new developments in earthquake engineering of steel and ... · a 3d 18 dof beam-column element was...

New Developments in Earthquake Engineering of Steel and Composite Structures

Jerome F. Hajjar, Ph.D., P.E.Professor and Narbey Khachaturian Faculty Scholar

Chair, Structures FacultyDepartment of Civil and Environmental Engineering

University of Illinois at Urbana-Champaign

North American Steel Construction ConferenceApril 3, 2008

Composite Beam-Column Behavior

COMPOSITE SEISMIC DESIGN

Composite ColumnsComposite Columns

Steel reinforced concrete (Steel reinforced concrete (SRCsSRCs, , encased composite columns)encased composite columns)

ConcreteConcrete--filled tubes (filled tubes (CFTsCFTs, filled , filled composite columns)composite columns)

From R. From R. KannoKanno, , Nippon Steel CorporationNippon Steel Corporation

Acknowledgements: Composite SystemsAcknowledgements: Composite SystemsSponsors: National Science FoundationSponsors: National Science Foundation

American Institute of Steel ConstructionAmerican Institute of Steel ConstructionUniversity of Illinois at UrbanaUniversity of Illinois at Urbana--ChampaignChampaignUniversity of MinnesotaUniversity of MinnesotaGeorgia Institute of TechnologyGeorgia Institute of Technology

InIn--Kind Funding: Atlas Tube CompanyKind Funding: Atlas Tube CompanyPDM Bridge PDM Bridge LeJeuneLeJeune Steel Co.Steel Co.

Composite Design and Testing:Composite Design and Testing:Roberto Leon, Tiziano Perea, Roberto Leon, Tiziano Perea, Georgia TechGeorgia Tech

Distributed Plasticity Fiber Model:Distributed Plasticity Fiber Model:

Mark DenavitMark Denavit

Cenk TortCenk Tort

Paul H. SchillerPaul H. Schiller

Alexander O. Alexander O. MolodanMolodanConcentrated Plasticity Macro Model:Concentrated Plasticity Macro Model:

Brett C. Brett C. GourleyGourley

Matthew C. OlsonMatthew C. OlsonPrototype CFT Building Designs:Prototype CFT Building Designs:

Jose Jose ZamudioZamudio

SeokkwonSeokkwon JangJangPerformancePerformance--Based Design:Based Design:

Steven GartnerSteven Gartner

Composite Connections:Composite Connections:Luis PallaresLuis Pallares

From R. From R. KannoKanno, Nippon Steel Corporation, Nippon Steel Corporation

New Limitations

•

Steel area = 0.01 Ag

min•

Rectangular HSS:

b/t ≤ 2.26 [E/Fy]0.5 = 54.4 for 50 ksi

•

Round HSS:D/t ≤ 0.15 E/Fy = 87 for 50 ksi

AISC 2005 Provisions for Composite Columns

•

For Pe

≥

0.44 Po

:Pn

= Po

[ 0.658Po/P

e

]

•

For Pe

< 0.44 Po

:Pn

= 0.877 Pe

•

Po

= As

Fy

+ Asr

Fyr

+ C2

f’c

Ac

•

C2

= 0.85

SRC, RCFT, 0.95 CCFT (confinement)

•

Pe

= π2

(EIeff

) / (KL)2

•

(EIeff

)

= Es

Is

+ Eyr

Iyr

+ C3

Ec

Ic

•

C3

= 0.1

+ 2(Ac

/Ag

) ≤

0.3 (SRC)

= 0.6 + 2(Ac

/Ag

) ≤

0.9 (CFT)

I2.1.2 Filled Composite Columns New Strength Model w/ Slenderness


•

Typically use Plastic Stress Distribution Method

Plastic Strength Equationso

Example CD Disk w/ AISC Manual

•

For axial compression:Square, rectangular, round HSS are in tables in AISC Manual for CFTsTabulated versus KL (effective length)f’c = 4, 5 ksi concrete


Axial force-bending moment interaction diagram

Slides from L. Griffis, Walter P. Moore & Assoc.

