Equivalent Static Force Procedure Research Articles

Seismic performance of eccentrically braced frames designed by the conventional and equivalent energy procedures

Eccentrically braced frame (EBF) is a robust structural system designed for seismic application. The design philosophy for EBF is to utilize the link beams to dissipate the earthquake energy. While such system has been proven to provide sufficient stiffness and strength to prevent the structure from collapse, the structural performance in terms of damage and resilience after strong earthquakes is not explicitly considered. In this paper, a novel design method, named the Equivalent Energy Design Procedure (EEDP), is adopted to design the EBF. EEDP is an alternative design procedure for fused structural systems, where engineers can design the structure to achieve the intended performance objectives at different earthquake hazard levels. To evaluate the performance of the EBF, a 5 storey EBF located in Vancouver, British Columbia, Canada is designed using both the EEDP and the Equivalent Static Force Procedure (ESFP) outlined in the 2015 National Building Code of Canada. Detailed nonlinear dynamic analyses were conducted. The results show that the EEDP designed EBF has better performance with lower initial and repair costs at different levels of earthquake shaking intensities.

An Optimal Seismic Force Pattern for Uniform Drift Distribution

The force distribution proposed by codes, which in many cases is framed in the equivalent static force procedure, likely leads to design structures with non-uniform drift distribution in terms of inter-storey drift and ductility demands. This can lead to an unbalanced drift demand at certain storeys. This phenomenon may also amass cyclic damage to the dissipative elements at this very storey, therefore increasing the probability of premature failure for low-cycle fatigue. This work proposes a new force design distribution that accounts for higher mode effects and limits the displacement concentration at any storey thus improving the dissipative capacity of the whole structures. The main advantage of the proposed method stands in its formulation, which allows to spare any previous set up with structural analyses. The proposed force distribution has been applied to multi-degree-of-freedom systems to check its effectiveness, and the results have been compared with other proposals. In addition, in order to obtain a further validation of the proposed force distribution, the results obtained by using a genetic algorithm have been evaluated and compared. Additionally, the results provided in this work validate the proposed procedure to develop a more efficient lateral load pattern.

Seismic Assessment of Existing Eccentrically Braced Frames According to NBCC and ASCE 41-13 Evaluation Procedures

The seismic performance of an existing 8-storey EBF with shear-critical links located in Victoria, BC, is assessed. The frame is designed according to 1995 NBCC and the CSA S16-94 steel design standard. Seismic assessment is first performed in accordance with recommendations of the User’s Guide to NBCC 2015 using equivalent static force procedure, response spectrum analysis and linear time history analysis. A Tier 3 systematic evaluation according to ASCE 41-13 is then carried out using a linear static and dynamic procedure. Even though the original frame design was based on capacity design principles, both procedure revealed an inadequate strength of the frame members and the need for strengthening. Although the ASCE 41 procedure resulted in a less severe assessment, failures were predicted for most of the columns and for some outer beams. Considering bending as deformation-controlled action alleviated outer beam response.

Performance evaluation of multi-storey cross-laminated timber structures under different earthquake hazard levels

The inter-storey drift limitations are meaningful reference values for structural seismic performance evaluation. This paper presents an analytical investigation into the seismic performance of multi-storey cross-laminated timber (CLT) structures to obtain the drift limitations under different earthquake hazard levels reasonably. The Pinching4 model was used to simulate the nonlinear mechanical behavior of three types of connections used in CLT structures, and a numerical model was further developed to capture the lateral load-resisting properties of CLT shear walls. Moreover, three benchmark multi-storey CLT apartment buildings were designed using the Equivalent Static Force Procedure according to National Building Code of Canada (NBCC), and simplified structural models were developed for these buildings. Depending on the results from numerous time-history dynamic analyses, the empirical cumulative distribution functions (CDFs) of the maximum inter-storey drifts were constructed for the three benchmark buildings. The probability of non-exceedance (PNE) of inter-storey drift thresholds under different earthquake hazard levels was proposed and validated. It is recommended that for low-rise CLT buildings within three stories, values of 0.30%, 0.75%, and 1.40% can be considered as the drift limitations for frequent, medium, and rare seismic hazard levels, respectively. For mid-rise or high-rise buildings without three stories, 0.25%, 0.70%, and 1.30% can be considered as drift limitations.

