Fundamental Period of Reinforced Concrete Moment-Resisting Frame Structures

This report investigates the rationale behind the approximate formula for computing the period of reinforced concrete frame structures recommended by the Structural Engineers Association of California (SEAOC) and adopted by the International Conference of Building Officials (lCBO). Pertinent studies and reports constituting the basis for that formula are critically reviewed. The discrepancies of the data base and procedure for compiling building periods from the data base are discussed. Results from various experimental studies are reported to illustrate the variation of building period with the increase of building vibrational response. The effects of building period on the response of structures under two orthogonal ground motion inputs are illustrated. The influence of structure characteristics and soil conditions are also discussed. The study introduces a methodology for inferring, in a consistent manner, building periods from actual strong motion instrument records. Based on this methodology, periods of 15 reinforced concrete frame buildings are compiled. The new data is correlated with approximate (empirical) period formulas prescribed in various code regulations and recommendations.

The new data set shows that the formulas T=0.035(hn)3/4 and T=O.IN represent lower limits of the period of reinforced concrete frames structures at the time where their response is controlled by the frame alone. However, there is no clear advantage in using the formula T=Ct(hn)3/4 over T=O.IN. The applications of approximate formulas should be limited to conventional buildings with similar stiffness distributions along their principal directions. The data does not support using either of these formula for buildings less than 50 feet or more than 250 feet in height.

It is shown that the period of reinforced concrete frame structures lengthens considerably while the structures are subjected to earthquakes, and therefore buildings do not present a single deterministic period value. The increase in period is related to the intensity of building response and to the participation of the nonstructural components into the lateral stiffness of the building. As a result, it appears more appropriate to prescribe a band of variation for the period of a structure and to select within that band, an effective period value that would be compatible with the seismic demands of interest in design. Additional studies should be devoted to define the bounds for that band of variation. Until such further studies are made, the code recommended formula or the simpler formula T=O.lN can be used to approximate the period value of conventional concrete ductile moment-resisting frame structures at a preliminary design stage.