Parametric shell structure

FUE
Future University in Egypt
Faculty of Engineering and Technology
Architectural Engineering Department
Course Name: Computer Applications for Architects 2
Course Code: ARC E02
Semester: Spring 2021
Instructor: Dr. Marwa Abd Elkader Elgendy
Teaching Assistants:
Arch. Sameh -Arch.Aya Osama - Arch. Somaya
Name I.D.
Mariam Najdy 20182828
Yomna Saad 20184627
Heba Mohamed 20183719
Yousef Hazem 20185014
Mayyar Abdelrahman 20182667
Shell parametric Structures

Table of content
1. Introduction
1.1 Introduction to shell structure
1.2 Introduction to parametric design
2. Examples
2.1 BUGA Wood Pavilion
2.2 RAPANA STREET LIBRARY
3. Steps to make a simple Parametric shell by
Rhino and Grasshopper

What is a shell structure?
Lattice and portal frame buildings consist of a frame which
supports slab, roof and wall covering. This frame serves purely as
the structural support and provides protection against weather.
The roof and wall covering add nothing to the strength the rigidity
of the structural frame.
A shell structure is a thin curved membrane or slab usually of
reinforced concrete that functions both as structure and covering.
The term “shell” is used to describe the structures which possess
strength and rigidity due to its thin, natural and curved form such
as shell of egg, a nut, human skull, and shell of tortoise.

Single or Double curvature shells
Single or Double curvature shells are curved on one linear axis
and are a part of a cylinder or cone in the form of barrel vaults
and conoid shells.
Double curvature shell are either part of a sphere, or a
hyperboloid of revolution.
The terms single curvature and double curvature do not
provide a precise geometric distinction between the form of
shell because a barrel vault is single curvature but so is a dome.
The terms single and double curvature are used to distinguish
the comparative rigidity of the two forms and complexity of
centering necessary to construct the shell form.

Forms of curvature
Surfaces of revolution
Surfaces of revolution are generated by the revolution
of a plane curve, called the meridional curve, about
an axis, called the axis of revolution.
E.G. Cylinders, cones, spherical or elliptical domes,
hyperboloids of revolution, toroids.

Surfaces of translation
Surfaces of translation are generated by sliding
a plane curve along another plane curve, while
keeping the orientation of the sliding curve
constant.
The latter curve, on which the original curve
slides, is called the generator of the surface.
In the special case in which the generator is a
straight line, the resulting surface is called a
cylindrical surface.
a) Elliptical paraboloid b)cylindrical
paraboloid c) hyperbolic paraboloid

Surfaces of translation
If two paraboloids are similar, the surface becomes a surface of revolution, called paraboloid of revolution.

Ruled surfaces
Ruled surfaces are generated by sliding each end
of a straight line on their own generating curve.
These lines are not necessarily at right angle to the
planes containing the end curves.

Surfaces with double curvature cannot be developed,
while those with single curvature can be developed.
In other words, surfaces with positive and negative
gaussian curvature cannot be developed, while those
with zero gaussian curvature can be developed.
Developable and Non- developable surfaces:

Developable surfaces
Developable surfaces is a surface that can be unrolled onto a flat plane without tearing or stretching it.
It is formed by bending a flat plane, the most typical shape of a developable shell is a barrel, and barrel shells is curved
only in one direction.
Barrel:
Arch action and beam action together make a barrel.
There are mainly two types of barrel:
-Long barrels, arch action is prominent
-Short barrels, beam action is prominent
Structural behavior of short barrel shells
These shells are typically supported at the corners and can behave in one or a combination of the following ways
Structural behavior of long barrel shells
These are typically supported at the corners and behave structurally as a large beam.

Non-Developable surfaces (Doubly-curved)
E.g., Sphere or hyperbolic paraboloid
There are many classified as 1)Synclastic 2)Anticlastic
Synclastic shells
These shells are doubly curved and have a similar curvature in each direction , e.g., domes
A dome is a good example of a synclastic shell, it is doubly curved and can be formed by
rotating a curved line around an axis.
A dome can be split up into two different directions, vertical sections separated by longitudinal
arch lines (also called meridians), and horizontal sections separated by hoops or parallels.
Structural behavior
Similar to arches under a uniform loading the dome is compression everywhere, and the
stresses act along the arch and hoop lines.

