Extension of direct displacement‐based design for quantifying higher mode effects on controlled rocking steel cores

Abstract

Direct displacement-based design (DDBD) procedure utilizes an equivalent singledegree-of-freedom model to predict seismic demands while neglecting the higher mode effects. Controlled rocking steel cores (CRSCs) vibrate in the first mode of vibration; however, higher modes greatly influence the member forces. Previous studies, in which DDBD has been utilized, have not quantified the contribution of higher mode demands to CRSC's assemblies. This paper aims to extend the DDBD (EDDBD) procedure for low-damage buildings, equipped with CRSCs. Modal responses are combined with modified SRSS at the design displacement. Design is formulated for the strength and stiffness of the CRSC components. The application of the proposed design approach is illustrated by 3-, 9-, and 15-story archetypes. Results verified by nonlinear dynamic analyses demonstrate the high precision of EDDBD in the design of low-to mid-rise CRSCs. The proposed procedure is applicable to commercial software. K E Y W O R D S controlled rocking core, direct displacement-based design, higher mode effects 1 | INTRODUCTION Current building codes implement both force-based design (FBD) and displacement-based design (DBD) methods for the seismic design of conventional buildings. Although FBD procedures are commonly used in most of the national seismic codes, DBD methods have provided a real correlation between displacement and damage extent. The DBD procedure can be categorized into "predesigned" and "design-led to analysis" (DLA) approaches. [1] In the predesigned method, the already-designed system is being checked to satisfy the drift requirement, [2,3] whereas in DLA methods such as DDBD and equal displacement-based procedures, the structure models by a single-degree-of-freedom (SDOF) system. The DDBD is an applicable design method, in which a multi-degree-of-freedom (MDOF) structure is substituted with an SDOF model, secant stiffness, and equivalent viscous damping associated with the design displacement. In the theoretical basis, the DDBD starts with desired target displacement, and it ends with the design demands. The pioneer efforts in proposing DDBD methods are related to Priestley et al., [4-8] as well as Calvi and Kingsley, [9] Kowalsky et al., [10] and Fardis and Panagiotakos. [11,12] This method is utilized for the design of a wide range of structural systems. For example, Priestley et al. [13,14] proposed a simplified DDBD method for precast concrete jointed structures and reinforced concrete frames. The efficient application of standard DBD for semirigid steel frames was investigated by Pirmoz and Liu. [15] Shahi e al. [16] examined the seismic performance of steel stud bracing walls and found that demands determined from standard DDBD method using inelastic spectra were in better agreement with NLTHA results than the equivalent damping approach. Comprehensive and well-validated studies have also been conducted in the recent past to use the DDBD procedure for masonry wall structures, [17,18] frame-wall structures, [19-21] and timber structures. [...

Scaled shaking table testing of higher‐mode effects on the seismic response of tall and slender structures

“…Tall buildings do not respond to seismic loading elastically, instead, they typically rely on the ductile plastic hinging mechanism at the base that limits seismic demands in a way similar to the rocking mechanism of the rocking-base specimen tested in this study. As demonstrated by previous analytical studies, [11][12][13][14] a single inelastic flexural mechanism (whether through rocking or plastic hinging) at the base of a cantilever structure only limits its first-mode responses and has negligible control over its higher-mode responses. This suggests that the observed reduction in the story shear demands of the rocking-base specimen was mainly due to the reduction in the first-mode response.…”

“…As demonstrated by the results of the shaking table tests, relying on a single inelastic flexural mechanism at the base of a cantilever structure is ineffective in limiting the seismic demands, especially the shear force demands at the base and along the height of the structure. Although ongoing research on higher‐mode effects has yielded many analytical equations that aim to capture the higher‐mode‐induced shear force amplification in the design process, 2–14 a broadly applicable methodology is not available yet to accurately account for the shear force amplification and changes in the shear force distribution along the height of structures due to higher‐mode effects 2,3 . As summarized in Christopoulos and Zhong, 3 most methods presented in codes and standards were based on early research on this topic that accounted for higher‐mode effects using a single amplification factor, based on the number of stories or the fundamental period of the structure under consideration, to amplify the story shear envelopes calculated by the code‐prescribed Equivalent Static Force Procedure (ESFP) or Response Spectrum Analysis (RSA) 58–61 .…”

“…To address this, a considerable amount of research has been conducted since the 1940s on this topic. While extensive analytical studies have yielded multiple amplification factors and equations that are intended to account for the amplified dynamic response due to the contribution of higher-mode vibrations, [2][3][4][5][6][7][8][9][10][11][12][13][14] limited number of experimental studies are available that provide measurable higher-mode effects on structures in shake table tests [15][16][17][18][19][20] and pseudo-dynamic hybrid tests. 21 As summarized in Rutenburg 2 and more recently in Christopoulos and Zhong, 3 a consensus is not yet available to account for higher-mode effects using analytical equations in the design process.…”

Seismic Evaluation of Self-Centering Bi-Rocking Walls via Micro Modeling of Rocking Joints: Locating the Rocking Section

“…Direct displacement-based design (DDBD) method utilizes an equivalent SDOF model to estimate the seismic demands ignoring the higher mode effects. Rahgozar and Rahgozar (2020) has generalized the DDBD procedure for self-centering systems. In this method, modal responses are combined via the modified SRSS at the design displacement point.…”

Optimization of relative-span ratio in rocking steel braced dual-frames

“…In the other studies, the efficiency of modern low-damage systems are also demonstrated, such as rocking-wall moment frames (Grigorian and Grigorian 2015a, b), confined-masonry rocking walls (Toranzo et al 2009), rocking-wall under the effect of axial stress ratio (Jafari et al 2017), rocking segmental bridge piers (Ahmadi and Kashani 2019), rocking spine in reinforced concrete frames with infills (Burton et al 2016), rocking moment frames (Tahmasebi et al 2014), pre-tensioned vertebral rocking columns (Kashani et al 2019) and quantifying higher mode effects on controlled rocking steel cores (Rahgozar and Rahgozar 2020). Recent research has shown very significant results for this type of self-centering systems.…”