RELIABILITY OF EXPOSED COLUMN-BASE PLATE CONNECTION IN SPECIAL MOMENT-RESISTING FRAMES

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1 October 1-17, 008, Beijin, China RELIABILITY OF EXPOSED COLUMN-BASE PLATE CONNECTION IN SPECIAL MOMENT-RESISTING FRAMES A. Aviram 1, B. Stojadinovic, and A. Der Kiurehian 3 1 Ph.D. Candidate, Department of Civil and Environmental Enineerin, University of California, Berkeley. aaviram@berkeley.edu Professor, Department of Civil and Environmental Enineerin, University of California, Berkeley. boza@ce.berkeley.edu 3 Taisei Professor and Vice Chair for Instruction, Department of Civil and Environmental Enineerin, University of California, Berkeley. adk@ce.berkeley.edu ABSTRACT : Many steel moment-resistin frame buildins suffered failure at their column base connections durin the 1995 Kobe, 1994 Northride and 1989 Loma Prieta earthquakes. System reliability analysis of an exposed moment-resistin base plate connection desined for a low-rise steel special moment resistin frame is carried out usin a structural reliability analysis software. Modes of failure of the column base are defined usin a limit-state formulation based on the AISC Desin Guide No The predominant failure modes of the exposed column base include: yieldin of the base plate on the compression side, crushin of concrete, and shear failure due to slidin of the base plate and bearin failure of the shear lus aainst the adjacent concrete. Sensitivity analysis is carried out to determine the influences of limit-state and distribution parameters on the reliability of the system. On the demand side, the cantilever lenth of the base plate extendin beyond the column cross section and the bendin moment at the column base are found to be the main parameters influencin the failure of the column base connection. On the capacity side, the thickness of the base plate and the strenth of steel are the main parameters influencin the reliability of the connection. Fraility curves are developed for each failure mode of the column base plate as well as for the connection as a system. These are expressed as a function of the spectral acceleration at the first mode period of the buildin. KEYWORDS: steel base plate connection, reliability analysis, moment resistin frame 1. INTRODUCTION A typical column-base connection between the column of a steel moment-resistin frame (MRF) and its concrete foundation, commonly used in US steel construction today, consists of an exposed steel base plate supported on unreinforced rout and secured to the concrete foundation usin steel anchor bolts. This moment-resistin connection is enerally subjected to a combination of hih bendin moments, axial and shear forces. A number of steel buildins, particularly low-rise moment resistin frame systems, developed failure at the column-base plate connection durin the 1995 Kobe, 1994 Northride and 1989 Loma Prieta earthquakes. It was found (Bertero et.al, 1994; Youssef et.al, 1995) that the rotational stiffness and strenth of the base plate assemblaes affected the damae these structures suffered not only directly in the column bases, but also in other reions of their lateral load resistin frames. A number of methodoloies for the desin of column-base plate connections under various load conditions are found in the literature. The most recent method presented in the AISC Desin Guide No (Fisher and Kloiber, 005) is already widely implemented in current US enineerin practice. Reliability analysis of a column base connection in a MRF, obtained usin the AISC Desin Guide No procedure, has not been carried out to date. Yet, such reliability analysis is needed to assess the safety of this important structural component with respect to its diverse failure modes and to evaluate the adequacy of the

