Tenth U.S. National Conference on Earthquake EngineeringFrontiers of Earthquake Engineering July 21-25, 2014 Anchorage, Alaska 10NCEE

Seismic assessment and rehabilitation of existing steel braced frames designed in accordance with the 1980 Canadian code

provisions

Yasaman Balazadeh-Minouei1, Sanda Koboevic2 and Robert Tremblay3

ABSTRACT The seismic deficiencies of a 10-storey steel braced frame designed in accordance with the 1980 NBCC and CSA-S16.1-M78 standard are evaluated using the linear and nonlinear procedures defined in the ASCE 41 standard. When the linear procedure is applied, all the braces and the columns at the 10th floor show sufficient strength. The resistance of all the other columns is inadequate. Nonlinear procedure on the other hand predicts excessive inelastic deformation demand in the braces at the upper levels and identifies the risk of column buckling in the lower levels. The columns are retrofitted based on the axial demand obtained from nonlinear procedure and the retrofit solution is validated through additional nonlinear analysis. The force-delivery reduction factor proposed in the ASCE 41 standard is also investigated.

1Graduate Student Researcher, 2Assistant Professor, 3Professor, Dept. of Civil Geological and Mining Engineering, Ecole Polytechnique of Montreal, Montreal, QC, Canada, H3T 1J4 Balazadeh-Minouei, Y., Koboevic, S., and Tremblay, R. T Seismic assessment and rehabilitation of existing steel braced frames designed in accordance with the 1980 Canadian code provisions. Proceedings of the 10th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.

Seismic assessment and rehabilitation of existing steel braced frames

designed in accordance with the 1980 Canadian code provisions

Yasaman Balazadeh-Minouei1, Sanda Koboevic2 and Robert Tremblay3

ABSTRACT The seismic deficiencies of a 10-storey steel braced frame designed in accordance with the 1980

NBCC and CSA-S16.1-M78 standard are evaluated using the linear and nonlinear procedures defined in the ASCE 41 standard. When the linear procedure is applied, all the braces and the columns at the 10th floor show sufficient strength. The resistance of all the other columns is inadequate. Nonlinear procedure on the other hand predicts excessive inelastic deformation demand in the braces at the upper levels and identifies the risk of column buckling in the lower levels. The columns are retrofitted based on the axial demand obtained from nonlinear procedure and the retrofit solution is validated through additional nonlinear analysis. The force-delivery reduction factor proposed in the ASCE 41 standard is also investigated.

Introduction Seismic design and detailing provisions for steel structures were integrated into the CSA S16 design standard in 1989. These provisions have since evolved significantly [1] as new studies on seismic hazard and seismic response of structures became available along with experience gained from recent earthquakes. In parallel, several changes have also been implemented in seismic design provisions of the National Building code of Canada ever since the seismic loads were first introduced for building design in 1941 [2]. The latest Canadian code, NBCC 2010 [3], and the steel design standard CSA S16-09 [4] reflect the most recent findings in the area of seismic engineering and are comparable to seismic design norms of other countries.

In the 1980’s, prior to the implementation of seismic requirements in CSA S16, steel braced frames with tension-only bracing and chevron bracing systems were commonly used to resist lateral loads in steel buildings in Canada. The bracing members were usually designed as back-to-back double angle sections while beams and columns were selected from W shapes. Bolted end brace connections were typically used with back-to-back legs directly connected to single vertical gusset plates by high strength bolts. Due to the absence of any explicit seismic design, these frames are likely to exhibit severe seismic deficiencies. This paper presents the seismic assessment of a tension-only X-braced frame used in a prototype 10-storey building located in Vancouver, British Columbia. The structure was designed in accordance with the 1980 NBCC [3]

1Graduate Student Researcher, 2Professor, 3Professor, Dept. of Civil Geological and Mining Engineering, Ecole Polytechnique of Montreal, Montreal, QC, Canada, H3T 1J4 Balazadeh-Minouei, Y., Koboevic, S., and Tremblay, R. T Seismic assessment and rehabilitation of existing steel braced frames designed in accordance with the 1980 Canadian code provisions. Proceedings of the 10th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.

