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Bioclimatic design of buildings considering heating requirements in Italian climatic conditions. A simplified approach
Building and Environment 46 (2011) 1624e1631
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Building and Environment journal homepage: www.elsevier.com/locate/buildenv
Bioclimatic design of buildings considering heating requirements in Italian climatic conditions. A simplified approach Rossano Albatici*, Francesco Passerini University of Trento, Department of Civil and Environmental Engineering, Via Mesiano 77, 38123 Trento, Italy
a r t i c l e i n f o
a b s t r a c t
Article history: Received 27 October 2010 Received in revised form 5 January 2011 Accepted 27 January 2011
This paper presents a parametric approach to the definition of a proper building shape compared to the building heating requirement in the very first stage of the design process. A new simplified index is introduced, namely the south exposure coefficient Cfs. In fact, as far as bioclimatic architecture is concerned, the relationship between buildings and natural environment is very important both for the control of indoor comfort conditions and energy requirements. The building shape is a fundamental aspect of this relationship. Usually, in thermal behavior analysis this parameter is considered only from the point of view of compactness. This is a reductive approach, because two buildings with the same coefficient could have different shapes and so a different thermal behavior. Some aspects such as orientation, openings, exposure to atmospheric agents and natural elements must also be strictly considered. Moreover, in scientific literature no indications are given to designers who operate in mild and warm climate conditions. This is why the results of a research activity focused on heating requirements of buildings with different shapes and laid in the Italian territory are presented. Monthly calculations have been performed following the quasi-steady-state method suggested in the European standard. Outputs show that better results in the building energy performance can be achieved considering a bioclimatic (though simplified) approach since the very beginning. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Building shape Solar exposure Energy efficiency Bioclimatic architecture Parametric approach
1. Introduction During the design process of a new building, one of the most important aspects to be taken into consideration is the definition of a proper building shape in compliance with a complex set of requirements mutually interacting. As for energy efficiency, the best way is a holistic approach which is related to three main aspects: human thermal comfort in inner spaces, exploitation of energy from renewables, effect of urbanization on city climatology [1]. But usually “the shape of a building of given volume was optimized taking the minimum heat energy loss as the criterion” [2]. The attention toward these issues is not new since it has been tackled in many review papers [3]. However, the relationship between shape and energy requirements is still an open question. In fact, “no definitive and simple correlations were established between the basic attributes associated with buildings (such as form, window size and glazing type) and their total annual energy use and/or heating/cooling loads” [4]. Lately, a multicriteria optimization approach has been developed [5e7]. It is a valid and a very comprehensive approach but at * Corresponding author. Tel.: þ39 0461282622; fax: þ39 0461282672. E-mail address: [email protected] (R. Albatici). 0360-1323/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.buildenv.2011.01.028
the same time a complex one when it comes to use. Very often, in fact, the designer points out the building shape, or at least its main lines and volume distribution, in the pre-design phase, i.e. at the very first stage of conception. So, simpler indexes, easy to understand, are needed to help designers to move in a field where, usually, these parameters are otherwise “adopted on the basis of experience or by intuition” [7]. In the professional practice, the most used index is the shape coefficient defined as the ratio between the envelope surface of the building S (i.e. the external skin surfaces) and the inner volume of the building V:
Cf ¼ S=V
(1)
Recently, some researchers have extended the previous works including, in addition to the building shape, even windows areas and glazing type. Anyway the main index remains the Relative Compactness RC, defined as the ratio of the reciprocal of the building shape coefficient and the reciprocal of the compactness of a reference building [8]. A simple formula is given at the end of the mentioned article, but it is valid only for office building in Kuwait. The relationship between the place where the building is positioned and the local climate is a fundamental problem. So, together
R. Albatici, F. Passerini / Building and Environment 46 (2011) 1624e1631
with the shape and the main envelope details, even the building orientation is to be considered [9]. In this field, Depecker et al. [10] studied the relationship between shape and energy requirements during the winter season in two French localities with different climate conditions, Paris and Carpentras (a town placed in southern France with a mild climate). In Paris they found a strong correlation between energy consumption and shape coefficient, in Carpentras they did not. So they did not give specific indications as far as building design in mild climates is concerned. With regard to climatic conditions similar to those of Carpentras they asserted: “A link between the energy consumption of a building and its shape can no longer be stated. As a consequence, that leaves architects to choose any shape”. It is opinion of the authors that the conclusion “in mild climates the architectural design can leave out of consideration the shape of buildings” is not appropriate. The main purpose of this research work is therefore to fill in that gap, in order to find relationships between buildings shape and heating requirements even in mild and warm climates. The matter is particularly important in Italy (and in countries with similar geographic conditions) since it is placed between the 47th and the 36th parallel north, more or less in the middle of the temperate zone in the northern hemisphere, with a prevalent northesouth development, going from the cold mountainous regions of the Alps (near the Austrian, Swiss and French border) to the warmer regions in the middle of the Mediterranean Sea, not too far from the Tunisian coasts in North Africa. To this end, not only does this work examine the relationship between building shape and energy requirements, but at the same time it considers both the shape coefficient and the facade orientation by means of the introduction of a new index, namely the south exposure coefficient Cfs.
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As far as the thermal properties of the envelope is concerned, the limit values given by the Italian legislation [11] have been considered for the city of Trento (194 m asl and 46 40 000 N 1170 000 E): - External walls U ¼ 0.34 W/(m2K) - Roof and ground floor U ¼ 0.30 W/(m2K) - Windows U ¼ 2.2 W/(m2K) The thermal bridges values correspond to standard EN ISO 14683:2007 [12] for external insulating layer and refer to internal dimensions of walls and roof: -
Connection external walleinternal partition Ji ¼ 0.1 W/(mK) Corner between two external walls Ji ¼ 0.15 W/(mK) Connection external walleroof Ji ¼ 0.15 W/(mK) Connection external walleground slab Ji ¼ 0.75 W/(mK) Connection external walleinner floor Ji ¼ 0.1 W/(mK)
The optical properties of glasses, ventilation and internal gains have been assumed considering the indications of technical standard UNI/TS 11300-1:2008 [13]: - Total solar energy transmittance of windows for Low E double glazing g ¼ 0.67 - 0.3 AC/h (air change/hour) - Internal gains of 3.9 W/m2
2.3. Modular models
2. Calculation models and methods
The research work has been divided into three main steps with increasing complexity. From the very beginning, together with the shape coefficient Cf, other two coefficients have been introduced, namely (the) south exposure coefficient Cfs that is the quotient of the area of south walls to the volume of the building:
2.1. Geometry
Cfs ¼ Ssouth =V
In the first part of the research, authors decided to work on a parallelepiped base module as in Depecker et al. [10], so to have a possible and meaningful comparison with previous researches results in this field. In particular, the base module, having a parallelepiped shape with a square floor, is defined as follows:
and the eastewest exposure coefficient Cfew that is the quotient of the area of east plus west walls to the volume of the building:
- Inner volume Vi ¼ 62.20 m3 - Floor surface Sf ¼ 23.04 m2 - External envelope surface Se ¼ 93.96 m2 See Fig. 1 where the main geometrical dimensions are represented. In order to give the model a clever energy feature from the very beginning, the north side and the roof have no openings while on the south side there is a glazing surface of 5.25 m2, equal to 40.6% of the total surface, net of delimitation elements. Both on the east and the west side there is a glazing surface of 1.54 m2, equal to 11.9% of the total surface, net of delimitation elements. The frame occupies the 9% of the hole for the big window, the 16% for the small one.
