1

Beam-Column Connections

Dawn Lehman

John Stanton and Laura Lowes University of Washington, Seattle

Jack MoehleUniversity of California, Berkeley

Force demands on joint

(a) moments, shears, axial loads acting on joint

(b) internal stress resultants acting on joint

Ts2 =1.25Asfy

C2 = Ts2

Ts1 = 1.25Asfy

C1 = Ts2

(c) joint shear

Vcol

Vcol

Vcol

Ts1 C2

Vu =Vj = Ts1 + C1 - Vcol

Vb1 Vb2

Beam

lnbV

wMpr

Mpr

Vp

Mpr

Vp

lc

Vcol

VcolMoehle

Classification/type

interior exterior corner

cont. column 20 15 12

Roof 15 12 8

Values of γ (ACI 352)

Joint shear strength- code-conforming joints -

hbfVV jcnu'φγφ ==

φ = 0.85

ACI 352

Current ACI seismic design provisions

Column Ties Continuous

Through Joint

hc/db> 20

Vu calculated using 1.25fy

' ( )n c jV f psi Aγ=

n uV Vφ >

ACI-318 02

Older-type beam-column connections Joint damage in previous eq.

2

-2.0 0E -01

0.00 E+ 00

PerformanceLevel

SeismicHazardLevel

+

SELECT PERFORMANCE OBJECTIVE

Seismic evaluation process

DEMAND ASSESSMENT

=

TST

VCCST

TSRCSL

Vj

VL

γ

DEMAND/PERFORMANCE RELATIONSHIPS

+

Seismic evaluation process:

Behavior

Experimental studies of older joints

Interior joint

No joint ties

Bars grooved

hc/db = 20

2/3 of full scale

P/(Agf’c) = 0.1

Study Parameters

Joint Shear StressDisplacement History

Interior joint

No joint ties

Bars grooved

hc/db = 20

2/3 of full scale

P/(Agf’c) = 0.1

Study Parameters

Joint Shear StressDisplacement History

Walker, Lehman and Stanton

-80

-60

-40

-20

0

20

40

60

80

-6 -4 -2 0 2 4 6

Col

umn

Shea

r (K

)

0.5% Drift 3% Drift

5% Drift

Damage progression

Walker, Lehman and Stanton

Standard Loading Impulsive Loading

Damage at 5% drift

Walker, Lehman and Stanton

Influence of joint shear stress

PEER-0850 PEER-4150PEER-0995Low Demand Intermediate Demand High Demand

Alire, Walker, Lehman and Stanton

3

Joint shear demandEffect on response

Join

t Stre

ss (p

si)

0

400

800

1200

1600

0 1 2 3 4 5 6

Drift Ratio (%)

Yield

Yield

• Joint “strength” closely linked to beam flexural strength• Plastic deformation capacity higher for lower joint shear

Alire, Walker, Lehman and Stanton

Joint shear “strength” Effect on damage mode and cyclic capacity

/fc’

0

0.1

0.3

0.4

0 10 20 30 40 50 60

Λ

0.2vj

Beam Hinging/Beam Bar Slip

Joint Shear Failure

Joint failure without yielding near 25.5√f’c

Failure forced into beams between 8.5√f’c and 11√f’c

Alire, Lehman and Stanton

Damage progressionexterior connections

Pantelides, 2002

Exterior jointhook detail

hook bent into joint

hook bent out of joint

Joint behaviorexterior connections

2 Clyde6 Clyde4 Clyde5 Clyde5 Pantelides6 Pantelides6 HakutoPriestley longitudinalPriestley transverse

psif

v

c

jo ,'

int

15

0 1 2 3 4 5 6 7

10

5

0

Drift, %bidirectional loading

Unreinforced Joint Strength

bhfV cj'γ=

γjointgeometry

4

6

10

8

12

FEMA 356 specifies the following:

• No new data. Probably still valid.

• Assuming bars are anchored in joint, strength limited by strength of framing members, with upper-bound of γ ≈ 15. For 15 ≥ γ ≥ 4, joint failure may occur after inelastic response. For γ ≤ 4, joint unlikely to fail.

• Assuming bars are anchored in joint, strength limited by strength of framing members, with upper bound of γ ≈ 25. For 25 ≥ γ ≥ 8, joint failure may occur after inelastic response. For γ ≤ 8, joint unlikely to fail.

