The results show four tables, where two are dedicated to show the results for the individual factors results and the ranking process results for both complexities.
Geometric Complexity Results
The geometric complexity results show the results in two tables; The table 11 shows the results for each factor and the Table 12 shows the ranking process results. The foundation, shell, and interior were used to test these factors. Table 11 shows the results of the test models mentioned above vertically while the building main parts are horizontal.
General Geometric General Entropy refers to the the entropy that can be found in the building main part as an entire solid or solids.
Building
Variety refers to the standard deviation of the individual entropies scores for all the instances that made a building main part Number of Elements refers to the numbers of solids that make a building main part.
Geometric Complexity Related Factor Results
Foundation Shell Interior
Building 2
Table 11 Geometric complexity results.
1 General Geometric Entropy
In table 11, the foundation results for this factor shows that the building 3 has a foundation with the highest general geometric entropy, while the building 4 has the lowest general geometric entropy. Building 1 and 2 have very close scores, but the building 1 is higher by 0.3. These last two buildings scores are higher than the building 4 and lower than building 3.
The test results for the shell shows that the building 4 has the highest general geometric entropy while the building 1 has the lowest. Similarly, building 2 has lower entropy than building 3 and a higher than building 1.
The general geometric entropy for the interior has a similar trending. Here the building 4 scored the highest and building 1 the lowest. Building 2 score is higher than building 1, but lower than building 3.
2 Variety
From the table 11 can be observed that the highest variety score for the foundation results is obtained by the building 3, on the other hand, all the other buildings scored zero.
For the shell variety, the building 3 has the highest variety; then the second highest is the building 4. The building 1 and 2 had the lowest scores, but the building 1 was higher by 0.3.
The interior results showed that the building 1 has a variety of zero, while the highest score was obtained by the building 2. Building 3 was the second highest, and building 4 was the third highest.
3 Number of elements
The table 11 shows that the foundation of the building 4 has a higher number of elements while the second highest is obtained by the building 3. The building 1 and 2 have only one element.
The shell highest score is obtained by the building 4; then the second highest is scored by the building 3, this was followed by the building 2 and 1 respectively.
The interior follows the same trending. Here the highest score is obtained by the building 4, then the second highest by the building 3, this was followed by the building 2 and 1 respectively Table 12b Foundation sorted results.
11.8 3 2.86 3 76 4
Table 12a Geometric complexity results.
Table 12c Shell sorted results.
Table 12d Interior sorted results.
The grouping factor process showed that the foundation for the building 3 is the one that has the highest geometric complexity, the score of the foundation of the building 4 followed this, then the building 1 and the least geometric complex is the foundation of the building 2. See table 12a,12b,12e,12f and 12i.
16.67 4 2.86 2 699 4
Table 12e Geometric complexity weighted results.
Table 12f Foundation weight summation. Table 12g Shell weight summation. Table 12h Interior weight summation.
Weight
Table 12i Foundation ranking. Table 12j Shell ranking. Table 12k Interior ranking.
Sorted
3 Highest 4 Highest 4 Highest
4 3 3
1 2 2
2 Lowest 1 Lowest 1 Lowest
The shell that has the highest geometric complexity is the shell of the building 4, followed by the building 3, then building 2 and finally building 1. See table
12a,12c,12e,12g and12j.
The interiors follow a similar trending. The interior of the building 4 is the most geometric complex, followed by the building 3, then building 2 and 1 respectively. See table 12a,12c,12e,12h and 12k.
Construction Complexity Results
The construction complexity results show the final values in two tables; The table 13 shows the results for each factor and the table 14 shows the ranking process results. Table 13 shows the results for the construction complexity factors showing two buildability and multidisciplinarity cases for each building.
Table 13 Construction complexity results.
1 Buildability
The buildability results in table 13 show a reduction in the buildability when the external building walls and structural frames are changed from cast in place to precast.
This reduction trending can be observed in every building.
For the cast in place score, the building 1,2,4 obtained the same results of 24.1 while the building 3 had a lower score of 22.36.
For the precast score, the building 1 and 2 had the same and the lowest score compared with the other buildings. Building 3 scored the highest in construction while building 4 scored the second highest.
2 Multidisciplinarity
The multidisciplinarity status where there are not finishes in the building showed less involved disciplines than the status where the finishes are included in the model. This trending can be observed in all the buildings.
The building 4 scored the highest for the status where there are no finishes included, this was followed by the building 3, then by the building 2 and 1, respectively.
The same logic trend is followed when the finishes were added to the building.
Here the building 4 scores the highest and building 1 the lowest.
3 Size
The size highest score is obtained by the building 4, followed by the building 3,2 and 1, respectively.
4 Group Factor Results
The ranking process results are applied to the building with all elements set as cast in place. The results showed that the building 4 is the one with the highest construction complexity, this building was followed by the building 3, 2 and 1 respectively. See table from14a to 14e.
Table 14a Construction complexity results.
Weight
Table 14b Construction complexity sorted results.
Table 14c Construction complexity weighted results.
Sorted
Table 14e Construction complexity ranking.
7 Discussion
In this research, a method to calculate two types of complexities directly from a building model was developed. Its approach to apparent cases confirmed the testing accuracy of the obtained scores by this method. However, this method has some limitations regarding its implementation and testing. Bellow, it will be discussed the relevant cases from the above-obtained results, also the implications and limitations obtained from the research.