Page 102 - Dynamic Loading and Design of Structures

Page 79

are values for the two dimensions evaluated separately. J1 is evaluated from the normalized
effective size HN1=He1/Ln (eqn (3.16)) for whichever dimension gives the larger value of H/Ln,
but the smaller normalized value is reduced for evaluation of J2, to HN2=(4/5.9)He2/Ln (Wyatt,
1981).
In the case of a clad structure such as a building, it is empirically established that the
correlation of pressure fluctuation over the upwind face is better than that of the free stream
velocity over the same distances (Cook, 1985). This effect is partly countered by relative
weakening of the effective load fluctuation on the downwind face; the net effect is not
addressed explicitly in Davenport based design formulations. The author’s personal practice is
to apply the lattice plate solution as above, but evaluated taking L =V/6n, an increase of one-
n
third over the free stream value. This procedure cannot be expected to offer precision
comparable to the line-like or true lattice plate cases, but may be sufficient for decision
whether specialist investigations are necessary, in particular for subjective comfort criteria.
Pressure fluctuations near the corners, especially in ‘glancing’ winds, are likely to be
important for lateral or torsional excitation.
The foregoing discussion has considered only the alongwind (u) component of turbulence.
Crosswind components may also be important, commonly treated in two independent
orthogonal components, v (horizontal) and w (vertical). A number of formulations are
available for spectra and net r.m.s. values. The HIT solution gives the upper-tail ordinates of
S and S as 4/3 times S at the given frequency. This can be used as a practical approximation
u
w
v
to Sv at frequencies such that Ln is less than (say) one-fifth of the height above ground, but
becomes increasingly conservative at lower frequencies. Sw can be treated similarly, but with
greater conservatism.
For modal analysis of response the forces are generally required in body axis components.
In the basic case of a vertical structure for which the drag coefficient has constant value C D
for all directions and the crosswind force coefficient is uniformly zero, which is a reasonable
approximation for many lattice towers, the body axis force perpendicular to the mean wind
direction is . The analysis then follows the alongwind treatment
described above, with (v/V)P replacing (2u/V)P, and thus S (or S ) replaces 4S . The HIT
w
v
u
solution for Ln for the v component on vertical separation (and likewise the w component on
horizontal separation) is, however, twice as large as the value for u, being V/4.43n when
integration extends over the full range, including negative ordinates of Rv or Rw. The
practical validity of this increase remains controversial, and some authorities retain the same
values as for u, a nonconservative assumption. The vectorial analysis leading to generalized
expressions for excitation of an element at an arbitrary inclination is highly complex
(Strømmen and Hjorth-Hansen, 1995). Practical approximations for inclined tower structures
are, however, available (Wyatt, 1992).
For bridges, gust dynamic response is generally dominated by vertical motion with
,
excitation based on dC /dαin which C is the lift force coefficient and αis the angle of
L
L
inclination of the wind to the deck. The analysis of correlation along