A c c e l e r a t i o n C o e f f i c i e n t ( S

a / g )

Period(s)

Fig. fromIS:1893-2002

130


Design Spectrum depends on Type I, II, and IIIsoils

Type I, II, III soils are indirectly defined inTable 1 of the code.

See Note 4 of Table 1: The value of N is to betaken 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 averageproperties in the top 30m rather than just at thefounding level.

132

Shape of Design Spectrum

The three curves in Fig. 2 have been drawnbased on general trends of average responsespectra shapes.

In recent years, the US codes (UBC, NEHRP andIBC) have provided more sophistication wherein

the shape of design spectrum varies from areato area depending on the ground motioncharacteristics expected.

8/20/2019 DCR-IS 1893 ppt

23/55

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 thestructure were to remain linear elastic

Earlier code just provided the required design force

It gave no direct indication that the real force may bemuch larger

Now, the code provides for realistic force for elasticstructure and then divides that force by (2R)

This gives the designer a more realistic picture of thedesign philosophy.

134

Response Reduction Factor (contd…)

For buildings, Table 7 gives values of R

For other structures, value of R is to be given inthe 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 newprovisions should be about the same as that in the oldcode.

For other building systems, lower values of R werespecified.

It is hoped that with time, these values will be refinedbased on detailed research.

136


Note 6 prohibits ordinary RC shear walls inzones IV and V.

Such a note is not there for OMRF.

This confuses people and they take it to meanthat the code allows Ordinary Moment ResistingFrames in zones IV and V.

As per IS:13920, all structures in zones III, IVand V should comply with ductile detailing (asper IS:13920). Hence, Ord. RC shear wallsprohibited in zones III also.

This needs to be corrected in the code.

137


Moreover, there are a number of other systemsthat are prohibited in high zones and those arenot listed in this table. For instance,

OMRF’s are also not allowed in zones III, IV and Vas per IS:13920.

Load bearing masonry buildings are required to

have seismic strengthening (lintel bands, verticalbars) 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 thatsome of the above systems are not allowed in

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

138

Response Reduction Factor (contd…)

Note the definition of R on page 14 contains thestatement:

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 lowestvalue 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.

8/20/2019 DCR-IS 1893 ppt

24/55

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 V B inproportion to their stiffness considering theirinteraction at all floor levels

• MRFs are designed to independently resist at least25% of V B

Shear Wall MRF

Response Reduction FactorResponse Reduction Factor ……

140

Design Spectrum for Stiff Structures

For very stiff structures (T < 0.1sec), ductili ty is nothelpful in reducing the design force.

Codes tend to disallow the reduction in force inthe period range of T < 0.1sec

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

T(seconds)

S p e c t r a l a c c e l e r a t i o n

Design spectrum assumes peak extends to T=0

Concept sometimes used by the codes forresponse 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, thevalue of Ah will not be taken less than Z/2

whatever be the value of I/R

This statement attempts to ensure a minimaldesign force for stiff structures.

Note that this statement is valid only when thefirst (fundamental) mode period T ≤ 0.1sec eventhough 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 theamplitude of vibration at the free surface ismuch higher (almost double) than that underthe 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 ofseismic inertia force on foundation under theground, say a well foundation for a bridge.

Hence, the wording Underground structures andfoundations

Note that in case of a bridge (or any above-ground structure) with foundation going deeperthan 30m: This clause (Cl. 6.4.4) can be used to calculate

seismic inertia force due to mass of foundationunder the ground, and not for calculation ofinertia 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 shouldhave had an independent clause number

Note the word “proposed” in this para ismisleading and should not be there.

8/20/2019 DCR-IS 1893 ppt

25/55

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 obtaindesign 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 designcriteria are developed

These take into account geology, seismicity, geotechnicalconditions and nature of project

Site specific criteria are developed by experts andusually 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 ForceCalculation

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 toemphasize the importance of structuralconfiguration for ensuring good seismicperformance.

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 t o provide band-aid – improve a basically poor solution as best as

he can. Conversely, if we start off with a goodconfiguration and a reasonable framing system, even a poor engineer can’t harm it sultimate performance too much.

