selection of the appropriate steel quality for efficient

Selection of the appropriate steel quality for efficient earthquake resistant structures Hervé Degée

IntroductionMany uncertainties in seismic design…

On seismic hazard Poor data base : - measurements since1950

- design return periods 475 years…or + Major earthquakes are rare events => approximative knowledge Extrapolation based on history repetition hypothesis … Knowledge of local geology approximate

all recent events make discover unknown faultsNorthridge (1994), Kobe (1995), Kocaeli (1999)

after each earthquake, seismicity revised: increased hazardIstanbul ag 0,2g => 0,4g after Kocaeli (1999)

on the response of structures

- dynamic, depend on real values & distribution of stiffnesses & massesnot known with precision

- often non linearbut NL computation not convenient

requires realistic data & model Ways to mitigate uncertainties

strength => overstrength plastic deformation capacity

Introduction

ACTION

+ Material

IntroductionMitigation of uncertainties

An earthquake imposes a relative displacementΔrequired= SDe(T) between center of mass & basisΔ ≈ independent of type of response elastic or inelastic

2 possible « mechanical » design in seismic codes

Elastic design resistances > action effects

EC8 DCL= Ductility Class Low

Dissipative or ductile design resistances > action effects

computed under reduced action accounting for energy dissipation in cyclic plastic mechanisms

capacity of deformationΔcapable > Δrequired

EC8 DCM= Ductility Class Medium // DCH = High

VEd

dSDe(T)

DCL

DCM

DCH

a)

b)

c)

Design base shear

Δrequired

Introduction

CD

E MF d=M.Sd(T)F e=M.S e(T)

F d=F e/qd

ds=q.dyde=dy

Why accept plastic deformations under earthquake?

To reduce cost: design is for Fd << Fe

To increase safety:much energy dissipated in a permanent way in plastic deformations

m ∫ u″(t)u′(t) + c ∫ [u′(t)]2dt + ∫ F(u) u′(t)dt = ∫ - m dg″(t) u′(t) dt

E kinetic + E viscous + E deformation = E input EQ

With E deformation = E Elastic+ E Plastic

Fd = Fe / q

← !!!ds = q. de

IntroductionConditions required for a very dissipative behaviour

Define the objective « global mechanism »

Moment resisting frames plastic hinges in beamsnot by plastic hinges in columnsnot by shear in beams&columnsnot in the connections

Diagonal concentric bracingsdiagonals in plastic tension

Eccentric bracingsSeismic link yielding in shearor bending

L

F1

F2

epst

p

e

p

Introduction

IntroductionHow to avoid reaching limits in components adjacent to dissipative ?

« capacity design » of all components other than the dissipative ones

=> overstrength of zones adjacent to the intended dissipative zone

ductile link F Other links K« fuse » « brittle »

Design resistance RdF ≥ Ed RdK ≥ γ RdF

RdK related to RdF not to action effect Ed

Ed

IntroductionCapacity design - examples

Normal Capacity

Connections in MRF

F 2

N Ed,G3

N Ed,E2

N Ed,E1 N Ed,E3

F 1

Columns in CBF

EEd, ovGEd,EdRd .1,1)( NΩNMN γ+≥

IntroductionCAPACITY DESIGN HAS TO BE BASED ON THE ACTUAL STEEL PROPERTIES

fy,design ≥ fy,max, real ≥ fy,nominal

Current possible optionsa) fy,max of dissipative zones is measured

is the value used in design => γ0v = 1

b) Do design, based on a single nominal yield strength fyfor dissipative & non dissipative zones

Use nominal fy for dissipative zones, with specified fy,maxUse higher nominal fy for non dissipative zones and connections

Ex: S235 dissipative zones, with fy,max = 355 N/mm2

S355 non dissipative zones

c) Design considering that in dissipative zones: fy,max = 1,1 γov fyγov material overstrength factor fy : nominalγ ov = fy,real / fyEuropean rolled sections: γ ov = 1,25

Ex: S235, γov = 1,25 => fy,max = 323 N/mm2

an upper value fy,max is specified for dissipative zones

OPUSRFCS Research Project OPUS“ Optimizing the seismic performance of steel and steel-concrete strUctures byStandardizing material quality control ”

What is the real sensitivity of seismic performances to material properties ??

