2013 Capacity-Design Infills

Natural Hazards and Risks in Structural Engineering

Lecture: Earthquake Engineering

Capacity Design

Analysis of frame structures considering the interaction with

infill walls

Dr. J. Schwarz and Lars Abrahamczyk

Bauhaus-Universität Weimar, Earthquake Damage Analysis Center

Bauhaus-Universität Weimar

1. Introduction • Motivation • Strategies

2. Strategies • overview • Details to “walls as masses” • Details to “walls as diagonal braces”

3. Simple diagonal braces

4. Example of calculation

5. Damage pictures

6. Conclusions

7. References

Table of contents Bauhaus-Universität Weimar

Introduction Bauhaus-Universität Weimar

Motivation:

Killari 1993 El Asnam 1980

Introduction

as masses

- no stiffness effect

- for damaged and weak infill walls

as diagonal braces

- consideration of stiffness

- possibility to define hinges and damage grades

as slabs

- exact characterization of the behavior

- use of exact material laws

- assignment of damage grades difficult

Strategies:


As masses

Example building SEM:


fundamental calculated

NS EW NS EW

2,50 Hz 2,97 Hz

SLang 2,46 Hz 3,10 Hz

ETABS 2,27 Hz 2,63 Hz 60% Young’s modulus

Created by GermanTaskForce 2002

Diagonal braces

overview • simple brace model

• consideration of stiffness for elastic and plastic behaviour

• failure modes:

• corner crushing (compression)

• diagonal compression mode

• diagonal cracking mode and/or bed joint sliding

• simple brace model with orthogonal bending stiffness

• additional failure mode: out of plane behaviour

• multi brace model

• consideration of effects from the infill to the frame elements

• possibility to describe failure modes on the frame elements


Diagonal braces acc. to FEMA 306 [1]

a) stiffness

4

1

inf

inf1

4

2sin

hE

tE

colfe

me

tinf thickness of infill panel and equivalent strut

Eme expected modulus of elasticity of infill material (2,10e+6)

Efe expected modulus of elasticity of frame material

Icol moment of inertial of column

tan-1(hinf / Linf), radians

hcol

hinf

Linf

Lcol

inf

4,0

1 )(175,0 rha col

rinf

a

material properties for the brace: masonry



b) strength I sliding-shear failure

hcol

hinf

Linf

Lcol

rinf

a

II compression failure

shear force horizontal component of the diagonal strut capacity

cos'

90inf mec ftaV

2

infinf me

i EtLVslide

f’me90 … expected strength of masonry in the horizontal direction (~50% f’me)

Modified version of the method suggested by Stafford-Smith and Carter (1969)

Based on the Mohr-Coulomb failure criteria

= tan f f … angle of sliding friction

… inter-story drift angle



b) strength

hcol

hinf

Linf

Lcol

rinf

a

III diagonal tension failure of panel

IV general shear failure of panel

inf

inf

inf

inf

inf22

L

h

h

L

tV cr

cr

'

infinf 2 memi ftLV mimf VV 3,0

Using the recommendation of Saneinejad and Hoobs (1995)

'20 mecr f

Based on the recommendation of FEMA 273 and [2] Vmi … initial shear capacity (during the first half-cyclic loading) Vmf … final shear capacity (as result of cyclic loading effects)



c) deformation

- no clear experimental results for the behavior modes (b)

- experimental evidence supports the following inter-story drift limit states for different masonry infill panels:

- brick masonry 1,5 %

- grouted concrete block masonry 2,0%

- un-grouted concrete block masonry 2,5 %


Diagonal braces acc. to [2] T. Paulay, M.J.N. Priestley

w = 0,25 dm

w - depends on the relative stiffness of frame and panel, stress-strain curves of the materials and the load level

h

hm

Lm

l

dm

w

Failure modes (compression force):

- compression failure of diagonal struts

- sliding shear failure of the masonry

td

lh

fR m

mS

3,01

03,0 '

sec3

2 '

mftzRC

2sin

4

2 tE

hIEz

m

mgc


Diagonal braces – behaviour

Hysteresis envelope of the brace elements: [5]


infinf

inf

3

inf

,2,1

1

tLG

h

IEC

hK

mememeF

hi

Assumptions: CE = 0; OZ = 0; CR = 0,5;

CF 3 cantilever action of filler-wall

12 filler-wall constrained at both ends

Ime moment of inertia of horizontal cross sectional area

Gme shear modulus of infill material

ftp between 4 and 8% of fc (masonry)

11

1,15,0

2infinf

, I

I

tp

hy CC

ftLF

inf

inf1,12h

LCI


Definition of nonlinear hinges in brace elements


d

hy

y

FF

cos

,

2

,

cos

hi

i

KK

i

y

yK

Fd 1,1

11 yu FF yu dd

2

ud

FF

4

ue

FF

u

F

udK

ddu

2

2

,

cos

1,0 hi

u

KK

2

4

u

u

K

F

de dd

0

5

10

15

20

25

30

35

40

45

50

0.0E+00 1.0E-03 2.0E-03 3.0E-03 4.0E-03 5.0E-03 6.0E-03

Zarnic 1 Zarnic 2 Sliding-shear

Compression Initial shear capacity Final shear capacity


Comparison of failure strength:


Diagonal braces – procedure

Modeling - calculation of the diagonal brace dimensions and the failure relationship

- modeling of the brace elements - without masses - pinned on the frame structure

- allocation of the infill masses on the frame structure (loads)

- definition of hinges (axial failure)

Analysis - run “push-over” analysis

- start iteration to determine the different limit states - slight damage - moderate damage - extensive damage

- apply the capacity spectrum method


Diagonal braces – capacity curve

Determination of the capacity curve


Roof Displacement

Base S

hear

Roof Displacement

Base S

hear

Diagonal braces – example [3]

Example building DUZ-1


Created by GermanTaskForce 2002


Calculated damage progression (ETABS)

North facade at slight damage state (HAZUS 99)

North facade

at extensive damage state (HAZUS 99)



First mode shape - transverse direction (DUZ-1).

at slight damage grade (HAZUS 99) at extensive damage grade (HAZUS 99)



Capacity curves of DUZ-1 (ETABS)

in transverse direction in longitudinal direction


Damage pictures

Compression failure of diagonal strut


GermanTaskForce 2003

Damage pictures Bauhaus-Universität Weimar


Damage pictures Bauhaus-Universität Weimar


Damage pictures

Short column effect


GermanTaskForce 2003 GermanTaskForce 2003

Conclusions

- existence of different possibilities in order to model infill walls

- as masses

- as braces

- as slabs

- tools to model infill´s

- stiffness acc. to FEMA 306

- strength and failure mode acc. to presented equations

- up to now, models of masonry infill walls based on a variety of assumptions

- a large field for researchers …


References

[1] FEMA 306

“Evaluation of earthquake damaged concrete and masonry wall buildings”, basic procedures manual, Washington D.C., USA, 1998.

[2] T. Paulay and M.J.N. Priestley

“Seismic design of reinforced concrete and masonry buildings”, New York : Wiley, 1992.

[3] Abrahamczyk L., Schott C., Schwarz J., Swain T.M.

“Vulnerability of RC frame structures in Turkish earthquake regions (Part 2): modeling and analysis” Proceedings of the 13th World Conference on Earthquake Engineering 2004, Vancouver, Canada; Paper no. 220.

[4] Fajfar P., Dolšek M., Žarnić R., Gostič S.

“Development of numerical methodologies for infilled frames”, Towards European integration in seimic design and upgrading of building structures, Euroquake-project, Final report, February 2001.


Documents

2013 Capacity-Design Infills