Nonlinear Finite Element Analysis of 3D Reinforced Concrete Beam-Column Joints Background and...

www.sgh.com

Nonlinear Finite Element Analysis of 3D Reinforced Concrete Beam-Column Joints

James B. (Ben) Deaton, Ph.D.

26 November 2013

Simpson Gumpertz & Heger Inc.www.sgh.com

Background and MotivationPrototype Constitutive Model in DIANA

Analysis of Beam-Column JointsCritical Appraisal and Recommendations

My Background and Contact Information

Graduate school at Georgia Institute of TechnologyPh.D. completed in 2012 in structural engineeringResearch in nonlinear constitutive modeling of concreteAdvised by Dr. Kenneth M. Will

Simpson Gumpertz & Heger, Inc.Joined Boston office in early 2013We design, investigate, and rehabilitate structures.Engineering Mechanics & Infrastructure (EMI) divisionHigh-end consulting service in engineering mechanicsApplication of state-of-the-art research and technology

Contact information:SGH: http://www.sgh.comEmail: JBDeaton@sgh.comLinkedIn: http://www.linkedin.com/in/bendeaton/

Ben Deaton NLFEA of Reinforced Concrete Beam-Column Joints

Simpson Gumpertz & Heger – Capabilities

Performance of Joints in EarthquakesVulnerability of Corner Beam-Column JointsState-of-the-art: Beam-Column Joint ModelingResearch Needs and Objectives

Outline

1 Background and MotivationPerformance of Joints in EarthquakesVulnerability of Corner Beam-Column JointsState-of-the-art: Beam-Column Joint ModelingResearch Needs and Objectives

2 Prototype Constitutive Model in DIANA

3 Analysis of Beam-Column Joints

4 Critical Appraisal and Recommendations

Reconnaissance Photos of Earthquake Joint Failure

Nonseismic Joint Design Details (pre-1970s)Beres, Pessiki, White, & Gergely (1996)

1 Column reinforcement ratio < 2%2 Column lap splices just above floor

level3 Widely spaced column ties4 No transverse shear reinforcement in

joint5 Insufficient beam bottom bar

anchorage6 Construction joints adjacent to joint7 Strong beam / weak column behavior

Previous Tests of Nonseismically Detailed Joints

Typical Joint Tests:

One-way, planar joints

No transverse beams

No floor slab

1/8 to 2/3 scale models

Unidirectional cyclic load

Quasistatic loading

Significant simplifications!

!"#$ %&'%$()*%$

$%&! '()*+! ,%(-*! )*!.)/01&!234!%5,! 1&)*6(17&8&*+!9&+5):,!8&&+)*/! +%&! 1&;0)1&8&*+,!(6! +%&!4<2=!

>?@!?(9&3! !$%),!9&+5):! 1&A1&,&*+,!5!B&1C!/((9!9&,)/*!6(1! +%5+! +)8&!90&! +(! +%&! :51/&!%((D,! +%5+!

7(**&7+! +%&! E&58! +(! +%&! 7(:08*3! ! $%),! 9&+5):! -5,! 0,&9! +(! 9&B&:(A! +%&! ,+10+F5*9F+)&! 8(9&:!

9),70,,&9!)*!+%),!?%5A+&13!!$%&!7(*71&+&!7(8A1&,,)B&!,+1&*/+%!0,&9!)*!+%&!5*5:C,),!-5,!6!7!G!HIH<2!

A,)I!(E+5)*&9!61(8!+&,+,!(6!+%1&&!7C:)*9&1,!'0,+!A1)(1!+(!+&,+)*/!+%&!'()*+3! !$%&!C)&:9!,+1&,,!(6!+%&!

B51)(0,!,)J&,!(6!,+&&:!E51,!-5,!5:,(!(E+5)*&9!61(8!+&,+,!5*9!),!,%(-*!)*!$5E:&!K3K3!!

$%&!7(:08*!-5,!,0E'&7+&9!+(!5!,+5+)7!5L)5:!:(59!(6!>!G!K"M!D)A,I!5*9!+%&!E&58!-5,!7C7:&9!

0A!5*9!9(-*!)*!5!;05,)F,+5+)7!7C7:)7!65,%)(*!0*+):!65):01&!(77011&93!!$%&!85L)808!:(59!7511)&9!

