1. Introduction
In the seismic design of secondary systems (SS) such as nonstructural components, inertial and relative displacement effects are usually considered independently. But the reason for this independence is not clarified enough. In past researches, response spectrum methods have been proposed to analyze three-dimensional piping. Those methods are too complicated to apply for the seismic design of SS in general buildings. It seems useful to obtain basic knowledge for the practical design of SS by studying both effects with a simple typical model.
In this paper, seismic responses due to both effects are studied for SS modeled as light-weight bending beams fixed to the upper and lower floors in a multistory building through response history analysis.
2. Mathematical model and analysis method
Lumped-mass shear-type models and uniform bending-beam models are used for structural frames and SS respectively. The boundary conditions of SS are pin-ends and fixed-ends. The former condition is for comparison and has no effect of relative displacement. Structural frames and SS are assumed to be linear.
A modal analysis method is derived. For inertial effect, responses of modes of structural frames are used as inputs to those of SS.
3. Response histories and peak sectional forces
A three-story model is used as a structural frame. The first natural period is set to be 0.6 sec. except for some cases, while those for SS with pin-ends and fixed-ends are set to be 0.4 and 0.176 sec. respectively for almost cases. Ground motion to the structural frame is an artificial one with a response spectrum corresponding to the lower seismic design level in Japan.
Response histories are shown to confirm the characteristics of responses of SS and phases of effects of inertia and relative displacements. Peak sectional forces along the height of SS are shown. Variations in those peak values due to the change of the natural period of structural frame and SS are shown in spectral form.
4. Conclusion
The results of this paper are summarized as follows.
(1) A modal analysis method has been derived.
(2) Characteristics of the responses of SS such as pseudo-static responses have been confirmed.
(3) The primary mode of SS is dominant in responses by inertial effects.
(4) Even if the natural frequency of SS is increased by changing the boundary condition from pin-ends to fixed-ends, it may be impossible to decrease seismic responses due to the effect of relative displacements.
(5) Because forces due to the effects of inertia and relative displacement are often in-phase, both effects should be appropriately combined in design.
(6) Seismic responses of SS increase with increase or decrease its natural frequency.
(7) While seismic responses of SS with pin-ends decreases as the natural frequency of the structural frame decreases, those with fixed-ends increase.
