Long Carbon Europe Sections and Merchant Bars. Design Guide for Floor Vibrations

Transcription

1 Long Carbon Europe Sections and Merchant Bars Design Guide for Foor Vibrations

2 Caude Vasconi Architecte - Chambre de Commerce de Luxembourg This design guide presents a method for assessing foor vibrations guaranteeing the comfort of occupants. This document is based on recent research deveopments (RFCS-Project Vibration of foors ). Guidance for the structura integrity, given in this document, is based on common approaches.

3 Contents 1. Introduction 3. Definitions 7 3. Determination of Foor Characteristics Cassification of Vibrations Design Procedure and Diagrams 19 Annex A Formuas for Manua Cacuation 31 Annex B Exampes 43 Technica assistance & Finishing 5 References 5 Your partners 53 1

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5 1. Introduction 3

6 1. Introduction Foor structures are designed for utimate imit state and serviceabiity imit state criteria: Utimate imit states are those reated to strength and stabiity; Serviceabiity imit states are mainy reated to vibrations and hence are governed by stiffness, masses, damping and the excitation mechanisms. For sender foor structures, as made in stee or composite construction, serviceabiity criteria govern the design. Guidance is given for: Specification of toerabe vibration by the introduction of acceptance casses (Chapter 4) and Prediction of foor response due to human induced vibration with respect to the intended use of the buiding (Chapter 5). The design guide comprehends simpe methods, design toos and recommendations for the acceptance of vibration of foors which are caused by peope during norma use. The given design methods focus on the prediction of vibration. Measurements performed after erection may ead to differences to the predicted vaues so that one cannot caim on the predicted resut. The design and assessment methods for foor vibrations are reated to human induced resonant vibrations, mainy caused by waking under norma conditions. Machine induced vibrations or vibrations due to traffic etc. are not covered by this design guide. The design guide shoud not be appied to pedestrian bridges or other structures, which do not have a structura characteristic or a characteristic of use comparabe to foors in buidings. An overview of the genera design procedure presented in Chapter 5 is given in Figure 1. For the prediction of vibration, severa dynamic foor characteristics need to be determined. These characteristics and simpified methods for their determination are briefy described. Design exampes are given in Annex B of this design guide.

7 1. Introduction Figure 1 Design procedure (see Chapter 5 ) Determine dynamic foor characteristics: - Natura Frequency - Moda Mass - Damping (Chapter 3; Annex A) Read off OS-RMS 90 Vaue (Chapter 5) Determine Acceptance Cass (Chapter 4) 5

8 ArceorMitta Photo Library

9 . Definitions 7

10 . Definitions The definitions given here are consistent with the appication of this design guide. Damping D Damping is the energy dissipation of a vibrating system. The tota damping consists of Materia and structura damping, Damping by furniture and finishing (e.g. fase foor), Spread of energy throughout the whoe structure. Moda mass M mod generaised mass Each mode of a system with severa degrees of freedom can be represented by a system with a singe degree of freedom: f 1 π K M mod mod where f is the natura frequency of the considered mode, K mod is the moda stiffness, M mod is the moda mass. Thus the moda mass can be interpreted to be the mass activated in a specific mode shape. The determination of the moda mass is described in Chapter 3.

11 . Definitions Natura Frequency f Eigenfrequency Every structure has its specific dynamic behaviour with regard to shape and duration T[s] of a singe osciation. The frequency f is the reciproca of the osciation time T(f 1/T). The natura frequency is the frequency of a free osciation without continuousy being driven by an exciter. Each structure has as many natura frequencies and associated mode shapes as degrees of freedom. They are commony sorted by the amount of energy that is activated by the osciation. Therefore the first natura frequency is that on the owest energy eve and is thus the most ikey to be activated. The equation for the natura frequency of a singe degree of freedom system is: f 1 π K M where K M is the stiffness, is the mass. The determination of frequencies is described in Chapter 3. OS-RMS 90 RMS- vaue of the veocity for a significant step covering the intensity of 90% of peope s steps waking normay OS: v RMS One step : Root mean square effective vaue, here of veocity v : v RMS T 1 ( t) T v 0 dt v Peak where T is the investigated period of time. 9

