Page 45 - Dynamic Loading and Design of Structures

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Chapter 2

Analysis for dynamic loading

George D.Monolis

2.1 INTRODUCTION

The purpose of this chapter is analysis of structures that are subjected to time varying loads.
Despite the fact that the majority of civil engineering structures are built on the assumption
that all applied loads are static, there are exceptions which require a distinction between static
and dynamic loads to be made, as in earthquake engineering. All loads in nature are time
dependent. In many cases, however, loads will be applied to a structure in slowly varying
ways, which implies that static conditions can be assumed. The term slow here is quantified
through comparison with an intrinsic time of the structure, which is none other than its natural
period. Thus, a load varies slowly or is fast only in relation to the time required for the
structure to complete a full cycle of oscillation.
There is growing interest nowadays in the process of designing civil engineering structures
to withstand dynamic loads (Biggs, 1965; Craig, 1981; Bathe, 1982). As examples, we
mention (i) structures which house moving or vibrating equipment, (ii) bridges under traffic,
(iii) multistory structures subject to wind and (iv) the case of earthquake induced loads
(Clough and Penzien, 1993; Newmark and Rosenblueth, 1971). Essentially, dynamic analyses
focus on evaluation of time dependent displacements, from which the stress state of the
structure in question can be computed (Paz, 1997; Argyris and Mlejnek, 1991; Chopra, 1995).
The most basic pieces of information needed for this are the natural period, which is a
function of the structure’s mass and stiffness, and the amount of available damping (or,
equivalently, the amount of energy that can be absorbed by the structure).

2.2 THE SINGLE DEGREE-OF-FREEDOM OSCILLATOR

The simplest dynamic model is the Single Degree-of-Freedom (SDOF) oscillator shown in
Figure 2.1 (a). It is an exact model for the simple orthogonal frame with slender columns and
a strong inflexible girder, where all the mass can be lumped. Three basic types of vibrations
can be considered, namely horizontal, vertical and