Cfew ¼ Seastþwest =V
(2)
(3)
The importance on the Cfs index is explained in the following Section 3.2. 2.3.1. First step: rectangular plant dimension In the first part of the work four extreme models composed by 16 base modules have been considered. They are presented in Fig. 2, going from the best to the worst compactness. As for compactness the best solution is MOD 1 (minimum Cf index), as for solar exposure the best solution is MOD 4 (maximum Cfs þ Cfew index) (see Table 1).
2.2. Thermal properties
2.3.2. Second step: free plant dimensions In the second part of the work, buildings with a parallelepiped shape have been considered as well, having the same glazing surface percentage for every orientation precisely as the models considered in the first part, but with free plant dimension, i.e. no more linkage to the base module dimensions and/or its multiple. In this way we have more freedom in finding the plant dimensional parameters that meet some certain fixed heating requirements.
In order to reach a simplified model that could be easily compared to real situations, standards, technical recommendations and laws in force in Italy have been considered.
2.3.3. Third step: halved building volume In the third part of the work, half of the volume of the previous models have been considered, since smaller models, such as those
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Fig. 1. Definition of the base model.
composed by 8 base models, whose volume is therefore 699.8 m3, allow a better evaluation of the influence of the volume on the relationship between shape and heating demand. Firstly, heating demands of four models composed by the base module 5.4 m 5.4 m 3 m have been calculated (Table 2). It is important to notice that Cfs and Cfew indexes are the same (both) for the smaller models and the corresponding previous ones, because halving the volume, the surfaces of the vertical facades have been halved as well. The extensions of the horizontal surfaces (roof and slabs) have been maintained constant. So the total envelope surfaces have not been halved, even if they have a smaller value. Therefore, the shape coefficients Cf of the smaller models are greater than the ones of the previous models. That means they are less compacted.
2.4. Calculation of heating requirements The calculation of heating requirements has been made using the monthly method presented in the standard EN ISO 13790:2008 [14]. It is a stationary calculation in which a coefficient, the “gain utilization factor”, is used to consider the non-stationary effects. The heating need is calculated as follows:
Qh;nd ¼ Qh;ht hh;gn Qh;gn
(4)
where Qh,ht is the total heat transfer from inside to outside, Qh,gn is the total heat gain, hh,gn is the gain utilization factor. Please refer to the standard itself for a complete description of the calculation code. The model prescribed by the standard to estimate the heating requirements is a simplified one. Nowadays, more advanced and
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Fig. 2. The four reference models composed by the base module.
detailed models are available working in dynamic state conditions. Anyway, spreadsheets based on a monthly method give results with a good level of accuracy and, in comparison with dynamic calculation software, need low calculus time and are easy to be used by all designers since the first stage of the design process. 2.5. Climatic data Depecker et al. [10] considered French localities whereas in the present research Italian localities have been taken into consideration, in order to give useful indications to designers working in climatic conditions milder and warmer than France. Four different localities have been selected, each one presenting different climatic conditions. Canazei and Trento, which are placed in northern Italy, in the Alpine region. Canazei is on a higher altitude (1465 m asl) and it is one of the coldest Italian localities. Florence is in north-central Italy, south of the Apennines. Rome is in the central part of Italy. The calculated energy requirements in Rome are very low and therefore no further south localities have been considered. Climatic data are taken from the Italian standard UNI 10349:1994 [15] and are shown in Table 3.
3. Results 3.1. Reference models The calculated annual heating requirements regarding the building models considered in the first step of the research work are presented in Fig. 3. Results are partially as expected. In fact MOD 2 e MOD 3 are less compacted and more exposed than MOD 1. So, in Canazei, a very cold locality, the energy need is higher than in the other towns. But in Trento, Florence and Rome this is no more true. This means that in mild and warm climates compactness is not a proper index to be used when designing an energy efficient building shape. However, in all the localities that have been considered models MOD 1, MOD 2 and MOD 3 show to have very similar energy requirements, while MOD 4, less compact than the other models and with a south facade not wider than MOD 1 and MOD 3, is more energy dispersant. 3.2. Free plant dimensions In the second part of the work, together with the models MOD 1e4, other models having different dimensions (though still parallelepipeds) have been introduced. In order to take into
Table 1 Dimensions concerning the models composed by the base module. Model
V [m3]
Si [m2]
Cf ¼ Si/V [m2/m3]
Cfs ¼ Ssouth/V [m2/m3]
Cfew ¼ SE
MOD MOD MOD MOD
1399.7 1399.7 1399.7 1399.7
751.7 881.7 894.2 1095.1
0.54 0.63 0.64 0.78
0.09 0.19 0.19 0.19
0.19 0.09 0.19 0.37
1 2 3 4
þ W/V
[m2/m3]
Awin,south [m2]
Awin,E
42.1 84.2 84.2 84.2
24.6 12.3 24.6 49.3
þ W
[m2]
V, Volume of the building; Cf, Shape coefficient; Cfs, South exposure coefficient; Cfew, East plus west exposure coefficient; Si, Surface of the envelope, ground floor slab included; Ssouth, Surface of the envelope - south side; SE þ W, Surface of the envelope east þ west side; Awin,south, Glazing surface - south side; Awin,E þ W, Glazing surface east þ west side.
