Deformation Capacity and Resilience of Structures

(1)

Deformation Capacity and

Resilience of Structures

Boyan Mihaylov

University of Liege, February 4

th

_{, 2013}





_t

(2)

Seismic Hazard Map of New Zealand 2010

Deformation Capacity and Resilience of RC Structures

  t c

Christchurch

0.22g

Boyan Mihaylov

(3)

Deformation Capacity and Resilience of RC Structures   t c

Devastation of Christchurch

12:51pm Feb 22nd 2011

182 people killed

50% of roads destroyed

600 buildings had to be

demolished

6000 homes destroyed

80% without power

80% of water and

sewerage damaged

Horizontal PGA ≈1.0g Vertical PGA ≈1.8g Return period ≈2500 years

(design PGA=0.22g)

(4)

Deformation Capacity and Resilience of RC Structures   t c

• Structural resilience

Design for Rare Events?

• Need for displacement-based

analysis of failure mechanisms

for direct

assessment / design for structural resilience

resilient

structure

non-resilient

structure

(5)

SOUTH ELEVATION

  t c

Building in Christchurch

Boyan Mihaylov

(6)



t c

Pushover Analysis by Ruggiero: Augustus-II

Failure Mechanisms and Deformation Capacity

of Structural Members

Deformation

???

??

?

Load

a ≤ 2.5d

d

Deep beams a/d ≤ 2.5

??

???

(7)

Deep Transfer Girder

  t c Photograph: Bentz 2008

Deep beam

Boyan Mihaylov

(8)

Deep Transfer Girder



t c

Photograph: Russell Berkowitz, Christchurch 14.03.2011

(9)

t Load Load +Load -Load a d 12 0 0 10 9 5 t Load

a/d=2.29

r

_v

=0.10%

a/d=2.29

r

_v

=0

a/d=1.55

r

_v

=0

a/d=1.55

r

_v

=0.10%



t c

Tests of Deep Beams

(10)

Tests of Deep Beams



t c

(11)

∆

=0 mm

x40

P

Behaviour of Deep Beams

  t c

P=0 kN

P=650 kN

0.2 mm

∆

P=0 kN

P=650 kN

0.2 mm

P=0 kN

P=650 kN

0.2 mm

P=0 kN

P=650 kN

0.2 mm Boyan Mihaylov

(12)

P=0 kN

P=650 kN

0.2 mm

P

Behaviour of Deep Beams

  t c

∆

=0.7 mm

x40

P=0 kN

P=650 kN

0.2 mm

P=0 kN

P=650 kN

0.2 mm

P=0 kN

P=650 kN

(13)

P=1300 kN

P=1680 kN

0.7 0.4 0.2 mm 2.0 0.5 0.3

P

Behaviour of Deep Beams

  t c

∆

=4.3 mm

x40

P=0 kN

P=650 kN

0.2 mm

P=0 kN

P=650 kN

0.2 mm

P=0 kN

P=650 kN

(14)

P=1300 kN

P=1680 kN

0.7 0.4 0.2 mm 2.0 0.5 0.3

P

Behaviour of Deep Beams

  t c

∆

=6.2 mm

x40

P=0 kN

P=650 kN

0.2 mm

P=0 kN

P=650 kN

0.2 mm

P=0 kN

P=650 kN

(15)

P=1864 kN

3.0

0.55

0.35

P

Behaviour of Deep Beams

  t c

∆

=8.4 mm

x40

P=0 kN

P=650 kN

0.2 mm

P=0 kN

P=650 kN

0.2 mm

P=0 kN

P=650 kN

(16)

P=1864 kN

3.0

0.55

0.35

P

Behaviour of Deep Beams

  t c

∆

=8.4 mm

x40

P=0 kN

P=650 kN

0.2 mm

P=0 kN

P=650 kN

0.2 mm

P=0 kN

P=650 kN

(17)

-10 -5 0 5 10 15 20 -2000 -1500 -1000 -500 0 500 1000 1500 2000 2500 _{, mm} P , k N -10 -5 0 5 10 15 -1000 -800 -600 -400 -200 0 200 400 600 800 1000 _{, mm} P , kN -10 -5 0 5 10 15 20 -2000 -1500 -1000 -500 0 500 1000 1500 2000 _{, mm} P , k N -15 -10 -5 0 5 10 15 20 25 -1500 -1000 -500 0 500 1000 1500 _{, mm} P , kN P  P  P  P  P  P  P  P  P  P  P  P  P  P  P  P  P  P  P  P 

cyclic

mono

cyclic

mono

Measured Load-Displacement Response



t c

(18)

FE Modeling of Deep Beams



t c

Program VecTor2, F.J. Vecchio, University of Toronto

(19)

Modeling of Deep Beams – Kinematic Approach



t c

Slender Beams

Plane sections remain plane hypothesis

Robert Hooke 1678

Measured deformations

Deep Beams

Measured deformations

Simple kinematic

conditions for deep

beams?

