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Selection of slab formwork system using fuzzy logicEmad Elbeltagi a , Ossama A. Hosny b , Ahmed Elhakeem b , Mohamed Emam Abd-Elrazek c &Ahmed Abdullah da Department of Structural Engineering, Mansoura University, Mansoura, Egyptb Department of Construction and Architectural Engineering, American University in Cairo,Cairo, Egyptc Department of Construction and Building Engineering, Arab Academy for Science andTechnology, Cairo, Egyptd Department of Construction and Building Engineering, Arab Academy for Science,Technology, and Maritime Transport, Alexandria, Egypt

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To cite this article: Emad Elbeltagi, Ossama A. Hosny, Ahmed Elhakeem, Mohamed Emam Abd-Elrazek & Ahmed Abdullah(2011): Selection of slab formwork system using fuzzy logic, Construction Management and Economics, 29:7, 659-670

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Selection of slab formwork system using fuzzy logic

EMAD ELBELTAGI1*, OSSAMA A. HOSNY2, AHMED ELHAKEEM2,MOHAMED EMAM ABD-ELRAZEK3 and AHMED ABDULLAH4

1Department of Structural Engineering, Mansoura University, Mansoura, Egypt2Department of Construction and Architectural Engineering, American University in Cairo, Cairo, Egypt3Department of Construction and Building Engineering, Arab Academy for Science and Technology, Cairo, Egypt4Department of Construction and Building Engineering, Arab Academy for Science, Technology, and Maritime

Transport, Alexandria, Egypt

Received 15 December 2008; accepted 17 May 2011

Formwork plays an important role in building construction. The selection of an appropriate formwork system

can reduce project cost, improve quality and speed up the construction process. Although the selection of an

appropriate formwork system requires years of experience in formwork design, few experienced personnel

may be available, especially in small/medium size contracting companies. With the lack of such experts, the

costly outsourcing option becomes essential otherwise the selection of a particular formwork system might

not be appropriate. A structured approach is developed to help decision makers in small/medium Egyptian

construction companies to select the appropriate horizontal formwork system(s) for their projects. This can

be achieved by recognizing the project governing factors affecting the selection process. Based on these fac-

tors, a knowledge base is developed to facilitate the process. A fuzzy logic system is used to automate the pro-

cess and overcome ambiguity and uncertainty in the selection process. The system is shown to be useful and

accurate in its application to a real-life case. A survey of formwork experts reveals its ease of use. Further

research will expand the system to consider vertical formwork selection to ensure full compatibility.

Keywords: Fuzzy logic, horizontal formwork selection, knowledge base.

Introduction

A formwork system is defined as ‘the total system of

support for freshly placed concrete, including the

mould or sheathing that contacts the concrete as well

as supporting members, hardware, and necessary

bracing’ (Hurd, 1989). Formwork systems for build-

ings are classified as either horizontal or vertical form-

work. Horizontal formwork systems are those used to

form the horizontal concrete work (slabs or roofs),

while vertical formwork systems are used to form ver-

tical concrete work (e.g. columns, cores and walls).

Although the selection of horizontal and vertical form-

work systems is usually made simultaneously, the

formwork types and the selection criteria are different.

This paper focuses on the selection of an appropriate

horizontal formwork system.

Formwork plays an important role in the construc-

tion industry. The selection of an appropriate

formwork system can reduce the project cost,

improve the quality of concrete and speed up the

construction process. The construction of a slab often

costs more than half of the whole structural framing

cost, except in extremely high rise buildings (Abdul-

lah, 2007). With the existence of several formwork

systems that can be used for building construction,

selecting an appropriate one becomes a challenge

considering the many factors (tangible and intangible)

governing the process. Accordingly, it requires years

of experience in formwork design to identify a suit-

able formwork system, and few such experienced per-

sonnel may exist, especially in small/medium size

contracting companies (Hanna and Sanvido, 1991).

The main objective of this paper is to develop a

structured approach to help decision makers in small/

medium construction companies in Egypt to select

the appropriate horizontal formwork system(s) for

their projects.