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Table 2 Dimensions concerning the smaller models composed by the base module. Model
V [m3]
Si [m2]
Cf ¼ Si/V [m2/m3]
Cfs ¼ Ssouth/V [m2/m3]
Cfew ¼ SE
MOD MOD MOD MOD
699.8 699.8 699.8 699.8
492.5 557.3 505.4 576.7
0.70 0.80 0.72 0.82
0.09 0.19 0.19 0.19
0.19 0.09 0.19 0.37
1S 2S 3S 4S
þ W/V
[m2/m3]
Awin,south [m2]
Awin,E
21.0 42.1 42.1 42.1
12.3 6.2 12.3 24.6
þ W
[m2]
V, Volume of the building; Cf, Shape coefficient; Cfs, South exposure coefficient; Cfew, East plus west exposure coefficient; Si, Surface of the envelope, ground floor slab included; Ssouth, Surface of the envelope - south side; SE þ W, Surface of the envelope east þ west side; Awin,south, Glazing surface - south side; Awin,E þ W, Glazing surface east þ west side.
account the importance of the building shape with reference to the solar irradiation (and so to interpret the misleading results presented in Section 3.1), a new index has been considered called “south exposure coefficient” Cfs (Eq. (2)). This index, all other geometrical factors being equal (specified in the following), gives an idea of how the shape changes so to allow the better surface exposure to solar irradiation. In particular, to determine the dimensions of a parallelepiped and therefore a point on a graph where the Cf and Cfs indexes are compared, three parameters are needed (being a parallelepiped defined by three dimensions). In a spreadsheet the equations concerning the relationships between shape parameters and heating requirement Qh,nd (Eq. (4)) have been set, considering the other parameters as constant (climate data, which are characteristic of the location, ventilation, thermal transmittances, total solar energy transmittance of glazing surfaces, the ratio between glazing surface and opaque surface for each orientation). Then three meaningful parameters have been fixed: volume V of the building, energy demand Qh,nd and building height. So the geometrical plant dimensions of a building having a chosen energy requirement Qh,nd have been determined and the corresponding point on the graph (Si/V; Ssouth/V) has been printed (Fig. 4 where, for the four Italian localities, three different values of Qh,nd has been considered). Therefore each point printed in the graph (using different symbols) corresponds to a chosen level of energy demand in a certain place and for a defined height of the model, changing plant dimensions. In the graphs, points corresponding to the models MOD 1, MOD 2, MOD 3 and MOD 4 are printed as well. Points corresponding to MOD 2 and to MOD 3 are very close (mostly overlapping). This is due to the fact that they have similar south exposure and shape coefficient, and so they have even very similar heating requirements. It is now easy to notice that buildings with the same shape coefficient Cf have lower heating requirements if south facade has a wider area. This is directly linked to the possible shape that the building can present even considering its section profile. Points linked to lower energy requirements correspond to lower average values of the shape coefficient. The linear regressions relative to each locality and to each level of heating demand have been considered. The deviations between the calculated points (Si/V; Ssouth/V) printed in Fig. 4 and the relative straight lines of linear regression
for each determined heating requirements are very little. The correlation C between shape coefficient and south exposure coefficient is very good for points relative to a specific heating demand (C going from 0.99 to 1.00). The slopes of the straight lines of linear regression for the 4 localities are shown in Table 4. We can observe that slopes values are higher in colder localities. This means that a greater increase in southerly exposure is needed to compensate for a given increase in the shape coefficient. It is important to notice that the formula proposed by the standard to calculate the heating requirements does consider solar radiation and not only external temperature. Anyway, in those locations with cloudy skies conditions for the great part of the year, the orientation of buildings with the same compactness is less important than in sunny climates. In fact, in places with higher solar radiation values during winter season, exposition to south direction is much more important. On the contrary, when external temperature is low, compactness become the most important factor.
3.3. Volume halved In the first step, buildings with same shape and geometry but halved volume have been considered. Energy requirements calculus has been made following the same procedure described in Section 2.4. Results are presented in Fig. 5. Heating requirements per surface unit are greater than in the case with a double volume. MOD 3 S has, in comparison with the other ones, both a good compactness and a good south exposure and therefore demands the smallest amount of energy. The differences among the other three models are smaller in Rome and Florence, while they are greater in the colder climates of Canazei and Trento. The same procedure used for the double volume buildings has been followed. In Fig. 6 results are summed up showing the comparisons between points relative to different volumes but regarding the same level of heating demand. It is possible to
Table 3 Climatic data concerning the four Italian localities. Locality
Altitude [m asl]
Latitude
Longitude
DD
Mean Hdh [MJ/m2]
Mean Hbh [MJ/m2]
Canazei Trento Florence Rome
1465 194 50 20
46 290 N 46 040 N 43 460 N 41 530 N
11 460 E 11 070 E 11 150 E 12 29 E
4918 2569 1821 1415
3.0 3.0 3.3 3.6
4.3 4.3 3.9 4.8
DD, Degrees day mean; Hdh, Mean of the daily diffuse solar radiation for the heating season mean; Hbh, Mean of the daily direct solar radiation on a horizontal plane for the heating season.
Fig. 3. Annual requirements for heating regarding the four models in the chosen localities.
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Fig. 5. Annual requirements for heating regarding the four smaller models (halved volume).
observe that changing the volume the straight lines of linear regression change as well, though not much. This means that shape coefficient together with south exposure coefficient can give useful indications regardless the volume V of the building because the angular coefficient of the regression lines is comparable. 4. Some important consideration on an invariant building parameter: windows area
Fig. 4. Graphs (Si/V; Ssouth/V) with representation of points having the same heating requirement and of their straight lines of linear regression.
Here follow some important considerations concerning a building parameter that has been considered invariant till now, but that usually has a great importance in defining the bioclimatic and energy characteristics of the building itself: the windows area. In fact, we have supposed that windows on southern facade have a wider area than those on eastern and western ones, fixing their dimensions. But how much does windows area bear on the total energy requirements? Here follows the analysis of the variation of heating demand depending on the windows area. Fig. 7 shows the relationship between the ratio glazed surface/ total surface and heating requirements. The case of MOD 1 for the locality of Trento is considered. All thermal properties are the same as previously presented in Section 2.2. Demand is decreasing with the ratio glazed surface/total surface relative to south facade and growing with the ratio glazed surface/ total surface relative to east and west facades. The same behavior has been obtained for the other models and in the other localities as well. This means that, considering only heating demand, southern windows should be as large as possible, while east and west openings do not have real benefits on the overall annual heating requirements of the building. Of course, while designing the windows of a building and choosing their size, heating demand is not the only aspect to be taken into consideration. Other aspects are important such as visual comfort, healthiness of inner environment, architectural features and so on. Thermal transmittance value of windows considered in the base model is Uw ¼ 2.2 W/m2K, the upper limit prescribed by Italian regulations. It is a high value compared to windows performances
Table 4 Slopes of the straight lines of linear regression of the points (Si/V; Ssouth/V) printed in Fig. 4.
