Research Article Mathematical Model of Hybrid Precast Gravity Frames for Smart Construction and Engineering

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1 Mathematical Problem in Engineering, Article ID , 14 page Reearch Article Mathematical Model of Hybrid Precat Gravity Frame for Smart Contruction and Engineering Seon-Chee Park, 1 Won-Kee Hong, 1 Sunkuk Kim, 1 and Xiangyu Wang 2,3 1 Department of Architectural Engineering, Kyung Hee Univerity, 1732 Deogyeong-daero, Giheung-gu, Yongin-i, Gyeonggi-do , Republic of Korea 2 Autralaian Joint Reearch Centre for Building Information Modelling, Curtin Univerity, GPO Box U1987, Perth, WA 6845, Autralia 3 Department of Houing and Interior Deign, Kyung Hee Univerity, 1732 Deogyeong-daero, Giheung-gu, Yongin-i, Gyeonggi-do , Republic of Korea Correpondence hould be addreed to Won-Kee Hong; hongwk@khu.ac.kr Received 28 February 2014; Revied 4 April 2014; Accepted 1 May 2014; Publihed 27 Augut 2014 Academic Editor: Changzhi Wu Copyright 2014 Seon-Chee Park et al. Thi i an open acce article ditributed under the Creative Common Attribution Licene, which permit unretricted ue, ditribution, and reproduction in any medium, provided the original work i properly cited. The tructural tability, contructability, economic feaibility, environmental-friendline, and energy efficiency of hybrid compoite frame ytem have been demontrated by practical application and reearch. A hybrid compoite frame ytem combine the economy of precat concrete tructure with the contructability of teel frame tructure, including erection peed. Novel compoite frame will ultimately maximize the efficiency of tructural deign and facilitate contruction. Thi paper preent hybrid precat frame, which are precat compoite frame baed on a imple connection between precat concrete column and beam. The hybrid precat frame deigned to reit gravity loading conit of PC column, PC beam, and teel inerted in the precat member. Steel ection located between the precat column were imply connected to teel inerted at each end of the precat beam. Dynamic analyi of a 15-tory building deigned with the propoed compoite frame wa performed to determine the dynamic characteritic of a building contructed of hybrid frame, including frequencie and mode hape. 1. Introduction The ue of hybrid precat compoite frame with hybrid precat beam and column for gravity loading offer advantage of both teel and precat concrete material. Effective interaction between the two material facilitate a reduction inizeofbothhybridprecatbeamandcolumn.thehybrid precat frame are connected by imple connection that upport only gravity load. In a previou tudy, Hajjar (2002) demontrated the benefit of compoite ytem relative to more common ytem [1]. Such advantage were determined by comparing the performance characteritic of beam ubjected to ervice and ultimate load. Hajjar alo analyzed the economic benefit of compoite tructure with repect to material uage and contruction cot. Fabbrocino et al. (2001) ued a refined theoretical model to invetigate the influence of teel reinforcement on the rotational capacity of compoite beam under negative bending [2]. Thi model wa validated through experimental teting. Yang and Tan (2014) conducted a erie of experiment to invetigate the failure mode and ductility of compoite beam-column joint under a middle-column-removal cenario and reported the ductility and load reitance of thee five pecimen in catenary action. They found that trengthened web cleat connection had a much higher load-carrying capacity than normal web cleat connection becaue the former could utain greater deformation [3].TeerandScotta(2013)tudiedcompoite teel true and concrete beam with an inferior precat concrete bae and compared their finding with theoretical evaluation of typical reitance mechanim of teel-concrete compoite and reinforced concrete tructure. They dicued the main qualitative and quantitative feature of the compoite teel tru and concrete beam [4]. Hwang and colleague (2011) evaluated the eimic reitance of concrete-filled, U- haped teel beam-to-rc column connection and provided

2 2 Mathematical Problem in Engineering eimic detail of concrete-encaed, U-haped teel beam-to- RC column connection. The pecimen exhibited required trength, deformation, and energy diipation capacitie. The deformation capacity exceeded an intertory drift angle of 4%, which i a requirement for pecial moment frame [5]. Haan and Khorow (2011) preented an analytical invetigation baed on FE model and uing ANSYS oftware to examine the effectivene of a precat beam column concrete connection of a jointed ytem. However, thi computer model did not examine the teel ection intalled in a columnbeam joint, a dicued in [6]. Another tudy by Ioani and Tripa (2012) dicued a new all-precat concrete ytem ued in Romania to contruct a reidential building. Deigned for contructability, a new all-precat concrete ytem compriing column, flat lab, and tructural wall were propoed. To validate the tructural