*Author for correspondence. E-mail: eelbelta@mans.edu.eg

Construction Management and Economics (July 2011) 29, 659–670

Construction Management and EconomicsISSN 0144-6193 print/ISSN 1466-433X online � 2011 Taylor & Francis

http://www.informaworld.comDOI: 10.1080/01446193.2011.590144

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Literature review

Many studies have been conducted to support the

formwork selection process. Some researchers used

knowledge-based systems and artificial intelligence

techniques, such as artificial neural networks. Elazouni

et al. (2005), for example, developed a neural network

model for estimating the degree of acceptability of new

formwork systems. This model is used to help decision

makers anticipate the acceptability of new formwork

systems before making the decision to acquire them.

The study included the most commonly used flat slab

systems in Egypt. Abdel-Razek (1999) developed a

knowledge base for the selection of the formwork sys-

tems used in the building construction industry in

Egypt. Hanna et al. (1992) described the development

of, and knowledge acquisition for, an expert system

developed to assist formwork designers in selecting

optimum formwork system(s). The system was devel-

oped by systemically capturing the expertise of people

involved in all phases of the life of the formwork, from

design through erection and concrete placement to its

removal. The three stages of knowledge acquisition:

familiarization, elicitation and organization were illus-

trated. Kamarthi et al. (1992) presented a neural net-

work approach for the selection of vertical formwork

systems for a given building. Hanna and Sanvido

(1991) developed a computer system ‘Slabform’ to

select the optimum slab formwork system. The com-

puter system was designed to help the contractor select

a horizontal formwork system. The expertise of several

formwork engineers/planners was gathered together to

create a body of decision rules and knowledge repre-

sented as an expert system. The system makes recom-

mendations on a variety of issues including the

selection of the shoring and re-shoring system and the

type of sheathing used. Hanna and Sanvido (1990)

introduced a tool to assist the formwork engineer/plan-

ner in selecting a vertical formwork system.

Despite the fact that the factors governing formwork

selection can be either tangible or intangible, making

such factors potentially suitable for application of fuzzy

logic, a review of the literature revealed very limited/no

applications (Chan et al., 2009). This paper presents a

knowledge-based system to assist construction person-

nel in selecting the appropriate horizontal formwork

system. Then it introduces a fuzzy logic system to auto-

mate the process of formwork selection. Finally a case

study is presented to validate the developed system.

Slab formwork systems

After investigating the most commonly used horizon-

tal formwork systems in Egypt, six systems are consid-

ered in the present study (Figure 1):

� Conventional wooden formwork system

� S-beam and props/shore-brace system

� Telescopic beam and props/shore-brace system

� Early striking panel (drop head) system

� Table form

� Multi-flex

Conventional wooden formwork

The conventional wooden formwork system (Figure 1

(a)) is widely used in most of the building construc-

tion projects in Egypt. A horizontal conventional

wooden system includes formwork for slabs and

beams. The system is generally built of lumber or a

combination of lumber and plywood. Formwork

pieces are made and erected in situ. For stripping,

conventional wooden systems are stripped piece by

piece, then cleaned, and may be reused several

times.

S-beam and props/shore-brace system

This system is composed of sheathing (either plywood

or lumber), joists, and stringers composed of S-

beams. The S-beam section is composed of two steel

channel sections placed back-to-back, far enough

apart to allow for a piece of lumber 5 � 5 cm placed

longitudinally to the inner space as shown in Figure 1

(b). The function of the lumber piece is to allow for

the plywood to be fixed to the S-beam. Adjustable

steel props or shore-brace frames are used for shoring

(Figure 1(c)).

Telescopic beam and props/shore-brace system

Telescopic beams are lightweight spans, as shown in

Figure 1(d) and (e), that provide a highly efficient,

simple and economical method of supporting and

stripping formwork. The design gives an exceptionally

high load-bearing capacity. Being manufactured from

high tensile steel makes it able to withstand the

toughest site handling, which reduces maintenance

costs. It can accommodate spans varying from 1 to 8

metres.

Early striking panel (drop head) system

This system consists of steel props with drop head

from two sides, lattice beam, in-fill beam and U-

form panel as shown in Figure 1(f). The concrete is

mixed with mixtures that accelerate the hardness of

the concrete therefore lattice beams and U-form

panels can be stripped and props are left to support

the slab until the concrete reaches its complete

strength. This system permits one set of lattice

beams and U-form panels and two sets of props to

be used. It increases construction progress rate (one

floor per three to four days).

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Table form system

Given sufficient crane capacity, table forms (Figure 1

(g)) are the most cost-effective solution where there is

a high degree of repetition and open facades.