Mean
Canazei
Trento
Florence
Rome
0.98 (Qh ¼ 45 kW h/m2) 1.00 (Qh ¼ 55 kW h/m2) 1.03 (Qh ¼ 65 kW h/m2) 1.00
0.86 (Qh ¼ 20 kW h/m2) 0.85 (Qh ¼ 25 kW h/m2) 0.88 (Qh ¼ 30 kW h/m2) 0.86
0.85 (Qh ¼ 13 kW h/m2) 0.84 (Qh ¼ 15.5 kW h/m2) 0.83 (Qh ¼ 18 kW h/m2) 0.84
0.78 (Qh ¼ 5 kW h/m2) 0.78 (Qh ¼ 6 kW h/m2) 0.78 (Qh ¼ 7 kW h/m2) 0.78
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Fig. 7. Relationship between the ratio glazed surface/total surface and heating requirements for MOD 1 in Trento.
order to exploit solar energy coming from east and west direction. Again, a clever bioclimatic design must take into account both the factors (geometry and thermal characteristics of the materials used) from the very beginning thus avoiding bitter surprises during the calculus and verification phase of the project.
Fig. 6. Graphs (Si/V; Ssouth/V) representing points having the same heating requirement and the straight lines of linear regression for the halved volume.
used nowadays. So, it is interesting to see what happens if windows thermal transmittance Uw is lower (Fig. 8). When Uw ¼ 1.4 W/m2K, an intermediate value of glazed area can be found that minimizes heating requirements. Moreover, if Uw is lower than 1.2 W/m2K, heating requirements are lower the greater the windows area is. This means that besides windows area, thermal properties of glasses and of window frame are important in
Fig. 8. Relationship between glazed surface/total surface ratio and heating requirements with lower windows thermal transmittances Uw.
R. Albatici, F. Passerini / Building and Environment 46 (2011) 1624e1631
5. Conclusions The present work focuses on energy requirements during winter season by means of a monthly calculation according to standard EN ISO 13790:2008 [14], a stationary method in which a gain utilization factor is introduced in order to consider the nonstationary effects of inertia. Results give indications about the importance of compactness and exposure to the sun in different Italian localities (mild and warm climate). Compared to Depecker et al. [10] the present research confirms that compactness is more important in cold localities than in warm ones but, in addition, it formalizes the question concerning solar exposure by means of the introduction of a new index called south exposure coefficient Csf ¼ Ssouth/V (south wall area/volume). It is now easy to notice that buildings with the same shape coefficient Cf have lower heating requirements if the south facade has a wider area. Taking into account four different Italian localities with four different climatic conditions (from the mountains to the sea and with different attitude), results can be well spread to other European countries. Anyway, it must be taken into account that considering a bioclimatic approach, solar radiation plays a very important role. In a climate with mainly cloudy days compactness could be again more important than orientation. Representation of points characterized by fixed values of heating demand in a graph comparing Cf with Cfs gives some interesting information. It has been demonstrated that shape coefficient together with south exposure coefficient can give useful indications regardless the volume V of the building. Moreover, it has been explained that windows area and their thermal transmittance values can strongly influence energy calculation results. So, in mild and warm climate a clever bioclimatic design must take into account both factors (geometry and thermal characteristics of the materials used) from the very beginning thus avoiding bitter surprises during the calculus and verification phase of the project (usually done with the help of more advanced software using a dynamic state condition approach). Considering that values on the graphs change even if the physical properties of constructive elements change, it is not possible to provide graphs suitable for each particular situation. Designers should therefore consider graphs provided in this work as indications and apply an appropriate calculus method to their project. Spreadsheets based on a monthly method, even if it is a simplified approach, give results with a good level of accuracy and, in comparison with dynamic simulation software, needs low
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calculus time and are easy to be used by all designers since the very first stage of the design process. Considering solar exposure, future developments of the research should also take into account the cooling season by means of dynamic simulation software that better considers the effect of mass inertia. Finally, it must be noticed that in summer time overheating problems do not come from south facades (the sun has a high elevation over the horizontal plane, the component of the radiation reflected by the glass is greater than the transmitted one and the facade can be easily shaded) but from the west ones. Here, in fact, even if incident solar radiation has the same value of the one on the east facade, the cumulative effect of radiation and temperature that occurs during evening is higher (heliothermic effect). References [1] Okeil A. A holistic approach to energy efficient building forms. Energy and Buildings 2010;42(9):1437e44. [2] Marks W. Multicriteria optimisation of shape of energy-saving buildings. Building and Environment 1997;32(4):331e9. [3] Engstrom L. Energy in the built environment. Stockholm: Swedish Council for Building Research; 1988. [4] Ourghi R, Al-Anzi A, Krarti M. A simplified analysis method to predict the impact of shape on annual energy use for office buildings. Energy Conversion and Management 2007;48(1):300e5. [5] Jedrzejuk H, Marks W. Optimization of shape and functional structure of buildings as well as heat source utilisation. Partial problems solution. Building and Environment 2002;37(11):1037e43. [6] Jedrzejuk H, Marks W. Optimization of shape and functional structure of buildings as well as heat source utilisation example. Building and Environment 2002;37(12):1249e53. [7] Jedrzejuk H, Marks W. Optimization of shape and functional structure of buildings as well as heat source utilization. Basic theory. Building and Environment 2002;37(12):1379e83. [8] AlAnzi A, Seo D, Krarti M. Impact of building shape on thermal performance of office buildings in Kuwait. Energy Conversion and Management 2009; 50(3):822e8. [9] Aksoy UT, Inalli M. Impacts of some building passive design parameters on heating demand for a cold region. Building and Environment 2006;41 (12):1742e54. [10] Depecker P, Menezo C, Virgone J, Lepers S. Design of buildings shape and energetic consumption. Building and Environment 2001;36(5):627e35. [11] L.D. 311/06. Corrective and additional disposal to the Legislative Decree 19 August 2005, n. 192, concerning the implementation of the Directive 2002/91/ CE on the Energy performance of building; 2007 [in Italian]. [12] EN ISO 14683 Thermal bridges in building construction - linear thermal transmittance - simplified methods and default values; 2007. [13] UNI/TS 11300-1 Energy performance of buildings - part 1: evaluation of energy needs for space heating and cooling; 2008. in Italian. [14] EN ISO 13790 Energy performance of buildings - calculation of energy use for space heating and cooling; 2008. [15] UNI 10349 Heating and cooling of buildings. Climatic data; 1994 [in Italian].
