A Super Element Beam-Column Joint Model Under Dynamic Loading

Proceedings of ESTE 2015 conference

A Super Element Beam-Column Joint Model Under Dynamic Loading Mark Adom-Asamoah, Jack Osei Banahene Department of Civil Engineering, Kwame Nkrumah University of Science and Technology

ABSTRACT Several analytical beam-column joint models with varying complexities have been proposed to give reliable estimate of joint response under seismic excitation. The inelastic seismic response of a super element consisting of 13 one-dimensional components which represents three types of inelastic mechanisms is evaluated. Its seismic performance is assessed at reverse quasi static loading of tested reinforced concrete joint assemblage, monotonic nonlinear pushover analysis (NPA) and nonlinear time history analysis (NTHA) with results compared to the conventional approach of modeling the beam-column connection as rigid. Results from reverse quasi static loading of sub-assemblages emphasized the importance of including joint flexibility, with the super element joint model closely matching the experimental response in terms of peak shear strength, pinching behaviour and amount of hysteretic energy dissipation. NPA results of a case study hypothetical frame also revealed that including joint flexibility may lead to a reduced initial stiffness and maximum base shear when compared with the conventional approach. NTHA revealed that explicit representation of the joint region using the super element approach may not change the dominant mode of failure but however may significantly impact the estimated average drift responses. One notably observation, is the rather increased drift responses for the rigid joint modeling approach when subjected to extreme ground motion intensities, which is being attributed to the fact that framing members may be subjected to large strain hardening at such levels of ground shaking.

KEYWORDS beam-column joint; reinforced concrete frames; pushover analysis; nonlinear time history analysis.

Introduction Gravity loading design reinforced concrete buildings have been found to possess major deficient detailing and inelastic deformations that are not suitable for ductile behaviour hence susceptible to severe damage under earthquake loading, Fig 1. These deficiencies may include one or more of the following; insufficient column confinement; short lap splice above beam level; short embedment length of bottom beam reinforcement; little or no joint hoops. Of these deficiencies, the absence of transverse reinforcement within the joint has

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been found to be the major contributor to the formation of inelastic mechanisms that can significantly increase the inter story drift ratio. An implication to this phenomenon will be to developed high fidelity analytical models that can capture these joint inelastic mechanisms to help understand the seismic behaviour of these older –type frames for effective risk mitigation strategies.

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reinf. ratio < 2%, Column longitudinal rei –usually weak column –strong beam Insufficient column confinement

Short lap splice right aabove beam level Construction joint Little or no joint hoops

Widely spaced open stirrups

Construction joint Short embedded length of bottom beam reinforcement

Fig 1: Typical sub-standard construction details, (Hassan 2011)

Several analytical beam-column joint models with varying complexities have been proposed to give reliable estimate of joint response under seismic action. (Celik and Ellingwood 2008) noted that the bond slip and shear deformation are primarily the inelastic deformations that govern joint behaviour, hence rotational and slip springs that are normally calibrated to experimental results are used to represent the constitutive behaviour (shear stress-strain and bond stress-slip relationship) of these components. A single zero length rotational spring element with rigid links that span the joint region, proposed by (Alath and Kunnath 1995) has been one of the widely used approaches to describe these mechanisms due to its simplicity and computational efficiency. However the modeling scheme does not decouple the contributions of the individual governing inelastic deformations and fails to capture the joint kinematics within the joint region, such as simulating the vertical translation of the upper and lower column across the joint, Fig 2. (Lowes and Altoontash 2003) also developed

a super-element consisting of thirteen one dimensional components that represents three kinds of inelastic mechanisms to help capture these kinematics and individually assess the contribution from the various mechanisms. In all these modeling schemes, quasi static loaded beam-column joint sub-assemblages have been for validation and subsequent calibration of spring elements. This study seeks to evaluate the impact of joint flexibility on non-ductile reinforced concrete (RC) frames by using the super-element joint modeling scheme to describe the joint response. The conventional approach of modeling joints of RC frames as rigid is used to make the necessary comparisons. Quasi static response of an unreinforced exterior joint sub-assemblage that can be used to assess local component behaviour, a monotonic nonlinear static pushover analysis and a nonlinear time history analysis will be employed in evaluating the global seismic performance.