Anti-clastic shells are doubly curved but each of the two
curves have the opposite direction to the other. E.g.,
saddle points
Conoids, hyperbolic paraboloid and hyperboloids are all
considered to the anticlastic shell because they are
saddled shape with different curvature in each direction
and straight lines can be drawn of the surface.
Conoids: Formed by moving a one end of a straight line
along a curved path and the other along the straight
path.
Hyperboloids: Formed by rotating a straight line around a
vertical axis.

Hyperbolic paraboloid:
Formed by sweeping a convex parabola along
a concave parabola pr by sweeping a straight
line over a straight path at one end and
another straight path not parallel to the first.
Structural behaviors:
Depending on the shape of the shell relative
to the curvature, there will be different stresses.
Shell roofs, have compression stresses
following the convex curvature and the
tension stresses follow the concave curvature.

Tension Tie
Figure A represents a doubly curved shell with no axis of
symmetry, shows a spherical dome supported on wall.
Whenever the shells are supported vertically at their
edges, a tension tie is required around the perimeter at
the intersection of the dome and the wall.
However, it is important to note that the tie will be
funicular for any shape or either the plan or elevation.
Figure B the shell has positive curvature and continuous
vertical support.

Tension Tie
The support may be a continuous wall or stiff beams between
adequately spaced columns. It is intersecting that the straight parts
of the tie do not require ties across the building.
The thrusts taken by shear forces through the width of the shell, and
only tension forces exist in the tie.

What is Parametricism?
In order to find the meaning of parametricism, we have to look into the origin of the word itself.

What is Para?
Besides, adjacent to, subsidiary.
Metric
A system or standard of measurement
Physics:
A binary function of a topological space which gives, for any two points of the space, a value equal
to the distance between them, or to a value treated as analogous to distance for the purpose of
analysis.
Mathematics:
An abstraction of the notion of distance in a metric space.

Parameter
A parameter generally, is any characteristic that can help in defining or classifying a particular system.
Mathematics:
A quantity whose value is selected for the circumstances and in relation to which another variable quantities may be
expressed.
A constant in an equation that varies in other equations of the same general form, especially such a constant in the
equation of a curve or surface that can be vaned to represent a family of curves or surfaces.
A quantity whose value can vary in general but is fixed when the quantity is used in specific mathematical expression
involving one or more other variables.
Computing science
In computing, a parameter is defined as “a reference or value that is passed to a function, procedure, subroutine,
command, or program.

Parametricism
Parametricism is a style within contemporary “avant-grade architecture, promoted as a successor to post-modern
architecture and modern architecture. The term was coined in 2008 by Patrik Schumacher, an architectural partner of
Zaha Hadid.
Avant grade: New and experimental ideas and methods in art, music or literature.
An avant-grade, computer aided style of architecture and urban planning in which the functions of spaces are
considered parametrically variable (dynamic) rather than static.
Parametricism is a method of digital design and a catalyst for complexity, it allows flexible work with liberty.
A computation, a fundamental base of an algorithm in which you iterate something, and it changes until something
happens.

Consider that a drawing is a visual representation of an idea, whereas an algorithm is a set of rules which
define that idea. A drawing has explicit dimensions, but the design decision processes by which those
dimensions were determined —the algorithms— are left implicit. Parametric modeling makes the design
decisions explicit as algorithms and allows the -model dimension to become implicit. The definition of systems
of rules which produce a model, rather than an explicit set of dimensions, becomes the focus of a design.
x
y
R
𝑥2
+ 𝑦2
= 𝑅2
Two incarnations of a circle. Drawing (left), algorithm (right).
Parametric modelling concept

Many of the fundamental concepts of parametric modelling derive from
mathematics and programming .nd like a program, rules in a parametric model
must not only be explicit in their operation but also applicable to all possible
scenarios within the bounds of the problem (Scheurer 2012).
Thus the designer’s task consist of defining rules their systematic application, and a
parametric model does not produce one solution but describes a collection of
potential solutions
A.(Concept)
Understanding
1.Intent and scope
2.interdependencie
s
B.(Abstraction)
Identifying
1.System
hierarchies
2.boundry,paramet
ers,
constraints
C.(Rules)
Defining
1.Explict
2.Relaationshaips and
operation between
parameters
And constraints
D.(Application)
Executing
A system or network of
independent
Rules and dependent
operations
,through which data
flows
Conceptual process of parametric design

sketching provides a good metaphor for the general
principles of parametric design. The manner in which
problems are framed and addressed is the same.
Subjects are first broadly blocked-in as linear
geometries. These are refined with increasing detail,
and always in relation the whole. For example,
drawing an apple follows the same steps of Concept,
Abstraction, Rules, and then Execution . Concept: it is
impossible to draw an actual apple, but easy to draw
a 2D representation of an apple. This general
description of the intended outcome situates the
design within geometric space. Abstraction: 2D
geometry can be described in 2D space. A very basic
frame of reference is constructed , here a two-
dimensional plane for orientation, with corners,
midpoints, and centre denoted. Rules: All points and
lines within this space can be described in relation to
the plane and its boundary . Broad outlines of any
subject can be drawn between points which freely
slide along the frame
Parametric drawing. Top, left to right: 2a) Reference
plane, 2b) Points 2c) Lines. Bottom left to right: 2d-2e)
Refining associations, 2f) Resultant form

