Civil Engineering Reference
In-Depth Information
displacements in Fig. 6.2 because the assumption of linear elastic structural behaviour
implies that the relationship between structural displacements and cross sectional forces
is also linear.
Fig. 7.1
Time and frequency domain representations
Thus, once the displacements have been determined, cross sectional forces may be
obtained directly from the structural stiffness properties and the derivatives of the
displacement functions according to usual structural mechanics procedures. While this is
an appropriate strategy for the determination of the mean value
F
, it is not an advisable
strategy for the determination of
. There are two reasons for this. First, dynamic
response displacements are in general obtained from a modal solution in frequency
domain that contains a chosen number of eigen modes which havebeen obtained from an
eigen value solution that is based on the distributed stiffness and mass properties of the
structure. The standard deviation of the total response displacements are then built up of
the sum of contributions from each of these modes, either in a mode by mode approach
σ
F