Standard table forms are fully pre-assembled form-

work available in different sizes. A table consists of

plywood sheathing supported by secondary girders of

steel or timber sections. The secondary girders are

S-Beam 8

1.20

0.80

1.60 1.

90

S-Beam 12 S-Beam 16 S-Beam 18

(b) S-beam sections(a) Conventional wooden formwork

(c) Shore-brace system (d) Telescopic beam (outer span)

(e) Telescopic beam (inner span) (f) Early striking (drop head) system

(g) Table form (h) Multi-flex slab formwork

Figure 1 Horizontal formwork systems

Horizontal formwork selection 661

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supported on main girders of the same sections. Each

table consists of two frames, which suit the required

height and area, four adjustable jacks and four caster

wheels.

Multi-flex system

The multi-flex slab formwork system is a flexible

formwork system that suits any shape and any type of

concrete slab. The system components (Figure 1(h))

include: sheathing of plywood, main girders and

cross-girders that could be of I-section timber solid

web girder or timber lattice beam. I-section chords

cross-section dimensions are 40 � 80 mm while the

total girder height is 200 mm. For the timber lattice

beam; the cross-section of a chord member is 60 �80 mm while the total beam height is 24 cm. Shoring

may be of galvanized steel props, aluminium props, or

galvanized steel stacking towers.

Factors affecting the selection of formworksystems

Usually, there are several formwork systems that can

be used to form a given concrete building. Although

searching for an appropriate system is challenging, it

deserves considerable attention to minimize cost.

Hanna et al. (1992) identified 38 factors classified

under four major groups that affect the selection of a

slab formwork system: (1) building design; (2) job

specifications; (3) local conditions; and (4) supporting

organization (Figure 2). In order to determine the

most important factors governing the selection of an

appropriate slab formwork system in Egypt, semi-

structured questionnaires were used. The views of

seven major formwork companies in Egypt were con-

sidered in semi-structured interviews. The purpose

was to solicit the interviewees’ opinions, via a ques-

tionnaire survey, on the 38 factors collected from the

literature, to understand their influence in the form-

work selection decision and their applicability in

Egypt. The questionnaire was designed to elicit the

experts’ opinions to rank the 38 factors based on

their relative importance. A numerical scale of 0 to

10 was used, where 0 implies null importance while

10 means high importance. The data gathered were

then analysed to assign a degree for each factor.

Finally, all factors were ranked according to their

degrees of importance in selecting horizontal form-

work systems. Factors with degrees above average (6

or more out of 10) are considered influential factors

in the selection process. These factors are identified

as: (1) speed of construction; (2) hoisting equipment;

(3) available capital; (4) slab type; and (5) area of

practice.

Factors Affecting Formwork Systems Selection

Building design Job specifications Local conditions Supporting organization

Area of Practice

Available Capital

Concrete Finish

Stripping

Potential reuse

Initial cost

Carrying capacity

Building location

Crane time

Troubleshooting experience

Safety management

No yard facility

Local yard facility

Regional yard facility

Labor cost

Labor quality

Cold weather

Hot weather

Size

Urban restricted

Sub-urban open site

Architectural concrete finish

Exposed concrete

As-cast concrete finish

Construction sequence

Rate of placement

Floor cycle

Speed of construction

Weather conditions

Site characteristics

Hoisting equipment

Office support

Support yard facility

Slab type

Lateral loads supporting

system (floor height)

One way slab supported by beams or bearing walls

Two way flat slab

Two way slab supported by beams

Waffle slab

One way slab, beams, and girder

Two way flat plate

One way joist slab

Rigid frame system

Shear walls

Framed shear wall

Framed tube

Tube in tube

Irregular

Uniform

Building shape

Figure 2 Factors affecting formwork systems selection (Hanna et al., 1992)

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Knowledge-based system for horizontalformwork selection

After identifying the main factors governing the form-

work selection and the most widely used formwork sys-

tems in Egypt, it is essential to quantify the effect of

each factor on the selection of a specific formwork sys-

tem. Details of the questionnaire used to solicit the

experience of formwork experts in Egypt and the

knowledge base representation are as follows.