Systematic design of unbonded fiber reinforced elastomeric isolators

Fiber reinforced elastomeric isolators (FREIs) comprise alternating bonded layers of elastomer and fiber reinforcement sheets. In an unbonded application the isolator is located in place without any bonding or mechanical fastening provided at its contact supports. The unbonded application results in an increased seismic isolation efficiency, however, it introduces few design limitations as it relies on friction to transfer shear loads, and no vertical tension can be taken by the isolator. These limitations may restrict the use of isolators where the superstructure overturning is of concern or in regions where large vertical ground accelerations are expected. This paper presents a systematic method for the design of structures supported on unbonded-FREIs. The design calculations conform the equivalent static force (ELF) procedure outlined in current seismic codes and account for the vertical component of earthquake in the analysis. A stability parameter has been introduced to verify both the overturning and sliding stability of the isolated system. The efficacy of the design method is illustrated by extensive response history simulations for several prototype frame structures.

Comparison of seismic design provisions for buckling restrained braced frames in Canada, United States, Chile, and New Zealand

Seismic design provisions for buildings in Canada, the United States, Chile and New Zealand are presented for buckling restrained braced frames, with focus on design requirements for seismic stability. P-delta effects are explicitly considered in seismic design in Canada, the U.S. and New Zealand. In Chile, stability effects are limited by means of more stringent drift limits. The provisions are applied to a 9-storey building structure located in areas in each country having similar seismic conditions. For this structure, comparable seismic loads are specified in Canada and Chile, whereas significantly lower seismic effects are prescribed in the U.S. In all countries, use of the dynamic (response spectrum) analysis method resulted in lighter and more flexible structures compared to the equivalent static force procedure. Seismic stability requirements had greater impact on designs in Canada and New Zealand. Frame design in the U.S. was only affected by stability effects when applying the stability requirements from AISC 360-10.

Analytical study on seismic force modification factors for cross-laminated timber buildings

With two producers in operation and over 20 buildings already constructed or in planning process, use of cross-laminated timber (CLT) is gaining popularity in Canada. Since CLT as a structural system is currently not included in the National Building Code of Canada (NBCC), one of the most important issues are the values for the force modification factors for seismic design of CLT structures when NBCC equivalent static force procedure is used. In this study, a test-calibrated numerical model for CLT shear walls was applied to develop the design resistances for typical CLT wall configurations. An estimation of a possible range of Rd-factors was obtained by developing design variations for three multi-storey CLT apartment buildings. By specifying the desired seismic performance in terms of inter-storey drift, it is concluded that an Rd-factor of 2.0 will likely provide desirable building performance during the design earthquake level event in Vancouver, B.C.

Seismic Design and Response of Crane-Supporting and Heavy Industrial Steel Structures

This paper presents an analytical study of the seismic behavior of two different types of industrial buildings; a regular mill-type crane-supporting steel structure and an irregular heavy industrial building housing a vertical mechanical process. For both structures, the seismic response is examined through elastic time-history dynamic analyses in order to validate the predictions from the equivalent static force procedure and the response spectrum analysis method prescribed in current building codes. The analyses also serve to assess the inelastic demand in crane-supporting structure. For the crane-supporting structure, analyses are performed for sites in Montreal and Vancouver in Canada and in Seattle in the United States. The results show that the median horizontal displacement and acceleration from the time-history analyses are generally well predicted by the code analysis methods. Inelastic response in these buildings is likely to develop in the form of buckling of the lower column segment, a failure mode that exhibits limited ductility. For the tall irregular building, the analyses are performed for the Montreal site only. The results show the equivalent static method provides fair displacements estimate, but may lead to unconservative predictions of column and brace forces. Response spectrum analysis method, as prescribed in design codes, appears to provide appropriate prediction of the seismic response of such highly irregular structures. For both building types, a good prediction from response spectrum and time-history analysis methods is possible only when a sufficient number of modes are used.

On calculating equivalent static seismic forces in the 2005 National Building Code of Canada

Several major changes were introduced in the seismic design provisions of the 2005 edition of the National Building Code of Canada (NBCC). The lateral earthquake design force at the base and the lateral force distribution along the building height depend on the design spectra and on modification factors that, in most cases, require a large number of interpolations and calculations. This note presents a spreadsheet that facilitates determination of the 2005 NBCC seismic design forces from the equivalent static force procedure.

