By Tyler B. Sease, E.I.T.
Practicing structural engineers typically design seismic force resisting systems (SFRS) for high seismic regions in one of two manners, either a capacity- or performance-based design. Capacity-based design refers to the process of analyzing a structure with the equivalent lateral force (ELF) procedure according to ASCE codes and then designing SFRS connections according to AISC’s Seismic Provisions. Performance-based earthquake engineering (PBEE) typically refers to the process of analyzing a structure with a modal pushover analysis (MPA) or response history analysis (RHA). With PBEE, the structural engineer is able to design the SFRS connections based on actual calculated loads in lieu of designing connections for the member’s strength with the ELF. This article is based on a study that sought to analyze and design a structure with both methods and determine if the PBEE methods would yield enough cost savings to a project to justify the complex analysis on the part of the structural engineer.
PBEE has matured as an analysis procedure over the past 20 years and is based on the dynamic properties of an individual structure. The MPA is a nonlinear static analysis procedure and the RHA is a nonlinear dynamic analysis procedure. With the MPA, gravity loads are applied to the structure and then lateral loads are applied and amplified until the structure’s roof reaches predetermined displacements. These displacements are plotted against the base shear, yielding a “pushover curve.” The lateral loads are applied with a minimum of three load patterns and are amplified for each case until enough stiffness is lost through plastic deformation that collapse is imminent.
RHA is the most precise procedure for seismic design. This precision stems from solving the equation of motion at each time step in a nonlinear manner. A minimum of seven sets of earthquake acceleration data are required in order to average critical values from each case, such as base shear, bracing loads, drift, etc. Scaled acceleration data should closely match the target spectrum for the maximum considered earthquake. The RHA calculated member forces do not require an overstrength factor, typically associated with the ELF procedure, but the RHA does include an ASCE requirement of a peer review in order to ensure proper implementation by the engineer-of-record.
The structure analyzed in the study was a five story multi-use commercial building located in the high-seismic region of Charleston, S.C. With a seismic design category of “D,” and having an occupancy category of III, this structure requires significant SFRS. This 80-foot tall structure consists of steel framing and composite slabs at each level. Typical building loads were used in the gravity design of this 200- by 200-foot structure. The SFRS is steel special concentrically braced frames (SCBF) with a response modification coefficient of 6. Typical wide flange shapes were used for beams and columns and square HSS sections for bracing members within the chevron braced frames.
The ELF procedure was used to analyze and design the structure for the capacity-based design, as well as provide a starting point for the PBEE procedures. The connections for the capacity-based design were designed according to AISC’s Seismic Provisions in such a manner that inelastic buckling and yielding may be allowed within the braces. The MPA requires approximately twice as much computing time from the engineer, and yielded a base shear 229 percent greater than that of the ELF procedure. However, the calculated loads that the SFRS connections should be designed for were on average 45 percent less than that of the ELF method. The RHA requires approximately four times as much computing time as the ELF, and a base shear 356 percent greater than the ELF was calculated. The loads calculated for the SFRS connections averaged 34 percent less than the capacity based method.
PBEE allows the engineer the flexibility to no longer be required to adhere to strict provisions of a seismic code, but rather perform complex analyses to create a more efficient structural system. With PBEE the engineer is able to locate precisely where nonlinear deformations are expected to occur within the SFRS. This permits the use of special detailing requirements as prescribed by the Seismic Provisions, to be provided for only those members in which nonlinear deformations are expected to occur. With both the MPA and RHA, the plastic deformations were confirmed to be located in the first level of the five levels of chevron bracing. Therefore, the first level was designed according to the Seismic Provisions, and the top four levels of SFRS connections were designed according to calculated loads. This is significant due to the highly complex connections that are required to develop member capacities, and the costs associated with them.
Based on the estimation of an AISC certified structural steel fabricator, the performance-based design would save approximately $23,400 per two-bay frame over the capacity-based design. This equates to a total savings of $187,200 for the SFRS, a savings of 44 percent over the capacity-based design. Beams were larger in the capacity-based design, due to requirements for beam design within chevron SCBF’s within the Seismic Provisions. Beam size reductions and material savings amounted to 114 tons of steel, and shop labor was reduced by 1,088 man-hours. These savings would likely be higher had column splices and axial transfer loads been taken into account in the pricing as these connections would vary significantly between the two methods.
Performance-based analyses certainly appear to be the logical and inherent methods of the future for seismic design in high-seismic regions. Performance-based design can provide significant cost savings for a project in an earthquake prone region, while providing a system tailored to a particular structure. This allows for more creativity from the engineer and opens the door for more efficient and sustainable designs. The structural engineer will be able to create a better system by verifying load paths, calculating more accurate transfer loads, verifying locations of plastic deformations, and ensuring the structure remains viable after a seismic event.
Tyler B. Sease, E.I.T., is a structural design engineer at the Greenville, SC based CMC Cary Engineering. Sease specializes is structural steel design and is a part-time graduate student at the University of South Carolina. He can be reached at Tyler.Sease@cmc.com.