Structural Engineering, Mechanics, and Materials

U.S. building codes refer to the ASCE 7 Standard for the design of nonstructural components in seismically isolated buildings. The current edition, ASCE 7-22, includes provisions permitting the use of nonlinear response history analysis (NLRHA) to determine the seismic design force on nonstructural components. This enables the calculation of forces that more accurately reflect the peak floor acceleration (PFA) demands of isolated structures. However, the standard also mandates a lower-bound seismic design force [ASCE 7-22 Eq. 13.3-3] regardless of the approach used. This lower bound is anchored to the short-period design spectral acceleration (S_DS ), and it often governs in the case of seismically isolated buildings. Concerns regarding this requirement were formally raised in Public Comment 23 during the ASCE 7-22 development cycle.

This study was undertaken in response to this issue, with the goal of evaluating both the current lower-bound equation and alternative formulations that better reflect the demands on nonstructural components in isolated structures. A wide range of seismically isolated building scenarios was considered, varying in isolation system type, number of superstructure stories, and site class. For each scenario, simplified structures were designed with isolation systems spanning a range of effective periods and damping ratios, and NLRHA was performed to quantify the resulting PFA demands. As prescribed in ASCE 7-22 Chapter 17, the target effective properties used in the isolation system design corresponded to the Risk-Targeted Maximum Considered Earthquake (MCE_R) level, while PFAs were evaluated using NLRHA with ground motions scaled to the Design Earthquake (DE) level, as required for nonstructural components in ASCE 7-22 Chapter 13.

The results of this study demonstrate that the current lower-bound force equation can vary from being overly conservative to unconservative, depending on isolation system properties and site conditions. It is shown that an equation anchored to S_DS is highly unreliable in predicting the PFA of seismically isolated structures, which are characterized by long periods. Instead, PFAs are found to correlate more strongly with the 1-second spectral acceleration at the DE-level (S_{D 1}), divided by the effective period of the isolation system at the DE-level (T_D ), among other parameters.

Based on these findings, a new lower-bound force equation is proposed for nonstructural components in seismically isolated structures. The proposed formulation captures the observed trends in PFA while remaining compatible with the terminology and framework of Chapter 17. It replaces the acceleration term “0.3 S_DS ” in the current equation with “0.8 (V_b /W),” where V_b is the total lateral seismic design force on the isolation system and W is the total weight of the structure. The ratio V_b /W serves as an estimate of the MCE_R-level acceleration, incorporating key quantities already determined in the design of the isolation system. The factor 0.8 then scales this acceleration to the DE level, accounting for the nonlinear behavior of the system.

This proposed formulation offers a practical and technically justified alternative to the current lower-bound equation. These results and recommendations are intended to inform the ongoing efforts of Task Committees 7 (Seismic Isolation and Damping Systems) and 8 (Nonstructural Components) of the ASCE 7-28 Seismic Subcommittee in developing improved provisions for the design of nonstructural components in seismically isolated buildings.

Mat foundations for high-rise buildings have traditionally been constructed as relatively thick members without shear reinforcement and with relatively low longitudinal reinforcement ratio. Laboratory tests demonstrate that unit shear strength decreases with increasing depth and with decreasing longitudinal reinforcement. These effects are represented in the one-way shear strength design equations of ACI 318-19, which results in significantly reduced nominal strength compared with design strengths that were successfully used for foundation mats for decades. The introduction of high-strength longitudinal reinforcement raises further questions about the effects of increased longitudinal reinforcement strains on one-way shear strength. To explore the effects of depth, reinforcement ratio, and high-strength reinforcement on one-way shear strength, a series of seven one-way shear laboratory tests were conducted. The tests were supplemented by nonlinear finite element studies to extrapolate the test results to alternate member geometries and boundary conditions. Design recommendations are proposed based on the findings of the experimental and analytical studies.

In collaboration with practicing structural engineers and experts in anchoring to concrete, the authors undertook a research project to explore the requirements for anchoring columns to reinforced concrete foundations. In early discussions it was realized that, while there were design procedures that were in use in different design offices, the design procedures differed from office to office and few of the methods had been verified by laboratory testing. Based on this knowledge, a series of laboratory tests was designed and carried out to develop benchmark data on the following types of column-foundation problems:

- Interior footings supporting columns in direct tension and anchored by multiple anchor bolts, either with or without additional footing transverse reinforcement to increase strength and deformation capacity.

- Interior footings supporting column in direct bending and anchored by multiple anchor bolts, either with or without additional footing transverse reinforcement to increase strength and deformation capacity.

The laboratory tests were supplemented by nonlinear finite element studies using the software ATENA, both to calibrate the model material parameters and to extrapolate results from the laboratory tests to geometries that were not tested in the laboratory. Together, the laboratory and numerical studies were used to derive a design method to calculate the strength of connections in either direct tension, direct moment transfer, or combinations of the two, with or without additional transverse reinforcement intended to increase strength and deformation capacity. The authors subsequently worked with ACI Committee 318 Structural Concrete Building Code of the American Concrete Institute to develop design provisions that were approved and adopted in ACI 318-25 Building Code Requirements for Structural Concrete and Commentary.

We introduce linear regression using physics-based basis functions optimized through the geometry of an inner product space. This method addresses the challenge of surrogate modeling with high-dimensional input, as the physics-based basis functions encode problem-specific information. We demonstrate the method using a proof-of-concept nonlinear random vibration example.