Partners:• Riva Acciaio (IT)• Université de Liège / Hasselt Universiteit (BE)• RTWH Aachen (DE)• University of Thessaly (GR)• ArcelorMittal (LU)• INSA Rennes (FR)• Universita di Pisa (IT)

First phase 2007-2011+ additional developments in the frame of Steel-Earth (2014-2015)

Flowchart of the research

Structural typologies and numerical modelling

Assessment of structural behaviour Collapse criteria individuation

Variability of mechanical properties Probabilistic modelling

Testing on steel specimens and stress-strain law modelling

Definition of the probabilistic procedure Estimation of the collapse probability of case studies

Analyses of actual recommendations included in productions standards and structural regulations

Influence of upper yielding stress limitation on dissipative areas γOV effectiveness in capacity design Recommendations and Guidelines

Structural Design Mechanical properties monitoring and modelling

Probabilistic Procedure

Research Outcomes

Mechanical properties monitoring and modelling Sampled steel products

Quality Production Standard φ : nominal diameter [mm]B450C Technical Code for Construction (2008) - Italy 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32B500B AFNOR NF A35-019-1 (2007) - France 14, 16, 18, 20, 22, 25

S500SD UNE 36065 (2000) - Spain 8, 10, 12, 16, 20, 25, 32Quality Production Standard t: thickness range [mm] - defined according to EN10025

S235 J0 AR EN 10025-2 7-16; 16-40; 40-63S275 J0 AR EN 10025-2 7-16; 16-40; 40-63; 63-80; 80-100S355 J0 AR EN 10025-2 7-16; 16-40; 40-63; 63-80; 80-100S355 J0 W EN 10025-5 7-16; 16-40; 40-63

S460 M EN 10025-4 16-40; 40-63Quality Production Standard Profile Series and designation

S235 JR/J0 EN 10025-2 HE 100 – 600; IPE 100 – 750; UPN 80 – 400

S275 JR/J0 EN 10025-2 HE 100 – 600; IPE 100 – 750; UPN 80 – 400

S355 J0/J2/K2 EN 10025-2 HE 100 – 600; IPE 100 – 750; UPN 80 – 400

S275 M EN 10025-4 HE 100 – 200; IPE 80 – 270; UPN 80 - 300

S355 M EN 10025-4 HE 100 – 200; IPE 80 – 270; UPN 80 - 300

S460M EN 10025-4 HE 100 – 600; IPE 100 – 750; UPN 80 – 400

Ste

el

rein

forc

ing

bars

Ste

el p

late

sS

teel

pro

files

0

50

100

150

200

250

300

354

376

399

421

444

466

488

511

533

555

578

600

Yielding stress [N/mm2]

Obs

erva

tions Gaussian Model

LogNormal Model

0

50

100

150

200

250

470

489

508

527

546

565

584

604

623

642

Tensile strength [N/mm2]

Obs

erva


LogNormal Model

0

50

100

150

200

250

20 21 23 24 25 26 27 28 30 31 31Elongation at failure [%]

Obs

erva


LogNormal Model

Yiel

ding

stre

ss

Tens

ile s

treng

th

Elo

ngat

ion

Mechanical properties monitoring and modelling Statistical analysis and modelling of mechanical properties: statistical investigation

concerned yielding stress, tensile strength and ultimate elongation and theirinterdependencies

=1

11

,,

,,

,,

tuyu

utyt

uyty

ff

fff

fff

R

εε

ε

ε

ρρρρρρ

X

Information recognized from statistical analysis were used to calibrate a multi-variedLog-Normal Model - LNM(fy,ft,εu)

The LNM was used as generation Kernel for theapplication of Monte-Carlo Method method

R ,R ,Ae,H m

S2751 0.736 0.276

C 0.736 1 0.4020.276 0.402 1

− = − − −

R ,R ,Ae,H m

S3551 0.851 0.382

C 0.851 1 0.5770.382 0.577 1

− = − − −

Mechanical properties monitoring and modelling

tf

yf

uthε y εεε

σ

εo

Tensile test on Structural Steels and Reinforcing bars (at least 30 tests for each steel product)

Simplified stress-strain law: bi-linear kinematic herdening based on tensile test results

Skeleton curve

0

100

200

300

400

500

600

700

0 5 10 15 20 25 30Strain - [%]

Stre

ss -

[MP

a] Reinforcing Bars

0

100

200

300

400

500

600

700

0.00 0.05 0.10 0.15 0.20 0.25Strain [-]

Tens

ile s

tress

[MP

a]Steel profiles Reinforcing bars

o ε

σ

ε ε εyε h t u

fy

ft

Model 1

σ

εo

tf

yf

uthε y εεε

Model 2

Mechanical properties monitoring and modelling Benchmarking of stress-strain model to capture hysteretic behaviour of steel member

(Moment-Rotation)

Simplified stress-strain law: bi-linear kinematic hardening based on tensile test results

σ

εo

tf

yf

uthε y εεε

Model 2

-1500

-1000

-500

0

500

1000

1500

-60 -40 -20 0 20 40 60Recorded displacement - SZ2 - SZ3 - [mm]

