Force-based Design Research Articles

Direct Displacement Based Design and Capacity Spectrum Method for Special Moment Resisting Frame

In designing seismic-resistant buildings, it is commonly used Forced-Based Design method. The concept of the Force-Based Design (FBD) method is based on an elastic analysis of the structure and indirectly shows the performance level of the structure towards the effects of the seismic forces. Therefore, it is required an approach that capable of analyzing and evaluating the performance of the inelastic structural response; it is called Performance-Based Design method. This paper uses two methods of Performance-Based Design, there are Direct Displacement-Based Design and Capacity Spectrum Method, by using pushover analysis. The objectives of the research are to analyze and compare the performance level of the building in inelastic condition by using these two methods. The structural model reinforced concrete special moment frames. Seismic design code that used in this study is SNI 1726:2012. The reviewed parameter values are displacement and story drift values, estimated plastic hinge response, and performance level of the building from two methods. As the results, all the parameter values of DDBD analysis are more significant than CSM. DDBD produces the drift and displacement values of 0.668 m with the rebar ratio is more significant than 1.00. While, the CSM produces the drift and displacement values of 0.501 m with the rebar ratio of 1.00. The failure mechanism of both methods indicates the strong column weak beam where the beams should fail before the columns. The structure performance level which refers to ATC-40 indicate that both DDBD method and CSM method are in Damage Control level despite displacement target of the two methods are different which is DDBD produces displacement target of 0.376 m while CSM produces the value of 0.345 m.

A Hybrid Seismic Design Method for Steel Irregular Space Moment Resisting Frames

ABSTRACT A performance-based hybrid force/displacement (HFD) seismic design method for space steel moment resisting frames irregular in plan view and in elevation is developed. Irregularity in elevation is either due to non-uniform distribution of mass or due to the presence of setbacks along the height of the frame. More specifically, 30 different frames irregular in plan view for the first case (plan-irregularities), 40 frames with setbacks (vertical stiffness irregularities) for the second case, and 18 frames with mass discontinuities (vertical mass irregularities) at the first, intermediate and top storey for the third case are considered. All these frames are designed according to Eurocodes 3 and 8 and subjected to 42 pairs of ordinary ground motions. Through nonlinear seismic analyses, seismic response databanks for these three types of irregular frames are generated corresponding to four performance levels. These databanks are then utilized for the development of simple expressions that determine the behavior (or strength reduction) factors of the frames. These are functions of frames geometrical/dynamic characteristics including measures of their irregularities as well as the target maximum interstorey drift ratio and member local ductility. The proposed design method, even though it is mainly a force-based design method, controls deformation and therefore damage through the proposed deformation-controlled behavior factors. Design examples are presented to validate the effectiveness of the method to account for the irregularity effects on the preliminary design stage while time-history analysis results demonstrate its advantages to control better the inelastic response of the frames over the conventional force-based seismic design method of Eurocode 8.

Evaluation of deflection amplification factor for steel buckling restrained braced frames

In the common force-based design method prescribed in seismic codes, displacements of a structure under reduced seismic forces are amplified by a deflection amplification factor, Cd, to estimate inelastic displacements. The present study evaluates Cd for steel buckling restrained braced frames (BRBFs). For this purpose, six low-to mid-rise structures comprising 2- to 12-story BRBFs are considered, and nonlinear dynamic analyses are performed. Results indicate that the recommended Cd by ASCE 7 (i.e., Cd = 5.0) underestimates the inelastic maximum interstory drift ratio (IMIDR) of lower stories in BRBFs under the design earthquake. Furthermore, estimation of IMIDR in upper stories of mid-rise structures using Cd = 5.0 leads to acceptable results. Therefore, by applying the particle swarm optimization (PSO) algorithm, a new equation is proposed for Cd to more realistically estimate IMIDR in steel BRBFs under the design earthquake. In the case of roof displacement, the results show that for low-rise structures the recommended value of Cd = 5.0 significantly underestimates the inelastic maximum roof drift ratio (IMRDR). On the other hand, for taller structures Cd = 5.0 overestimates the IMRDR. Thus, another new equation is proposed using the PSO algorithm for CdRoof in order to better estimate the IMRDR. Moreover, effects of variation in strain hardening ratio on Cd and CdRoof are investigated. In the last part of this study, variations of the ratios of Cd and CdRoof to response modification coefficient (R) with ductility reduction factor (Rμ) are investigated.