A

C

D

B

P-M Interaction Diagram

φMn (kip-ft)

φ Pn

(kip

s)


A


φMn (kip-ft)

φ Pn

(kip

s)

0.85f’c Fy

PA = As Fy + 0.85f’c AcMA = 0As = area of steel shapeAc = Ag - As


B


φMn (kip-ft)

φ Pn

(kip

s)

0.85f’c

hn

Fy

CL

PNA

PB = 0

M M Z F 12 Z (0.85f' )B D sn y cn c= − −

Z 2t hsn w2n

=

Z h hcn 12n

=

[ ]h0.85f' A

2 0.85f' h 4t Fh2n

c c

c 1 w y

2=+

≤


C


φMn (kip-ft)

φ Pn

(kip

s)

0.85f’c

hn

Fy

CL

PNA

PC = 0.85f’c Ac

MC = MB


D


φMn (kip-ft)

φ Pn

(kip

s)

Fy

CL

PNA

0.85f’c

M Z F 12 Z (0.85f' )D s y c c= +

Z full y - axis plastic section modulus of steel shape

s =

Zh h

4 0.192rc1

2

i3= −2

P0.85f' A

2Dc c=


A

C

B


φMn (kip-ft)

φ Pn

(kip

s)

D

Unsafe design

Stability reduction (schematic)

AISC interaction


Project Goals

•

Facilitate use of composite systems in buildings up to 20 stories and in areas of low, moderate, and high seismicity

•

Develop system performance factors (e.g., R, Cd

, and Ωo

) for composite braced and unbraced

structural systems

•

Provide practical guidelines for the analysis and design of composite structures

•

Upgrade the computational models available for analyzing complete composite systems and provide detailed documentation to help researchers pursue similar studies

Assessment of Capacity: Database Development for ModelingAssessment of Capacity: Database Development for Modeling• Worldwide test results of RCFT tests were documented:

•• Each database consists of four sections including:Each database consists of four sections including:–– Test Description:Test Description:–– Material Properties:Material Properties:–– Geometric Properties:Geometric Properties:–– Experimental Results:Experimental Results:

•• Failure modesFailure modes•• Deformation and load capacitiesDeformation and load capacities•• Occurrence of local damage in terms load and deformation levelsOccurrence of local damage in terms load and deformation levels

RCFT Tests

0

50

100

150

200

250

Columns Beam-Columns

Pinned-Conn. MomentConn.

Panel Zones Frames

Num

ber

of S

peci

men

s

MonotonicCyclic

•• Created deformationCreated deformation--based and energybased and energy--based damage functions (e.g., based damage functions (e.g., concrete crushing, steel yielding, local buckling)concrete crushing, steel yielding, local buckling)

•• The damage function values at specific damage levels were correlThe damage function values at specific damage levels were correlated to ated to the structural parameters (e.g., the structural parameters (e.g., ff’’cc

, , ffyy

, , D/t, PD/t, Pcc

/P/Poo

, P, Pss

/P/Poo

etc.)etc.)

P/Po Ps/Po

dty

/do

μ = 7

μ = 13

μ = 10μ = 10

μ = 4

μ = 12

μ = 12 μ = 10

μ = 4

μ = 12

μ = 12

85.328.547.1 +−=o

s

oo

ty

PP

PP

dd

Damage Assessment in RCFT Members and Frames

Example: Tension flange yielding occurspre-peak for thick-walled RCFTs with low axial force

0.00

0.15

0.30

0.45

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16Specimen

E

0.0

3.0

6.0

9.0

12.0

15.0

18.0

Duc

tility

YCF

YTF

LBF

LBW

A parametric study was conducted on the equations to estimate the range of probable damage function values

Database Development for Testing

•

Work of previous researchers (Leon, Goode, Morino) combined to create a comprehensive worldwide database

•

Database used to identify gaps in test data and calibrate computational model

P/Po

RCFT CCFT SRC

P/PoP/Po

λλ

M/MdM/Md

λ

M/Md

CCFT RCFT SRC

Columns 762 455 119

Beam-

Columns

395 189 120

Number of Tests

Gaps In Test Data

•

Fewer tests for slender members (λ > 1.5) Flexural Buckling

•

Fewer tests for slender sections (b/t

> 50) Local Buckling

•

Few with both slender members and sections•

Other gaps in material properties

0.0

0.5

1.0

1.5

2.0

0.00 0.50 1.00 1.50 2.00

Pexp/Po

AISC

P/P

o

λ

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

0.0 50.0 100.0 150.0 200.0 250.0 300.0

λ

b/t

MAST Facility

•

The MAST facility permits the comprehensive testing of a wide range of composite beam-

columns subjected to three dimensional loading at a realistic scale.

