JANUARY 2022 41
structural ANALYSIS
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 authorsā
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 codeās seismic provisions
is the equivalent lateral force (ELF) procedure, predicated on the
assumption of approximately equal deformation distribution in one
dimension over the structureās 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 sim-
plification 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
(Ļ) values. Consistent with the procedureās imposition of a static
force at the top of the rigid base, the lower portion is designed
using the ELF procedure.
Code Provisions
The two-stage analysis procedure provisions from ASCE 7-16, Section
12.2.3.2 are listed below:
a. The stiffness of the lower portion must be at least 10 times the
stiffness of the upper portion.
b. The period of the entire structure shall not be greater than 1.1
times the period of the upper portion considered as a separate
structure fixed at the base.
c. The flexible upper portion shall be designed as a separate
structure using the appropriate values of R and Ļ.
d. The rigid lower portion shall be designed as a separate struc-
ture using the appropriate values of R and Ļ. The reactions
from the upper portion shall be those determined from the
analysis of the upper portion amplified by the ratio of the R/Ļ
of the upper portion over R/Ļ of the lower portion. This ratio
shall not be less than 1.0.
e. The upper portion is analyzed with the equivalent lateral force
or modal response spectrum procedure, and the lower portion
is analyzed with the equivalent lateral force procedure.
To the main point, these provisions strain the obligation to validate
the simplification. Only (a) and (b) provide restrictions to apply the
procedure; the other items specify how the procedure is used. While
item (a) imposes a relative stiffness requirement, the stiffness param-
eter is undefined. More importantly, the stiffness obligation does not
mandate that the lower portion have properties that provide support
equivalent to āfixed at the base.ā While item (b) imposes a require-
ment to compare dynamic properties of the two portions, the period
comparison does not ensure the lower portion responds rigidly as the
procedure allows the engineer to assume. In the authorsā opinion,
although compliance with item (b) is not uniformly adhered to, the
provision at least helps diligent practitioners and code enforcement
officials keep designs closer to the code intent of a fixed base.
Figure 1. Example building's finite element model.
continued on next page
Two-Stage Analysis Loophole
By Steven Shepherd, S.E., and James McDonald, S.E.