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Building and Environment journal homepage: www.elsevier.com/locate/buildenv
Bioclimatic design of buildings considering heating requirements in Italian climatic conditions. A simplified approach Rossano Albatici*, Francesco Passerini University of Trento, Department of Civil and Environmental Engineering, Via Mesiano 77, 38123 Trento, Italy
a r t i c l e i n f o
a b s t r a c t
Article history: Received 27 October 2010 Received in revised form 5 January 2011 Accepted 27 January 2011
This paper presents a parametric approach to the definition of a proper building shape compared to the building heating requirement in the very first stage of the design process. A new simplified index is introduced, namely the south exposure coefficient Cfs. In fact, as far as bioclimatic architecture is concerned, the relationship between buildings and natural environment is very important both for the control of indoor comfort conditions and energy requirements. The building shape is a fundamental aspect of this relationship. Usually, in thermal behavior analysis this parameter is considered only from the point of view of compactness. This is a reductive approach, because two buildings with the same coefficient could have different shapes and so a different thermal behavior. Some aspects such as orientation, openings, exposure to atmospheric agents and natural elements must also be strictly considered. Moreover, in scientific literature no indications are given to designers who operate in mild and warm climate conditions. This is why the results of a research activity focused on heating requirements of buildings with different shapes and laid in the Italian territory are presented. Monthly calculations have been performed following the quasi-steady-state method suggested in the European standard. Outputs show that better results in the building energy performance can be achieved considering a bioclimatic (though simplified) approach since the very beginning. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Building shape Solar exposure Energy efficiency Bioclimatic architecture Parametric approach
1. Introduction During the design process of a new building, one of the most important aspects to be taken into consideration is the definition of a proper building shape in compliance with a complex set of requirements mutually interacting. As for energy efficiency, the best way is a holistic approach which is related to three main aspects: human thermal comfort in inner spaces, exploitation of energy from renewables, effect of urbanization on city climatology [1]. But usually “the shape of a building of given volume was optimized taking the minimum heat energy loss as the criterion” [2]. The attention toward these issues is not new since it has been tackled in many review papers [3]. However, the relationship between shape and energy requirements is still an open question. In fact, “no definitive and simple correlations were established between the basic attributes associated with buildings (such as form, window size and glazing type) and their total annual energy use and/or heating/cooling loads” [4]. Lately, a multicriteria optimization approach has been developed [5e7]. It is a valid and a very comprehensive approach but at * Corresponding author. Tel.: þ39 0461282622; fax: þ39 0461282672. E-mail address: [email protected] (R. Albatici). 0360-1323/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.buildenv.2011.01.028
the same time a complex one when it comes to use. Very often, in fact, the designer points out the building shape, or at least its main lines and volume distribution, in the pre-design phase, i.e. at the very first stage of conception. So, simpler indexes, easy to understand, are needed to help designers to move in a field where, usually, these parameters are otherwise “adopted on the basis of experience or by intuition” [7]. In the professional practice, the most used index is the shape coefficient defined as the ratio between the envelope surface of the building S (i.e. the external skin surfaces) and the inner volume of the building V:
Cf ¼ S=V
(1)
Recently, some researchers have extended the previous works including, in addition to the building shape, even windows areas and glazing type. Anyway the main index remains the Relative Compactness RC, defined as the ratio of the reciprocal of the building shape coefficient and the reciprocal of the compactness of a reference building [8]. A simple formula is given at the end of the mentioned article, but it is valid only for office building in Kuwait. The relationship between the place where the building is positioned and the local climate is a fundamental problem. So, together
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with the shape and the main envelope details, even the building orientation is to be considered [9]. In this field, Depecker et al. [10] studied the relationship between shape and energy requirements during the winter season in two French localities with different climate conditions, Paris and Carpentras (a town placed in southern France with a mild climate). In Paris they found a strong correlation between energy consumption and shape coefficient, in Carpentras they did not. So they did not give specific indications as far as building design in mild climates is concerned. With regard to climatic conditions similar to those of Carpentras they asserted: “A link between the energy consumption of a building and its shape can no longer be stated. As a consequence, that leaves architects to choose any shape”. It is opinion of the authors that the conclusion “in mild climates the architectural design can leave out of consideration the shape of buildings” is not appropriate. The main purpose of this research work is therefore to fill in that gap, in order to find relationships between buildings shape and heating requirements even in mild and warm climates. The matter is particularly important in Italy (and in countries with similar geographic conditions) since it is placed between the 47th and the 36th parallel north, more or less in the middle of the temperate zone in the northern hemisphere, with a prevalent northesouth development, going from the cold mountainous regions of the Alps (near the Austrian, Swiss and French border) to the warmer regions in the middle of the Mediterranean Sea, not too far from the Tunisian coasts in North Africa. To this end, not only does this work examine the relationship between building shape and energy requirements, but at the same time it considers both the shape coefficient and the facade orientation by means of the introduction of a new index, namely the south exposure coefficient Cfs.
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As far as the thermal properties of the envelope is concerned, the limit values given by the Italian legislation [11] have been considered for the city of Trento (194 m asl and 46 40 000 N 1170 000 E): - External walls U ¼ 0.34 W/(m2K) - Roof and ground floor U ¼ 0.30 W/(m2K) - Windows U ¼ 2.2 W/(m2K) The thermal bridges values correspond to standard EN ISO 14683:2007 [12] for external insulating layer and refer to internal dimensions of walls and roof: -
Connection external walleinternal partition Ji ¼ 0.1 W/(mK) Corner between two external walls Ji ¼ 0.15 W/(mK) Connection external walleroof Ji ¼ 0.15 W/(mK) Connection external walleground slab Ji ¼ 0.75 W/(mK) Connection external walleinner floor Ji ¼ 0.1 W/(mK)
The optical properties of glasses, ventilation and internal gains have been assumed considering the indications of technical standard UNI/TS 11300-1:2008 [13]: - Total solar energy transmittance of windows for Low E double glazing g ¼ 0.67 - 0.3 AC/h (air change/hour) - Internal gains of 3.9 W/m2
2.3. Modular models
2. Calculation models and methods
The research work has been divided into three main steps with increasing complexity. From the very beginning, together with the shape coefficient Cf, other two coefficients have been introduced, namely (the) south exposure coefficient Cfs that is the quotient of the area of south walls to the volume of the building:
2.1. Geometry
Cfs ¼ Ssouth =V
In the first part of the research, authors decided to work on a parallelepiped base module as in Depecker et al. [10], so to have a possible and meaningful comparison with previous researches results in this field. In particular, the base module, having a parallelepiped shape with a square floor, is defined as follows:
and the eastewest exposure coefficient Cfew that is the quotient of the area of east plus west walls to the volume of the building:
- Inner volume Vi ¼ 62.20 m3 - Floor surface Sf ¼ 23.04 m2 - External envelope surface Se ¼ 93.96 m2 See Fig. 1 where the main geometrical dimensions are represented. In order to give the model a clever energy feature from the very beginning, the north side and the roof have no openings while on the south side there is a glazing surface of 5.25 m2, equal to 40.6% of the total surface, net of delimitation elements. Both on the east and the west side there is a glazing surface of 1.54 m2, equal to 11.9% of the total surface, net of delimitation elements. The frame occupies the 9% of the hole for the big window, the 16% for the small one.
