A non-conventional design philosophy for seismic resistance of building structures was preliminary evaluated. The main concept was to design the vertical elements of the structure (columns and walls) for gravity loads and to determine the characteristics of added damping devices required to satisfy certain maximum level of deformation in the building under a strong seismic excitation. The buildings under consideration are meant to respond in the linear range. Alternative damping mechanisms considered in the analyses included; (i) metallic yielding devices, (ii) frictional devices, and (iii) linearly viscous damping devices. Low to high rise buildings (corresponding to 0.2, 0.5, 1.0, and 2.0s periods) were considered in the analyses and their “flexible counterparts” were investigated under the alternative seismic design scheme.

It is found that very different damping characteristics are required for long period single degree of freedom (SDOF) systems as compared to short period SDOF in order to reduce the stiffness and still produce the same maximum displacement under a strong seismic excitation. For short period SDOF the demand of external damping (either from viscous or metallic yielding devices) is higher as compared to long period SDOF systems. It is also found that the relative viscous damping demand of short and long period Multiple Degree of Freedom Systems (MDOF) is considerably different than the relative viscous damping demand in short and long period SDOF. Long period MDOF require more viscous damping per story than short period MDOF.

Considerably efforts have been invested throughout the world for a number of years in order to develop seismic design criteria and procedures to achieve specified performance objectives. Innovative techniques to improve building performance under strong ground motions include: seismic isolation, supplemental energy dissipation systems, and active or hybrid structural control.

This study is focused on the use of some supplemental energy dissipation devices as a mechanism that allows reducing the elastic stiffness of a structure and still obtaining the same maximum displacement under a strong ground motion. Elasto-plastic metallic yielding and frictional devices, and fluid viscous dampers are considered in the analyses.

1) Problem Statement

Assuming an idealized structural system with stiffness “K₀”, mass “M”, and linear viscous damping C_0.05 (Figure 1.a), find the damping characteristics required in a companion “softened” structure (Figure 1.b) in order to have the same maximum displacement when both systems are subject to the same strong ground motion. The damping factor for the base case structure “C_0.05” is assumed to be equal to 5% of the critical damping factor (2(K₀M)^0.5).

Damping devices considered in this study includes linear viscous dampers and elasto-plastic yielding devices. A particular case of the elasto-plastic devices in which the initial stiffness equals infinity corresponds to frictional devices.

It is noticed from Figure 2 that the viscous damping demand for short period SDOF is considerably higher than the damping demand for long period SDOF. This observation can also be stated as follows; for the same damping ratio, the reduction in the response is higher for long period structures than for short period structures. This conclusion is implicitly stated in Table 2 of the monograph by Hanson and Soong (2001).

It is noticed from Figure 3 that for the same reduction of the stiffness in the base case structure, the maximum damping force is considerably higher in short period structures (T₀=0.2s) than in long periods structures (T₀=2.0s). For instance, decreasing the stiffness by a factor of two (2) in a T₀=0.2s SDOF would require a damping device generating a damping force five (5) times larger than the maximum damping force induced in the base case structure. An excessive extra damping force might limit the use of this type of dissipating energy devices because the structural design should also specify a mean to transmit such forces to the foundation.

The resulting system (structure plus yielding device) has a bilinear force-deformation relationship defined by:

Post-yielding stiffness:             (2)

The yielding force, F_y, of the composed system is given by:

where g is a parameter (inverse of base shear coefficient), and V_max(K₀/a, x = 0.05.a^0.5) is the maximum induced shear force in a linear SDOF with mass M, stiffness K₀/a,  .. and damping ratio x = 0.05.a^0.5.

For all the cases, it is noticed that:

It is also important to notice that for short period SDOF (T₀=0.2 sec), there is no combination of the parameters b and g (for 0<b<10, and 1.5<g<10) in the softened system allowing to obtain the same maximum displacement than the base case structure. This is observed even for a stiffness reduction factor of 1.5. Contrarily to this, for intermediate and long period SDOF (T₀=0.5, 1.0, 2.0 s), it is possible to find combinations of g and b in the softened system with a=2.0, allowing to obtain the same displacement than the base case structure. This suggests that the use of elasto-plastic yielding (and frictional) devices is less efficient in short period SDOF than in intermediate and long period SDOF. In fact, it can be claimed that for short period SDOF the use of such devices would not permit achieving the selected performance criterion.

The conclusions stated in Section 2 correspond exclusively to SDOF systems. The selection of the parameters a, b, and g was completely arbitrary and might not have practical meaning in an actual structure. In this section, boundaries are established for some of those parameters to realistically evaluate the efficiency of viscous dampers in short, intermediate, and long period building structures. The relative efficiency of metallic yielding devices is not evaluated here because of time constrains during this study.