Further refinements are made in relation to the previous outlines in a recursive manner until the
geometry satisfies the design criteria of a more specific objective and then details can be filled-in to
complete the model Execution: a systematic representation of how the apple drawing would look like as
a symbolic model (Woodbury 2010) is shown in the circle process below
shade
lines
points
plane
Iterations
Symbolic model showing the process of
drawing as a parametric system

To understand the tools and methods of predecessors, a conceptual frame needed to be applied which would relate prior
work to the objectives of this research. Structural design of complex geometries varies depending on the role which the
engineer is allowed to take, and these approaches have been categorized in the past on different rationales. Kloft (2003)
differentiates on the spatial boundaries dictated by the architect in which the engineer may operate, Manglesdorf (2010)
on geometric types and their implications for the structural designer. To embed structural design into the form finding
practise, rather than focusing on final forms and spaces, architectural-structural relationships can be placed in a 4-tiered
system to reflect how early the structural engineer is brought into the design process:
1) Architect->Concept->Algorithm->Geometry->Structural Design
2) Architect->Concept, physics-based geometry acknowledges action of structure- >Algorithm->Geometry->Structural
Design 3) Architect->Concept->Algorithms->Geometry->Consults engineer and manufacturer on Materials, Fabrication
Process->Optimization of Shape->Structural Design
4) Architect-> Concept->designs with engineer and manufacturer on physical behaviour, materials, fabrication->Algorithms-
>Preliminary Structural Design->Optimization/Tradeoffs->Geometry->Final Structural Design.
Approaches to Structural Design of Parametric Architecture

▪ Location: Heilbronn, Germany
▪ Architects: ICD/ITKE University of Stuttgart
▪ Area: 500 m²
▪ Year: 2019
▪ Construction System: parametric shell structure

Concept
The design of the wood shell is based
on biological principles found in the
plate skeleton of sea urchins.

• Digital manufacturing by Rhino
Construction

The cassette data fle acts as the direct and
curated interface between design and fabrication.
The types of data stored in the cassette data fle that is relevant for the robotic
fabrication were as follows:
1. Explicit three-dimensional meshes.
2. Explicit three-dimensional solids represented as Boundary Representation
objects (BREPs), available in the CAD Rhinoceros software.
3. NURBS Curves.
4. Geometrically defined planes, structured as single objects or lists, depending on
what they represent.
5. Basic numeric data and strings of text.

• Each section of the pavilion is
divided in pairs of cassette
groups. This allows the
scheduling of prefabrication
following both similar
cassette shapes and assembly
sequence on site.

▪ Location: Varna, Bulgaria.
▪ Architects: Downtown studio
▪ Year: 2017
▪ Construction System: parametric shell structure

Concept
Varna is a city located by the sea " This
is the main reason why the chosen
concept shape of the library resembles
the shell of a sea snail one might find
on the beaches of this city, sitting on
the edge of the Black Sea.

Steps to make a simple Parametric shell
by Rhino and Grasshopper

• At this video, we are going to look at using
grasshopper to make a tensile shell, this is created by
Rhino, and now we will create it in Grasshoper
“parametric”
This is a geometry created by Rhino, then now
lets’s see how it’s created by grasshopper.

Select the object and delete what was created by
Rhino.
• The object after deleting the one created by Rhino.

• We can raise the shell by rising the
vertical line from PT 5.
• We can raise the shell by rising the vertical
line from PT 3.

• So, let’s start and know how we can do this.
First, Edit → New Document
• Then show what we have hidden in Rhino.

• Then, enter the number of sliders to
control the radius of the polygon.

• Then, right click on slider

• Then, choose slide type and then choose
integers.

• Then, click on Slider
• Then, rename it

• Then, rename it any type radius
• Then, change the range to be 120, as it’s
the greatest value we going to need.

• Then, connect radius to R.

• Then, type the radius to be 60.
• Then, copy and paste.

