The Advisory Desk has received a number of queries asking for guidance on vi- bration of steel staircases. In fact, guidance is already given in several parts of SCI publication Design of floors for vibration: A new approach (P354). This AD collects that guidance and adds references to other sources of information that may be relevant when analysing the vibration behaviour of steel staircases. This AD also identifies some other design considerations that may be relevant.
Steel staircases are, by their nature, highly susceptible to vibration as they combine low levels of damping (typically ζ ≈ 0.5%), low mass and high levels of human-induced excitation. The general approach outlined in Chapter 6 of SCI P354 can be used to determine the dynamic behaviour of the staircase, but clearly the applied forces will be different for people travelling up and down staircases than for walking across floors, and acceptable levels of vibration also differ.
In P354, the response is determined from the modal properties of the staircase (frequencies, modal masses and mode shapes) and the frequency and ampli- tude of the applied vertical load. The peak amplitude of the load in each mode is generally given in terms of Fourier coefficients, αn, which represent the proportion of a person’s weight that is acting at each harmonic of the activity frequency. These Fourier coefficients are given in Human induced loading of flexible staircases (Bishop, Willford & Pumphrey, 1995 and Kerr & Bishop, 2001), and depend on the speed of ascent or descent. ISO 10137: 2007 (Bases for design of structures – Serviceability of buildings and walkways against vibrations) reproduces the worst case of these in Table A.4, and these are also given in Table 3.2 of P354 :
In P354 floors are categorised as either low-frequency or high-frequency, the latter case responding to impulsive excitations rather than responding reso- nantly. No specific analysis is given by Bishop et al for the impulsive loads that will be experienced by staircases with natural frequencies that exceed the up- per limits of the Fourier terms given in ISO 10137. Further Fourier coefficients (up to the 6th harmonic) are presented in the paper; these could be used to determine a more comprehensive response.
Bishop et al. also give guidance on the acceptability criteria for staircases, and their research indicates that for multi-person excitation, a maximum mul- tiplying factor of 64 applies. Typically this is achieved by designing staircases for a limiting multiplying factor of 32 for light use (such as offices) or 24 for heavy use (such as public buildings and stadia) under single person excitation using the Fourier terms given above. The limits for staircases are higher than for floors because the frequency of exposure to staircase vibration is gener- ally significantly lower than for a floor, and the audio and visual stimuli that ac- company the movement reduce the associated level of annoyance. For narrow staircases with no landings, it is unlikely that there will be stationary people on the stairs to receive the vibration, and as vibration is, in the main, a service- ability issue, in these cases the level or response is less critical.
Other design considerations
An additional design consideration for staircases is to ensure that the interac- tion between a staircase and the floors it links is such that excessive vibration does not carry onto the floor plate and therefore affect nearby rooms. This can generally be achieved by attaching the staircase in the vicinity of columns, and by avoiding features such as cantilever beams which are highly suscepti- ble to vibration issues.
Contact: Andy Smith
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