Civil Engineering Reference
In-Depth Information
Load effects (i.e. member forces and internal stresses) resulting from overall building
response in two orthogonal directions (
x
and
y
) can very accurately be combined by the
following formula:
(9.24)
where is total combined maximum peak load effect (e.g. the axial load in a column);
the load effect derived from the mean response in the
x
-direction (usually derived from
the mean base bending moment in that direction); the load effect derived from the
mean response in the
y
-direction; the peak load effect derived from the response in the
x
-direction and the peak load effect derived from the response in the
y
-direction.
Equation (9.24) is quite an accurate one, as it is based on the combination of
uncorrelated Gaussian random processes, for which it is exact. Most responses dominated
by resonant contributions to wind have been found to be very close to Gaussian and if the
two orthogonal sway frequencies are well separated, the dynamic responses will be
poorly correlated.
As an alternative approximation, the following load cases can be studied:
(a) [Mean
x
load+0.75 (peak − mean)
x
] with [mean
y
load+0.75 (peak − mean)
y
];
(b) [Mean
x
load+(peak − mean)
x
] with [mean
y
load];
(c) [Mean
x
load] with [mean
y
load+(peak − mean)
y
].
The case (a) corresponds to the following approximation to Equation (9.24) for peak load
effect:
(9.25)
Equation (9.25) is a good approximation to Equation (9.24) for the range:
The other two cases (b) and (c) are intended to cover the cases outside this range, i.e.
when
is much larger than
and vice versa.
9.7
Torsional loading and response
The significance of torsional components in the dynamic response of tall buildings was
highlighted by the Commerce Court Study of the 1970s (Section 9.2), when a building of
a uniform rectangular cross-section experienced significant and measurable dynamic
twist due to an eccentricity between the elastic and mass centres. Such a possibility had
been overlooked in the original wind-tunnel testing. Now, when considering accelerations
at the top of tall building, the possibility of torsional motions increasing the perceptible
motions at the periphery of the cross-section may need to be considered.