2 October 1-17, 008, Beijin, China desin method and limit-state formulation. A sensitivity analysis of the different components of the column base connection is needed to identify the critical parameters in the desin process. These issues are the focus of the present paper.. RELIABILITY ANALYSIS Seismic desin of an exposed column base connection in a typical low-rise moment resistin frame is carried out in the US followin the AISC Desin Guide No procedure. In this paper, the column base connection of an exterior column of the ATC-58 3 story-3 bay MRF office buildin, which is located on the University of California at Berkeley campus (Yan et.al, 006), is used as an example. This connection is shown in Fiure 1. Steel column Steel base plate Anchor bolts Steel anchor bolts Unreinforced rout A P V M A B Concrete foundation N Section A - A Fiure 1 Confiuration of a typical exposed base plate connection The loads used for the desin of the connection are obtained from a series of nonlinear time history analysis (NL THA) of the MRF model with fixed column bases. The median values of the joint reactions obtained from a suite of 7 round motions correspondin to the desin earthquake hazard level (10% in 50 years probability of exceedance (PE)) are used to desin the connection. Several load combinations from each NL THA are considered to find the critical load combination Random Variables The followin table summarizes the random variables (RVs) used in the reliability analysis of this column base connection. These RVs and their distributions represent different column base components and parameters that influence the behavior of the selected column base connection at different hazard levels defined for a site in Berkeley, California Table 1 Summary of column base connection random variables RV Description Distribution μ-mean Units c.o.v. Reference/Source Dimensions d c Column depth Normal 6.0 in 0.01 ASTM A6-05 b f Column flane width Normal in 0.01 ASTM A6-05 N Base plate lenth Normal 38.0 in 0.05 ASTM A6-05 B Base plate width Normal 5.0 in ASTM A6-05 t PL Base plate thickness Normal 3.75 in 0.03 ASTM A6-05 l sl Shear lu depth Beta 3.5 in 0.15 ASTM A6-05 b sl Shear lu lenth Normal 5.0 in 0.05 ASTM A6-05 d b Anchor bolt diameter Normal.0 in 0.05 ASTM F d ede Ede distance from bolt centerline Normal 3.0 in AISC-Code Standard Practice, 000 t Grout thickness Beta.0 in 0.5 AISC-Code Standard Practice, 000

3 October 1-17, 008, Beijin, China Table 1 Continued RV Description Distribution μ-mean Units c.o.v. Reference/Source Material Strenth F y,pl Base plate steel yield stress, Gr. 36 Lonormal 50 ksi 0.07 ASTM A99-04; Liu, 003 F ub Anchor bolt ultimate stress, Gr. 105 Lonormal ksi 0.10 ASTM F f c Concrete compressive strenth (4 ksi) Lonormal 4.8 ksi 0.15 MacGreor, 005 Coefficients μ Friction coefficient Beta Fisher and Kloiber, 005 Loads Hih hazard level- Collapse Prevention (% in 50 yr PE): Case M max P m Seismic axial load (includin ravity) Lonormal 43.6 kips 0.07 NL THA V m Seismic shear force Lonormal 41.6 kips 0.13 NL THA M max Seismic bendin moment Gumbel kip-in 0.08 NL THA Hih hazard level- Life Safety (5% in 50 yr PE) : Case M max P m Seismic axial load (includin ravity) Lonormal kips 0.01 NL THA V m Seismic shear force Gumbel 18.4 kips 0.09 NL THA M max Seismic bendin moment Lonormal kip-in 0.03 NL THA Moderate hazard level- Immediate Occupancy (10% in 50 yr PE): Case M max P m Seismic axial load (includin ravity) Lonormal 48.8 kips 0.01 NL THA V m Seismic shear force Gumbel 06.5 kips 0.08 NL THA M max Seismic bendin moment Lonormal kip-in 0.09 NL THA Low hazard level- Operational (50% in 50 yr PE): Case M max P m Seismic axial load (includin ravity) Lonormal kips 0.08 NL THA V m Seismic shear force Gumbel 11.4 kips 0.3 NL THA M max Seismic bendin moment Lonormal kip-in 0.1 NL THA The friction coefficient is taken to have a relatively hih mean value of 0.80 because net tension rarely occurs in this specific column base connection, even under severe round motions correspondin to the hihest seismic hazard level. The load case correspondin to the maximum bendin moment (M max ) and the correspondin shear (V m ) and axial (P m ) loads occurrin at the same time instant is found to be the most critical for the connection, resultin in the hihest failure probabilities. Additional load cases are also considered in the analysis but are not presented in this paper for brevity. The correlation coefficients between the seismic shear, bendin moment and axial loads are determined based on 7 records for each hazard level. The Nataf joint distribution model (Liu and Der Kiurehian, 1986) is assumed for the loads. 