Seismic Performance of Concentrically Braced Steel Frames in Multistory Buildings with Mass Irregularity

The influence of mass irregularity on building seismic response is examined for an eight-story concentrically braced steel frame with different setback configurations resulting in sudden reductions in plan dimensions and seismic weight along the height of the structure. Three locations of mass discontinuity were considered (25, 50, and 75% of the building height), together with two ratios of seismic weight (200 and 300%). A reference regular structure was also considered for comparison. The design of each structure was performed according to the proposed 2005 National Building Code of Canada NBCC provisions using two analysis methods: The equivalent static force procedure and the response spectrum analysis method. Although severe, the mass irregularity conditions considered in this study were found to have a limited negative impact on the seismic performance of the structures designed with the static analysis method. The performance of irregular structures exhibiting lower performance could be improved by...

Application of the equivalent static force procedure for the seismic design of multistorey buildings with vertical mass irregularity

The seismic forces and deformations obtained from the equivalent static force procedure and the dynamic analysis method proposed for the 2005 National Building Code of Canada are compared for 4-, 8-, 12-, and 16-storey buildings with structural mass irregularity. Setbacks resulting in 200% and 300% mass discontinuities located at 25%, 50%, or 75% of the building height were considered. The buildings are located in Vancouver and Montréal, and lateral loads are resisted by concentrically braced steel frames. The storey shear forces, overturning moments, and storey drifts obtained from static analysis were found to exceed the values determined from dynamic analysis for all irregular structures except at the base of "podium-type" buildings located at the Vancouver site.Key words: mass, static, dynamic, seismic, shear, overturning moment, deflections, braced steel frames.

Efficient seismic analysis of multi-story buildings

The equivalent static force procedure and the response spectrum analysis method are widely used for seismic analyses of multi-story buildings. The equivalent static force procedure is one of the most simple but less accurate method in predicting possible seismic response of a structure. The response spectrum analysis method provides more accurate results while it takes much longer computational time. In the response spectrum method, dynamic response of a multi-story building is obtained by combining modal responses through a proper procedure such as SRSS or CQC method. Since all of the analysis results are expressed in absolute values, structural engineers have difficulties to combine them with the results obtained from the static analysis. Design automation is interrupted at this stage because of the difficulty in the decision of the most critical design load. Pseudo-dynamic analysis method proposed in this study provides more accurate seismic analysis results than those of the equivalent static force procedure since the dynamic characteristics of a structure is considered. And the proposed method has an advantage in combination of the analysis results due to gravity loads and seismic loads since the direction of the forces can be considered.

Seismic torsional response and design procedures for a class of setback frame buildings

AbstractThis paper presents results of an analytical study of the inelastic earthquake torsional response of a class of setback frame buildings. In the first part of the study, the modal response spectrum analysis procedure is utilized to determine the yielding strengths of structural members in an idealized but representative setback frame building model. Results are then presented for the inelastic dynamic response of this setback building model subjected to an ensemble of six earthquake ground motions. The results indicate that the modal response spectrum analysis procedure is inadequate for preventing excessive response leading to concentration of damage in vulnerable structural members, such as those in the tower near the notch and those in the base (the part of the structure below the tower) near the perimeter at the opposite side of the tower. The second part of the study develops a modified equivalent static force procedure for strength design of such setback frame buildings. Response analyses show that the proposed procedure results in improved and satisfactory inelastic performance of the selected class of setback frame buildings, having a wide range of realistic configurations.

A modified static procedure for the design of torsionally unbalanced multistorey frame buildings

AbstractSeismic building codes include design provisions to account for the torsional effects arising in torsionally unbalanced (asymmetric) buildings. These provisions are based on two alternative analytical procedures for determining the design load for the individual resisting structural elements. A previous study has shown that the linear elastic modal analysis procedure may not lead to conservative designs, even for multistorey buildings with regular asymmetry, when such structures are excited well into the inelastic range of response. The equivalent static force procedure as recommended by codes may also be deficient in accounting for additional ductility demand in the critical stiff‐edge elements. This paper addresses the non‐conservatism of existing static torsional provisions and examines aspects of element strength distribution and its influence on inelastic torsional effects. A recommendation is made for improving the effectiveness of the code‐type static force procedure for torsionally unbalanced multistorey frame buildings with regular asymmetry, leading to a design approach which estimates conservatively the peak ductility demand of edge elements on both sides of the building. The modified approach also retains the simplicity of existing code provisions and results in acceptable levels of additional lateral design strength. It has recently been adopted by the new Australian earthquake code, which is due to be implemented early in 1993.