EC!+%&! '()*+!901)*/! +%&!&LA&1)8&*+!-5,!N!G!HK!D)A,3! !$%&! :(75+)(*!(6!5L)5:! :(59I!>I!5*9!:5+&15:!

:(59I! NI! ),! ,%(-*! )*! .)/01&! 23KI! -%)7%! 5:,(! ,%(-,! +%&! +&,+! ,&+0A3! ! $%&! ,+10+F5*9F+)&! 8(9&:!

9&B&:(A&9!-5,!E5,&9!(*!+%&!0A-519!,+1(D&3! !$%&!1&,0:+,!6(1! +%&!9(-*-519!,+1(D&!51&!+%&!,58&!

90&!+(!+%&!,C88&+1C!(6!+%&!'()*+3!!!

+,-"$!"#$$%./0$/.012$

More realistic experimental studies conductedPampanin et al. (2010): of 45° to the principal axis! of the column at the particular drift

level. ! is the measured angle of any points to the principal axesalong the loading path. The loading protocol is illustrated inFig. 6.

The axial load was applied by means of a vertical hydraulicactuator, acting on a steel plate connected to the column baseplate by vertical external post-tensioned bars. Following the test-ing procedure recommended by Pampanin et al. "2007a! forpoorly detailed exterior beam-column joint, the axial load, N, wasvaried around the gravity load value "i.e., based on tributary area!in proportion to the lateral force acting on the column, Vc, as itwould occur due to the frame lateral sway: N=Ngravity"#Vc. Theproportionality coefficient # is a function of the geometry of thebuilding "i.e., number of stories, and number and length of bays!and can be derived by simple hand calculations or pushoveranalyses of the prototype frame.

The two test series were performed under different axial loadlevels in order to investigate the effect of prototype building con-figurations on the performance of the specimens: Set 1 specimenswere subjected to moderate variation of axial load with tributarygravity load of 75 kN with varying axial load coefficient # of 1.8,whereas Set 2 specimens were tested under high variation of axialload corresponding to 110 kN of gravity load and # coefficient of4.63 and 2.35 for 2D and 3D specimens, respectively.

It is important to note that a constant-axial load of 75 kN

Fig. 4. Sequence of implementation of the GFRP retrofit intervention as illustrated in Fig. 3

Fig. 5. Test setup for quasi-static cyclic testing under uni- orbi-directional loading regime

Fig. 6. Bidirectional load history: "a! loading pattern; "b! displacement components; and "c! schematic representation of rose curve load path

JOURNAL OF COMPOSITES FOR CONSTRUCTION © ASCE / JANUARY/FEBRUARY 2010 / 97

Downloaded 16 Jan 2010 to 130.207.50.192. Redistribution subject to ASCE license or copyright; see http://pubs.asce.org/copyright

Park & Mosallam (2010): Engindeniz (2008):

#$%&'(!)*)!+!,(-.!-(.&/*!

0('(!12230(4*!

,5(! 2314$6%! /'37(4&'(! -$8&21.(4! 1! 7972$7! 21.('12! 2314$6%! 3:! 1! ;&$24$6%! 71''9$6%!

-('<$7(! %'1<$.9! 2314-*! ='$3'! .3! .5(! 7972$7! 2314$6%! 3:! .5(! ;(18->! 1! 732&86! 1?$12! 2314! 3:!

@AB! 3:! .5(! 732&86C-! 738/'(--$<(! 2314! 71/17$.9! 01-! 1//2$(4>! 164! ;3.5! ;(18-! 0('(!

;'3&%5.!.3!1!6(%1.$<(!D430601'4E!4$-/217(8(6.!2(<(2!.51.!'(-&2.(4!$6!1!-.'36%F1?$-!;(18!

838(6.! 738/1'1;2(! .3! .51.! (-.$81.(4! .3! 377&'! $6! .5(! 834(2(4! :'18(! ;&$24$6%! &64('!

-('<$7(!2314-*!,5(!;(18-!0('(!.5(6!7972(4!1'3&64!.5$-!4(:3'8(4!/3-$.$36!1.!4$-/217(8(6.!

2(<(2-!73''(-/364$6%!.3!GA*H)B>!G@*IAB>!164!G@*JKB!$6.('-.3'9!4'$:.!'1.$3-!1-!-5306!$6!

