Load-bearing capacity and resonance stability of inelastic beams and plane trusses with initial defects

Abstract

PurposeThe purpose of this paper is to contribute to the solution of the buckling and resonance stability problems in inelastic beams and wooden plane trusses, taking into account geometric and material defects.Design/methodology/approachTwo sources of non-linearity are analyzed, namely the geometrical non-linearity due to geometrical imperfections and material non-linearity due to material defects. The load-bearing capacity is obtained by the rheological-dynamical analogy (RDA). The RDA inelastic theory is used in conjunction with the damage mechanics to analyze the softening behavior with the scalar damage variable for stiffness reduction. Based on the assumed damages in the wooden truss, the corresponding external masses are calculated in order to obtain the corresponding fundamental frequencies, which are compared with the measured ones.FindingsRDA theory uses rheology and dynamics to determine the structures' response, those results in the post-buckling branch can then be compared by fracture mechanics. The RDA method uses the measured P and S wave velocities, as well as fundamental frequencies to find material properties at the limit point. The verification examples confirmed that the RDA theory is more suitable than other non-linear theories, as those proved to be overly complex in terms of their application to the real structures with geometrical and material defects.Originality/valueThe paper presents a novel method of solving the buckling and resonance stability problems in inelastic beams and wooden plane trusses with initial defects. The method is efficient as it provides explanations highlighting that an inelastic beam made of ductile material can break in any stage from brittle to extremely ductile, depending on the value of initial imperfections. The characterization of the internal friction and structural damping via the damping ratio is original and effective.

Theoretical and Numerical Simulation Study on the Ultimate Load Capacity of Triangular and Quadrilateral Truss Structures

“…Krajewski et al [14] conducted a study on the stability and load-bearing capacity of elastic support trusses. Milašinović et al [15] investigated the load-bearing capacity of non-elastic beams and planar trusses, considering geometric and material defects. Krajewski et al [16] provided linear buckling analysis results and nonlinear static analysis results for truss-shell models and obtained the relationship between the truss support stiffness and buckling as well as the ultimate load capacity.…”

Modeling of porous-hardened concrete by rheological-dynamical analogy

“…The state of damage in this case can be represented by a scalar damage variable. In the case of an SDOF dynamic system, the scalar damage variable represents a decreasing linear function of the square of the quotient of the natural frequency of the damaged and undamaged SDOF dynamic system (Milašinović et al ., 2022a). The generalization of the SDOF dynamic system to the case of a multi-degree-of-freedom (MDOF) dynamic system leads to a structure damage matrix (Milašinović et al ., 2018).…”