Cfew ¼ Seastþwest =V
(2)
(3)
The importance on the Cfs index is explained in the following Section 3.2. 2.3.1. First step: rectangular plant dimension In the first part of the work four extreme models composed by 16 base modules have been considered. They are presented in Fig. 2, going from the best to the worst compactness. As for compactness the best solution is MOD 1 (minimum Cf index), as for solar exposure the best solution is MOD 4 (maximum Cfs þ Cfew index) (see Table 1).
2.2. Thermal properties
2.3.2. Second step: free plant dimensions In the second part of the work, buildings with a parallelepiped shape have been considered as well, having the same glazing surface percentage for every orientation precisely as the models considered in the first part, but with free plant dimension, i.e. no more linkage to the base module dimensions and/or its multiple. In this way we have more freedom in finding the plant dimensional parameters that meet some certain fixed heating requirements.
In order to reach a simplified model that could be easily compared to real situations, standards, technical recommendations and laws in force in Italy have been considered.
2.3.3. Third step: halved building volume In the third part of the work, half of the volume of the previous models have been considered, since smaller models, such as those
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Fig. 1. Definition of the base model.
composed by 8 base models, whose volume is therefore 699.8 m3, allow a better evaluation of the influence of the volume on the relationship between shape and heating demand. Firstly, heating demands of four models composed by the base module 5.4 m 5.4 m 3 m have been calculated (Table 2). It is important to notice that Cfs and Cfew indexes are the same (both) for the smaller models and the corresponding previous ones, because halving the volume, the surfaces of the vertical facades have been halved as well. The extensions of the horizontal surfaces (roof and slabs) have been maintained constant. So the total envelope surfaces have not been halved, even if they have a smaller value. Therefore, the shape coefficients Cf of the smaller models are greater than the ones of the previous models. That means they are less compacted.
2.4. Calculation of heating requirements The calculation of heating requirements has been made using the monthly method presented in the standard EN ISO 13790:2008 [14]. It is a stationary calculation in which a coefficient, the “gain utilization factor”, is used to consider the non-stationary effects. The heating need is calculated as follows:
Qh;nd ¼ Qh;ht hh;gn Qh;gn
(4)
where Qh,ht is the total heat transfer from inside to outside, Qh,gn is the total heat gain, hh,gn is the gain utilization factor. Please refer to the standard itself for a complete description of the calculation code. The model prescribed by the standard to estimate the heating requirements is a simplified one. Nowadays, more advanced and
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Fig. 2. The four reference models composed by the base module.
detailed models are available working in dynamic state conditions. Anyway, spreadsheets based on a monthly method give results with a good level of accuracy and, in comparison with dynamic calculation software, need low calculus time and are easy to be used by all designers since the first stage of the design process. 2.5. Climatic data Depecker et al. [10] considered French localities whereas in the present research Italian localities have been taken into consideration, in order to give useful indications to designers working in climatic conditions milder and warmer than France. Four different localities have been selected, each one presenting different climatic conditions. Canazei and Trento, which are placed in northern Italy, in the Alpine region. Canazei is on a higher altitude (1465 m asl) and it is one of the coldest Italian localities. Florence is in north-central Italy, south of the Apennines. Rome is in the central part of Italy. The calculated energy requirements in Rome are very low and therefore no further south localities have been considered. Climatic data are taken from the Italian standard UNI 10349:1994 [15] and are shown in Table 3.
3. Results 3.1. Reference models The calculated annual heating requirements regarding the building models considered in the first step of the research work are presented in Fig. 3. Results are partially as expected. In fact MOD 2 e MOD 3 are less compacted and more exposed than MOD 1. So, in Canazei, a very cold locality, the energy need is higher than in the other towns. But in Trento, Florence and Rome this is no more true. This means that in mild and warm climates compactness is not a proper index to be used when designing an energy efficient building shape. However, in all the localities that have been considered models MOD 1, MOD 2 and MOD 3 show to have very similar energy requirements, while MOD 4, less compact than the other models and with a south facade not wider than MOD 1 and MOD 3, is more energy dispersant. 3.2. Free plant dimensions In the second part of the work, together with the models MOD 1e4, other models having different dimensions (though still parallelepipeds) have been introduced. In order to take into
Table 1 Dimensions concerning the models composed by the base module. Model
V [m3]
Si [m2]
Cf ¼ Si/V [m2/m3]
Cfs ¼ Ssouth/V [m2/m3]
Cfew ¼ SE
MOD MOD MOD MOD
1399.7 1399.7 1399.7 1399.7
751.7 881.7 894.2 1095.1
0.54 0.63 0.64 0.78
0.09 0.19 0.19 0.19
0.19 0.09 0.19 0.37
1 2 3 4
þ W/V
[m2/m3]
Awin,south [m2]
Awin,E
42.1 84.2 84.2 84.2
24.6 12.3 24.6 49.3
þ W
[m2]
V, Volume of the building; Cf, Shape coefficient; Cfs, South exposure coefficient; Cfew, East plus west exposure coefficient; Si, Surface of the envelope, ground floor slab included; Ssouth, Surface of the envelope - south side; SE þ W, Surface of the envelope east þ west side; Awin,south, Glazing surface - south side; Awin,E þ W, Glazing surface east þ west side.
