Automation in Construction 20 (2011) 56–65

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Automation in Construction

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Automatic optimal design algorithm for the foundation of tower cranes

Sun-Kuk Kim a,⁎, Jang-Young Kim b, Dong-Hoon Lee a, Sang-Yeon Ryu a

a Dept. of Architectural Eng., Kyung Hee Univ., Yongin 446-701, Republic of Koreab Gyeonggi Provincial Office of Education, Suwon, Republic of Korea

⁎ Corresponding author.E-mail addresses: kimskuk@khu.ac.kr (S.-K. Kim), kj

0926-5805/$ – see front matter © 2010 Elsevier B.V. Adoi:10.1016/j.autcon.2010.07.004

a b s t r a c t

a r t i c l e i n f o

Article history:Accepted 3 May 2010

Keywords:Tower craneOptimal designFoundationOptimization algorithmStability

As buildings become taller and larger, the lifting plan safety review has become more important inconstruction project management. However, the cost and safety aspects of the lifting plan are contradictoryto each other. Therefore, an optimization algorithm needs to be devised as a solution to this problem. Inmany cases at construction sites, the selection and stability review of the tower cranes are assigned to theequipment suppliers or the field managers, which causes problems for the safety and cost of a project. Toprove this aspect of the current situation, this study examines an automatic optimization algorithm fordesigning the foundation of tower cranes. This algorithm can be implemented by a computerized system andeasily and promptly utilized by field managers without the need for substantial knowledge.

angy801@goe.go.kr (J.-Y. Kim).

ll rights reserved.

© 2010 Elsevier B.V. All rights reserved.

1. Introduction

Tower cranes are widely used for the construction of high-rise andcongested urban buildings all over the world. It is very important toselect an appropriate crane based on the lifting load and to guaranteeits structural safety in order to keep the cost and duration of a projectas well as its productivity at adequate levels. The Korea OccupationalSafety & Health Agency reported in July 2007 that crane-related safetyaccidents represent approximately 32% of all accidents that occurredat construction sites in Korea [14]. In contrast, only 8% of the accidentsat construction sites in the US between 1991 and 2002 were crane-related [7]. This means that additional efforts need to be made toreduce the number of crane-related fatalities in Korea.

The stability of a tower crane basically depends on the choice ofthe model, which is based on its lifting load, and the construction siteconditions, more specifically the length of the jib, its self-standingheight, the lateral supports, the foundations, etc. Collision preventionand the resistance levels for gust and earthquake loadings are alsoimportant factors. Various research such as those on the selection ofan appropriate crane for a construction site [3,22], the stability of thelateral supports for cranes [2,5,12], and crane collision prevention[20,24] have been performed in the past. The stabilities of tower cranefoundations have been examined in some studies [8,10,13], but theregulations require only a simple structural safety check. This lim-itation seems to exist due to the fact that the design and constructionof the foundation are conducted based on the standard drawingsprovided, in most cases, by the equipment vendors. However, thismay not be an optimal solution since it does not consider otherstructural safety factors that are specific to construction site con-

ditions, thus leading to the design of a crane foundation that is neitherstable nor economically feasible.

Although the stability of a tower crane is a very important factor, itshould be balanced with economical feasibility. For instance, if thesite-specific conditions are not considered, a loss of economicfeasibility may result. Consequently, it is required to find an optimaldesign for tower crane foundations by considering these two factorssimultaneously. Since it is not easy to manually create an optimaldesign for tower crane foundations, this system should be automated.

In this paper, we aim to develop an automatic algorithm to op-timize the design of tower crane foundations while achievingstructural stability during its installation and operation and costefficiency of the final product. Among the many parameters involvedin the design procedure of tower crane foundations, this workevaluates stability by focusing on overturn, shear, and bearingcapacities. As shown in Fig. 1, this research only considers normalisolated foundations and fixed trolley-type tower cranes, the mostcommonly used types at construction sites in Korea. In addition, it isassumed that other supports such as lateral supports or pilefoundations are not used because the construction site ground hassufficient bearing capacity to allow for the use of a shallow foundation.

The following list shows the sequence used in this study to obtainthe automatic optimal design algorithm.

