Performance-Based Plastic Design Method · Performance-Based Plastic Design Method ... 1 Review of Current Seismic Design ... Dr. Swapnil B. Kharmale Fundamentals of Structural Dynamics

One Week FDPFundamentals of Structural Dynamics and Application to

Earthquake Engineeringin Sanjay Ghodawat Group of Institute

Performance-Based Plastic Design Method

Dr. Swapnil B. Kharmale

Assistant Professor, Applied MechanicsGovernment College of Engineering and Research, Avasari

[email protected]

December 11, 2015Dr. Swapnil B. Kharmale Fundamentals of Structural Dynamics and Application to Earthquake Engineering

Content

1 Review of Current Seismic Design Procedure

Design Standards (Viz IS 1893, ASCE7)

Calculation of Base Shear Vb

Response reduction or modification factor R

Equivalent Static Lateral Force Distribution

Design of members of LLRS

Displacement ductility of LLRS µ

2 Weaknesses in Current Seismic Design Procedure

3 Perfomance-Based Seismic Design (PBSD)

4 Performance-Based Plastic Design (PBPD)

Basis of Design Method

Application of PBPD to Various LLRS

PBPD for Steel MRF by Lee and Goel (2001)

Dr. Swapnil B. Kharmale Fundamentals of Structural Dynamics and Application to Earthquake Engineering

Content















Content















Content















Review of Current Seismic Design Procedure

Current codes

Structures expected toundergo large inelasticdeformations during majorearthquake

Design approach is simpleelastic force/strength-based

Inelastic behaviour isaccounted in somewhatimplicit or indirect way(through, R)

Figure: Typical spectral responseacceleration and seismic responsecoefficient for Vb


Review of Current Seismic Design Procedure: Calculationof Vb

ASCE 7

Vb = CsW

where, Cs is seismic responsecoefficient

Cs =SDSRI

IS:1893

Vb = AhW

where, Ah is design horizontalseismic coefficient

Ah =Z

2

Sag

I

R

About R: Response reduction or modification factor

Depends upon perceived seismic damage performance of thestructure, characterised by ductile or brittle deformations.

Based on professional experience and judgment.

For example OMRF R = 3, SMRF R = 5.


Review of Current Seismic Design Procedure: Calculationof Vb

ASCE 7

Vb = CsW

where, Cs is seismic responsecoefficient

Cs =SDSRI

IS:1893

Vb = AhW

where, Ah is design horizontalseismic coefficient

Ah =Z

2

Sag

I

R

About R: Response reduction or modification factor

Depends upon perceived seismic damage performance of thestructure, characterised by ductile or brittle deformations.

Based on professional experience and judgment.

For example OMRF R = 3, SMRF R = 5.


How Seismic Design Code Considers Inelastic Response ofSystem

Figure: Base shear Vb versus lateral displacement for elastic and inelasticsystem


Review of Current Seismic Design Procedure: Equivalentstatic lateral force distribution

Based on elastic response ofstructure and considersfundamental mode of vibration

Generic expression

Fi = CviVb

Cvi =wih

ki∑n

i=1 wihki

Value of k for

UBC k = 1

IBC k = f (T1)

IS k = 2Figure: Equivalent static lateralforce distribution




Generic expression

Fi = CviVb

Cvi =wih

ki∑n

i=1 wihki

Value of k for

UBC k = 1

IBC k = f (T1)





Generic expression

Fi = CviVb

Cvi =wih

ki∑n

i=1 wihki

Value of k for

UBC k = 1

IBC k = f (T1)



Review of Current Seismic Design Procedure: Selection ofmember sizes

After calculation of Vb and Fi

Structure with trial sizes of members analysed using elasticanalysis

Member sizes are finalised for reqiured strength(Strength≥Action)

Drift calculated from elastic analysis is amplified usingdeflection amplification factor so as to keep it within codespecified limit

Appropriate detailing provisions are followed to met theexpected ductility demand


Review of Current Seismic Design Procedure:Displacement ductility µ

How much displacement ductilityis targeted implicitly

Displacement ductility ratio

µ =∆m

∆y

Implicitly

µ =R

Ωo

No direct inclusion of µ incalculation of Vb

Figure: General Structural Response[Uang 1991]


Review of Current Seismic Design Procedure:Displacement ductility µ

How much displacement ductilityis targeted implicitly

Displacement ductility ratio

µ =∆m

∆y

Implicitly

µ =R

Ωo

No direct inclusion of µ incalculation of Vb

Figure: General Structural Response[Uang 1991]


Review of Current Seismic Design Procedure: Design FlowChart

Figure: Typical design flow chart of current seismic design procedure(Say ASCE7)


Review of Current Seismic Design Procedure: Weaknessesin design procedure

Force/strength-based and not displacement-based asdisplacements/drifts are better measure of damages

More iterative and never provide good or optimal design asdesired

Current design procedure is unable to utilize the significantinelastic deformation capacity of system

Structure designed by current design procedure whensubjected to severe strong motion have been found to undergolarge inelastic deformation in “un-controlled manner” (Say“soft storey” an unlike collapse mechanism)




















Performance-Based Seismic Design (PBSD)

Performance-Based SeismicDesign (PBSD)

Developed in USA after1994 Northridge Earthquake

Structure should meetmultiple performanceobjectives when subjected toearthquake

Fully opreational(with 50% probability ofexeedance in 50 years)Life saftey(with 10% probability ofexeedance in 50 years)Collapse prevention(with 2% probability ofexeedance in 50 years)

