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Presentation VII:

Modelling and Analysis of Multistorey Buildings

Yogendra Singh, Ph.D.Professor, Department of Earthquake EngineeringIndian Institute of Technology Roorkeewww.iitr.ac.in

Indo-Norwegian Training ProgrammeIndo-Norwegian Training Programme

Seismic Design of Multi-Storey Buildings:

IS 1893 vs. Eurocode 8

Seismic Design of Multi-Storey Buildings:

IS 1893 vs. Eurocode 8

New Delhi,

26–28 May 2014

New Delhi,

26–28 May 2014

CLASSICALMETHODS

APPROXIMATEMETHODS

DIRECT STIFFNESSMETHOD

FINITE ELEMENTMETHOD

COMPUTER BASEDMETHODS

MATHEMATICAL MODELLING

MODELLING METHODS

COMPUTER BASED MODELLING

• Structure is considered as assemblage of members and elements

• Stiffness matrix of each member elements is obtained

• Stiffness matrices of various elements are assembled using compatibility

• System of linear equations is solved

MODELLING OF FRAME STRUCTURE

STIFFNESS MATRIX OF FRAME MEMBER

L

EIz

L

EIz

L

EIz

L

EIL

EI

L

EI

L

EI

L

EIL

GI

L

GIL

EI

L

EI

L

EI

L

EIL

EIz

L

EI

L

EIz

L

EIL

EA

L

EAL

EIz

L

EIz

L

EIz

L

EIL

EI

L

EI

L

EI

L

EIL

GI

L

GIL

EI

L

EI

L

EI

L

EIL

EI

L

EI

L

EI

L

EIL

EA

L

EA

S

Z

YYYY

XX

YYYY

ZZ

Z

YYYY

XX

YYYY

ZZZZ

4000

60

2000

60

04

06

0002

06

00

0000000000

06

012

0006

012

00

6000

120

6000

120

0000000000

2000

60

4000

60

02

06

0004

06

00

0000000000

06

012

0006

012

00

6000

120

6000

120

0000000000

22

22

2323

2323

22

22

2323

2323

MODELLING OF SHEAR WALL

1

4

2

65

3

L

EI

L

EI

L

EI

L

EIL

EI

L

EI

L

EI

L

EIL

EA

L

EAL

EI

L

EIL

EIL

EA

S

)4(6

0)2(6

0

6120

6120

00

0)4(6

0

120

)1(

1

22

2323

2

3

RGAL

EI2

12

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MODELLING OF FINITE SIZE OF JOINTS

A A' B' B

aL cL bL

HSHS T

1000

100

0010

001

bL

dL

H

MODELLING OF COUPLED SHEAR WALLS

MODELLING BEAM COLUMN OFFSET

MODELLING BEAM COLUMN OFFSET

MODELLING OF BEAM-COLUMN JOINTS

(a) (b) (c)Beam-column Joint Model as per ASCE/SEI-41 Supplement-1 (2007)for EffectiveStiffness, when Ratio of Flexural Strength of Columns and Beams Framing intoJoint is: (a) 0.8, (b) in between 0.8 and 1.2, and (c) greater than 1.2.

STIFFNESS OF RC MEMBERSRC Member Eurocode-8 (2004)

ASCE/SEI-41 Supplement-1 (2007)

Non-prestressed Beam

0.5EcIg

0.3EcIg

Columns with design gravity loads ≥0.5Agfc

’ 0.7EcIg

Columns with design gravity loads ≤0.3Agfc

’ Linear interpolation

Columns with design gravity loads ≤0.1Agfc

’ or with tension0.3EcIg

Beam-column joint with -Rigid beam end zones with the

column flexibility extending to the joint centerline

Beam-column joint with -Rigid column end zones with the beam flexibility extending to the

joint centerline

Beam-column joint with -50% of the end zones of both beam and column within the joint extents

are rigid

8.0

b

c

M

M

2.18.0

b

c

M

M

2.1

b

c

M

M

where, Ec is Modulus of elasticity of concrete, Ig is moment of inertia of gross concrete section, Ag is gross cross sectional area, fc

’ is compressive strength of concrete, Mc and Mb are nominal flexural strength of column and beam, respectively.

