On the effectiveness of local modifications as dynamic instability modifiers

Collapse during strong ground motions requires the effective tangent stiffness matrix to lose positive definiteness at some point in time. However, this loss alone does not guarantee collapse, since the velocity distribution at that instant rarely aligns with the unstable mode. Thus, inertia and, to a lesser degree, damping provide a temporary stabilizing effect, making a negative eigenvalue necessary but not sufficient for dynamic instability. In structural design, especially for multistory structures, constraints ensure the lowest eigenvalue of the second-order elastic stiffness remains substantially above zero. Under earthquake loads, plasticity may reduce this eigenvalue, potentially leading to statically unstable configurations and collapse. Assessing stability, therefore, requires understanding how a given distribution of plastic hinges alters tangent stiffness (for practicality, a lumped plasticity model is used). Thus, we explore how to raise the ground motion intensity required for instability by a scaling factor α. Simply increasing yield strength uniformly by α is possible but inefficient. Instead, strategically distributing strength increases—termed “local modifications”—can shift governing plasticity distributions toward more favorable ones. This approach is most relevant for tall buildings, which can reach unstable configurations without forming mechanisms, making dynamic instability critical. Effectiveness of local modifications is judged by tracking changes in the lowest eigenvalue of the effective tangent stiffness. Selected modifications are then validated through nonlinear second-order time history analyses, confirming their role in delaying collapse.