Controlled Rocking of Steel-Framed Buildings with Replaceable Energy

Dissipating Fuses

MUST-SIM Meeting February 5, 2007

Matt Eatherton, MS SEUniversity of Illinois at Urbana-Champaign

MUST-SIMMUST-SIM

Organization

1. Introduction

2. Controlled Rocking System

3. Parametric Study & Prototype Building

4. UIUC Half-Scale Test Program

5. Conclusions

Current Building Codes - Expected Building Performance?

Two story steel-framed office building in Santa Clarita suffered residual drift in the first story due to the Northridge Earthquake.

From EERI Earthquake Recon. Report, Jan. 1996 & May 1990

Building with a Red Tag restricting access after the Northridge Earthquake

Industrial Structure that experienced brace

buckling and residual drift during Loma Prieta

Current Building Codes - Expected Building Performance?

• Seismic loads prescribed in current building codes assume a considerable amount of inelastic damage in structural elements.

• In a severe seismic event, structural damage can be distributed throughout the structure and extensive enough to make repair uneconomical.

• Residual drifts also make repair difficult if not financially unreasonable.

• The goal of current building codes is to provide life safety during large earthquakes – not limiting structural damage or ensuring repairability.

• To construct a building that is easy to repair, two attractive performance goals would be to 1. eliminate residual drifts and 2. concentrate all the structural damage in replaceable fuses.

Controlled Rocking System

Component 1 – Stiff braced frame, designed to remain essentially elastic - not tied down to the foundation.

Component 2 – Post-tensioning strands bring frame back down during rocking

Component 3 – Replaceable energy dissipating fuses take majority of damage

Bumper or Trough

Controlled Rocking Systemin the Rocked Configuration

Corner of frame is allowed to uplift.

Fuses experience more shear strain than drift angle – amplification

One challenge is limiting floor damage while transferring diaphragm shear to frame.

Variations

A. Fuse Type / Material

1. Steel Panel

a) Slit Steel Panel

b) Butterfly Panel

2. Engineered Cementitous Composite (ECC) Panels with various reinforcement schemes.

3. Aluminum

4. Others. . .

Variations (Cont’d)

B. Fuse Distribution Among Stories - may not need fuses at every story

C. Frame Bracing Configuration

1. Chevron 2. Chevron at top to resist post-tensioning load and single braces below

4. Steel plate shear walls (SPSW)

3. Two-Story X

Variations (Cont’d)

D. Post-Tensioning Location – at columns or in middle

E. Single Frame vs. Dual Frame

Dual Frame with P/T at Mid-point of Frame

Dual Frame with P/T at Columns (P/T loops

in foundation to allow enough P/T strain capacity)

Single Frame with Fuses on Either Side

Research Program

Research Team:

PI Greg Deierlein – Project Manager, Stanford University

Co-PI Sarah Billington – ECC & HPFRCC Fuses, Stanford Unviersity

Co-PI Jerome Hajjar – Simulation and Half-Scale Tests, University of Illinois

Helmut Krawinkler, Stanford University

Mitsumasa Midorikawa – E-Defense, Building Research institute in Japan

David Mar - Industry Collaborator, Tipping and Mar Engineers

Current Graduate Students: Xiang Ma (Stanford), Eric Borchers (Stanford), Matt Eatherton (UIUC)

Past Graduate Students: Paul Cordova (Post-Doc at Stanford), Kerry Hall (UIUC),

Project is funded by a grant from NSF - NEESR-SG

E-DEFENSE

JAPAN

Research Program

A. Schematic Design and Analysis (Entire Team)

A. Single degree of freedom study.

B. Iterations on system design (such as variations described above).

C. Planer MDOF models.

B. Fuse Panel Design and Testing (Stanford)

A. Engineered Cementitous Composites (ECC) panels.

B. Steel slit panels.

C. Steel butterfly panels.

C. Parametric Study (UIUC)

A. Define a prototype structure.

B. Nonlinear time history analyses to examine effect of each variable.

C. Use results to inform decisions about testing program.

Research Program

D. Half-Scale Tests (UIUC)

A. Test several half-scale specimens representing prototype frames.

B. Validate the performance of the controlled rocking system.

C. Examine forces realized in the fuses.

D. Study and improve details not common in steel structures.

E. Large-Scale Shake Table Tests (E-Defense / Stanford)

A. Study ability of system to self-center.

B. Further validation of the system performance.

F. Design Implications and Recommendations (Entire Team)

A. Characterize performance of the controlled rocking system

B. Summarize design recommendations

Controlled Rocking System – Mechanism for Resisting Overturning

BAVA

FM pPTresist

22

FPT

Vp/3

Vp/3

Vp/3

F1

F2

F3FPT

“A” “B” “A”