A Framework to Incorporate Probabilistic Performance in Force-based Seismic Design of RC Buildings as per Indian Standards

ABSTRACT A framework for incorporating probabilistic seismic performance during prescriptive design of reinforced concrete buildings using Indian building codes is presented. The second-generation performance-based design procedure is considered. Thirty special RC frame buildings have been numerically analyzed through nonlinear static and time history analyses. Effects of seismicity, building height, bay-width, and number of bays on building performance are investigated. A generalized expression for the overstrength factor is proposed. Expression for response reduction factor to achieve the desired level of performance objective is also proposed. Low- and mid-rise buildings in the high seismic region designed using current codes are found to be deficient.

Performance assessment of RC frame designed using force,displacement & energy based approach

Force based design (FBD) approach is prevalent in most of the national seismic design codes world over. Direct displacement based design (DDBD) and energy based design (EBD) approaches are relatively new methods of seismic design which claims to be more rational and predictive than the FBD. These three design approaches are conceptually distinct and imparts different strength, stiffness and ductility property to structural members for same plan configuration. In present study behavioural assessment of frame of six storey RC building designed using FBD, DDBD and EBD approaches has been performed. Lateral storey forces distribution, reinforcement design and results of nonlinear performance using static and dynamic methods have been compared. For the three approaches, considerable difference in lateral storey forces distribution and reinforcement design has been observed. Nonlinear pushover analysis and time history analysis results show that in FBD frame plastic deformation is concentrated in the lower storey, in EBD frame large plastic deformation is concentrated in the middle storeys though the inelastic hinges are well distributed over the height and, in DDBD frame plastic deformation is approximately uniform over the height. Overall the six storey frame designed using DDBD approach seems to be more rational than the other two methods.

Quantitative Definition of Seismic Performance Levels for Precast Bridge Piers with Continuous Reinforcement

For construction sites within cities, which require fast construction because of restrictions in road occupation time, or for other occasions where construction period is an important factor because of similar reasons, application of a modular construction method using precast members is efficient in terms of shortening the construction period. The substructures of bridges are normally constructed using cast‐in‐place, which has been a major cause of delays in construction. Application of a modular construction method could decrease the occupation time in the sites. A prime example is the Accelerated Bridge Construction (ABC) by the Texas Department of Transportation (TDOT) and Federal Highway Administration (FHWA). Precast members are the key components of ABC. The main purpose of this paper is to provide clear seismic performance standards for precast bridge piers. Current seismic design codes require force‐based design checks and provide qualitative evaluation of the overall structure. They do not provide specific qualitative criteria for individual structures with particular types. Previous research has been focused on reinforced‐concrete bridge piers, while lacking on research towards prefabricated bridge piers with continuous reinforcements. In order to quantitatively evaluate the seismic performance level of prefabricated bridge piers, the seismic performance was quantitatively suggested in accordance with the classification of four which are operational, immediate occupancy, life safety, and collapse prevention. These criteria are cracking of cover concrete, crushing of cover concrete, yielding of axial steels, and fracture of axial steels. Based on the given seismic performance evaluation criteria, evaluation and verification were conducted on four prefabricated bridge piers with continuous reinforcement that have undergone quasistatic cyclic experiments. The moment‐curvature analysis model was constructed for the parametric study and verified through experimental results. Based on the developed M‐Phi model, prefabricated bridge piers with continuous reinforcement, which were designed force‐based using response correction factor, were evaluated. In addition, parametric study was also conducted focusing on concrete strength, magnitude of prestress, and transverse reinforcement. Depending on the level of individual performance produced by ranges of these variables within possible runs on actual piers, the impact of 3 variables was analyzed. Furthermore, in response to changes in each variable, the impact on the relevant seismic performance level was verified through response spectrum analysis.