and the assessment is performed using the ASCE 41-13 standard [5]. This U.S. standard provides requirements for the analysis and assessment of existing buildings and includes acceptance criteria for the structural components. The Tier 3 systematic procedure was followed to asses the behavior at the collapse prevention performance level for 2% in 50 years hazard, which corresponds to the basic NBCC performance objective in the 2010 NBCC design spectrum was used in the analyses and member capacities were determined using the provisions of the current CSA S16-09 steel design standard.

The selection of the seismic assessment method is usually done considering the objectives

of the assessment program, the cost and the available time. The analytical procedures used to determine seismic demand vary greatly in their complexity to represent structural behavior and the easiness of use for practical applications. Because the linear analyses are more often applied in practice, it is of interest to establish if the seismic structural assessment based on such analyses is consistent with the one determined using more sophisticated analysis methods. In this study, the analysis was performed using both the linear and nonlinear dynamic procedures proposed in the ASCE 41 standard and different numerical modeling techniques were considered to assess the seismic demand on the structure. The study focused on the bracing members and columns of the braced frames. The columns were found to be deficient and a strengthening scheme is proposed and validated through nonlinear response time history analysis. The force-delivery reduction factor proposed in ASCE 41 is also investigated.

Design of the Building Studied The building studied has a regular structural arrangement in plan with five 9.144 m wide bays in each orthogonal direction. The storey heights are 4.572 m at the first floor and 3.962 m at the other nine levels [6]. The structure was designed following the 1980 NBCC provisions. This code edition was selected because the design seismic loads are much lower than those specified in the 2010 NBCC. The building is of the normal importance category and is situated on a firm ground site in Vancouver, British Colombia. Lateral loads are resisted by two tension-only X-braced frames in the N-S direction and two chevron braced frames in the E-W direction. This study focuses on the assessment of the X-braced frames. In 1980, the design seismic base shear was determined from:

V = ASKIFW (1) In this equation, A is the design acceleration ratio, S is the seismic response factor (S = 0.5/T0.5 ≤ 1.0, where T is the fundamental period of the structure), K is a coefficient related to the type of construction, I is the importance factor, F is the foundation factor and W is the seismic weight. For this structure, A = 0.08, I = 1.0, F = 1.0, and W is equal to 83756 kN for the entire building. The fundamental period of the structure was obtained using the Rayleigh method, as was permitted in the 1980 NBCC and would have been done in practice in the early 1980’s. An iterative design procedure was therefore applied in which the periods and loads were recalculated until member selection converged. The fundamental period of the final X-braced frame is 2.77 s. In the NBCC, K = 1.3 for the tension-only X-bracing, which resulted in seismic force coefficient, V/W = 0.032. The equivalent static force procedure was used to determine earthquake effects in the structure, as was permitted for regular structures in the 1980 NBCC. A concentrated lateral force Ft = 7.74% V was applied at the roof level and the remaining seismic load, V – Ft, was

distributed along the height of structure as a function of the relative product of the seismic weight and the height measured from the ground to the level under consideration. The overturning moment reduction factor, J, was equal to 1.0. In-plane accidental torsion and P-delta effects were accounted for in the design.

The braced frames were designed based on the requirements of CSA-S16.1-M78 steel design standard [7]. The structural members were made of CSA-G40.21-300W steel (Fy = 300 MPa, Fu = 450 MPa). All bracing members were double angle sections with equal legs in back-to-back position. The overall slenderness ratio was limited to 300 for the tension-only braces and the unsupported length was taken equal to half of the total brace length. All braces were connected to single vertical gusset plates using high-strength ASTM A325 bolts, 19.1 mm in diameter. The design of the bracing members was governed by axial strength requirements, except at the roof level where the maximum brace overall slenderness limits were critical. For these braces, the connections were designed for 50% of the factored brace tensile resistance, as prescribed in CSA S16.1-M78. Governing design requirements for top storey braces resulted in beneficial brace and brace connection overstrengths. Shear lag effects and block shear failure were not considered in the design standard at that time, which led to smaller brace connections compared to current designs performed today. The beams and columns were selected from W sections. Two-storey column tiers were used. The beams were assumed to be laterally supported by the floors and thus were selected to resist shear and flexure from gravity loads and strong axis buckling under combined axial compression and bending.