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(b)

(a)

Fig 2 : Scissors model (a) Model kinematics, FEMA 451 (b) drawback of missing joint translation , (Theiss 2005).

Analytical Modeling of Structural Components The nonlinear open source platform, OpenSees, (McKenna 2010) was employed in numerically simulation of the responses of structural components. The beams and columns are modeled using line elements that can account for both material and geometric nonlinearities. The “nonlinear beamColumn element”, based on a distributed inelasticity formulation, along with fibre element modeling of the various component that make up the element cross-section, i.e , confined, unconfined and reinforcing steel, was used to model the beams and columns. The

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concrete properties were modeled using the “Concrete02” material object that assumes zero tensile strength. In order to account for the marginal increase in compressive strength due to confinement, the model of (mander et al 1988) was employed. The reinforcing steel was modeled using the “steel02” material object that uses a bilinear response envelope and Menegotto-Pinto (1973) hysteretic curves to describe the cyclic behaviour as well as accounting for the bauschinger effect. The joint region was modeled using the “beamColumnJoint” element that requires 22 modeling parameters to describe the one dimensional behaviour of the thirteen spring components, Fig 3a. The hysteretic material model,”Pinching4” was employed to characterize the backbone curve of each element using an appropriate joint shear strength model. It approximates the element shear stress-strain response by using a quadlinear envelope and a trilinear unload-reload path to control the hysteretic damage, Fig 3c. (Jeon 2013) used an extensive database of 261 quasi statically loaded sub-assemblages, and proposed a joint shear strength model that depends on typical design parameters such as the compressive strength, the joint confinement factor, number of transverse beams and beam reinforcement index. This model was adopted to estimate the maximum joint strength. For the remaining key points on the backbone, the suggestions made by (Anderson et al 2008) were utilized Fig 3b.

external node shear panel

zero-length interface shear spring

internal node

beam element rigid internal interface plane

(γj,2, vj,2)= (0.006, 0.95vj,max)

Joint shear stress (vj)

zero-length bar-slip shear spring

column element


(γj,3, vj,3=vj,max)

(γj,1, vj,1) =(0.00043, 0.48√fcj)

rigid external interface plane

(γj,4, vj,4)=(γj,res, 0.2vj,max)

Joint shear strain (γj)

(b) backbone curve Load

(a) Super element joint model

(dmax, f(dmax)) Pd2, ePf2) (e

(ePd3, ePf3)

(ePd1, Pf e 1) (ePd4, ePf4)

(*, uForceP·ePf3)

(rDispP·dmax, rForceP·f(dmax))

(rDispN·dmin, rForceN·f(dmin)) (eNd 4, eNf 4)

Deformation (*, uForceN·eNf3)

(eNd1, eNf1) (eNd3, eNf3)

(eNd2, eNf2) (dmin, f(dmin))

(c) Pinching4 material model Fig 3: Super element joint model and constitutive realtionship

Quasi Static Responses of SubAssemblage The exterior beam-column joint subassembalge of (Pantelidis et al 2002) is selected to investigate the adequacy and importance of including joint flexibility in vulnerability assessment of non-ductile RC frames. (Pantelidis et al 2002) assessed the impact of column axial load and joint embedment length in exterior joint with substandard details. In evaluating the seismic performance of such joint details, the longitudinal reinforcement were increased, so that a shear failure mode can be exhibited in order to quantify the seismic performance of shear-dominated exterior joints. Two levels of axial compressive loads (10% and 25%) as well

as three extent of embedment length in the joints was studied. The experimental validation of test unit 1, possessing an axial compressive load of 10% with a 6 inches embedment length of bottom bars is selected.