12 SINGLE Speed IMAGE - Peter Vanderwarker - Pau Pedini

13 3. Determination of Foor Characteristics 11

14 3. Determination of Foor Characteristics The determination of foor characteristics can be performed by simpe cacuation methods, by Finite Eement Anaysis (FEA) or by testing. As the design guide is intended to be used for the design of new buidings, testing procedures are excuded from further expanations and reference is given to [1]. Different finite eement programs can perform dynamic cacuations and offer toos for the determination of natura frequencies. The mode mass is in many programs aso a resut of the anaysis of the frequency. As it is specific for each software what eements can be used, how damping is considered and how and which resuts are given by the different programs, ony some genera information is given in this design guide concerning FEA. If FEA is appied for the design of a foor with respect to the vibration behaviour, it shoud be considered that the FE-mode for this purpose may differ significanty to that used for utimate imit state (ULS) design as ony sma defections are expected due to vibration. A typica exampe is the different consideration of boundary conditions in vibration anaysis. If compared to ULS design: a connection which is assumed to be a hinged connection in ULS may be rather assumed to provide fu moment connection in vibration anaysis. For concrete, the dynamic moduus of easticity shoud be considered to be 10% higher than the static moduus E cm. For manua cacuations, Annex A gives formuas for the determination of frequency and moda mass for isotropic pates, orthotropic pates and beams. Damping has a big infuence on the vibration behaviour of a foor. Independent on the method chosen to determine the natura frequency and moda mass the damping vaues for a vibrating system can be determined with the vaues given in Tabe 1. These vaues are considering the infuence of structura damping for different materias, damping due to furniture and damping due to finishes. The system damping D is obtained by summing up the appropriate vaues for D 1 to D 3. In the determination of the dynamic foor characteristics, a reaistic fraction of imposed oad shoud be considered in the mass of the foor (m, M). Experienced vaues for residentia and office buidings are 10% to 0% of the imposed oad.

15 3. Determination of Foor Characteristics Tabe 1 Determination of damping Type Damping (% of critica damping) Structura Damping D 1 Wood 6% Concrete % Stee 1% Composite (stee-concrete) 1% Damping due to furniture D Traditiona office for 1 to 3 persons with separation was % Paperess office 0% Open pan office 1% Library 1% Houses 1% Schoos 0% Gymnastic 0% Damping due to finishes D 3 Ceiing under the foor 1% Tota Damping D D 1 + D + D 3 Free foating foor 0% Swimming screed 1% 13

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17 4. Cassification of Vibrations 15

18 4. Cassification of Vibrations The perception of vibrations by persons and the individua feeing of annoyance depends on severa aspects. The most important are: The direction of the vibration, however in this design guide ony vertica vibrations are considered; Another aspect is the posture of peope such as standing, ying or sitting; The current activity of the person considered is of reevance for its perception of vibrations. Persons working in the production of a factory perceive vibrations differenty from those working concentrated in an office or a surgery; Additionay, age and heath of affected peope may be of importance for feeing annoyed by vibrations. Thus the perception of vibrations is a very individua probem that can ony be described in a way that fufis the acceptance of comfort of the majority. It shoud be noted that the vibrations considered in this design guide are reevant for the comfort of the occupants ony. They are not reevant for the structura integrity. Aiming at an universa assessment procedure for human induced vibration, it is recommended to adopt the so-caed one step RMS vaue (OS-RMS) as a measure for assessing annoying foor vibrations. The OS-RMS vaues correspond to the harmonic vibration caused by one reevant step onto the foor. As the dynamic effect of peope waking on a foor depends on severa boundary conditions, such as weight and speed of waking of the peope, their shoes, fooring, etc., the 90% OS-RMS (OS-RMS 90 ) vaue is recommended as assessment vaue. The index 90 indicates that 90 percent of steps on the foor are covered by this vaue. The foowing tabe cassifies vibrations into severa casses and gives aso recommendations for the assignment of casses with respect to the function of the considered foor.

