Slides Frame YS

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Yogendra Singh, Ph.D.Professor, Deptt. of Earthquake Engg.

Indian Institute of Technology Roorkee, India

Indo‐Norwegian Training Programme on

Nonlinear Modelling and Seismic Response Evaluation of StructuresDecember 14‐16, 2014 – Continuing Education Center, IIT Roorkee

Nonlinear modelling of frame‐shear wall buildings

Table of contents

Introduction: Sources of nonlinearity

Material nonlinearity, Section nonlinearity and Member nonlinearity

Concept of chord rotation

Behaviour of steel and RC frames

Behaviour of braced and infilled frames

Behaviour of shear walls

Behaviour of beam‐column joints in steel and RC frames

Modelling parameters as per ASCE 41

Moment and shear capacity

Plastic deformation capacity

Backbone curves

Nonlinear Modelling

During earthquakes, the structures undergo:

1. Large displacements triggering geometric nonlinearity

2. Stresses beyond yield material nonlinearity

Linear modelling is limited to simulation of stiffness of different components;

Information required Sectional dimensions

Elastic material properties

Cracking of RC members (reinforcement details?)

Nonlinear modelling involves simulation of stiffness, strength and ductility

All the information required in linear analysis

Strength in different failure modes (reinforcement in case of RC members)

Reinforcement detailing, confinement, anchorage and splicing, axial force

ratio, shear force ratio

Understanding of behaviour and failure modes and mechanisms is the key to

successful modelling

Material Nonlinearity

Unconfined and confined concrete


Reinforcing Steel


Reinforcing Steel

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Section Nonlinearity

RC Sections


Steel Sections

d d'

dp

dp

y

y

fy


RC Sections

Member Nonlinearity

RC Sections

Member Nonlinearity

RC Sections

Member Nonlinearity

RC Sections

spspcp LLkLL 2

blyesp dfL 022.0

08.012.0

y

u

f

fk

cL = length from the critical section to thepoint of contra-flexure

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Member Nonlinearity

RC Sections

Member Nonlinearity

RC Sections

3

2spy

y

LH

HLpyuyu

cdor

csycy

y

cdor

csucc

u

dcdcscsc

Chord Rotation

θ

θθ

Chord Rotation

Usable strain limits

RC Sections

ASCE 41‐2013

10.3.3.1 Usable Strain Limits Without confining transverse reinforcement, the maximum usable strain at the extreme concrete compression fiber shall not exceed 0.002 for components in nearly pure compression and 0.005 for other components,… Maximum compressive strains in longitudinal reinforcement shall not exceed 0.02, and maximum tensile strains in longitudinal reinforcement shall not exceed 0.05. Monotonic coupon test results shall not be used to determine reinforcement strain limits. If experimental evidence is used to determine strain limits, the effects of low-cycle fatigue and transverse reinforcement spacing and size shall be included in testing procedures.

Effect of cyclic loading

Backbone curve

ASCE 41‐2013

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Backbone curveASCE 41‐2013

Behaviour of frames

Behaviour of frames Behaviour of frames

Behaviour of frames

BMD SFD

Behaviour of frames

Beams can yield in Flexure or Shear

Columns can yield under Axial‐Flexure (P‐M‐M) interaction or Shear

Joints (panel zones) can yield

in Shear

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Behaviour of frames Behaviour of frames

Behaviour of joints Behaviour of joints

Behaviour of joints Behaviour of joints

cjh VTCV cosRVTCV cjh

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Lumped plasticity model of a frame

P-M-M Hinges

Shear Hinges

Moment Hinges

Concentrically braced steel frames

Single Diagonal Inverted V- Bracing V- Bracing

X- Bracing Two Story X-Bracing

Concentrically braced steel frames Concentrically braced steel frames

Tension Brace: Yields

Columns and beams: remain essentially elastic

Compression Brace: Buckles

Concentrically braced steel frames

P

Eccentrically braced steel frames

e

e

e e e e

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Eccentrically braced steel frames Eccentrically braced steel frames

pp

p = link plastic rotation angle (rad)

Eccentrically braced steel frames

p

p = link plastic rotation angle (rad)

Behaviour of RC shear‐wallse

V V

M M

V

M

M

Shear yielding occurs when: V = Vp = 0.6 Fy (d - 2tf ) tw

Flexural yielding occurs when:

M = Mp = Z Fy

Behaviour of RC shear‐walls

e

V V

M M

V

2Me

p

p

V

M1.6e PREDOMINANTLY SHEAR YIELDING LINK:

PREDOMINANTLY FLEXURAL YIELDING LINK:p

p

V

M2.6e

COMBINED SHEAR AND FLEXURAL YIELDING:p

p

p

p

V

M2.6e

V

M1.6

Behaviour of infilled frames

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Infills have been 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

inf4.0

1175.0 rha col

4

1

inf

inf1 4

2sin

hIE

tE

colfe

me

colh

infh

feE

meE

colI

infL

infr

inft

Effective Stiffness of URM Infills Failure modes in infilled frames

ReferenceTension

failure of columns

Compression failure of columns

Short-column effect

shear failureof

beam/column

Flexural failure of columns

Failure of beam-column joints

Smith (1967) ● ○ ○ ● ○ ○Smith and Carter

(1969) ● ○ ○ ● ○ ○Paulay and Priestley

(1992) ● ○ ● ● ● ○Mehrabi et al. (1996) ○ ○ ○ ● ● ○Fiorato et al. (1970) ● ● ○ ● ○ ○El-Dakhakhni et al.