– Survey the literature concerning an automatic optimal designalgorithm for tower crane foundations.

– Examine theories on generic tower crane foundation designs anddefine the optimization concept.

– Develop an optimal tower crane foundation design concept andoptimization equations.

– Analyze the factors affecting the stability of a tower cranefoundation and propose an optimal design process involving anautomation algorithm.

Fig. 1. Scope of the research.

Fig. 3. Optimization concept.

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– Review the stability of the tower crane foundation and automatean estimation of theminimum crane foundation construction costsin relation to such stability.

2. Theoretical considerations

2.1. Literature survey

Much research has been conducted with regard to the lifting planof a tower crane, the selection of a model and its location on theconstruction site, crane operation efficiency, and crane safety analysis.Hornaday et al. [6] studied the computer-aided lift planning of mobilecranes in 1993, and Ajmal Deen Ali et al. [20] proposed an approach togenerate a collision-free path during multiple heavy lifts. In 2003,Sivakumar et al. [23] presented cooperative crane lifts using a heu-ristic search, and Varghese et al. developed a heavy lift planningsystem for crane lifts [25].

To research the safety and efficiency issues of a lifting deviceduring its operation, in 1997, Bernold et al. [16] introduced a mobilecrane monitoring system using intelligent technology. Everett andSlocum [11] proposed a video communication system to improve theproductivity and safety of a tower crane, and, in 1999, Leung and Tam[17] performed a study to develop a lifting time estimation model fortower cranes. These studies on the planning and operation of liftingdevices aimed to improve their effectiveness and to reduce safetyaccidents.

Furusaka and Gray [22] developed a model for the selection of theoptimum crane for each specific construction site. Rodriguez-Ramosand Francis [26] proposed a mathematical prescriptive model toestablish the optimal location for a crane within a construction site.Gray and Little [3] presented a systematic approach for selecting anappropriate mobile crane consistent with design work during theearly design process. Tam et al. [4] suggested a site layout algorithmmodel by optimizing supply locations around a tower crane, and Linand Haas introduced a computer-aided planning process model for

Fig. 2. Generic de

the optimization of multiple heavy lifts [15]. Shapira and Glascock [1],Zhang et al. [21], and Ali-Hussein et al. performed other relatedresearch for the optimal selection and location of cranes [19]. Theaforementioned studies on the selection and location of tower craneshave a different purpose than those researching design algorithms oftower crane foundations.

There have been several approaches to reviewing the safety issuesof a tower crane. Ho et al. [9] performed a study to optimize towercrane selection and stability examination as per construction siteconditions. Ho [8] also surveyed the tower crane operation status inKorea and introduced a development program for tower cranestability examination. In a subsequent study, Ho et al. [10] proposeda simulation program for improving the efficiency of the tower cranestability examination preceded by its type selection. Lee and Ro [18]categorized some examples of tower crane collapses that have oc-curred in Korea and proposed reinforcing methods to preventaccidents based on the result of a structural analysis for eachcategorized case. Han et al. [13] presented a method to examine thestabilities of foundations using the OptiCRANE program, a computer-ized program that selects a tower crane and designs its foundation. Allof this research deals with the analyses of disaster cases, the generaldesign and stability examination of the foundations, or the reinforce-ment of their supporting structures. Instead, we intend to focus on thedevelopment of an automatic optimum design algorithm to ensurethe stability and economic feasibility of a crane foundation.

2.2. Generic design process

Fig. 2 summarizes a generic tower crane foundation design process[13]. The tower crane stability is examined in reference to dataacquired by a pre-installation review, and the site or foundationconditions are modified to reflect the stability examination feedbackdetermined prior to construction. However, such a process is designedto only handle generic items and is limited in that it only produces afoundation design at an adequate level. In other words, the concept ofoptimal design is missing.

2.3. Foundation of a tower crane

The foundation of a tower crane includes the fixing anchor and theconcrete that holds it. As for the foundation of the fixed tower crane

sign process.

Fig. 4. Optimal foundation design concept.

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targeted in this study, the fixing anchor is held to the ground by aconcrete block using a basic installation approach that is usually usedfor reinforced concrete apartment buildings and low-rise structures.As mentioned above in relation to the scope of this study, such afoundation structure is applicable when a sufficient amount of bearingcapacity is available, and the strength of the concrete block with afixing anchor must be 255 kg/cm2 or more.