Numerical Modelling

Four analytical models were considered for the analysis. Model A is a three dimensional representation of the entire structure with elastic beam elements employed to model the braces, columns and beams. Rigid diaphragm response was assumed at every level. This model was used for the elastic response spectrum analysis procedure. The results confirmed that the structure had limited in-plane torsional response. Thus it was possible to use two-dimensional model of one of the two X-braced frames for the subsequent application of the nonlinear analysis procedure. Three such nonlinear braced frame models were developed using the OpenSees platform [8] considering the type of analysis to be performed for the seismic assessment. In Model B, the braces were represented by nonlinear beam-column elements whereas elastic beam-column elements were used for the columns and beams. This model permitted partial study of nonlinear frame response accounting only for the cyclic tensile yielding and inelastic buckling responses of the braces. Each angle of the bracing members was modelled using 16 nonlinear beam-column elements, with 4 integration points per element and fiber discretization of the section to reproduce distributed plasticity. The two series of angle elements were connected at their ends and at the locations of the stitch connectors. The Giuffré-Menegotto-Pinto (Steel 02) material with kinematic and isotropic hardening properties was assigned to the fibers representing the angle cross-sections. Initial out-of-straightness and residual stresses were also considered [6-9]. Elastic beam elements were used to model the beams and columns in order to evaluate the elastic force demand on these members. Zero-length elements with high axial and negligible flexural stiffness were considered to model the beam-to-column connections. Column bases were assumed to be pinned.

In a third model (Model C) nonlinear beam-column elements were employed for both the braces and the columns while the beams were represented by elastic beam elements. Model C permitted to examine the influence of column inelastic buckling on the braced frame response. Braces and columns representation in this model is the same as that used for the braces in Model B except that 10 nonlinear beam-column elements with 4 integration points placed along each element were used for the column segments at every level of the columns. The cross section of each element was discretized by fibers. The Steel02 material was used with a residual stress pattern typical for W shaped columns. Initial in-plane and out-of-plane out-of-straightness was assigned to the columns with a half-sine wave deformation having a maximum amplitude of 1/1000 of the unsupported storey height. This amplitude corresponds to the limit prescribed in CSA-S16.1-M78. A fourth model (Model D) was used to assess the adequacy of the strengthening scheme proposed for the columns based on axial demand obtained from the nonlinear response analysis. Model D is identical to Model C except that the cross-sections of the column elements were modified by adding the strengthening plates after the application of the gravity loads, prior to subjecting the structure to the seismic demand. Residual stresses were not modelled in the column reinforcement plates.

The load combination in the analyses was as specified in the NBCC, i.e.

1.0D+0.5L+0.25S+1.0E, where D, L, S and E respectively refer to the dead load, the floor live load, the roof snow load and the earthquake load. P-delta effects were considered in all models. Damping equal to 5% of critical was considered in the response spectrum analysis while 3% Rayleigh damping in modes 1 and 2 was specified in Models B to D.