From NEES@Minnesota

Degree of Freedom

Load Stroke/ Rotation

X-Translation ±880 kips ±16 in

X-Rotation ±8,910 kip-ft ±7°

Y-Translation ±880 kips ±16 in

Y-Rotation ±8,910 kip-ft ±7°

Z-Translation ±1,320 kips ±20 in

Z-Rotation ±13,200 kip-ft ±10°

Maximum non-concurrent capacities of MAST DOFs

CFT Test Series

Preliminary SRC Test Series

Label Steel Axis f ' c F y Long. Trans. ρ L λ L/r

b (in) d (in) Section (ksi) (ksi) Reinf. Reinf. (%) (ft) √Pe/Po

SRC1 24 24 W10x49 Strong 5 50 8#8 #4@12 2.3 14 1.00 23.3

SRC2 24 24 W10x49 Strong 5 50 8#8 #4@12 2.3 20 2.00 33.3

SRC3 16 16 W10x100 Strong 5 50 8#6 #4@12 10.3 14 1.25 35.0

SRC4 16 16 W10x100 Strong 5 50 8#6 #4@12 10.3 20 2.50 50.0

SRC5 16 16 W10x100 Weak 5 50 8#6 #4@6 10.3 14 1.25 35.0

SRC6 16 16 W10x100 Biaxial 5 50 8#6 #4@12 10.3 20 2.50 50.0

SRC7 16 16 W10x100 Strong 8 65 8#6 #4@12 10.3 20 2.50 50.0

SRC8 16 16 W10x100 Strong 12 65 8#6 #4@12 10.3 20 2.50 50.0

RC Section

Load Histories

•

Proportional; Non-proportional; Non-symmetric

From AISC 2005M

P

Strain C.

Plastic

2005Simp.Axial capacity of MAST System

θx

θx

θyΔz

Assessment of Demand: Computational ModelingAssessment of Demand: Computational Modeling

Δy

Δx

θz

Δyc

Δxc

Δxs

Δys θy

ΔzcΔzs

θz

A 3D 18 DOF Beam-Column element was formulated:

•

Separate translational DOFs

for steel tube and concrete core were defined

•

Differential displacement allowed in the axial direction

•

Distributed plasticity fiber formulation: stress and strain modeled explicitly at each fiber of cross section

•

Suitable for static and transient dynamic analysis

slip

MzMy

Ps Pc

MxVsz

Vcz

Vsy

Vcy

•

Implemented in OpenSEES

Physical Characteristics of Rectangular Physical Characteristics of Rectangular CFTsCFTs

Cyclic Behavior of RCFT membersCyclic Behavior of RCFT members

Elastic Unloading concrete + steel

Decreasing Elastic Zone concrete + steel

Strength Degradation concrete + steel

Bauschinger Effect steel

Gradual Stiffness Reduction concrete + steel

Bounding Stiffness steel

Softening concrete + steel

Sakino and Tomii (1981)

Slip (mm)

Shakir-Khalil (1993)

0 2 4 6 8 100

-100

-200

-300

-400

-500

Load

(k

N)

-600 Elastic Unloading andReloading

Concrete Constitutive FormulationConcrete Constitutive Formulation

•

Cyclic constitutive model proposed by Chang and Mander

(1994) was adapted and modified extensively to simulate strain vs. stress response of concrete

Accounts for confinement implicitly through slope of softening branch

Tension stiffening

Cycle into tension and back into compression

Robust formulation at section iteration level to capture softening

-25

-15

-5

5

-0.008 -0.006 -0.004 -0.002 0 0.002

Strain

Stre

ss (M

Pa)

0

5

10

15

20

25

30

35

0 0.002 0.004 0.006 0.008

ExperimentComputation

0

5

10

15

20

25

0 0.002 0.004 0.006 0.008

Experiment

Computation

0

30

60

90

0 0.01 0.02 0.03 0.04 0.05


0

5

10

15

20

25

30

0 0.002 0.004 0.006 0.008


Strain

Stre

ss (M

Pa)

Strain

Stre

ss (M

Pa)

Strain

Stre

ss (M

Pa)

Strain

Stre

ss (M

Pa)

Karsan and Jirsa (1964)

Sinha et al. (1969)

Calibration of Concrete Constitutive FormulationCalibration of Concrete Constitutive Formulation