1.. Limit-State Formulation and Failure Mode Hierarchy The limit-state for each failure mode of the base-plate connection is formulated based on the AISC Desin Guide No procedure. This Guide assumes a rectanular stress distribution in the supportin concrete foundation, consistent with the LRFD method for desin of reinforced concrete structures used in the US. Accordin to the LRFD methodoloy, different components of the connection are considered to be at their plastic or ultimate capacities and their relative stiffnesses are disrearded for determination of internal forces. The flexibility of the base plate is nelected for calculatin the bearin stress. The dimensions of the plate and the anchor bolts required to achieve the desired strenth are obtained from lobal vertical and moment equilibrium equations. The yield-line theory is used to model the bendin behavior of the base plate. The resultin base plate desin is also checked for shear-friction resistance and anchor bolt shear. If the shear capacity is insufficient, bearin action to resist shear can be developed by addin shear lus under the base plate. Shear checks are performed assumin no interaction between the shear and moment resistances. The limit-state functions (x) for all failure modes used for the component and system reliability analysis are defined as the difference between the correspondin capacity and demand values: (x) = Capacity Demand (see Table ). Failure is defined as the event where demand exceeds capacity, i.e. (x)<0, and does not necessarily correspond to a physical collapse of the connection. For the ductile failure modes, a redistribution of forces amon the components of the connection is expected to occur. Such behavior is disrearded in this formulation.

4 October 1-17, 008, Beijin, China Table Limit-state functions Component Description i (X)- Limit-state function 1 Concrete crushin P M ( ) ( ) = 1 X 0.85kf ' c + NB 1/ 6 BN Yieldin of the base plate due to cantilever bendin on the compression side 3 Yieldin of the base plate due to cantilever bendin on the tension side 4 Tensile yieldin of anchor bolts ( X ) ( X ) 3 A = F = ( t ) y, pl p P M 1 B 0.80b f 4 ( 1/ 6) + NB BN F ( ) ( ) ( ) y, plb t p N dc dede = 0.85kf ' c B A P 4 P ( ) ( ) ( M P + N dede) N d N d ede ede 0.85kf ' B n π d b 4 ( X ) = ( Cub 1 ) Fub ( 0.85kf ' c B A P) 4 C ub1 =0.75 is a coefficient for ultimate stress of the anchor bolts in tension. X = μp 5 Friction failure or slidin of plate ( ) V 6 Shear failure of anchor bolts 7 Bearin failure of shear lus aainst the adjacent concrete 5 b 6 ( X ) = CubFub 4 C ub =0.50 is a coefficient for ultimate stress of the anchor bolts in shear. Only two bolts are assumed to be effective in resistin shear in the connection. π d ( X ) = C f ' n b ( l t ) V 7 br c sl sl sl rout C br =0.80 is a concrete bearin coefficient Selection of base plate dimensions and material strenths followin the AISC Desin Guide method resulted in some hihly unlikely failure modes (i.e. these failure modes have hih safety factors). They are: concrete ede breakout, anchor bolt pull-out failure, bearin failure of the base plate, bendin failure of the shear lus, and column-to-base-plate weld failure. These failure modes are therefore inored in this paper. A hierarchy of column base connection failure modes used in the reliability analysis is shown in Fiure. V c Concrete crushin 1 3 Cantilever bendin, compression side Cantilever bendin, tension side Yieldin of base plate 4 5 Tension yieldin of anchor bolts Friction 6 7 Anchor bolt shear Bearin of shear lus Shear failure Fiure Hierarchy of column base connection failure modes The minimum cut-set formulation of the system is: C min ={(1)()(3)(4)(5,6)(5,7)}, i.e., the failure of the system can occur due to 6 failure modes. The component and system reliability analyses are carried out usin the first-order reliability method (FORM) for the four seismic hazard levels shown in Table 1. Computations are carried out usin the CalREL software (Der Kiurehian, Haukaas and Fujimura, 006). 3. DISCUSSION OF RESULTS 3.1. System Reliability Analysis Results Usin the minimum cut-set formulation for the column base connection system, component reliability analysis

