António Xavier Gonçalves Frazão da Rocha Pinto

Transcription

1 SOFTWARE FOR AUTOMATIC APPLICATION OF THE CALCULATION MODELS OF EN IN BUILDING ACOUSTICS António Xavier Gonçalves Frazão da Rocha Pinto DECivil, Instituto Superior Técnico, Av Rovisco Pais, 1, Lisbon, Portugal October, 2011 ABSTRACT Knowing that the correct application of the calculation models presented in the standard series EN demands an accurate management of a great amount of data and a meticulous choice of some given calculation options, its automation ensures an error minimization and a considerable decrease of the time spent in each project. Based on some previous analyses developed in Instituto Superior Técnico on the assessment of the detailed calculation models of parts 1 and 2 of the standard EN applied to casestudies, the present thesis aims to create a software for automatic application of the models. The program was conceived in a CAD platform chosen for its important role in design and communication between each entity involved in building design and construction. The program validation was made using the same case-studies mentioned above. The results obtained by automatic calculation prove to be equivalent to results obtained in the previously mentioned studies, thus confirming the correct use of the calculation models. Impact sound insulation prediction model seems to be more accurate than the airborne sound insulation prediction model for the considered case-studies. KEYWORDS: Estimation of sound transmission; EN ISO 12354; Automation; AutoCAD; Software

2 1. INTRODUCTION Considering that the first Portuguese law concerning building acoustics is less than twenty five years old, the study of this subject still has great relevance. More recently, the European Standard series EN ISO presented the first calculation model in European, and therefore Portuguese, legislation. The study of building acoustics itself is a rather new subject for which there is yet no model capable of fitting to every construction solution nor a perfect adjustment between the models and field results. Being so new these Standards are still incomplete and its accuracy is not properly quantified. Therefore, the software developed throughout this thesis aims, not only to ease the calculation model application, by reducing the time spent in the calculation process as well as minimizing errors, but also to contribute to the study of the mentioned model by increasing the number of available results. Once it was proven that the detailed model gives better results than the simplified model, only the first one was implemented. Although the Standards EN ISO [1] and EN ISO [2] give primacy to the use of experimental data regarding construction elements and junctions, the developed software calculates its behavior using theoretical models hence it only allows the introduction of material properties and element dimensions. This option lays on the absence of information regarding the most used elements and junctions in the National scene. The validation of the software was made by calculating the case-studies used by Dias [3] and Galante [4] in their previous papers - which compared the results of the detailed model with several simplified models and field results. 2. STATE OF THE ART Four commercial computer programs were analyzed when conceiving the presented software: Cypevac Acoubat, CAEd and SONarchitect. Although many of these computer programs also verify other Standards from the EN ISO series, only the first two standards verification were taken into account. Cypevac is the simplest. It has no visual representation of the building, nor does it spatially relate the construction elements. The results are obtained simply by applying the empirical expression as function of the mass per unit area to each element. The elements can be chosen from a lot of preset elements or introduced by the user. The results are shown in a Portuguese written report with graphic representation of the element s section. Acoubat has a tridimensional graphic interface that can represent one, two or four rooms in the same floor or in adjacent floors. The calculation is based on laboratory measurements so that it 2

3 is only possible to use elements from the database provided. The database has about 3000 entries. The CAEd has a similar structure to Acoubat s. It also has a tridimensional graphic interface but this one can only represent two rooms at a time. Although the database has the most common elements used in Portuguese construction, its 100 entries prove to fail at more original solutions. The management of the database is less intuitive than Acoubat s. SONarchitect is the high-end software in building acoustics. It is the only software capable of calculating the entire building at once, identifying the sound reduction index corresponding to each transmission path. It is also the only software capable of importing.dwg drawing files although it also includes a drawing tool. The building is represented in two or three dimensions, allowing almost any type of architectural variation. 3. CALCULATION MODEL The first step before using the calculation model presented in the Standards is the homogenization of the constructive solution. It is required that each element has a single value for its dimensions, density, Poisson ratio and Young s modulus. In case of additional lining or floating floors the structural element should be considered independently from any other layer. Since there is no specification concerning heavy double leaf walls, this type of element was considered as a single leaf heavy element. (1) Once the element is homogenized some parameters must be calculated: the critical frequency (f c ), phase speed of longitudinal waves (c L ), and the frequencies f p and f 11, as the following formulae expose: (2) (3) (4) (5) Where E is the Young s modulus, l 1 and l 2 are the element dimensions and t is the element thickness. 3