“H1”

“H2”

“H3”

ovtresist MM

FPT = Initial post-tension force

Vp = Fuse yield strength in shear

Overturning moment =

Resistance comes from Post-Tensioning and Fuses:

In an LRFD context use a resistance factor to design:

iiovt HFM

Can also include gravity loads

Controlled Rocking System – Mechanism for Self-Centering

BAVA

F pPT

22

In the rocked configuration, the fuses resist self-centering. The restoring moment due to P/T must overcome the restoring resistance:

FPT

Vp/3

Vp/3

Vp/3

FPT

“A” “B” “A”

Other sources of resistance not considered in this equation include:

• Stiffness of gravity system

• Stiffness of interior partitions that have undergone inelastic damage

• P-delta effect

Can also include effect of gravity load in restoring force.

Controlled Rocking System –Fuse Shear Strain Capacity

effeff B

BARDR

B

)( BARDR Fuse Shear Strain, =

Shear strain in the fuses is amplified compared to the roof drift ratio (RDR).

Using small angle assumption:

Example:

068.0'33.5

'6'1202.0

0 0.005 0.01 0.015 0.020

50

100

150

Roof Drift Ratio (mm/mm)

Ba

se S

he

ar

(kN

)Controlled Rocking System –

Representative Hysteretic Response

4

1

3

2 5

6

FLAG SHAPED HYSTERESIS

1. Begin Loading

2. Frame Uplifts

3. Fuses Yield

4. Load reversal. If pushed far enough P/T would yield

5. Zero force in fuses

6. Fuses yield in other direction

7. Frame sets back down and forces in the frame relax.

8. Elastic strain energy remains in frame and fuses

7

8

Controlled Rocking System – Other Considerations

1. Global Overturning (FPT > Vp)

2. Initial P/T stress: Stressing the P/T strands 0.4 Fu may require special procedures to anchor post-tensioning (post-blocking).

3. P/T strain capacity: If performance criteria includes not replacing P/T after a severe earthquake then ensure adequate strain capacity.

Fuse Strength

VP

Initial Post-

Tensioning, FPT

To Prevent Dual

Frame Rocking:

FPT > VP

Preventing Global Overturning

Prototype Structure

Use prototype structure to apply controlled rocking to a realistic structure

Based on SAC Building configuration

Tests and analysis simulate the controlled rocking frames in this structure.

Prototype Structure – CR Frames

12'-0" 6'-0" 12'-0"

13'-0"

13'-0"

13'-0"

W12X26

W12 X30

W12X26

W12 X30

W12

X12

0

W12

X17

0

W12

X17

0

W12

X12

0

W12 X30

W12X26

W12 X30

W12X26

W12

X10

6 W12X

96

W12X

53

W12

X87

W12

X96

W12X

53

W12X

106W12

X96

W12

X53

W12X

87

W12X

96

W12

X53

OpenSees Model

1 2 3 414 5

10 11

114

214

314

105

205

305

101

201

301

104

204

304

110

310

6

102

202

302

111

311

103

203

303

7 8 9

DIMENSION “A” “B” “A”

Ground Motions

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3 3.5 4

Period (sec)

Pse

udo-

Acc

eler

atio

n (g

)

• Based on Medina Dissertation (2002)

• Used the LMSR-N group (40 grnd mtns)

• Design spectrum is based on site in LA

• Scaled to one-second spectral accel.

• Scaled to three hazard levels

• Ground motions that required scaling greater than 4.0 were thrown out.

Parametric Study

)( BAV

FA

M

MSC

P

PT

resist

restore

Parameters Studied

1. A/B ratio – geometry of frame

2. Overturning Ratio (OT) – ratio of resisting moment to design overturning moment. OT=1.0 corresponds to R=8.0, OT=1.33 means R=6.0, and OT=0.8 means R=10.