Questionnaire design and data collection

A sample of 37 formwork experts currently working in

Egypt was interviewed. The questionnaire was designed

to determine the degree of suitability of each formwork

system against each factor governing the selection pro-

cess. A scale between 0 and 10 was used to reflect the

degree of fulfilment capability, where 0 means that the

formwork system has no capability and 10 means that

the system has high capability. For example (as shown

in Table 1), the ‘table form’ which was assigned a suit-

ability degree of 9, is more suitable to speed up the

construction (less cycle time) if compared to the

‘conventional wooden formwork’ which was assigned 6

on the suitability scale. The results obtained from the

questionnaire are summarized in Table 1.

Knowledge base representation

In accordance with the analysis of the questionnaire

results, an effective knowledge-based system was built

to facilitate the selection process. It includes the basic

information about the capability of each formwork

system to fulfil the various slab formwork selection

factors. Each factor is divided into its sub-factors,

then linked to the characteristics of each formwork

system. A summary table (Table 2) is presented as a

knowledge-based system for the slab formwork

selection problem. Table 2 can also be used to filter

out the unsuitable formwork systems after checking

the governing factors. Accordingly, the formwork

designer/contractor can easily arrive at an appropriate

formwork system for a specific task.

Proposed fuzzy logic model for horizontalformwork selection

Since Zadeh (1965) introduced the concept of a fuzzy

set, it has been employed in numerous areas. The

concept is founded on the fact that some notions,

though meaningful, may not be clearly defined. The

beauty of fuzzy logic based systems is that they can

handle linguistic inputs—called variables—and keep

processing them to develop outputs or decisions. A

fuzzy linguistic variable is defined as a variable, the

values of which are words, phrases, or sentences in a

given language. For example, cycle time can be con-

sidered as a linguistic variable with values such as

‘low cycle time’, ‘medium cycle time’, or ‘high cycle

time’, while numerical variables use numbers as val-

ues. Since words are usually less precise than num-

bers, linguistic variables provide a method to enable

complex systems that are ill defined to be described

in traditional quantitative terms (Zadeh, 1975). Fuzzy

set theory is a tool that transforms this linguistic con-

trol strategy into a mathematical control method. It

has been applied successfully in many areas such as

plant layout (Dweiri and Meier, 1996), project sched-

uling (Lorterapong and Moselhi, 1996), and evaluat-

ing alternative construction technologies and contract

selection strategies (Chao and Skibniewski, 1998;

Sayed, 2009). Good background material on fuzzy set

theory can be found in Ross (1995).

In this paper, a fuzzy logic model is used to select the

most appropriate horizontal formwork system. The five

governing factors affecting the formwork selection are

presented as fuzzy input variables and the six output

variables representing various slab formwork systems

are converted to fuzzy forms.

Fuzzy input variables

As discussed earlier, five input variables were identified

as the most influential factors governing the slab form-

work selection. These factors are: speed of construc-

tion, hoisting equipment, available capital, slab type

and area of practice. Referring to the knowledge-based

system presented in Table 2, each main factor can be

Table 1 Questionnaire results

SystemFactor

Conventionalwoodenformwork

Multi-flex

Tableform

Telescopic beamand props/shore-brace

S-beamand props/shore-brace

Early strikingpanel

(drop head)

Speed of construction (less cycle time) 6 7 9 8 7.5 9Hoisting equipment (capacity) 6 7 9 7 8 7Available capital (cost) 6 8 8 7 7 7Slab type (complexity) 9.5 8 6 8 8 7Area of practice (available skilled labours) 9 8 7 7 7.5 7

Horizontal formwork selection 663

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Table

2Knowledge-basedsystem

forselectionofslabform

work

Form

work

system

influen

cefactor

Conven

tionalwooden

form

work

Multi-flex

Table

form

Telesco

pic

beam

andprops

shore-brace

S-beam

and

props/

shore-brace

Earlystriking

panel

(drophead)

Speedof

construction

Cycletime

Typicallyonefloorevery15

workingdays.

Faster

cyclecan

beaccommodatedatadditional

cost

(more

stories

tobeshored

andre-shored)

Onefloorevery10

days

Oneflooreverythreeto

fourdays

Onefloorevery10

days

Onefloor

every10days

Oneflooreveryfourto

fivedays(only

oneday

tostriking,dep

endingon

slabdep

thandco

ncrete

strength)

Rate

of

placemen

tUsuallynotafactorin

horizontalco

ncretework

averagerate

19.23m

3/hr

Construction

sequen

cePouringco

lumns,

beamsandslabs.

