Finite Element Simulation of Link-to-Column Connections in Steel

Proceedings of the 8th U.S. National Conference on Earthquake Engineering April 18-22, 2006, San Francisco, California, USA Paper No. 1526

FINITE ELEMENT SIMULATION OF LINK-TO-COLUMN CONNECTIONS IN STEEL ECCENTRICALLY BRACED FRAMES Taichiro Okazaki 1 and Michael D. Engelhardt 2

ABSTRACT In an eccentrically braced frame, the link-to-column connection plays a critical role in the seismic performance and safety of the frame. However, very few linkto-column connection details meet the validation criteria prescribed in the US code provisions. Large-scale cyclic loading tests were conducted to evaluate connections typical of pre-Northridge construction as well as connections incorporating improvements in welding, design, and detailing. The test results demonstrated that link-to-column connections typically fail prematurely due to fracture of the link flange near the groove welds. Finite element analyses provided some insight into the stress and strain environment that caused the fracture observed in the tests. Limitations of the analysis to predict the occurrence of fracture is discussed. Introduction The link-to-column connection is a critical element affecting the safety and performance of seismic-resistant steel eccentrically braced frames (EBFs). In the US, the 2002 AISC Seismic Provisions for Structural Steel Buildings (AISC 2002) requires that satisfactory performance of link-to-column connections be verified by testing under a prescribed loading protocol. To-date, very few link-to-column connection details have passed these testing criteria. Consequently, the availability of link-to-column connection details with demonstrated satisfactory performance remains a largely unsolved problem for construction of EBFs in the US. The writers conducted a research program to address this issue. The program combined large-scale cyclic loading tests of link-to-column connections and an analytical study including detailed finite element analysis simulations. A total of sixteen large-scale link-column specimens were tested to investigate the effect of link length, connection details, and loading protocol on the performance of link-tocolumn connections. Detailed finite element analyses were performed to study the correlation between experimental observation and simulation results. This paper provides an overview of this program with emphasis on the analytical study. Details of this research are reported in Okazaki (2004).

1

Assistant Professor, Department of Civil Engineering, University of Minnesota, Minneapolis, MN 55455 Professor, Department of Civil, Architectural, and Environmental Engineering, University of Texas at Austin, Austin, TX 78712-0275

2

Experimental Program The test setup devised for this investigation is shown in Fig. 1. The link-column specimen (shaded segment in the figure) was connected to the test setup using high-strength bolts. Lateral bracing was provided near the four reaction points at the top and bottom of the column, and near the two ends of the horizontal beam. The loading ram supplied quasi-static vertical motion to the bottom of the column, which in turn, imposed large cyclic shear deformation on the link. The loading system subjected the link to constant shear along its length, and reverse-curvature bending moment, with higher moment at the column end of the link than at the beam end. The force and deformation environment produced in the specimen is a reasonable representation of what is realized in an EBF arrangement with one end of the link connected to a column. A total of sixteen link-column specimens were tested in this program. All specimens were constructed from W18x40 links and W12x120 columns, both of ASTM A992 steel. The sizes of the link and column sections as well as the column height of 2.44-m were selected to represent full or near full-scale dimensions in actual EBFs. The links were detailed per the 2002 AISC Seismic Provisions. The column was provided with continuity plates, but with no doubler plate. The primary test parameters for this investigation were the connection type, link length, and loading protocol. As shown in Table 1, the specimen names represent the three test parameters: the first two letters (PN / MW / FF / NA) represent the connection type; the following letters (S / SL / I / M) represent the link length. The absence of suffix “–RLP” indicates that the specimen was tested using the cyclic loading protocol prescribed in the 2002 AISC Seismic Provisions. The presence of the suffix “–RLP” indicates that the specimen was tested using the revised loading protocol developed by Richards and Uang (2003). As illustrated in Fig. 2, the connection details included a detail representing the preNorthridge practice in design and fabrication (PN-connection), a detail which implemented modifications in welding procedures over the PN-connection (MW-connection), a free flange connection proposed by Choi et al. (2002) adapted for use as link-to-column connections (FFe = 635, 985, 1270, or 1905 mm e