Linear Analysis Procedure Linear procedure is permitted for regular structures, which is the case for the frame studied. The response spectrum analysis is selected and conducted using Model A. ASCE 41 standard classifies steel components as either deformation controlled (ductile) or force controlled (non-ductile) elements. Also, different actions for a same element can be classified in different categories. For instance, axial actions on braces are considered as deformation-controlled, whereas bending moments in beams and columns can be considered as force- or deformation-controlled actions depending on the amplitude of the axial loads. Shear and bending moment actions on brace connections must be treated as force-controlled. Moreover, structural elements should be categorized as primary or secondary components. A primary component resists seismic forces to provide the selected performance level for the structure while a structural component not designed to resist seismic forces and achieve the selected performance level is categorized as a secondary component. In the linear analysis procedure, deformation- and force-controlled actions are evaluated using: Deformation-controlled actions: mκQCE ≥ QUD (2) Force-controlled actions: κQCL ≥ QUF (3) where m is the component demand modification factor to account for the expected ductility related to this action at the selected structural performance level, κ is the knowledge factor, QCE is the expected strength of a component at the deformation level under consideration for deformation-controlled actions, QUD is the deformation-controlled design action due to gravity loads (QG) and earthquake loads (QE), QCL is the lower-bound strength of a component at

the deformation level under consideration for force-controlled actions, and QUF is force-controlled design action determined by Eq. 4: QUF = QG ± QE / (C1 C2 J) (4)

where C1 is the modification factor that relates the expected maximum inelastic displacements to displacements calculated using linear elastic response, C2 is a modification factor that considers the effect of pinched hysteresis shapes, cyclic stiffness degradation, and strength deterioration on maximum displacement response, and J is the force delivery reduction factor, calculated as the smallest demand capacity ratio (DCR = QUD/QCE) of all components in the load path delivering forces to the component being examined.

For tension-only bracing members, the m-factor in is equal to 4.0 when the systems are

evaluated for the collapse prevention performance level. The knowledge factor, κ, was taken equal to 1.0 because comprehensive data was available. The member capacities were determined based on the CSA S16-09 standard with resistance factors equal to 1.0. For the braces, QCE was computed with expected steel yield strength Fye taken as 1.1 times the nominal value Fy = 300 MPa (Fye = 330 MPa). For the columns (force-controlled), the lower bound steel yield strength corresponding to Fy = 300 MPa was used to determine QCL. In ASCE 41-13, the C1 and C2 coefficients are equal to 1.0 for periods longer than 1.0 s and 0.7 s, respectively. The period of the studied building was 2.77 s thus both coefficients were taken equal to 1.0 to assess the force controlled actions of components.

The resulting demand-to-capacity ratios for the braces and the columns from linear analysis using Model A are shown in Figs. 1 a, and 1 b respectively. All bracing members have sufficient strength while none of the columns have sufficient axial compressive resistance except for the columns located at the 10th storey. Linear analysis procedure indicates that the columns at level 1 are the most critical.

Figure 1. Assessment of the braces (a) and columns (b) using linear (Model A) and nonlinear (Model B) procedures.

Nonlinear Analysis Procedures

Response history analyses were used for the nonlinear analysis procedures. Twenty historical ground motions were first selected on basis of the magnitude-distance scenarios contributing the most to the

hazard at the site, as proposed by Atkinson [10]. The records were scaled such that the average value of the response spectra did not fall below the NBCC 2010 spectrum for periods ranging from 0.2T to 1.5T, where T is the fundamental period of the structure [11]. Out of twenty records, the three records with the target spectrum-to-the record spectrum between 0.5 and 2.0 and with the lowest standard deviation over the 0.2T-1.5T period range were retained. A second, larger subset of 7 records was also selected form the same initial ensemble using the same procedure. These 7 records were used to evaluate the seismic response of the retrofitted structure.

In ASCE 41 standard, the axial actions on braces are considered as deformation-controlled

and the acceptance criteria for nonlinear procedures are therefore expressed in terms of specific deformation limits. For braces in tension, categorized as primary components and evaluated for the collapse prevention performance level, the limit in ASCE 41 is 9ΔT, where ΔT is the axial deformation of the brace at the expected tensile yielding load (based on Fye = 330 MPa). Models B and C were considered in the nonlinear procedures assessment. Results obtained for Model B were used to assess the elastic demand on columns. The combined axial and flexural force demands are compared to the column force capacities using the CSA S16-09 interaction equations. To calculate capacities, resistance factors equal to 1.0 and nominal yield strength was used. In Model C, inelastic buckling of the columns under axial and flexural demands is explicitly verified.