Slabongradeneednotbein

place,butco

stcanbereducedifslabongradeisin

place

Hoistingequipment

Locationof

building

and

obstruction

Gen

erallynotafactor

Minim

um

free

space

should

beavailable

for

cranemovem

ent

Amajorfactor;

system

must

beopen

space

at

least

1.5

length

ofthe

largetable

from

theface

ofthebuilding

Minim

um

free

space

should

beavailable

for

cranemovem

ent

Minim

um

free

space

should

beavailable

forcrane

movem

ent

Minim

um

free

space

should

beavailable

for

cranemovem

ent

Cranetime

Craneisusedonly

for

materialplacing

Craneshould

have

adeq

uate

carrying

capacity

atmaxim

um

and

minim

um

radii

Craneisusedonly

for

materialplacing

Craneisused

only

for

material

placing

Craneisusedonly

for

materialplacing

Availablecapital

Stripping

Handstrip;highstrippingco

stHandstrip;low

strippingco

stM

inorstrippingco

st;

table

isbeenstroked

as

oneunit

Handstrip;low

strippingco

stespeciallyifusedwith

U-form

panelsfor

sheathing

Handstrip;

highstripping

cost

Handstrip;low

stripping

cost

Reu

seUpto

10reuses

Upto

50reuses

Upto

65reuses

Slabtype

Allslabsystem

s;most

suited

for

two-w

ayslabsupported

by

beamsorone-wayslab,beam,

girder

Allslabsystem

s;most

suited

fortw

o-w

ayslab

supported

bybeamsor

one-wayslab,beam,

girder

Most

effectivewithflat

plates

Allslabsystem

s;most

suited

fortw

o-w

ayslab

supported

bybeamsor

one-wayslab,beam,

girder

Allslab

system

s;most

suited

fortw

o-

wayflatplate

Areaof

practice

Work

bestin

areasofhigh

quality,low

cost

labourforce

Work

bestin

areasof

highquality,highco

stlabourforce

Work

bestin

areasoflow

quality,highco

stlabour

force

Work

bestin

areasof

highquality,highco

stlabourforce

Work

bestin

areasofhigh

quality,low

cost

labour

force

Work

bestin

areasof

highquality,highco

stlabourforce

664 Elbeltagi et al.

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divided into sub-factors to determine the overall value

of this factor.

A family of fuzzy sets has been formulated in which

each variable was expressed by three membership func-

tions low (L), medium (M) and high (H), as shown in

Figure 3. The shape and range of values of the three

membership functions (L, M and H) were determined

based on the questionnaire conducted during the

course of this research. The low and high membership

functions are matched with minimum and maximum

experts’ responses (i.e. frequency of each value) and

represented in a way to cover the whole scope of the

variable. Then, the medium membership function is

placed to overlap with both the low and high member-

ship functions. Accordingly, triangular and trapezoidal

shapes were adopted as shown in Figure 3. These two

shapes are also the most frequently used in the litera-

ture (Ross, 1995; Elbeltagi and Hegazy, 2001).

The five main factors mentioned earlier are divided

into quantitative and qualitative factors. Quantitative

factors are the speed of construction, the hoisting

equipment needed and the available capital. Qualita-

tive factors however are the slab type and the area of

practice. In order to obtain the input variables, each

factor should be expressed in a numerical form to suit

the fuzzy logic model. In view of the fact that

qualitative factors are much more challenging com-

pared to quantitative factors in terms of converting

them to fuzzy variables, new measurable criteria are

proposed to handle this conversion. In the present

study it is proposed to measure both slab type and

area of practice by two new measures called ‘degree

of complexity’ as per Table 3 and ‘labour quality’ as

per Table 4, respectively. Accordingly, a numerical

scale ranging from 0 to 10 is used for both factors.

For example, the degree of complexity measure is

used to reflect how complex it is to form a given slab

(i.e. flat plates are an easier slab to form; on the other

hand, two-way slabs with dropped beams are more

complex to form). Hence, a two-way flat plate which

represents the simplest slab type to form would

receive low degree of complexity from 0 to 2.

