Modelowanie odwrotne jako narzędzie w nauczaniu konceptualnego kształtowania synergicznych form architektoniczno-konstrukcyjnych – badanie recepcji metody

Wojciech Gilewski

doi:10.37190/arc250312

Streszczenie

W artykule autor przedstawił własne doświadczenia w nauczaniu kształtowania synergicznych form architektoniczno-konstrukcyjnych, czyli takich, w których forma architektoniczna i forma konstrukcyjna stanowią jedność. Szczególną determinantę osiągania w praktyce tej jedności stanowią odpowiednie relacje pomiędzy profesjami architektoniczną i konstrukcyjną.

Autor występuje z pozycji inżyniera budownictwa z wieloletnim stażem w nauczaniu konstrukcji na poziomie akademickim (studentów architektury). Z jego doświadczeń wynika, że efektywne w tej mierze są metody wykorzystujące modelowanie fizyczne, w tym tzw. kształtowanie odwrotne. W artykule zaprezentował sposób prowadzenia zajęć opartych na tych właśnie podstawach i opisał przykłady uzyskanych podczas nich efektów. Autor zbadał też recepcję metody kształtowania odwrotnego wśród studentów Wydziału Architektury Politechniki Wrocławskiej, zestawiając wady i zalety zgłoszone przez blisko 90 osób.

Obecnie proces edukacji inżynierów budownictwa rzadko wykorzystuje manualne metody modelowania fizycznego jako narzędzia kształtowania formy architektoniczno-konstrukcyjnej. W tych celach stosuje się głównie metody obliczeniowe i modelowanie cyfrowe. Zdaniem autora metody te są właściwe dopiero w drugim etapie weryfikacji konstrukcji, po wcześniejszym stworzeniu unikalnego konceptu i zarysu obiektu podczas wstępnego modelowania fizycznego. Do podobnych wniosków można dojść, obserwując warsztat i dorobek słynnych projektantów, łączących często równocześnie kompetencje inżyniera i architekta. Model fizyczny, zbudowany poprawnie już we wstępnej fazie projektowej i przy ścisłej współpracy architekta i konstruktora, może zawierać około 70% trafnych ideowo rozwiązań, a te mogą stanowić podstawę dalszych faz koncepcyjnego doskonalenia synergicznej formy architektoniczno-konstrukcyjnej.

Słowa kluczowe

kształtowanie konstrukcji, architektura konstrukcji, modelowanie fizyczne, forma architektoniczno-konstrukcyjna, przepływy sił

Podgląd pełnego artykułu jest możliwy wyłącznie na większych ekranach.

2025

3(83)

Michał Szczęsny Pelczarski*

Inverse modelling as a tool in teaching the conceptual formation

of synergistic architectural and structural forms

– exploring the reception of the method

DOI: 10.37190/arc250312

Published in open access. CC BY NC ND license

Abstract

The article describes the author’s experiences in teaching the creation of synergistic architectural and structural forms, meaning those where the ar-

chitectural form and the structural form are unied. A key factor is the unity in practice achieved through proper collaboration between the architectural

and structural professions.

The author, as a civil engineer with experience in teaching structural design at the academic level to architecture students, found that methods based

on physical modelling have proven to be very eective, particularly those employing reverse shaping. The article presents a teaching method based on

these principles and describes its results. The author also analyses students´ perception of the inverse shaping (form-nding) method, comparing the

advantages and disadvantages reported by nearly 90 students.

Currently, the process of educating civil engineers rarely utilizes manual physical modelling methods as a tool for shaping architectural and structural

form. For these purpose, computational methods and digital modelling are primarily used. In the author’s opinion, these methods are only suitable for the

second stage of project verication, after the initial creation of a unique concept. Similar conclusions can be drawn by observing the design workshop

and the work of famous designers, who often combine the skills of an engineer and an architect. A properly constructed physical model, developed at

the initial stage of design in close cooperation between the architect and the structural engineer, may already contain approximately 70% of solutions

consistent with the project’s ideology. Therefore, they can serve as a basis for further stages of designing a synergistic architectural and structural form.

Key words: shaping of the structure, structure’s architecture, physical modelling, architectural-structural form, ow of forces

Introduction

The development of construction, initiated by the indus-

trial revolution, brought about the end of an era in which

the terms “engineer” and “architect” meant the same thing.

