BIM As The Future Standard In Elaboration Of Building
Designs Based On Parametric / Mathematical Formulae
Piotr Nabzdyk
BIM As The Future Standard Elaboration Of Building Designs Based On Parametric / Mathematical Formulae
The Introduction
BIM
As The Future
Presentation
title Standard In Elaboration Of Bulding Designs Based On Parametric /
Mathematical Formulae
What is BIM?
• BIM (Building Information Modelling) is both a tool and a process, and one cannot realistically exist without the other
• It creates the digital models of the building objects in conjunction with all the other design branches that are mutually coordinated and linked • It is a digital representation of physical and functional characteristics of a designing abstract that acts as a shared knowledge resource for information about a facility forming reliable basis for decisions during its life cycle from inception onward
• It is the design tool that enables implementation of information to programmable environment, describing in an unambiguous way the digital model which is internally linked between the particular design views
BIM
As The Future
Presentation
title Standard In Elaboration Of Bulding Designs Based On Parametric /
Mathematical Formulae
CAD Project
CAD‐based workflow
BIM Project
BIM‐based workflow
Differences between designing cultures are shown on the diagrams above.
Source: Mastering Revit Architecture
BIM
As The Future
Presentation
title Standard In Elaboration Of Bulding Designs Based On Parametric /
Mathematical Formulae
Why BIM?
• It downsizes the amount of the design files, eliminates errors and reveals any design collisions (e.g. between the branches), even in the preliminary stage of the project
• The process of BIM generates information models and their associated information that are used throughout the lifecycle of building/infrastructure facilities or assets
• BIM eliminates the constant pressure of control of expenditures
• All tools integrated in one programme facility /suite
• More effective cooperation with engineers & consultants
• No need to save the project files using various file extensions
• Competitive advantage through high quality visualisations & virtual walks
• Optimalisation of building construction process & maintaining building assets
BIM
As The Future
Presentation
title Standard In Elaboration Of Bulding Designs Based On Parametric /
Mathematical Formulae
Why BIM?
• BIM environment and its parametric nature can be developed by user through introduction of the mathematic formulae into the programme components.
BIM As The Future Standard Elaboration Of Building Designs Based On Parametric / Mathematical Formulae
The Purpose
BIM
As The Future
Presentation
title Standard In Elaboration Of Bulding Designs Based On Parametric /
Mathematical Formulae
What is the purpose of this presentation?
• To prove that parameters used by the creation of the component with the use of BIM‐based application return the series of types of windows dependent on a mathematical formula related to its general physical dimensions • To show that components created with the use of parameters dependent on each other and defined with the use of mathematical formulae, can return the group of components being proportionally the same
• To prove that the more formulae entered the higher the control of the
component is
BIM As The Future Standard Elaboration Of Building Designs Based On Parametric / Mathematical Formulae
The Research
BIM
As The Future
Presentation
title Standard In Elaboration Of Bulding Designs Based On Parametric /
Mathematical Formulae
The research consist of two parts
First Part
• The first part concerns constructing a single window with the arch.
The window has the parameters which define its basic sizes as follows (parameters' names in the brackets) :
‐ height (Height)
‐ width (Width)
BIM
As The Future
Presentation
title Standard In Elaboration Of Bulding Designs Based On Parametric /
Mathematical Formulae
‐window frame recess i.e. towards the plane of the external elevation (Frame Recess)
‐ the width of the external sill (Ext Sill Width) ‐ the height of the window arch (Arch Height)
To add & assign the parameters to the dimensioned window, we have to find the Family Type tab (or press “FT”) in the “Modify” tool in the “properties” panel and click it.
BIM
As The Future
Presentation
title Standard In Elaboration Of Bulding Designs Based On Parametric /
Mathematical Formulae
The Family Types window opens. Let’s add the parameter named Arch Height
which is responsible for changing the arch height in window (in Parameter
Properties window). BIM
As The Future
Presentation
title Standard In Elaboration Of Bulding Designs Based On Parametric /
Mathematical Formulae
To bind the window extrusion in the wall (void extrusion) with the window frame, let’s indicate the edge of window opening and then choose Edit Extrusion tab on the contextual Mode panel
BIM
As The Future
Presentation
title Standard In Elaboration Of Bulding Designs Based On Parametric /
Mathematical Formulae
The sketch mode opens. While in sketch mode, we need to assign the Arch Height parameter to the arch of the window (dimensioned from the tangent of the arch to the lower end of the arch)
Let’s assign the parameter (defined earlier) to the dimension of the arch ‐ select the label “Arch Height”
BIM
As The Future
Presentation
title Standard In Elaboration Of Bulding Designs Based On Parametric /
Mathematical Formulae
The same way we can assign the parameters to the other main dimensions of the window (Height, Width, Default Sill Height) – diagram to the left. The diagram to the right shows the window with the assigned parameters with the arch height equal to 300mm.