2.4. Optimal design algorithm

Optimal design refers to a foundation design that maintains liftingstability from the installation of the tower crane through its removal,

Fig. 5. Optimal foundat

at a minimum cost. In other words, the goals that an optimalfoundation design must fulfill include secure stability and minimumcost.

As shown in Fig. 3, the generation model of the conventionalfoundation design includes a single review of each stability attribute,while this study's simulation model of the foundation design processrepeatedlymodifies the foundation size inmultiple rounds of analysis.An optimization model refers to the use of simulations to derive anoptimal design solution that creates an optimal foundation design.

Therefore, this study aims to conduct research on an optimalfoundation design by optimizing the stability and costs.

3. Optimal design algorithm

3.1. Concept of the optimal foundation design

This research focuses on the determination of an optimal foun-dation size involving the examinations of stability and cost. Thecorrelation between stability and cost is analyzed in order to developand conceptualize an optimal foundation design, as shown in Fig. 4. Ascan be seen in Fig. 4, the concept of optimal foundation design is basedon the assumption that the foundation size and cost have positivecorrelations as the concrete, formwork, and rebar quantities increaserelative to the foundation size.

Examining the stability and rangeof the foundation size that satisfieseach stability examination item produces a feasible range. Allcoordinates in the feasible region are deemed to represent a foundationsize that enables stable installation, operation, and removal of the towercrane. However, if costminimization is considered in the optimal designand the objective function is limited to cost minimization, a coordinate

ion design process.

Fig. 6. Automatic foundation size and reinforcement adjustment process.

59S.-K. Kim et al. / Automation in Construction 20 (2011) 56–65

that maximizes the objective function value is said to be the ‘optimalsolution’ or the ‘optimal value’ and represents the optimal foundationdesign point where stability is secured and cost is minimized.

The equation of the optimal isolated spread footing design basedon the above concept and the linear function is presented in Eq. (1). Inthis equation, Costfoundation represents the sum of all costs that arerequired to put together the concrete, formwork, and rebar necessaryto build an isolated spread footing whose features are finalized in theoptimal design automation process proposed herein.

Minimize Costfoundationsubject to σb≤ f a bearing capacityð Þ

e ≤ Ls = 3 overturnð ÞVu≤ ΦVc shearð Þ

ð1Þ

The value of the objective function minimizes Costfoundation in theoptimal design algorithm proposed herein, and this valuemust ensurethe bearing capacity and stability against the constraints of overturnand shear. To put it differently, the features of the footing are deter-mined automatically by the simulation of the structural stability of thetower crane. Accurate quantities and minimum costs are estimatedsubject to the footing features in the simulation.

3.2. Optimal foundation design process

Fig. 5 shows the optimal foundation design process through theadaptation of the generic design process with the addition of the itemsnecessary for optimal design. The stability is examined with regard tosite conditions, the selected tower crane attributes, and the initialfoundation size, which aremodified in each step, and the rebar spacingis reviewed. Once the foundation size is determined, the concrete,formwork, and rebar quantities are calculated, and the costs of not onlythe materials but also the equipment and labor are calculated. Then,both the stability and costs are examined, and the analysis of thecorrelation between them is used to optimize the foundation design.

The conditions of the automatic optimal foundation designalgorithm for a tower crane are summarized as follows.

– Design conditions include site conditions, the selection of thetower crane attributes, and the initial foundation size.

– Stability review includes the overturn review, the bearing capacityreview, and the shear review.

– Reinforcement review includes the number of rebar pieces, therebar diameter, the required rebar quantity, and the rebar spacing.

– Quantity and cost estimations include the concrete cost, theformwork cost, and the reinforcement cost.

3.3. Concept of the automatic foundation design

Automating the optimal tower crane footing design as proposedherein requires a concept described in Fig. 6. As part of the initialdesign conditions, the footing is sized at 3 m×3 m×1 m (LL×Ls×h)and is expanded in increments of 0.1 m to simulate tower cranestability and to derive the final footing size. The initial size reflects theminimum footing size adopted for tower cranes in Korea. However, asthe initial value slightly varies depending on the tower crane type, it isdefined as a nearly constant variable herein.

