# Input requirements for P354 floor vibration

# General

The simplified method for the analysis of the vibration of floors given in the SCI Publication P354, on which the Tekla Structural Designer check is based, is only applicable to regular structures which, by and large, are created from rectilinear grids.

Of course the floor layouts of 'real' multi-storey buildings are rarely uniform and Tekla Structural Designer therefore provides you with the opportunity to select the more irregular floor areas to be assessed with grids that are other than rectilinear.

In so far as the selection of the beams to be used in the analysis is concerned, only beams with Non-Composite or Composite attributes are valid for selection and, within these confines, you are able to:

• select a single beam

• select a beam span as critical plus an adjoining span (in a two or three span configuration)

In all cases, and subject to the above restrictions, which beams from the selected area of floor are chosen is entirely at your discretion and under your judgment, but it is expected that the beams chosen will be those that are typical, common or the worst case. Irrespective, Tekla Structural Designer will take these beams as those that form the idealized floor layout. There is no validation on what the you select (although there is some validation on which beams are selectable i.e. beams which have no slab for part of their length, beams from angle sections, beams with no adjoining span when a 2-span configuration is chosen, and beams with no adjoining span at both ends when a 3-span configuration is chosen will not be selectable).

# Data Derived from Tekla Structural Designer (P354)

Note that, where appropriate, the derived data is for each design combination under SLS loads only.

** Unit mass**

The unit mass in kg/m^{2} is used to establish the 'participating mass' of the floor - that is the mass of floor and its permanent loading that has to be set in motion during vibration of the floor. It is taken as the slab self-weight (and to be accurate, the beam self-weight), other permanent 'Dead' loads and the proportion of the 'Imposed' loads that can be considered as permanent. The latter is usually taken as 10% and, whilst this is the default, the value is editable since imposed storage loads, for example, would warrant a higher value.

The unit mass is obtained by summing all the loads (or the appropriate percentage in the case of imposed loads) that act over or in the selected area. This includes any blanket, area, line and spot loads that are present within the selected area. The component of any of these load types that lie outside of the selected area are ignored. Nodal loads directly on columns are also ignored. The total load is then divided by the area selected.

The slab self-weight will usually be in the Slab Dry loadcase - note that in the case of composite slabs this includes the weight of decking. The beam self-weight is in a separate protected loadcase. For simplicity this component of the unit mass is ignored. This leads to a slight inaccuracy in the participating mass that is conservative (more mass is advantageous).

Note that the use of imposed load reductions has no effect on the floor vibration check.

**Slab data**

If there are more than one set of slab attributes in the selected area then you have to choose which of these it is appropriate to use. From the designated slab attributes the following information/data is obtained,

• the un-transformed inertia in c m 4 per metre width. For profiled decking this takes account of the concrete in the troughs and is independent of the direction of span of the decking.

• the short-term modular ratio for normal or lightweight concrete as appropriate.

If the designated slab attributes are for a 'generic' slab, then you are asked for the inertia and the dynamic modular ratio.

** Secondary beam data**

When these are non-composite beams, the inertia is obtained from the sections database. When these beams are of composite construction the inertia is the gross, uncracked composite inertia based on the dynamic modular ratio that is required. Steel joist inertias from the database are assumed to be 'gross' inertias of the chords and are editable. Following guidance contained in AISC Steel Design Guide 11
^{Ref. 3}, section 3.6, the gross steel joist inertia is factored by quantity C_{r} and displayed as the 'effective' inertia in the results viewer.

The span of the critical/base beam and the adjoining beams is required.

The deflection of the critical beam under the permanent loads is required. To calculate this value, the deflection under the Dead loads and the appropriate percentage of the Imposed load deflection is summed.

** Primary beam data**

The same data is required as that for the secondary beams.

** Floor plate data**

The dimensions of the floor plate in the idealized cases are defined in one direction by the number of secondary beam bays and in the orthogonal direction by the number of primary beam bays. In practice, given that the idealized case may not attain, the floorplate dimensions are derived from the slab items you select as participating in the mass.

# User Input Data (P354)

**Secondary Beam Spacing**

You must confirm the spacing of the secondary beams - an average value when the spacing is non-uniform.

**Proportion of Imposed Loads**

You are required to specify the proportion of the imposed loads that is to be used in the vibration analysis.

**Number of bays used to establish Modal mass**

You are required to specify the number of bays in the direction of the secondary beam span, n y, and the number of bays in the direction of the primary beam span, n x, that are to be used to establish the modal mass. The number of bays ranges from 1 to 4 for both directions.

** Mode Shape Factors**

You are required to specify the mode shape factors, μ_{e} and μ_{r}, which are to be used in the evaluation of the root mean square response acceleration. The default value is 1.0 for both variables.

** Damping ratio**

Floors do not vibrate as a free mass but have some damping i.e. dissipation of the energy in the system. Four values of damping ratio are recommended in P354 as a percentage,

- 0.5%, for fully welded steel structures, e.g. staircases,
- 1.1%, for completely bare floors or floors where only a small amount of furnishings are present,
- 3.0%, for normal, open-plan, well-furnished floors (the default),
- 4.5%, for a floor where the designer is confident that partitions will be appropriately located to interrupt the relevant mode(s) of vibration i.e. the partition lines are perpendicular to the main vibrating elements of the critical mode shape.

Since an even higher damping ratio might be justified for storage floors for example, a range of up to 10% is offered.

** Maximum corridor length**

This is used in the calculation of the "Resonance Build-up Factor" that makes an allowance for the time it takes for someone walking across the floor to begin to excite the floor - vibration is not instantaneous upon the first footfall. Hence, a "walking time" is required and is calculated from the "walking distance" (maximum corridor length) divided by the "walking velocity".

The designer will often not know, reliably, the maximum corridor length. The default is therefore taken as the longer of the floor plate dimensions.

If the designer does not wish to estimate the maximum corridor length or accept the default, then the Resonance Build-up Factor can be set to 1.0 by selecting Not known for the maximum corridor length. This sets the Resonance Build-up Factor to 1.0.

**Walking Pace**

The walking frequency (pace) must be selected in the range 1.7 to 2.4 Hz. This range is equivalent to a walking velocity of 2.5 to 5.7 mph (4.0 to 9.1 kph). Walking velocities less than and greater than this are achievable - slow walking 1.0 to 1.5 mph (1.6 to 2.4 kph) or running 6.0 to 12.0 mph (9.6 to 19.2 kph). However, the range of validity of the formula for calculating the walking velocity is given as that quoted. Thus any consequent value outside of the range 1.7 to 2.4 Hz is given a Warning that this is outside of the range given in Equation 16 of SCI P354. The default value is 1.8 Hz.

** Resonance build-up factor**

This is calculated data and has an upper bound
of 1.0. However, you are able to specify that the calculations should use 1.0
perhaps because there is insufficient information at the time to make a more
accurate and reliable estimate (see: **Maximum corridor length** above). Setting
the value to 1.0 is conservative.

** Required Response Factor**

You must enter the response factor that you expect the floor to achieve. This will be based on your engineering judgment and the advice given in P354. Tables 5.2 and 5.3 of that publication give a range of values with the common values being 2, 4, and 8.

** Vibration Dose Value (VDV)**

You have to specify the VDV value to be used if this analysis is performed (see: Vibration Dose Values).