probabilistic fracture mechanics based design of seismic

Probabilistic Fracture Mechanics Based Design of Seismic Column Splices

Amit Kanvinde

Kimberly Stillmaker (UC Davis)

Carmine Galasso

(University College London)

24th June, 2016 Hydra, Greece

Acknowledgments

• Dimitrios!! • Sean Shaw (former PhD student) • American Institute of Steel

Construction • Jim Malley (Degenkolb) • Mark Saunders (Rutherford and

Chekene) • AISC Committee on Seismic Effects • Herrick Corporation

Earthquake induced fracture in steel structures (Northridge)

Photo Acknowledgment - AISC

4 Sharp crack like flaw – resulting in fracture

Earthquake induced fracture in steel structures (Northridge)

Pre-Northridge column splices

Partial Joint Penetration (PJP) welds

Risk of fracture

Elimination of notch (use only CJP)

Use of notch tough weld filler material and base metal

2010 AISC Seismic Provisions

For Intermediate Moment Frames and Special Moment Frames “Where welds are used to make the splice, they shall be complete-joint-penetration groove welds.”

Currently required

Inconvenient field weld

13


14


Excellent performance of tough, PJP welded base plates and other details

Can we use PJPs in splices? If so, under what conditions?

The aim – a safe and reliable PJP welded splice

Understanding of seismic stress demands and uncertainty

The aim – a safe and reliable PJP welded splice

Understanding of fracture stress capacity and uncertainty

Understanding of seismic stress demands and uncertainty

Stress

Distance ahead of crack

Fracture occurs

if KI (which

characterizes

the stress field)

exceeds KIC

(a material

property)

High KI

Lower KI

To understand capacity, fracture mechanics is necessary

What stress does the splice fracture at?

𝜎𝑓𝑟𝑎𝑐𝑡𝑢𝑟𝑒 = 𝑓( 𝐾𝐼𝐶, 𝑎, 𝑡𝑢𝑝𝑝𝑒𝑟 , 𝑡𝑙𝑜𝑤𝑒𝑟)

Conceptually



Conceptually

Material Toughness (CVN – KIC)



Conceptually


Crack Length



Conceptually


Crack Length

Geometry

How to determine 𝜎𝑓𝑟𝑎𝑐𝑡𝑢𝑟𝑒 in a general

manner?

1. Experiments - Expensive - Limited data set in terms

of geometry, material properties

- 5 full scale experiments = 1 PhD + $200K


manner?

2. Finite Element Simulations - Allow investigation of

many parameter sets But, - Not tests! - Still a bit expensive

25 simulations = 30-40 weeks


manner?

2. Finite Element Simulations - Allow investigation of

many parameter sets But, - Not tests! - Still a bit expensive

25 simulations = 30-40 weeks

35 40 45 50 55 60 65 70 75 8035

40

45

50

55

60

65

70

75

80

Str

ess f

rom

Full

Scale

Te

st at

Failu

re

Stress from FEM


manner?

- Can characterize any

configuration - Introduces additional

error

s capacity,estimate

flange =KIC

p ´ (h / 2x )´ tupper

´1

x a ´ f1(h)´ f2(x )´ g1(h)´ g2(x )

0 10 20 30 40 50 60 700

10

20

30

40

50

60

70

Str

ess fro

m F

EM

Stress from Formula

3. Semi-analytical regressed expressions

Monte Carlo simulations to characterize capacity

s capacity,estimate

flange =KIC


´1

x a ´ f1(h)´ f2(x )´ g1(h)´ g2(x )

Sources of uncertainty (simulated as RVs):


s capacity,estimate

flange =KIC


´1

x a ´ f1(h)´ f2(x )´ g1(h)´ g2(x )


Material toughness


s capacity,estimate

flange =KIC


´1

x a ´ f1(h)´ f2(x )´ g1(h)´ g2(x )


Material toughness

CVN is random

CVN KIC conversion error


s capacity,estimate

flange =KIC


´1

x a ´ f1(h)´ f2(x )´ g1(h)´ g2(x )


Material toughness

CVN is random


Geometry


s capacity,estimate

flange =KIC


´1

x a ´ f1(h)´ f2(x )´ g1(h)´ g2(x )

flange

estimatecapacityflange

estimatecapacity

flange

FEMcapacity

flange

FEMcapacity

flange

truecapacityflange

truecapacity ,

,

,

,

,

,


Material toughness

CVN is random


Geometry

35 40 45 50 55 60 65 70 75 8035

40

45

50

55

60

65

70

75

80

Str

ess f

rom

Full

Scale

Te

st at

Failu

re

Stress from FEM

0 10 20 30 40 50 60 700

10

20

30

40

50

60

70

Str

ess fro

m F

EM

Stress from Formula

Errors in FE and semi-analytical

relationship

Application

s capacity,estimate

flange =KIC


´1

x a ´ f1(h)´ f2(x )´ g1(h)´ g2(x )

Toughness

Geometry f

capacity

Is this Pf acceptable?

Application

s capacity,estimate

flange =KIC


´1

x a ´ f1(h)´ f2(x )´ g1(h)´ g2(x )

capacity

f

demand

Toughness

Geometry

Assessment of splice safety

f

Pf is acceptable if - 85% Penetration is maintained - Thicker flange is 15% thicker than

thinner flange - Some other detailing considerations

demand

Is this Pf acceptable?

capacity

Summary • NLTHA to determine demands • Full scale experiments • Fracture mechanics simulations • Reliability analysis • Determination of acceptable geometries • For the first time since 1994, cracks are explicitly

allowed in demand critical welds in seismic steel structures in the USA

Thank you for your attention!

probabilistic fracture mechanics based design of seismic

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