#$%&'(!)*I*!,3!;(..('!16129L(!.5(!(::(7.-!3:!;$4$'(7.$3612!2314$6%>!&6$4$'(7.$3612!2314$6%-!

$6! .5(!MN! 164! .5(6! .5(!OP! 4$'(7.$36-!0('(! /(':3'8(4! :$'-.*! ,5(! 1//2$(4! 4$-/217(8(6.!

2(<(2-! 0('(! -(2(7.(4! 1-! @*A>! @*">! 164! Q*A! .$8(-! .5(! 4$-/217(8(6.! 1.! :$'-.! 9$(24! D !! E!

8(1-&'(4!4&'$6%! .5(!&6$4$'(7.$3612! 2314$6%! 3:!P/(7$8(6!@*!,(-.$6%!3:!P/(7$8(6!Q!01-!

.('8$61.(4! 1:.('! .5(! G@*IAB! 4'$:.! 7972(-! D1.! /3$6.! H7! $6! #$%&'(! )*IE! .3! '(/'(-(6.! 1! 2(--!

-(<('(!4181%(!2(<(2!.516!P/(7$8(6!@!$6!.5(!-&;-(R&(6.!'(.'3:$.!-.&4$(-!05$75!1'(!3&.-$4(!

.5(!-73/(!3:!.5$-!751/.('*!

Tests of nonseismically detailed joints with floor membersunder bidirectional loading resulted in damage modesoverlooked in simplified one-way tests.

Value of Finite Element Analysis of Deficient Joints

Challenges of full-scale experimental studies:Significant cost: time and moneyParametric investigation prohibitive

NLFEA provides useful complementRapidly assess various configurationsInternal representation of state-of-stress, damageprogression and force-transfer mechanisms

Literature Survey: Types of Joints Analyzed

Type I (19) Type II (17) Type III (3) Type IV (9)

Type V (6) Type VI (1) Type VII (2) Type VIII (4)

Type IX (1) Type X (2) Type XI (2) Type XII (1)

Need for Numerical Analysis of Deficient Joints

Realistic joints have not been analyzedIt is not known whether NLFEA is suitable for simulation ofseismically deficient jointsACI 352R-02 cites need for further in-depth study ofnonseismically detailed jointsValidation now possible with recent experimental studiesNumerous immediate applications:

Parametric investigations of factors affecting joint failure,design of innovative rehabilitation measures, planning ofexperiments, calibration of simplified models, advancementtoward predictive nonlinear analysis.

Research Question and Objectives

Research sought to answer:

Can nonlinear FEA simulate the cyclic response of realistic RCbeam-column joints with seismic deficiencies?

Research Objectives1 Assemble a prototype model suitable for joint simulation

Lit review, experimental validation, & parameter studies2 Analyze four seismically deficient exterior corner joints.

Increasing complexity and deficiencySlab, transverse beams, bidirectional lateral loading, cycliccolumn compression, and multiple seismic deficiencies

3 Critical appraisal of prototype model.

Concrete Constitutive FrameworkSteel Reinforcement Plasticity ModelBond-Slip and Anchorage ResponseShear Failure

Outline

1 Background and Motivation

2 Prototype Constitutive Model in DIANAConcrete Constitutive FrameworkSteel Reinforcement Plasticity ModelBond-Slip and Anchorage ResponseShear Failure

Software and Constitutive Model Selection

DIANA Release 9.4.4Total strain rotating crack model by Selby & Vecchio (1997)

Stress-strain relationships evaluated in the principaldirections of the strain tensorCrack orientations allowed to “rotate” during analysisProven approach for shear-dominated failure mechanisms

Cyclic responseUnloading/reloading follows the secant stiffness

Evolution of compressive strength4-parameter Hsieh-Ting-Chen plasticity modelIncrease due to lateral confinement (Selby 1996)Decrease due to prior lateral cracking (Vecchio 1993)

Mat’l properties: Ec (ACI), ft (MC90), Gf (Remmel)

Compression Response

Thorenfeldt (1987) compression hardening/softening function

σ = f ′c

(εε0

n−1+(

ε0 =f ′cEc· n

n−1 n = 0.80 +f ′c17 k =

{1.0 , ε0 > ε

0.67 +f ′c62 ≥ 1.0, ε > ε0

0.000 0.001 0.002 0.003 0.004 0.005 0.006

Strain (mm/mm)