(a) Speed of construction (b) Hoisting equipments 10 164

MediumLow

0

1

Membership

Cycle time

(day)

High

0

1Low

Crane capacity

(ton)

Medium HighMembership

2.5 4 1

Low Medium High

Membership

Cost

(LE/m2)36 54180

1

0

1

Membership

5 8 2

Degree of

complexity

Low Medium High

(c) Available capital (d) Slab type

(e) Area of practice (f) Fuzzy output variable

0

1 Poor Fair Good

Membership

1 2 3 4 5 6 7 8 9 100

1

Membership

8 2

Labor

quality

Low Medium High

5

Suitability

degree

Figure 3 Fuzzy input and output variables

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Consequently, such a slab would mainly relate to the

low membership function. Figure 3(a) to (e) shows

the fuzzy input variables along with their linguistic

values and membership functions.

Fuzzy output variables

Each of the six formwork systems included in this

study is considered to be a possible output. As these

outputs represent qualitative variables, ‘suitability

degree’ is proposed to measure the ability of a given

system to fulfil the fuzzy input values. For a given set

of inputs, the output variable provides the degree of

suitability for all formwork types. Thus, one family of

membership functions (poor, fair and good) is used to

represent all the six types of formwork systems (output

variables), as shown in Figure 3(f). The range of each

fuzzy set is based on the experts’ opinions obtained

from the questionnaire results. Because the lowest

score given by experts was 6 (Table 1), then full mem-

bership in the ‘poor’ fuzzy set is considered 6 or less.

The mean degree was 7.5, which is considered full

membership in the fuzzy set ‘fair’. Full membership in

fuzzy set ‘good’ is considered from 8.5 and above.

Fuzzy decision rules

Fuzzy rules define the values or levels of a decision

maker in controlling a system using fuzzy control.

Since each of the fuzzy input variables has three

membership functions, there could be a total of 35

(243) different combinations of preconditions that

affect the selection of the slab formwork system

(determining the formwork suitability). These precon-

ditions are stored in the form of fuzzy rules. To

develop the rules, first the average degrees of each of

the five factors for each formwork system were

obtained from the questionnaire results presented in

Table 1 and translated into linguistic terms. For

example, the ‘available capital’ for the conventional

wooden formwork system had an average degree of 6.

It can be seen that a degree of 6 for the available cap-

ital factor is in the medium range. Hence, the suitable

linguistic term to be given for the available capital for

the conventional wooden formwork system is ‘med-

ium initial cost’. The same procedure is followed with

all other factors for each system. These linguistic

terms represent the best condition in which a factor

should be in order that the formwork system’s suit-

ability can be expressed as ‘good suitability’. For

example, if the construction progress rate is ‘high’,

then the ‘table form’ and ‘early striking panel form’,

are of ‘good suitability’. As discussed before, each fac-

tor is represented in three forms: ‘low’, ‘medium’ and

‘high’. This was done in such a way that if the pre-

condition of a certain factor is for example ‘low’ and

the linguistic term for this factor for a certain form-

work system is also ‘low’ then the suitability can be

considered ‘good’. But, if the linguistic term was

‘medium’ then the suitability can be considered ‘fair’.

Consequently, if the linguistic term was ‘high’ then

the suitability can be considered ‘poor’. Table 5 pre-

sents the suitability of each output formwork system

against each input possible condition of each affecting

factor.

In this study, in order to compose the fuzzy rules,

scores of 1, 2 and 3 are given to the suitability

indicators ‘poor’, ‘fair’ and ‘good’ respectively. When

a rule is composed, the sum of the scores of the

preconditions is determined and compared to a pre-

set value that relates to the conclusion ‘good’, ‘fair’

and ‘poor’. If the total score is between 12 and 15,

then the conclusion is ‘good’. If the preconditions

total score is between 9 and less than 12, the con-

clusion is ‘fair’; otherwise, the conclusion is ‘poor’.

For example, one rule may read: If cycle time is

low, crane capacity is low, cost is low, degree of

complexity is medium, and labour quality is high

then the conventional wooden formwork is good, the

table form is poor, . . ., and the multi-flex is fair

Table 3 Degree of complexity of different slab types

No. Slab type Degree of complexity

1 Two-way flat plate⁄ 0 to 22 Two-way flat slab with drop panels or column heads More than 2 up to 43 One-way flat slab More than 4 up to 64 One-way beam and slab More than 6 up to 85 Two-way beam and slab More than 8 up to 10

Note: ⁄One-way and two-way joist slabs (waffle slab) use the same formwork system with special moulds above sheathing.