8/20/2019 DCR-IS 1893 ppt

26/55

26

151

Importance of Configuration (contd…)

Quote from NEHRP Commentary:

The major factors influencing the cost of complying with theprovisions are:

1. The complexity of the shape and structural framing system forthe building. (It is much easier to provide seismic resistance in abuilding with a simple shape and framing plan.)

2. The cost of the structural system (plus other items subject tospecial seismic design requirements) in relation to the total costof the building. (In many buildings, the cost of providing thestructural system may be only 25 percent of the total cost of theproject.)

3. The stage in design at which the provision of seismic resistanceis first considered. (The cost can be inflated greatly if noattention is given to seismic resistance until after theconfiguration of the building, the structural framing plan, and thematerials 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 I rregularities in Plan

Table 5 and Fig. 4 for I rregularities in Elevation

153

A Remark on IS:13920

Recently, BIS has issued some amendments toIS:13920-1993 (see next slide).

In the context of Table 7, note that provisions ofIS:13920 are now mandatory for all RCstructures 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% ofimposed 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 twomethods: seismic coefficient method andresponse spectrum method.

There have been instances of designercalculating seismic design force for each 2-D

frame separately based on tributary massshared by that frame.

This is erroneous since only a fraction of thebuilding mass is considered in the seismic loadcalculations.

156

EQx

Mass being considered forcalculation of inertia force

due to earthquake

EQx

Mass that causesEarthquake Forcein X-Direction

Plan of building

Calculation of design seismicforce on the basis of

tributary mass on 2-D framesleads to significant under-design.

8/20/2019 DCR-IS 1893 ppt

27/55

27

157

• Seismic Weight of Building W

– Dead load

– Part of imposed loads

50 Above 3.0

25Up to and including 3.0

% of Imposed Load

to be considered

Imposed UniformlyDistributed 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 entirebuilding first and then distribute it to differentframes/ walls.

Cl. 7.5.2 does not mean that one has tonecessarily 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 reallyimplies 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 withmasonry infills clearly showed that T = 0.1n significantlyover-estimates the period. For instance, see

Jain S K, Saraf V K, and Mehrotra B, “Period of RC FrameBuildings 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 RCMRF Buildings with URM Infill Walls,” The Indian ConcreteJournal , 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

8/20/2019 DCR-IS 1893 ppt

28/55

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 heightdepends 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 straightline (with regular distribution of mass andstiffness)

For tall buildings, contribution of higher modescan be significant even though the first modemay still contribute the maximum response.

166

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

Hence, NEHRP provides the following expression forvertical 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 i n the range 0.5 secto 2.5 sec.

In IS:1893 over the years, k = 2 has been takenregardless of natural period This is conservative value and has been retained

in the code.

∑=

=n

j

k

j j

k

ii Bi

hW

hW V Q

1

167

Horizontal Distribution... (Cl. 7.7.2)

Floor diaphragm plays an important role inseismic 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 beamwidth equal to slab thickness.

Being a very deep beam, it does not deform inits own plane, and it forces the frames/walls tofulfil the deformation compatibility of no in-planedeformation of floor.

This is rigid floor diaphragm action.

168

Concept of FloorDiaphragm Action

Fig. from Jain S K, “A Proposed Draft for IS:1893…Part II:Commentary and Examples,” J. of StructEngg, Vol. 22,No. 2, July 1995, pp 73-90

8/20/2019 DCR-IS 1893 ppt

29/55

29

169

Horizontal Distribution... (Cl. 7.7.2) (contd…)

Implications of rigid floor diaphragm action:

In case of symmetrical building and loading, theseismic forces are shared by different frames or

walls in proportion to their own lateral sti ffness.

170

Fig. from Jain S K, “A Proposed Draft for IS:1893…Part II:Commentary and Examples,” J. of StructEngg, Vol. 22,No. 2, July 1995, pp 73-90

Lateral Load DistributionDue to Rigid FloorDiaphragm: SymmetricCase – No Torsion

171

When building is not symmetrical, the floorundergoes rigid body translation and rotation.

172

Fig. from Jain S K, “A Proposed Draft for IS:1893…Part II:Commentary and Examples,” J. of StructEngg, Vol. 22,

No. 2, July 1995, pp 73-90

Analysis of Forces Inducedby Twisting Moment (RigidFloor Diaphragm)

173

Rigid Diaphragm Action

In-plane rigidity of floors is sometimes misunderstood tomean 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-planebehavior of slab and beams.