A new relationship emerged between architects and struc-

tural engineers, which led to a separation of competences in

common design and construction practice and frequent an-

tagonism between these misunderstood specialists. Respon-

sibility for the design process has shifted from one to two

people, and this has given rise to the need for dialogue to

achieve a unied view. However, its participants must have

common ground – so that the conceptual design stage is not

lost (Todisco 2016). This crucial stage is based on a holis

tic, creative view, qualitative analyses and synergies, rather

than the dominance of one party. Exceptions are the few

outstanding creators, called structural artists by David P.

Billington (1985), among them Rafael Gustavino, Antonio

Gaudí, Robert Maillart, Pier Luigi Nervi, Eduardo Torroja,

Félix Candela, Eladio Dieste, Nikolaus Otto or Heinz Isler,

who combined architectural, engineering and construction

skills – and thus created works that have gone down in ar-

chitectural and construction history.

Interviews with Wacław Zalewski (Zalewski, Allen and

Iano 1998), an eminent Polish engineer and professor at the

Department of Architecture at MIT, show that he clearly

noticed this discrepancy, as well as the fact that the lack of

a common ground does not favour the achievement of syner-

gistic, high-quality design eects on the part of both profes-

sions, which are equally responsible for creating architectural

* ORCID:

0000-0002-4563-4694. Faculty of Architecture, Wrocław

University of Science and Technology, Poland, e-mail: michal.pelczarski@

pwr.edu.pl

122

Michał Szczęsny Pelczarski

and structural forms. In view of the above, they should work

closely together, especially in the rst, crucial, conceptual

phases of the design process.

The author’s many years of experience in developing

an awareness of the synergy of architectural and structur-

al forms among students of the Faculty of Architecture at

Wrocław University of Science and Technology shows

that the best way to achieve this goal is through physical

modelling methods, especially since manual skills are de-

clining among young people. This is because these meth-

ods engage – already in the initial stages of the conceptual

search for form – the natural perceptual abilities, the ability

to experience and intuitively predict the behaviour of ma-

terial form in the eld of external forces, the spatial imag-

ination and the creative potential of the designer (Ilkovič,

Ilkovičová and Špaček 2014). Gaudí, in his statements, re-

veals that man can think mainly in two dimensions. Only

the sight and touch of a nished object allow him to truly

understand space (Hensbergen 2015, 250). The use of so-

phisticated software at the stage of conceptual form-seek-

ing (Popovic Larsen, Tyas 2003), which supports the cal-

culation of forces and deformations in construction, and

various types of form generators, will therefore never re-

place the independent, physical modelling of matter. As

Zalewski said, the computer method does not, after all,

produce the form it investigates, despite advanced research

in this direction (Mueller, Fivet and Ochsendorf 2015;

Mueller, Ochsendorf 2011; Gedig 2010). This form has to

be materialised in an earlier process, when only qualitative

analysis is sucient When creating a model, the physical

designer, like a sculptor, moulds the material in specic

spatial congurations; he or she simultaneously controls

aesthetics, plasticity, rigidity and functionality. Any soft-

ware incorporated into the design process at this stage will

interfere with the already advanced, often subconscious

process going on in his mind.

State of research

The history of the application of methods for the shaping

of momentless forms intended for natural materials (stone,

clay, ceramics, brick) that do not stretch, according to mod-

ern knowledge, is as follows. The rst “creator” of this type

of form is nature, which eliminates the stretched parts of

matter through erosion. The result is then highly durable

arched or dome-shaped rock formations, known from moun-

tain or coastal caves, shaped in the earth’s eld of gravity so

that only compression occurs in their cross-sections. It is

most likely that man picked up on these forms and tried to

imitate them, initially by trial and error and, over time, in

a more rened and precise way. The hanging chain method

(at hanging model) was used by Robert Hooke in 1675

and Giovanni Poleni in 1748 to determine momentless pro-

les of arches and domes. To achieve purely compressible

forms, Antoni Gaudí used three-dimensional hanging mod-

els (made of strings and sandbags) between 1880 and 1926,

notably in the design of the Colònia Güell and intuitively

in the Park Güell (the landmark here is the use of inclined

columns and curving in line with the pressure line of the

retaining wall – the Portico De La Lavandera).

For further work, the Catalan architect used measure-

ments, reversed photographs and probably a mirror reec-

tion. Heinz Isler, on the other hand, worked between 1950

and 1960 on hanging reversed cloth membranes, coated with

plaster and then dried or poured with water and frozen, to

obtain funicular forms after reversal, used in the design of

momentless, extremely slender reinforced concrete shells

with large spans.

