## 4 Design Values of Shape Coefficients
### Pitched Roofs  
Owing the fact that few data for pitched roofs have been collected in the framework of the European Snow Load Research Project [15], in the present study the main reference is the previously mentioned database of Hoibe [24,25], which contains information on more than 200 buildings located in various Norwegian areas. In these areas, the ground snow  
Figure 5: Design shape coefficient for flat roofs (\(\mu_{1,d}\)) as a function of the coefficient of variation of ground snow load (\(COV_{g}\)), parameterized in terms of exposure conditions (sheltered: green lines, normal: blue lines). (**a**) Norwegian database; (**b**) Norwegian database assuming \(COV_{\mu_{1}}=0.4\). loads associated with an annual probability of exceedance \(p=0.02\) belong to the interval \(\left[0.5-4.5\ \mathrm{kN/m^{2}}\right]\), and mostly vary between 1.0 and 2.0 \(\mathrm{kN/m^{2}}\). That database, representing one of the most comprehensive collections of measurements for snow load on roofs, has been also used for the development of the new model for gabled/pitched roofs provided in the new version of the EN1991-1-3 [17]. Following [16], the observed data are grouped in different exposure classes as a function of the so-called asymmetry coefficient (\(C_{a}\)), which is the ratio between the snow load on the leeward side and the snow load on the windward side of the roof. The asymmetry coefficient \(C_{a}\) usually satisfies the inequalities of  
\[1.0\leq C_{a}\leq 1.1, \tag{10}\]  
in sheltered conditions,  
\[1.1\leq C_{a}\leq 1.8 \tag{11}\]  
in normal conditions, and  
\[C_{a}>1.8 \tag{12}\]  
in exposed conditions. Starting from the data collected in the above recalled database, design shape coefficients (\(\mu_{2,d}\)) have been evaluated for pitched roofs of different slopes, according to the procedure already presented for flat roofs in the previous section. The results are summarized in Figure 7, which illustrates the variation of design shape coefficients as a function of the pitch angle \(\alpha\) and \(COV_{g}\) for different exposure conditions (exposed, normal, and sheltered) in the leeward and windward sides of the roofs. Figure 6: Design shape coefficient for flat roofs (\(\mu_{1,d}\)) as a function of the coefficient of variation (\(COV_{g}\)) of ground snow load, parameterized in terms of exposure conditions (sheltered: green lines, normal: blue lines, exposed: red lines) and distribution of the snow load on ground (log-normal: circular markers, Gumbel: lozenge markers) for 25 Italian weather stations. The outcomes are compared with the provisions of the EN1991-1-3 model (in cyan) and the prEN1991-1-3 model (in magenta). The diagram shows the so-called \"leeward+windward\" curves, which correspond to a \"balanced\" situation and are obtained as the mean value between the leeward and windward side values. Similar to those given in Figure 4, the \(\mu_{2,d}-COV_{g}\) curves can be derived for pitched roofs for given intervals of the pitch angle. The curves thus obtained, again characterized by an annual probability of exceedance \(p=0.02\), are compared with the \(\mu_{2,d}\) values given in EN1991-1-3:2003 or in prEN1991-1-3:2020 in Figures 8-10. In these figures, solid horizontal lines represent constant shape coefficients (\(\mu_{2,d}\)) provided in EN1991-1-3:2003, while the dashed horizontal lines represent constant shape coefficients provided in prEN1991-1-3:2020 for gabled roofs. Due to the lack of information in exposed conditions for such roofs, in Figure 8, which refers to pitch angles \(10^{\circ}<\alpha<15^{\circ}\), only two exposure conditions are considered: sheltered (green curves) and normal (blue curves). In Figures 9 and 10, which refer to pitch angles \(25^{\circ}<\alpha<30^{\circ}\) and \(40^{\circ}<\alpha<45^{\circ}\), respectively, the exposed condition is also taken into account.