Furthermore, as the tower crane footing is rectangular-shaped, itslong side lengths (LL) and short side lengths (Ls) are adjusted at thesame time, and its height (h) is adjusted separately to produce avariety of executable solutions that are subject to an integratedstability review.

In addition, the automatic optimal design algorithm for the towercrane footing uses data from the unit price database as well as theinitial footing size inputs. Therefore, the quantities of materials to bemobilized for construction after the final size is determined and their

aggregate costs are able to be estimated automatically. Cost=Q×UP,as mentioned in Section 4.3, and U/P (unit price) are provided as theinitial inputs to be used for the final cost estimation. In other words,the algorithm proposed herein can review the stability to finalize thefooting size and to automatically estimate the required quantities andcost.

In addition, as Fig. 6 shows, the automatic reinforcement ad-justment process utilizes the sum of the required rebar cross-section(qrebar) and the rebar diameter-specific cross-section data foundationdetermined in the footing size stability review. As shown in Table 2,value i is the first item of the rebar diameter-specific cross-sectiondatabase, and each item includes the name, diameter, nominal cross-section data, etc of the chosen rebar. The details of the reinforcementreview items and processes are described in the following section.

In addition, as Fig. 6 shows, the automatic reinforcementadjustment process utilizes the sum of the required rebar cross-section (qrebar) and the rebar diameter-specific cross-section datafoundation determined in the footing size stability review.

Section 4.2.4 herein details the reinforcement review items andprocess.

4. Optimal foundation design

4.1. Design condition

4.1.1. Site conditionThe site conditions refer to the attributes of the applicable project

site and other conditions generically applicable to the constructionproject, including the bearing capacity of the applicable site identifiedin the ground survey, the compressive strength of the concrete, the

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covering thickness, the rebar strength, etc. The applicable safety factoris also one of the site conditions.

4.1.2. Selected tower crane attributesThe selected tower crane attributes are selected from the

manufacturer's specifications in consideration of the payload weight,structure height, construction scope, crane rental charge, and otherconditions. Such attributes include the vertical force, horizontal force,moment, and dead weight of the tower crane and provide basic inputsto the stability review.

4.1.3. Foundation sizeAlthough this study aims to optimize the tower crane foundation

design, the foundation size in this step refers to a generic foundationsize to be used. The generic foundation size for the stability review isprovided and modified in each step of the stability and cost review.The initial foundation size information includes the foundation heightand the dead weight as the lengths of the X and Y axes, respectively.

4.2. Stability review

4.2.1. Overturn reviewFor the overturn stability calculation, Korean Industrial Standards

(KS B ISO 12486) specify that a tower crane is stable when thealgebraic sum of the stability moments is equal to or greater than thesum of the overturn moments. As for the overturn review, the bearingcapacity must first be secured against the vertical load, and it must bedetermined whether the overturn moment can be supported by thefoundation dead weight and anchor structure. The basic information

Fig. 7. Overturn re

necessary for the overturn review, review process, and to determinethe relationships among the calculation items are described in Fig. 7.

The overturn review can be conducted on the basis of the verticalforce, horizontal force, and moment acquired automatically upon theselection of the tower crane, and the foundation lengths on the X/Yaxes, the height, and the dead weight are available as parts of theinitial foundation configuration. The formula for overturn is describedin Table 1. In other words, the overturn stability can be ensured whenthe eccentricity (e) calculated by the equation in Table 1 is equal to orless than the minimum length of each side of the footing plate so thatit is less than the aforementioned e value (e≤Ls/3).

4.2.2. Bearing capacity reviewThe basic information necessary for the bearing capacity review,

the review process, and the determination of the relationships amongthe calculation items are described in Fig. 8. Once the overturn reviewis conducted, the e acquired in the overturn review, the site con-ditions, the foundation size, and the vertical force of the tower craneare entered to initiate the bearing capacity review.

If the foundation size needs to be modified, as it does notguarantee a sufficient bearing capacity, the review process starts overagain at the overturn review. Once the overturn and bearing capacityreviews are completed, the shear review is initiated. The formula forthe bearing capacity is described in Table 1.