19 4. Cassification of vibrations Tabe Cassification of foor response and recommendation for the appication of casses OS-RMS 90 Function of Foor Cass Lower Limit Upper Limit Critica Workspace Heath Education Residentia Office Meeting Retai Hote Industria Sport A B C D E F Recommended Critica Not recommended 17

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21 5. Design Procedure and Diagrams 19

22 5. Design Procedure and Diagrams An overview of the genera design procedure is given in Figure. The design is carried out in 3 steps where the determination of the dynamic foor characteristics is the most compex one. Thus Annex A gives detaied hep by simpified methods; genera expanations are given in Chapter 3. When moda mass and frequency are determined, the OS-RMS 90 -vaue as we as the assignment to the perception casses may be determined with the diagrams given beow. The reevant diagram needs to be seected according to the damping characteristics of the foor in the condition of use (considering finishing and furniture), see Chapter 3. The diagrams have been eaborated by TNO Bouw, the Netherands, in the frame of [1]. Figure Design procedure Determine dynamic foor characteristics: - Natura Frequency - Moda Mass - Damping (Chapter 3; Annex A) Read off OS-RMS 90 Vaue (Chapter 5) Determine Acceptance Cass (Chapter 4)

23 5. Design Procedure and Diagrams Figure 3 Appication of diagrams The diagram is used by entering the moda mass on the x-axis and the corresponding frequency on the y-axis. The OS-RMS vaue B A and the acceptance cass can be read-off at the intersection of extensions at both entry points. Frequency of the foor [Hz] E D C F Moda Mass of the foor [kg] : means out of the range of a toerabe assessment 1

24 5. Design Procedure and Diagrams Figure 4 OS-RMS 90 for 1% Damping Cassification based on a damping ratio of 1% A B C Eigenfrequency of the foor [Hz] F E D Moda mass of the foor [kg]

25 5. Design Procedure and Diagrams Figure 5 OS-RMS 90 for % Damping Cassification based on a damping ratio of % A B C Eigenfrequency of the foor [Hz] F E D Moda mass of the foor [kg] 3

26 5. Design Procedure and Diagrams Figure 6 OS-RMS 90 for 3% Damping Cassification based on a damping ratio of 3% A B C Eigenfrequency of the foor [Hz] F E D Moda mass of the foor [kg]

27 5. Design Procedure and Diagrams Figure 7 OS-RMS 90 for 4% Damping Cassification based on a damping ratio of 4% A B C Eigenfrequency of the foor [Hz] F E D Moda mass of the foor [kg] 5

28 5. Design Procedure and Diagrams Figure 8 OS-RMS 90 for 5% Damping Cassification based on a damping ratio of 5% B A C Eigenfrequency of the foor [Hz] F E D Moda mass of the foor [kg]

29 5. Design Procedure and Diagrams Figure 9 OS-RMS 90 for 6% Damping Cassification based on a damping ratio of 6% A B C Eigenfrequency of the foor [Hz] F E D Moda mass of the foor [kg] 7

30 5. Design Procedure and Diagrams Figure 10 OS-RMS 90 for 7% Damping Cassification based on a damping ratio of 7% A B C Eigenfrequency of the foor [Hz] F E D Moda mass of the foor [kg]

31 5. Design Procedure and Diagrams Figure 11 OS-RMS 90 for 8% Damping Cassification based on a damping ratio of 8% A B Eigenfrequency of the foor [Hz] E D C F Moda mass of the foor [kg] 9

32 5. Design Procedure and Diagrams Figure 1 OS-RMS 90 for 9% Damping Cassification based on a damping ratio of 9% A B Eigenfrequency of the foor (Hz) F E D C Moda mass of the foor (kg)

33 Annex a formuas FOR MANUAL CALCULATION A.1 Natura Frequency and Moda Mass for Isotropic Pates 3 A. Natura Frequency and Moda Mass for Beams 34 A.3 Natura Frequency and Moda Mass for Orthotropic Pates 35 A.4 Sef Weight Approach for Natura Frequency 36 A.5 Dunkerey Approach for Natura Frequency 37 A.6 Approximation of Moda Mass 38 31

34 A.1 Natura Frequency and Moda Mass for Isotropic Pates The foowing tabe gives formuas for the determination of the first natura frequency (acc. to []) and the moda mass of pates for different support conditions. For the appication of the given equations, it is assumed that no atera defection at any edges of the pate occurs. Support Conditions: camped hinged Frequency; Moda Mass α f 3 E t 1m (1 υ ) ; M mod β M b α α ( 1 + λ )) β λ Ratio λ /b L/B b α α λ λ λ λ β λ Ratio λ /b L/B b α α λ λ λ + 44 λ β λ Ratio λ /b L/B

