distributed yielding concept for improved seismic g 5 v · develop simplified numerical models of...

Distributed Yielding Concept for Improved Seismic Collapse Performance of Rigid Wall- Flexible Roof

Diaphragm Buildings

Maria Koliou, Ph.D. Candidate

Advisor: Andre Filiatrault, Ph.D., Eng.

Department of Civil, Structural and Environmental Engineering

University at Buffalo – The State University of New York

Rigid Wall – Flexible Roof Diaphragm (RWFD) structures are buildings framed with:

Exterior concrete (cast-in-place or precast) or masonry walls

Interior columns

Horizontal roof diaphragms (wood, steel or “hybrid”)

Rigid Wall – Flexible Diaphragm (RWFD) structures Structures

with large footprint !!!

Applications:

Light industrial and low-rise commercial construction (i.e. warehouses, storage units & shopping complexes)

Introduction

Performance in past earthquakes Poor seismic response during past earthquake events:

1. Structural damage at wall panel – to – roof connections & wall panel –to – wall panel connections (1964 Alaska, 1971 San Fernando & 2010/2011 Christchurch)

2. Seismic response dominated by flexible roof diaphragms

partial building collapses (1987 Whittier Narrows, 1989 Loma Prieta & 1994 Northridge)

Photo courtesy of Doc Nghiem

1994 Northridge

Photo courtesy of Doc Nghiem

1994 Northridge

Problem statement & Research objectives

Problem Statement:

Current design provisions do not account for this type of structure:

• Unrealistic design & prediction of seismic response

• Diaphragm flexibility is not accounted into the design

• Response modification factors (R-values) based on vertical elements of SFRS

• Fundamental design period: significantly underestimated by the code formula

Research Objectives:

Develop simplified numerical models of RWFD buildings with relative good accuracy and efficient computational overhead

Evaluate the seismic collapse capacity of RWFD buildings

Develop, propose & validate a stand-alone simplified seismic design of RWFD buildings

2D numerical framework based on a three step sub-structuring approach:

Step 1: hysteretic response database for roof diaphragm connectors

Step 2: 2D inelastic diaphragm model incorporating local hysteretic connector responses

Step 3: 2D simplified building model incorporating global hysteretic diaphragm model responses

Steps 2 and 3 of numerical framework were validated with experimental and analytical studies available in the literature

Sensitivity study conducted on the modeling assumptions of simplified building model (step 3)

Concept of distributed roof diaphragm yielding Current design of large diaphragms intentionally reduces the shear capacity towards the center of the diaphragm

Inelastic roof diaphragm behavior remains concentrated towards the diaphragm boundaries

Localized inelastic response limited ability to dissipate large amounts of energy that can lead to premature building failure

Concept of distributed yielding intentionally weakening certain intermediate diaphragm zones below current code-based force demands

Roof segment/spring 1

Center of roof diaphragm

Roof diaphragm boundary









Conventional (ASCE7-10)

diaphragm design

(a) (b)



Fo

rce

Displacement

Fo

rce

Displacement

Diaphragm distributed

yielding design

(c)



0 5 10 15 20 25 30-0.2

-0.1

0

0.1

0.2

0.3

Time[sec]

Acce

lerati

on [g

]

Direction of shaking

Potential advantages:

Protection of perimeter diaphragm boundary areas from excessive inelastic demand

Reduction/control of premature diaphragm permanent deformations & consequent building collapse

Cost-effective enhancement of seismic collapse resistance of RWFD buildings

Possible increase of natural period of vibration reduced seismic

demand in terms of spectral acceleration

Potential disadvantage:

Possible increase in spectral displacement due to increase in natural period of vibration

But: spectral displacement maybe reduced within acceptable limits due to an increase of effective damping of the building system

CASE STUDY: RWFD building with steel roof diaphragm

Single story concrete tilt – up building Plan dimensions: 400ft X 200ft

Use: Warehouse or distribution center

Walls: Precast concrete walls 30ft tall, 3ft tall parapet & 9.25in thick

Roof: panelized 1.5’’ deep wide-rib steel roof deck

Vertical SFRS: Intermediate precast shear walls (R=4)