Contemporary “convenient” experimental physical me-

th ods used for the conceptual design of funicular structures

are realised by the author with students by constructing an-

ti-funicular rib physical models or anti-funicular shell mod-

els. The former are realised from chains of dierent weights,

reecting proportionally the level of materiality of the struc-

tural elements (ballasted, for example, with plasticine at the

points of future concentrated forces), then stiened with hot

glue or resin. The latter are formed from a combination of

chains and gauze coated with dental plaster.

In the digital world, tools are being developed for the

early stages of mesh mould design, such as CADenary, TL

Catenary, JTB Catenary, Grasshopper Catenary and Kanga-

roo or Food4Rhino-Spider, which simulate the behaviour

and geometry of hanging models and allow relatively easy

parametric exploration of moulds. There are also programs

based on the force density method (FDM), among them:

Rhino Vault 2, Sostik, Easy or Tensyl, Formnder, and

the thrust network analysis (TNA) method from the Block

Research Group at ETH Zurich, used in Rhino Vault and

Compas.

The use of such software and physical modelling has

enabled some exceptional contemporary developments.

These include the stone-built exceptionally large Global

Vipassana pagoda in Mumbai (96 m high and 85 m in di-

ameter dome; inside it accommodates approx. 8,000 peo-

ple), the steel-tubed, single-skin atrium at the Smithsonian

Institution in Washington, D.C., the Great Courtyard at the

British Museum in London (Schlaich Bergermann Partner

and Foster+Partners) and the impregnated cardboard tubes

for the Japanese Expo 2000 pavilion in Hanover (designer:

Shigeru Ban).

Basic concepts of inverse modelling method theory

Physical model

The physical model is understood here as a material

structural system, made on a reduced scale, reecting the

spatial form and mode of operation (in terms of force trans-

mission) of a real building object on a real scale of 1 : 1.

The author’s many years of experience in teaching conrm

the usefulness of physical modelling in developing struc-

tural awareness among students of architecture. The great

advantage of this method is that it can be used by almost

anyone, even an inexperienced user with only a prelimi-

nary knowledge of structural mechanics theory. All that is

needed is to follow a few basic principles, and the results

quickly illustrate the play of forces at the initial stage of the

conceptual search for form. The simplied model, which is

easy to make from commonly available materials, allows

many ideas to be tested, encouraging experimentation. This

Inverse modelling as a tool in teaching the conceptual formation of synergistic architectural and structural forms

123

allows observation of the behaviour of the assumed form

of the object under load, as well as qualitative assessment

of the structural system and its rapid verication. Constant

physical contact with the model fosters a subconscious pro-

cess of creating modications to the model and immediately

applying new solutions to it. It also contributes to maintain-

ing the high emotional involvement required to create new

solutions. However, the so-called reverse modelling, used

by the author in his work with students, plays a special role

in physical modelling.

Thrust line theory

Inverse modelling, in the form of planar or spatial mod-

els, is known in the literature as the hanging models meth-

od (Rippmann 2016), the catenary and the line of thrust

(Graefe 2021), inverted tensile models (Tomlow 1989) or

anti-funicular structures (Todisco 2016). This method was

used, for example, by Gaudí when he designed the church

in Colonia Güell, and his model was faithfully attempted

to be reproduced in 1989 by a team led by Frei Otto (Tom-

low 1989). In contrast, a contemporary method of inverse

shell formation was used by Heinz Isler (Campbell et al.

1980; Chilton 2001). Knowledge of the pressure lines is

particularly important in materials incapable of carrying

tension (stone, brick), limits the occurrence of corrosion

of scratch-sensitive materials (reinforced concrete), but

also allows the design of material-economical momentless

structures. It is worth mentioning that exural load-bearing

elements are less ecient than tensile ones in terms of util-

ising the strength properties of the load-bearing structure

material.

The mechanics of stone and brick arches, which are sen-

sitive to the tension arising during bending, is brilliantly

discussed in his work by Santiago Huerta (2005). In it, the

author investigates the ultimate load capacity of arch struc-

tures using models. This makes it possible to observe the

eects of pressure lines approaching the inner or outer edge

of the arch, leading to the formation of hinges in the arch.

Particularly noteworthy is the earthquake simulation meth-

od implemented on a hanging model by tilting the support

lines by, for example, an angle of ±15°.

In the methodology of physical, preliminary modelling

of structural forms, the full analogy between the drawing

line and the pressure line reecting it is essential. Both lines

represent the resultant action of all forces acting on the ob-

ject under investigation.