Four (4) different base case building structures are considered in the analyses; the structures are N = 2, 5, 10, and 20-story planar frames (Figure 9) having a single bay of length L=30 ft. Each base structure represents an interior frame of an infinitely long and infinitely wide building. The out-of-plane distance between consecutive frames is assumed to be equal to the frame’s span (L = 30 ft). W_story = 200 lbf/ft² story weight is assumed. Girders are L/24 wide by L/12 deep in all cases. The modulus of elasticity of the girder and columns’ material is 4,000 ksi, which roughly corresponds to f’_c = 5 ksi concrete. Column sizes are selected on each case to produce a first mode period of the structure equal to N/10 seconds. Column sections are square.

The column size of each on the base case structures defined in the Section 3.1 (Figure 9) is consecutively reduced and the corresponding stiffness reduction factor, a, is calculated. For each column size, C, the compression stress, sc, on the first story columns is estimated as:

               (4)

Figures 10 (a)-(d) show the variation of a with column size and compression stress on the first story columns (normalized by f’c = 5 ksi) for the N = 2, 5, 10, and 20-story structures.

Notice that although the large column size corresponding to the base case structure (a = 1.0) might not be realistic (this is associated to the large story weight assumed), the purpose of these analyses is to determine reasonable values of a for different types of structures.

It is noticed from Figure 10 (and Table 1) that:

                 (5)

The assumptions involved in the derivation of this equation include: (i) linear elastic response of the structure, (ii) harmonic excitation of the structure, (iii) structure response is governed by first mode.

(6.a)

where:
(6.b)

M_story: story mass (m_i = M_story)

In Equation 6, it is assumed that dampers are located in diagonal running from the base of one column to the top of the next column on each story.

It is noticed from Figure 11 that a considerably higher damping constant per story is needed in long period structures as compared to short period structures in order to obtain the same increase in the overall damping ratio. Thus, even though for SDOF the damping ratio required to produce the same displacement for a given stiffness reduction factor is considerably smaller for long period structures than for short period structures, the required damping constant per story might be similar in both types of MDOF structures. In order to investigate this issue, the base case MDOF structures defined above were subject to the AIJ acceleration design spectrum defined at engineering bedrock (Otani et. al, 2000):

            (7)

where, S_a(T) is the acceleration spectrum ordinate (cm/s²), and T (=T₀) is the structure period.

-Calculate the spectral displacement for the base structure using Equation 7.

-Calculate the required damping constant per story using Figure 11.

Figure 12 show the resulting damping constant per story for the different base case structures considering both: (i) a uniform distribution of dampers along the height, (ii) an optimized distribution assuming at most two (2) dampers per story (but same number of dampers in the structure as in case (i), i.e., N dampers).

It is noticed that the required damping factor per floor is closely the same for short and intermediate period structures (T₀<1.0s) and it is higher for long period structures (T₀ = 2.0s). This conclusion is almost opposite to the conclusion made for SDOF systems in Section 2.1 concerned with the use of viscous damper devices as a mechanism allowing to reduce the stiffness of the structure.

Considering the scheme of reducing the stiffness of a system and adding damping in order to obtain the same maximum displacement under the same excitation, the following conclusions are drawn:

The use of metallic yielding and friction devices in MDOF structures as a mechanism allowing to reduce the stiffness of the structure was not investigated in this study due to time constrains.

An evaluation of the generality of the findings reported here must be carried out by considering other types of base excitation.

Other types of damping devices commercially available; non-linear viscous dampers, viscoelastic (VE) solid devices, and metallic yielding devices with more general force-displacement relationship must be evaluated under the scheme of achieving a maximum reduction of the stiffness of the building and obtaining the same response than a base case structure.

Hwang Jenn-Shin (2002), Seismic Design of Structures with Viscous Dampers, International Training Program for Seismic Design of Building Structures, National Center for Research on Earthquake Engineering of Taiwan.

Hanson, R. D., and Soong, T. T. (2001), Seismic Design with Supplemental Energy Dissipation Devices, Earthquake Engineering Research Institute (EERI) Monographs, 135p.

Otani, S., Hiraishi, H., Midorikawa, M., and Teshigawara, M. (2000), New Seismic Design Provisions in Japan, Uzumeri Symposium-2000 ACI Annual Fall Convention in Toronto.

Garcia , L. E. (1998), Structural Dynamics Applied to Seismic Design (In Spanish), Universidad de los Andes, Facultad de Ingenieria Civil, Bogota-Colombia, 574p.

The author wishes to express his deepest gratitude to the Monbukagakusho program, the U.S and Tokyo National Science Foundation (NSF) for making the summer program a dream come true.

Special thanks also to Professor Otani for his continuous guidance during this research. Sincere gratitude also extended to Professor Shiohara, Suzuki-san, and all the members of the Otani-Shiohara laboratory at the University of Tokyo for all the hospitality and kindness during the summer program.

Table 1 Maximum Stiffness Reduction Factor and Minimum Column size for Different Base Case Structures