Force Based Design and Direct Displacement Based Design for Dual System Structure

The Force Based Design (FBD) and the Direct Displacement-Based Design (DDBD) are methods for designing seismic-resistant buildings. Building structures designed, are expected to be suitable with the purpose and usefulness of a building. For this reason, this study compares the performance of dual system structures using the DDBD and FBD methods that aim to prove better performance with consideration of safety against users during an earthquake. This research method uses design analysis method to compare the value of the base shear force, reinforcement ratio, and performance level using software for static nonlinear pushover analysis. The results showed the value of the base shear force x direction of the DDBD method was 17.57% smaller than the FBD method, whereas for the y direction the DDBD value was greater than 9.38% of the FBD. The value of the reinforcement ratio of the beam, column and shear wall results is greater DDBD than FBD. The actual drift of the DDBD and FBD methods is slightly different. So that both are at the same level of performance, namely damage control. The performance level has not reached the performance target of life safety design in DDBD, but the structure has met the level performance requirements for offices.

Comparative performance evaluation of RC frame structures using direct displacement-based design method and force-based design method

Force-based design (FBD) method has been practiced for a long time which focuses on the seismic force over the structure. Problems associated with FBD are assumed stiffness of structural elements, inappropriate R factors and others. Thus, a new alternative method is required to overcome these differences. Direct displacement-based design method (DDBD) provides an efficient alternative. It is more straightforward which aims to achieve a specified acceptable level of damage under the design earthquake. The main aim of DDBD is to define the target displacement profile for the structures. In this study, the performance of low- and medium-rise building is evaluated using FBD and DDBD method and results have been compared. Both structures are designed according to Indian standard loading in compliance with IS 1893 (part 1) 2016. Non-linear analyses have been carried out for evaluating structural performance like base shear, maximum displacement and inter-storey drift ratio (IDR%). From the study, it can be concluded that DDBD method is more effective than FBD method.

Direct Displacement Based Design of Reinforced Concrete Elevated Water Tanks Frame Staging

Elevated water tanks supported by the reinforced concrete (RC) Staging are classified as inverted pendulum structures. These are considered as structures of high post-earthquake importance and should remain functional after the seismic events. National codes of various countries recommend Force-Based Design (FBD) procedure for water tank staging, which does not ensure nonlinear performance level for a given hazard. Therefore, it becomes necessary to design these structures with a performance-based design approach like Direct Displacement-Based Design (DDBD). Many design engineers consider that the behavior of frame staging of the elevated water tank is similar to the building's frame and generally adopt the same design principles for both types of structures. However, the seismic behavior of the building frame is significantly different from frame staging due to the absence of diaphragm action at the bracing level and concentrated mass at the top level only. Therefore, it may not be rational to utilize the same DDBD procedure of the building's frame for the design of frame staging of the elevated water tanks. The present study proposes some modification in existing DDBD procedure (used for the design of frame building) based on the nonlinear time history analysis of twenty meters high RC frame staging with four different configurations. The modifications are proposed in terms of inelastic displacement profile, design displacement, effective height, and effective mass calculation. Further, the performance of the same RC frame staging designed using the proposed DDBD procedure has been assessed using nonlinear static and dynamic analyses to verify the suitability of proposed modifications.

Seismic Performance and Cost Comparison of Concentrically Braced Frames Designed By Performance-Based Plastic Design and Force-Based Design Method

Comparative study of 5, 10 and 15 storied steel Concentrically Braced Frames (CBF) designed by Performance Based Plastic Design (PBPD) method and Force Based Design (FBD) method is presented here. The parameters selected for comparison of the frames are (a) Lateral load distribution (b) Design sections of members (c) Seismic performance and (d) Cost. It is observed that the lateral load's distribution in case of PBPD frames is found more factual. The column sections of PBPD frames are heavier, and brace sections are lighter compared to FBD frames given the fact that PBPD is designed for higher ductility factor. The PBPD method gives a better seismic performance by achieving the predetermined failure mechanism and avoiding total collapse. Taller structures offer cost-effectiveness for PBPD method.

