Civil Engineering Reference
In-Depth Information
Chapter 4
BASIC THEORY OF STOCHASTIC
DYNAMIC RESPONSE
CALCULATIONS
The general finite element theory of wind induced dynamic response calculations for
civil engineering line-like structures is presented in Chapter 9. In the chapter below the
theory is presented in a continuous version tailored for the response and cross sectional
force calculations in Chapter 6 and 7 where it is taken for granted that the necessary
mode shapes are known and that they may be assembled in separate
y
,
z
and θ direc-
tion components. The reason for this choice is that it represents an effective solution
focusing directly on the important wind load and displacement degrees of freedom.
4.1 Modal Analysis and Dynamic Equilibrium Equations
The relevant cross sectional displacements and forces are illustrated in Fig. 4.1. (See also
Fig. 1.3.) It is assumed that displacements and loads (all referred to the
Fig. 4.1
Cross sectional displacements and loads