Appl

ied

Forc

e [k

N]

Experimental testingNumerical simulation Model 2











Research Outcomes

Design of case studies• 16 different 3D buildings have been design according to EN1998• Bare steel and other steel-concrete solutions have been considered• Some structures have been designed for Low Seismicity zones (PGA=0.1g; soil type C; other

for High Seismicity zones (PGA=0.25g; soil type B)• Three main building types have been considered: office building; car park; industrial building;

(also tank will be examined)• TOTAL: 34 typical plane configurations are defined and will be analyzed• Different steel grades have been employed – S235, S275, S355, S460

bare steel & composite

Car Park

Multi-storey industrial buildingSingle-storey industrial building

Numerical Models of case studies• Four software : ABAQUS, DYNACS, FINELG, OPENSEES – To strengthen the coherence

between results a preliminary benchmarking action is adopted

PP

V

L

H

±δ

∆

L

sect. 1

sect. 2

sect. 3

sect. 41 2 3

PP

V

L

H

Numerical Models of case studies

0

2

4

6

8

10

0.00 1.00 2.00 3.00 4.00

Period (S)

Acce

lera

tion

(m/s

2 )

asart

asd

Discrepancy

Vu

dmax

Vbase

droof

Vy= 0.60 Vu

dy

sd

arts

statice

u

aa

qu

,

,

×=λλϑ

ϑ

ydesigny

realy

realy

u

y

u

designy

u

y

u

qqqVV

VV

dd

VV

ddq

⋅⋅=⋅⋅=

=⋅=Ω⋅=

Ωµ

µ

,

,

,

,

Seismic performance: evaluation of behaviour factor - q Incremental Dynamic Analysis Static Push-Over

Numerical Models of case studies

Oversizing in Low Seismicity with higher q

q factors using bending link appear over-estimated in EN1998

For High Seismicity, EN1998 works properly

Recalibration of q factor using modified Ballio-Setti procedures could help in the improvement of design procedure











Research Outcomes

Applicative probabilistic approach STEP 1. Deep knowledge of structural systems. Structural behaviour of the case studies

(fulfilled by q factor estimation).

STEP 2. Nonlinear modelling and collapse modalities assessment. Individuation of therelevant collapse criteria and definition of PGA levels activating the collapse modes relevantfor each structural type

STEP 3. Characterization of seismic hazard. Parameters and hazard proposed by EN1998-1-1; seven seismic inputs to be adopted in the numerical simulations (artificially generated fromresponse spectra adopted in the design)

STEP 4. Probabilistic model of mechanical variables. Scattering of steel products wasrepresented by a multi-variable model LN[Re,H, Rm, A] - Monte Carlo simulation.

STEP 5. Execution of nonlinear analyses and optimal planning of numerical simulations.Correlation between seismic demand and structural response through IDA technique:correspondence between PGA and activation of collapse modes [in the analysis bothscattering of seismic inputs and material variability were considered.

STEP 6. Probabilistic procedure for Pf estimation. Numerical results coming from dynamicanalyses were analyzed employing a statistical procedure that furnishes fragility curves andyearly threshold exceedance probability referred to relevant collapse modes.

Applicative probabilistic approach STEP 2 Moment Resisting Frames

Eccentrically braced frames Concentrically braced frames

Applicative probabilistic approach STEP 2

Type Reference Criteria A Dynamic instability (Global) - Limit B Maximum roof drift ratio (Global) FEMA 356 Indicative C Inter-storey drift ratio (Global) FEMA 356 Indicative D Ultimate rotation of plastic hinges (Local) EN1998-3 Limit E Shear capacity (Local) EN1993-1 Limit F Lateral torsional buckling (Local) EN1993-1 Limit G Global buckling (Local) EN1993-1 Limit H Joint forces - Evaluation I Foundation forces - Evaluation

Type Reference code Criteria A Dynamic instability (Global) - Limit B Maximum roof drift ratio (Global) FEMA 356 Indicative C Inter-story drift ratio (Global) FEMA 356 Indicative N Ultimate rotation of link (Local) FEMA 356 Limit E Shear capacity (Local) EN1993-1 Limit G Global buckling (Local) EN1993-1 Limit H Joints forces - Evaluation I Foundation forces - Evaluation

Type Reference Code Criteria A Dynamic instability (Global) - Limit B Maximum roof drift ratio (Global) FEMA 356 Indicative C Inter-storey drift ratio (Global) FEMA 356 Indicative L Ultimate deformation, tension (Local) EN1998-3 Limit M Ultimate deformation, compres. (Local) EN1998-3 Limit E Shear capacity (Local) EN1993-1 Limit F Lateral torsional buckling (Local) EN1993-1 Limit G Global buckling (Local) EN1993-1 Limit H Joint forces - Evaluation I Foundation forces - Evaluation