Earthquake loss assessment of steel moment-resisting frames designed according to Eurocode 8

Current design and assessment guidelines define several seismic performance levels, aiming to ensure that structures exhibit adequate behaviour at different seismic intensity levels. Typically, the acceptance criteria at different performance levels are met by ensuring that local deformation demands are lower than pre-defined capacities. Despite the proven effectiveness of such an approach, it provides an ambiguous measure of the performance of the building, which, in most cases, is neither meaningful nor appropriate for building owners, stakeholders or decision-makers. The main objective of the research presented in this paper is to evaluate the expected direct economic seismic losses of steel moment-resisting frame structures designed according to Eurocode 8 (EC8). A set of 120 archetype buildings, representative of the current building stock in Portugal, were designed according to Part 1 of EC8 using three different behaviour factors, q: a) code-prescribed upper bound limits for medium and high ductility classes; b) behaviour factor defined according to an Improved Force-Based Design (IFBD) procedure. The PEER-PBEE methodology with the improvements proposed by Ramirez and Miranda [1] was employed for the estimation of expected seismic losses evaluated for the seismic intensity levels considered in Part 3 of EC8. The results obtained indicate that the buildings designed in accordance with EC8 comply with the non-collapse criteria. However, the level of damage could imply significant repair costs. Importantly, the results also highlight that a rational selection of the behaviour factor can result in a reduction of steel weight but still ensuring acceptable levels of expected annual losses.

Seismic assessment of RC frame building designed using gross and cracked section as per Indian standards

This study presents the comparative seismic assessment of 2-, 4-, 8- and 12-storey RC frame buildings designed with gross/uncracked section (IS 1893-2002) and effective/cracked section (IS 1893-2016) properties of RC members using conventional force-based design approach. RC frames of similar height are designed using the same seismic base shear coefficient based on empirically obtained period of the building as recommended in IS 1893. All the considered frames are analyzed using nonlinear static pushover analysis and nonlinear time history analysis (NLTHA). The results of the pushover analysis and NLTHA show that the inter-storey drift at design load of RC frames designed using gross section property is well within the prescribed limit of maximum permissible inter-storey drift ratio. Whereas the inter-storey drift of RC frame designed using effective section properties of beams and columns for the force criteria alone is observed much higher as compared to RC frame designed using gross section and beyond the limit of maximum permissible inter-storey drift ratio. The RC frame buildings designed using the modified cracked section for the force as well as drift criteria of IS 1893 show the improved structural performance and its inter-story drift ratio observed is within the prescribed limit.

Simplified force-based seismic design procedure for linked column frame system

Dual structural systems with structural fuse such as linked column frame system (LCF) have two main performances, including the resistance to lateral seismic loads and the proper function of structural fuse to control deformation of the other members to remain in elastic phase. The achievement of these two functions is necessary for appropriate seismic design of these systems. Undoubtedly, despite the practical complexity, displacement-based seismic design methods are generally the best method for this purpose. In contrast, conventional force-based methods are relatively simple, but it cannot easily guarantee the desired performance. In this paper, a simplified force-based seismic design method is presented for linked column frame system based on parametric studies on different structures, which are designed with displacement-based method. In addition to simplicity, the proposed method has an appropriate accuracy in terms of achieving the performance objectives. For the parametric study, 18 prototype structures with various relative lateral stiffness of moment frame and linked column system are designed with the displacement-based method. Based on the results of the structures designed with desirable performance, the criteria are proposed for the force-based design method. Based on evaluating results, the structures designed by the proposed simplified force-based method properly reached the performance objectives.

A more rational selection of the behaviour factor for seismic design according to Eurocode 8

The main objective of the research presented in this paper is to assess the influence of a more rational selection of the behaviour factor (q) for the seismic design of steel moment-resisting frames (MRFs) according to Eurocode 8 (EC8). To this end, a large set of steel MRFs were designed using for code-prescribed behaviour factors as well as using the Improved Force-Based Design (IFBD) methodology for a more consistent selection of q. The seismic performance of the archetypes was assessed through nonlinear static and response-history analysis. The results point to the discrepancy between the design assumptions and the real response of the structures, as significant differences between the design base shear and the lateral strength of the frames were observed for frames designed with code-prescribed behaviour factors. Moreover, it is shown that IFBD-designed steel frames exhibit more uniform inelastic demands over the building height, as well as ductility demands more compatible with the design assumptions. Finally, the fragility and seismic risk assessment conducted shows that all building archetypes, regardless of the q-scenario considered, exhibit values of mean annual frequency of collapse that comply with limits available in the literature.