3. Self-Centering Ratio (SC) – ratio of restoring moment to restoring resistance.

4. Initial P/T stress

5. Frame Stiffness

6. Fuse type including degradation

OVT

PPT

OVT

resist

M

BAVFA

M

MOT

)(

“A” “A”

FPT FPT

Vp/3

Vp/3

Vp/3

“B”

Parametric Study Results

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Res

idua

l Upl

ift (

mm

)

1.5 2.0 2.3 2.5 3.0

A/B Ratio OT Ratio

0.75 1.0 1.25 1.5 2.0

SC Ratio

0.5 0.75 1.0 1.5 2.0

0.00%

0.01%

0.02%

0.03%

0.04%

0.05%

0.06%

Res

idua

l Roo

f Drif

tR

atio

(R

DR

) (p

erce

nt)

1.5 2.0 2.3 2.5 3.0

A/B Ratio OT Ratio

0.75 1.0 1.25 1.5 2.0

SC Ratio

0.5 0.75 1.0 1.5 2.0

0

1

2

3

4

5

6

7

8

50% / 50 Median

50% / 50 Median + Std. Dev.

10% / 50 Median

10% / 50 Median + Std. Dev.

2% / 50 Median

2% / 50 Median + Std. Dev.

1.5 2.3 2.5 3.0

OT Ratio

0.75 1.0 1.25 1.5 2.0

SC Ratio

0.5 0.75 1.0 1.5 2.0

OT=1.0

SC=1.0

A/B=2.3

SC=1.0

A/B=2.3

OT=1.0

Parametric Study Results

0

2,000

4,000

6,000

8,000

10,000

Pe

ak

Ba

se S

he

ar

(kN

)

1.5 2.0 2.3 2.5 3.0

A/B Ratio OT Ratio

0.75

1.0 1.251.5 2.0

SC Ratio

0.5 0.75

1.0 1.5 2.0

0

20

40

60

80

100

120

140

160P

eak

Upl

ift (

mm

)

1.5 2.0 2.3 2.5 3.0

A/B Ratio OT Ratio

0.75 1.0 1.251.5 2.0

SC Ratio

0.5 0.75 1.0 1.5 2.0

0

1

2

3

4

5

6

7

8

50% / 50 Median

50% / 50 Median + Std. Dev.

10% / 50 Median

10% / 50 Median + Std. Dev.

2% / 50 Median

2% / 50 Median + Std. Dev.

1.5 2.3 2.5 3.0

OT Ratio

0.75 1.0 1.25 1.5 2.0

SC Ratio

0.5 0.75 1.0 1.5 2.0

OT=1.0

SC=1.0

A/B=2.3

SC=1.0

A/B=2.3

OT=1.0

Parametric Study Results

0

0.01

0.02

0.03

0.04

0.05

Roo

f D

rift

Rat

io D

eman

d (m

m/m

m)

1.5 2.0 2.3 2.5 3.0

A/B Ratio OT Ratio

0.75 1.0 1.25 1.5 2.0

SC Ratio

0.5 0.75 1.0 1.5 2.0

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

Pea

k F

use

She

arS

trai

n D

eman

d (m

m/m

m)

1.5 2.0 2.3 2.5 3.0

A/B Ratio OT Ratio

0.75 1.0 1.25 1.5 2.0

SC Ratio

0.5 0.75 1.0 1.5 2.0

0

1

2

3

4

5

6

7

8

50% / 50 Median

50% / 50 Median + Std. Dev.

10% / 50 Median

10% / 50 Median + Std. Dev.

2% / 50 Median

2% / 50 Median + Std. Dev.

1.5 2.3 2.5 3.0

OT Ratio

0.75 1.0 1.25 1.5 2.0

SC Ratio

0.5 0.75 1.0 1.5 2.0

OT=1.0

SC=1.0

A/B=2.3

SC=1.0

A/B=2.3

OT=1.0

Parametric Study - Conclusions

1. Reduction in the A/B ratio resulted in a decrease in the fuse shear strains, but requires steeper bracing in the braced frames, and yields slightly higher displacements.