Mander et al. (1984)

Okamato (1976)

-400

-200

0

200

400

-0.003 -0.002 -0.001 0 0.001

Plastic Strain

Stre

ss (M

Pa)

Loading Surface

Local Buckling

Steel Constitutive FormulationSteel Constitutive Formulation

• Cyclic constitutive model proposed by Mizuno at el. (1992) was adapted and modified to simulate strain vs. stress response of cold- formed steel tube

• Uniaxial bounding surface model with local buckling

Bounding Surface

Calibration of Steel Constitutive FormulationCalibration of Steel Constitutive Formulation

-800-600-400-200

0200400600800

0 0.01 0.02 0.03 0.04 0.05 0.06ExperimentAnalysis

-700

-500

-300

-100

100

300

500

700

-0.02 0 0.02 0.04

ExperimentAnalysis

StrainStrain

Str

ess

(MPa

)

Str

ess

(MPa

)

0

90

180

270

360

450

540

0 0.005 0.01 0.015

flat - testflat - analysiscorner - test

corner - analysis

Str

ess

(MPa

)

Strain

Sully and Hancock, 1991

Mizuno et al., 1991 Mizuno et al., 1991

εpo

= 0.0006

(corner)εpo

= 0.0004(flat)

0

100

200

300

400

500

0 0.002 0.004 0.006 0.008

flat - testflat - analysiscorner - testcorner - analysis

Strain

Str

ess

(MPa

)

Furlong, 1968

εpo

= 0.0006

(corner)εpo

= 0.0004(flat)

Cantilever:Cantilever:

LL--Frame:Frame:

M

L = 1 inch A = 1000 inch2

I = 1 inch4 E = 1 ksi

3 elements

Verification of RCFT BeamVerification of RCFT Beam--Columns: Geometric NonlinearityColumns: Geometric Nonlinearity

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

Axial Displacement (inch)

Tra

nsv

erse

Dis

pla

cem

ent

(inch

)

Theory

-25

0

25

50

75

100

125

-25 0 25 50 75 100 125 150 175

Displacement (inch)

Dis

plac

emen

t (in

ch)

L

= 120 inch E

= 7.2 x 106 ksi

A

= 6 inch2 I

= 2 inch4

L/5

LL

V

Steel girder

RCFT column

-15000

-10000

-5000

0

5000

10000

15000

20000

25000

0.0 0.5 1.0

Normalized Displacement

She

ar F

orce

(kip

s)

theory

theory

6 elements

6 elements

10 elements

10 elements

Axially Loaded RCFT ColumnsAxially Loaded RCFT Columns

0

1500

3000

4500

0 2 4 6 8 10 12Axial Deformation (mm)

Axia

l For

ce (k

N)

ExperimentAnalysisCY - AnalysisCC - AnalysisLB - AnalysisCY - Tort and Hajjar (2003)CC - Tort and Hajjar (2003)LB - Tort and Hajjar (2003)

Nakahara and Sakino, 1998CR4-D-2D/t

= 73.7fy

= 262.0 MPaf’c

= 25.4 MPaL/D

= 3

0

2000

4000

6000

8000

10000

12000

14000

16000

0.0 2.0 4.0 6.0 8.0 10.0 12.0Axial Deformation (mm)

Axi

al F

orce

(kN

)

Experiment CY - ExperimentCC - Experiment LB - ExperimentAnalysis CY - AnalysisCC - Analysis LB - AnalysisCY - Tort and Hajjar (2003) CC - Tort and Hajjar (2003)LB - Tort and Hajjar (2003)

Varma, 2000SC32-80 D/t

= 34.3fy

= 600.0 MPafc

= 110.6 MPaL/D

= 4

RCFT BeamRCFT Beam--ColumnsColumns

• Proportionally Loaded Columns:

• Non-Proportionally Loaded Columns:

0

200

400

600

0.0 0.3 0.6 0.9

experiment analysis

Mid-Height Disp (inch)

Axi

al F

orc

e (

kips)

D/t = 20, f’c

= 5.4 ksi

fy

= 45 ksi, L/D

= 10.5

SHC3 (Bridge, 1976)

0

40

80

120

160

0 0.5 1 1.5 2

experiment analysis

Mid-Height Disp (inch)

Axi

al F

orc

e (k

ips)