Building A B C D E F G H I L M N 1 X X X 2 X X 3 X X X X 4 X X X X 5 X X X X X 6 X 7 X 8 X 9 X

10 X X X 11 X X X 12 X X X X X X 13 X X X X X X 14 X X X 16 X X X X

Activable collapse modes Moment Resisting Frames

Eccentrically braced frames Concentrically braced frames

Applicative probabilistic approach STEP 3 and 4

( ) kgR0gR akaH −⋅= 1.0E-05

1.0E-04

1.0E-03

1.0E-02

1.0E-01

0.0 0.5 1.0 1.5

Exce

edan

ce p

roab

ility

agR - Peak Ground Acceleration - [g]

High Seismic Zones - Hazard - EN1998-1-1

TL = 1 year

TL = 50 years

1.0E-06

1.0E-05

1.0E-04

1.0E-03

1.0E-02

1.0E-01

0.0 0.5 1.0 1.5

Exce

edan

ce p

roab

ility

agR - Peak Ground Acceleration - [g]

Low Seismicity Zones - Hazard - EN1998-1-1

TL = 1 year

TL = 50 years

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0T [s]

S a [g

]

Hazard EN1998

7 artifical Seismic inputs

-4,0

-3,0

-2,0

-1,0

0,0

1,0

2,0

3,0

4,0

0 5 10 15 20

grou

nd a

ccel

erat

ion

[m/s

²]

Time [s]

-4,0

-3,0

-2,0

-1,0

0,0

1,0

2,0

3,0

4,0

0 5 10 15 20

grou

nd a

ccel

erat

ion

[m/s

²]

Time [s]

MonteCarlo simulation of material scattering

seismicity Low high p.g.a. 0.10 g 0.25 g

spectrum Type 2 Type 1 soil Type C Type B

total duration

15 s 20 s

strong motion

5 s 10 s

LN[Re,H, Rm, A]

C1 C2

C3 C4

C5 C6

B1

B2

B3

B4

B5

Br1 Br2

Br3 Br4

Br5 Br6

Br7 Br8

Br9Br10

ID m

embe

rs w

ithdi

ffere

nt p

roba

bilis

ticva

riabl

es

Grade Mean µStd. Dev.

σModel

N/mm2 N/mm2 fy ft εu

S275 fy 350 32 Log-Normal fy 1 0.74 -0.276

S275 ft 460 21 Log-Normal ft 0.736 1 -0.402

S275 εu 25 1.75 Log-Normal εu -0.276 -0.4 1

S355 fy 430 27 Log-Normal fy 1 0.85 -0.382

S355 ft 550 25 Log-Normal ft 0.851 1 -0.577

S355 εu 25 1.75 Log-Normal εu -0.382 -0.6 1

Correlation Matrix

Sources of uncertainty


IM - p.g.a.

DM - analysis output

Integration of the probabilistic variables was executed adopting IDA techniquesadopting, as PGA levels, the activation of collapse (obtained in the STEP 2)

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

14.00%

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00

p.g.a. [g-units]

Inte

rsto

rey

drift

[%]

The number of simulations executed for each PGA level were determined according topilot analyses carried out in order to check the stabilization of failure probability

IM - p.g.a.p.g.a.criteria 1

p.g.a.criteria 2

p.g.a.criteria 3

p.g.a.criteria 4

identified collapse criteria

DM - structural response

Plastic Hinge 5 - Collapse Criteria

0,35

0,4

0,45

0,5

0,55

0 1000 2000 3000 4000 5000Samples

Pfa

il

Normal Model LogNormal ModelNumerical CrudeMonteCarlo - Inf - 95%CrudeMonteCarlo - Sup - 95% CrudeMonteCarlo - Average


0,3

0,35

0,4

0,45

0,5

0,55

0,6

0 200 400 600 800Samples

Pfai

l

Normal model LogNorma modelNumerical CrudeMonteCarlo - Inf - 95%CrudeMonteCarlo - Average CrudeMonteCarlo - Sup - 95%


0,3

0,35

0,4

0,45

0,5

0,55

0,6

0 200 400 600 800SamplesPf

ail

Normal model LogNorma modelNumerical CrudeMonteCarlo - Inf - 95%CrudeMonteCarlo - Average CrudeMonteCarlo - Sup - 95%


( ) ( ) ( ) ( ) ( )∫∫ λ⋅⋅⋅=λ IMdIMDMdGDMMVdGMVEDPGEDP

The results obtained from IDA were employed for calculating the exceedance probabilityof relevant collapse criteria for the structural type