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Table 2 Dimensions concerning the smaller models composed by the base module. Model
V [m3]
Si [m2]
Cf ¼ Si/V [m2/m3]
Cfs ¼ Ssouth/V [m2/m3]
Cfew ¼ SE
MOD MOD MOD MOD
699.8 699.8 699.8 699.8
492.5 557.3 505.4 576.7
0.70 0.80 0.72 0.82
0.09 0.19 0.19 0.19
0.19 0.09 0.19 0.37
1S 2S 3S 4S
þ W/V
[m2/m3]
Awin,south [m2]
Awin,E
21.0 42.1 42.1 42.1
12.3 6.2 12.3 24.6
þ W
[m2]
V, Volume of the building; Cf, Shape coefficient; Cfs, South exposure coefficient; Cfew, East plus west exposure coefficient; Si, Surface of the envelope, ground floor slab included; Ssouth, Surface of the envelope - south side; SE þ W, Surface of the envelope east þ west side; Awin,south, Glazing surface - south side; Awin,E þ W, Glazing surface east þ west side.
account the importance of the building shape with reference to the solar irradiation (and so to interpret the misleading results presented in Section 3.1), a new index has been considered called “south exposure coefficient” Cfs (Eq. (2)). This index, all other geometrical factors being equal (specified in the following), gives an idea of how the shape changes so to allow the better surface exposure to solar irradiation. In particular, to determine the dimensions of a parallelepiped and therefore a point on a graph where the Cf and Cfs indexes are compared, three parameters are needed (being a parallelepiped defined by three dimensions). In a spreadsheet the equations concerning the relationships between shape parameters and heating requirement Qh,nd (Eq. (4)) have been set, considering the other parameters as constant (climate data, which are characteristic of the location, ventilation, thermal transmittances, total solar energy transmittance of glazing surfaces, the ratio between glazing surface and opaque surface for each orientation). Then three meaningful parameters have been fixed: volume V of the building, energy demand Qh,nd and building height. So the geometrical plant dimensions of a building having a chosen energy requirement Qh,nd have been determined and the corresponding point on the graph (Si/V; Ssouth/V) has been printed (Fig. 4 where, for the four Italian localities, three different values of Qh,nd has been considered). Therefore each point printed in the graph (using different symbols) corresponds to a chosen level of energy demand in a certain place and for a defined height of the model, changing plant dimensions. In the graphs, points corresponding to the models MOD 1, MOD 2, MOD 3 and MOD 4 are printed as well. Points corresponding to MOD 2 and to MOD 3 are very close (mostly overlapping). This is due to the fact that they have similar south exposure and shape coefficient, and so they have even very similar heating requirements. It is now easy to notice that buildings with the same shape coefficient Cf have lower heating requirements if south facade has a wider area. This is directly linked to the possible shape that the building can present even considering its section profile. Points linked to lower energy requirements correspond to lower average values of the shape coefficient. The linear regressions relative to each locality and to each level of heating demand have been considered. The deviations between the calculated points (Si/V; Ssouth/V) printed in Fig. 4 and the relative straight lines of linear regression
for each determined heating requirements are very little. The correlation C between shape coefficient and south exposure coefficient is very good for points relative to a specific heating demand (C going from 0.99 to 1.00). The slopes of the straight lines of linear regression for the 4 localities are shown in Table 4. We can observe that slopes values are higher in colder localities. This means that a greater increase in southerly exposure is needed to compensate for a given increase in the shape coefficient. It is important to notice that the formula proposed by the standard to calculate the heating requirements does consider solar radiation and not only external temperature. Anyway, in those locations with cloudy skies conditions for the great part of the year, the orientation of buildings with the same compactness is less important than in sunny climates. In fact, in places with higher solar radiation values during winter season, exposition to south direction is much more important. On the contrary, when external temperature is low, compactness become the most important factor.
3.3. Volume halved In the first step, buildings with same shape and geometry but halved volume have been considered. Energy requirements calculus has been made following the same procedure described in Section 2.4. Results are presented in Fig. 5. Heating requirements per surface unit are greater than in the case with a double volume. MOD 3 S has, in comparison with the other ones, both a good compactness and a good south exposure and therefore demands the smallest amount of energy. The differences among the other three models are smaller in Rome and Florence, while they are greater in the colder climates of Canazei and Trento. The same procedure used for the double volume buildings has been followed. In Fig. 6 results are summed up showing the comparisons between points relative to different volumes but regarding the same level of heating demand. It is possible to
Table 3 Climatic data concerning the four Italian localities. Locality
Altitude [m asl]
Latitude
Longitude
DD
Mean Hdh [MJ/m2]
Mean Hbh [MJ/m2]
Canazei Trento Florence Rome
1465 194 50 20
46 290 N 46 040 N 43 460 N 41 530 N
11 460 E 11 070 E 11 150 E 12 29 E
4918 2569 1821 1415
3.0 3.0 3.3 3.6
4.3 4.3 3.9 4.8
DD, Degrees day mean; Hdh, Mean of the daily diffuse solar radiation for the heating season mean; Hbh, Mean of the daily direct solar radiation on a horizontal plane for the heating season.
Fig. 3. Annual requirements for heating regarding the four models in the chosen localities.
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Fig. 5. Annual requirements for heating regarding the four smaller models (halved volume).
observe that changing the volume the straight lines of linear regression change as well, though not much. This means that shape coefficient together with south exposure coefficient can give useful indications regardless the volume V of the building because the angular coefficient of the regression lines is comparable. 4. Some important consideration on an invariant building parameter: windows area
Fig. 4. Graphs (Si/V; Ssouth/V) with representation of points having the same heating requirement and of their straight lines of linear regression.
Here follow some important considerations concerning a building parameter that has been considered invariant till now, but that usually has a great importance in defining the bioclimatic and energy characteristics of the building itself: the windows area. In fact, we have supposed that windows on southern facade have a wider area than those on eastern and western ones, fixing their dimensions. But how much does windows area bear on the total energy requirements? Here follows the analysis of the variation of heating demand depending on the windows area. Fig. 7 shows the relationship between the ratio glazed surface/ total surface and heating requirements. The case of MOD 1 for the locality of Trento is considered. All thermal properties are the same as previously presented in Section 2.2. Demand is decreasing with the ratio glazed surface/total surface relative to south facade and growing with the ratio glazed surface/ total surface relative to east and west facades. The same behavior has been obtained for the other models and in the other localities as well. This means that, considering only heating demand, southern windows should be as large as possible, while east and west openings do not have real benefits on the overall annual heating requirements of the building. Of course, while designing the windows of a building and choosing their size, heating demand is not the only aspect to be taken into consideration. Other aspects are important such as visual comfort, healthiness of inner environment, architectural features and so on. Thermal transmittance value of windows considered in the base model is Uw ¼ 2.2 W/m2K, the upper limit prescribed by Italian regulations. It is a high value compared to windows performances
Table 4 Slopes of the straight lines of linear regression of the points (Si/V; Ssouth/V) printed in Fig. 4.