Horizontal Beam: W18x76

2420 mm

445 kN Load Cell Column: W12x120 Link: W18x40

670 kN Load Cell 1300 kN Load Cell

(a) Represented EBF

2360 mm

2360 mm

Column Stub: W12x120

(b) Test Setup and Dimensions

Figure 1. Test Setup

445 kN Load Cell Hydraulic Loading Ram

2440 mm

5080 mm for shear or intermediate link 3810 mm for moment link

Table 1. Test Specimens Specimen

e (mm)

e/(Mp/Vp)

Required γp (rad)

Achieved γp (rad)

Observed Failure

PNS PNI PNM MWS MWI MWM FFS FFI FFM FFS-RLP FFSL-RLP NAS NAI NAM NAS-RLP NASL-RLP

635 1270 1905 635 1270 1905 635 1270 1905 635 985 635 1270 1905 635 985

1.11 2.22 3.34 1.11 2.22 3.34 1.11 2.22 3.34 1.11 1.72 1.11 2.22 3.34 1.11 1.72

0.08 0.043 0.02 0.08 0.043 0.02 0.08 0.043 0.02 0.08 0.073 0.08 0.043 0.02 0.08 0.073

0.041 0.018 0.008 0.051 0.018 0.008 0.060 0.046 0.016 0.031 0.019 0.071 0.027 0.017 0.119 0.058

Fracture of link flange Fracture of link flange Fracture of link flange Fracture of link flange Fracture of link flange Fracture of link flange Fracture of link web around shear tab Fracture of link flange and link web Fracture of link flange and link web Fracture of link web Fracture of link web Fracture of link web at stiffener welds Fracture of link flange Fracture of link flange Fracture of link flange Fracture of link flange

E70T-6 Remove weld tabs

10 30°

E70T-4 10 30°

E71T-8 Weld B.U. bar to column

E71T-8

E71T-8 6 45°

6 45°

W18X40

W18X40

E70T-6 Remove B.U. Bar Remove weld tabs

W12X120

E70T-4

E71T-8

10 30°

(a) Pre-Northridge (PN) Connection E70T-6 Remove weld tabs E71T-8 Weld B.U. bar to column