For both models, only the results obtained for the most critical ground motion are presented.

The results from Model B are shown in Fig. 1. In Fig. 1a, the deformation demand in all braces remained with the brace capacities except at levels 8 and 9. This result differs from the one obtained from linear procedure. Similarly, excessive force demand is observed in levels 8 and 9 columns. The time histories of the storey drift and brace axial deformations at the 8th level obtained for Models B and C are illustrated in Figs. 2a and 2b, respectively. In Model B, large storey displacements excursions developed at level 8, which led to the high brace axial deformation demands. The large axial deformation of the braces at 8th floor induced the flexural demands on the columns at that level, as shown in Fig. 2d. Note that the columns were continuous over two storeys. This high flexural demand dominated the interaction equation results shown in Fig. 1b. Such demand on the top floor columns could not be predicted using Model A. In Fig. 2c, Model B shows that the axial load in the left-hand side (LHS) column at level 1 significantly exceeds the column lower-bound compressive strength PCL. Since column buckling was not reproduced in that model, the analysis continued to the end of the ground motion record.

Column buckling response is included in Model C. The results shown in Fig. 2c indicate

that the 1st storey LHS column buckled when the load reached and slightly exceeded PCL. This in turn led to the entire collapse of the structure when the post-buckling strength of the column reduced to the force level corresponding to gravity loading. In Fig. 2b, the axial deformation in the braces and the flexural demand on the columns at the 8th level were reduced significantly when column buckling occurred in the first storey.

Figure 2. Response time history results from Models B and C: a) Storey drift at level 8; b) Brace axial deformations at level 8; c) Axial demand on the LHS column (LC) at level 1; and d) Flexural demand in the columns at level 8.

Structural Rehabilitation

The columns were strengthened to prevent buckling during future seismic events. The results from Model C analyses suggested that column buckling was induced by excessive axial loading rather than by high flexural demands causing plastic hinging. The design of the column retrofit was therefore based on the axial load demand obtained from the analysis performed with Model B. That demand is plotted in Fig. 3a. Only the columns exhibiting a Puf/Pcl ratio greater than 1.0 were retrofitted, that is the columns from the 1st to the 7th levels and the columns at the 9th level. Columns at the 8th level have column demand-to-capacity ratio less than one and thus do not need to be reinforced even if the nonlinear assessment procedure indicates that these columns are the most critical ones (Fig. 1b). The retrofit scheme consisted in welding steel plates to the flanges of the columns, as illustrated in Fig 3b. Figure 3c shows the ratio of the required total cross section area, Areq, to the area of the existing columns, Aexis, to reach Puf/Pcl = 1.0 for the deficient columns. That ratio varies from 1.45 to 1.90. Model D includes the columns’ reinforcement plates. Fig. 4 shows time history results obtained for the retrofitted building under the same critical ground motion record. Fig. 4a shows that the retrofitted columns at the 1st floor have sufficient axial strength and did not buckle. In Fig. 4b, the axial deformations of the braces at the 8th level from Model D are comparable to those obtained using Model B where elastic column response was assumed (see Fig. 2b). Similar comparison can be made for the storey drift at the 8th level. That large deformation demand induced large flexural demand on the columns at the 8th level. As shown in Fig. 4c, the axial strength of the columns at the 8th level is adequate and the columns could withstand the earthquake even if their flexural capacity was reached and plastic hinges formed at the top and bottom (Fig. 4d). The rehabilitation improved the performance of the studied building.

Figure 3. a) Axial load demand on the columns from Model B analysis; b) Proposed column retrofit scheme; and c) Required column cross-section area (Areq) vs existing column cross-section area (Aexis.).