Physically, the tension line is a virtual accid rope or

chain (i.e., funicular line) arising in a structural element

from a load applied to it, causing it to stretch (Kuś 2008;

Mueller, Ochsendorf 2011; Mueller, Fivet and Ochsendorf

2015). For the forces, this line represents the only possible

“transmission channel”, beyond which they are unable to

physically “pass” between the supports.

Each change in load changes the geometry of the rope,

creating the image of a new and unique string line as a new

system in static equilibrium. The line of draughts also ap-

pears in graphical statics as a string polygon, i.e., a graph-

ical system that balances the concentrated loads acting on

the object.

By creating an object of structural material within de-

ned boundaries in space, we reduce the number of possible

string lines or pressures that can physically pass through that

object. The designer’s objective may therefore be to adapt

the geometry of the structure so that these lines, arising from

all possible loads and their real combinations, run in the vi-

cinity of the core of the cross-section – for the lines that run

in the cores of the cross-sections of the structure under study

induce in them only tension or only compression. When, on

the other hand, the pressure or tension line goes outside the

section core, the section is subject to bending. The section

bres closer to the pressure line will be compressed and on

the opposite side will be stretched.

Thus, if the designer, for various reasons, cannot main -

tain the pressure line in the core area or even in the cross-sec-

tional area, he or she has to reckon with an increase in the

volume of structural material required to carry the bend-

ing in that section where the line will extend beyond the

structure (the greater the further the line is from the axis

of the cross-section). It is this excessive deformation that

will force the designer to use more material in order for the

structure to meet performance and safety requirements.

The modelling of this type of semi-funicular solution

amounts to creating truss systems inside the available con-

tour. A rod-and-column system is then created, redirecting

the naturally formed funicular ows of force into the de-

signer’s accessible contour. The geometry of such semi-fu-

nicular constructions is based on parabolas, so that the axial

forces created in the top and bottom bands of this structure

are often of constant value.

This is because the distance between bands (i.e., the in-

ternal force arm) in parabolic systems is proportional to the

parabolic bending moment diagram. The constant force in

the bands of such a truss theoretically means that there is

no need for diagonal trussing and allows the use of a single

section along the length of the truss, such as a xed diameter

tube, which aects the architecture of the overall structure.

Inverse modelling method

– conclusions and a methodology

From the ndings of the theory of lines of pressure and

lines of drag demonstrated above, concerning the full anal-

ogies occurring between them, it follows, benecial for the

design of structures, that the path of static equilibrium be-

tween the forces acting on the designed object in the space

between supports can be considered in an inverted state, so

as to take advantage of the features of the chain curve giving

an image of the line of drag.

By inverting the modelled object or reversing only the

direction of the forces, it is therefore possible to simulate

the action of dead weight, ground pressure, water and wind

pressure on the designed structure (Fig. 1).

Inverse modelling makes it possible to visualise how, un-

der load in the contour accessible to the structure, cooper-

ative compressive force streams and tensile force channels

form. Systems built in this way are usually close to optimal,

due to the amount of material needed to ensure a favourable

ow of forces from the structure to its foundations. It is, of

course, possible to create many other geometries of force

124

Michał Szczęsny Pelczarski

Fig. 1. Catalogue of selected

applications of inverse modelling

in structural analysis and design

(elaborated by M. Pelczarski)

Il. 1. Katalog wybranych

zastosowań modelowania

odwrotnego w analizie

konstrukcji i w projektowaniu

(oprac. M. Pelczarski)

I – thin line: flexible connector used to suspend and hang, through deviators, the ballast simulating an external

load; thicker line: flexible connector forming and stabilising semi-funicular and/or funicular bands in a bar-ten-

sion truss system, visible in the working diagram of the frame and beams

II – flexible connector which, when the model is inverted to its final position, will act as a bar or compression ring

III – flexible connector (chain) loaded with ballast to simulate the self-weight of the arch, which after reversing

the direction of the forces or after inverting the model to the target position will be a funicular or semi-funicular

compression band

IV – a strut which, when inverted to the target position, will act as a tensile element in the form of a tie or

reinforcement in plane systems, or a ring in spatial systems

ux systems in the available contour, but these will consume

more material as they move away from the optimum systems.

The observation of the play of forces and the shaping of

structural forms that are most favourable in terms of force

ows can be carried out on 2D planar models or, for more

complex structures, on 3D spatial models, as Gaudí has

done (Huerta 2006).

