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. [...