Chapter 2.12 Dynamics

Figure 2.12.2 First to Third Modes Natural Frequency

Vibration is a subject in the text books and on any structural engineering course which is too often off putting to all but the most mathematically able. It is argued that engineers should have at least a rudimentary working knowledge of the principles; particularly with a modern tendency for clients and architects to demand long span lightweight structures – which are especially prone to dynamic excitation.

The first part recaps on the main elements of dynamics followed by simple rules for finding fundamental natural frequencies.

A review of simplistic methods to assess peak structural response, together with examples which demonstrate how to identify areas of concern, is followed by a short summary of some response criteria. In conclusion aspects of building sway (dynamic response to wind loading and earthquakes) are discussed.

figure 2.12.10 Response Chart
A general practitioner, in other words, a structural engineer working on structures such as buildings or bridges, should have a basic understanding of vibration. It is unfortunate that engineers tend to fear this aspect of design by the complexity of the subject. Engineers are practical people who want to gain an intuitive understanding of the structure in hand.
Stadium Tier Response (B) (continued…)
The crowd weight is 1kN/m2 (damping 3%) and is jumping at a frequency of 2.5 Hz. The crowd is jumping to a rock concert.

Natural frequency (2.5) equals forcing frequency (2.5)…

The 1st harmonic response (assuming resonance) is: 1.3xαxwp/(2xρxW) a/g = 1.3×1.5×1 /(2×0.03×8) = 4.1g

(ie an acceleration of 410%g)

Resonance and the extreme motion causes a significant response (4xg) which may also have strength implications).

The Institution of Structural Engineers published recommendations (IStructE 2001, reference 6.) which noted that for spectator stands hosting sports events vertical frequencies greater than 3.5Hz may generally be demonstrated to perform satisfactorily. Whereas stadium structures hosting pop concerts will generally behave within acceptable limits with vertical natural frequencies greater than 6Hz minimum