Modal behavior factors for the performance-based seismic design of R/C wall-frame dual systems and infilled-MRFs

Modal behavior (strength reduction) factors q̅k for the performance-based seismic design of plane reinforced concrete wall-frame dual systems and infilled moment resisting frames are proposed. Instead of using a single and constant behavior (strength reduction) factor q (R) as all modern seismic design codes do, herein are proposed different such factors for the first few significant modes of the structure. Moreover, these q̅k are constructed as functions of period, different deformation targets and soil types and thus, they are suitable for a performance-based design in a force-based design scheme. A linear analysis in conjunction with an elastic acceleration response spectrum with its ordinates divided by q̅k provides a design base shear which is able to produce seismically designed frames which account for both strength and deformation requirements. In contrast to the code-based seismic design procedure which is accomplished in two steps, i.e., first for strength and second for deformation satisfaction, the proposed method eliminates the second step due to its deformational dependent q̅k. Moreover, these q̅k can be used to design for up to four performance levels depending on the design needs. Explicit expressions for q̅k are derived from extensive parametrical studies involving non-linear tiime-history analyses of 19 wall-frame dual systems and 19 infilled moment resisting frames under 100 far-fault historical ground motions corresponding to the four soil classes of Eurocode 8, for six deformation targets and four performance levels. The proposed method is demonstrated and validated with realistic design examples, which show its advantages over the force-based design method of Eurocode 8.

Characteristics of FBD and DDBD techniques for SMRF buildings designed for seismic zone-V in India

This paper presents the results of the nonlinear time history analysis of six different reinforced concrete moment frames. The frames were designed using two major seismic design methods as Force Based Design (FBD) and Direct Displacement Based Design (DDBD) in which former is a conventional method while later one is a performance based approach of design. However, in this study, 4, 8 and 12 stories RC framed building with two × three bays were designed according to Indian standard and the Federal Emergency Management Agency (FEMA) considering two design approaches (FBD and DDBD) studied. Analysis and design for this study performed using SAP2000 v15.1 tool. Both design approaches performed using nonlinear time history analysis for five different real recorded ground motions of north-eastern region, India. The parameters such as inter-storey drift, displacement, material strain, and ductility demand obtained from the analyses of the frames designed using both design methods are noted and compared. This study examined, discussed and shown about the applicability of existing methods adopted considering the FBD and DDBD in a cost-effective manner to achieve desired level of performance.

Seismic behavior of K-type eccentrically braced frames with high strength steel based on PBSD method

In eccentrically braced steel frames (EBFs), the links are fuse members which enter inelastic phase before other structure members and dissipate the seismic energy. Based on the force-based seismic design method, damages and plastic deformations are limited to the links, and the main structure members are required tremendous sizes to ensure elastic with limited or no damage. Force-based seismic design method is very common and is found in most design codes, it is unable to determine the inelastic response of the structure and the damages of the members. Nowadays, methods of seismic design are emphasizing more on performance-based seismic design concept to have a more realistic assessment of the inelastic response of the structure. Links use ordinary steel Q345 (the nominal yielding strength fy>=345 MPa) while other members use high strength steel (Q460 fy>=460 MPa or Q690 fy>=690 MPa) in eccentrically braced frames with high strength steel combination (HSS-EBFs). The application of high strength steels brings out many advantages, including higher safety ensured by higher strength in elastic state, better economy which results from the smaller member size and structural weight as well as the corresponding welding work, and most importantly, the application of high strength steel in seismic fortification zone, which is helpful to popularize the extensive use of high strength steel. In order to comparison seismic behavior between HSS-EBFs and ordinary EBFs, on the basis of experimental study, four structures with 5, 10, 15 and 20 stories were designed by PBSD method for HSS-EBFs and ordinary EBFs. Nonlinear static and dynamic analysis is applied to all designs. The loading capacity, lateral stiffness, ductility and story drifts and failure mode under rare earthquake of the designs are compared. Analyses results indicated that HSS-EBFs have similar loading capacity with ordinary EBFs while the lateral stiffness and ductility of HSS-EBFs is lower than that of EBFs. HSS-EBFs and ordinary EBFs designed by PBSD method have the similar failure mode and story drift distribution under rare earthquake, the steel weight of HSS-EBFs is 10%-15% lower than ordinary EBFs resulting in good economic efficiency.

