---

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.

---

Despite widespread application of grillage structures in many engineering fields such as civil, architecture, mechanics, their analysis and design make them more complex than other type of skeletal structures. This intricacy becomes more laborious when the corresponding
analysis and design are based on plastic concepts.
In this paper, Finite Element Method is utilized to find the lower and the upper bounds solutions of rectangular planner grids and this method is compared with analogues Finite Difference Method to indicate the efficiency of proposed approach.
 

---

In this study, the investigation of maximum inelastic displacement demands in steel moment- resisting (SMR) frames designed using the Performance-Based Plastic Design (PBPD) method is conducted under both near-fault and far-fault earthquake records. The PBPD method utilizes a target drift and predetermined yield mechanism as the functional limit state. To accomplish this, 6 steel moment frames having various heights were scaled using well-known sa(T1)  method and, then, were analyzed by OPENSEES software. A total of 22 far-fault records and 90 near-fault records were compiled and employed for parametric nonlinear dynamic analysis. The near-fault records were classified into two categories: T1/Tp≥1  and T1/Tp<1 . The study aimed at investigate their impacts on the inter-story drift and the relative distribution of base shear along the height of the structure. The results revealed that the records with T1/Tp≥1   exerted the greatest influence on the drift demands of upper stories in all frames. Conversely, the near-fault records with T1/Tp<1  demonstrated the most significant impact on the lower stories of mid-rise frames. Additionally, the distribution of relative story shears was examined through genetic programming for optimum PBPD design of steel moment frame structures. As a result, a proposed relationship, denoted as b (seismic parameter for design lateral force distribution), was developed and optimized for both near-fault and far-fault records. This relationship depends on the fundamental period of vibration and the total height of the structure. The accuracy of the predicted model was assessed using R2 , which confirmed the reliability of the proposed relationship.