Steel Designers Manual - TheBestFriend.org

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Steel Designers' Manual - 6th Edition (2003)
Note: displacement y measured
relative to static
equilibrium position.
Displacement, velocity and
acceleration measured
positive upwards.
L
Fundamentals of dynamic behaviour 355
It is beyond the scope of this book to address all these issues, and references are
suggested for more detailed guidance. The following sections are intended to give
an overview of the fundamental features of dynamic behaviour and to introduce
some of the terminology employed and analysis procedures available. It must be
borne in mind that dynamic behaviour is influenced by a larger number of parameters
than static behaviour, and that some of the parameters cannot be predicted
precisely at the design stage. It is often advisable to investigate the effects of varying
initial assumptions to ensure that the most critical situations that may occur have
been examined.
12.2 Fundamentals of dynamic behaviour
The principal features of dynamic behaviour may be illustrated by the examination
of a very simple dynamic system, a concentrated mass M supported on a light
cantilever of flexural rigidity EI and length L as illustrated in Fig. 12.1. The mass is
subjected to forces P which vary with time t.
12.2.1 Dynamic equilibrium
One of the basic methods of dynamic analysis is the examination of dynamic equilibrium
to formulate an equation of motion. Consider the dynamic equilibrium of
the mass illustrated in Fig. 12.1. If at some time t the mass is displaced upwards from
its static equilibrium position by y, and has velocity y · and acceleration ÿ (positive
upwards) the mass is in general subjected to the following forces:
Fig. 12.1 Example of a dynamic system
_—(
Ky
Forces acting on mass
M at time