The structural response was presented in terms of collapse indicator of the ith modethrough the auxiliary variable

uii DMDM100Y ⋅= DMi: response paramter; DMu: isentification of collapse mode

All outputs where analyzed in a first step obtaining fragility curves for relevant collapsemodes (PGA vs. Exceedance probability ) statistically analyzing Yi variable for each PGAlevel

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80

Prob

ablit

y of f

ailu

re -

Dem

and

> Ca

pacit

yPeak ground acceleration - [g]

Quake 1Quake 2Quake 3Quake 4Quake 5Quake 6Quake 7MeanNormal CDF

Pro

babi

lity

Linear Stepwise

Upper tailNumerical fitting

Lower tailNumerical fitting

G(X )iG(X)=1

PG(x)=1

0

100

200

300

400

500

600

700

800

52 61 71 80 90 99 108 118 127 137 146 155 165

Expe

rimen

tal o

bser

vatio

ns

Failure mode index [100]

statistic model fragility

Main results about failure probability

1,0E-09 1,0E-08 1,0E-07 1,0E-06 1,0E-05 1,0E-04 1,0E-03 1,0E-02 1,0E-01 1,0E+00

5CB355

5CB355

5CB460

5CB460

5MRFX355

5MRFX355

5MRFX460

5MRFX460

5MRFX460

12CB355

12CB355

13CB235

13CB275

13CB235

13CB275

13MRFX235

13MRFX235

13MRFX235

13MRFX235

13MRFX235

Buc

klin

gD

riftC

olu

mn

buck

ling

Drif

tC

olum

n bu

cklin

gC

olum

n bu

cklin

gB

race

s/T

Bra

ces/

CD

rift L

TBC

olum

n bu

cklin

g

1,0E-06 1,0E-05 1,0E-04 1,0E-03 1,0E-02 1,0E-01 1,0E+00

6MRFX235

6MRFX235

6MRFX355

7MRFX235

7MRFX235

8MRFX355

8MRFX355

9MRFX235

PH

rot

1,0E-06 1,0E-05 1,0E-04 1,0E-03 1,0E-02 1,0E-01 1,0E+00

B1B2B3B4B5B6

Br1Br2Br3Br4Br5Br6C1C2C3C4

Drift1Drfit2

PH

Rot

.B

uckl

ing

Buc

klin

gLi

mit

1,00E-07 1,00E-06 1,00E-05 1,00E-04 1,00E-03 1,00E-02 1,00E-01 1,00E+00

1MRFX235

1MRFX235

2CBFX235

2CBFX235

14MRFX355

14MRFX355

15MRFX355

15MRFX355

15CBFY355

15CBFY355

10CBFY

11CBFY

11EBFX

10EBFX

PH

rot.

Bra

ce/T

PH

rot.

Bra

ce/T

Buc

klin

gP

H ro

t.


1,00E-05 1,00E-04 1,00E-03 1,00E-02 1,00E-01 1,00E+00

3EBFX

3EBFX

3EBFX

3EBFX

3EBFX

3EBFX

3EBFX

3EBFX

3EBFX

3EBFX

3EBFX

3EBFX

B1

B2

B3

B4

B5

Drfi

t1

Drfi

t2

Drfi

t3

Drfi

t4

Drfi

t5

Br1

Br2

1,00E-08 1,00E-07 1,00E-06 1,00E-05 1,00E-04 1,00E-03 1,00E-02 1,00E-01 1,00E+00

3EBFY

3EBFY

3EBFY

3EBFY

3EBFY

3EBFY

3EBFY

3EBFY

3EBFY

3EBFY

3EBFY

3EBFY

3EBFY

3EBFY

3EBFY

3EBFY

3EBFY

3EBFY

3EBFY

B1

B4

B5

B8

B9

B12

B13

B16

B17

B20

Drif

t2

Drif

t3

Drif

t4

Drif

t5

Br1

Br2

C1

C2

C4

1,00E-15 1,00E-13 1,00E-11 1,00E-09 1,00E-07 1,00E-05 1,00E-03 1,00E-01

4EBFX

4EBFX

4EBFX

4EBFX

4EBFX

4EBFX

4EBFX

4EBFX

4EBFX

4EBFX

4EBFX

4EBFX

4EBFX

4EBFX

4EBFX

4EBFX

4EBFX

4EBFX

4EBFX

4EBFX

4EBFX

B1

B3

B4

B6

B7

B9

B10

B12

B13

B15

Drf

it1

Drf

it2

Drf

it3

Drf

it4

Drf

it5

Br1

Br2

C1

C2

C3

C4

1,00E-07 1,00E-06 1,00E-05 1,00E-04 1,00E-03 1,00E-02 1,00E-01 1,00E+00

4EBFY

4EBFY

4EBFY

4EBFY

4EBFY

4EBFY

4EBFY

4EBFY

4EBFY

4EBFY

4EBFY

4EBFY

B1

B4

B5

B8

B9

B12

B13

B16

Br1

Br2

Drf

it1D

rift2


properly works in the protection of not dissipative elements.