Results and discussion The quasi static reverse cyclic test results, indicated that even though the full moment capacity of beam element cannot be utilized upon failure, the reduction in strength due to anchorage failure from short embedment length can be appreciable. Fig 4b shows this phenomenon with a factor of about 2.12 for the lateral load capacities in the two opposing directions from experimental base shear-drift responses. The super element joint model was 685


able to capture the highly pinched behavior of the joint region as well as reduced strength due to anchorage failure. However the rigid joint model, in which framing element is assumed to intersect at the centerline, showed a much larger energy dissipation mechanism which deviates from results of experimental test. In terms of the maximum shear capacity, Fig 4d, which illustrates the base shear-drift relationship for the super element joint model, was able to closely match the peak shear capacity of the specimen in the two opposing directions as compared to the rigid joint model, Fig 4c, that overestimates the shear capacity along with its inability to account for the reduced strength due to anchorage failure in the negative direction.

(a) Test specimen

(b) Experimental responses 60

60 Rigid joint model

40 Lateral Force (kip)

Lateral Force (kip)

40 20 0 - 20 - 40 - 60 - 10

-6

-4

-2 0 2 Drift Ratio (%)

(c) Rigid joint model

4

6

8

20 0 −20 −40

Simulation Experiment -8

Super element joint model

10

−60 −10

Simulation Experiment −8

−6

−4

−2 0 2 Drift Ratio (%)

4

6

8

10

(d) Super element joint model

Fig 4: Base shear-drift hysteretic responses of exterior joint sub-assemblage.

Evaluation of Nonlinear Static and Dynamic Responses of Case Study Rc Frame. Two hypothetical six story – three bay gravity loading design RC frame, Fig 5, that represents the interior frame of an office building are implemented in the open source finite element framework, OpenSees. These RC frames differ only in their joint representation, where for one realization; the super element joint modeling scheme that has been validated is implemented, whereas the other entails the conventional approach to modeling beam-column connection as rigid.

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Fig 5: Hypothetical model frame

A preliminary assessment of the variation in the seismic responses was investigated by performing a monotonic nonlinear static pushover analysis, where the laterals load distribution along the floors is distributed linearly using the relation:

Cx =

wx hx

(1)

n

∑w h i =1

i i

where Cx is the normalized load at floor level x, wi and wx are the proportion of the total effective seismic weight of the structure (W) located or assigned to level i and x, respectively; hi and hx are the height from the base to level i and x. Analysis results were assembled at maximum base shear, which indirectly signifies structural capacity, and at failure for the two studied joint modeling schemes.

In order to adequately quantify the seismic performance, a non-linear time history analysis that involve subjecting these RC frame models to a suite of ground motion was also carried out to address the impact of strength and stiffness deterioration of framing members under seismic excitation. The stochastic time-series simulation model developed by (Baker et al 2011) which uses the wavelet packet transform that easily modulate the time and frequency characteristics of the ground motion is selected because it has been validated for a wide range of magnitude, structure specific modal periods, shear wave velocities, etc. A cumulative sample of 60 synthetic records were generated conditioning on a moment magnitude of 7.0,with a source to site distance of 10km and a 30m depth shear wave velocity of 400cm/s. From this a latin hypercube experimental design that models the variation in the compressive strength of 687


concrete, tensile yield strength of steel and damping ratio were constructed with each realization randomly mapped to one sample

of the suite of ground motions. The statistical property of theses random variables is shown in Table 1.