Table 4 Degree of labour quality

No. Labour quality Degree of labour quality

1 Low 0 to 42 Medium More than 2 up to 83 High More than 8 up to 10

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(Table 6 shows the composition of the complete

rule). For example, in this rule and according to

Table 6 for the conventional wooden formwork, if

cycle time is low, crane capacity is low, available

capital is low, slab complexity is medium, and labour

skill is high, then the suitability of a wooden form-

work system is poor (score of 1), good (score of 3),

good (score of 3), fair (score of 2), and good (score

of 3), respectively. These inputs result in a total

score of (1 + 3 + 3 + 2 + 3 = 12) which means

good suitability of the wooden formwork system to

the given inputs.

Determining formwork system using fuzzy rule-

based system

With the membership functions and fuzzy rules for-

mulated, it is possible to use them with specific values

of the input variables to compute a numeric value of

the output variable. This process is known as the

fuzzy rule-based inference. The typical steps used in a

fuzzy rule-based system can be summarized as follows

(Ross, 1995):

� Input the numeric values for the input variables

(e.g. cycle time, initial cost, etc.).

� Fuzzify the inputs by applying the input values

to the rules to get their corresponding member-

ship values.

� Calculate the firing strength of each rule using

the minimum operator, Fi = min (x1, x2, x3, x4,

x5), where: Fi = firing strength of rule number i;

x1, x2, x3, x4 and x5 represent the memberships

of the input variables: cycle time, crane capacity,

cost, slab type and area of practice respectively.

This is based on the degree to which the input

elements meet the preconditions of a rule, which

is measured by the obtained membership values

from the fuzzy set concerned.

� Proportion the consequence of each rule to its

firing strength using the minimum operator in

order to determine how much the consequence

of a rule contributes to the output value.

� Aggregate the consequences of all rules to form

the overall membership function of the output

variables.

� Defuzzify the overall membership function to

convert it to a crisp (non-fuzzy) value through a

defuzzification process. Various methods can be

used to defuzzify the overall membership func-

tion, among which the centre of area method is

the most common.

Implementation and example application

To facilitate the implementation process and the use

of the developed fuzzy logic model, MATLAB� was

used to code and automate the process (MathWorks

Inc., 2006). To demonstrate the applicability of the

developed fuzzy logic model, three real-life projects

were used and the analysis of the results showed the

ability of the developed model to select an appropriate

formwork system for a real project on hand. One of

these case studies is the construction of a commercial

building with seven typical floors. The following

parameters represent the model inputs: the slabs of

the building are two-way flat plate type; the formwork

Table 5 Capability of formwork systems with respect to input variables

Input variables Values

Output variables

Conventionalwoodenformwork

S-beamand props/shore-brace

Telescopic beamand props/shore-brace Early striking Table form Multi-flex

Cycle time Low Poor Fair Good Good Fair FairMedium Fair Fair Fair Poor Fair FairHigh Good Poor Poor Poor Poor Poor

Crane capacity Low Good Poor Good Poor Poor PoorMedium Poor Fair Fair Fair Fair FairHigh Poor Fair Poor Fair Good Fair

Cost Low Good Poor Poor Poor Poor PoorMedium Fair Fair Fair Fair Fair FairHigh Poor Fair Fair Fair Good Good

Complexity Low Poor Poor Poor Poor Good PoorMedium Fair Fair Fair Fair Fair FairHigh Good Good Good Fair Poor Good

Labour skill Low Poor Poor Poor Poor Good PoorMedium Fair Fair Fair Fair Fair FairHigh Good Fair Fair Fair Poor Good

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cycle time is considered as 10 days; the formwork was

handled by a tower crane with 5 tons capacity; the

cost (available capital) for formwork system was lim-

ited to LE70/m2 (about $12/m2) per one time use;

and the labour force available in the project location

have low skills. The solution process is started by

fuzzifying the input data. The fuzzification process is

carried out to assign the degree of membership of

each numerical input versus each of the membership

functions representing the linguistic values of the

input linguistic variables. Next, the firing strength of

each rule is calculated. For example, the firing

strength of rule 20: ‘If cycle time is low, crane capac-

ity is high, available capital is high, degree of com-

plexity is low, and labour quality is low then

conventional wood formwork is poor, table form is

good, early striking is fair, S-beam and props/shore-

brace is poor, telescopic beams and props/shore-brace

is poor and multi-flex is poor’ is calculated as the

minimum of (0.5, 1, 1, 1, 0.667) which equals 0.5.