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MODELLING OF DUAL SYSTEMS

Imbedded beam elements

(a) Wall-Frame Structure (b) Analysis Model

MODELLING OF IN-FILLS

inf4.0

1175.0 rha col

41

inf

inf1 4

2sin

hIEtE

colfe

me

MODELLING OF IN-FILLSInfills canbe modelled as Equivalent Diagonal Compressive Strut having width

where,

=column height between centerlines of beams

=height of infill panel

=expected modulus of elasticity of frame material (concrete)

=expected modulus of elasticity of infill material

=moment of inertia of column

=length of infill panel

=diagonal length of infill panel

=thickness of infill panel and equivalent strut

colh

infh

feE

meE

colI

infL

infr

inft

41

inf

inf1 4

2sin

hIEtE

colfe

me

inf4.0

1175.0 rha col

EQUIVALENT PLANE FRAME MODELLING

Y

X

C1 C4 C7 C10

C3 C6 C9 C12

C2 C5 C8 C11

• Symmetric plan about both the axes

• Symmetric distribution of stiffness

• Symmetric distribution of mass

EQUIVALENT PLANE-FRAME MODELIN X-DIRECTION

C1

Rigid Link Members

C4 C10 C7 C5 C2 C8 C11 C6 C3 C9 C12

• Rigid link members have high axial stiffness (say 1000 times of columns)

• Beams are also assigned high axial stiffness

EQUIVALENT PLANE-FRAME MODELIN Y-DIRECTION

• Rigid link members have high axial stiffness (say 1000 times of columns)

• Beams are also assigned high axial stiffness

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12

Rigid Link Members

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SPACE FRAME MODELLING

1. 3D Modelling with 6 DOF per node

2. Rigid floor modelling, the floor slab is rigid in its plane and distributes the lateral force in various lateral load resisting elements

3. In the absence of rigid floor modelling, there may be error in free vibration characteristics, column torsion and beam bending moment

RIGID FLOOR MODELLING

x

y

U1

U2

U3

u1

u2

u3

Θ

100

sincoscossin

cossinsincos

yx

yx

B

TRANSFORMATION MATRIX

RIGID BODY MOTION

RIGID FLOOR MODELLING

Y

X

C1 C4 C7 C10

C3 C6 C9 C12

C2 C5 C8 C11

EQUIVALENT PLANE FRAME MODELLING FOR FRAMED TUBE

EQUIVALENT PLANE FRAME MODELLING FOR MULTI-CELL TUBE

EQUIVALENT PLANE FRAME MODELLING FOR MULTI-CELL TUBE

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SEQUENTIAL ANALYSIS FOR DEAD LOAD

ERROR IN SIMULATNEOUS ANDCONVENTIONAL ANALYSIS

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FLAT SLAB SYSTEMS

Drop Panel

Column Head

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FLAT SLAB SYSTEMS

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FLAT SLAB SYSTEMS

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FLAT SLAB SYSTEMS

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FLAT SLAB SYSTEMS

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FLAT SLAB SYSTEMS

0

1

2

3

4

5

0 0.2 0.4 0.6 0.8 1

Max

imu

m I

nte

r S

tore

y D

rift

(%

)

Gravity Shear Ratio

Hueste and Wright

ASCE/SEI 41 [NC]

ASCE/SEI 41 [C]

ACI 318-05

MODELLING OF FLAT SLAB•ACI equivalent frame method

Load transfer system in this method involves three distinct interconnected elements:i) Slab-beam member (Ks)ii) Column (Kc)iii) Torsional member (Kt)

Members of ACIEFM, Detail A

Members of 3-D structure, Detail A

Definition of equivalent frame

MODELLING OF FLAT SLAB

•Extended equivalent column method

• Slab is represented by beam element•Arrangement of column elements incorporate the column flexibility and torsionalflexibility of attached torsional members

KcKs

Kt

Kc

Extended Equivalent column method [Cano and Klinger, 1988]

MODELLING OF FLAT SLAB

•Extended equivalent beam method

• Column is modelled directly•Arrangement of slab-beam elements incorporate the slab flexibility and torsionalflexibility of attached torsional members

Kc

Ks

Kt

Extended Equivalent beam method [Cano and Klinger, 1988]

MODELLING OF FLAT SLAB

•Explicit Transverse Torsional Element Model

Torsional element

Column

Equivalent beam member

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MODELLING OF FLAT SLAB

•Explicit Transverse Torsional Element Model (ACI 318)

3

222 1

9

lcl

ECKt

363.01

3 yx

y

xC

THANK YOU !