D/t

= 24, f’c

= 6.8 ksify

= 42 ksi, L/D

= 24

1 (Cederwall

et al., 1990)

0

500

1000

1500

2000

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035

experiment analysisBR4-6-10-02

(Nakahara and Sakino, 1998)

D/t

= 32, f’c

= 17.3 ksi,fy

= 45 ksi, P/Po

= 0.20

End-Rotation (rad)

Mom

ent

(ki

ps.

inch

)

244 (Tomii

and Sakino, 1979)

0

60

120

180

0 0.01 0.02 0.03 0.04

experimentanalysis

End-Rotation (rad)

Mom

ent

(ki

ps.

inch

)D/t = 24

f’c

= 2.7 ksi

fy

= 41 ksi

P/Po

= 0.40

4 elements 3 integration points

2 elements 3 integration points

ThreeThree--Dimensional Verification of RCFT ResponseDimensional Verification of RCFT Response

2264 m

m

1738 mm

1188 m

m

-40

-30

-20

-10

0

10

20

30

40

-0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04

Rotation (%)Sh

ear (

kN)

experiment analysis

D/t

= 21.8 L/D = 9f’c

= 20 MPa f y = 395 MPaMorino et al., 1993 –

3D Subassemblage

-24.0

-18.0

-12.0

-6.0

0.0

6.0

-0.035 -0.025 -0.015 -0.005 0.005

Strain

Stre

ss (M

Pa)

-500.0

-300.0

-100.0

100.0

300.0

500.0

-0.03 -0.02 -0.01 0 0.01

Strain

Stre

ss (M

Pa)

3 elements4 integration points

Kawaguchi, 2000

Specimen

21C30C

D/t

= 21.6

f’c

= 17.9 MPa

fy

= 404 MPa

L/D

= 8

P/Po

= 0.30

Constant Axial Load

Cyclic Shear Force

Connections remain elastic

RCFT Frame Response RCFT Frame Response 10

00 m

m

1500 mm

-80

-60

-40

-20

0

20

40

60

80

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0

analysis

experiment

1

32

4

5

1

2

3

5

1-TC 2-CY 3-TY

4-CC 5-LB

3 elements4 integration points

STRAIN

STR

ES

S (k

si)

-80

-60

-40

-20

0

20

40

60

80

-0.025 -0.020 -0.015 -0.010 -0.005 0.000 0.005 0.010 0.015

-80

-60

-40

-20

0

20

40

60

80

-0.020 -0.015 -0.010 -0.005 0.000 0.005 0.010 0.015

-80

-60

-40

-20

0

20

40

60

80

-0.015 -0.010 -0.005 0.000 0.005 0.010

-70

-60

-50

-40

-30

-20

-10

0

10

-0.0050 -0.0040 -0.0030 -0.0020 -0.0010 0.0000 0.0010

-40

-30

-20

-10

0

10

20

-0.0015 -0.0010 -0.0005 0.0000 0.0005 0.0010

-35-30-25-20-15-10

-505

101520

-0.0015 -0.0010 -0.0005 0.0000 0.0005 0.0010

-25

-20

-15

-10

-5

0

5

10

-0.0008 -0.0006 -0.0004 -0.0002 0.0000 0.0002 0.0004

-12

-10

-8

-6

-4

-2

0-0.00040 -0.00035 -0.00030 -0.00025 -0.00020 -0.00015 -0.00010 -0.00005 0.00000

Steel Stress-Strain

Curves

Flange

Corner

Web

Web

RCFT Frame Response: Steel StressRCFT Frame Response: Steel Stress--Strain Curves Strain Curves

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

-0.015 -0.010 -0.005 0.000 0.005 0.010 0.015 0.020

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

-0.005 -0.004 -0.003 -0.002 -0.001 0.000 0.001

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

-0.015 -0.010 -0.005 0.000 0.005 0.010

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

-0.020 -0.015 -0.010 -0.005 0.000 0.005 0.010 0.015

-2.5

-2

-1.5

-1

-0.5

0

0.5

-0.0012 -0.0010 -0.0008 -0.0006 -0.0004 -0.0002 0.0000 0.0002 0.0004 0.0006

-1.0

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.00.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

