Two-Stage Analysis Loophole
Engineering projects and building code provisions can often seem like Rorschach tests where two people looking at the same thing can draw sharply different conclusions. This article reviews the two-stage analysis procedure in ASCE 7-16, Minimum Design Loads for Buildings and Other Structures, to consider if the provisions are an innocent inkblot or possibly may be interpreted differently by some.
Engineers simplify what is too complex to solve and what is too complex to solve efficiently in practice. The simplification imposes the obligation to validate that it does not result in a solution that works for the simplified model but is invalid for the complex realities. Because simplification is often an imperfect step away from reality, simplification incurs the obligation of conservatism. The authors’ purpose is to explain how the two-stage analysis simplification can be applied inappropriately to allow for designs that do not provide the level of safety intended by the code. This article also offers remedies to prevent future misuse of this procedure.
A bold and useful simplification in the code’s seismic provisions is the equivalent lateral force (ELF) procedure, predicated on the assumption of approximately equal deformation distribution in one dimension over the structure’s height. But an efficient and ubiquitous building type like podium construction with several stories of light framing perched on one or more levels of concrete (or concrete with concrete masonry) framing is not consistent with the assumptions inherent in the ELF procedure. Using ELF for podium construction can result in mass from the heavier base being applied as inertial loads to the flexible upper portion. Rather than subject podium construction to the rigors and expense of a dynamic analysis, code authors opted for another simplification to keep the ELF procedure on the table for the design of podium construction by adopting the two-stage analysis provisions first introduced in the 1988 Uniform Building Code (UBC).
Conceptually, the two-stage analysis introduces a reasonable simplification to reflect the physical phenomenon of a rigid base not amplifying ground motions to more flexible stories perched above. Further, it appropriately builds in conservatism because analyzing a single building as two separate shorter buildings results in shorter periods for individual building portions, and therefore, equal or greater base shear coefficients for each portion of the structure. However, as demonstrated by the example building described later, this conservatism can be insufficient compensation if the two-stage analysis technique masks the deleterious effects of a base with a torsional irregularity. The two-stage analysis allows the flexible upper portion to be designed as a separate structure fixed at its base using the ELF or modal response spectrum procedure. The reactions from the upper portion are transferred to the rigid base (lower portion), amplified, not reduced, as appropriate for relative seismic response modification factor (R) and redundancy factor (ρ) values. Consistent with the procedure’s imposition of a static force at the top of the rigid base, the lower portion is designed using the ELF procedure.