• Then, click on radius to rename it.
• Type # of slides.

• Then connect it to S and control it to be 3
as we need only 3 sides.
• Then, insert a text from here.

• Then, click on it and start typing.
• Type triangle, then click OK.

• Then start rotating the red
triangle to a 90 degree.
• Type rotate.

• Since we want to rotate the polygon, so
we have to connect rotate to polygon
• Then, copy and paste

• And rename it to rotation >

• And change the range to be 90

• This message says that it looks for a number
that is radian, so we need a component that
converts degrees to radians.
• Type a component that named radian.

• Then, plug that rad to the angle
• Then, plug that rad to the Rotate.

• Now, the triangle is rotated.
• Now, turn the original polygon off.

• Then, select all these and ctrl+g to group it.
• Now, they are grouped, and you can
change the color.

• Right click, and then choose color.
• And then choose the color you want.

• For example, we have chosen this color.
• Now, it’s changed.

• Insert a text
Name it Divide Triangle, then click OK.
• Then, type divide triangle

• Now, insert a divide curve component.
• Then, plug it to Rotate and by default it
gives 10 divisions, so go and copy and
paste the number of slider.

• After copying the number of
slider, right click
• Then, rename it to # of divisions.

• Then, plug it into N in Divide.
• Then, change the range to 6.

• As we see, no. of divisions changed to 6.
• Now, we are going to call the points, so
type point list.

• After calling the points, plug it.
• Plug it into Divide (P for points).

• And we need to control the number of
sides.
• So, plug it the number of sides into points.

• As we can see, the points are numbered.
• Then, select all the components of Divide
triangle to group them.

• Ctrl+G to group it.
• Then, change its color.

• The color of this group is changed.
• Now, wen need to call the points, so we
have to create List of items.

• Rename it, and type list items.
• List items.

• Now, we are going to call all the points
except zero.
• Type List item

• Now, copy and paste the number of
sliders.
• Then, rename it.

• Rename it, and type item #.
• Change the range into 1.

• Then, plug it into item and plug Divide into
item, as the list of points come out of
Divide P.
• As we can see here, point 1 is active, so we
have to repeat the same steps with the
other 4 points.

• Copy the item and paste.
• Change the range to 2.

• Then, copy it one more time.
• Then, change the range into 3.

• Then, group it together and choose the color.

• Now, we want to create the vertical line at
no. 3, so type line SDL.
• The start is going to be from point 3.

• So, plug no.3 to the line.
• The direction by default is z-axis

• Then, copy and paste no. of slider for the line.
• Then, rename it to Length.

• Then, plug it to L.
• Then, change the range into 25, and insert end.

• Type end point, as we need the curve to
be from point 2 to 3 and then from 3 to 4,
then plug it into Line, and then type arc.
• Then plug point 2 and 4 into arc, then
plug end into arc. And as we can see the
green curve is drawn.

• So, let’s change the shape and color of arc into red.

• Now, the color is changed.
• Type hide in the command bar to hide the
lines created by Rhino and group the arc.

• Then, insert a text and rename it to vertical
from PT3.
• Then, group it.

• Then, insert a text and rename it to Diagonal
lines.
• Then, insert a line component.

• Then, plug point 2 and 5 into line.
• Then, copy and paste and plug points 1
and 4 into line.

• Then, inset vertical from intersection and
create line and end components, then
plug line from diagonal into it.
• Repeat the same steps with the vertical
from PT 5.

• Then, create Evaluate Arc, then copy the
number of sliders and change the range.
• Then, create Edge surface and Polar array.

• As we see the curve is created.

• https://www.researchgate.net/figure/Computational-design-to-fabrication-
interrelations-of-different-models-direct-digital_fig2_345308591
• https://parametrichouse.com/buga-wood-pavilion/
• https://www.archdaily.com/916758/buga-wood-pavilion-icd-itke-university-of-stuttgart
• https://www.designboom.com/architecture/buga-wood-pavilion-icd-itke-04-18-2019/
• https://www.slideshare.net/SusmitaPaul12/shell-structure
• https://issuu.com/danielkandersen/docs/parametric_modelling_for_point_supp
• https://www.treehugger.com/street-library-made-wood-parametric-design-downtown-
studio-4855643
• https://parametric-architecture.com/rapana-by-downtown-studio/
• http://www.iaacblog.com/programs/animated-systems-rapana-street-library/
• http://www.iaacblog.com/programs/animated-systems-rapana/
• https://www.youtube.com/watch?v=PxNrNGL4EY0
References

Parametric shell structure

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