-2

-1.5

-1

-0.5

0

0.5

-0.0010 -0.0008 -0.0006 -0.0004 -0.0002 0.0000 0.0002 0.0004

-2.5

-2

-1.5

-1

-0.5

0

0.5

-0.0012 -0.0010 -0.0008 -0.0006 -0.0004 -0.0002 0.0000 0.0002 0.0004 0.0006

STRAIN

STR

ES

S (k

si)

Flange

Corner

Web

Web

Concrete Stress-Strain

Curves

RCFT Frame Response: Concrete StressRCFT Frame Response: Concrete Stress--Strain Curves Strain Curves

RCFT Frame Response: PseudoRCFT Frame Response: Pseudo--Dynamic ExperimentDynamic Experiment

- 5 0 0- 4 0 0- 3 0 0- 2 0 0- 1 0 0

01 0 02 0 03 0 0

0 5 1 0 1 5 2 0

C o m p u t a t i o n a lE x p e r i m e n t

- 3 0 0

- 2 0 0

- 1 0 0

0

1 0 0

2 0 0

3 0 0

4 0 0

0 5 1 0 1 5 2 0

C o m p u t a t i o n a lE x p e r i m e n t

Time (sec)D

ispl

acem

ent (

mm

)

2%50

10%50m1

= 145 tonsm2

= 145 tonsm3

= 145 tonsm4

= 105 tons

Rigid Link

LeanerColumn

Loading Beam

Girders:fy

= 345 MPaGround – W460x681st – W460x682nd – W410x603rd – W410x464th – W310x33RCFT Columns:fy

= 552 MPaHSS 305x305x10f’c = 55 MPa

Ground

1st

2nd

3rd

4th

RCFTColumn

SteelGirder

1.4 m

3.0 m

2.3 m

2.3 m

2.3 m

5.5m 5.5 m

m1

m2

m3

m4

-2000

-1500

-1000

-500

0

500

1000

1500

2000

-100 -50 0 50 100

C om putationalE xperim ent

-2000

-1500

-1000

-500

0

500

1000

1500

2000

-150 -100 -50 0 50 100 150

C om puta tional

E xperim ent

Inter Story Drift (mm)

Stor

y Sh

ear

(kN

) 1st Story

10%50

4th Story

1st Story

2%50

4th Story

Herrera et al. (2005)

- Pseudo-dynamic testing

- Loading is applied at the mid-point of girders

- High strength materials

11.0 m

11.1

m

Computational Modeling of Computational Modeling of RCFTsRCFTs

1st Story Column Steel

Tube Stress vs. Strain

1st Story Column Concrete

Core Stress vs. Strain

1st Story Column and Girder P-M Interaction

Girder

Column

1st Story

Shear vs. Drift

1st Story Girder

Moment vs. Rotation

4th Story

Displacement vs.

Time

1st Story Column

Moment vs. Rotation10% in 50 year Northridge ground motion

070612 Herarra Frame Movie.mpg

Computational Model

•

Extending now to circular CFTs

and SRCs

2264 m

m

1738 mm

1188 m

m

-10

-8

-6

-4

-2

0

2

4

6

8

-0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04

Rotation (%)

Shea

r (ki

ps)

experiment analysis

Upcoming: Parametric Studies

•

Parametric studies will be performed to document the performance limit states of composite systems, leading to the development of new recommendations for non-seismic and seismic design of composite beam-

columns.

Upcoming: Equivalent Stiffness for AISC

•

A simplified, mechanistically based equation for the prediction of the equivalent stiffness, EIeq

, of composite beam-columns will be developed.

•

Equations similar to the current ones for buckling of composite sections in the 2005 AISC Specification will be derived.

EIeff

= Es

Is

+ 0.5 Es

Isr

+ C1

Ec

Icwhere C1

is a simple parameter based on the reinforcement ratio.

Upcoming: System Performance Factors

•

Rational system performance factors (e.g., R, Cd

, and Ωo

) will be developed. •

Currently, they are based on a perceived equivalence to either concrete or steel systems.Seismic-Force-Resisting Systems R Ωo Cd

Composite eccentrically braced frames 8 2 ½ 4

Composite concentrically braced frames 5 2 4 ½

Ordinary composite braced frames 3 2 3

Special composite moment frames 8 3 5 ½

Intermediate composite moment frame 5 3 4 ½

Ordinary composite moment frame 3 3 2 ½FEMA 450-1/2003 Edition

new developments in earthquake engineering of steel and ... · a 3d 18 dof beam-column element was...

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