The next step is to aggregate the conclusions of the

different rules to generate the overall membership

function for each output. The output overall member-

ship function is then defuzzified in order to obtain a

crisp output value for each output variable. The

defuzzification method used here is the centre of area.

The result of this example application is presented in

Table 7, where the table form system had the highest

score of 8.86, followed by the multi-flex and the S-

beam systems with the same score 7.5. Consequently,

the table form system is considered as the most

appropriate system for this building. The multi-flex

and S-beam systems are acceptable alternative sys-

tems. The other three systems: conventional wooden

formwork, telescopic and early striking, have scores

less than 5.0, which implies their unsuitability for this

building.

Referring to the knowledge-based system presented

in Table 2, using the case parameters, it can be

concluded that the table form system is the most suit-

able system for the current application. This shows

the conformity of the results using both the developed

simplified knowledge-based system and the fuzzy logic

model. The results of the three case studies were,

then, discussed with formwork selectors; favourable

comments were received. The flexibility of the system

was a major point of appeal. With few inputs, the sys-

tem was able to determine the appropriate formwork

system that the experts agreed on.

System validation

Based on the fact that the knowledge-based system

reflects experts’ knowledge regarding the best matchTable

6Compositionofafuzzydecisionrule

Outputvariable

Inputvariables’

linguisticvalues

Numericalscores

Sco

reConsequen

ce

Speedof

construction

Hoisting

equipmen

tAvailable

capital

Slabtype

Areaof

practice

12

34

5Cycletime

Capacity

Cost

Complexity

Labourskill

Wooden

form

work

LL

LM

H1

33

23

12

Good

Table

form

LL

LM

H2

11

21

7Poor

Earlystriking

LL

LM

H3

11

22

9Fair

S-beam

andprops/shore-brace

LL

LM

H2

11

22

8Poor

Telesco

pic

beam

andprops

LL

LM

H3

11

22

9Fair

Multi-flex

LL

LM

H2

11

23

9Fair

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of a formwork system against a governing set of

formwork selection factors, the developed fuzzy logic

model with its consistency to the knowledge-based

system (as shown in the application example) repre-

sents the first verification and validation. However,

the developed model had been additionally validated

through distributing a questionnaire to 10 experts to

evaluate its performance and credibility. Interviews

were undertaken with the experts prior to their

answering the questionnaire to illustrate the model’s

description, functions and main features. The experts

were also allowed to try the model by themselves

individually and apply it to real projects based on

their past experience. Next, each expert was asked to

evaluate the model based on seven criteria. Each of

those seven criteria was to be given a score from 1

to 5, where 1 indicates ‘poor’ and 5 indicates ‘excel-

lent’. The average score given by the users for each

criterion is shown in Table 8. The overall average

score was almost 4 out of 5, which can be consid-

ered acceptable.

Conclusions

Six slab formwork systems were recognized as the

most commonly used systems in Egypt and five fac-

tors were identified as the most influential governing

factors affecting slab formwork selection. These fac-

tors are: speed of construction, hoisting equipment,

available capital, slab type and area of practice. The

slab formwork systems are: conventional wood form-

work system, S-beam and props/shore-brace system,

telescopic beam and props/shore-brace system, early

striking (drop head) system, table form, and multi-flex

system. Two significant developments were intro-

duced in this paper. First, a knowledge-based system

was structured in a simple to use table/matrix form to

systematically guide decision makers in selecting a

suitable formwork system. Second, a fuzzy logic sys-

tem was presented to automate the process and over-

come ambiguity and uncertainty in the selection

process. The model was implemented on MATLAB�

with five input variables, 243 fuzzy decision rules and

six output variables. The decision maker inputs the

data related to the project and the system provides

him/her with the different formworks ranked accord-

ing to their suitability. The system proved to be useful

and accurate when applied to a real-life case. In addi-

tion, a survey of formwork experts revealed its ease of

use and an overall average satisfaction level of 80%.

Research is going on to use fuzzy logic for the selec-

tion of vertical formwork systems and to integrate it

with the current development to ensure consistency

and practicality of the overall selection of all building

formworks.

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Table 7 Final results of the example application

Formwork system Degree Percentage Rank Evaluation

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Table 8 System validation questionnaire results

Criterion Average

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