When reviewing the stability of the bearing capacity, the bearingcapacity is deemed secure when the maximum soil pressure (σb) isequal to or less than the bearing capacity (fa) of the soil (σb≤ fa). If thebearing capacity simulation result shows that the bearing capacity issmaller than the maximum soil pressure (σbN fa), the isolated spread

view process.

Table 1Stability review items and calculation formulas.

Review items Calculation formula

Overturn review In operation e=(Mon+Hon×h)/(Pon+G)Out of operation e=(Moff+Hoff×h)/(Poff+G)

Bearing capacity review In operation σb=2×(Pon+G)/(3×LL×Ls/2-e)Out of operation σb=2×(Poff+G)/(3×LL×Ls/2-e)

Shear review One direction Vu=1.7×σb×LL×L′ΦVc=0.85×0.53×√fck×LL×d

Two directions Vu=1.7×σb×(Ls×LL−(ℓ+d)2)ΦVc=0.85×1.06×√fck×Bo×d

LL: length of foundation's long side, e: eccentricity, Ls: length of foundation's short side,m: mast size, h: foundation height, G: dead weight of foundation, Mon: operationalmoment, Moff: non-operational moment, Hon: horizontal force in operation, σb:maximum soil pressure, Hoff: horizontal force in non-operation, fa: bearing capacity,Pon: vertical force in operation, n: foundation section area, Poff: vertical force in non-operation, Vc: design shear strength of concrete, Vu: shear strength at a critical section, L′: anchor distance, ΦVc: nominal shear strength of concrete, fck: concrete strength, σb:maximum soil pressure in operation, Bo: circumference at a critical section of thefoundation={(m×100+d)×4}, and d: distance between the compressive section andthe center of the tension bar.

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footing cannot be used, and another reinforcement alternative such aspile footing needs to be considered. As this paper assumes that asufficient bearing capacity is available on site, the scope of thisresearch is limited to the optimal design of the isolated spread footing.

4.2.3. Shear reviewThe basic information necessary for the bearing capacity review,

the relationships among the calculation items, the review process, andthe foundation size modification steps are described in Fig. 9.

Fig. 8. Review process of

The shear review is initiated when the foundation size modifiedin the overturn and bearing capacity reviews, the compressivestrength of the concrete, and the rebar strength in the site conditionsare entered. Even if the foundation size has already proven to bestable in terms of possible overturn and the bearing capacity, if it isshown to be unstable with regard to shear, the foundation has to bemodified again. The foundation size modified to ensure shearstability must go through a reiterative overturn, and the bearingcapacity and shear review processes are to be conducted using thepreceding steps. The formula to calculate shear capacity is describedin Table 1.

Conversely speaking, if the shear strength (Vu) is found to beequal to or less than the nominal shear strength of the concrete (Vc)in a review of both Directions 1 and 2, stability is deemed secure(Vu≤ΦVc).

Once the foundation size is proven to be stable in terms of theoverturn, bearing capacity, and shear, the foundation design processin which the rebar spacing is modified and the foundation design isbased on the above modified foundation size is initiated.

4.2.4. Reinforcement reviewFig. 10 outlines the rebar placement process. As the footing size

that ensures the required bearing capacity, overturn stability, andshear strength is determined in the foregoing stability review, thesum of the required rebar cross-section (qrebar) is also estimated.Then, the initial nominal rebar diameter (i=0) is defined, and, if it issmaller than the sum of the required rebar cross-section, the initialvalue is adjusted with regard to the rebar diameter-specific cross-section database.

the bearing capacity.

Fig. 9. Shear review process.

Fig. 10. Automatic simulation process of the reinforcement review.

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In other words, the simulation is iterated until the sum ofthe cross-sectional area is greater than or equal to the value of thereinforcement area (qrebar) required for the structural stability of thefoundation (qrebar≤sum of the rebar cross-section). Table 2 showsthe rebar data, including the bar designation, the actual diameter, thenominal weight, and the cross-sectional area (KS (Korean IndustrialStandards), KSD3504).