8

10 30°

W12X120 8

(b) Modified-welding (MW) Connection

DO NOT PLACE FILLET WELD CLOSE TO WELD ACCESS HOLE

10 30°

11 76

8

E71T-8

E70T-6 Remove weld tabs E71T-8

E71T-8 Weld B.U. bar to column

PL 13

6 45°

E70T-6 Remove B.U. Bar Remove weld tabs

E71T-8

10 30°

64

W12X120

East View

E71T-8

11

95 165

8

11

76

E71T-8

West View

(c) Free flange (FF) Connection

8

E71T-8 8 8

W18X40

229

368

W18X40

10 30°

E71T-8 Weld B.U. bar to column

E70T-6 Remove weld tabs

8

W12X120 10 30°

(c) No-weld-access-hole (NA) Connection

Figure 2. Connection Details

connection), and a no-weld-access-hole connection (NA-connection) developed in Japan (Suita et al. 2000). The third and fourth connection details are improved details recently developed for beam-to-column moment frame connections. The FF-connections are intended to minimize the shear force transmitted through the link flange welds, and thereby reduce the local secondary bending produced near the link flange welds. The NA-connection removes a source of stress and strain concentration by eliminating the weld access holes. The FF and NA-connections adopted the same modified welding procedures used in the MW-connection. The link length were varied from the shear yielding range (link length, e = 1.1Mp/Vp), intermediate length range (e = 1.7Mp/Vp and e = 2.2Mp/Vp), to flexure yielding range (e = 3.3Mp/Vp). Cyclic loading was applied by controlling the link rotation angle, which was measured as the relative displacement of the link ends divided by the link length. The loading protocols ask to repeat elastic cycles, followed by inelastic cycles with increasing amplitudes. During the course of this project, it was realized that the loading protocol prescribed in the 2002 AISC Seismic Provisions demanded too many inelastic cycles to shear yielding links (Richards and Uang 2003). Richards and Uang developed a revised loading protocol, which is now adopted in the 2005 edition of the AISC Seismic Provisions. Key Observations The 2002 AISC Seismic Provisions define the inelastic link rotation capacity, γp, depending on the link length: 0.08 rad for links shorter than e = 1.6Mp/Vp; 0.02 rad for links longer than e = 2.6Mp/Vp; linear interpolation is used for links of 1.6Mp/Vp ≤ e ≤ 2.6Mp/Vp. The inelastic rotation angle was evaluated by removing the elastic component from the link rotation angle. The γp values listed in Table 1 were evaluated based on the last full cycle of loading prior to either the shear force or moment at the column face dropping to below 80% of their respective maximum values measured during the test. Table 1 also provides brief descriptions of the failure mode observed in each specimen. The PN-specimens showed poor performance, unable to develop half of the required inelastic rotation. Consequently, existing EBFs constructed prior to the Northridge Earthquake may be prone to premature failure at the link-to-column connections under severe earthquake loading. The MW-specimens showed little improvement over the PN-specimens, The results from the FF and NA-specimens demonstrated that significant improvement in connection performance can be achieved through modifications in welding practices combined with modifications in connection design and detailing. However, these connections still did not provide the levels of inelastic rotation required by the 2002 AISC Seismic Provisions. Consequently, further research is needed to identify satisfactory link-to-column connection details. Regardless of the connection type, link length, and loading protocol, the majority of specimens failed by fracture of the link flange. The fracture occurred either in the top or bottom flange, or in both flanges, at the interface of the weld metal and flange base metal. The effect of loading protocols can be seen by comparing the performance of Specimens NAS and NAS-RLP. These two specimens were identical but were tested using different loading protocols. Specimen NAS-RLP, which used the more realistic revised loading protocol, achieved an inelastic rotation 50% greater than that achieved by Specimen NAS. Therefore, the loading protocol used for testing has a significant influence in the measured inelastic rotation capacity. The poor behavior of Specimens FFS-RLP and FFSL-RLP was attributed to these two specimens

having the link web cut short of reaching the column flange, as opposed to having the link web welded directly to the column flange as in the other FF-specimens. Finite Element Analysis The behavior of link-column specimens was studied by finite element analysis simulations. The correlation between simulations and experimental observations was a primary interest of this analytical study. As discussed above, the majority of link-column specimens failed due to fracture of the link flanges, at the interface of the weld metal and link flange base metal. Simulations of the specimens provided detailed information on the stress and strain environment at this local region of concern. Model and Analysis The general-purpose finite element analysis program ABAQUS was used to perform nonlinear three-dimensional (3-D) finite element simulations of link-column test specimens. Each finite element simulation was performed in two stages. First, a “global model” representing the entire link-column test specimen was analyzed. Subsequently, a more detailed “submodel” including a limited region of the structure surrounding the weld access hole at the link bottom flange was analyzed. The results from the “submodeling” analyses were used for the detailed study of stress and strain environment which caused the fracture observed in the tests. Fig. 3 illustrates the global model and submodel. Material nonlinearity was considered using the von Mises yield criterion and the associative flow rule. Hardening was modeled by an isotropic hardening rule. The constitutive rule was modeled by a tri-linear rule, as shown in Fig. 4. The figure compares the A992 steel model and weld metal model against selected tension coupon test results. Geometric nonlinearity was considered in all analyses by a large strain-large displacement formulation. The global models were subjected to a monotonically increasing load, subjecting the bottom link flange to increasing tension. For each connection type, a beamcolumn subassemblage model with a W18x40 beam and W12x120 column was analyzed in addition to link-column models. The length of the beam measured from the face of the column was 90-inches, providing a span-to-depth ratio of 10 for the beam-column models. The beamcolumn models were denoted, for example, as MWB for the model with an MW-connection. Fig. 5 shows a comparison between skeleton curves constructed from the cyclic test Beam

M-link

Column

Column Flange

Link Web

Static Load Global Model

Link Bottom Flange Submodel

Figure 3. Finite Element Model

Specimen FFI Link K-area

200

Link Flange 80

Link Web

60 40

Tension Coupons A992 Steel Model Weld Model

20 0

Link Shear Force: V (kips)

Cauchy Stress (ksi)

100

Vp

150

100

Positive Skeleton Negative Skeleton FE Simulation

50

0 0

0.1

0.2

0.3

Logarithmic Strain

Figure 4. Material Model

0

0.02

0.04

0.06

0.08

0.1

Rotation / Skeleton Rotation: γ (rad)