Protected member as columns in MRF and CBF and braces in EBF exploit beneficialeffects of Ω also that, as seen during the design, produce in some case over-sizing.

It is interesting to observe that over-strength data associated to generated samples

The analysis of IDA outputs according to the proposed procedure allowed theassessment of material scattering influence of exceedance probability of limit statesassociated to relevant collapse modes

The results of all analyzed case studies showed Pfail lower than acceptance limit fixedequal to 10-4. This confirm that γOV =1.25 in EN1998 and capacity design approach

ESdOV

GSdEd EEE ×Ω××+= γ1.1

Mean value

Standard deviation

5% 95%

1.40 0.070 1.30 1.52

1.20 0.060 1.11 1.30 1.17 0.060 1.07 1.26

1.08 0.040 1.02 1.14 1.46 0.100 1.31 1.64 1.32 0.120 1.14 1.56 1.32 0.080 1.18 1.44

1.18 0.060 1.08 1.291.32 0.083 1.06 1.191.12 0.030 1.16 1.47

Percentile

Steel Quality

S235J0JR (+M)(*)

S275J0JR (+M)(*)

S355J0 (+M)S460M

S235J0JR (+M)S275J0JR (+M)S355J2K2 (+M)

S460MS275MS355M

were characterized by high values of γOV for 95% fractile (e.g.1.52, 156, 1.64,….).

The design provision effectively mitigated the high over-strength values at material level due, also, to the over-sizingoften imposed by seismic design provisions or when seismiccombination is not predominant.











Research Outcomes

Influence of upper limitation on fy

430

480

530

580

630

680

350 400 450 500

Tens

ile st

reng

th -

[MPa

]

Yielding stress - [MPa]

430

480

530

580

630

680

350 400 450 500

Tens

ile st

reng

th -

[MPa

]


Data have been analyzed also considering an additional quality control on EN10025 imposed on steel in dissipative zones by actual seismic codes

25.1,

max, ≤nomy

edissipativy

ffEN10025 EN10025 + ISO24314 (S345S)

Failure probability associated to collapse criteria was re-calculated with different upper limitation onyielding stress Re,H (fy)

-6%

-5%

-4%

-3%

-2%

-1%

0%

1%

2%

- 1,375 1,350 1,300 1,250

Varia

tion

of A

nnua

l Pfa

il(R

isk)

Limitation of fy - (fy,max/fy,nom)

3EBFX Br1 3EBFX Br2 3EBFY Br1 3EBFY Br2

-2%-1%0%1%2%3%4%5%6%7%8%

- 1,375 1,350 1,300 1,250

Varia

tion

of a

nnua

l Pfa

il(R

isk)

Limitation on fy - (fy,max/fy,nom)

3EBFX B1 3EBFX B2 3EBFY B1 3EBFY B4 3EBFY B5 3EBFY B8


430

480

530

580

630

680

350 400 450 500

Tens

ile st

reng

th -

[MPa

]


430

480

530

580

630

680

350 400 450 500

Tens

ile st

reng

th -

[MPa

]



25.1,

max, ≤nomy

edissipativy

ffEN10025 EN10025 + ISO24314 (S345S)


-40%

-35%

-30%

-25%

-20%

-15%

-10%

-5%

0%

5%

- 1,375 1,350 1,300 1,250

Varia

tion

of A

nnua

l Pfa

il(R

isk)



-5%

0%

5%

10%

15%

20%

25%

30%

- 1,375 1,350 1,300 1,250Va

riatio

n of

ann

ual P

fail

(Risk

)


4EBFX B1 4EBFX B3 4EBFX B4 4EBFX B6 4EBFY B1


430

480

530

580

630

680

350 400 450 500

Tens

ile st

reng

th -

[MPa

]


430

480

530

580

630

680

350 400 450 500

Tens

ile st

reng

th -

[MPa

]



25.1,

max, ≤nomy

edissipativy

ffEN10025 EN10025 + ISO24314 (S345S)