(a) In-plane floordeformation, (b) Out-

of-plane floordeformation.

Fig. from Jain S K, “A ProposedDraft for IS:1893…Part II:Commentary and Examples,” J. ofStruct Engg, Vol. 22, No. 2, July1995, pp 73-90

174

Buildings without Diaphragm Action

When the floor diaphragm does not exist, orwhen the diaphragm is extremely flexible ascompared to the vertical elements

The load can be distributed to the verticalelements in proportion to the tributary mass

8/20/2019 DCR-IS 1893 ppt

30/55

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 carefullyanalyzed considering in-plane floor flexibility.

Note 1 of Cl. 7.7.2.2 gives the criterion on when thefloor 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)

Fig. from Jain S K, “A ProposedDraft for IS:1893…Part II:Commentary and Examples,” J. ofStruct Engg, Vol. 22, No. 2, July1995, pp 73-90

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 inlateral load distribution

177

Fig. from Jain S K, “A ProposedDraft for IS:1893…Part II:Commentary and Examples,” J. ofStruct Engg, Vol. 22, No. 2, July

1995, pp 73-90

Lateral Load Distribution

Considering Floor DiaphragmDeformation: Vertical

Analogy Method

178

Analysis for Flexible Floor Diaphragm Buildings (contd…)

Alternatively, one can take the design force asenvelop of (that is, the higher of) the twoextreme assumptions, i.e.,

Rigid diaphragm action

No diaphragm action (load distribution inproportion to tributary mass)

179

Section 7.8: Dynamic Analysis

IS:1893-2002(Part I)

180


Sub-sections

Cl. 7.1: Regular and I rregular Configurations

Cl. 7.2: Importance Factor I and Response Reduction Factor R

Cl. 7.3: Design Imposed Loads for Earthquake Force Calculation

Cl. 7.4: Seismic Weight

Cl. 7.5: Design Lateral Force

Cl. 7.6: Fundamental Natural Period


Cl. 7.8: Dynamic Analysis

Cl. 7.9: Torsion

Cl. 7.10: Buildings with Soft Storey

Cl. 7.11 Deformations

Cl. 7.12 M iscellaneous

This lecture covers sub-section 7.8

8/20/2019 DCR-IS 1893 ppt

31/55

31

181

About This Lecture

The intent is not to teach Structural Dynamics or

to teach how to carry out dynamic analysis of abuilding.

Interested persons may learn Structural Dynamicsfrom numerous excellent text books available onthis subject.

182

Requirement of Dynamic Anal. Cl. 7.8.1

Ht > 12 mHt > 40 mIV and V

Ht > 40 mHt > 90 mII and III

IrregularBuildings

RegularBuilding

SeismicZone

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 basedon assumptions

Fundamental mode dominates the response

Mass and stiffness distribution are evenlydistributed with building height

Thus, giving regular mode shape

184

Why Dynamic Analysis? (contd…)

In tall buildings, higher modes can be quitesignificant.

In irregular buildings, mode shapes may bequite irregular

Hence, for tall and irregular buildings, dynamicanalysis is recommended.

Note that industrial buildings may have large

spans, large heights, and considerableirregularities:

These too will require dynamic analysis.

185

Lower Bound on Seismic Force (Cl. 7.8.2)

This clause requires that in case dynamicanalysis gives lower design forces, these bescaled up to the level of forces obtained basedon 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 modelinga building for dynamic analysis, e.g., Stiffness contribution of non-structural elements

Stiffness contribution of masonry infills

Modulus of elasticity of concrete, masonry andsoil

Moment of inertia of RC members

Depending on how one models a building, therecan be a large variation in natural period.

Ignoring the stiffness contribution of infill wallsitself can result in a natural period several timeshigher

8/20/2019 DCR-IS 1893 ppt

32/55

32

187

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

Empirical expressions for period

Based on observations of actual as-builtbuildings, and hence

Are far more reliable than period from dynamicanalysis based on questionable assumptions

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

The load distribution with building height and todifferent 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 forabout 40% higher seismic force than a similarRC building.

The code should specify 5% damping for bothsteel and RC buildings.

