A presentation about the scope of footfall analysis is shown under SCI P354. In tandem with the theory, a case study example of a very thin slab (i.e. Comflor 60 130mm) is also examined on Robot Structural Analysis 2015 under four (4) different structural arrangements. Through the FE approach, the Resonant Response Factors are presented for each case, providing a good reflection of the solution and the mitigation measured that should be sought for slab vibrations under walking load.

1. Footfall Vibration Analysis
Theory & Case Study Review
27/11/2016
Konstantinos Vazouras
CEng | PhD

2. Scope
Footfall 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

3. 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.

4. 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).

5. Footfall Theory
Two 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)

6. Footfall Theory
 Footfall harmonic Force Equation:
(continuous excitation)

7. Footfall Theory
 Activity Frequencies:
 Applied loading density:
 Recommended factors for single person excitation:

8. Footfall Theory
Basic 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.

9. 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 C30
Metal Sheeting Comflor 60
Span 3.50m (y-y)
Loading
DL: 5.5 kN/m2 (excl steelwork)
LL: 5 kN/m2
Mass: G+0.3Q
Dumping 3%

10. 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)

11. Case Study
Potential Solution A
 Flat Slab (no metal deck)
200mm
 Decent solution (Rf<4)
 Increase SW deflections

12. Case Study
Potential Solution B
 Amended Slab Results – Add secondary
beams – UB203x152x23
 Decrease slab span
 Similar solution.

13. Case Study
Potential Solution C
 Reduce edge span
 Induce transverse 1.75m wall at edges
(symmetry)
 Not a solution

14. Case Study
Potential Solution D
 Increase Slab thickness at mid-span
to 230mm, forming a ridge
 Still trapezoidal sheeting Comflor60
to be used
 Decent solution.

15. Case Study
 Summarising the Footfall Analysis Results:
Examined Solutions Rf (max)
A) Flat Slab 4.69
B) Add Secondary Beam 7.26
C) Add Walls 8.65
D) Inclined Comflor Slab 6.91
 A combination of the above solutions may be a possible final application
for the slab under investigation.

16. 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-
products/learn-
explore/caas/CloudHelp/cloudhelp/2015/ENU/Robot/files/GUID-3AD2F89E-
BA01-415F-80C5-C83E3902A470-htm.html