Page 101 - Dynamic Loading and Design of Structures

Page 78

‘inertia loading’ given by the product for all masses of mass and acceleration per unit modal
displacement (i.e. Yj=1m), i.e.

(3.21)

in which iF(z) is the conventional static influence function for load effect F and µj is the mode
shape function.
The response to lower frequency input components is effectively quasi-static, and space
does not permit detailed consideration in this dynamics text. The r.m.s. value for load effect F
is commonly denoted , ‘B’ signifying spectral broadband of frequencies. It can be
evaluated by purely static correlation analysis (Wyatt, 1981), which is particularly well-suited
to cases where the load on some part of the structure has the effect of relieving the net load
effect. is equivalent to the ‘background factor’ in Davenport based design codes and
recommendations, and can also be inferred from conventional static results such as the
detailed method of BS 6399 Part 2. Denoting the codified peak quasi-static value as FQS
(prior to application of dynamic factor C ) and the hourly mean value as F, and writing
r
, the crest factor for quasi-static response can be taken as gs=4.1–
B
0.25log10He (Wyatt, 1981), for He expressed in metres. σ(F) is then readily evaluated.
The static (broadband) and dynamic (narrowband) effects are statistically independent, and

can be combined by root sum square . Design is commonly based on the
expected maximum value ,in which g is the ‘crest factor’ (Davenport,
1/2
1/2
)
1964) given by g=(In 2vτ +0.577/(In 2vτ . In the latter, τs the storm-strength averaging
)
i
time (e.g. 3,600 sec) and v is the effective frequency, which can be
taken as . The upper tail nature of both spectrum and admittance function are
such that the first mode dominates dynamic gust response, but if necessary further mode
contributions can be added to σ(F) by root sum square.
T
3.1.4 Further cases of gust load spectra

In the case of a lattice tower of significant face width compared to the integral scale L , the
n
foregoing presumption that the load on any element is fully defined by a single-point
windspeed remains acceptable but it is necessary to allow for the correlation in two
dimensions (i.e. with reference to location co-ordinates z and z ). This case is referred to as
1
2
the ‘lattice plate’. The numerator of the admittance function thus becomes a quadruple
integral. For the case where L is small compared to the structure dimensions H and H in
2
n
1
two orthogonal directions, the analogue to the approximation for a single line
becomes , in which . For the exponential
approximation to . For the HIT form, (considering only positive
ordinates of Ru). The resulting approximation to the admittance (J) is given to a good
,
approximation by J=J ×J where J and J 2
1
2
1