35 Annex A Formuas for Manua Cacuation E t m υ M Young's moduus [N/m²] Thickness of pate [m] Mass of foor incuding finishing and a representative amount of imposed oad (see chapter 3) [kg/m²] Poisson ratio Tota mass of foor incuding finishes and representative amount of imposed oad (see chapter 3) [kg] Support Conditions: Frequency; Moda Mass 3 α E t f ; M mod β M camped hinged 1m (1 υ ). ( λ ) α λ λ 4 b α Ratio λ β λ /b L/B b α λ + 5 α λ λ. 44 λ Ratio λ β λ /b L/B 4 b α α λ λ λ + 44 λ β 0.17 λ Ratio λ /b L/B 33

36 A. Natura Frequency and Moda Mass for Beams The first Eigenfrequency of a beam can be determined with the formua according to the supporting conditions from Tabe 3 with: E Young's moduus [N/m²] I Moment of inertia [m 4 ] µ Distributed mass m of the foor (see page 33) mutipied by the foor width [kg/m] Length of beam [m] Tabe 3 Determination of the first Eigenfrequency of Beams Support Conditions Natura Frequency Moda Mass f 4 3 EI π µ 4 M 0 mod. 41 µ f 3 EI π 0. µ 4 M 0 mod. 45 µ f 3 EI π µ 4 M 0 mod. 5 µ f 1 3 EI π 0. 4 µ 4 M mod µ

37 A.3 Natura Frequency and Moda Mass for Orthotropic Pates Annex A Formuas for Manua Cacuation Orthotropic foors as e.g. composite foors with beams in ongitudina direction and a concrete pate in transverse direction have different stiffnesses in ength and width (EI y > EI x ). An exampe is given in Figure 13. The first natura frequency of the orthotropic pate being simpy supported at a four edges can be determined with: Where: m is the mass of foor incuding finishes and a representative amount of imposed oad (see chapter 3) [kg/m²], is the ength of the foor (in x-direction) [m], is the width of the foor (in y-direction) [m], is the Young's moduus [N/m²], b E I x is the moment of inertia for bending about the x-axis [m 4 ], I y is the moment of inertia for bending about the y-axis [m 4 ]. f π EI y m b 4 b + EIx EI y Formuas for the approximation of the moda mass for orthotropic pates are give in Annex A.6. Figure 13 Dimensions and axis of an orthotropic pate b y z x 35

38 A.4 Sef Weight Approach for Natura Frequency The sef weight approach is a very practica approximation in cases where the maximum defection δ max due to the mass m is aready determined, e.g. by finite eement cacuation. This method has its origin in the genera frequency equation: f 1 π K M The stiffness K can be approximated by the assumption: K M g 3 4 δ where: M g δ is the tota mass of the vibrating system [kg], is the gravity [m/s ] and is the average defection [mm]. The approximated natura frequency is f 1 π K M 1 π 4g 3δ max δ max 18 [ mm] where: δ max is the maximum defection due to oading in reference to the mass m.

39 A.5 Dunkerey Approach for Natura Frequency Annex A Formuas for Manua Cacuation The Dunkerey approach is an approximation for manua cacuations. It is appied when the expected mode shape is compex but can be subdivided into different singe modes for which the natura frequency can be determined, see A.1, A.3 and A.. Figure 14 shows an exampe of a composite foor with two simpy supported beams and no support at the edges of the concrete pate. The expected mode shape is divided into two independent singe mode shapes; one of the concrete sab and one of the composite beam. Both mode shapes have their own natura frequency (f 1 for the mode of the concrete sab and f for the composite beam). According to Dunkerey, the resuting natura frequency f of the tota system is: 1 f 1 f 1 f 1 f Figure 14 Exampe for mode shape decomposition Initia System Mode of concrete sab Mode of composite beam 37

