An Inverted V-Braced Frame System Exhibiting Bilinear ... · • Canadian code provisions • Seismic stability of an 16-storey ... Design Seismic Load NBCC 2015 RdRo= 4.8 ... •

Robert TremblayPolytechnique Montreal, Canada

An Inverted V-Braced Frame System Exhibiting Bilinear Response

for Seismic Stability underLong Duration Subduction Earthquakes

Overview

• Steel SFRSs

• Seismic stability

• Cascadia subduction earthquakes

• Canadian code provisions

• Seismic stability of an 16-storey braced frame

• Column continuity

• Proposed chevron braced frame

• Conclusions

Robert Tremblay, Polytechnique Montreal, Canada 3

Plastic Hinge (typ.)

Shearyielding


Tensionyielding

Plastic HingeTension

yielding

Tensionyielding

Compressionyielding e


Plastic Hinge

End-plateBending

Shearyielding

Current Steel SFRSs

CBF BRBF EBF

MRF PW

Main achievements

• Systems have reliable energy dissipation

through robust ductile response

• Comprehensive design provisions to achieve

this energy dissipation capacity and allow

reduced design seismic forces

• Structural damage confined to a limited

portion of the structure to minimize repair


Tensionyielding

Compressionyielding

Buckling Restrained Braced Frames


Graphite

Molybdenum disulphide

UHMW

PTFE


Eccentrically Braced Steel FramesShearyielding

e

Use of Modular Links

with N. Mansour& C. Christopoulos, University of Toronto



with L. Tirca, Concordia University& Pall Dynamics


Friction Braced Frames (FBFs)


BRBFs

FBFs

EBFs


Main Shortcomings

• Residual deformations

• Prone to soft-storey response

and dynamic instability


Braced Frame (typ.)

Braced FrameBuilding Plan View

F

F yk

1

V

PP

kk



M Vh P Fh 0

k, Fy

F

F yk

1

1

V

LossF y

V V

P P

P/h

P

F

h

Equilibrium:

Elastic response:

Inelastic response:

F V P / h

y yV F P / h

k, FW

y

F

Fy

k

1

P

h


Seismic Conditions in Southwest British Columbia

Rogers, G., Halchuck, S. Adams, J., and Allen, T. (2015). 5TH Generation (2015) Seismic Hazard Model for Southwest British Columbia, Proc. 11th Can. Conf. Earthquake Eng., Paper no. 94198.

Subduction deep-in-slab EQs

Subduction interface EQs

Shallow crustal EQs


Typical ground motions expected in Southwest BC

Subduction deep-in-slab EQ motions

Subduction interface EQ motions

Shallow crustal EQ motions


P- effects under subduction deep-in-slab EQ motions


P- effects under subduction interface EQ motions



P‐ effects reduce lateral strength

P‐ effects create an unsymmetrical SFRS=> Progressive drifting

F

-F

V+

+-V > V

y

y

V 1P/h

V =S(Ta) Mv IE W

Ro Rd

S

S(T )

Period, TTa

a

Site SpecificDesign Spectrum



RdRo = 4.8

RdRo = 7.5

V =S(Ta) Mv IE W

Ro Rd

k, FW

y

P

aT = 1.8 s

Victoria, BCFirm Ground




V =S(Ta) Mv IE W

Ro Rd

S

Period, T

Minimum

2 s Ta


F

Fy

k

1

1

V Target Drift

F U F

y

t

2 y

P/h

U F 2 y


RdRo = 4.8


RdRo = 7.5



BRBF or FBF : RdRo = 4.8Firm Ground, Vancouver, BC

5 @ 9.0 = 45.0 m

Frame Studied

Frame ElevationPlan View

4.5 m

5 @

9.0

= 4

5.0

m

15 @

4.0

= 6

0 m

N

Gravity loads: Roof: Dead = 3.0 kPa Snow = 1.64 kPa Floor: Dead = 3.6 kPa Partitions = 1.0 kPa Live = 2.4 kPa Exterior walls = 1.2 kPa

0.25 m(typ.)

BRBF

FBF



Design BWith Stab. Provisions

102 tons3.52 s

Design ANo Stab.

Provisions

81 tons3.99 s

TonnageT1 (s)

0 1 2 3 4 5T (s)

0.00

0.04

0.08

0.12

0.16

0.20

Design Seismic LoadNBCC 2015RdRo = 4.8

Vancouver, BC (Site C)

Design B

Design A

0 0.02 0.04 0.06V / W

0

4

8

12

16

Leve

l

Design ADesign B

1.0 1.1 1.2 1.3 1.4U2

0

4

8

12

16

0.0 0.5 1.0 1.5 2.0d (%hs)

0

4

8

12

16


5 @ 9.0 = 45.0 m

Frame Studied

Plan View

5 @

9.0

= 4

5.0

m

N

1x 2y 3y

4x 4y 2x

1y

1xx1

1xx1

2xx2

1yx1

4xx4

3yx2

2yx2

1yx1

4yx4

Analysis using 2D model and SAP2000Braces: elastic‐plastic hysteresis using NL link elementsBeams and columns: elastic beam elements with P–M plastic hingesColumns pinned at their basesGravity columns with pinned splices at every second level


a g a g

a gn

(%h n

)

n (%

h n)

n (%

h n)