5 October 1-17, 008, Beijin, China results are combined to obtain the conditional system failure probability of the connection for the four seismic hazard levels considered. The desin of the connection remains unmodified throuhout. The failure probabilities for each failure mode and for the system are presented in Table 3. Table 3 Conditional failure probabilities computed for different hazard levels P f1 - Failure probability Hazard level (PE in 50 yr) Failure Mode Description % 5% 10% 50% 1 Concrete crushin 5.818x x x x10-4 Yieldin of base plate (compression side).956x x x x Yieldin of base plate (tension side) 5.554x x x x Tensile yieldin of bolts 1.695x x x x Friction & bolt shear.370x x x x Friction & bearin of shear lus.19x x x x10-4 System- Failure probability P f x x x x10-3 System- Reliability index β The total failure probability for each failure mode and for the system are obtained by combinin the correspondin conditional failure probabilities at each hazard level presented above weihted by the correspondin probabilities of the hazard levels. Table 4 presents the total failure probabilities for 1 year and for the expected 50 year lifespan of the structure. Also shown in Table 4 is the correspondin system reliability index. Table 4 System failure probability P f1 and reliability index β Failure Mode Description P f1,t=50 yr (%) P f1,t=1 yr (%) 1 Concrete crushin 3.34x x10-4 Yieldin of base plate (compression side).06x x Yieldin of base plate (tension side) 1.983x x Tensile yieldin of bolts 6.054x x Friction & bolt shear 9.469x x Friction & bearin of shear lus.373x x10-4 System- Failure probability P f1.431x x10-3 System- Reliability index β The larest contribution to the system failure probability is due to yieldin of the base plate on the compression side, which is a ductile and desirable failure mode. The other dominant failure modes are undesirable brittle failures includin concrete crushin and shear failure due to slidin of the base plate and bearin failure of the shear lus aainst the adjacent concrete. Tension yieldin of the anchor bolts also has an important contribution. The remainin failure modes have neliible contribution to the system s failure for this connection desin. The resultin system reliability index β of 1.97 and failure probability P f1 of.43% computed for the expected 50 year lifespan of the structure may be considered relatively low and hih, respectively. The desin, carried out for the 10% in 50 year PE hazard level, also results in relatively hih conditional failure probability of 9.17% for an earthquake of relatively moderate intensity. For the hihest seismic hazard level of % in 50 year PE, the failure probability of 34.31% is also relatively hih. Based on the results of this reliability analysis, the AISC Desin Guide No column base plate connection desin procedure should be modified by reducin resistance factors to increase connection reliability. It is also important to incorporate a capacity desin approach to promote the occurrence of ductile failure modes over brittle failure modes. The failure probability estimates presented above, which employ the well known PEER formula, entail an error due to the presence of non-erodic variables (Der Kiurehian, 005). The oriinal PEER formula was intended to compute the mean annual rate of a performance measure exceedin a specified threshold. Approximation of the exceedance probability usin this formula may result in as much as 0% error for probabilities around 0.05 and 30% error for probabilities around For failure probabilities less than 0.01 the approximation has a neliible error. In the present project the total failure probability of the connection computed for one year is less than 0.01.