4

Seismic evaluation process:

Demand/capacity assessmentEvaluation of FEMA-356 modelinterior connections

0

2

4

6

8

10

12

14

16

18

0 0.005 0.01 0.015 0.02 0.025 0.03

Joint Shear Strain

Join

t She

ar F

acto

r

FEMAPEER-14CD15-14CD30-14PADH-14PEER-22CD30-22PADH-22

Alire, Walker, Lehman and Stanton

0

20

40

60

80

100

120

1 4 7 10 13 16 19 22 25 28 31 34

Cycle Number

Perc

ent C

ontr

ibut

ion

Joint Shear

Bar Slip

Beam

Column

Specimen CD15-14

Contributions to driftinterior connections

“Joints shall be modeled as either stiff or rigid components.” (FEMA 356)

Walker, Lehman and Stanton

Simulation models: simple spring

Secant Shear Modulus of Joint

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 5 10 15

Shear Stress Demand (MPa)

Gse

c/G

el

CrackingYieldingSpalling

Alire, Lehman and Stanton

Suggested envelope relationinterior connections with continuous beam bars

psif

v

c

jo ,'

int 25

20

15

10

5

0

0.015

0.04 0.02

8

strength = beam strength but not to exceed

psifc ,25 '

stiffness based on effective stiffness to yield:

Moehle

0.3 0.05 cG−

Suggested envelope relationexterior connections with hooked beam bars

psif

v

c

jo ,'

int 25

20

15

10

5

0

0.010

0.02

strength = beam strength but not to exceed psifc ,12 '

stiffness based on effective stiffness to yield

0.01

connections with demand less than have beam-yield mechanisms and do not follow this model

'4 cf

axial-load stability unknown, especially under high axial loads

Moehle

5

Simulation models: simple spring

-100

-80

-60

-40

-20

0

20

40

60

80

-6.00 -4.00 -2.00 0.00 2.00 4.00 6.00

Drift (%)

Col

umn

shea

r (k)

PEER 1450 eyl

Yield of BeamLongitudinal Reinforcement

-80

-60

-40

-20

0

20

40

60

80

-4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0

Drift (%)

Col

umn

shea

r (k

)

PEER 1450 Inelastic Damage Pts Rigid

InitialSpalling

Yielding

Cracking

-80

-60

-40

-20

0

20

40

60

80

-6.0 -4.0 -2.0 0.0 2.0 4.0 6.0

Drift (%)

Col

umn

shea

r (k

)

CD30 1450 Inelastic Damage Pts

Initial Spalling

Yielding

Anderson, Lehman and Stanton

Simulation models: macro-element

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

-0.05 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05

Joint Shear Strain (radians)

Join

t She

ar S

tres

s (k

si)

CD15-1450 ModelAnderson, Lehmanand Stanton

Seismic Evaluation Process:

Performance Models

=

TST

VCCST

TSRCSL

Vj

VL

γ

DEMAND/PERFORMANCE RELATIONSHIPS

+0

5

10

15

20

25

30

0 0.01 0.02 0.03 0.04 0.05 0.06

plastic drift angle

psif

v

c

jo ,'

int

Note: the plastic drift angle includes inelastic deformations of the beams

InteriorExterior

Plastic drift capacity(20% loss in lateral strength)

Moehle

Methods of repair (MOR)

Spalling >80% of jt. area

Spalling <80% of jt. area

crack width ≥0.02 in.

crack width < 0.02 in

Repair finishes

MOR1

Epoxy Injection

MOR2

Replace ConcretePatching

MOR4MOR3

Pagni and Lowes

Fragility relations for interior joints

0.0 1.0 2.0 3.0 4.0 5.0 6.000.10.20.30.40.50.60.70.80.91

Drift (%)

MOR 0MOR 1MOR 2MOR 3MOR 4

0.0 1.0 2.0 3.0 4.0 5.0 6.000.10.20.30.40.50.60.70.80.91

Drift (%)

MOR 0MOR 1MOR 2MOR 3MOR 4

MOR 0MOR 1MOR 2MOR 3MOR 4

MOR 0MOR 1MOR 2MOR 3MOR 4Pr

obab

ility

of R

equi

ring

a M

OR

Cosmetic repairEpoxy injectionPatchingReplace concreteReplace joint

Cosmetic repairEpoxy injectionPatchingReplace concreteReplace joint

Pagni and Lowes

6

EDP for MOR

Mean Drift Ratio*0.5%

Repair Finishes

MOR1

1.3%

Epoxy Injection

MOR2

3%2.4%

Replace ConcretePatching

MOR4MOR3

* Includes drift resulting from beam and column deformations

Pagni and Lowes

SummaryTypically, strength of sub-assemblage depends on flexural strength of beam or column and joint performance is not limited by joint shear stress capacity

Increase in joint shear stress demand leads to decrease in deformation capacity:

Drift ratios range from 4% (10 √f’c) to 2.5% (25√f’c ) for interior joints.

