---

This article introduces three simple ideas that lead to the efficient design of regular moment frames. The finite module concept assumes that the moment frame may be construed as being composed of predesigned, imaginary rectangular modules that fit into the bays of the structure. Plastic design analysis aims at minimizing the demand-capacity ratios of elements of ductile moment frames by inducing the strength and stiffnesses of groups of members in accordance with certain design criteria, rather than investigating their suitability against the same rules of compliance. Collapse modes and stability conditions are imposed rather than investigated. In short, theory of structures is applied rather than followed. Plastic displacement control suggests that in addition to conducting failure analysis, the maximum displacements of plausible failure modes at incipient collapse should also be taken into consideration. While two collapse mechanisms may share the same carrying capacity, their maximum displacements may be different.

---

This study was prompted by the need to elaborate on recent developments in plastic design of, parallel chord Vierendeel girders (VG). The paper proposes exact, general solutions to two novel classes of VG under practical loading conditions, a-VG of uniform section, where the chords and the verticals may be composed of two different prismatic sections, and b-VG of uniform strength, where the constituent elements are selected in such a way as to induce a state of equal stress for all members of the structure. It has been shown that the total weight of both classes of VG can be minimized by the proper selection of the relative strengths of the members of each system. The essence of the paper is based on a novel failure mechanism presented for the first time in this article. It has been shown that racking moments can be utilized to conduct spot checks on final solutions. Several generic examples have been provided to demonstrate the applications and the validity of the proposed solutions.

---

The research leading to this paper was prompted by the need to estimate strength and stiffness of Rigid Rocking Cores (RRCs) as essential elements of resilient earthquake resisting structures. While a limited number of such studies have been reported, no general study in terms of physical properties of RRCs, their appendages and adjoining structures have been published. Despite the growing knowledge on RRCs there are no design guidelines on their applications for seismic protection of buildings. The purpose of the present article is to propose effective rigidity limits beyond which it would be unproductive to use stiffer cores and to provide basic guidelines for the preliminary design of RRCs with a view to collapse prevention, re-centering and post-earthquake repairs/replacements. Several examples supported by computer analysis have been provided to demonstrate the applications and the validity of the proposed solutions.