2. Higher OT factors minimize displacement response, including residual displacements and fuse shear strain demands. The advantages of increasing OT must be tempered by the cost of larger forces that must be transmitted through the frame and foundation, and slightly larger accelerations.

3. The system exhibited excellent self-centering capability. The SC ratio does not need to be larger than 1.0 to self-center the system, but configuration must be checked to preclude global overturning. Also, it is expected that upon removal of the fuses (for replacement), any residual uplift or roof drift would be eliminated.

4. The system has to rock to work. None of the configurations considered eliminated uplift for even the smaller event considered (50% in 50 years). The OT ratio had the most effect in limiting peak uplift.

5. Peak roof drift ratios and peak uplifts were in acceptable ranges even for OT = 0.75 (R=10).

6. Based on median for 2% in 50 year event, the following are limits that might be imposed on fuse design:

For A/B ratio = 1.5, use fuses with shear strain capacity of 0.08For A/B ratio = 2.0, use fuses with shear strain capacity of 0.10For A/B ratio = 2.5, use fuses with shear strain capacity of 0.11For A/B ratio = 3.0, use fuses with shear strain capacity of 0.13

Potential Fuse Shear Strain Capacity

Fuse tests are underway.

Fuse configurations include steel slit panel, steel butterfly panel, and ECC panels

UIUC Half-Scale TestsGoals:

1. To test and improve details – post-tensioning and base connections are not typical to steel structures.

2. Study the forces realized in the fuses and distribution of force between fuses. Geometric nonlinearity and indeterminacy creates complexity.

3. Examine effect of out-of-plane motion while rocking.

4. Determine whether typical P/T strands and anchorage can be stressed to yield without fracturing or slipping.

5. Establish whether there is inelasticity or relaxation in the P/T that would require replacement or re-stressing.

6. Investigate whether inelasticity occurs in the frame.

VERIFY THE PERFORMANCE OF THE SYSTEM FOR IMPLEMENTATION IN PRACTICE

UIUC Half-Scale Tests

Front View Side View

Current Test MatrixTest ID

Dim “B”

A/B Ratio

OT Ratio

Initial P/T Stress and

Force

Fuse Type and Fuse Strength

Time Req’d

Testing Protocol

Reason for Test

A1 3.09’ 1.75 1.0(R=8)

0.359 Fu(103.9 kips)

Steel Slit 1(82.6 kips)

4 weeks

Quasi-Static

This is our best shot at getting the system to work. If there is a problem here, we still have a chance to reconfigure the remaining tests.

A2 3.09’ 1.75 1.0(R=8)

0.359 Fu(103.9 kips)

ECC 1 (82.6 kips)

1 week

Quasi-Static

If the system works in the first test, try an ECC fuse in this best-case configuration.

A3 3.09’ 1.75 1.0(R=8)

0.359 Fu(103.9 kips)

Steel Slit 3(82.6 kips)

2 week

Hybrid Simu-lation

Now that we know how well this configuration responds, conduct a hybrid simulation to find out how the system will perform in a real building.

A4 3.09’ 1.75 1.5(R=5.3)

0.539 Fu(155.8 kips)

Steel Slit 2(123.9 kips)

1 week

Quasi-Static

Increase the OT to 1.5. The higher OT would result in lower ductility demands, so if it works, this would be the configuration proposed for better performance in a PBD. This is also our best shot at yielding the P/T before the fuse is completely destroyed.

B1 2.16’ 2.5 1.5(R=5.3)

0.471 Fu(155.8 kips)

Steel Slit 4(139.1 kips)

4 weeks

Quasi-Static

Now that we have an idea how well the system works, push the A/B to 2.5, but with an OT of 1.5. This configuration still produced reasonable fuse shear strain demands in the parametric study.

B2 2.16’ 2.5 1.0(R=8)

0.314 Fu(103.9 kips)

Steel Slit 5(92.7 kips)

1 week

Quasi-Static

Drop the OT back to 1.0. This configuration pushes the envelope with regards to fuse shear strain demand predicted by the parametric study.

B3 2.16’ 2.5 1.0(R=8)

0.314 Fu(103.9 kips)

ECC 2(92.7 kips)

1 weeks

Quasi-Static

If the previous test with A/B = 2.5 and OT = 1.0 works, try an ECC fuse. *We will cast another set of ECC fuses based on A/B=2.0, in case system isn’t performing as well as expected.