4 The junction vibration reduction index is obtained using the Annex E from the Standard EN ISO [1]. For each junction type and each sound path there is an equation which describes its behaviour, as it is shown in the image bellow for the case of heavy cross junction: K 13 = 8,7 + 17,1 M + 5,7 M 2 db; 0 db / octave (6) K 12 = 8,7 + 5,7 M 2 (= K 23) db; 0 db / octave (7) (8) It is then calculated the absorption coefficient for bending wave field at each border k of an element: (9) Being f ref the reference frequency (1000 Hz) and f c,j the the critical frequency of the element j in the sound transmission path ij. Finally the sound reduction index and the normalized sound pressure level for direct transmission are defined by: (10) (11) These formulae are the result of a sequence of complex calculations described in Annex C of the EN ISO which, for its complexity and length will not be described here. Other transmission paths are considered through the following expressions: (11) ; (12) (13) All the previous values are calculated for all the one third octave bands. The single number value is obtained by shifting a reference curve towards the measured curve until de sum of unfavourable deviations is as large as possible but not more than 32,0 db, as defined in ISO 4

5 717-1 [5] and ISO [6] for airborne and impact sound insulation respectively. The single number value is the 500 Hz value of the reference curve. In the case of airborne sound insulation, the additional linings are considered as a single number value, for each of the considered transmission paths as listed in the following table: Table 1 Weighted sound reduction index improvement by a lining, depending on the resonance frequency [1]. Where f 0 is Resonance frequency f 0 ΔR w of the lining (Hz) (db) R w / R w / R w / R w / > (14) (15) For elastic or rigid connections to the heavy element, as explained in annex C of EN ISO In the case impact sound insulation thecontribution of the additional layers is considered as a single number in the direct path and spectrum distributed in flanking paths. (db) (16) If elements are constructed of several parts (in parallel), its sound reduction index should be summed: (db), (17) Finally, to provide the user a quantity that can be compared with legally required values, standardized level difference and normalized sound pressure level are computed: (db); (18) 5

6 (db). (19) 4. PROGRAM STRUCTURE The developed software stands out from other computer programs for its interaction with a CAD platform and its independence from databases. Unlike what happens with other programs, the developed software is not based on a sender-receiver pair. In fact, it relies on the construction of an element network so that elements may be part of different sender-receiver pairs. To begin with, the user must define the elements involved, its dimensions and materials. There are three types of elements: walls, homogeneous floors and floating floors. The second step is defining the junctions. For each element, four junctions should be defined. Since there is no coordinate system implemented in the program, the position of any lining must be defined at this point. Finally, the calculation of the sound reduction index or impact sound pressure level only needs the designation of the separating element and the volume of the receiving room. In order to reduce the minimum time needed to get the first results, it was allowed a simplification of the calculation method. Thus instead of demanding the definition of the four junctions per element in contact with the separating element, these definitions are optional. For each element whose junctions are not defined the program assumes the laboratory values as equivalent to field values. The quantification of the effect this abridgement has in the final result can be observed in the results chapter bellow. The user is always informed on the number of transmission paths that were subject to this simplification. 5. RESULTS The program was submitted to four validation tests, two for the airborne sound insulation and two for the impact sound insulation. The first test for either procedure was the calculus of the example given in annex H and E of the standards EN ISO [1] and EN ISO [2], respectively. In addition to the results provided by the program were also considered the results of manual calculation, the results given in the annex and, in the case of airborne sound, the results of Cypevac. 6