With only a qualitative type of model analysis in mind,

the cross-section of the object to be analysed is divided into

strips, e.g., of equal width, and the ballast weights are se-

lected in proportion to the area of the structure delimited by

the strip in question. These elds, cut out of cardboard, are

numbered and suspended from a chain where it intersects

the centreline of the strip in question. Equal elements, e.g.,

washers or nuts, come in handy when applying the princi-

ple of proportional incremental loading, e.g., reecting the

length of a band of matter or ground pressure with increas-

ing depth.

In general, the inverse shaping method can involve pro-

ceeding iteratively in a ve-step process:

REVERSE

MODELLING

AREAS OF

APPLICATION

WHEN THE FUNICULAR FLANGE OF A

GIRDER OR RETAINING WALL IS IN

TENSION, INVERSION OF THE MODEL OR

FORCES IS NOT APPLIED

SIMULATION OF CANTILEVER BEHAVIOUR

SHAPING OF A

COMPRESSED

FUNICULAR FLANGE

REQUIRES INVERSION

OF THE MODEL

SIMULATION OF RETAINING WALL LOADING

EARTH PRESSURE WITHOUT

FRICTION

EARTH PRESSURE WITH

FRICTION

SIMULATION OF FRAME

BEHAVIOUR

SEMIFUNICULAR CHAIN ADAPTED

TO THE OUTLINE GEOMETRY OF

THE GIVEN SPACE, THANKS TO THE

STRUT-AND-TIE SYSTEM

SIMULATION OF SELF-

WEIGHT, BUTTRESS AND

FLYING BUTTRESS

ACTION

FORCE INVERSION

SIMULATION

WIND LOAD

AND / OR

SELF-WEIGHT

EIFFEL TOWER

–

SHAPING OF

THE

FUNICULAR

GIRDER

SIMULATION OF RINGS IN A DOME

HORIZONTAL EDGE

GIRDER OF A HALL

SIMULATED WITH A

PROP

TENSION RING

SIMULATED

WITH A PROP

COMPRESSION RING

SIMULATED

WITH A TIE

SIMULATION OF BEAM BEHAVIOUR

SIMPLE BEAM

(TYPE 1 AND 2)

FIXED BEAM

CANTILEVER BEAM

(TYPE 1 AND 2

)

SIMULATION OF EARTHQUAKE EFFECTS

MASSIVE WALLLS

DESCRIPTION

IN THE TEXT

LEGEND

PINNACLES – BUTTRESSES

MODEL INVERSION

OR INVERTED MODEL ROTATED BY AN ANGLE OF 10–15°

SHAPING

OF COMPRESSED

FUNICULAR

GIRDER

EXCEPTIONS

Inverse modelling as a tool in teaching the conceptual formation of synergistic architectural and structural forms

125

– Stage I: Initial denition of the designed function-

al-spatial form in the form of a template model.

– Stage II: Inversion of the assumed model (or direction

of forces), followed by shaping of the chain curves (lines

of pull) by gravity so that the chain falls within the area of

the template, and recording of the achieved result from the

dead weight.

– Stage III: Loading with a set of expected alternating

loads (as these often signicantly alter the geometry of the

predetermined drawing line conguration) and then record-

ing the new drawing line layout.

– Stage IV: Comparison of the results of stages II and III,

followed by an adjustment of the ballast values at critical

points, where the drawing line approaches or goes beyond

the edge of the bar-band. This corresponds to a proportional

change in the width of the critical section in question or to

the application of ballast in the form of, for example, a pin-

nacle or lantern or other ornamentation that is also architec-

turally advantageous. The changed section geometry should

ensure that the chain curves run as close as possible to the

central zone of the section, i.e., in the core of the section.

– Stage V (optional): Working on the inverted model and

inputting the digital model, possibly scanning or stiening

the chain model by covering it with, e.g., resin or hot glue

and inverting the model to the target position.

Description of own research

Principle of instruction and examples

of student work using the inverse modelling method

Selected examples of work (Fig. 2) were carried out by

students completing assignments under the guidance of the

author as part of the course “Structures in contemporary

architecture” during the master’s degree programme at the

Faculty of Architecture, Wrocław University of Science and

Technology in the winter semester 2021. The modelling as-

signment is usually conducted in several stages. These are

as follows: selection of one of approximately 60 topics, re-

search of available information materials on the selected ob-

ject, construction of a 2D at model demonstrating the op-

eration of the main structural system, construction of a 3D

model in a simplied version (A4 format), introduction by

the student of the author’s innovation and construction of

the target model (A3 format), preparation of a report on the

course of the research work, its stages, corrections, history

of good and faulty solutions, techniques applied and an in-

ventory of materials used (Fig. 3).

