Simplified Seismic Analysis of Building Structure with Rocking Rigid Core(s) and Link Beams

In conventional design methods, buildings are designed such that during an earthquake materials of the structure can enter into inelastic zone in all stories of the building. The problem with this method is that in a regular n-story building with rigid diaphragm, which has 3n degrees of freedom, the inelastic behavior subjected to future earthquakes cannot be estimated easily. Therefore, in spite of the detailed design, it is likely that the stories’ displacements have an inappropriate distribution under a particular earthquake and these inelastic displacements may be concentrated in certain stories and lead to failure of those stories and eventually collapse of the entire structure. To overcome this difficulty, in the current article, a structural system with one or two rocking rigid core(s) and link beams is introduced for n-story buildings, and a simplified method is presented for its seismic analysis. Because of the existence of the rigid core(s) the entire building has a behavior very similar to a one-degree of freedom system in each of the main lateral directions. In this way, estimating the behavior of the structure under the influence of the possible future earthquakes will be easier with a higher level of precision. In addition, concentration of plastic deformations in columns of some stories of the building, and creation of soft stories is not likely in the proposed system.
To show the efficiency of the proposed system and its simplified analysis method, a 15-story steel building has been considered, once with one rigid core, and once more with two rigid cores. The rigid core is consisted of a one bay by one bay braced frame, designed to remain quite elastic under the seismic loads. The connections between the core and the building’s frames are all hinges at all stories to accommodate the relative rotation between the core and the surrounding frames during an earthquake, leading to the vibration of the building to take place basically in the first mode in each lateral direction. In case of two rigid core there are some link beams between them with capability of plastic deformation in shear, by which the integrity of the system and its stability will be provided. The link beams are designed in such a way that result in the minimal amount of bending moment in the rigid core to make it oscillate basically in its first mode and therefore better do its main duty, which is creating the uniform drift in all stories of the building, and eliminating the higher modes effects, resulting a more reliable seismic behavior of the building. For decreasing the amount of shear forces imposed to the link beams, the hinge supports of the two rigid cores has been shifted to their external sides; since in this case, the distance between the support is maximum, leading to minimum shear force in link beam, which is around 58% of its values in case of hinges at the middle.
Regarding that the proposed system behaves similar to a one-degree-of-freedom system, for its dynamic analysis, first the equations of motion have been developed for the n-degree-of-freedom system and then by dynamic compatibility conditions, the mass and height of the equivalent SDOF system have been obtained. Besides, stiffness and yielding displacement of the equivalent SDOF system have been determined so that they result in hysteretic loops similar to the original structure. To investigate the inelastic seismic behavior of the original building and its equivalent SDOF system, the three-component accelerograms of a set of 15 selected earthquakes, including six ones happened outside Iran, four ones of Iranian earthquakes, and five artificial ones, have been used, all corresponding to the soil type III. The PGA values of all records have been scaled to 0.5 g. Finally, elastic and inelastic seismic responses of the original 15-story building and its equivalent SDOF system have been compared. Comparisons show that there is less than 3% and 11% differences in elastic and inelastic responses, respectively.