Table 1. Material and structural uncertainty parameters (Healy et al. 1980). Parameter Probability distribution Mean Coefficient of variation Concrete strength Normal 5.0 ksi 0.18 Steel strength Lognormal 50.0 ksi 0.11 Damping ratio Lognormal 0.0426 0.76

Results and Discussion

a larger maximum base shear when compared to the model with explicit representation of joint flexibility, that is, the super element modeling scheme. This of the order approximately 3.0, but decreases appreciable as the roof drift increases. This phenomenon lead to maximum inter story drift ratio being observed at the first floor, which can be attributed to the loss of lateral capacity of the first floor columns, hence initiates a soft story collapse mechanism, as seen in Fig 6b and Fig 6c. However the super element joint model produce the largest interstory drift at maximum base shear, occurring at the third floor level order than the first floor for the rigid joint. In all cases, the super element model underestimated the story drift at the roof level when compared with the rigid joint.

Pushover Analysis Fig 6 presents the comparative results of the pushover analysis of the studied hypothetical frames. It illustrates the base shear- roof drift relationship and the inter-story drift distribution at both maximum base shear and failure, where failure is defined here as the 1% roof drift that conforms to the immediate occupancy limit state in the FEMA 2003. The story level that corresponding to the maximum inter-story drift can be an indicator of floor that corresponds to the global failure mechanism the frame exhibits. It is observed that the rigid joint model RC frame experiences a much higher initial stiffness with

1400

Rigid joint model Super element joint model

1200

Base Shear (KN)

1000 800 600 400 200 0

0

1

2

3 Roof Drift (%)

4

5

6

(a) Base shear-roof drift relationship Rigid joint model Super element joint model

5

5

4

4

3

3

2

2

1

1

0

0.2

0.4 0.6 Inter−story Drift (%)

0.8

(b) Inter story drift distribution at

maximum base shear


6

Story Level

Story Level

6

1

0

0

0.5

1

1.5 2 Inter−story Drift (%)

(c) Inter story drift distribution at

failure

Fig 6 : Pushover analysis results

688

2.5

3

3.5


Nonlinear Time History Analysis. Fig 7 also illustrates the inter story drift responses along the various floor of the studied RC frame under a suite of 60 ground motion as already discussed. The suite average, median and maximum drift responses are presented. It evident that the major failure mechanism is that of a soft story collapse with the peak inter story drift being observed at the first floor for both rigid joint and super element joint model among the studied suite characteristics. For the suite average and median responses, the super-element joint model produced the largest drift responses at this floor, 1.51% and 1.03% respectively. This corresponds to 26% increase in the suite average drift response of the rigid joint model and a 100% increase in the suite median response. To better understand this

trend, the suite maximum of the drift responses reveal that the rigid joint model may exhibit larger drifts, that is, 7.59% when compared to 6.71% for the super element model. This shows that for extreme ground motion intensities that are likely to cause collapse of the building, framing members may have then being subjected to large strain hardening in the rigid joint model, hence causing this trend in responses. This also show that using the suite median, which represents the drift at which 50% of the records responses will be exceeded, may not be robust metric to be employed for comparison. Finally in all cases the super element model underestimates the drift responses at the roof level when compared to the rigid joint model, which is in unison with results from monotonic pushover analysis.


6

Story Level

5 4 3 2 1 0

0

0.2

0.4

0.6 0.8 1 Inter−story Drift (%)

1.2

1.4

1.6

(a) Suite average drift responses Rigid joint model Super element joint model

5

5

4

4

3

3

2

2

1

1

0

0.2

0.4


1.2

1.4

(b) Suite median drift responses


6

Story Level

Story Level

6

1.6

0

0.2

0.4


1.2

1.4

1.6

(c) Suite maximum drift responses

Fig 7: Nonlinear time history analysis result.