Drift capacity for exterior joints also depend on the anchorage detail

SummaryJoints are not rigid. Equivalent elastic stiffness values from Gc (prior to cracking); 0.3Gc to 0.05Gc (yield). Additional flexibility from anchorage condition (i.e. bar slip)

To model cyclic degradation, advanced hysteretic models needed for joint shear and anchorage

On average, repair of an interior joint needed at the following drift ratios:

≈ 1.5% : epoxy injection≈ 2.5% : patch cover concrete≈ 3.0% : replace concrete

References• Clyde, C., C. Pantelides, and L. Reaveley (2000), “Performance-based evaluation of exterior reinforced

concrete building joints for seismic excitation,” Report No. PEER-2000/05, Pacific Earthquake Engineering Research Center, University of California, Berkeley, 61 pp.

• Pantelides, C., J. Hansen, J. Nadauld, L Reaveley (2002, “Assessment of reinforced concrete building exterior joints with substandard details,” Report No. PEER-2002/18, Pacific Earthquake Engineering Research Center, University of California, Berkeley, 103 pp.

• Park, R. (2002), "A Summary of Results of Simulated Seismic Load Tests on Reinforced Concrete Beam-Column Joints, Beams and Columns with Substandard Reinforcing Details, Journal of Earthquake Engineering, Vol. 6, No. 2, pp. 147-174.

• Priestley, M., and G. Hart (1994), “Seismic Behavior of “As-Built” and “As-Designed” Corner Joints,”SEQAD Report to Hart Consultant Group, Report #94-09, 93 pp. plus appendices.

• Walker, S., C. Yeargin, D. Lehman, and J. Stanton (2002), “Influence of Joint Shear Stress Demand and Displacement History on the Seismic Performance of Beam-Column Joints,” Proceedings, The Third US-Japan Workshop on Performance-Based Earthquake Engineering Methodology for Reinforced ConcreteBuilding Structures, Seattle, USA, 16-18 August 2001, Report No. PEER-2002/02, Pacific Earthquake Engineering Research Center, University of California, Berkeley, pp. 349-362.

• Hakuto, S., R. Park, and H. Tanaka, “Seismic Load Tests on Interior and Exterior Beam-Column Joints with Substandard Reinforcing Details,” ACI Structural Journal, Vol. 97, No. 1, January 2000, pp. 11-25.

• Beres, A., R.White, and P. Gergely, “Seismic Behavior of Reinforced Concrete Frame Structures with Nonductile Details: Part I – Summary of Experimental Findings of Full Scale Beam-Column Joint Tests,”Report NCEER-92-0024, NCEER, State University of New York at Buffalo, 1992.

• Pessiki, S., C. Conley, P. Gergely, and R. White, “Seismic Behavior of Lightly-Reinforced Concrete Column and Beam Column Joint Details,” Report NCEER-90-0014, NCEER, State University of New York at Buffalo, 1990.

• ACI-ASCE Committee 352, Recommendations for Design of Beam-Column Connections in Monolithic Reinforced Concrete Structures,” American Concrete Institute, Farmington Hills, 2002.

References (continued)Fragility functions:

•Pagni, C.A. and L.N. Lowes (2006). “Empirical Models for Predicting Earthquake Damage and Repair Requirements for Older Reinforced Concrete Beam-Column Joints.” Earthquake Spectra. In press.Joint element:•Lowes, L.N. and A. Altoontash. “Modeling the Response of Reinforced Concrete Beam-Column Joints.” Journal of Structural Engineering, ASCE. 129(12) (2003):1686-1697.•Mitra, N. and L.N. Lowes. “Evaluation, Calibration and Verification of a Reinforced Concrete Beam-Column Joint Model.” Journal of Structural Engineering, ASCE. Submitted July 2005. •Anderson, M.R. (2003). “Analytical Modeling of Existing Reinforced Concrete Beam-Column Joints” MSCE thesis, University of Washington, Seattle, 308 p.

Analyses using joint model:•Theiss, A.G. “Modeling the Response of Older Reinforced Concrete Building Joints.” M.S. Thesis. Seattle: University of Washington (2005): 209 p.

Experimental Research•Walker, S.*, Yeargin, C.*, Lehman, D.E., and Stanton, J. Seismic Performance of Non-Ductile Reinforced Concrete Beam-Column Joints, Structural Journal, American Concrete Institute, accepted for publication.•Walker, S.G. (2001). “Seismic Performance of Existing Reinforced Concrete Beam-Column Joints”. MSCE Thesis, University of Washington, Seattle. 308 p.•Alire, D.A. (2002). "Seismic Evaluation of Existing Unconfined Reinforced Concrete Beam-Column Joints", MSCE thesis, University of Washington, Seattle, 250 p.•Infrastructure Review•Mosier, G. (2000). “Seismic Assessment of Reinforced Concrete Beam-Column Joints”. MSCE thesis, University of Washington, Seattle. 218 p.