(20)



_c h

DOF



_c



_c k L



_t

DOF



_t,avg



_t,min

a



_t,avg

(1+ )



_x





_z

 

_c k L

Two Parameter Kinematic Model

Below the crack:

Above the crack:



_c h

DOF



_c



_c

a



_t,avg

V

P

b1

(V/P)L

b1

L



_c



r

(1+ )

CLZ

=0 b1e

L =

d



k L





v



t,min



t,max



_t,avg

x

z



_t

DOF



_t,avg k l =l₀



_t,min

a



_t,avg

(1+ )



_x





_z

 

_c

+

=

 

x

z

_t_avg

x

,



,





 

z

h

x

z

x

t avg z



_

2 ,

,





 











_x

x

,

z



_t_,_avg

h



z

cot

 

tavg c z

x

z





x









,

_,

cot

a _t,avg V P b1 (V/P)L b1 L



_c  r (1+ ) CLZ =0 b1e L = h



 v  t,min  t,max _t,avg x z Rigid block Boyan Mihaylov

(21)

Components of Shear Resistance

T

_min

V

_d

V

A

_v

f

_v

v

_ci



a

V

_s



1 d=

10

95 m

m

=

Aggregate interlock

d

s

ci

CLZ

V





Critical Loading Zone

∆

_c

V

_CLZ

V

(22)



t c

2PKT for Complete Response of Deep Beams

V

_CLZ

V,

V

_ci

V

_d

V

_s



_c

Diagonal

crack

Bottom

Reinforcement

DOF

∆

_c

DOF

ε

_t,avg

∆

V

Exp

2PKT

V,∆

∆

Boyan Mihaylov

(23)

2PKT for Ultimate Response of Deep Beams

1. Degrees of Freedom (1) s s t avg t A E d Va    9 . 0 min , ,   (2) c30.0035lb1ecot

2. Geometry 3. Compatibility 4. Shear Strength V=VCLZ+Vci+Vd+Vs

Effective loading plate

(3) l_b1_e(V/P)l_b13a_g Dowel length (4) lk l₀d



cotcot₁







1 max 0 1.5h d cot s l    





d d h d s l b  0.28 2.5 max  (Ref. 1) Crack angle (5) 1max(,)

 – based on Simplified MCFT (Ref. 2) or 35˚

Area of effective stirrups

(6)Avevb



dcot1l01.5lb1e



0

Displacement field

– below critical crack

(7) _x_t_,_avgx (8) z h x avg t z _ 2 ,  

– above critical crack

(9) _x_t_,_avg



hz



cot (10)_z _t_,_avgxcot_c Crack width (11) 1 min , 1 sin 2 cos    t k c l w  Stirrup strain (12) d d avg t c v 9 . 0 cot 25 . 0 _, 2₁   

Critical loading zone, CLZ

(13) 2 1 8 . 0 sin ' 43 . 1 c be CLZ f kbl V  cot 2 1 2 1 0k    Dowel action (14) k b ye b d l d f n V 3 3  0 500 1 2 min ,                     MPa f E f f y s t y ye  Aggregate interlock (15) bd a w f V g c ci 16 24 31 . 0 ' 18 . 0    (Ref. 3) Stirrup capacity (16) V_sA_vef_v yv v s v E f f    c c k l P b1 l c _t,min _ t,max CLZ b1e l d _t,avg x z h  1  v _x _z x _z c _t,min x z d V   a+ d cot_t,avg  a+ d cot_t,avg  b1e l 1 w b d b n bars b2 l s A g a V 0 l _l 1. Degrees of Freedom (1) (2)

2. Geometry 3. Compatibility 4. Shear Strength V=VCLZ+Vci+Vd+Vs

Effective loading plate

(3) Dowel length (4) (Ref. 1) Crack angle (5)