7 Table 2 Results from manual and automatic calculation of the example given in Annex H of EN [1]. Example 1 D nt,w (db) Annex H of EN Manual Calculation 58 Automatic Calculation 57 Cypevac Results 52 Table 3 Results from manual and automatic calculation of the example given in Annex E of EN [2]. Example 2 L nt,w (db) Annex E of EN Manual Calculation 40 Automatic Calculation 40 The difference between automatic and manual calculation in airborne sound level difference is due to rounding errors in all sound reduction indexes of each frequency band in each of the transmission paths. The difference between the value obtained with the program and the value given in the standard cannot be properly explained for the calculation method is not extensively described in the annex. Nevertheless, the results prove to be satisfactory. The second test for either of the calculation models was made by comparison of the results obtained with the results given by Dias [3] and Galante [4] in their thesis. Five of the seven elements (four slabs and one internal wall) studied in Dias s work were included in the analysis as well as three of the four elements (three slabs) analyzed by Galante. Some aspects must be taken into account to fully understand the meaning of the results exposed above. In Graphics 1 and 2 the references LA(4T) and LA(2X+2T) correspond to the same element, only in Dias s work were considered four T junctions which, in the author s opinion, is not the best approach to the real architecture. In Graphics 3 and 4 the calculation for impact sound pressure level for slabs LB and LC was made considering two different volumes in the receiving room: first only the volume limited by the analyzed slab and second the volume corresponding to the whole receiving room. The first results prove to be more accurate. 7

8 Graphic 1 Difference between the results of two automated methods compared to manual method by Galante [4], given in db (percussion sound) db Detailed automatic forecast Fast automatic forecast Graphic 2 Difference between the results of two automated methods and the manual method by Galante [4] against the results of measurements in situ, given in db (percussion sound) 12 db Detailed manual forecast Detailed automatic forecast Fast automatic forecast Graphic 3 Difference between the results of two automated methods compared to manual method by Dias [3], given in db (airborne sound) db Detailed automatic forecast Fast automatic forecast 8

9 Graphic 4 Difference between the results of two automated methods and the manual method by Dias [3] against the results of measurements in situ, given in db (airborne sound) db Detailed manual forecast Detailed automatic forecast Fast automatic forecast In general, when compared to the results calculated by Dias [3] and Galante [4], the results prove to be accurate enough (with a difference below 3 db) Graphics 1 and 3. The simplified method has a bigger impact in the sound reduction index which was predictable for its greater number of flanking paths. These results are not to be trusted as a precise description of the element s behaviour. When compared to field results, the impact sound insulation gives more accurate results proving to be trustworthy. These conclusions are only valid to elements similar to the ones tested. Therefore no precise conclusions can be taken, for instance, on floating floors (rather than what the first validation test may allow to assume). 6. CONCLUSIONS Several aspects should be taken into account so that conclusions can be taken. Starting with the results it is clear that the ones given by the software are equivalent to the ones calculated by other authors, proving the correct implementation of the calculation model. As for its accuracy, more cases should be studied before a correct quantification can be made. The Standards estimate a standard deviation of 1,5 db to 2,5 db for airborne sound. As for impact sound, it is said that the results are in a range of ±2 db in 60% of the predicted values and ±4 db in 100% of the predicted values. The standard deviation obtained is of 6,3 db in airborne sound insulation and 1,5 in impact sound insulation. 9

10 The program reveals several improvement opportunities naturally inherent to any software or thesis. First of all the introduction of a coordinate system. This would allow a great reduction in the time spent in the definition of junctions and would automatically locate the position of the lining. An upgrade on the graphic interface would also be important, especially in the definition of the junctions so that, for instance, horizontal junctions would be represented differently from vertical junctions. Although one of the main goals of the present thesis was to conceive a program independent of any kind of database, the introduction of a data structure, at least for the most common building elements, might reduce the operating time. Furthermore, one unavoidable weakness of the developed software is its dependence of the host software. Therefore, for each version of AutoCAD, there must be a different version of the software. There is also some liability on Microsoft Excel used for data storage. This could be minimized by using CVS system. 7. REFERENCES [1] EN ISO (2000): Building acoustics Estimation of acoustic performance of buildings from the performance of elements Part 1: Airborne sound insulation between rooms, British Standard. [2] EN ISO (2000): Building acoustics Estimation of acoustic performance of buildings from the performance of elements Part 1: Impact sound insulation between rooms, British Standard. [3] Dias, R (2010). Análise comparativa dos métodos normalizados de previsão da transmissão sonora por via aérea. Instituto Superior Técnico. [4] Galante, R. (2010). Análise comparativa dos métodos normalizados de previsão da transmissão sonora por via estrutural. Instituto Superior Técnico. [5] EN ISO (1996) Acoustics Rating of sound insulation in buildings and of building elements Part 1: Airborne sound insulation; British Standard [6] EN ISO (1996), Acoustics Rating of sound insulation in buildings and of building elements Part 2: Impact sound insulation, British Standard. 10