Figure: PBEE frame work


Salient features of PBSD

PBEE allows to choose owner or designer

level of ground shaking

level of performance/protection for that ground motion

Hence abvantages of PBSD

Better characterization of structural damage and dueconsideration to uncertainties

Explicit (Direct) consideration to inelastic behaviour in thedesign


Salient features of PBSD

PBEE allows to choose owner or designer

level of ground shaking

level of performance/protection for that ground motion

Hence abvantages of PBSD

Better characterization of structural damage and dueconsideration to uncertainties

Explicit (Direct) consideration to inelastic behaviour in thedesign


Appraches in PBSD

Performance-Based designMethod differ depending uponthe performance objectives anddesign and analysis approaches

Comprehensive DesignApproach

Displacement DesignApproach

Energy Based DesignApproach

General Force or StrengthApproach

Perspective DesignApproach

Figure: Performance Based DesignFlowchart (FEMA 445)


Performance-Based Plastic Design (PBPD) Method

Developed at University of Michigan by Prof. Goel andResearch Associates

PBSD approaches based on plastic analysis and designconcepts

Pre-selected yield/failure mechanism and a uniformtarget drift (based on inelastic behaviour) are considered asperformance objectives.

Accounts for structural inelastic behaviour directly

Practically eliminate the need for assesment or iteration afterinitial design

Seismic force calculations are based on the concept ofenergy balance


Performance-Based Plastic Design (PBPD) Method: Basisof Design

Concept of energy balance

Considers inelasticenergy demand: topush the structuremonotonically uptothe target drift

Equated to inelasticwork (through theplastic deformations)required by equivalentEPP SDOF system toachieve same inelasticstate Figure: Structural idealised response and

energy balance conceptDr. Swapnil B. Kharmale Fundamentals of Structural Dynamics and Application to Earthquake Engineering

Performance-Based Plastic Design (PBPD) Method:Application to various system

Application to various lateral load resisting system

Steel MRF: Leelataviwat et al. (1999) and Lee and Goel(2001)

Steel Buckling Restrained Braced frame: Dasgupta et al.(2005)

Steel Braced frame: Chao and Goel (2005)

Steel Special Truss Moment Resisting Frames: Chao andGoel (2008)

Steel Plate Shear Walls: Ghosh et al. (2009) and Kharmale(2011)



Performance objectives

To design steel MRF for

a target ductility demandµt = Du/Dy

a pre-selected yieldmechanism

Figure: Pre-selected yieldmechanism


PBPD for Steel MRF : Design yield base shear Vby

Total strain energy imparted to inelastic system as sum of elasticand plastic vibrational energy

Ee + Ep = γ

(1

2MS2

v

)=

1

2γM

(T1

2π

Sagg

)2

where,

M = total seismic mass of structure

Sa and Sv spectral acceleration and spectral velocity of MRF

γ = energy modification factor

γ =2µt − 1

R2µ

where,

µt = target displacement ductility ratio

Rµ = ductility reduction factor


PBPD for Steel MRF : Design yield base shear Vby

Elastic vibrational energy can be written, assuming that the entirestructure is reduced into SDOF

Ee =1

2M

(T1

2π

Vby

Wg

)2

Thus,

Plastic energy demand, Ep

Ep =WT 2

1 g

8π2

(γ(Sa/g)2 −

(Vby

W

)2)


PBPD for Steel MRF: Design yield base shear Vby

Inelastic work done (Wp)

Wp =

(n∑

i=1

Fihi

)θp

Equating Ep to Wp and solving

Vby

W=

−α +√α2 + 4γ(Sa/g)2

2

where

α =

(n∑

i=1

Cvihi

)8θpπ

2

T 21 g

and Cvi =FiVby


PBPD for Steel MRF: Design of Floor Beams

Steps

After Vby calculationdistribute it using suitablelateral force distribution.

Rigid floor diaphragm actionresult zero axial force infloor beams.

Calculate Mpc to avoid softstorey collapse mechanism.

Calculate Mpbi using virtualwork principle.

Soft storey collapse mechanism


PBPD for Steel MRF : Design of Floor Beams

Mpc

Mpc =Vbyh1

4

Calculation of Mpbi

Calculate shear proportionfactor, βi = Vi/Vn.

Use virtual work principle

Calculation of Mpbr

Virtual work principle(n∑

i=1

Fihi

)θp = (2Mpc) θp +

(2Mpbr

n∑i=1

βi

)θp


PBPD for Steel MRF : Design of Columns

At ultimate drift level, updatedlateral force at ith floor Fiu

Fiu = (βi − βi + 1)Fnu

Updated lateral force at roof Fnu

Fnu =Mpc +

∑ni=1Mpbi∑n

i=1(βi − βi+1)hi

Free body diagram for exteriorcolumn

Mc(h) and Pc(h)

Mc(h) =n∑

i=1

Mpbi −n∑

i=1

Fiu(hi − h)

Pc(h) =1

L

n∑i=1

Mpbi


PBPD for Steel MRF: Design Flow Chart

Figure: Flow chart for PBPD of steel MRF


THANK YOU!


Documents

Performance-Based Plastic Design Method · Performance-Based Plastic Design Method ... 1 Review of Current Seismic Design ... Dr. Swapnil B. Kharmale Fundamentals of Structural Dynamics