Figure 5. Verification of FE Simulation

response and the monotonic simulated response. The figure shows the relation between link rotation and link shear force. The skeleton curve is known to very closely represent the monotonic loading curve. The two skeleton curves shown in the figure correspond to the positive and negative loading sides of the cyclic test response. The similarity between the three curves indicates that the response of the global model analysis is reasonable to represent the response of the test specimen. Similar agreement was seen for all other specimens. Note that the effect of loading protocol, which was one of the three key parameters in the experimental program, was not considered in the finite element analysis. Discussion of Results Ductile Fracture Criteria Mao et al. (2001) and Tabuchi et al. (2002), among others, used a combination of finite element analysis and ductile fracture criteria to estimate the deformation capacity of welded beam-to-column connections. The ductile fracture criteria for steel are generally provided as a relation between stress triaxiality and effective plastic strain, stating that increase in stress triaixlity tends to reduce plastic strain capacity (Hancock and Mackenzie 1976; Kuwamura and Yamamoto 1997). Stress triaxiality, τ, and effective plastic strain, εeff, are defined as follows:

τ=

σ ave 1 2 s ij s ij ; σ ave = s ii ; σ Mises = 3 3 σ Mises

ε eff = ∫

(1)

2 p p dε ij dε ij 3

(2)

In the above equations, sij are the deviatoric stress components, ε ij are the plastic strain components. By relating the detailed stress and strain information obtained from finite element analysis with the ductile fracture criteria, the occurrence of fracture initiation can be evaluated. These procedures provide a rational basis to estimate the location where fracture initiates. Moreover, the stage when fracture initiates can be taken as a lower-bound estimate for the p

deformation capacity of the beam-to-column connection or link-to-column connection. Fig. 6 shows the stress triaxiality vs. plastic strain relation plotted for selected models, along with the ductile fracture criteria developed by Kuwamura and Yamamoto (1997). Fig. 6(a) compares four shear link models with different connection details, as the link rotation angle increased from 0 to 0.24 rad. Fig. 6(b) compares four MW-connection models with different link lengths. The values were sampled at mid-width of the link flange, at the outer-face of the flange, as indicated in the figure. This was the location identified as the critical point in many models, based on the simulation results. The sampling point was selected to be close enough to the weld interface to capture the stress and strain concentration caused by the material and geometrical discontinuities, but far enough from the weld interface to assure that the values from neighboring finite elements agreed with each other. Fig. 6(a) indicates that the stress triaxiality vs. plastic strain relation is affected significantly by the connection detail. In Specimens PNS and MWS, the stress triaxiality and plastic strain approach closer to the curve expressing the ductile fracture criteria than in Specimens FFS and NAS. Therefore, Specimens PNS and MWS may be more susceptible to fracture at the sampled point. Fig. 6(b) suggests that the stress triaxiality vs. plastic strain relation follows the same trajectory for a given connection detail, regardless of the link length. Nonetheless, susceptibility to fracture can depend on the link length. The instant when the link or beam reached the required inelastic rotation is indicated in the figure: 0.08 rad for Model MWS; 0.043 rad for Model MWI; 0.02 rad for Model MWM; and 0.03 rad for Model MWB. The figure suggests that Model MWI is twice as susceptible to fracture at the sampled point as Model MWB. The results suggests that intermediate length links, which develop a combination of large shear force and large bending moment at the link ends, generates the most severe stress and strain environment at the link-to-column connection. Fig. 6 also indicates that, by the end of the analysis which was performed up to a fairly large rotation level (e.g. 0.24 rad for shear links, which is nearly three times the required link rotation), the stress triaxiality and plastic strain values is far from reaching the critical level suggested by Kuwamura and Yamamoto (1997). Since the most critical location found based on the simulation results was chosen as the sampling point, the simulation suggests that no fracture occurs at this extreme rotation level. Therefore, the simulation combined with the ductile fracture criteria was not capable of predicting the fracture observed in the link-column test specimens. Some of the important limitation of the fracture evaluation procedure may be 1.2

Kuwamura (1997)

