Footfall Vibration Analysis

Theory & Case Study Review27/11/2016

Konstantinos VazourasCEng | PhD

ScopeFootfall vibration analysis should be of a concern, but Why? Where? When? Design codes – BS and IBC recommend that floor vibrations be checked (SCI P354). Commercial – on lively floors, computer users complain because their screens wobble,

making it difficult to work. Bridges – need to comply with bridge codes. Laboratories – equipment, such as optical and electron microscopes and laser

research systems, are very sensitive to vibrations. Floors for such equipment floors must comply with the BBN or ASHRAE standards.

Hospitals – operating theatres require the utmost stability for delicate operations, and the latest scanning technologies require even lower vibration levels.

Airports – Airport owners are concerned that floor vibrations in heavily trafficked waiting areas can upset seated travellers.

Retail – many major retailers require assurance that vibrations on display floors, such as a display of glasses on glass shelves, will not be excessive. If the floor is too lively, then the glasses will rattle

The vibration problem For many years, serviceability requirements have been a part of structural design (i.e.

deflection limits to prevent finishes from cracking and building occupants noticing floors sagging).

This SLS approach proved inadequate for lighter structures, such as composite beam or post-tensioned slab floors, and more open-plan areas.

The proposed remedy to this problem was to restrict the natural frequency of the floor beams, since it was thought that if this were kept above walking pace, then resonance should not occur. For simple floor layouts, the fact that this frequency could be found by a simple hand calculation encouraged this approach.

However, a number of problems emerged with this solution. The first was that floors can be excited into resonance at higher harmonics of a pedestrian’s footstep frequency.

The second was that while shorter spans had higher natural frequencies, they also had lower mass, making them easier to excite. This, combined with the modern trend for irregular floor bays, open plan offices and electronic storage rather than filing cabinets (reducing the mass and damping of floors) made the vibration problem more difficult to assess and solve.

Footfall Theory Footfall examines the effect of the walking loading, which induces

vibrations on a structure, by means of a harmonic force in a certain frequency interval.

Usually linear elastic analysis is only concerned (why?) The objective of the analysis is to evaluate a vertical response (e.g. Rf ,

acceleration, velocity, displacement) for the nodes of the structure, caused by the harmonic force applied to the nodes.

Reminder!: The harmonic force varies with time and also considers damping (ζ).

Footfall TheoryTwo approaches to analyse the footfall effects: Self Excitation: Analyse the response in the same node, where the force is applied Full Excitation: Analyse the response in ANY node to the effect of the force applied to

another node. (Time consuming!!)

Both methods entail the division in 20 intervals considering additional points for the frequency of eigenvectors.

Two types of analysis: Resonant Response Analysis (if mode 1 to mode 4 < 8-10Hz) Transient Response Analysis (if mode 1 to mode 4 >8-10Hz)

Footfall Theory Footfall harmonic Force Equation:

(continuous excitation)

Footfall Theory Activity

Frequencies:

Applied loading density:

Recommended factors for single person excitation:

Footfall TheoryBasic Analysis Steps: Assess the natural frequency of the floor system; Determine the modal mass during vibration; Determine the damping factor of the flooring system; Calculate the critical Rms acceleration & the response factor; Compare the response factor with the acceptance criteria;

Handy Tips: As a rule of thumb we should have fn > 3Hz If hand calculations are not fulfilled by the Response factor

criteria, use FEA or more sophisticated tools.

Case Study – Comflor60 Slab Simplified Analysis Slab

Model(RSA 2015)

Castellated Beams over 17.5m span

FE model 0.25m coons 300mm RC wall

Analysis Properties:Slab type

Thickness: 130mm Concrete C30Metal Sheeting

Comflor 60

Span 3.50m (y-y)

LoadingDL: 5.5 kN/m2 (excl steelwork)LL: 5 kN/m2

Mass: G+0.3QDumping 3%

Case Study Existing Slab Results

Problematic arrangement The slab should be amended

Note: Red Regions are where Rf>4 (i.e. exceeds limit for shopping malls)

Case StudyPotential Solution A

Flat Slab (no metal deck) 200mm

Decent solution (Rf<4) Increase SW

deflections

Case Study Potential Solution B

Amended Slab Results – Add secondary beams – UB203x152x23

Decrease slab span Similar solution.

Case StudyPotential Solution C Reduce edge span Induce transverse 1.75m wall at edges

(symmetry) Not a solution

Case StudyPotential Solution D

Increase Slab thickness at mid-span to 230mm, forming a ridge

Still trapezoidal sheeting Comflor60 to be used

Decent solution.

Case Study Summarising the Footfall Analysis Results:

Examined Solutions

Rf (max)

A) Flat Slab 4.69B) Add Secondary Beam

7.26

C) Add Walls 8.65D) Inclined Comflor Slab

6.91 A combination of the above solutions may be a possible final application for the slab under investigation.

References SCI_P354 : 2009 – Design of Floors for Vibration Debney P., Willford M.; “Footfall Vibration and Finite Element

Analysis”, Sound & Vibration, Nov 2009 https://knowledge.autodesk.com/support/robot-structural-analysis-pro

ducts/learn-explore/caas/CloudHelp/cloudhelp/2015/ENU/Robot/files/GUID-3AD2F89E-BA01-415F-80C5-C83E3902A470-htm.html