189

Value of Damping Cl. 7.8.2.1 (contd…)

Damping value depends on the material and thelevel of vibrations

Higher damping for stronger shaking

Means that during the same earthquake,damping will increase as the level of shakingincreases.

We are performing a simple linear analysis, whilethe real behaviour is non-linear.

Hence, one fixed value of damping is used in ouranalysis.

190

Value of Damping Cl. 7.8.2.1 (contd…)

Choice of damping has implications on seismicsafety.

Hence, damping value and design spectrumlevel go together.

Most codes tend to specify 5% damping forbuildings.

What value of damping to be used in “static

procedure” of Cl. 7.5?

Not specified. I recommend 5% be mentioned inthe code.

191

A Note on Static Procedure

The procedure of Cl.7.5 to 7.7 does not requiredynamic analysis.

Hence, this procedure is often termed as static

procedure or equivalent static procedure or seismic coefficient method.

However, notice that this procedure doesaccount for dynamics of the building in anapproximate manner

Even though its applicability is limited to simplebuildings

192

Number of Modes Cl. 7.8.4.2

The code requires sufficient number of modesso that at least 90% of the total seismic mass isexcited 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 analysisshould be such that the sum total of modalmasses in all modes considered i s at least 90percent of the total seismic mass and missingmass correction beyond 33 percent.

The portion highlighted in red should be deleted.

8/20/2019 DCR-IS 1893 ppt

33/55

33

193

Number of Modes Cl. 7.8.4.2 (contd…)

Last sentence reads as:

The effect of higher modes shall be included byconsidering missing mass correction using well

established procedures

It should read as:

The effect of modes with natural frequencybeyond 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 themodes are well-separated and when the modesare closely-spaced.

Many computer programs have CQC methodbuilt in for modal combination.

195

Modal Combination Cl. 7.8.4.4 (contd…)

Response Quantity could be any responsequantity 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) ifthe natural modes are not c losely-spaced.

Use Absolute Sum for closely-spaced modes

To appreciate the alternative method, considertwo examples.

....24

2

3

2

2

2

1 ++++= λ λ λ λ λ

...4321 ++++= λ λ λ λ λ

197

Example 1 on Modal Combination:

For first five modes of vibration, natural period/natural frequency and maximum response aregiven. Estimate the maximum response for thestructure.

1201502303501100ResponseQuantity

9.097.145.002.861.05NaturalFrequency

0.110.140.200.350.95NaturalPeriod

54321Mode

198

Example 1 on Modal Combination (contd…)

All natural frequencies differ from each other bymore 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) methodto obtain resultant response as

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

8/20/2019 DCR-IS 1893 ppt

34/55

34

199

Example 2 on Modal Combination

For first six modes of vibration, natural period/

natural frequency and maximum response aregiven. Estimate the maximum response for thestructure.

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 lowerfrequency.

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 canbe 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 theprocedure 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 canperform dynamic analysis: it is not sufficient.

One needs to develop in-depth understanding ofdynamic analysis. There are approximate methods (such as

Rayleigh’s method, Dunkerley’s method) thatone should use to evaluate if the computerresults are right.

It is not uncommon to confuse between theunits of mass and weight when performingdynamic analysis. Leads to huge errors.

204

Lecture 3

This lecture covers

Sections 7.9 to 7.11

IS:1893-2002(Part I)

8/20/2019 DCR-IS 1893 ppt

35/55

35

205


Sub-sections

Cl. 7.1: Regular and I rregular Configurations Cl. 7.2: Importance Factor I and Response Reduction Factor R

Cl. 7.3: Design Imposed Loads for Earthquake Force Calculation

Cl. 7.4: Seismic Weight

Cl. 7.5: Design Lateral Force

Cl. 7.6: Fundamental Natural Period


Cl. 7.8: Dynamic Analysis

Cl. 7.9: Torsion

Cl. 7.10: Buildings with Soft Storey

Cl. 7.11 Deformations

Cl. 7.12 M iscellaneous

This lecture covers sub-sections 7.9 to 7.11

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

b050e51of Worste

.

..

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 toaccidental 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 accidentaleccentricity to 1.5 times calculated eccentricity.