Designed with current US design provisions

Fastener pattern:

12 23 3

50ft 60ft 90ft 90ft 60ft 50ft

Zone Conventional (ASCE 7-10)

diaphragm design


yielding design

1 Button punches @ 12’’ o.c. Button punches @ 12’’ o.c.

2 Top seam welds @ 12’’ o.c. Button punches @ 24’’ o.c.

3 Top seam welds @ 6’’ o.c. Top seam welds @ 6’’ o.c.

Numerical framework

-1 -0.5 0 0.5 1-300

-200

-100

0

100

200

300

400

Displacement (inches)

Fo

rce(l

bs)

Test

-1 -0.5 0 0.5 1-300

-200

-100

0

100

200

300


Fo

rce(l

bs)

SAWS model-estimated

-1 -0.5 0 0.5 1-300

-200

-100

0

100

200

300


Fo

rce(l

bs)

Wyane-Stewart model-estimatedConnector Database (1/3) Roof Diaphragm Model (2/3) Simplified Building Model (3/3)

-1 -0.5 0 0.5 1-300

-200

-100

0

100

200

300

400


Fo

rce(l

bs)

Test

-1 -0.5 0 0.5 1-300

-200

-100

0

100

200

300


Fo

rce(l

bs)


-1 -0.5 0 0.5 1-300

-200

-100

0

100

200

300


Fo

rce(l

bs)

Wyane-Stewart model-estimated

Connector DatabaseDiaphragm model

V

4rx 3rx2rx 1rx

-1 -0.5 0 0.5 1-300

-200

-100

0

100

200

300

400


Fo

rce(l

bs)

Test

-1 -0.5 0 0.5 1-300

-200

-100

0

100

200

300


Fo

rce(l

bs)


-1 -0.5 0 0.5 1-300

-200

-100

0

100

200

300


Fo

rce(l

bs)

Wyane-Stewart model-estimatedV

xr4 –xr3-1 -0.5 0 0.5 1

-300

-200

-100

0

100

200

300

400


Fo

rce(l

bs)

Test

-1 -0.5 0 0.5 1-300

-200

-100

0

100

200

300


Fo

rce(l

bs)


-1 -0.5 0 0.5 1-300

-200

-100

0

100

200

300


Fo

rce(l

bs)


xr3 –xr2-1 -0.5 0 0.5 1

-300

-200

-100

0

100

200

300

400


Fo

rce(l

bs)

Test

-1 -0.5 0 0.5 1-300

-200

-100

0

100

200

300


Fo

rce(l

bs)


-1 -0.5 0 0.5 1-300

-200

-100

0

100

200

300


Fo

rce(l

bs)


xr2 –xr1-1 -0.5 0 0.5 1

-300

-200

-100

0

100

200

300

400


Fo

rce(l

bs)

Test

-1 -0.5 0 0.5 1-300

-200

-100

0

100

200

300


Fo

rce(l

bs)


-1 -0.5 0 0.5 1-300

-200

-100

0

100

200

300


Fo

rce(l

bs)


xr1

Simplified Building Model

md2

md3

xiw

xd1xd2

xd3xd4

md1 miw

xd5

md5

0

5

10

15

20

25

30

-0.2

-0.1

0

0.1

0.2

0.3

Time[s

ec]

Acc

eler

atio

n [g

]

kd5kd4

kd3kd2

kd1

kiw

md4

0

100

200

0

100

200

0

10

20

30

X (ft)Y (ft)

Heig

ht

Z (

ft)

0

100

200

0

100

200

0

10

20

30

X (ft)Y (ft)

Heig

ht

Z (

ft)

T1=0.57 s

Conventional diaphragm design

Center of

roof diaphragm

T1=0.52 s

Diaphragm distributed yielding design

Center of

roof diaphragm

Short direction excitation

Minor influence on the RWFD building’s mode shapes and fundamental periods associated

Measured periods considerably longer than predicted by the design

empirical formula of ASCE 7-10

0.75 0.750.02 0.02 30 0.26secT h

Modal analysis:

Dynamic time history analysis:

IDA conducted using the FEMA P695 Far Field Ground Motion Ensemble

Damage measure (DM): Building Drift Ratio (BDR)