BIM
As The Future
Presentation
title Standard In Elaboration Of Bulding Designs Based On Parametric /
Mathematical Formulae
After the parameters are assigned, the window requires analysis of its behaviour
when the changes are applied to the arch and other general dimensions. After typing “FT” (Family Type) the programme creates new window types (e.g. 150x150cm f=30cm or 200x200 f=40cm). At this stage no formulae are entered, however the parameters created allow to model any window with the arch of almost any “f” value (height of the arch).
BIM
As The Future
Presentation
title Standard In Elaboration Of Bulding Designs Based On Parametric /
Mathematical Formulae
Second Part
• The second part concerns the creation of the dependencies between main parameters (defined earlier) in order to obtain the series of window types of specific proportions. The proportions for the new window types are based on the golden ratio formula (φ)
(a + b) / a = a / b = φ)
where a is a longer segment of a line
b is a shorter segment of a line
φ is a golden ratio
BIM
As The Future
Presentation
title Standard In Elaboration Of Bulding Designs Based On Parametric /
Mathematical Formulae
The golden ratio (φ or phi) is represented as the relation between two unequal segments (longer "a" and shorter "b") of a line, in such a way that the ratio of the sum of "a" and "b" to segment "a" is equal to ratio of segment "a" to the "b" segment.
a + b
a
=
a
b
The golden ratio formula can also be expressed with the use of numerical values as shown in the following equation:
φ = (1 + √5) / 2 = 1.6180339887…
BIM
As The Future
Presentation
title Standard In Elaboration Of Bulding Designs Based On Parametric /
Mathematical Formulae
The golden ratio formula will look in the BIM programme as shown below:
φ = (sqrt (5) + 1)/2 where
sqrt ‐ square root
digit in brackets ‐ the number from which the root is extracted.
Let’s go back to the previous formula:
(a + b) / a = a / b = φ)
Let"a" represent half of the width of a window (“1/2 * Width” parameter) and "b" represent the height of arch (“Arch Height” parameter).
BIM
As The Future
Presentation
title Standard In Elaboration Of Bulding Designs Based On Parametric /
Mathematical Formulae
"a" represents half of the width of a window (“1/2 * Width” parameter) and "b" represents the height of arch (“Arch Height” parameter).
Let’s make Arch Height dependant on the Width of the window.
We need to derive the mathematical formula for the quotient of 1/2 * Width and Arch Height to obtain the Arch Height value.
φ = (sqrt (5) + 1)/2 = 1/2 * Width / Arch Height //*2
(sqrt (5) + 1) = Width / Arch Height //* Arch Height (sqrt (5) + 1) * Arch Height = Width //:(sqrt (5) +1)
Arch Height = Width / (sqrt (5) +1)
BIM
As The Future
Presentation
title Standard In Elaboration Of Bulding Designs Based On Parametric /
Mathematical Formulae
Arch Height = Width / (sqrt (5) +1)
Let’s place this formula by "Arch Height" parameter under "Formula" column as shown in the diagram to the right. After the formula is placed the value (under “Value” column) for Arch Height changes automatically to 309mm.
BIM
As The Future
Presentation
title Standard In Elaboration Of Bulding Designs Based On Parametric /
Mathematical Formulae
The diagram below shows the window with Arch Height changed automatically
to 309mm. BIM
As The Future
Presentation
title Standard In Elaboration Of Bulding Designs Based On Parametric /
Mathematical Formulae
Let’s check how the height of the arch of the window is driven by the formula.
I’ve created new Window type 200x200cm (Reference no. "1"), then changed the Value of Width parameter to 2000 (mm) (Ref. no. "2") while the formula of Arch Height is still "Width / sqrt (5) +1)" (Ref. no. "3"). The result is that Arch Height is changed automatically to 618mm (Reference no. “4”).
BIM
As The Future
Presentation
title Standard In Elaboration Of Bulding Designs Based On Parametric /
Mathematical Formulae
The graphic representation of that window type is shown below.
