TIMBERTECH BUILDINGS – TECNICAL REPORT – FLOOR VIBRATION CHECKS

TECHNICAL DESIGN CALCULATION REPORT Design Of Timber Structures

Project: Timber floor vibration checks with TimberTech Buildings software

Location: Villazzano

Address: Via della Villa 22/A

City: Trento

State: Italy

Client: Timber Tech srl

Building company: Timber Tech srl

Structural designer: Mauro Andreolli

Date: March 20, 2017

Floors vibrations (SLS) Vibrations on floors are carried out according to § 7.3 of EN 1995-1-1. In case of floors with a fundamental frequency greater or equal than 8 Hz, it will be evaluated the maximum value of vertical deflection induced by a vertical, static and concentrated force F acting on every point of the slab and the unit impulse velocity induced by an impulsive load acting in the point of the floor that provides the maximum response. In case of floors with a fundamental frequency lower than 8 Hz, it will be evaluated the maximum value of vertical acceleration induced by a dynamic load.

Stiffness of elements

Stiffness values for floor elements are taken as: ,

,

,

,

,

,

,

where: ,

is the stiffness of principal elements “Layer 0”, along the span

,

is the stiffness of principal elements, perpendicular to the span

,

is the stiffness of secondary element “Layer 1”, perpendicular to the span

,

is the stiffness of secondary element “Layer 2”, perpendicular to the span

The following table shows, for every single floor, the stiffness used in the evaluation of vibration criterion.

Floor name Floor 1 Floor 2

(EJ)0,l [Nm2/m] 3.68E6 3.68E6

(EJ)0,b [Nm2/m] 0.00E0 0.00E0

(EJ)1,b [Nm2/m] 3.66E3 3.66E3

(EJ)2,b [Nm2/m] 5.72E5 5.72E5

(EJ)TOT,l [Nm2/m] 3.68E6 3.68E6

(EJ)TOT,b [Nm2/m] 5.75E5 5.75E5

Minimum frequency criterion

The fundamental frequency of floors should satisfy the following expression: ,

where: www.timbertech.it

is the fundamental frequency of the floor ,

is the minimum frequency value, which depends on the chosen level of demand.

The minimum value

,

is taken as in the following table.

f1,min

High demand

Normal demand

4.5 Hz

4.5 Hz

It is considered a permanent combination for loads in the calculation of the mass of the floor.

The value of effective width deflection, is taken as:

, wich consider the effect of the transverse stiffness on the vertical

1,1

,

∙

,

where: is the length of the grater span is the width of the floor is taken at least equal to the spacing between the joists, in case of joists floors, or at least equal to the width of the panel, in case of solid wood floors.

The following tables show, for every single floor (relative to the element in which the minimum frequency criterion is the most severe), the representation of the fundamental mode of vibration, values, modal mass values M*, fundamental frequency values and relative checks.

Floor name

f1 [Hz]

Floor 1

26.22

Fundamental vibration mode

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Floor 2

5.52

Floor name

Demand required

beff [m]

M* [kg]

f1 [Hz]

f1,min [Hz]

Check

Floor 1

Normal demand

1.57

507

26.22

4.5

17%

Floor 2

Normal demand

3.36

2526

5.52

4.5

81%

Stiffness criterion – Static deflection under a concentrated load

Stiffness criterion checks are conducted evaluating the maximum instant deflection under a static concentrated force. This deflection should satisfy the following expression: ,

where: is the vertical deflection caused by a static vertical force assumed equal to 1 kN ,

is the limit value for deflection, which depends on the chosen level of demand

Limit values

,

are taken as in the following table.

Beam on two supports

Cantilevering beams

High demand

Normal demand

0.5 mm

1 mm

1 mm

2 mm

The following tables show, for every single floor (relative to the element in which the stiffness values and relative checks. criterion is the most severe), the deformation under static force,

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Floor name

W1kN [mm]

Floor 1

0.07

Floor 2

0.34

Static deformation

Floor name

Demand required

Most restrictive check

W1kN [mm]

W1kN.lim [mm/kN]

Check

Floor 1

Normal demand

Internal span

0.07

1

7%

Floor 2

Normal demand

Internal span

0.34

1

34%

Acceleration criterion (Floors with fundamental frequency lower than 8 Hz)

Acceleration criterion checks are conducted evaluating the maximum acceleration value caused by periodic actions: 0,4

∙ ∗

∙

1 1

2

where: is the weight force of a person, equal to 700 N is the fundamental frequency of the floor is the forcing frequency is the Fourier coefficient in dependence of the fundamental frequency of the floor is the modal damping ratio www.timbertech.it

∗

is the modal mass of the floor is the limit value for acceleration, which depends on the chosen level of demand

The following table shows the parameters needed in the definition of maximum acceleration value.

Fundamental frequency 4,5 5,1

[Hz]

Fourier coefficient

Forcing frequency

5,1

0,2

f

6,9

0,06

f

6,9

0,06

[Hz]

f f 6,9

, evaluated at the point of application of the force , it is Note the maximum acceleration calculated the acceleration a in the generic point of the element in function of the modal shape, assumed as shown in the following table, in function of the comparing this value with the value required level of requirement.

High demand

Normal demand

Beam on two supports

0.05 m/s2

0.15 m/s2

Cantilevering beams

0.1 m/s2

0.2 m/s2

The following table shows, for every single floor (relative to the element in which the acceleration criterion is the most severe), the parameters needed in the definition of maximum acceleration value and relative checks.

Floor name

Demand required

Floor 1 Floor 2

Normal demand Normal demand

f1 [Hz] N/D 5.52

[-] N/D 0.06

M* [kg] N/D 2525.89

Most restrictive check

ξ [-] 0.03 0.03

N/D Internal span

a [m/s2] N/D 0.11

alim [m/s2] N/D 0.15

Check Not applicable 74%

Velocity response criterion (Floors with fundamental frequency higher than 8 Hz)

Unit impulse velocity response criterion checks are conducted evaluating vibration velocity response of the floor under a unit impulse equal to 1 Ns, limiting the upper frequency components to a value of 40 Hz. The vibration velocity response should satisfy the following expression:

where: is a parameter wich depends on the chosen level of demand is the fundamental frequency of the floor is the modal damping ratio is the limit value for the unit impulse velocity The unit impulse velocity response , is taken as: 4 ∙ 0,4

0,6 200

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where: is the number of first-order modes with natural frequencies up to 40 Hz is the mass of the floor is the length of the greater span The value of

is taken as: 40

Limit values

,

1 ∙

,

∙

,

are taken as in the following table.

b

High demand

Normal demand

150

120

The following table shows, for every single floor (relative to the element in which the unit impulse velocity response criterion is the most severe), the parameters needed in the definition of maximum unit impulse velocity response value and relative checks.

Floor name Floor 1 Floor 2

Demand required Normal demand Normal demand

f1 [Hz] 26.22 N/D

ξ [-] 0.03 0.03

n40 [-] 1.40 N/D

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v [m/(Ns2)] 3.01E-3 N/D

vlim [m/(Ns2)] 3.60E-1 N/D

Check 1% Not applicable