40 A.6 Approximation of Moda Mass The moda mass may be interpreted as the fraction of the tota mass of a foor that is activated when the foor osciates in a specific mode shape. Each mode shape has its specific natura frequency and moda mass. Figure 15 Appication of oad to obtain approximated oad shape (exampe) For the determination of the moda mass the mode shape has to be determined and to be normaised to the maximum defection. As the mode shape cannot be determined by manua cacuations, approximations for the first mode are commony used. As an aternative to manua cacuations, Finite Eement Anaysis is commony used. If the Finite Eement software does not give moda mass as resut of moda anaysis, the mode shape may be approximated by the appication of oads driving the pate into the expected mode shape, see Figure 15. Expected mode shape: Appication of oads: If the mode shape of a foor can be approximated by a normaised function δ(x,y) (i.e. δ (x,y) max 1.0) the corresponding moda mass of the foor can be cacuated by the foowing equation: When mode shape defections are determined by FEA: M ( x, y) df M mod mod µ δ δ F i dm i Nodes i Where: µ is the distribution of mass δ(x,y) is the vertica defection at ocation x,y Where: δ i dm i is the vertica defection at node i (normaised to the maximum defection) is the mass of the foor represented at node i If the function δ (x,y) represents the exact soution for the mode shape the above described equation aso yieds to the exact moda mass.

41 Annex A Formuas for Manua Cacuation The foowing gives exampes for the determination of moda mass by manua cacuation: Exampe 1 Pate simpy supported aong a four edges, ~ y x y x Approximation of the first mode shape: δ ( x, y) sin π x sin π y x y ( δ ( x, y 1. 0 max Mass distribution µ M x y Moda mass M mod y x M µ δ ( x, y) df sin 0 0 F x y π x x sin π y y dx dy M 4 39

42 Exampe Pate simpy supported aong a four edges, x << y y x x x Approximation of the first mode shape: x 0 y y y y : x 1. and δ ( x, y) 1. 0 max δ ( x, y) sin πx sin π y x y. x π x x y y : δ ( x, y) sin 1. 0 x δ ( x, y) 1. 0 max Mass distribution µ M x y Moda mass M mod µ δ ( x, y) F df y x M x x y x π sin sin dx dy + x 0 0 y x 0 y x π y y π sin 0 x x dx dy M 4 x y

43 Annex A Formuas for Manua Cacuation 41 Exampe 3 Pate spans uniaxia between beams, pate and beams simpy supported Approximation of the first mode shape: With δ x Defection of the beam δ y Defection of the sab assuming the defection of the supports (i.e. the defection of the beam) is zero δ δ x + δ y Mass distribution Moda mass + y y x x y x y x π δ δ π δ δ sin sin ), ( x y M µ x y 1 0 ), ( max y x δ δ δ π δ δ δ y x y x M + mod sin sin ), ( π δ δ π δ δ µ y y x x y x F dx dy y x M df y x M x y 0 0 δ δ δ

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45 Annex B Exampes B.1 Fiigree sab with ACB-composite beams (office buiding) 44 B.1.1 Description of the Foor 44 B.1. Determination of dynamic foor characteristics 47 B.1.3 Assessment 47 B. Three storey office buiding 48 B..1 Description of the Foor 48 B.. Determination of dynamic foor characteristics 50 B..3 Assessment 51 43

46 B.1 Fiigree sab with ACB-composite beams (office buiding) B.1.1 Description of the Foor In the first worked exampe, a fiigree sab with fase-foor in an open pan office is checked for footfa induced vibrations. The sab spans uniaxiay by over 4. m between main beams. Its overa thickness is 160 mm. The main beams are ArceorMitta Ceuar Beams (ACB) which act as composite beams. They are attached to the vertica coumns by a fu moment connection. The foor pan is shown in Figure 18. For a vibration anaysis it is sufficient to check ony a part of the foor (representative foor bay). The representative part of the foor to be considered in this exampe is indicated by the hatched area in Figure 18. Figure 16 Buiding structure Figure 17 Beam to coumn connection Figure 18 Foor pan y x [m]