6 October 1-17, 008, Beijin, China Therefore this approximation of the failure probability has a neliible error. For the lifespan of the structure of 50 years, the error in the failure probability of.43% may be as much as 0%. However, since the error is on the conservative side (Der Kiurehian, 005), this approximation of the connection reliability is found to be acceptable. Fraility curves are obtained relatin the conditional failure probabilities of occurrence of each failure mode and occurrence of system failure to an earthquake intensity measure (IM). In this study, IM is the spectral acceleration at the first mode period (S a,t1 ) of the MRF. This measure was computed at each hazard level usin the hazard data for a location in Berkeley, California. The fraility curves are obtained usin a lonormal fit to the data presented in Table 3 and a least-square approximation of the error (see Fiures 3 and 4). System Pf,1- Failure probability Pf,1- Failure probability Concrete crushin Base plate yieldin (compression side) Friction and bearin failure of shear lus S a,t1 - spectral acceleration [] at 1 st mode period of MRF Fiure 3 Lonormal fit to failure probabilities of base plate connection S a,t1 - spectral acceleration [] at 1 st mode period of MRF Fiure 4 Fraility curves for the system and predominant failure modes 3.. Relative Importance of Random Variables Determinin the order of importance of random variables for column base connection behavior is performed by perturbin the mean values of these variables (on the order of 10%), determinin the resultin variations in connection reliability, and computin the importance value δ=( β/ μ)σ for each variable. The characterization as a capacity or demand variable is established for each RV accordin to the sin of the correspondin element in vector δ. The results computed for the % in 50 year PE hazard level are presented in Table 5. Table 5 Importance vector δ obtained from system reliability analysis RV δ=( β/ μ)σ Order of Importance Approximate Classification RV δ=( β/ μ)σ Order of Importance Approximate Classification d c.40x Capacity t -7.5x10-9 Demand b f 8.65x10-7 Capacity F y,pl 3.0x Capacity N.7x Capacity F ub 4.09x Capacity B -5.3x Demand f c 1.0x Capacity t PL.0x Capacity μ 7.80x10-8 Capacity l sl.86x Capacity P -.80x Demand b sl 3.46x Capacity V -5.7x10-10 Demand d b 3.00x Capacity M -4.90x10-1 Demand d ede -4.17x Demand On the demand side, the base plate dimension affectin directly the cantilever lenth and bendin moment of the column base plate has the hihest influence on the failure of the connection. On the capacity side, the base plate thickness and base plate steel strenth represent important components of the system resistance. The strenth of the concrete foundation and the friction coefficient between the base plate and rout are the next important aspects affectin the reliability of the column base connection.

7 October 1-17, 008, Beijin, China 3.3. Sensitivity Analysis of Limit-State Parameters The sensitivity of the failure probability P f1 of the system with respect to the limit-state parameters, denoted θ, are obtained throuh a small perturbation in the parameter values (on the order of 5%) and the computation of the resultin variations in P f1. The results for the % in 50 year PE hazard level are presented in Table 6. The confinement coefficient k, which for the present desin is equal to.0 based on the assumption of adequate transverse reinforcement and lare cross section of the concrete pedestal, has a sensitivity θ P f (θ /P f ) of For example, this corresponds to an increase of (or 8.9%) in the system failure probability P f1 for the % in 50 year hazard level if the value of parameter k is reduced by 10% due to inadequate confinement. The remainin limit-state parameters have small to neliible effect on the failure probabilities of the connection, even for the hihest hazard level. Table 6 Sensitivities of P f1 of the system to variation in limit-state parameters θ Parameter Description θ - Value θ P f (θ /P f )-Sensitivity k Concrete confinement coefficient for maximum stress C ub1 Coefficient for tension in anchor bolts C ub Coefficient for shear in anchor bolts C br Coefficient for bearin of shear lus CONCLUSIONS The reliability of an exposed column base desined accordin to the AISC Desin uide No provisions was evaluated in this paper. A sample column base was desined for the moment resistin frame of the ATC-58 buildin located in a hih seismic zone. Random variables describin this desin were characterized usin ASTM and AISC desin code data. The demands on the column base were characterized usin data from suites of non-linear time history earthquake response analyses of the ATC-58 buildin frame conducted at four different seismic hazard levels (, 5, 10 and 50% in 50 year probabilities of exceedance). A hierarchy of