A very important stage undertaken during the course: the

analysis of the work of the structure allows students to fa-

miliarise themselves with the possible force ow systems

in an existing prominent object, and enables them to shape

and make their own modications to it. At this stage Inverse

modelling enables students to design structures with a high

economy of materials and an architecturally attractive ex-

pression of forces, which consists in making the structur-

al system explicit in the architecture of the building. The

inability to apply the inverse method explicitly during the

analysis or creation of a given object indicates that the struc-

ture – or rather its form and geometry – is moving away

from funicular systems, which implies the need for semi-fu-

nicular and/or funicular truss systems with a larger volume

of structural material and a less clear system operation for

the observer.

Summary

– conclusions and demands

One of the most important factors determining the quality

of an architectural work and its sustainable ecological cha-

racteristics is the unity between functional-spatial form and

the structural form it represents. The two professions, archi-

tecture and construction, should work more closely together,

especially during the formation phase of a common design

concept. Both are equally responsible for creating a synergi-

stic architectural and structural form. This requires, among

other things, the strengthening of architectural awareness

on the part of the constructors and, conversely, of structural

awareness on the part of the architects, and its development

should begin at a very early level of academic education.

Based on this conviction, the author postulates the need for

more extensive training in this area than is currently the case

at the faculties of building and architecture. The creation of

a new course of study is also worth considering: “design of

synergistic architectural-structural forms” and, in the long

term, perhaps even a new professional specialisation.

The above statements form the ideological basis of the

author’s scientic and didactic activities at the Faculty of Ar-

chitecture of Wrocław University of Science and Technology.

They are also the basis for searching for the most appropriate

methods of teaching architecture students to understand the

work of structural systems and their inuence on architectur-

al forms. From the author’s 10 years of teaching activity, it

is evident that the methods using physical modelling, espe-

cially using inverse shaping, produce the best results. They

are well adapted to the perceptual and creative abilities of

future architects, and are similar in terms of technique to the

methods used in basic subjects teaching architectural design

skills. The executional simplicity of the models makes stu-

dents perfectly capable of building them at home, and the

general friendly principles of physical modelling allow them

to carry out the required range of analyses and experiments

and reach valuable conclusions on their own (see Fig. 3).

During the project, the student’s relationship with the in-

structor is more personal and more frequent; the instructor,

via a popular instant messenger, can provide precise com-

ments and graphic, audio and video comments at key mo-

ments for the student. An important value is the students’

inventiveness in solving micro-engineering problems, often

used when constructing models on their own under condi-

tions of an always limited budget.

The scope of the term paper closure report on structur-

al modelling requires students to comment on their chosen

modelling method. Among the positives, they mention the

use of spatial models, which facilitates, among other things,

an understanding of how a system works, examining it

with the sense of sight and touch. They also considered it

valuable to simulate the operation of well-known structures.

They often pointed out that research work during mod-

elling, based on experience, strengthens condence in one’s

126

Michał Szczęsny Pelczarski

Fig. 2. Inverse modelling – selected examples of student work:

a) inspiration: retaining wall according to the design of A. Gaudí, Park Güell in Barcelona (photo by M. Pelczarski),

b) analysis of the inspired cross-section using inverse modelling (reversing the direction of forces,

ballast is in the form of steel nuts which simulating earth pressure with friction, the main line of thrust/tension is created

as a loop stretched by inverted forces from soil pressure

– terrace cantilevers shaped by struts forming a funicular compression flange (author: A. Łuksik),

c) inverted chain model of Nervi’s dome, Palazzetto dello Sport (Little Sports Palace) in Rome,

d) chain model fixed withplaster (author: K. Indyk),

e) author’s proposal of a simplified inverse model representing the structural work of the water tower,

Fedala Reservoir in Mohammedia, Morocco (author: U. Śliwińska),

f) inverse model of the Global Vipassana Pagoda in Mumbai (2009),

g) sketch of the actual structure, a hall for 8,000 people, monitored by the Auroville Earth Institute studio (author: S. Krawczyk),

h) model inspired by the dome of Santa Maria del Fiore in Florence, Italy (architect: Filippo Brunelleschi),

i) flat cross-section model at the location of the tension ring with an applied strut (authors: E. Naworska, S. Kiciński, W. Włodarczyk)

g i

Inverse modelling as a tool in teaching the conceptual formation of synergistic architectural and structural forms