B4 2.16’ 2.5 1.0(R=8)

0.314 Fu(103.9 kips)

Steel Slit 6(92.7 kips)

2 week

Hybrid Simu-lation

For the finale, try a hybrid simulation at A/B = 2.5. Along with other hybrid simulation, this will tell us how well the system might perform in a real building.

UIUC Half-Scale Tests

3/8"PL

TYP

3/8"PL

TYP

Test A3 – A/B=1.75 Test B1 – A/B=2.5

Proposed Mixed Mode Control

Degree of Freedom Left LBCB Right LBCB

Force Movement Force Movement

U - horizontal Free USE THIS AS

CONTROL

Constrain to Match Force of left LBCB

Free

U - vertical Gravity Load Specified

Free Gravity Load Specified

Free

U - out-of-plane Free Constrain to be 0

Free Constrain to be 0

θ - in-plane As necessary to simulate applying

gravity load to exterior columns

Free As necessary to simulate applying

gravity load to exterior columns

Free

θ - out-of-plane Free Constrain to be 0

Free Constrain to be 0

θ - torsion Free Constrain to be 0

Free Constrain to be 0

The horizontal movement of the Left LBCB would be used to control the test. The Right LBCB will match the horizontal force in the left LBCB. This will apply the same amount of load to both frames, but allow differential rocking between the frames.

EBF Loading Protocol

From Richards and Uang (2006) and Okazaki (2005)

Proposed Static Loading Protocol

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0 5 10 15 20 25 30 35 40

Number of Cycles

Roo

f Drif

t Rat

io (

in/in

)

Max Stroke = 8", Corresponding RDR = 0.036

Target RDR = 0.02

Hybrid Simulation

Reasons for conducting the hybrid simulation:

1. Ground motions will be applied in both directions (parallel and perpendicular to the frame being tested), the ability of the frame to withstand out-of-plane motion, and rock while sustaining out-of-plane rotation will be examined.

2. The lateral stiffness of the gravity framing and/or the stiffness of interior partitions will be modeled, so the ability of the system to self-center in a real building can be demonstrated.

3. The level of damage and repairability of the system after a realistic earthquake motion will be demonstrated.

4. We may try to model a building taller than 3 stories.

5. Account for P-Delta effect with a leaning column in the model.

Conclusions / Summary

1. Seismic loads prescribed in current building codes assume considerable inelasticity in the structure during a severe earthquake. This can result in structural damage and residual drift that cannot be economically repaired.

2. To provide a building that is relatively easy to repair after an earthquake, two attractive performance criteria are:a) Eliminate residual drift.b) Concentrate bulk of structural damage in replaceable fuses.

3. The controlled rocking system satisfies these performance goals.

4. The controlled rocking system consists of three major components:a) Stiff steel braced frame designed to remain essentially elastic, but

not tied down to the foundation.b) Post-tensioning that provides self-centering capability.c) Highly ductile energy dissipating fuses.

Conclusions / Summary

5. A multi-institution, international research project is underway to examine, improve, and validate the performance of this innovative system.

6. A parametric study was conducted to optimize A/B ratio, OT ratio, and SC ratio. Results were presented.

7. Some considerations in the design of the controlled rocking system include:a) Proportioning fuses and P/T to resist overturning, but still self-

center.b) Insuring enough P/T strain capacity.c) Using fuses with enough shear strain capacity based on frame

geometry (fuse shear strain is amplified compared to roof drift ratio).d) Preclude global overturning.

Conclusions / Summary

8. Half-scale tests will be conducted later this year at the UIUC MUST-SIM Facility to improve details and validate the performance of the controlled rocking system for implementation in practice.

9. Loading protocol has significant effect on EBF link tests. A loading protocol based on state-of-the-art EBF protocol will be used.

10.Hybrid simulation tests will further validate the system performance and demonstrate the self-centering and repairability of the controlled rocking system when subjected to a realistic ground motion.

Controlled Rocking of Steel-Framed Buildings with Replaceable Energy

Dissipating Fuses

Matt Eatherton, MS SEUniversity of Illinois at Urbana-Champaign

QUESTIONS?