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Recent earthquakes that have stuck densely populated regions have demonstrated the urgent need for reliable design methodologies for non-structural elements. Acceleration-sensitive non-structural elements behave in a similar way as structural systems during earthquakes with the differences that they are characterized by different dynamic characteristics and that the seismic demand comes from the movement of the structure on which they are supported. Since many non-structural elements are designed to undergo inelastic deformations during a design level earthquake, damage in these elements is usually caused by excessive displacements relative to the supporting structure. With this in mind, Filiatrault et al. (2018) recently extended the direct displacement-based design procedure, originally proposed for structures (Priestley et al. 2007), to non-structural elements. The proposed methodology applies to acceleration-sensitive elements that are attached to a single point in the supporting structure and for which damage is the result of excessive displacements. Some example of non-structural elements that can be designed using the direct displacement-based approach are suspended piping systems, suspended ceiling systems and heavy anchored or vibration isolated equipment.
In contemporary seismic design standards in Europe and North America, the seismic design of non-structural elements is based on a simplified force-based procedure. Information on the supporting structure must be gathered to start the design process. For example, Eurocode 8 (CEN 2004) requires the seismic hazard at the construction site (in terms of peak ground acceleration, ag), the height of the supporting structure, H, and its elastic fundamental period, T. The next step includes gathering information on the non-structural element including the height at which the component is attached, z, its weight, Wa, its elastic period, Ta, a force reduction factor greater than one, qa, and an importance factor also greater than one, γa. These quantities are used to compute the equivalent static force to be applied at the center of mass of the non-structural element, Fa:
where S is a factor that accounts for soil effects and is assumed as 1.0 for rock sites and larger than 1.0 for softer soil conditions. The equivalent static force, Fa, is used to design the lateral restraints of the non-structural element or the non-structural element itself.
Despite the current force-based approach being very simple, it includes several limitations including:
- The empirical linear amplification factor, 1 + z/H, that estimates the amplification of the peak floor acceleration relative to the peak ground acceleration has been demonstrated, by many past studies, to be over conservative. This is mainly due to ignoring the nonlinear behavior of the supporting structure and the influence of higher structural modes on the peak floor acceleration;
- The component amplification factor, 3/(1 + (1-Ta/T)2), that predicts the amplification of the peak acceleration of the non-structural element relative to the peak floor acceleration, ignores the damping of the non-structural element, the nonlinear response of both the supporting structure and the non-structural element, and the dynamic amplification caused by the higher structural modes;
- The code procedure initiates with an estimate of the elastic period of the non-structural element. This period is difficult to establish due to all the uncertainties involved and the lack of guidelines in design codes. Additionally, for many non-structural elements the global elastic stiffness of the element, and hence its period, are dependent on its total strength. The latter implies that a proper force-based design approach would have to be iterative;
- The force reduction factors, qa, are based on judgement rather than on the lateral force-displacement response of non-structural elements;
- The use of force reduction factors depends on the equal displacement assumption between elastic and inelastic systems. This assumption is not only inadequate for short period non-structural elements, but its validity also depends on the hysteretic and elastic damping models used for comparing elastic and inelastic displacements using nonlinear time history analysis (Priestley et al. 2007).
- Despite limiting displacements is paramount to preventing damage to non-structural elements, contemporary building standards fail to define, quantitatively, displacement limit states for non-structural elements.
Because of the limitations of contemporary building codes for the seismic design of non-structural elements, the direct displacement-based design is an appealing alternative. Direct displacement-based design is based on the concept of designing a non-structural element to achieve a target displacement relative to the supporting structure given a level of seismic hazard intensity. Figure 1 presents a flowchart outlining the various steps required to perform the direct displacement-based seismic design of non-structural elements.
Figure 1
The first step of the direct displacement-based procedure is the definition of the target displacement, Δt,a, relative to the supporting structure that the non-structural element should not exceed under a given seismic hazard intensity.
The seismic hazard level associated with this target displacement is also defined in this step. For non-structural elements, the seismic hazard has to be defined in terms of relative displacement floor response spectra (Merino et al. 2019). The second step consists in the definition of an appropriate level of equivalent non-structural viscous damping, ξeq,a, to capture the energy dissipation characteristics of the non-structural element. The level of equivalent viscous damping is dependent on the target displacement of the non-structural element and could be determined by processing hysteretic curves gathered from cyclic tests conducted on non-structural elements. The third step consists in entering the properly damped design relative displacement floor response spectrum with the target displacement and determining the equivalent non-structural period, Teq,a. In step 4, the equivalent non-structural stiffness, keq,a, is determined using the equivalent period from the previous step and the mass of the non-structural element, Wa/g (g is the acceleration of gravity). Finally, step 5 consists in computing the force acting at the center of mass of the non-structural element, Fa. It is defined as the product of the equivalent stiffness, keq,a, and the target displacement, Δt,a. This force is then used to design the lateral restraint system of the non-structural element or the non-structural element itself.
The effectiveness of this design procedure was appraised by Filiatrault et al. (2018) through the design of the lateral restraint system of a suspended piping system supported on a reinforced concrete frame located in Italy. The results of nonlinear time history analysis demonstrated that the direct displacement-based design methodology is more reliable with respect to the Eurocode 8 force-based methodology.
References:
Filiatrault A, Perrone D, Merino RJ, Calvi GM. (2018) Performance-based seismic design of non-structural building elements. Journal of Earthquake Engineering, DOI: 10.1080/13632469.2018.1512910.
Priestley MJN, Calvi GM, Kowalsky MJ. (2004) Displacement-Based Seismic Design of Structures, IUSS Press, Istituto Universitario di Studi Superiori di Pavia, Pavia, Italy.
CEN, (2004) Eurocode 8 – Design provisions for earthquake resistant structures, EN-1998-1:2004, Comite Europeen de Normalization, Brussels, Belgium.
Merino RJ, Perrone D, Filiatrault A. (2019) Estimating consistent relative displacement and absolute acceleration floor response spectra in elastic buildings. 4th International SPONSE Workshop. At: Pavia, Italy, doi: 0.7414/4sponse.ID.4
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