Human-induced vibration in structural engineering
Static and dynamic structural analyses are performed to check if the structure can meet all relevant strength, stability and serviceability requirements set out in applicable design codes. With respect to the serviceability of the structure, the first thing that comes to mind is certainly the structure’s vertical and horizontal deflection. This blog, however, will focus on one aspect of serviceability that might not be the first thing that pops to mind, yet is pivotal for structural design – vibration limits.
Sources of vibration and structural impacts of vibration
The sources of vibration are multiple – they can be induced by human activity (walking, running, rhythmic activities such as dancing and jumping), machine operation, traffic or cranes, hoists and other equipment moving along the structure, wind, etc.
The impacts of vibration on the structure can also be diverse. The effect on people, namely, the sense of discomfort and annoyance, is a consequence of vibration that requires verification when serviceability limit states are analysed. The impacts of vibration on strength and stability are another consequence that needs to be considered as well. Specifically, if the dynamic excitation from vibration is greater than the static or quasistatic actions acting on the structure, adequate ultimate limit state checks need to be performed. Last, but in no way the least, are the impacts of vibration fatigue, where the fatigue is reflected in the formation and propagation of cracks under cyclic loading. Slender structures such as chimneys, masts and towers are a prime example of this vibration-induced impact, where vibration occurring due to wind may cause cyclic loading on the structure’s connections.
Structures susceptible to human-induced vibration
As suggested in the title, this blog looks at vibration caused by human activity and how it affects structures and people.
Typical examples of structures for which the impacts of vibration need to be eliminated are footbridges, floor structures in building construction, staircase towers and various industrial platforms where human presence can be expected. Obviously, these structures are primarily designed to enable pedestrian activity and traffic so eliminating potential discomfort caused by vibrating structures is crucial in their design. In addition to the discomfort to the occupants, vibration may have a detrimental effect on the functioning of sensitive equipment often supported by process platforms, or on motion-sensitive activities such as surgery, in cases where operating rooms are located on floor structures in hospital buildings. All of the above clearly suggests that, in such cases, human-induced vibration essentially represents a serviceability issue.
Dynamic response of the structure and vibration control
The structure’s dynamic response depends on dynamic loading conditions and the dynamic properties of the structure itself. The structure’s dynamic properties that are relevant for the assessment of its response are the natural frequency of oscillation, modal mass, and damping. The structure’s frequency and modal mass can be manually calculated using associated formulas or by applying a modal analysis in FEA. Damping represents the dissipation of energy of an oscillating system and can be in the function of the structure’s geometry, static system, material used, etc. The primary and prevailing method of vibration control is to change (increase) the structure’s frequency (so-called frequency tuning) achieved by improving the structure’s rigidity. Various standards and guidelines (EN 1990, SETRA, HiVoSS, AISC Design Guide 11, to name a few) define frequency limits based on the structure’s type and design intent, so vertical oscillation frequencies for pedestrian structures (such as footbridges) can be prescribed at above 5.0-6.0 Hz, depending on the standard, whereas vertical frequencies higher than 9.0 Hz are recommended for floor structures in school, business and sports facilities.
However, if the impacts of vibration cannot be eliminated by raising the natural frequency of the structure, forced vibrations need to be calculated and their impact on the structure analysed. The parameters and limits to be checked by this analysis are also given in some of the above standards and guidelines.
Finally, if this design method cannot be applied or fails to provide satisfactory results, special vibration mitigation measures must be applied, such as installing special devices – vibration absorbers, for instance.
Our design case studies
Our past design projects include a number of structures which needed to be checked for susceptibility to vibration.
A pedestrian bridge project in the UK is one of the projects where vibrational impacts needed to be considered. As suggested above, with this type of structures, pedestrian can experience discomfort due to vibration caused by footfall in the events where significant vibration resonance occurs when the pedestrian frequency and natural frequency of the bridge coincide. A simply-supported truss was proposed as the initial solution for the bridge’s structural system. This solution arose as the first choice in the project’s conceptual phase since the purpose of the truss would be to serve as a railing apart from the structure’s main girder, given that the pedestrian walkway is set at the height of the truss’s lower chord. The addition of the truss would significantly improve the stiffness of the structure. However, the client wanted faster fabrication of the elements, which in this case meant that the truss was not suitable. We opted for a beam girder instead, which increased the mass of the bridge itself. The initial static analysis showed that the bridge’s deflection was the governing factor in girder design, so the girder section was selected accordingly. The modal analysis further checked the natural frequencies of the bridge oscillation. It found that the first vertical mode of oscillation had a frequency of around 7.5 Hz, so the bridge met the vibration criteria recommended by corresponding standards.