1,00E-07

1,00E-06

1,00E-05

1,00E-04

1,00E-03

1,00E-02

1,00E-01

1,00E+00

- 1,375 1,3 1,25

Failu

re p

roba

bilit

y es

timat

ion

Material Over-stength coefficient

14MRFX355 1_bottom 14MRFX355 3_bottom15MRFX355 3a_top 15MRFX355 5a_top

1,0E-06

1,0E-05

1,0E-04

1,0E-03

1,0E-02

1,0E-01

1,0E+00

- 1,375 1,350Upper limit - (fy,act/fy,nom)max

16EBFX B1 16EBFX B2 16EBFX B3 16EBFX Br1 16EBFX Br216EBFY B1 16EBFY B2 16EBFY B5 16EBFY B6 16EBFY Br116EBFY Br2 16EBFY Br3 16EBFY Br4

1,0E-07

1,0E-06

1,0E-05

1,0E-04

1,0E-03

1,0E-02

1,0E-01

1,0E+00

- 1,375 1,3 1,25Upper limit - (fy,max/fy,nom)max

Diag1L 10CBFY Link S5 10EBFX Diag1L 11CBFY Link S5 11EBFX


The pre-conditioning of material samples for the estimation of failureprobability (Pfail) associated to collapse modes showed in many casesonly a slight modification.

In particular, it was observed that the variation is in many cases of theorder of 5%; the low sensitivity of designed case studies to the upperlimitation of fy is related to the design process.

Only in one case, the complete optimisation of the design (Frame 4)produced a structure in which quite all design checks were equal toone: in such a case the variation of the failure probability was equal toabout 30%. It remains much lower for other cases.


-1%

0%

1%

2%

3%

4%

5%

6%

7%

8%

- 1,375 1,3 1,25

Varia

tion

of A

nnua

l Pfa

il(R

isk)


1_bottom 3_bottom 3a_top 5a_top

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

-5%0%5%

10%15%20%

- 1,375 1,350

Varia

tion

of A

nnua

l Pfa

il(R

isk)


16EBFX Br1 16EBFX Br2

16EBFY Br1 16EBFY Br2

16EBFY Br3 16EBFY Br4

-4,0%

-3,5%

-3,0%

-2,5%

-2,0%

-1,5%

-1,0%

-0,5%

0,0%

- 1,375 1,3 1,25

Varia

tion

of A

nnua

l Pfa

il(R

isk)


6MRFX235 6MRFX355 8MRFX355

-6%

-5%

-4%

-3%

-2%

-1%

0%

1%

2%

- 1,375 1,350 1,300 1,250

Varia

tion

of A

nnua

l Pfa

il(R

isk)



-2%-1%0%1%2%3%4%5%6%7%8%

- 1,375 1,350 1,300 1,250

Varia

tion

of a

nnua

l Pfa

il(R

isk)


3EBFX B1 3EBFX B2 3EBFY B1 3EBFY B4 3EBFY B5 3EBFY B8

-5%

0%

5%

10%

15%

20%

25%

30%

- 1,375 1,350 1,300 1,250

Varia

tion

of a

nnua

l Pfa

il(R

isk)


4EBFX B1 4EBFX B3 4EBFX B4 4EBFX B6 4EBFY B1

-1%

0%

1%

2%

3%

4%

5%

6%

7%

8%

- 1,375 1,3 1,25

Varia

tion

of A

nnua

l Pfa

il(R

isk)


1_bottom 3_bottom 3a_top 5a_top

-40%

-35%

-30%

-25%

-20%

-15%

-10%

-5%

0%

5%

- 1,375 1,350 1,300 1,250

Varia

tion

of A

nnua

l Pfa

il(R

isk)



Pfail associated tonot-dissipativeelements

Pfail associated todissipative elements

Influence of upper limitation on fy The pre-conditioning of material samples for the estimation of failure probability (Pfail)

associated to collapse modes showed in many cases a slight modification.

In particular, it was observed that the variation is in many cases of the order of 5%; thelow sensitiveness of designed case studies to the upper limitation of fy is related to thedesign process.

Only in one case, the complete optimisation of the design (Frame4) produced a structurein which quite all design checks were equal to one: in such a case the variation of thefailure probability was equal to about 30%. Other cases much lower.

The upper limitation on fy produced an increasing of Pfail associated to ductile collapsemodes while protected members as braces presented a decreasing of probabilityassociated to their collapse modes.

An upper limitation of fy about 1.375÷1.30 showed a balance between ductile and brittlefailure modes guaranteeing a not negligible decreasing of Pfail associated to protectedmembers (only braces because columns where over-sized, i.e. Pfail ~0)

Definition of an upper limitation at production level anyway showed a small improvementof existing situation, combining EN10025 and EN1998, already judged as generally safefor all case studies

Capacity Design and γOV effectiveness Results coming from IDA analyses were also used to assess the effectiveness of

(material) over-strength factor in the capacity design framework as proposed by EN1998.