47 Annex B Exampes Figure 19 Cross section 160 For the main beams (span of 16.8 m) ACB/HEM400/HEB400 profies in stee S460 have been used, see Figure 19. The main beams with the shorter span of 4. m are ACB/HEM360 in S HE400B The cross beams which are spanning in goba x-direction may be negected for the further cacuations, as they do not contribute to the oad transfer of the structure HE400M [mm] The nomina materia properties are Stee S460: E s N/mm², f y 460 N/mm² Concrete C5/30: E cm N/mm², f ck 5 N/mm² As stated in Chapter 3, the nomina eastic moduus of the concrete wi be increased for the dynamic cacuations: Ec, dyn 1.1 Ecm N/ mm² Figure 0 Expected mode shape of the considered part of the foor corresponding to the first Eigenfrequency The expected mode shape of the considered part of the foor which corresponds to the first Eigenfrequency is shown in Figure 0. From the mode shape it can be concuded that each fied of the concrete sab may be assumed to be simpy supported for the further dynamic cacuations. Regarding the boundary conditions of the main beams (see beam to coumn connection in Figure 17) it is assumed that for sma ampitudes as they occur in vibration anaysis, the beam-coumn connection provides sufficient rotationa restrain, i.e. the main beams are considered to be fuy fixed. 45

48 Section properties Sab The reevant section properties of the sab in goba x-direction are: Loads Sab Sef weight (incudes 1.0 kn/m² for fase foor):, 160 mm A c x mm 3 g sab kn m, I c x mm mm Main beam Assuming the previousy described first vibration mode, the effective width of the composite beam may be obtained from the foowing equation: b eff b eff,1 + b eff, 0 8 The reevant section properties of the main beam for serviceabiity imit state (no cracking) are: A a,net 1936 mm A a,tota 914 mm A i 9830 mm I i x 10 9 mm m 8 Live oad: Usuay a characteristic ive oad of 3 kn/m² is recommended for foors in office buidings. The considered fraction of the ive oad for the dynamic cacuation is assumed to be approx. 10% of the fu ive oad, i.e. for the vibration check it is assumed that q sab Main beam Sef weight (incudes.00 kn/m for ACB): 4. g beam kN m Live oad: kn m 4. q sab kn m

49 Annex B Exampes B.1. Determination of dynamic foor characteristics B.1.3 Assessment Eigenfrequency The first Eigenfrequency is cacuated based on the sef weight approach. The maximum tota defection may be obtained by superposition of the defection of the sab and the defection of the main beam, i.e. Damping The damping ratio of the stee-concrete sab with fase foor is determined according to tabe 1: With Based on the above cacuated moda properties the foor is cassified as cass C (Figure 6). The expected OS-RMS vaue is approx. 0.5 mm/s. According to Tabe, cass C is cassified as being suitabe for office buidings, i.e. the requirements are fufied. δ max δ sab + δ beam D 1 D D (stee-concrete sab) 1.0 (open pan office) 1.0 (fase foor) With ( ) δ sab 1. 9 mm δ 1 ( ) beam mm the maximum defection is δ max mm Thus the first Eigenfrequency may be obtained (according to Annex A.4) from 18 f Hz 6. 6 Moda Mass The tota mass of the considered foor bay is M ( ) kg According to Chapter A.6, Exampe 3, the moda mass of the considered sab may be cacuated as M π 6 mod 1746 kg 47

50 B. Three storey office buiding B..1 Introduction Figure 1 Buiding overview The method eads in genera to conservative resuts when appied as singe bay method using the mode reated to the fundamenta frequency. However, in specia cases in which the moda mass for a higher mode is significanty ow, aso higher modes need to be considered, see the foowing exampe. B.. Description of the Foor The foor of this office buiding, Figure 1, spans 15 m from edge beam to edge beam. In the reguar area these secondary foor beams are IPE600 sections, spaced in.5 m. Primary edge beams, which span 7.5 m from coumn to coumn, consist aso of IPE600 sections, see Figure. Figure Pan view of foor with choice of sections IPE600 IPE600 IPE600 IPE600 IPE600 IPE600 IPE600 IPE600 IPE600 IPE600 IPE600 IPE600 IPE A IPE600 B IPE600 C IPE600 D 9 x.5 [m]