column base connection failure modes was established. Reliability analysis was carried out usin the FORM approximation to compute the reliability index of the connection. Fraility curves for each failure mode and the system were developed usin a lonormal fit. The most likely failure modes of the connection were yieldin of the base plate on the compression side (ductile), concrete compression crushin (brittle), and shear failure due to base plate slidin and bearin failure of shear lus (brittle). In order to promote ductile failure modes and a desirable failure mode sequence, resistance factors in AISC Desin Guide No should be decreased and a capacity desin approach should be riorously adhered to. Althouh relatively hih failure probabilities were computed for the column base connection at the hih hazard level (34.31%), a lower probability of failure equal to.43% (β=1.97) was obtained as the combined total failure probability of the connection in 50 years. This failure probability can still be considered as relatively hih for a critical structural connection. The column base connection desin procedure proposed in AISC Desin Guide No.1 can therefore be considered unconservative. A sensitivity analysis was carried out to evaluate the importance of the random variables, as well as the sensitivity of the failure probabilities to variations in the limit-state function parameters. On the demand side, the larest cantilever lenth of the base plate has the hihest importance for the connection s failure. This dimension should be minimized durin the desin process to minimize the bendin demand on the plate. The thickness of the plate and its yield strenth are also important variables controllin failure. Finally, a reduction in the confinement of the foundation can lead to an important increase of the failure probability of the connection due to crushin of concrete. Steel frame and foundation desiners should interact to ensure adequate confinement of the foundation, particularly for column bases of the perimeter columns. Resistance to slidin of the column base should be studied further to better understand the interaction between the

8 October 1-17, 008, Beijin, China different shear resistance mechanisms and their sequence. Different column base confiurations should also be investiated because other failure modes may be triered. Data from laboratory tests is needed to perform additional component and model uncertainty analyses, and to calibrate the resistance factors in the desin equations. REFERENCES American Institute of Steel Construction (000). Code of Standard Practice for Steel Buildins and Brides, American Institute of Steel Construction, Inc., Chicao, Illinois. ATC-58 (in proress). Development of Next-Generation Performance-Based Seismic Desin Procedures for New and Existin Buildins, Applied Technoloy Council, Committee 58, ASTM A99 (004). Standard Specification for Structural Steel Shapes, American Standards for Testin and Materials, ASTM International, West Conshohocken, Pennsylvania. ASTM A6 (005). Standard Specification for General Requirements for Rolled Structural Steel Bars, Plates, Shapes, and Sheet Pilin, American Standards for Testin and Materials, ASTM International, West Conshohocken, Pennsylvania. ASTM F1554 (004). Standard Specification for Anchor Bolts, Steel, 36, 55, and 105-ksi Yield Strenth, American Standard for Testin and Materials, ASTM International, West Conshohocken, Pennsylvania. Bertero V.V., Anderson J.C., and Krawinkler, H. (1994). Performance of Steel Buildin Structures durin the Northride Earthquake, Report No. UCB/EERC-94/09, Earthquake Enineerin Research Center, University of California at Berkeley. Der Kiurehian, A. (005). Non-erodicity and PEER s Framework Formula. Earthquake Enineerin and Structural Dynamics 34, Der Kiurehian, A., T. Haukaas and K. Fujimura (006). Structural reliability software at the University of California, Berkeley. Structural Safety, 8(1-): Fisher, J.M. and Kloiber, L.A., 005. AISC Desin Guide No.1- Column Base Plates, American Institute of Steel Construction. Liu, P-L., and A. Der Kiurehian (1986). Multivariate distribution models with prescribed marinals and covariances. Probabilistic Enineerin Mechanics, 1, MacGreor, J. G. and Wiht, J. K. (005). Reinforced Concrete: Mechanics and Desin, 4 th Edition, Prentice Hall, Upper Saddle River, New Jersey. Yan, T.Y., Moehle, J., Stojadinovic, B., and Der Kiurehian, A. (006). An Application of PEER Performance-Based Earthquake Enineerin Methodoloy. Proceedins, Eihth National Conference on Earthquake Enineerin, San Francisco, California, April 18-, 006, CD, Paper #171. Youssef, N.F.G., Bonowitz, D., and Gross, J.L. (1995). A Survey of Steel Moment-Resistin Frame Buildins Affected by the 1994 Northride Earthquake, NISTIR 565. National Institute of Standard and Technoloy, Gaithersbur, Maryland.