Elsevier

Engineering Structures

Volume 28, Issue 4, March 2006, Pages 495-502
Engineering Structures

A rationale for determining the natural period of RC building frames having infill

https://doi.org/10.1016/j.engstruct.2005.09.004Get rights and content

Abstract

Building design codes generally impose some upper limit on the magnitude of the natural period determined from a rational numerical analysis if the period is longer than that predicted by empirical code equations since the code equations are derived on the basis of measuring the period of real buildings during an earthquake. In this study, the fundamental periods of vibration of a series of regular RC framed buildings are studied using 3D FE modeling and modal eigenvalue analysis including the effects of infill. It has been found that when the models do not include infill, as is done in conventional analysis, the period given by the analysis is significantly longer than the period predicted by the code equations justifying the imposition of upper limit on the period by the code. However, when the effect of infill is included in the models, the time periods determined from eigenvalue analysis were remarkably close to those predicted by the code formulas. It is also observed that the randomness in the distribution of infill does not cause much variation of the period if the total amount of infilled panels is the same for all models. It is also observed that varying amount of infilled panels causes some changes in the determined period. Based on the findings of the study, some guidelines are suggested for determining the period. The findings of the study have shown us a practical way to determine the fundamental period of RC frames using rational approaches like modal analysis, and eliminate the necessity of imposing code limits.

Introduction

Building codes provide empirical formulas for estimating the fundamental period. These formulas are developed on the basis of observed periods of real buildings during ground motion and the period is generally expressed as a function of building height, type (frame or shear wall), etc. Building periods predicted by these empirical equations are widely used in practice although it has been pointed out by many [2], [3], [8], [15] that there is scope for further improvement in these equations. With the wide availability of high-speed personal computers it is now possible to develop a rigorous finite element (FE) model of a structure and determine its natural period by means of the exact eigenvalue analysis or by any rational method like Rayleigh’s method. However, the period obtained by such rational methods has been generally found to be significantly longer than the observed period of the buildings [4], [2], [3]. For this reason, code specifications (BNBC [5], UBC [7], BSLJ [11]) generally put a limit on the period value if it is obtained by eigenvalue analysis of the FE model. This, in fact, discourages the use of periods obtained from computational modeling. Conventional FE modeling of reinforced concrete (RC) structures, which are widely used in strength analysis and design, renders the structures more flexible than they actually are due to the fact that the effect of secondary components like the infills are not considered in the modeling. In reality, the additional stiffness contributed by these secondary components increases the overall stiffness of the building, which eventually leads to shorter time periods as they are observed during earthquakes.

The objective of this paper is to investigate the natural period of vibrations of RC buildings by means of FE modeling under various conditions of geometric and other parameters including the effect of regular as well as randomly distributed infill. The diagonal strut model of infill proposed by Saneinejad and Hobbs [14] and later enhanced by Madan et al. [10] has been adopted in the present study. Three-dimensional finite element modeling of a series of some idealized regular shaped building frames is analyzed, and their time periods are determined by means of modal (eigenvalue) analysis. These periods are then compared with the code formulas as well as periods obtained from analysis without considering infill. The study has been conducted under varying conditions of number of floors, floor heights, number of spans, amount of infilled panels, etc. Infilled panels were distributed over the structure in regular as well as in a random pattern. Comparisons of the periods obtained for different parametric conditions revealed the relative accuracy of the different methods and established the importance of incorporating the structural effect of infill in FE modeling to more accurately reflect the dynamic behavior of RC frames which is otherwise not possible to obtain in conventional frame modeling.

Section snippets

Infill in RC structure

Infills of brick or stone masonry are frequently used in RC framed buildings. Although these are primarily intended to serve as partitions, their structural contribution in increasing the lateral stiffness of the frame is long recognized. There are several analytical models of infill available in the literature, which can be broadly categorized as (a) continuum models such as the models proposed by Lourenco et al. [9] and Papia [13] and (b) diagonal strut models such as the model proposed by

Computational modeling

In this study common two-noded frame elements having six degrees of freedom per node has been used for the columns. For beams, similar elements with node offset capabilities has been used to model the web of T-beams (monolithic beam and slab). The floor slab has been modeled using common four-noded plate elements. Point mass elements are used to represent the non-structural dead load like floor finish, partition walls, etc. The infills are modeled as diagonal struts using two-noded truss

Code equations for time period

The empirical formula for the fundamental period of vibration of RC buildings specified in the Uniform Building Code (UBC) and Bangladesh National Building Code (BNBC) is of the form T=Cth3/4s, where h is the height of the building above the base. For framed RC buildings the numerical coefficient Ct=0.03 for UBC when h is in feet and Ct=0.073 in BNBC when h is in meters. Both codes permit an alternative way to calculate the fundamental period T using the structural properties and deformational

Sensitivity analysis

Earlier studies on the sensitivity of different structural parameters [1] reveals that when infill is considered in the analysis of building, the nature of the stiffness contribution of structural elements like beams and columns or the effect of building parameters like the number of spans or floor panel size are significantly altered. Other parameters commonly established to have effect on the period are the number of floors and floor height or building height. In each case a complete 3D Fet

Period with randomly distributed infill

It is already apparent from the results presented in the previous section that the building period obtained by the analytical method is close to the period predicted by codes when infill is present in the FE model. In all the results presented in previous section, the number of infilled frame panels was fixed at 40%. In practical cases, the amount of infill will vary from building to building. Also their arrangement or location will be different from building to building. Therefore, the effect

The rationale

Based on the preceding discussion, a rationale for estimating the period of an RC framed building having infilled panels can be suggested. Among the different code equations, the BNBC (or UBC) equation for determining the period has been found to be closest to the numerical results with infill. Although the code equations are reasonably accurate, further refinement can be made so that the period is estimated more accurately. This shall result in more accurate determination of base shear which

Conclusion

A computational investigation has been performed on the fundamental natural period of vibration of RC framed buildings having infills. Some sensitivity analysis has been performed in the present study which shows that, in presence of infill, the beam and column stiffness have negligible effect on the period. The span length of the panel, number of spans in the direction of motion and amount of infill in the structure are some important parameters in influencing the period which the code

References (15)

  • K.M. Amanat et al.

    A reappraisal of time period formulas of design codes for framed reinforced concrete buildings

  • R.K. Goel et al.

    Period formulas for moment-resisting frame buildings

    Journal of Structural Engineering, ASCE

    (1997)
  • R.K. Goel et al.

    Period formulas for concrete shear wall buildings

    Journal of Structural Engineering, ASCE

    (1998)
  • Hossain M.Z.. Influence of structure parameters on period of frame structures for earthquake resistant design. MSc...
  • Housing and Building Research Institute and Bangladesh Standards and Testing Institution. Bangladesh National Building...
  • Indian Standards Institution (IS). Criteria for earthquake resistant design of structures. India;...
  • International Conference of Building Officials. Uniform building code. California: Willier;...
There are more references available in the full text version of this article.

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