Hence, the first equation should be taken tomean having + and - sign for the second term,whichever is critical:

1.5esi ± 0.05biedi =

209

– Two cases of Design Eccentricity

CM CSCM*

ib05.0

isi be 05.0−isi be 05.05.1 +

sie5.0

sie i

b05.0

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…)

8/20/2019 DCR-IS 1893 ppt

36/55

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 computedeccentricity.

Hence, factor 1.5 is not applied to the computedeccentricity.

Again, this equation also should be understoodto 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

• Incorporating the provision in practice…– Effect of shear only

• Analysis B


CMCS

216

• Incorporating the provision in practice…– Effect of shear, torsion esi and 0.05bi

• Analysis C


CMCSCM*

0.05bi

8/20/2019 DCR-IS 1893 ppt

37/55

37

217

• Incorporating the provision in practice…

– 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 ortorsion about vertical axis), the point throughwhich the resultant of the restoring forces acts isthe 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 willnot distinguish between the terms Centre ofRigidity 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 pointslocated one on each floor, through whichapplication of lateral load profile would causeno rotation in any floor.

As per this definition, location of CR isdependent on building stiffness properties aswell as on the applied lateral load profile.

221

All Floor Definition of CR

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

F jy

CR

CR

CR

CR

CR

CRF(j+1)y

F1y

F2y

F(j-1)y

Fny

No rotation in anyfloor

Fig. DhimanBasu

222

Single Floor CR Definition

Centre of rigidity of a floor is defined as thepoint on the floor such that application of lateralload passing through that point does not causeany rotation of that particular floor, while the

other floors may rotate. This definition is independent of applied lateral load.

8/20/2019 DCR-IS 1893 ppt

38/55

38

223

Single Floor Definition of CR

CR j th floor does notrotate(other floors mayrotate)

Fig. DhimanBasu

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 notconcern ourselves about it.

Results could be somewhat different dependingon which definition is used. But, the difference isnot substantial for most buildings. Use any definition that you find convenient to use.

For computer-aided analysis, the all-floordefinition 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 massdistribution, we take it at geometric centre of thefloor.

Locating CR is not so simple for a multi-storeybuilding.

226

To Locate CR

The way we defined it, one needs to applylateral loads at the CR.

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

Notice the condition that the floor should notrotate.

Hence, we could apply the load at CM, andrestrain the floor from rotation by providing rollers

The resultant of the applied load and reactionsat the rollers will pass through CR

227

To Locate All-Floor CR

(b) Free body diagram of aparticular floor

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

constrained model

Central nodes of both ends ofthe diaphragm are constrainedto ensure equal horizontaldisplacement

Columnshear

Resultant of columnshears passes throughthe center of rigidity of

the floor

Central nodes of both ends ofthe diaphragm are constrainedto ensure equal horizontaldisplacement

Lateral load

proportional to

the massdistributiondistributedalong the floorlength

Fig. Dhiman Basu

228

To Locate Single-Floor CR

(b) Free body diagram of a

particular floor

Column

shear

Resultant of columnshears passes throughthe center of rigidity of

the floor

(a) Lateral load is applied at theconstrained floor

Lateral loadproportional to

the massdistributiondistributedalong the floorlength

Central nodes of both ends ofthe diaphragm are constrained

to ensure equal horizontaldisplacement

Fig. Dhiman Basu

8/20/2019 DCR-IS 1893 ppt

39/55

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 andChopra (ASCE, Vol 119, No. 10).

230

Superposition Method

Apply lateral load profile at the CM’s and analyse

the building; say the solution is F1 This incorporates the effect of computed

eccentricity (without dynamic amplification oraccidental ecc.)

Apply lateral load profile at CM’s but restrain thefloors from rotating; say this solution is F2 This amounts to solving the problem as i f the

lateral loads were applied at the CRs since the

floors did not rotate.

The difference of F1 and F2 gives the solutiondue 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 timescomputed 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 toload profile times accidental eccentricity; saysolution 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 bedeleted:

However, negative torsional shear shall beneglected

This statement is needed only when secondequation of design eccentricity is not specified.

Notice that Cl.7.8.4.5 says if highly irregularbuildings are analyzed as per 7.8.4.5, while7.8.4.5 says that it is applicable only for regularor nominally irregular buildings! Indeed, 7.8.4.5 is not applicable to buildings

highly irregular in plan.

8/20/2019 DCR-

Documents

DCR-IS 1893 ppt