0.000 0.002 0.004 0.006 0.008 0.010

Strain (mm/mm)

Karsan & Jirsa (1969) Sinha et al. (1964)

Tension Response

Hordijk (1991) tension softening function

σcr = ft[(

c1εcrεult

c2εcrεult

)− εcrεult

(1 + c13)e−c2

]εult = 5.136 Gf

hftc1 = 3 c2 = 6.93

0.0000 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006 0.0007

Strain (mm/mm)

0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030 0.0035 0.0040

Displacement (mm)

Gopalaratnam & Shah (1985) Reinhardt (1984)

Steel Reinforcement Model – Von Mises Plasticity

Isotropic, kinematic, mixed, or no hardening (EPP)Bauschinger effect (Menegotto-Pinto / Monti-Nuti)Verification with Ma, Bertero, and Popov (1976):

f (σ, κ) =√

3J2 − σ̄(κ) g ≡ f b = EshE = 0.02

0.01 0.00 0.01 0.02 0.03 0.04 0.05

Strain (mm/mm)

0.01 0.00 0.01 0.02 0.03 0.04 0.05

Strain (mm/mm)

Bond Slip Simulation

Modeling approach for bond-slip in DIANA:

Line-to-solid interface (spring) elements connect steel to concrete

Nonlinear (multi-linear) shear-slip backbone curve (only input req’d)

Prototype bond-slip law: CEB-FIP Model Code 1990 Guidelines

ing analyses a fixed value, equal to 0.2, was assumed for suchparameter. The Hordijk’s model for the softening behavior in ten-sion was adopted, where the fracture energy Gf is assumed as aninput property of the material and the crack band is related tothe characteristic element length h (Fig. 7). Regarding the compres-sive behavior the Thorenfeldt’s model [15] was adopted, and theeffects of confinement and of lateral cracking were taken into ac-count. Such a model is based on Popovics’ relationship [16] andmodified by adjusting the descending branch of the concretestress–strain law to ensure a steeper descending part of the curvefor high-strength concrete.

The interface between the bar and the surrounding concretewas simulated with specific zero-thickness elements (springs),which can be used in both 2D and 3D problems. The behavior ofsuch elements is expressed in terms of tangential stresses vs. rela-tive slip of the node, respectively, on the top and on the bottom ofthe element. In this paper the proposed bond stress–slip relation-ship for long anchored bar has been adopted. It is worth notingthat, similarly to the MC90 formulation [3], the proposed relation-ship is not properly a ‘‘constitutive law’’ of the bar-concrete inter-face but rather an average formulation able to reproduce thestructural behavior of the concrete–bar assembly under specificconditions.

Finally, regarding the steel elements, an elasto-plastic modelwith isotropic hardening was used.

All the details of the concrete and steel constitutive laws and ofthe adopted software may be found in Ref. [11].

4. Validation of the bond-slip formulation

4.1. Engström’s tests

A number of pull-out tests on long anchored bars, addressed toinvestigate the effects of confinement on bond capabilities was car-ried out by Engström et al. [7]. The aim of such an experimentalcampaign was to study the anchorage behavior of ribbed bars inlinear structural members (i.e. beams and columns) in normaland high strength concrete. Several tests were performed varyingthe concrete cover, from a maximum of 12 bar diameter (well con-fined condition) to 1 bar diameter (splitting failure).

Here the results relative to the well confined specimen are con-sidered: a 16 mm diameter rebar was embedded for 290 mm along

fracture energy

traction

gf =Gf /h!j

compression

Fig. 7. Loading–unloading path for concrete smeared crack model.

CONCRETESPECIMEN

STEEL REBAR

SUPPORT BEAM

DISPLACEMENTTRASDUCER

HYDRAULIC JACKLOAD GAUGE

Fig. 8. Engström’s tests set up [7].

Table 2Materials properties in Engström’s tests.

Concrete Steel

Test fcm[MPa]

fctm Gf

[N/mm]fy[MPa]

Eel[MPa]

ft[MPa]

et ‰

N290a 26 2.1 0.11 569 2E6 648 140N290b 30 2.5 0.11

0 2 4 6 8 10 12 140

slip [mm]

N290b exp.

N290b F.E.long anch.

yield capacityN290a exp.

