Designing to the Strongest Ground Motions

Every structure has a certain capacity to deform. If the deformation demand exceeds the deformation capacity, the structure collapses. This chapter deals with the deformation demand imposed by ground motion. Ground motions for engineering applications are measured by accelerometers (acceleration sensors) oriented in three orthogonal directions: usually east, north, and up. A linear-elastic structure can be represented by one or more single-degree-of-freedom systems. The tripartite plot is a very concise and elegant way of displaying the response spectrum of a ground motion. Acceleration-deformation plot of the response spectrum (ADRS) is helpful in estimating the response of nonlinear systems. When shaken strongly, a “ductile” structure yields on reaching its maximum strength. After yielding, the structure no longer behaves in a linear fashion. ADRS and cyclic-demand response spectra directly affect the response of structures.

Future ground motions are predicted by a probabilistic seismic hazard analysis probabilistic seismic hazard analysis. In this chapter, the predicted ground motions are compared with the strongest recorded ground motions. The 10,000-year mean return period (MRP) predicted ground motions at two sites in the United States are much stronger than any ground motions in 200,000 instrument-years of recorded data. The energy demand of 20,000-year MRP ground motions is completely unrealistic, even though 20,000-year ground motion also has nearly a 100% chance of exceeding 200,000 years of recorded data. Overprediction of hazards (and risks) is harmful because it increases the cost of insurance, results in inefficient allocation of resources; deprives the public of the benefits of projects that are deemed “too risky” or “too costly” because of overprediction; and causes others to doubt the predictions and not take them seriously.

Strength, deformability, and damping play equally important roles in seismic design. Buildings are not expected to withstand extreme ground motions by strength alone. Two example buildings are selected: a 3-story steel special moment frame (SMF) building and a 20-story steel eccentric braced frame building. Both buildings are designed to possess high strength, deformability, and damping by utilizing ordinary materials and established technologies. The lateral strength and deformability of a building are defined by its pushover curve, which is a plot between the lateral force and the deflection of the building’s center of gravity. The SMF is an excellent system for low- to mid-rise buildings because of its high deformability and damping. With an increase in height, both elastic and inelastic deflections of the SMF increase. Greater elastic deflection reduces the overall damping of the system because damping in the elastic range is low.

Nonlinear-dynamic analysis requires the numerical solution of coupled nonlinear equations of motion (EOM). Nonlinear-dynamic analysis can be more “accurate” than nonlinear-static analysis, but it can also be easily corrupted by numerical errors. Nonlinear-dynamic analysis is used only to confirm that the responses are not underestimated. In this chapter, both methods of analysis are used to calculate the responses of 3-story steel SMF and 20-story steel EBF buildings to the TAPS ground motion. Ground motions impose both amplitude and cyclic demands on structures. From both static and dynamic analyses, the damage suffered by the building during the TAPS ground motion is negligible. Because the damping-adjustment is less than the seismic toughness, the building cannot collapse, but it can be damaged by the TAPS ground motion. The response of a 20-story steel EBF building to TAPS ground motion is determined by the intersection of demand and capacity curves.

In this chapter, the weakest ground motions that can collapse the 3-story steel SMF and 20-story steel EBF buildings are determined. Because energy demand (ED) is proposed as a measure of the strength of ground shaking, the weakest ground motions are those with the lowest energy demand. Deformability and hysteretic damping are highly important in collapse prevention, but in prescriptive seismic design, deformability and hysteretic damping are not explicitly considered. Their effect is considered by applying judgment-based load reduction factors. This makes the prescriptive seismic design quite arbitrary. In collapse prevention, deformability and hysteresis are as important as strength; hence, they should be explicitly considered in seismic design. The most important seismic characteristic of a building is the minimum ED needed to collapse that building.

In this chapter, the 3-story and 20-story buildings are subjected to 11 of the strongest ground motions. The buildings’ responses are calculated by using both static and dynamic methods of nonlinear analysis. Cumulative fatigue damage from cycles of various amplitudes is considered, and the main results are discussed. Tarzana’s ground motion cannot collapse the 3-story building, but it can damage the building. If the building had no hysteretic damping, it would collapse because the capacity curve stops short of the magenta demand curve. The maximum damage to the 3-story steel SMF building was caused by the ground motion recorded at TCU084 station during the 1999 magnitude M 7.6 Chi-Chi, Taiwan, earthquake. The effect of aftershocks is expected to be small for extreme ground motions because they are much stronger than any other ground motion, including aftershocks.

Collapse-proof structures cannot be collapsed by any of the recorded ground motions. Collapse-proof structures are characterized by very high values of seismic toughness and damping. This chapter discusses the seismic design of a collapse-proof structure. The 11 response spectra are enclosed within a smooth envelope, as shown by the thick magenta curve. Envelope response spectra are similarly generated for other values of damping. Buckling-restrained braces (BRB) can yield both tension and compression. A normal brace buckles in compression before it can yield. But a BRB has an outer encasement, which prevents it from buckling, whereas the inner core yields in compression. The capacity and damping curves are regenerated using new values of elastic period and damping. Soil-structure interaction increases the elastic period of the system and increases its initial (elastic) damping.

The overstrength factor Ω₀ and the deflection amplification factor C_d can vary from one building to another even if the buildings have the same lateral load resisting system. Also, the response modification factor R is very sensitive to the frequency composition of the ground motion. It is unreasonable to assume the same R for all ground motions. In addition, elastic analysis does not capture the true strength, deformability, and damping of a structure. R, C_d and Ω₀ factors are used to mitigate the shortcomings of an elastic analysis, but these factors are arbitrary. Collapse-proof seismic design should be carried out by using true capacities and true demands without the use of R, C_d and Ω₀ factors.

A ground motion is defined by its acceleration-deformation response spectra (ADRS) and cyclic-demand response spectra for various values of damping. The size of an ADRS is captured by energy demand; its shape is captured by the energy centroid and normalized velocity. From the perspective of collapse prevention, the important characteristics of a structure are its seismic toughness, damping at ultimate deflection, and cyclic capacity. Seismic toughness and damping can be rolled into the minimum energy-demand needed to collapse the structure. The physics of the earth is too complex to be captured by any models in the near future. Therefore, predictions of future ground motions will remain highly subjective and uncertain for a long time. When uncertainty is not an option, structures should be designed to withstand the strongest recorded ground motions.