(2003) ○ ○ ○ ○ ● ●● – Failure mode considered; ○ – Failure mode not considered

Failure modes in infills

Sl. no. Reference

Identified failure modes of infill panelsSliding shear failure

Diagonal tension

Diagonal compression

Corner crushing

1 Smith (1967) ○ ● ● ○2 Smith and Carter (1969) ● ● ● ○3 Mainstone (1971) ○ ● ○ ●4 Wood (1978) ● ● ○ ●5 Liauw and Kwan (1985b) ○ ○ ● ●6 Smith and Coull (1991) ○ ○ ○ ●7 Priestley and Calvi (1991) ● ● ● ○8 Paulay and Priestley (1992) ● ○ ● ○9 Saneinejad and Hobbs (1995) ● ● ● ●

10 Flanagan and Bennett (1999) ○ ○ ○ ●11 Al-Chaar (2002) ● ○ ● ○12 ACI 530 (2005 ) ● ○ ● ●13 ASCE-41 (2007) ● ○ ○ ○

○ – Failure mode not considered; ● – Failure mode considered

Infills are constructed after completion of frame Construction sequence does not allow a full contact between infill

and soffit of the beam above

Realistic model of infills

Evaluation of efficacy of 1‐, 2‐, and 3‐strut models of infills

Reference of experimental study

Column

shear strength

(kN)

Shear force applied to column

(kN)Experimental

observation1-strut

model

2-strut

model

3-strut

model

RC frame with unreinforced solid

concrete block masonry infill(Mehrabi et al. 1996)

92.95 130.98 65.49 32.74Shear failure of

columns

RC frame with burnt clay brick

infill (Al-Chaar 1998)29.06 124.41 62.20 31.1

Shear cracks in

column

RC frame with concrete masonry

infill (Al-Chaar 1998)29.06 345.55 172.77 86.39

Shear cracks in

column

Non ductile RC frame with burnt

clay brick infill (Kaushik andManchanda 2010)

51.14 57.75 28.88 14.44Shear cracks in

columns

Ductile RC frame with URM

infill (Kaushik and Manchanda2010)

60.31 66.00 33.00 16.50Columns suffer

shear damage

Shear Failure of RC columns caused due to strut action of URM infill

(Mehrabi et al. 1996)

Failure of exterior & interior column observed in 2003 Bingöl earthquake

(Özcebe et al. 2003) (Kaushik and Manchanda2010)

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Modelling of URM infills Effective stiffnessASCE 41‐2013

Plastic hinge propertiesASCE 41‐2013




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Nominal strength vs. expected strength

Mean or Expected strength, fe=fmean

Nominal or characteristic strength, fck

f

n

64.1 cke ff


Structural Steel


Concrete and Reinforcement

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Shear strength models of RC columns Shear strength models of RC beam‐column joints

Modeling of Beam‐Column Joints Behaviour of shear‐walls

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Boundary confinement

Boundary Elements

Plastic hinges in shear‐wallsASCE 41‐2013

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Drop Panel

Column Head

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

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• Flexural failure of slab• Flexural failure of slab-column

connectionDuctile mode of failureCracks appear on bottom surface

• Punching shear failureBrittle mode of failureCracks appear on top surface

Failure of flat slab systems

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• Out of total unbalanced moment, part is transferred through flexure and part is transferred through torsion

• Shear stress at critical section is resultant of gravity and torsional actions

J

cM

db

Vv uvg

n

0

Flat slab systems

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fv 1

2

1

3

21

1

b

bf

f = factor for unbalanced moment transferred by flexure at slab-column connections

= factor for unbalanced moment transferred by torsion atslab-column connections

v

Flat slab systems

•Explicit Transverse Torsional Element Model

Modelling of flat slab systems

•Equivalent width of slab

32 1

12

lcl

61

12

lcl

•Interior Supports

•Exterior Supports


•Stiffness of Torsional Element

3

222 1

9

lcl

ECKt

363.01

3 yx

y

xC


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0

1

2

3

4

5

0 0.2 0.4 0.6 0.8 1

Max

imu

m I

nte

r St

orey

Dri

ft (

%)

Gravity Shear Ratio

Hueste and Wright

ASCE/SEI 41 [NC]

ASCE/SEI 41 [C]

ACI 318-05


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