Plastic Analysis, Stability, and Natural Frequency of Two-Dimensional Frames of Variable Section Beams

Abstract

This paper focuses on calculating the load level and the ultimate state of steel plane frames consisting of straight slender nonprismatic rods. The plastic behavior is modeled in the theory of second order with a step-by-step method that only considers the bending moment effect and leads to the formulation of sudden concentrated plastic hinge. The plastic process results in the loss of stiffness, leading to lower strength of the section of the structure as a whole. Therefore, it also affects the stability of the whole, which is checked during the loading process each time a new plastic hinge is formed by the equations of stability. Thus, it is well known that it is necessary to suggest the static equilibrium in the deformed or actual configuration. The plastic design allows saving materials as well as ensuring the safety, functionality, and durability of the structure. In addition to the static analysis, the ability to evaluate the frequencies and the associated vibration modes is included. All this enables a tracking process of the structure response for each load state until the collapse.