This type of check has also been applied on the tall and slender industrial platforms we have designed. A prime example of that is a 1.0m wide walkway supported by a single row of 5.3m high columns, designed for automobile industry purposes in the US. In addition to a vertical vibration check, this walkway also required lateral oscillations to be checked due to low lateral stiffness. In this case, the vibration limit was relevant for girder design, so the structural solution and sections were selected based on this criterion.
Another example of a platform we have checked for dynamic structural behaviour is available in our Projects section. Those are access platforms for aircraft maintenance and inspection (docks). One of these docks is around 13.8m high and given that it is lightly loaded (imposed load comes solely from a few concentrated forces set in the least favourable position based on client information on maximum allowable number of people simultaneously present on the dock), smaller sections were selected at the static analysis and initial design of steel sections (smaller in relation to the sections that could be used for a medium-load platform of the same height), which in turn reduced the structure’s mass. To top it all, the dock also had overhangs of around 1.5 meters in length. You can probably imagine the level of discomfort one would feel walking along the dock almost fourteen meters above ground level with the structure beneath shaking. This is why we checked it for potential impacts of vibration and adopted structural measures that prevent the occurrence of vibration resonance on the dock.
We have also designed a number of staircases, both industrial ones and those in residential and office buildings, where this type of dynamic analysis is now part of the standard and mandatory serviceability checks for stairs.
Even though there are papers suggesting that process platforms and staircases need not be checked for the impacts of human-induced vibration (this, of course, does not apply to platforms supporting various sensitive equipment) since the discomfort caused by vibration is regarded as an occupational risk of the jobs performed on such structures, our opinion (and the author’s personal opinion) is that the structure’s dynamic behaviour should certainly be checked for these conditions. With fast checks (either by FEA or even manual calculation) and perhaps minor structural modifications, which does not require too much time or other resources, we can achieve more acceptable behaviours of the structure at human excitation and thus avoid potential problems and subsequent changes in the design.
We have listed here some checks of the structure’s dynamic behaviour by comparing the natural frequencies obtained by the modal analysis with the limits prescribed by applicable standards, guidelines, and various papers. One way to prevent the occurrence of this phenomenon is to change the structural system, increase the cross-section and various other reinforcements of the structure with the aim of improving structural rigidity, which in turn increases the natural frequency. However, there are cases where none of the above is on the table. A good illustration of this is an analysis of a footbridge with strict size and appearance requirements that must be complied with because of the structure’s architecture and the bridge aesthetic that can be crucial and cannot be deviated from. In this case a direct dynamic analysis (time history analysis) is needed to model pedestrian motion in terms of the speed and intensity. This will provide precise data on how the structure behaves over time – deflections, velocities, and accelerations at specific nodes of the structure at specific intervals. In this way, by checking the above parameters against the standards, we can determine if the structure meets all serviceability requirements.
The choice of design method, of course, is at the discretion of the structural engineer. In some cases, such as in the described pedestrian bridge example where other factors dictate the very geometry of the structure, the direct dynamic analysis is inevitable. Another possible scenario is that the prevention through frequency increase is not economically viable. Conversely, there are cases where we have the freedom to select which verification method to use. The time history analysis requires advanced engineering knowledge and a time-consuming design analysis, which very often is a vital factor for decision-makers (in most cases it certainly is more cost-efficient to increase the cross-section of the industrial staircase girder than to perform an advanced dynamic analysis). Or your software package might not comprise this feature (various advanced software options often require payment). In this case, using the modal analysis to determine the structure’s dynamic properties and solving this issue by adopting different structural solutions is completely justifiable.
Finally, if the advanced dynamic analysis proves it necessary, specific measures are applied to reduce the impact of vibration. As described above, such measures can comprise the application of vibration absorbers or dampers.
