Structural Instability due to P-Delta Effects: Analysis and Modifications by Local Adjustments

This thesis examines the phenomenon of structural instability from second-order effects (P-Delta effects) in structures subjected to seismic excitations. A necessary condition for instability during the response to a strong earthquake is that, at a certain point in time, the lowest eigenvalue of the effective stiffness becomes negative. This is equivalent to stating that the effective tangent stiffness, in these instants, is not positive definite. Design constraints in multistory structures are such that the lowest eigenvalue of the second-order elastic stiffness is large when the behavior is elastic. During intense ground motion, however, plasticity develops and the associated loss of stiffness, depending on the spatial distribution, can lead to configurations that are statically unstable. Whether a given distribution of plasticity implies a negative eigenvalue in the effective stiffness can be determined without the need to simulate the dynamic response. Therefore, the question is whether earthquake excitation will drive the structure into any of these configurations and whether some will persist long enough to result in collapse. This brings us to one of the central ideas in this thesis, namely, we examine the possibility of affecting the distribution of plasticity in a favorable way by using local modifications. It is opportune to note that although plasticity distributions associated with kinematic mechanisms are always unstable (neglecting hardening), unstable configurations can be (and often are) reached even though a kinematic mechanism has not formed. One intuitive way to say this is that plasticity softens the structure, and in some cases, the extent is to such that the gravity loading exceeds the buckling strength of the structure (as a system), although no kinematic mechanism has formed. The previously described matter is, as one gathers, increasingly important for high-rise structures. As noted, the central idea explored in this thesis is that of affecting the degree of plasticity needed to reach unstable configurations by local strength modifications. While it is evident that increasing the building’s strength should raise the threshold required to induce collapse, the key question is whether local modifications can realize this objective in a manner that is more efficient and cost-effective than a global strengthening approach.