Ductility reduction factor formulations for seismic design of RC wall and frame structures

Seismic design of standard structures is typically founded on a force-based design approach. Over the years this approach has proven robust and easily applicable by design engineers and – in combination with capacity design principles – it provides a good protection against premature structural failures. However, it is also known that the force-based design approach as it is implemented in the current generation of seismic design codes suffers from some shortcomings; among these is the fact that the base shear is computed using a pre-defined force reduction factor, which is constant for a given structural system. Thus, for the same design input, structures of an identical type but different geometry are subjected to varying ductility demands and may perform differently during an earthquake. The objective of this research is to present an alternative formulation for computing force reduction factors for RC wall and frame structures, using simple analytical models which only require input data already available at the beginning of the design process. Such analytical models allow to link global to local ductility demands and therefore to compute an estimate of the force ductility reduction factors that lead to equal local ductility demands and expected damage levels. A series of pushover and nonlinear time history analyses are run on simplified numerical models of a set of wall and frame structures. The results show that the proposed alternative formulation yields a more accurate ductility reduction factor than the current Eurocode 8 design approach.

Implementation of the structural performance factor (Sp) within a displacement-based design framework

This paper discusses the application of the Structural Performance factor (SP) within a Direct Displacement-Based Design framework (Direct-DBD). As stated within the New Zealand loadings standard, NZS1170.5:2004 [1], the SP factor is a base shear multiplier (reduction factor) for ductile structures, i.e. as the design ductility increases, the SP factor reduces. The SP factor is intended to acknowledge the better-than-expected structural behaviour of ductile systems (both strength, and ductility capacity) by accounting for attributes of response that designers are unable to reliably estimate. The SP factor also recognizes the less dependable seismic performance of non-ductile structures, by permitting less of a reduction (a larger SP factor) for non-ductile structures. Within a traditional force-based design framework the SP factor can be applied to either the design response spectrum (a seismic hazard/demand multiplier), or as a base shear multiplier at the end of design (structural capacity multiplier) – either of these two approaches will yield an identical design in terms of the required design base shear and computed ULS displacement/drift demands. However, these two approaches yield very different outcomes within a Direct-DBD framework – in particular, if SP is applied to the seismic demand, the design base shear is effectively multiplied by (SP)2 (i.e. a two-fold reduction). This paper presents a “DBD-corrected” SP factor to be applied to the design response spectrum in Direct-DBD in order to achieve the intent of the SP factor as it applies to force-based design. The proposed DBD-corrected SP factor is attractive in that it is identical to the SP relationship applied to the elastic site hazard spectrum C(T) for numerical integration time history method of analysis within NZS 1170.5:2004 [1], SP,DDBD = (1+SP)/2.

A hybrid force/displacement seismic design method for reinforced concrete moment resisting frames

A performance-based seismic design method for plane reinforced concrete (R/C) moment-resisting frames (MRF) is proposed. This method is based on a hybrid force/displacement (HFD) seismic design scheme, which has been successfully applied to the seismic design of steel structures and is extended in this paper to plane RC-MRFs. The proposed HFD method combines the familiar to engineers force-based design (FBD) method, used in all seismic design codes, with the displacement-based design (DBD) method, which efficiently controls the deformation and hence the damage in a performance-based design (PBD) framework. This is accomplished by constructing explicit empirical expressions for a behavior (strength reduction) factor, which incorporates target non-structural and structural deformation metrics such as inter-storey drift ratio (IDR) and member plastic rotation (θpl). Use of this factor in conjunction with the elastic acceleration spectrum of EC8, can produce designs in one step, by simply conducting a strength checking, since the deformation restrictions are automatically satisfied. Those expressions for the behavior factor in terms of target deformation metrics, number of storeys, column to beam strength ratios and beam to column stiffness ratios are derived through extensive parametrical studies involving 38 RC-MRFs, under 100 ordinary ground motions (25 for each of the four soil classes of EC8) for seven deformation targets. Comparison of the proposed method with the EC8 seismic design through examples, with the aid of non-linear time-history (NLTH) analyses, demonstrates its advantages.