PNS MWS

0.2

FFS NAS

Link Flange Sampling Point

0 0

0.1

0.2

0.3

Plastic Strain: ε

0.4 eff

(a) Connection Detail

Weld

0.5

0.8

MWM MWB

Kuwamura (1997)

Link Web

0.6 0.4 0.2

Link Flange

MWI

0.4

MWS MWI

MWB

Link Web

0.6

1

MWM

γ = 0.24 rad

0.8

Stress Triaxiality: τ

Stress Triaxiality: τ

1

MWS

1.2

Sampling Point

0 0.6

0

0.1

0.2

0.3

Plastic Strain: ε

0.4 eff

(b) Link Length

Figure 6 Stress-Strain Trajectory and Ductile Fracture Criteria

Weld

0.5

0.6

summarized as follows. While the simulation performed in this study used monotonic loading, cyclic loading effects, or more specifically, low cycle fatigue effects, can be detrimental to the occurrence of fracture. While the finite element model contained a sharp discontinuity of material properties at the weld interface, the actual material near the weld fusion line is characterized by a gradual transition of properties from the base metal, heat affected zone, weld interface, to the weld metal. On the other hand, to the knowledge of the authors, the currently available ductile fracture criteria do not account for low cycle fatigue effects and the distribution of material properties near the weld fusion line are not well known. These issues need to be address to enhance the capability of analytical procedures to evaluate the performance of steel seismic connections governed by fracture. Link Length In the following, the connection performance is discussed based on the bending stress distribution in the link flanges, instead of the ductile fracture criteria. The bending stress roughly equaled to the principal stress at the concerned locations. The bending stress is also relevant to the crack opening mode of fracture for fracture through the thickness of the link flange. Fig. 7 compares the bending stress distributions in MW-connections with different link lengths. The bending stress values were sampled along the link flange weld interface, at the inner face (Line-U) and outer face (Line-L) of the link flange. Each model was at an inelastic rotation equal to 1.1 times the skeleton rotations achieved by the corresponding test specimen: 0.108 rad for Model MWS; 0.058 rad for Model MWI; and 0.039 rad for Model MWM. Model MWB was at an inelastic beam rotation of 0.046 rad. The figure shows remarkable similarity in bending stress distribution between Models MWI, MWM, and MWM, implying that test specimens MWI and MWM were subjected to similar stress and strain environment when they failed. The bending stress distribution in Model MWS was very different from that in the other three models. While all four models showed higher tensile stresses along Line-L than along LineU. Model MWS developed compressive stress along Line-U and tensile stress along Line-L. The difference in tensile stress values between Lines-U and L indicate that all four models developed secondary bending in the link flange, which added tensile stress to the outer side of the flange 150

150 125

Max Strength

100 75

Bending Stress (ksi)

Bending Stress (ksi)

125

Yield Strength

50 Link Web

25 Line-U

0 -25

Link Flange

-50

MWS MWI MWM MWB

-3

-2

-1 0 1 2 Distance from Center (in)

(a) Line-L

75 50

Yield Strength

25 0 -25 -50

Line-L

-75

Max Strength

100

-75 3

-3

-2

-1 0 1 2 Distance from Center (in)

(b) Line-U

Figure 7. Influence of Link Length on Bending Stress Value across Width of Link Flange

3

and compressive stress to the inner side of the flange. Model MWS was more significantly influenced by secondary bending than the other four models. Although the net tensile force developed in the link flange is much smaller in Model MWS than in other models, Model MWS is equally susceptible to fracture along Line-L as the other models. This result agrees with the experimental observation that fracture of the link flange can occur even in shear link specimens, which develop relatively small bending moment at the link-to-column connection. Connection Details Fig. 8 compares the bending stress distributions in four shear link models with different connection details, PN, MW, FF, and NA. The simulations do not address the different properties of the weld metal, which was one of the key differences between the PN- and MWconnections in the test program (see Fig. 2). The bending stress values were sampled along Lines-U and L, as in Fig. 7, when the inelastic link rotation was at 0.108 rad. The figure shows that Model FFS barely yielded along either Lines-L or U. The relatively similar stress values between Lines-U and L suggest that the link flanges in Model FFS was subjected to small secondary bending. On the other hand, Models PNS, MWS, and NAS showed significantly higher bending stress values along Line-L than along Line-U, indicating substantial influence of secondary bending in these three models. The variation in bending stress along Line-U in Models PNS and NAS was caused by the restraint near mid-width of the link flange provided by the link web. The large weld access hole in Models MWS and FFS relaxed this restraint, and led to a more uniform bending stress distribution along Line-U than in Model PNS and NAS. The bending stress distributions along the link flange weld interface correlate well with the different performance levels achieved by the test specimens. The substantially smaller bending stress values obtained in Models FFS and NAS compared to Models PNS and MWS agreed with the improved level of performance achieved by the Specimens FFS and NAS over Specimens PNS and MWS (see Table 1). Therefore, the finite element simulation is an effective tool to gain better insights into connection behavior. Although not discussed in this paper, similar observations were made for intermediate length link and moment link models. 150

