Benefits of Nonlinear Systems Nonlinear systems have several advantages over elastic systems that make them the preferred solution for resisting seismic loads. First of all, the issue of what happens if yielding occurs has already been taken care of in the design. It is very difficult to keep structural elements from yielding in a large earthquake, so a structure designed to yield will have much more predictable, ductile response than one that is designed to remain elastic and is overloaded. Limit Forces Nonlinear systems also limit the forces the structure experiences. A structural member or protective device exhibits force- displacement behavior which limits the forces to the ultimate strength of the member or device, as shown below. The forces in an elastic system, on the other hand, are limited only by the earthquake forces. Limit Accelerations Since nonlinear systems limit forces, by Newton's 2nd law they must also limit accelerations. Control Damage Distribution In addition, nonlinear systems allow the designer to control the damage distribution. Except for the base-isolated system, the systems shown below are statically determinate at the near-collapse limit state and thus the forces in all members and the foundation are known. The designer chooses locations where local damage is acceptable, and designs the rest of the structure to be stronger, thus limiting damage to the designated areas. The Displacement Question The major difficulty with designing systems to respond nonlinearly is determining the design displacements. A large part of this course will be devoted to various ways of estimating expected displacements. Several ways of doing this are: Simple nonlinear spectral displacement estimates Estimates based on elastic demands using empirical relationships Nonlinear analysis - static for local deformations - dynamic for global and residual deformations