Civil Engineering Reference
In-Depth Information
Figure 5.2(a) shows the characteristics of the time histories of an along-wind (drag)
force; the structural response for a structure with a
high
fundamental natural frequency is
shown in Figure 5.2(b), and the response with a
low
natural frequency in Figure 5.2(c). In
the former case, the resonant, or vibratory component, clearly plays a minor role in the
response, which generally follows closely the time variation of the exciting forces.
Figure 5.1
Response spectral density for a
structure with significant resonant
contributions.
However, in the latter case, the resonant response in the fundamental mode of vibration is
important, although response in higher modes than the first can usually be neglected.
In fact, the majority of structures fall into the category of Figure 5.2(b), and will
not
experience significant resonant dynamic response. A well-known rule of thumb is that the
lowest natural frequency should be below 1 Hz for the resonant response to be
significant. However, the amount of resonant response also depends on the damping,
aerodynamic or structural, present. For example, high-voltage transmission lines usually
have fundamental sway frequencies which are well below 1 Hz; however, the
aerodynamic
damping is very high—typically around 25% of critical—so that the
resonant response is largely damped out. Lattice towers, because of their low mass, also
have high aerodynamic damping ratios. Slip-jointed steel lighting poles have high
structural
damping due to friction at the joints—this energy-absorbing mechanism will
limit the resonant response to wind.
Resonant response, when it does occur, may occasionally produce complex
interactions, in which the movement of the structure itself results in additional aeroelastic
forces being produced (Section 5.5). In some extreme cases, for example the Tacoma
Narrows Bridge failure of 1940 (see Chapter 1), catastrophic failure has resulted. These
are exceptional cases, which of course must be avoided, but in the majority of structures
with significant resonant dynamic response, the dynamic component is superimposed on
a significant or dominant mean and background fluctuating response.