-2 -1 0 1 2s (%hs)

1

3

5

7

9

11

13

15

Leve

l

-2 -1 0 1 2s (%hs)

1

3

5

7

9

11

13

15

-4 -3 -2 -1 0 1 2 3 4s (%hs)

1

3

5

7

9

11

13

15

Individuals RecordsMean Values

CR Ground Motions IS Ground Motions SI Ground Motions

T1 T1T1

Shear Storey Drift Demands / Design A - No P- in Analysis


5 10 15 20 25Time (s)

-0.5

0

0.5 (%

h s)

-1.0

-0.5

0.0

0.5

1.0

1.5

(%h s

)

Shear Storey Drift, s

Bending Storey Drift, b

Total Storey Drift, s + b

SI1 - 2011 M9.0 Tohoku EQ, AOM0281103111446_NS

CR1 - 1989 M6.9 Loma Prieta EQ, Bran 0oLevel 16

Level 9

40 60 80 100 120Time (s)

-1.0

0.0

1.0

2.0

3.0

(%h s

)

Level 9

-2.0

-1.0

0.0

1.0

2.0

(%h s

)

Level 16

Design A

No P-in Analysis


SI1 SI2 SI3

SI4 SI5

Collapse Patterns under Subduction Interface (SI) Motions


-1.0 0.0 1.0 2.0 3.0 4.0Storey Shear Drift, s (%hs)

-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

Stor

ey S

hear

(kN

)

Design A

-4.0 -3.0 -2.0 -1.0 0.0 1.0Storey Shear Drift, s (%hs)

-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

Stor

ey S

hear

(kN

)

Storeys Shears fromBraces OnlyBraces + Columns

Design B

Storey shear-Shear storey drift response at level 9 - SI1 motion:

0.0 1.0 2.0Roof / hn (%)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

V / (

V D

esig

n A)

Design ADesign B



k, Fy

F

F yk

1

1

V

LossFy

V

P

P/h

P

h

P (3 )

P (3 )

3 h

3 h

3

s

s

s

s

s

n = 3

ss

3 h 2 h

P

P (2 )

P (2 )

P PP-Delta shear = P-Delta stiffness =

2 h

2 h

h h

2

n = 2

s

s

s

s

s

s s

s

P

P P

F

-F

V+

+-V > V

y

y

VF

-F

V > V+ -

+-V V<

y

y

V V

P

k

k’

h

+ =

11

k’

k’ > P/hP/h


Known solution: provide k’ > P/h


0 1 2 3 4T (s)

0.00.20.40.60.81.01.2

k' = P/hk' = 2 P/h

0 1 2 3 4T (s)

0 1 2 3 4T (s)

CR Ground Motions IS Ground Motions SI Ground Motions

0 20 40 60 80 100 120 140 160 180 200Time (s)

-0.2

0

0.2-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

h = 2/3 hn; P = 1.2 W; T = 3.05 s; Rd = 4.0No P- in AnalysisP- in Analysis - k' = 0P- in Analysis - k' = P/hP- in Analysis - k' = 2 P/h

SI5 - 2011 M9.0 Tohoku EQ, YMTH121103111446_NS2

FW s

Vy

k

k’

1

1

P

h

s scsc s

s s

P n n k 'if : k ' n 1nh P h


0.75

csc 3

s

EIk '

h

Note: Valid if P, EIc, and hs same at all levels

Stiffness k’s supplied by column continuity:


n k’sc / (P/hs)

Level 9

scs

n k ' 1P h

?


Stiffness k’s supplied by a back-up moment frame:

FBF

MRF

V

V

V

S y,F

+

FBF MRF

S

11 K

K

F

By,F

y,f may be limited $$$ :

• Rigid beam-column connections• MRF provided with minimum ductile detailing


Stiffness k’s from a modified chevron BF configuration:


Stiffness k’s from a modified chevron BF configuration:

VV’

V

V

y

m

k

s

s

k’

1

1

1

B

A

s

sm s

sy

’

L

s

P/hs

sk’ P/h>

P

h

P

BeamA , I

Elastic Brace, Ad

bbs

V

V

s sy s s3g sd

L L V0 : V ; k4EA 4EA cos θ

3 2sy s sm s s3g g sd

L L L tan θ V ': ' V ' ; k '2EA 48EI '2EA cos θ


m ysm sy

s

V Vk '

Point B - Beam Yielding

VV’

V

V

y

m

k

s

s

k’

1

1

1

B

A

s

sm s

sy

’

PP

V - 0.5 V

wgrav

0.5 V ym y

y,de,d

L

s

P/hs

sk’ P/h>

P

h

P

BeamA , I

Elastic Brace, Ad

bbs

V

V

b y b b,grav

At Point B :