51 Annex B Exampes The sab is a composite pate of 15 cm tota thickness with stee sheets COFRASTRA 70, Figure 3. More information concerning the COFRASTRA 70 are avaiabe on The nomina materia properties are: Stee S35: E s N/mm², f y 35 N/mm² Concrete C5/30: E cm N/mm², f ck 5 N/mm² For dynamic cacuations (vibration anaysis) the eastic moduus wi be increased according to Chapter 3: Figure 3 Foor set up with COFRASTRA 70 E c, dyn 1.1 E cm N/mm² Section properties Sab (transversa to beam, E N/mm ) A 1170 cm²/m I 0355 cm 4 /m Composite beam (b eff,5 m; E N/mm²) A 468 cm² I cm 4 Loads Sab Sef weight: g 3.5 kn/m² g 0.5 kn/m² g + g 4.0 kn/m² (permanent oad) Life oad q 3.0 x kn/m² (10% of fu ive oad) Composite beam Sef weight: g ( ) x kn/m Life oad: q 0.3 x kn/m 49

52 B..3 Determination of dynamic foor characteristics Supporting conditions The secondary beams are ending in the primary beams which are open sections with ow torsiona stiffness. Thus these beams may be assumed to be simpy supported. Eigenfrequency In this exampe, the Eigenfrequency is determined according to three methods: the beam formua, negecting the transversa stiffness of the foor, the formua for orthotropic pates and the sef-weight method considering the transversa stiffness. Appication of the beam equation (Chapter A.): p kn/ m µ / kg/ m f π 3 EI 0.49 µ π Hz Appication of the equation for orthotropic pates (Chapter A.3): f 1 π π EI m y 4 b Hz b + 4 EI EI 8 x y

53 Annex B Exampes B..4 Assessment Appication of the sef weight approach (Chapter A.4): δ max δ sab + δ beam δ sab 0. 3mm 5 Based on the above cacuated moda properties the foor is cassified as cass D (Figure 6). The expected OS-RMS 90 vaue is approximatey 3. mm/s. According to Tabe, cass D is suitabe for office buidings, i.e. the requirements are fufied. δ beam 13. 9mm 4 δ max mm 18 f Hz 14. Moda Mass The determination of the Eigenfrequency shows that the oad bearing behaviour of the foor can be approximated by a simpe beam mode. Thus this mode is taken for the determination of the moda mass: M 0. 5 µ kg mod Damping The damping ratio of the steeconcrete sab with fase foor is determined according to Tabe 1: D D1 + D + D % With D 1 D D (stee-concrete sab) 1.0 (open pan office) 1.0 (ceiing under foor) 51

54 Technica assistance & Finishing Technica assistance We are happy to provide you with free technica advice to optimise the use of our products and soutions in your projects and to answer your questions about the use of sections and merchant bars. This technica advice covers the design of structura eements, construction detais, surface protection, fire safety, metaurgy and weding. Our speciaists are ready to support your initiatives anywhere in the word. To faciitate the design of your projects, we aso offer software and technica documentation that you can consut or downoad from our website: Finishing As a compement to the technica capacities of our partners, we are equipped with high-performance finishing toos and offer a wide range of services, such as: driing fame cutting T cut-outs notching cambering curving straightening cod sawing to exact ength weding and fitting of studs shot and sand basting surface treatment Buiding & Construction Support At ArceorMitta we aso have a team of muti-product professionas speciaised in the construction market: the Buiding and Construction Support (BCS) division. A compete range of products and soutions dedicated to construction in a its forms: structures, façades, roofing, etc. is avaiabe from the website References [1] European Commission Technica Stee Research: Generaisation of criteria for foor vibrations for industria, office, residentia and pubic buiding and gymnastic has, RFCS Report EUR 197 EN, ISBN , 006, [] Hugo Bachmann, Water Ammann: Vibration of Structures induced by Man and Machines IABSE-AIPC-IVBH, Zürich 1987, ISBN X

55 Your partners Authors ArceorMitta Commercia Sections 66, rue de Luxembourg L-41 Esch-sur-Azette Luxembourg Te: Fax: Prof. Dr.-Ing. Markus Fedmann Dr.-Ing. Ch. Heinemeyer Dr.-Ing. B. Vöing RWTH Aachen University Institut und Lehrstuh für Stahbau und Leichtmetabau We operate in more than 60 countries on a five continents. Pease have a ook at our website under About us to find our oca agency in your country. Athough every care has been taken during the production of this brochure, we regret that we cannot accept any iabiity in respect of any incorrect information it may contain or any damages which may arise through the misinterpretation of its contents.

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