In addition, the number of required rebar is determined as a wholenumber by the interface of the rebar diameter-specific cross-sectiondatabase. Then, interrelations among the rebar diameter-specificcross-section, the rebar quantity, and the footing size are reviewed,and the rebar diameter is adjusted as necessary. Lastly, the rebarspacing is reviewed as described in Eqs. (2) and (3).

The relationships among the long/short side lengths and thecovering thickness C, the rebar spacing, and the diameter can beexpressed as shown in Fig. 11. The covering thickness, rebar diameter,and spacing must be equal to or smaller than the length of side LL,which also applies to side Ls.

LL≥ drebarLs × nð Þ + 1:5drebarLs n−1ð Þ + 2C→ok ð2Þ

Ls≥ drebarLL × nð Þ + 1:5drebarLL n−1ð Þ + 2C→ok ð3Þ

The rebar placement spacing is reviewed by the automatic processin Fig. 10, where the rebar quantity or diameter is adjusted to arrive atthe final rebar spacing. However, as the footing rebar placementdesign varies as much as the variety of the tower crane manufacturersor models, model-specific manuals need to be referred to for furtherdetails.

Table 2Rebar diameter-specific cross-section database.

Bar designation(KSD3504)

Actualdiameter(mm)

Nominalweight(kg/m)

Cross-sectionalarea (cm2)

Remark

D10 9.53 0.56 0.7133D13 12.7 0.995 1.267D16 15.9 1.56 1.986D19 19.1 2.25 2.865D22 22.2 3.04 3.871D25 25.4 3.98 5.067D29 28.6 5.04 6.424D32 31.8 6.23 7.942D35 34.9 7.51 9.566D38 38.1 8.95 11.40: : : :

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4.3. Cost estimation

Once the characteristics of the isolated spread footing are finalizedin the optimal footing design process, the construction cost inreference to the quantity to be built is estimated. The constructioncost of the isolated spread footing consists of the costs of the concrete,formwork, and rebar. Each cost item is estimated by multiplying therequired quantity by the unit price, as shown in Eq. (4). As assumedabove, the unit price is retrieved from the quantity and the unit pricedatabase provided, along with the initially defined footing size data.

Costfoundation = Costconc + Costform + Costrebar ð4Þ

4.3.1. Concrete work costThe concrete quantity can be calculated using the following formula

in reference to the foundation size finalized in the stability review andthe rebar spacing modification. Characters LL, Ls, and h used in theformula carry the meanings shown in Fig. 12.

As shown in Eqs. (5) and (6), the concrete quantity (Qconc) iscalculated in the same manner as the volume of a generic rectangularbox and is multiplied by the unit price (UPconc/m³) of the concretework, which includes the concrete, equipment, and labor costs.

Costconc = Q conc × UPconc ð5Þ

Q conc = LL × Ls × h m3ð Þ ð6Þ

4.3.2. Formwork costAs is the case with the concrete quantity calculation, the formwork

cost (Costform) described in Eq. (7) can be calculated on the basis ofthe foundation size acquired in the preceding steps. This value is

Fig. 11. Relationships between the long/short sides and the spacing of the rebar.

found using the calculated formwork quantity (Qform) with the unitprice (UPform/m²) as shown in Eq. (8), which also includes the form,equipment, and labor costs in the same manner as in the genericformwork quantity calculation formula.

Costform = Q form × UPform ð7Þ

Q form = LL + Lsð Þ × 2 × h m2ð Þ ð8Þ

4.3.3. Reinforcement work costThe rebar quantity can be calculated after the rebar spacing is

reviewed in consideration of the selected tower crane attributes andthe finalized foundation size. As shown in Eq. (10), the rebar quantity(Qrebar) is calculated by multiplying the sum of the long side rebar(LL), short side rebar (LS), and hoopwith the unit weight of each rebar.The reinforcement cost is calculated by multiplying the unit price perrebar diameter. The reinforcement cost calculation formula is shownin Eq. (9).

Costrebar = Q rebar × UPrebar ð9Þ

Q rebar = fðWrebarLL × ∑LrebarLLÞ + ðWrebarLs × ∑LrebarLsÞ

+ Wrebarhoop × ∑Lrebarhoopð Þg = 1000 tonð ÞLrebarLL : cutting length of the rebar long side mð ÞLrebarLs : cutting length of the rebar short side mð ÞLrebarhoop : rebar hoop cutting length mð ÞWrebarLL : unit weight of the rebar long side kg =mð ÞWrebarLs : unit weight of the rebar short side kg =mð ÞWrebarhoop : unit weight of the rebar hoop kg=mð Þ

ð10Þ

The calculated cross-section of the reinforcement is divided by thecross-sectional area, and the number of necessary rebar strands iscalculated using the roundup function.