Mean
Canazei
Trento
Florence
Rome
0.98 (Qh ¼ 45 kW h/m2) 1.00 (Qh ¼ 55 kW h/m2) 1.03 (Qh ¼ 65 kW h/m2) 1.00
0.86 (Qh ¼ 20 kW h/m2) 0.85 (Qh ¼ 25 kW h/m2) 0.88 (Qh ¼ 30 kW h/m2) 0.86
0.85 (Qh ¼ 13 kW h/m2) 0.84 (Qh ¼ 15.5 kW h/m2) 0.83 (Qh ¼ 18 kW h/m2) 0.84
0.78 (Qh ¼ 5 kW h/m2) 0.78 (Qh ¼ 6 kW h/m2) 0.78 (Qh ¼ 7 kW h/m2) 0.78
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Fig. 7. Relationship between the ratio glazed surface/total surface and heating requirements for MOD 1 in Trento.
order to exploit solar energy coming from east and west direction. Again, a clever bioclimatic design must take into account both the factors (geometry and thermal characteristics of the materials used) from the very beginning thus avoiding bitter surprises during the calculus and verification phase of the project.
Fig. 6. Graphs (Si/V; Ssouth/V) representing points having the same heating requirement and the straight lines of linear regression for the halved volume.
used nowadays. So, it is interesting to see what happens if windows thermal transmittance Uw is lower (Fig. 8). When Uw ¼ 1.4 W/m2K, an intermediate value of glazed area can be found that minimizes heating requirements. Moreover, if Uw is lower than 1.2 W/m2K, heating requirements are lower the greater the windows area is. This means that besides windows area, thermal properties of glasses and of window frame are important in
Fig. 8. Relationship between glazed surface/total surface ratio and heating requirements with lower windows thermal transmittances Uw.
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5. Conclusions The present work focuses on energy requirements during winter season by means of a monthly calculation according to standard EN ISO 13790:2008 [14], a stationary method in which a gain utilization factor is introduced in order to consider the nonstationary effects of inertia. Results give indications about the importance of compactness and exposure to the sun in different Italian localities (mild and warm climate). Compared to Depecker et al. [10] the present research confirms that compactness is more important in cold localities than in warm ones but, in addition, it formalizes the question concerning solar exposure by means of the introduction of a new index called south exposure coefficient Csf ¼ Ssouth/V (south wall area/volume). It is now easy to notice that buildings with the same shape coefficient Cf have lower heating requirements if the south facade has a wider area. Taking into account four different Italian localities with four different climatic conditions (from the mountains to the sea and with different attitude), results can be well spread to other European countries. Anyway, it must be taken into account that considering a bioclimatic approach, solar radiation plays a very important role. In a climate with mainly cloudy days compactness could be again more important than orientation. Representation of points characterized by fixed values of heating demand in a graph comparing Cf with Cfs gives some interesting information. It has been demonstrated that shape coefficient together with south exposure coefficient can give useful indications regardless the volume V of the building. Moreover, it has been explained that windows area and their thermal transmittance values can strongly influence energy calculation results. So, in mild and warm climate a clever bioclimatic design must take into account both factors (geometry and thermal characteristics of the materials used) from the very beginning thus avoiding bitter surprises during the calculus and verification phase of the project (usually done with the help of more advanced software using a dynamic state condition approach). Considering that values on the graphs change even if the physical properties of constructive elements change, it is not possible to provide graphs suitable for each particular situation. Designers should therefore consider graphs provided in this work as indications and apply an appropriate calculus method to their project. Spreadsheets based on a monthly method, even if it is a simplified approach, give results with a good level of accuracy and, in comparison with dynamic simulation software, needs low
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calculus time and are easy to be used by all designers since the very first stage of the design process. Considering solar exposure, future developments of the research should also take into account the cooling season by means of dynamic simulation software that better considers the effect of mass inertia. Finally, it must be noticed that in summer time overheating problems do not come from south facades (the sun has a high elevation over the horizontal plane, the component of the radiation reflected by the glass is greater than the transmitted one and the facade can be easily shaded) but from the west ones. Here, in fact, even if incident solar radiation has the same value of the one on the east facade, the cumulative effect of radiation and temperature that occurs during evening is higher (heliothermic effect). References [1] Okeil A. A holistic approach to energy efficient building forms. Energy and Buildings 2010;42(9):1437e44. [2] Marks W. Multicriteria optimisation of shape of energy-saving buildings. Building and Environment 1997;32(4):331e9. [3] Engstrom L. Energy in the built environment. Stockholm: Swedish Council for Building Research; 1988. [4] Ourghi R, Al-Anzi A, Krarti M. A simplified analysis method to predict the impact of shape on annual energy use for office buildings. Energy Conversion and Management 2007;48(1):300e5. [5] Jedrzejuk H, Marks W. Optimization of shape and functional structure of buildings as well as heat source utilisation. Partial problems solution. Building and Environment 2002;37(11):1037e43. [6] Jedrzejuk H, Marks W. Optimization of shape and functional structure of buildings as well as heat source utilisation example. Building and Environment 2002;37(12):1249e53. [7] Jedrzejuk H, Marks W. Optimization of shape and functional structure of buildings as well as heat source utilization. Basic theory. Building and Environment 2002;37(12):1379e83. [8] AlAnzi A, Seo D, Krarti M. Impact of building shape on thermal performance of office buildings in Kuwait. Energy Conversion and Management 2009; 50(3):822e8. [9] Aksoy UT, Inalli M. Impacts of some building passive design parameters on heating demand for a cold region. Building and Environment 2006;41 (12):1742e54. [10] Depecker P, Menezo C, Virgone J, Lepers S. Design of buildings shape and energetic consumption. Building and Environment 2001;36(5):627e35. [11] L.D. 311/06. Corrective and additional disposal to the Legislative Decree 19 August 2005, n. 192, concerning the implementation of the Directive 2002/91/ CE on the Energy performance of building; 2007 [in Italian]. [12] EN ISO 14683 Thermal bridges in building construction - linear thermal transmittance - simplified methods and default values; 2007. [13] UNI/TS 11300-1 Energy performance of buildings - part 1: evaluation of energy needs for space heating and cooling; 2008. in Italian. [14] EN ISO 13790 Energy performance of buildings - calculation of energy use for space heating and cooling; 2008. [15] UNI 10349 Heating and cooling of buildings. Climatic data; 1994 [in Italian].