N290a F.E.long anch.

N290b F.E.short anch.N290a F.E.short anch.

tensile capacity

Fig. 9. Experimental tests and numerical simulation of Engström’s pull-out tests.

CADWELD COUPLER

CONCRETE BLOCK

CONCRETEBLOCK

LOAD CELL

HYDRAULIC JACKFOR AXIAL LOADING

(1330kN)

HYDRAULICJACK (530KN)

HYDRAULICJACK (530KN)CONCRETE

LOAD CELLHORIZONTALSUPPORTS

CONCRETEBLOCK

TIE DOWNSTRAPS

Fig. 10. Viwathanatepa’s tests set up [13].

Table 3Materials properties in Viwathanatepa’s tests.

Concrete Steel

fcm [MPa] fctm [MPa] Gf [N/mm] fy [MPa] Eel [MPa] ft [MPa] et ‰

30 2.5 0.06 460 2E6 700 120.0

E. Mazzarolo et al. / Engineering Structures 34 (2012) 330–341 333

Eligehausen, Bertero, & Popov (1983) DIANA Cyclic Bond RulesBen Deaton NLFEA of Reinforced Concrete Beam-Column Joints

Cyclic Bond-Slip Validation — Viwathanatepa (1979)Verification of Cone Formation (Pull-Out Failure)

Cyclic Anchorage Response of Hooked BarsVerification with Hawkins, Lin and Ueda (1987)

15” 66”

18” 3” 3”

#8 bars

#3 ties

2.125”

#8 bar

#6 bars

Cyclic Anchorage Response of Hooked BarsVerification with Hawkins, Lin and Ueda (1987)

4 2 0 2 4 6 8 10

Displacement (mm)

Shear Failure

Can the prototype model capture shear-dominated failure?Investigate the response of panels subjected to shearData from tests at University of Toronto (Vecchio 1999)

Shear Panel Response – Vecchio (1999)Panel Finite Element Mesh and Boundary Conditions

Shear Panel Response – Vecchio (1999)Shear Stress-Strain Response

0.000 0.001 0.002 0.003 0.004 0.005

Shear Strain (mm/mm)

Shear Panel Response – Vecchio (1999)Observed vs. Predicted Crack Pattern

Summary of Validated Model Parameters in DIANA

Type Model CharacteristicSoftware DIANA 9.4.4Concrete framework Total strain rotating crack modelConcrete constitutive theory Selby and Vecchio (1997)Tension softening Hordijk et al. (1991)Tension stiffening Vecchio (1993)Compression softening Thorenfeldt (1987)Concrete Elastic Modulus ACI 318Concrete Tensile Strength CEB-FIP Model Code 1990Concrete Fracture Energy Remmel (1994)Concrete element HX24LSteel framework Von Mises plasticityHardening type KinematicHardening ratio 0.02Steel element L6TRU/L13BEBond Response CEB-FIP Model Code 1990Bond interface element HX30IFNonlinear solution type Quasi-newton, Broyden formulationMax # iterations 1000 (20-30 iterations typical)

1-Way Exterior Joint – Pantelides et al. (2002)2-Way Corner Joint – Akgüzel et al. (2011)2-Way Corner Joint w/ Slab – Park et al. (2010)2-Way Corner Joint w/ Slab – Engindeniz et al. (2008)

Outline

3 Analysis of Beam-Column Joints1-Way Exterior Joint – Pantelides et al. (2002)2-Way Corner Joint – Akgüzel et al. (2011)2-Way Corner Joint w/ Slab – Park et al. (2010)2-Way Corner Joint w/ Slab – Engindeniz et al. (2008)

Joint Response Definitions

Displacement

nxminnxFminn

xFmaxnxmaxn

xminnxFminn

Kppn =Fmaxn−Fminn

xFmaxn−xFminn

τ ′jh =Cb−Vc

hb·hc√

f ′cγave = ∆∠ABC−∆∠BCD+∆∠CDA−∆∠DAB

Experiment conducted by Pantelides et al. (2000)

One-way half-scale exterior joint

Designed per ACI 318-63

No joint transverse reinforcement

Beam reinforcement ratio increasedto induce joint shear failure

Column lap splice

Quasistatic cyclic loading

Column compression = 0.10f ′c Ag

f ′c = 6700 psi

Tested at University of Utah