A-9.23.4.2.(2) Numerical Method to Establish Vibration-Controlled Spans for Wood Frame Floors.

In addition to the normal strength and deflection analyses, the calculations on which the floor joist span tables are based include a method of ensuring that the spans are not so long that floor vibrations could lead to occupants perceiving the floors as too “bouncy” or “springy”. Limiting deflection under the normal uniformly distributed loads to 1/360 of the span does not provide this assurance. Normally, vibration analysis requires detailed dynamic modelling. However, the calculations for the span tables use the following simplified static analysis method of estimating vibration-acceptable spans:

• The span which will result in a 2 mm deflection of a single joist supporting a 1 kN concentrated midpoint load is calculated.
• This span is multiplied by a factor, K, to determine the “vibration-controlled” span for the entire floor system. If this span is less than the strength- or deflection-controlled span under uniformly distributed load, the vibration-controlled span becomes the maximum span.
• The K factor is determined from the following relationship: ln(K) = A – B • ln(S_i /S₁₈₄) + G where A, B = constants, the values of which are determined from Tables A-9.23.4.2.(2)-A or -B G = constant, the value of which is determined from Table A-9.23.4.2.(2)-C S_i = span which results in a 2 mm deflection of the joist in question under a 1 kN concentrated midpoint load S₁₈₄ = span which results in a 2 mm deflection of a 38 x 184 mm joist of same species and grade as the joist in question under a 1 kN concentrated midpoint load.

For a given joist species and grade, the value of K shall not be greater than K3, the value which results in a vibration-controlled span of exactly 3 m. This means that for vibration-controlled spans 3 m or less, K always equals K3, and for vibration-controlled spans greater than 3 m, K is as calculated.

Note that, for a sawn lumber joist, the ratio S_i /S₁₈₄ is equivalent to its depth (mm) divided by 184.

Due to rounding differences, the method, as presented here, might produce results slightly different from those produced by the computer program used to generate the span tables.

Constants A and B for Calculating Vibration-Controlled Floor Joist Spans - General Cases

Notes to Table A-9.23.4.2.(2)-A:

(1) Gypsum board attached directly to joists can be considered equivalent to strapping.

Constants A and B for Calculating Vibration-Controlled Floor Joist Spans - Special Cases

Notes to Table A-9.23.4.2.(2)-B:

(1) Wood furring means 19 x 89 mm boards not more than 600 mm o.c., or 19 x 64 mm boards not more than 300 mm o.c. For all other cases, see Table A-9.23.4.2.(2)-A.

(2) 30 mm to 51 mm normal weight concrete (not less than 20 MPa) placed directly on the subflooring.

Constant G for Calculating Vibration-Controlled Floor Joist Spans

Notes to Table A-9.23.4.2.(2)-C:

(1) Common wire nails, spiral nails or wood screws can be considered equivalent for this purpose.

(2) Subfloor field-glued to floor joists with elastomeric adhesive complying with standard CAN/CGSB-71.26-M, “Adhesives for Field-Gluing Plywood to Lumber Framing for Floor Systems”.

Additional background information on this method can be found in the following publications:

• Onysko, D.M. Serviceability Criteria for Residential Floors Based on a Field Study of Consumer Response.

Project 03-50-10-008. Forintek Canada Corp., Ottawa, Canada 1985.

• Onysko, D.M. Performance Criteria for Residential Floors Based on Consumer Responses. 1988 International Conference on Timber Engineering, Seattle, September 19-22, Forest Products Research Society, Vol.1, 1988, pp. 736-745.
• Onysko, D.M. Performance and Acceptability of Wood Floors - Forintek Studies. Proceedings of Symposium/Workshop on Serviceability of Buildings, Ottawa, May 16-18, National Research Council of Canada, Ottawa, 1988.