P 0.5 V V '; M V ' tanθ L 4 M

y,b y b,grav y,b p,bp,b b,grav

m yy,b p,b

P 0.5 V 0.85M P MM MV V min ;

tanθ L 4 1 0.85 tanθ L 4 P M

b b by,b p,b p,b

P M MBeam yielding : 0.85 1.0 ; 1.0P M M


Point B - Beam Yielding

VV’

V

V

y

m

k

s

s

k’

1

1

1

B

A

s

sm s

sy

’

PP

V - 0.5 V

wgrav

0.5 V ym y

y,de,d

L

s

P/hs

sk’ P/h>

P

h

P

BeamA , I

Elastic Brace, Ad

bbs

V

V

m ye,d

m yc

At Point B :

V V 2P

cosθ

V VP

2 tanθ


0 10 20 30 40 50P/hs, k's (kN/mm)

0

4

8

12

16

Leve

l

P/hsDesign CDesign DDesign E

0.0 0.5 1.0 1.5 2.0sm (%hs)

0

4

8

12

16


0 0.005 0.01 0.015 0.02 0.025s/hs

0.0

0.4

0.8

1.2

1.6

2.0

V/V y

W760x147 (Design E) W360x421 (Design D)

W310x289

W610x113 (Design C)

P/hs

2 P/hsLevel 9:


0.0 1.0 2.0Roof / hn (%)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

V / (

V D

esig

n A)

Design ADesign BDesign CDesign DDesign E

0 10 20 30 40 50P/hs, k's (kN/mm)

0

4

8

12

16

Leve

l

P/hsDesign CDesign DDesign E

0.0 0.5 1.0 1.5 2.0sm (%hs)

0

4

8

12

16

-1.0 0.0 1.0 2.0 3.0Storey Shear Drift, s (%hs)

-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

Stor

ey S

hear

(kN

)

Design C

-2.0 -1.0 0.0 1.0 2.0Storey Shear Drift, s (%hs)

-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

Stor

ey S

hear

(kN

)

Design D

-2.0 -1.0 0.0 1.0 2.0Storey Shear Drift, s (%hs)

-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

Stor

ey S

hear

(kN

)

Design E


1

3

5

7

9

11

13

15

-3 -2 -1 0 1 2 3s (%hs)

-5 -4 -3 -2 -1 0 1 2 3 4 5s (%hs)

1

3

5

7

9

11

13

15

Leve

l

Design Ck's = P/hs - sm = 1% hs

-2 -1 0 1 2s (%hs)

1

3

5

7

9

11

13

15

Design Ek's = 2 P/hs - sm = 1% hs

Design Dk's = 2 P/hs - sm = 2% hs

Storey shear-shear-storey drift response at level 9 - SI1 motion:

Peak shear storey drift demands:


Design

V/W (%)T1 (s)

Tonnage (t)

A

4.443.9981

B

5.463.52102

C

4.443.8587

D

4.443.35153

E

4.443.5199

a gn

(%h n

)


0.0 1.0 2.0Roof / hn (%)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

V / (

V D

esig

n A)

Design ADesign DDesign EDesign F

1

3

5

7

9

11

13

15

-3 -2 -1 0 1 2 3

s (%hs)

Design D

-2 -1 0 1 2

s (%hs)

1

3

5

7

9

11

13

15

Design E

1

3

5

7

9

11

13

15

-3 -2 -1 0 1 2 3

s (%hs)

Design F

Design F

Same as Design Eexcept that no minimum V/W

0 1 2 3 4 5T (s)

0.00

0.04

0.08

0.12

0.16

0.20

V / W

Design Seismic LoadNBCC 2015RdRo = 4.8

Vancouver, BC (Site C)

Minimum V/W

Designs D E F A


Design

V/W (%)T1 (s)

Tonnage (t)

A

4.443.9981

B

5.463.52102

C

4.443.8587

D

4.443.35153

E

4.443.5199

F

3.333.8693

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300Time (s)

-0.2

0

0.2

a g

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

n (%

h n)

Design ADesign BDesign DDesign EDesign F

SI2 - 2011 M9.0 Tohoku EQ, FKS0211103111446_EW

• Collapse of tall braced frames with limited post-yielding stiffness expected under subduction interface EQs

• Current design provisions (strength amplification, column continuity) and/or systems (limited post-yield stiffness) need to be modified

• Positive post-yielding stiffness appears as a possible solution; proposed modified chevron BF configuration appears as a promising application:

– System exhibits stable response and offers re-centring capacity with reduced peak and residual storey drifts

– Number of yielding braces reduced by 50% and limited additional steel required for the beams

– Possibility of relaxing current code limits (heigth, V/W)

Conclusions


• Further studies needed to:

– Positive post-yielding stiffness concept to be further validated for other multi-storey applications

– Design guidance needed for key parameterssuch as Rd, k’s, sm, etc.

Conclusions


Documents

An Inverted V-Braced Frame System Exhibiting Bilinear ... · • Canadian code provisions • Seismic stability of an 16-storey ... Design Seismic Load NBCC 2015 RdRo= 4.8 ... •