Following analysis was performed in order to test the ability of capacity design in theprediction of real internal solicitations regime inside protected members as columns orbraces

EelSdOV

GelSdEd EEE ,, 1.1 ×Ω××+= γ

Internal forces, coming from IDA, were used as reference (‘real’) forces; γOV wasconsidered as a design parameter to be varied; EG and EE are the solicitations comingfrom the design in the seismic combination: gravity and earthquake contribution.

The statistical distribution of G function was analyzed considering different γOV values

( )irealIDA

designeliEOV

designeliG

gOV EEE

aXG,,

.,min

., 1.1

,,×Ω××+

=γ

γ

Capacity Design and γOV effectiveness

0

20

40

60

80

100

120

140

1.14

1.16

1.18

1.20

1.22

1.24

1.26

1.28

1.30

1.32

1.34

1.36

1.38

1.40

1.42

1.44

1.46

1.48

1.50

1.52

1.54

1.56

Stat

istic

al o

ccur

ence

Value of limit state function - G(X,γOV)

0

20

40

60

80

100

120

140

1.09

1.11

1.13

1.15

1.17

1.19

1.21

1.23

1.25

1.27

1.29

1.31

1.33

1.34

1.36

1.38

1.40

1.42

1.44

1.46

1.48

1.50

Stat

istic

al o

ccur

ence


0

20

40

60

80

100

120

140

1.05

1.07

1.09

1.11

1.12

1.14

1.16

1.18

1.20

1.22

1.24

1.25

1.27

1.29

1.31

1.33

1.35

1.37

1.38

1.40

1.42

1.44

Stat

istic

al o

ccur

ence


The introduction of real forces obtained from IDA allowed the statistical analysis of thelimit state function G(X,γOV,ag)

γOV=1.35 γOV=1.25 γOV=1.15

Then the estimation of probability, that the capacity design formula was not able in theprediction of real forces, allowed the definition of fragility curves combining prob. andp.g.a. of seismic action.

00.10.20.30.40.50.60.70.80.9

1

0.00 0.20 0.40 0.60 0.80 1.00 1.20

Exce

edan

ce P

roba

bilit

y Re

al F

orce

> C

.D. F

orce

Peak Ground Acceleration - [g]

γOV protection in C.D. framework

1.50 1.45

1.40 1.35

1.30 1.25

1.20 1.15

1.10

The C.D. approach with γOV equal to 1.25 seemsappropriate: in the column and braces IDA forcesresulted in many cases much lower than capacitydesign with materials characterized by high over-strength. This means that in C.D. γOV works atstructural level and not directly related to material

Mean value

Standard deviation

5% 95%

1.40 0.070 1.30 1.52

1.20 0.060 1.11 1.30 1.17 0.060 1.07 1.26

1.08 0.040 1.02 1.14 1.46 0.100 1.31 1.64 1.32 0.120 1.14 1.56 1.32 0.080 1.18 1.44

1.18 0.060 1.08 1.291.32 0.083 1.06 1.191.12 0.030 1.16 1.47

Percentile

Steel Quality

S235J0JR (+M)(*)

S275J0JR (+M)(*)

S355J0 (+M)S460M

S235J0JR (+M)S275J0JR (+M)S355J2K2 (+M)

S460MS275MS355M

Conclusions and perspectives

The probability levels associated to all relevant collapse modes were lower than thefixed acceptance limit (i.e. defined as nominal probability) showing a good fit betweenEN10025 and EN1998-1-1.

This was essentially due to the oversize of steel sections induced by the capacitydesign procedure and to the higher yielding threshold presented by steel products withrespect to nominal values assumed in the design.

The introduction of an upper limit on fy as additional check for the seismic qualificationof EN10025 steel products results in a moderate improvement of the of mitigation ofexceedance probability associate to brittle collapse modes (e.g. Buckling of protectedmembers).

On the contrary the exceedance probability associated to ductile collapse modesincreased significantly (e.g. Exhaustion of plastic deformation).

Fictitious upper value equal to 1.25 would produce a too high increment of Pfailassociated to ductile modes, while the decrement of Pfail associated to brittle modes forlimits lower than 1.35 does not change.

Conclusions and perspectives

It is also important to underline that the capacity design approach properly worksadopting γOV equal to 1.25 also with steel product that have an upper fractile (95%) ofmaterial overstrength equal to 1.4 or higher.

This means that coefficients inserted in C.D. formula works at structural level and thatany possible future upper limitation on fy at the production level cannot be directlytransferred in the C.D.

More appropriate appears to modify C.D. formula using an over-strength coefficientrelated to ductility behaviour, structural type or other parameter, γRD

EelSdRD

GelSdEd EEE ,, 1.1 ×Ω××+= γ

selection of the appropriate steel quality for efficient

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