The Compactness Indicators of Solids Applied to Analysis of Geometric Efficiency of Buildings

Abstract

The authors redefine and generalize the so-called relative ratio of compactness of solid with respect to sphere and cube introduced by Mahdavi and Gurtekin. The authors propose such new indicators as a relative ratio of solid compactness in the shape of a prism-shaped solid related to a cuboid with a square base and a given height (e.g. the height of the analyzed storey), a solid compactness indicator defined for the basis of the prism relative to the square. They introduce also other indicators: a relative defect of the perimeter and area. The test of indicators formulated and described in the paper was carried out in two groups of buildings: existing (spotted locally) and those whose designs can be found in the selected catalog available on the website. In addition to the compactness ratios calculated for existing and designed buildings, an analysis of the size of the indicators for the adopted building research models was made. Proposed indicators allow for a description of the compactness of the building model with an indication of the deviation from the real ideal solid. The introduced geometric determinants of solids may be useful in the initial phase of searching for satisfactory design solutions.

Geometric Aspects of Assessing the Amount of Material Consumption in the Construction of a Designed Single-Family House

“…usable area of 100-150 m 2 (data according to the Central Statistical Office-the most statistically popular range of selected houses in Poland and Europe); -free-standing buildings with a rectangular plan; -single-story (one-story) buildings with no usable attic, no basement, and no garage; -basic building materials for the housing: H + H blocks, concrete, and steel; (a) with a large 81% area defect, A R − A = 88 u 2 , RDA = 0.81 and zero's perimeter defect, RDP = 0, (b) with a 57% perimeter defect, P -P R = 24 u, RDP = 0.57 and, with a 35% area defect, A R − A = 38 u 2 , RDA = 0.35, and (c) with a 95% perimeter defect, P − P R = 40 u, RDP = 0.95 and, with a 41% area defect, A R − A = 44 u 2 , RDA = 0.41 (taken from [14] with permission from the authors). with a large 81% area defect, AR − A = 88 u 2 , RDA = 0.81 and zero's perimeter defect, RDP = 0, (b) with a 57% perimeter defect, P -PR = 24 u, RDP = 0.57 and, with a 35% area defect, AR − A = 38 u 2 , RDA = 0.35, and (c) with a 95% perimeter defect, P − PR = 40 u, RDP = 0.95 and, with a 41% area defect, AR − A = 44 u 2 , RDA = 0.41 (taken from [14] with permission from the authors). a rectangular polygon with a perimeter defect equal to zero, and (c) a rectangular polygon with a perimeter defect greater than zero (Figure taken from [14] with approval from the authors).…”

“…with a large 81% area defect, AR − A = 88 u 2 , RDA = 0.81 and zero's perimeter defect, RDP = 0, (b) with a 57% perimeter defect, P -PR = 24 u, RDP = 0.57 and, with a 35% area defect, AR − A = 38 u 2 , RDA = 0.35, and (c) with a 95% perimeter defect, P − PR = 40 u, RDP = 0.95 and, with a 41% area defect, AR − A = 44 u 2 , RDA = 0.41 (taken from [14] with permission from the authors). a rectangular polygon with a perimeter defect equal to zero, and (c) a rectangular polygon with a perimeter defect greater than zero (Figure taken from [14] with approval from the authors).…”

“…The search for cheap buildings in construction and energy consumption led to the concept of geometric building efficiency [14] and then to the geometric compactness of the building structure-the basic parameter characterizing this efficiency. Many different indicators have been formulated in the literature regarding the geometric shape of a building, including compactness indicators, and many of them are used to describe and estimate construction costs and energy consumption [15][16][17][18][19].…”

“…Instead of the A/V ratio, A/S is assumed, where A is the external envelope area of a building and S is the heated area. In [14], a whole family of compactness indicators was introduced; some of these are described in Section 3.…”

“…The geometric efficiency of a building [14] that meets the assumed size parameters (cubic capacity, usable area) is a set of geometric features that makes the building functional, economical (with a low energy demand) in construction and maintenance, safe in use, and aesthetic. An important geometric feature of the building is its compactness.…”