127

Il. 2. Modelowanie odwrotne – wybrane przykłady prac studenckich:

a) inspiracja: ściana oporowa według projektu A. Gaudíego, Park Güell w Barcelonie (fot. M. Pelczarski),

b) analiza inspirowanego przekroju za pomocą modelowania odwrotnego (odwrócenie kierunku działania sił,

balasty w postaci nakrętek stalowych symulujących parcie gruntu z tarciem

– wsporniki tarasów kształtowane z rozpór tworzących funikularny pas ściskany

(autorka: A. Łuksik),

c) odwrócony łańcuchowy model kopuły Nerviego, Palazzetto dello Sport w Rzymie,

d) model łańcuchowy usztywniony gipsem (autorka: K. Indyk),

e) autorska propozycja uproszczonego modelu odwrotnego przedstawiającego pracę konstrukcji wieży ciśnień Fedala Reservoir w Mohammedia,

Maroko (autorka: U. Śliwińska),

f) model odwrotny Global Vipassana Pagoda w Bombaju (2009),

g) szkic przekroju hali na 8000 osób monitorowanej przez studio Auroville Earth Institute (autor: S. Krawczyk),

h) model inspirowany kopułą Santa Maria del Fiore we Florencji (architekt: Filippo Brunelleschi),

i) model płaski przekroju z rozporą zastosowaną w miejscu pierścienia rozciąganego (autorzy: E. Naworska, S. Kiciński, W. Włodarczyk)

Student’s own guidelines for building a 3D model

PROBLEM NO. 1

PROBLEM NO. 2

PROBLEM NO. 3

● Research on the available documentation of

the facility.

● Information about designers and their inspirations.

● Development of a work pattern of the structure.

● Verification of correct understanding of structure

work in the selected facility

● Proposed scope and type of research

● Verification of model

construction technic

● Support for innovation

concept

PHYSICAL MODELING OF THE SYNERGIC ARCHITECTURAL / STRUCTURAL

FORMS

● METHODOLOGY OF THE DIDACTIC PROCESS ●

TUTOR

STUDENT

CONSULTATION 5

SUMMARY – FINAL CONCLUSIONS

● 3D model verification

(A4 base + details)

● Assessment of the innovation of the form

● Assessment of the innovation of the structure

● Assessment of architectural and construction

synergy

● Evaluation of the technological innovation of the

model

CONSTRUCTION OF THE 3D MODEL

OF THE AUTHOR'S OBJECT (the base: A3)

ELABORATION OF THE REPORT

● Weaknesses and strengths of the modeling method

used

● Chronological documentation of the modeling

● Applied materials ● Conclusions for the future

CONSULTATION 3

● Verification of the 3D model,

(base: A4)

CONSULTATION 4

● Choice of 3D model construction

technology

● Contact with models photo archive

● Physical contact with archival models

CONCLUSIONS

Ending the task

Continuation

of the task

CONSTRUCTION OF A 3D MODEL

the base of the model: A4

A PROPOSAL OF OWN FORM, INSPIRED BY

AN EXISTING OBJECT

CONSTRUCTION OF THE 3D MODEL

OF THE AUTHOR'S OBJECT (the base: A4)

● inspiration by form ● inspiration by structure

PRESENTATION OF THE GENERAL

ASSUMPTIONS OF THE COURSE

Handing over a catalog of 60 topics (database of

existing facilities: stadium, hall, pavilion, engineering

facility)

SUBJECT SELECTION AND ITS INITIAL

ANALYSIS

The student has the option of submitting his

own proposal of a topic that is not included in

the tutor's catalog.

CONSULTATION 1

CONSULTATION 2

CHOICE

OF PHYSICAL

MODELING METHOD

MODELING:

● classic

● inverted

● membranes

● rod-tension

structures

VERIFICATION OF CONCLUSIONS

CONSTRUCTION OF A 2D MODEL

MODEL RESEARCH

●

Searching for

the maximum

stiffness of

the model

●

Recognition of

justifications

for the used

solution

●

Searching for

synergy of

architectural and

structural forms

Fig. 3. Physical modelling

of synergistic architectural and

construction forms

– a methodology of

the teaching process

(elaborated by M. Pelczarski)

Il. 3. Modelowanie

fizyczne synergicznych form

architektoniczno-konstrukcyjnych

– metodyka procesu dydaktycznego

(oprac. M. Pelczarski)

128

Michał Szczęsny Pelczarski

own intuition. On the other hand, they mentioned the fol-

lowing as disadvantages: labour-intensive, the need for

manual precision, patience, the need for assistance from

another person, confusion resulting from the reversal of

forces. There were also comments about the benecial ef-

fect of physical contact with a collection of models made in

previous years, which allows a quicker understanding of the

working principles of physical models through touch and

the models’ reactions to the applied force. The advantages

and disadvantages of the inverse shaping method reported

by nearly 90 students and the author are summarised in Ta-

ble 1 (the advantages outweigh the disadvantages, and the

indicated disadvantages are solvable).