150

Max Strength

100 75 50 Link Web

25

Yield Strength

Line-U

0 -25

Link Flange

-50

PNS MWS FFS NAS

-3

-2

-1 0 1 2 Distance from Center (in)

(a) Line-L

100 75

Yield Strength

50 25 0 -25 -50

Line-L

-75

Max Strength

125 Bending Stress (ksi)

Bending Stress (ksi)

125

-75 3

-3

-2

-1 0 1 2 Distance from Center (in)

3

(b) Line-U

Figure 8. Influence of Connection Details on Bending Stress Value across Width of Link Flange

Concluding Remarks The experimental program demonstrated that further research is needed to develop safe and reliable link-to-column connections in seismic-resistant steel EBFs. Finite element simulations of the test specimens provided valuable insight into the stress and strain environment that caused the premature fracture of the link flange observed in the experiments. The simulation results can be used to develop further improved connection details. However, in order to predict the occurrence of fracture based on the simulation results, and to evaluate connection performance, ductile fracture criteria which account for low cycle fatigue effects is needed. Also lacking is information on the distribution of material properties immediately near the weld interface. Testing is continuing at the University of Texas on other link-to-column connection details that were not discussed in this paper. Acknowledgments The authors gratefully acknowledge primary funding provided for this project by the National Science Foundation (Grant No.CMS-0000031) and supplementary funding provided by the American Institute of Steel Construction. References American Institute of Steel Construction, Inc. (AISC). 2002. Seismic provisions for structural steel buildings, Standard ANSI/AISC 341-02, Chicago, IL. Choi J., Stojadinovic B., and Goel S.C. 2002. Development of free flange moment connection. Report No. UMCEE 00-15, Department of Civil and Environmental Engineering, University of Michigan, Ann Arbor, MI. Federal Emergency Management Agency (FEMA). 2000. FEMA-350. Recommended seismic design criteria for new steel moment-frame buildings, Washington, DC. Hancock J.W. and Mackenzie, A.C. 1976. On the mechanisms of ductile failure in high-strength steel subjected to multi-axial stress-states. Journal of the Mechanics and Physics of Solids, 24, 147-169. Kuwamura, H. and Yamamoto, K. 1997. Ductile crack as trigger of brittle fracture in steel. Journal of Structural Engineering, ASCE, 123(6), 729-735. Okazaki, T. 2004. Seismic performance of link-to-column connections in steel eccentrically braced frames. Ph.D. Dissertation, Department of Civil Engineering, University of Texas at Austin, Austin, TX. Mao C., Ricles J.M., Lu L.-W., and Fisher J.W. 2001. Effect of local details on ductility of welded moment connections. Journal of Structural Engineering, ASCE, 127(9), 1036-1044. Richards P. and Uang C.-M. 2003. Development of testing protocol for short links in eccentrically braced frames. Report No. SSRP-2003/08, Department of Structural Engineering, University of California, San Diego, LaJolla, CA. Suita, K., Nakashima, M., and Engelhardt, M.D. 2000. Comparison of seismic capacity between postNorthridge and post-Kobe beam-to-column connections, The third International Conference on Behavior of Steel Structures in Seismic Areas, STESSA 2000, Montreal, Canada. Tabuchi, M., Tanaka, T., and Iguchi, T. 2002. Effects of end-tab shapes on plastic deformation capacity of wide-flange beams connected with SHS column. Journal of Steel Construction Engineering, Japan Society of Steel Construction, 9(35), 1-16. (in Japanese).