Summary and Conclusion The joint contribution to the seismic response of gravity loading design RC frames was evaluated. The comparative assessment was investigated by implementing the conventional approach of simulating frames, which assumes

the joint region to be rigidly connected and an explicit joint modeling schemes that uses thirteen one-dimensional spring element to describe the inelastic mechanisms govern joint responses. Results from reverse quasi static loading of sub-assemblages emphasized the importance of including joint flexibility, with 689


the explicit joint modeling scheme closely matching the experimental response in terms of peak shear strength, pinching behaviour and amount of hysteretic energy dissipation. Pushover analysis of a case study hypothetical frame also revealed that including joint flexibility may lead to a reduced initial stiffness and maximum base shear when compared with the conventional approach. In order to study the effect of strength and stiffness deterioration of framing members due to load reversals, a

nonlinear time history analysis revealed that explicit representati on of the joint region using the super element approach may not change the dominant mode of failure but however may significantly impact the estimated average drift responses. One notably conclusion, is the rather increased drift responses for the rigid joint modeling approach when subjected to extreme ground motion intensities, attributing it to the fact that framing members may subjected to large strain hardening.

References Alath, S. and Kunnath, S. K. (2005),“Modeling inelastic shear deformations in RC beam-column joints,” Engineering Mechanics Proceedings of 10th Conference, May 21–24, University of Colorado at Boulder, Boulder, Colorado, ASCE, New York, 2, 822–825. Anderson, M., Lehman, D., and Stanton, J. (2008) “A cyclic shear stress-strain model for joints without transverse reinforcement”, Engineering Structures, Vol. 30, No. 4, pp. 941–954. Baker, J.W., Shahi, S.K., and Jayaram, N. (2011) “New ground motion selection procedures and selected motions for the PEER Transportation Research Program”, PEER Report 2011/03, Pacific Earthquake Engineering Research Center, University of California, Berkeley, CA. Celik, O. C., and Ellingwood, B. R. (2008), “Modeling beam-column joints in fragility assessment of gravity load designed reinforced concrete frames.” J. Earthquake. Eng., 12(3), pp. 357-381 FEMA (2003). “HAZUS-MH MR4 technical manual”, earthquake model, Federal Emergency Management Agency, Washington, DC. FEMA 451, “Structural Analysis for Performance-Based Earthquake Engineering”, Federal Emergency Management Agency, Washington D.C Hassan W. M. (2011), “Analytical and Experimental Assessment of Seismic Vulnerability of BeamColumn Joints without Transverse Reinforcement in Concrete Buildings”, PHD thesis, University of California, Berkeley. Healy, J. J., Wu, S. T., and Murga M. (1980). “Structural Building Response Review.” NUREG/ CR-1423, Vol. 1, US Nuclear Regulatory Commission, Washington, DC. Jeon J. S. (2013), “Aftershock vulnerability assessment of damage reinforced concrete buildings in california”, PHD thesis, Georgia Institute of Technology, Atlanta.

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Lowes, L. N., and Altoontash, A. (2003), “Modeling reinforced-concrete-column joints subjected to cyclic loadings.” J. Struct. Eng., ASCE, 129(12), 1686-1679. Menegotto, M., P. Pinto (1973), “Method of analysis of cyclically loaded reinforced concrete plane frames including changes in geometry and inelastic behavior of elements under combined normal geometry and inelastic behavior of elements under combined normal force and bending”, Proceedings of the IABSE Symposium on the Resistance and Ultimate Deformability of Structures Acted on by Well-Defined Repeated Loads. Lisbon Mander, J. B., Priestley, M. J. N., and Park, R. (1988). “Theoretical stress-strain model for confined concrete.” J. Struct. Eng., ASCE, 114(8), 1804-1826. McKenna, F., Scott, M. H., and Fenves, G. L. (2010), “Nonlinear finite-element analysis software architecture using object composition.” J. Comput. Civil Eng., ASCE, 24(1), 95-107. Pantelides, C.P., Hansen, J., Nadauld, J., and Reaveley, L.D. (2002) Assessment of reinforced concrete building exterior joints with substandard details, PEER 329 Report 2002/18, Pacific Earthquake Engineering Center, University of California,Berkeley, CA. Theiss A.G, (2005), “Modeling the earthquake response of older reinforced concrete beam-column building joints”, MSc thesis, University of Washington.

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