The seismic performance of retrofitted structure was further evaluated using the second

ensemble of 7 ground motion records. In that case, ASCE 41permits to use the average value of each response parameter in the assessment. Table 1 gives the average and maximum values of P/Py, P/Pcl and M/Mp for the columns at the 1st and 8th levels. The reinforced columns at the 1st floor have sufficient axial and flexural strengths. The columns at the 8th level also have adequate axial strength but the flexural demand of the columns at this level is significant, as a result of the large axial deformation of the braces in the upper levels. The average values of Δ/9ΔT ratios for the left and right braces at the 8th floor are respectively 0.56 and 0.82, and thus the braces are assessed as adequate. Note that the corresponding maximum values are 1.01 and 1.63, indicating that some individual records still induce large inelastic demand consistently with what was previously observed.

Figure 4. a) Column axial demand at the 1st level; b) Brace axial deformation demand at the 8th level (LB = LHS brace, RB = RHS brace); c) Column axial load demand at the 8th level; and d) Column flexural demand at the 8th level.

Table 1. Assessment of the retrofitted structure using the 7 record ensembles

Action Ratio

Left Column-1st Level

Right Column-1st Level

Left Column-8th Level

Right Column- 8th Level

AVG MAX AVG MAX AVG MAX AVG MAX P/AFy 0.63 0.71 0.59 0.67 0.68 0.72 0.69 0.73 P/Pcl 0.77 0.88 0.72 0.82 0.83 0.87 0.84 0.89

M/Mp 0.16 0.24 0.17 0.26 1.05 1.13 1.04 1.08

Evaluation of the ASCE 41 Force-delivery Reduction Factor J According to ASCE 41, the smallest demand capacity ratio (DCR) of the components in the load path delivering force to the component should be considered as the force-delivery reduction factor J. In Fig. 5a, two cases are considered for the J factor used to calculate the axial forces in the columns. The first value, J-Minimum, corresponds to the factor as defined in ASCE 41. For the second J factor, J-individual, the demand capacity ratio (DCR) of the components at each level is considered to deliver the force to the component located at that level. In Fig. 5a, the column axial loads determined with J-Minimum are much larger than the column forces calculated with J-Individual. Column forces calculated with the J-Individual are similar to the maximum demand determined from nonlinear response history analysis with Model B from the three ground motions TH11, TH14 and TH15. In Fig. 5a, PG is the column axial force induced by gravity loading and PCL is the lower-bound compressive strength of the retrofitted columns. Figure 5b shows that only the columns at the 6th and 10th levels have adequate strength when J-Minimum is used to calculate the axial force demand on the columns; however, the columns at all levels have sufficient strength when using J-Individual for the calculation of the axial forces. Using J-Individual for the force-delivery reduction factor provides more realistic estimates of QUF in the linear procedures compared to currently specify as J-Minimum. If J-Minimum is considered as a force-delivery reduction factor, more components of structures would need to be retrofitted.

Figure 5. a) Axial force demands on the columns; and b) Assessment of the columns.

Conclusion The seismic performance of a 10-storey X-braced frame of a regular building structure located in Vancouver, British Columbia was assessed according to the ASCE 41-13 standard. The structure was designed in accordance with the design provisions of the 1980 Canadian codes. Different

assessment results were obtained for the studied building when using the linear and nonlinear procedures proposed in ASCE 41. The linear procedure showed that all of the braces have sufficient strength and none of the columns have adequate resistance except those at the 10th floor. The nonlinear analysis revealed a significant flexural demand for the columns at the 8th level which was induced by the large inelastic deformations of the braces in the upper levels. When column buckling was represented in nonlinear analysis, the structure collapsed because of buckling of the column at the 1st level. The large flexural demand in the columns at the 8th floor did not lead to buckling. Only the columns lacking axial resistance were retrofitted and this retrofit approach was validated through additional nonlinear analyses. Force-delivery reduction (J) factor -proposed in ASCE 41 was found to be too conservative for the assessment of braced frame columns.

Acknowledgments The authors gratefully acknowledge the financial support provided by the Natural Sciences and Engineering Research Council of Canada (NSERC) for the Canadian Seismic Research Network (CSRN).

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