BIM
As The Future
Presentation
title Standard In Elaboration Of Bulding Designs Based On Parametric /
Mathematical Formulae
So far the height of the window (Height parameter) was not associated with the other parameter. Let’s link this parameter with the width (Width parameter) as if they are related to each other. Let the Height be longer ("a") than Width ("b") parameter.
The formula for Height from the use of Width parameter and the golden ratio is
derived as follows:
φ = (sqrt (5) + 1) / 2 (a+b) : a = a : b
where
“a” is a Height parameter
“b” is a Width parameter.
BIM
As The Future
Presentation
title Standard In Elaboration Of Bulding Designs Based On Parametric /
Mathematical Formulae
(Height + Width) / Height = Height / Width = (sqrt (5) + 1) / 2 Height / Width = (sqrt (5) + 1) / 2 //* Width Height = 0.5 * (sqrt (5) +1) * Width
This formula is placed in the "Height" parameter under “Formula" column (Ref. no. “1”) as shown in the diagram to the right. The Height of the window changes to 1618mm. Let’s rename the window to 100x162cm (Ref. no. “2”). The Arch Height value does not change ‐ it remains the same as in the window.
BIM
As The Future
Presentation
title Standard In Elaboration Of Bulding Designs Based On Parametric /
Mathematical Formulae
The graphic representation of that window type is shown to the left.
At this point the Height parameter depends on Width as far as Arch Height parameter, i.e.
While changing the width of the window, programme changes the height and arch height proportionally.
BIM
As The Future
Presentation
title Standard In Elaboration Of Bulding Designs Based On Parametric /
Mathematical Formulae
The ratio of the two parameters used for the window in the equation below
indicates that, for every increase of 1cm of width of the window, the height proportionally increases by 1,62cm.
Height = Width * φ
Height = Width * (1 + √5) / 2
Let’s check if the height of the arch and height of the window are driven by the formulae. Let’s create a new window type of width of 200cm
(=2000mm).
The formulae inserted at Height and Arch Height parameters values change these to 3236.1 (mm) and 618 (mm) respectively.
The change of the window name to “200x324cm” follows.
BIM
As The Future
Presentation
title Standard In Elaboration Of Bulding Designs Based On Parametric /
Mathematical Formulae
The graphic representation of that window type is shown to the left
(Elevation) and below (Plan).
BIM As The Future Standard Elaboration Of Building Designs Based On Parametric / Mathematical Formulae
Research Results
BIM
As The Future
Presentation
title Standard In Elaboration Of Bulding Designs Based On Parametric /
Mathematical Formulae
• The results of this research is a series of the parameterized window types in which the height of the window and height of the arch change, depending on the defined width of the window. • The series of the window types maintain constant proportions based on golden mean in:
‐ half of width of window and height of the arch
‐ the width and the height of the window.
• The formula can be based on any ratio between any parameters defined earlier. It must be noted that formulae used in the design cannot be mutually exclusive and contradictory.
BIM As The Future Standard Elaboration Of Building Designs Based On Parametric / Mathematical Formulae
Conclusions
BIM
As The Future
Presentation
title Standard In Elaboration Of Bulding Designs Based On Parametric /
Mathematical Formulae
• The results of this simple research based on mathematical formulae allow for in‐depth research of the dependencies between particular parameterized values (physical dimensions) of the window (or any other modelled object).
• The results obtained in the research prove that the method based on parameters and their mutual dependencies is an appropriate one. It helps the designer to produce the entire range of the types of the components without the necessity of modelling each of them separately. Therefore, such a method can be used while modelling any physical object with the various types of the same component. This research also proves the superiority of BIM based
programmes over the CAD based programmes.
• This research shows the programming possibilities within the BIM environment in relation to any modelled entity.
BIM As The Future Standard Elaboration Of Building Designs Based On Parametric / Mathematical Formulae
References
BIM
As The Future
Presentation
title Standard In Elaboration Of Bulding Designs Based On Parametric /
Mathematical Formulae
This research would not be possible without the references to few books or
publications.
[1] P Read, E Krygiel & J Vandezande. Mastering Autodesk Revit Architecture,
John Wiley & Sons, Inc., Indianapolis, Indiana, USA, 2012.
[2] British Standards Institution. PAS 1192‐2:2013. Specification for information management for the capital/delivery phase of construction projects using building information modelling, BSI Standards Limited 2013.
[3] National Institute of Building Sciences, www.nibs.org
[4] P Read, E Krygiel & J Vandezande. Autodesk Revit Architecture. Essentials,
John Wiley & Sons, Inc., Indianapolis, Indiana, USA, 2012. Piotr Nabzdyk