Tall buildings - Wind Loading of Structures - page 232

From Equation (9.14), taking natural logarithms of both sides,
(9.16)
The mode and scale factor of the Type I extreme value distribution of the process p(t) can
be estimated by the following procedure.
• Plot the natural logarithm of the rate of upcrossings against the level, p .
• Fit a straight line. From Equation (9.16), the slope is (−1/ a ), and the intercept ( p =0) is
(u T /a) .
• From these values, estimate u T and a, the mode and scale factor of the Type I extreme
value distribution of p .
9.4.5 Strength characteristics of glass in relation to wind loads
Direct wind loading is a major design consideration in the design of glass and its fixing in
tall buildings. However, the need to design for wind-generated flying debris (Section
1.5)—particularly roof gravel—in some cities also needs to be considered (Minor, 1994).
As has been discussed, wind pressures on the surfaces of buildings fluctuate greatly
with time, and it is known that the strength of glass is quite dependent on the duration of
the loading. The interaction of these two phenomena results in a complex design
problem.
The surfaces of glass panels are covered with flaws of various sizes and orientations.
When these are exposed to tensile stresses they grow at a rate dependent on the
magnitude of the stress field, as well as relative humidity and temperature. The result is a
strength reduction which is dependent on the magnitude and duration of the tensile stress.
Drawing on earlier studies of this phenomenon, known as 'static fatigue', Brown (1972)
proposed a formula for damage accumulation which has the form of Equation (9.17), at
constant humidity and temperature:
(9.17)
where D is the accumulated damage, s(t) the time varying stress, T the time over which
the glass is stressed and n a higher power (in the range of 12-20).
The expected damage in time, T, under a fluctuating wind pressure, p(t), in the vicinity
of a critical flaw can be written as Equation (9.18):
(9.18)
where K is a constant and m a different power, usually lower than n, but dependent on the
size and aspect ratio of the glass, which allows for the non-linear relationship between
load and stress for glass plates due to membrane stresses (Calderone and Melbourne,
1993). E{} is the expectation or averaging operation.