 – based on Simplified MCFT (Ref. 2) or 35˚

Area of effective stirrups

(6)

Displacement field

– below critical crack

(7) (8)

– above critical crack

(9) (10) Crack width (11) Stirrup strain (12)

Critical loading zone, CLZ

(13) Dowel action (14) Aggregate interlock (15) (Ref. 3) Stirrup capacity (16) Boyan Mihaylov

(24)

Predicted Shear Strength, 434 Tests

  t c 0 0.5 1 1.5 2 2.5 3 0

V

exp

/V

pred

Avg. COV

1.10 13.7%

1.25 24.6%

1.30 29.0%

2PKT

Canadian Standards

Association

American Concrete

Institute

Conservative 5% 0 0.5 1 1.5 2 2.5 3 0

V

exp

/V

pred Boyan Mihaylov

(25)

Tests by Zhang & Tan, 2007

Size Effect in Deep Beams

100 1000 3000 0 0.05 0.1 0.15 0.2 0.25

d, mm

KT

v

d

v

ci

v

CLZ CSA strut-and-tie a/d=1.1 Lb1=0.16d Lb2=0.16d V/P=1 l=1.26% fy=506MPa fc’=28.5MPa ag=10mm a/d=1.1 Lb1=0.16d Lb2=0.16d V/P=1 l=1.26% fy=484MPa vfyv=1.75MPa fc’=27.6MPa ag=10mm

V

bd f

c’ 40 in. 120 in. 4 in. 0.25d d 0.25d d 0 .0 7 5 d 0 .0 7 5 d 0.25d d 0.25d d 0 .0 7 5 d 0 .0 7 5 d

Transfer girder

in building

~

3

0

0 m

m

  t c 2PKT Boyan Mihaylov

(26)









d

a

L

d

_k _t _k t

c





,max

cot









,min







0 2 4 6 8 10 12 14 16 18 0 2 4 6 8 10 12 14 16 18



pred

, mm



ex p

,

m

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7



pred

, in



ex p

,

in

a _t,avg V P

_

c  r (1+ ) CLZ =0 d



 v  t,min  t,max _t,avg x z

Predicted Displacement Capacity, 53 Tests



t c

(27)

Predicted Deformed Shapes

a/d = 1.55

a/d = 2.29

Pred.

Exp.

P/P

_u

= 92%

P/P

_u

= 78%

P/P

_u

= 91%

P/P

_u

= 100%

P/P

_u

= 100%

P/P

_u

= 97%

P/P

_u

= 92%

P/P

_u

= 93%

P

Boyan Mihaylov

(28)



t c

Double-Curvature Bending of Deep Beams

transfer girder

deep beam slender

beam

Test of Continuous Deep Beam

Specimen Construction

1 2 0 0 m m 3475 mm 3475 Spreader beam Specimen

P

Continuous

Deep Beam in

Building

Boyan Mihaylov

(29)



t c

Double-Curvature Bending of Deep Beams

(30)



t c

Predicted Deformed Shapes

Pred.

Exp.

P

D

0 2 4 6 8 10 12 14 16 18 20 0 200 400 600 800 1000 1200 1400 1600 1800 _{, mm} P , k N Boyan Mihaylov

(31)



t c

Short Coupling Beams

Adapted from Subedi 1999

Shear wall Coupling beam

Adapted from Paulay 1971

Cracked

CLZ?

N

(32)



t c

D Regions in Slender Beams/Columns

D

B

D

Tests by Yoshida, U of Toronto, 2000

Pred.

Exp.

(33)



t c

Wall Type Bridge Piers

Passerelle, Liège Passerelle, Liège

Pont d’Ougrée, Standard Viaduc de Remouchamps

(34)



t c

Wall Type Bridge Piers

(35)



t c

Empirical Models for Deformation Capacity

Biskinis and Fardis, 2010

(36)



t c

3PKT for Wall Type Piers

0.86 1.59 1.6 3.35 2.2 9.06 3.2 11.4 5.4 10

Test by Bischas and Dazio, 2010

P, kN ∆, mm -60 -1000 , ∆ Exp. Boyan Mihaylov

(37)



t c

Macro Models for D Regions Combined with Sectional

Models for B regions to Study Structural Resilience

Augustus-II (Bentz 2011)

Structural Resilience Analysis



t

c

(38)



t c

Tоwards More Resilient Urban Infrastructure

Toronto Canada

(39)

Merci!



t c