## Info

Notes relating to (EI)b

(1) The flexural stiffness is calculated as (EI)b using the mean value of the modulus of elasticity of the floor decking and discontinuities at the ends of floor boards or at the edges of floor panels may be ignored.

(2) Where plasterboard ceilings are fixed directly to the soffit of the floor joists, the flexural rigidity of the plasterboard can be added. It is to be assumed that Epiasterboard = 2000 N/mm2.

(3) Where the floor comprises open web joists fitted with a continuous transverse member secured to all joists within 0.1£ from mid-span, (EI)b may be increased by adding the bending stiffness of the transverse member (in N mm2) divided by the span I (in metres).

(b) High-frequency effects (heel impact effect).

Under the action of a unit impulse force of 1.0 N s at the centre of the floor simulating heel contact, the maximum initial value of the vertical floor vibration velocity v (in m/s) must comply with equation (7.4) in EC5:

v < b(/1Z-1) m/(Ns2) (EC5, equation (7.4)) (4.51)

Where:

• v is the unit impulse velocity response in m/(N s2) units; i.e. the maximum value of the floor vibration velocity (in m/s) in a vertical direction caused by an impulse of 1.0 N s, simulating the heel impact condition applied at the point on the floor giving maximum displacement.

• b is a constant for the control of unit impulse response and is related to the floor deflection a as shown in EC5, Figure 7.2. It can be expressed in equation format as follows, b = 150 - (30 (a - 0.5) /0.5) = 180 - 60a when a < 1 mm (4.52) b = 120 - (40 (a - 1)) = 160 - 40a when a > 1 mm (4.53)

where a is in mm and is obtained from equation (4.49).

• /1 is the natural frequency of the floor obtained from equation (4.46) (in Hz).

• Z is the modal damping ratio of the floor and for typical UK floors NA.2.6 of the UKNA to EC5 states that a value of 0.02 is appropriate.

To derive the actual unit impulse velocity response of the structure, the EC5 requirement is as follows:

For a rectangular floor with overall dimensions bxl and simply supported on four sides, the approximate value for v can be obtained from equation (7.6) in EC5 as follows,

where b is the floor width (in metres), I is the design span of the floor (in metres), m is as defined in equation (4.46) (in kg/m2), and n4o is the number of first-order vibration modes with natural frequencies up to 40 Hz.

The value of n4° can be calculated from the approximate expression given in equation (7.7) of EC5, where (EI)b is as defined in equation (4.50), but the units to be used for this equation are N m2/m, and (EI)lis the equivalent plate bending stiffness of the floor in the direction of the span of the joists as defined in equation (4.46) (in N m2/m) and (EI)b < (EI)l.

It is to be noted that when using Z = 0.02 for the modal damping ratio, the UKNA to EC5 states that the unit impulse velocity will not normally govern the size of the joists used in residential timber floors.

See Example 4.8.4.

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