Response of structures to earthquakes: approximate analysis techniques for lateral loads

Response of structures to earthquakes: approximate analysis techniques for lateral loads

Abstract: Approximate methods provide the basis for selecting preliminary member sizes for rigorous analysis to determine whether design criteria are met. Hence simplified analyses are often used for preliminary design and for gaining valuable insight into system performance. The zero moment point method for single bay multi-storey frame and portal, cantilever, factor and stiffness centre methods for multi-storey and multi-bay frames are discussed and a comparison is made.

Key words: zero moment point, portal, cantilever, contra-flexure, stiffness centre.

Introduction

Even in today’s high-speed computer-oriented world with all its sophisticated analysis capability, there is still a need for approximate analysis of structures. First it provides a basis for selecting preliminary member sizes because the design of a structure, no matter how simple or complex, begins with a tentative selection of members. With the preliminary sizes, an analysis is made to determine if design criteria are met. If not, an analysis of the modified structure is made to improve its agreement with the requirements and the process is continued until a design is obtained within the limits of acceptability.

When it comes to earthquakes, earthquake-resistant structural design often requires the ability to analyse complex frames for lateral loads arising from systematic loading. Sophisticated, very accurate analysis may not be necessary since large uncertainties are involved in seismic loading. Hence simplified analyses are often used for preliminary gaining and for getting valuable insight into system performance. Preliminary designs are very useful in locating weak solutions.

In order to model a structure subjected to earthquake loading several assumptions and approximations are made. Hence the results arising from these will not reflect the true behaviour. It is customary to assume a structure has a shear frame for the purposes of determining natural frequencies, periods and mode shapes. For such an idealization the beam slab system is assumed to be infinitely rigid in comparison with columns. Even though it is deviating from reality, this reduces the dynamic degrees of freedom quite significantly.

Frames with uniform distribution of mass and stiffness are called regular frames and they may be idealized as a single multi-storeyed frame for the purpose of analysis in elevation. Structures which are unsymmetrical in plan produce torsion in plan and introduce more shears on perimeter and corner columns. When a diaphragm is discontinuous, it will significantly affect the distribution of forces between the vertical lateral load resisting (VLLR) elements. Usually codal guidelines are given for ensuring good seismic performance in the absence of detailed analysis tools.

Simplified analysis for lateral loads

The following assumptions are made:

•       Horizontal loads are concentrated at floor levels.

•       The effect of shear on deformation is neglected. This is valid for frames but not for walls.

•       The effect of axial force in deformation is neglected. This is true as long as total length is not small with respect to the height.

The methods of analysis are:

•       For multi-storey, single bay frame

•       Zero moment point method

•       Continuum method (only for buildings with large degree of uniformity)

•       For multi-storey, multi-bay frames

•       portal method,

•       cantilever method,

•       factor method,

•       stiffness centre method.

These will be discussed in more detail in the following sections.