In addition, the rebar quantity can be calculated more accurately ifthe bendingmargin is considered. According to a previous study [20], thebending margin refers to the phenomenon where a high-tension steelbar is lengthened by 2.5 times its diameter after processing (see Fig. 13).

If the rebar is cut without consideration of the bending margin,about 1% rebar loss is incurred, and the rebar is not adequatelycovered by concrete, requiring additional labor, material, and trans-portation costs.

Therefore, the bending margin warrants consideration in rebarwork if rebar loss is to be reduced. In otherwords, the rebar needs to becut 2.5 times the rebar diameter shorter than the rebar length in thedrawing asmany times as the number of bending locations in advance.To minimize potential rebar loss, this bending margin is reflected inthe algorithm herein (see Eqs. (11), (12), and (13)). Furthermore, anadditional rebar quantity calculation required by each tower cranetype, depending on its specific attributes, is excluded from the scopeof this research, and only the generic rebar quantity calculation isaddressed herein.

Therefore, in the case of the tension rebar,

LrebarLL = LL−2Cð Þ + 40drebarLL × 2− 2:5drebarLL × 2ð Þ ð11Þ

LrebarLs = Ls−2Cð Þ + 40drebarLs × 2− 2:5drebarLs × 2ð Þ ð12Þ

Lrebarhoop = LL−2Cð Þ + Ls−2Cð Þ × 2 + 2 × 10dhoop– 2:5dhoop × 5� �

;

ð13Þ

Fig. 12. Foundation size.

64 S.-K. Kim et al. / Automation in Construction 20 (2011) 56–65

and the rebar quantity can be calculated using Eq. (14). As mentionedin the beginning of this section,

Qrebar = ðWrebarLL × ∑LrebarLLÞ + ðWrebarLs × ∑LrebarLsÞ+ ðWrebarhoop × ∑Lrebarhoop

: ð14Þ

5. Conclusions

This study was intended to improve the efficiency of thefoundation design upon the recognition that the stability of a towercrane has not been thoroughly examined, as the installation of towercranes is dictated by a field manager or installation specificationspresented by the equipment supplier in most construction sites ofKorea.

The research scope of this paper was limited to the shallow foun-dation of a fixed tower crane and a foundation design process adaptedfrom the generic design process with the addition of optimizationelements was proposed. The following conclusions are derived fromthe aim of this study, an optimal tower crane foundation designalgorithm.

Firstly, the optimal tower crane footing design concept isestablished, and an optimal equation based on the linear function isdesigned. The objective function is the minimization of costs requiredfor the tower crane footing construction, and the securing of thebearing capacity, the overturn stability, and the shear strength at therequired level are defined as constraints. The introduction of theoptimal design concept is considered in order to build a platform thatcan produce an optimal footing design that optimizes the stability andminimizes costs in comparison with those of the conventional towercrane footing design approach that focuses on simply ensuring theadequacy of the footing stability and the construction cost.

Secondly, the factors that potentially affect tower crane stability areanalyzed, and an optimal design process that adopts a concept of an

Fig. 13. Bending margin.

automatic footing size adjustment process is proposed. This process isdesigned to determine the tower crane footing features by validatingits stability and automatically estimating the minimum input costs.

Thirdly, the algorithm developed in this study saves the time andcosts needed to determine the stability of the tower cranes in thefoundation design stage. In other words, the automatic algorithmproposed herein will deliver a more efficient tower crane footingdesign process which will require far less dependence on expertknowledge.

Finally, for future research, the automatic design algorithmdeveloped in this paper will be applied to the computerized programfor the optimum foundation design of tower cranes.

Acknowledgements

This research was supported by the Basic Science ResearchProgram through the National Research Foundation of Korea (NRF)and funded by the Ministry of Education, Science and Technology (No.2009-0063383).

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