Intensity Measure (IM): Median spectral acceleration at the 1st mode of vibration

,% 100

2

in planewallsmid roof

wallroof

xxBDR

hL

0 1 2 3 4 5 60

0.2

0.4

0.6

0.8

1

IM = Sa (T1) [g]

P[C

oll

ap

se]



Median()

Conventional diaphragm

design=1.49


yielding design=2.66

0 2 4 6 80

0.2

0.4

0.6

0.8

1

IM = Sa (T1) [g]

P[C

oll

ap

se]



Median()

Conventional diaphragm

design=2.68


yielding design=3.45

Displacement ductility ratio:

Δu is the ultimate/maximum displacement of the diaphragm segment & Δy is the yield displacement of the same diaphragm segment

Median MCE ductility evenly distributed along the span of

diaphragm for the building by applying the distributed yielding concept

Diaphragm hysteretic response for one earthquake motion (Friuli, Italy) scaled at the MCE intensity level

u y

-15 -10 -5 0 5 10 15-1000

0

1000

-15 -10 -5 0 5 10 15-1000

0

1000

-15 -10 -5 0 5 10 15-1000

0

1000

-15 -10 -5 0 5 10 15-1000

0

1000

-15 -10 -5 0 5 10 15-1000

0

1000

-15 -10 -5 0 5 10 15-1000

0

1000

-15 -10 -5 0 5 10 15-1000

0

1000

-15 -10 -5 0 5 10 15-1000

0

1000

-15 -10 -5 0 5 10 15-1000

0

1000

Fo

rce (

kN

)

-15 -10 -5 0 5 10 15-1000

0

1000

-15 -10 -5 0 5 10 15-1000

0

1000

-15 -10 -5 0 5 10 15-1000

0

1000

-15 -10 -5 0 5 10 15-1000

0

1000

-15 -10 -5 0 5 10 15-1000

0

1000

-15 -10 -5 0 5 10 15-1000

0

1000

-15 -10 -5 0 5 10 15-1000

0

1000

-15 -10 -5 0 5 10 15-1000

0

1000

-15 -10 -5 0 5 10 15-1000

0

1000

x=0 ft


x=12.5 ft

x=37.5 ft

x=62.5 ft

x=87.5 ft

x=112.5 ft

x=137.5 ft

x=162.5 ft

x=187.5 ft

x=200 ft

μ=3.5

μ=3.2

μ=1.1

μ=1.0

μ=1.0

μ=1.0

μ=1.0

μ=1.0

μ=1.0

μ=2.6

μ=2.0

μ=1.2

μ=1.2

μ=1.2

μ=1.0

μ=1.0

μ=1.0

μ=1.0

Displacement [in]

Fo

rce [

kip

s]

Fo

rce [

kip

s]

Displacement [in]

Conventional design Distributed diaphragm yielding design

Collapse fragility results

Significant increase of median collapse intensity

TOWARDS A DESIGN PERSPECTIVE

Response modification (R) factor for diaphragm design

Overstrength factor for the edges of roof diaphragm roof perimeter stronger &

ensure distributed yielding in the roof diaphragm

Conclusions

Simple & cost effective solution to improve the seismic collapse performance of RWFD buildings & reduce damage during extreme ground shaking

Better ductility distribution along the diaphragm span less damage at roof

boundaries

Simple design methodology adopting this concept is currently being developed & verified

Acknowledgements Mr. D. J. Kelly, Simpson Gumpertz & Heger (SGH)

Prof. J. Lawson, Cal Poly San Luis Obispo

Federal Emergency Management Agency (FEMA) & National Institute of Building Sciences (NIBS)

Project Management Committee: Mr. B. Holmes (Rutherford & Chekene), Mr. J. Harris (J.R. Harris & Co.), Mr. J. Hooper (Magnusson Klemencic Associates) & Mr. B. H. Welliver (BHW Engineers, L.L.C. )

Prof. R. Tremblay, Ecole Polytechnique, Montreal

Prof. C. Rogers, McGill University

distributed yielding concept for improved seismic g 5 v · develop simplified numerical models of...

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