The research shows that this method, properly commu-

nicated to students and supported by interactive exercises

or scripts available on the web, can contribute to a signif-

icant increase in their self-reliance and condence when

designing new, as yet unknown optimal forms that can be

independently veried by them using the inverse modelling

technique. The modelling of new forms based on the phys-

ical laws of nature used during inverse modelling should

and, as the research shows, can become a cornerstone of the

contemporary architect’s workshop, making him or her an

informed creator of new solutions, well prepared for dia-

logue with all branches of the design process.

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Disadvantages Advantages

Labour-intensive Simple and proven techniques for making physical models

Need for manual precision Strengthening of intuition

Assistance by another person required Bolder and independent design

Difficulty in force reversal interpretation Further development of research tools

High cost of experiments Independent evaluation of one’s own solution

Better understanding of the workings of the design used

Ability to introduce modifications to the model

Simultaneous control over form, function, and structure

Developing design decision-making skills

Searching for new modelling techniques

Adaptation of the method to the students’ perceptive abilities

Encouraging micro-engineering problems solving

Table 1. Study of students’ reception at the faculty of architecture of reverse modelling methods as a tool for designing optimal architectural

construction forms (elaborated by M. Pelczarski)

Tabela 1. Wady i zalety modelowania fizycznego synergicznych form architektoniczno-konstrukcyjnych

przy zastosowaniu metody modelowania odwrotnego (oprac. M. Pelczarski)

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Streszczenie

Modelowanie odwrotne jako narzędzie w nauczaniu konceptualnego kształtowania synergicznych form architektoniczno-konstrukcyjnych

– badanie recepcji metody

W artykule autor przedstawił własne doświadczenia w nauczaniu kształtowania synergicznych form architektoniczno-konstrukcyjnych, czyli takich,

w których forma architektoniczna i forma konstrukcyjna stanowią jedność. Szczególną determinantę osiągania w praktyce tej jedności stanowią odpo-

wiednie relacje pomiędzy profesjami architektoniczną i konstrukcyjną.

Autor występuje z pozycji inżyniera budownictwa z wieloletnim stażem w nauczaniu konstrukcji na poziomie akademickim (studentów architektury).

Z jego doświadczeń wynika, że efektywne w tej mierze są metody wykorzystujące modelowanie zyczne, w tym tzw. kształtowanie odwrotne. W arty-

kule zaprezentował sposób prowadzenia zajęć opartych na tych właśnie podstawach i opisał przykłady uzyskanych podczas nich efektów. Autor zbadał

też recepcję metody kształtowania odwrotnego wśród studentów Wydziału Architektury Politechniki Wrocławskiej, zestawiając wady i zalety zgłoszone

przez blisko 90 osób.

Obecnie proces edukacji inżynierów budownictwa rzadko wykorzystuje manualne metody modelowania zycznego jako narzędzia kształtowania

formy architektoniczno-konstrukcyjnej. W tych celach stosuje się głównie metody obliczeniowe i modelowanie cyfrowe. Zdaniem autora metody te

są właściwe dopiero w drugim etapie werykacji konstrukcji, po wcześniejszym stworzeniu unikalnego konceptu i zarysu obiektu podczas wstępnego

modelowania zycznego. Do podobnych wniosków można dojść, obserwując warsztat i dorobek słynnych projektantów, łączących często równocześnie

kompetencje inżyniera i architekta. Model zyczny, zbudowany poprawnie już we wstępnej fazie projektowej i przy ścisłej współpracy architekta i kon-

struktora, może zawierać około 70% trafnych ideowo rozwiązań, a te mogą stanowić podstawę dalszych faz koncepcyjnego doskonalenia synergicznej

formy architektoniczno-konstrukcyjnej.

Słowa kluczowe: kształtowanie konstrukcji, architektura konstrukcji, modelowanie zyczne, forma architektoniczno-konstrukcyjna, przepływy sił