quality and performance of thi type of tructure, an extenive program of theoretical analye and tructural tet (including hake table tet) wa conducted [7]. Thi product propoed by Ioani and Tripa differ from theonepropoedhere.thetructuralytemdeveloped bytheauthoriahybridcompoitebeam-columnframe that demontrate the tructural behavior of building frame ytem. We deigned hybrid precat compoite frame with imple teel connection inerted between precat concrete columnandbeamtoreitonlygravityloading.thefirt objective of the tudy by Chou and Uang (2007) wa to examine the effect of the two factor of continuity plate and the amount of tranvere reinforcement on the concrete hear trength in the connection region. The econd objective wa to develop an analytical procedure to quantify the connection hear force developed in concrete. Thi continuity platewillbeuedforthehybridcompoiteframeofthe author in later experiment [8]. Ju andkim (2005) developed thetechnical,economical,andconvenient(tec)compoite beam with experimental invetigation uing a erie of monotonic loading tet [9]. However, thi beam i not free from the requirement of being fire-proof. Thee tudie did not expand their interet to hybrid compoite tructure for practical application which were covered in thi paper. We alo preent novel tructural ytem with dynamic analyi to examine the hybrid behavior of a building, which take advantage of material, tructural, and contruction hybrid feature and capabilitie. The hybrid precat compoite frame ytem how how material, tructural, and contruction hybridityareetablihedtouniquelyprovideeconomyand contructability, making thi technology ignificant to the contruction indutry. We alo deigned hybrid precat compoite frame with imple teel connection inerted between precatconcretecolumnandbeamtoreitonlygravity loading. The hybrid compoite frame ytem introduced in thi paper i intended to provide the economy of precat concrete tructure with the contructability of teel frame tructure. Structural deign efficiency, facilitie planning, contruction, and building management could be maximized uing the propoed compoite frame ytem. Implementation of integrating augmented reality with building information modeling [10 13] will help project the chedule and cot of contruction utilizing mart frame for ite engineer and repone to any demand for change can be provided in time. We have previouly [14, 15] invetigated dual-frame ytem compoed of hybrid precat frame. The dual-frame ytem conit of a moment frame and a bearing wall or braced frame. Seimic force are ditributed in proportion to the lateral tiffne of each frame. The moment frame ha to reit at leat 25% of the deign eimic force. However, the dual frame ytem with moment connection including much more complicated contruction detail require ignificant time and cot than imple connection which are ued in building frame ytem for gravity loading. Building frame ytem with imple connection are commonly ued with teel frame to provide fat and eay contruction for building. In thi paper, new tructural ytem to provide implified contruction method wa preented for building frame ytem for gravity loading fabricated with hybrid precat compoite frame coniting of imple connection between column and beam. The building frame ytem wa deigned for the reearch; the frame reit gravity loading, while the bearing wall reit lateral force. 2. Precat Compoite Structural Sytem (Hybrid Precat Frame) 2.1.DetailoftheFramewithGeneralizedSteelJoint.The hybrid precat frame propoed in thi tudy repreent a hybrid compoite tructural ytem with the advantage of both teel frame and reinforced concrete tructure. Hybrid precat frame are compoed of generalized teel joint, reinforcing teel, and precat concrete. Apartment building have been outfitted with thee hybrid precat frame to reolve problem uch a the increae in floor height when contructed with concrete Rahmen. Thee frame can maintaintheamefloorheightathatofabearingwallytem, providing architectural flexibility and cot-effectivene [14, 15]. We developed a precat teel column with teel connection to effectively erect and aemble the compoite frame.thejointofhybridprecatframeintalledtoacorewall were imple connection to upport vertical loading only. The joint of the gravity frame were not filled with concrete, allowing for pin-joint behavior, which enhance the contructability and economic feaibility of the gravity frame. The contruction of the core-wall wa followed by contruction of hybrid precat frame, including column, beam, and lab. Hybrid precat frame were compoed ofhybridprecatbeamunitandhybridprecatcolumn unit with enhanced joint connection capable of reiting vertical load, enabling more efficient erection with tructural tability. Specifically, the introduction of teel ection for joint connection make the contruction of hybrid precat frame a timely a that of teel frame. Hybrid precat frame contruction i illutrated in Figure 1. Hybrid precat frame were manufactured either at a plant or on ite [16]. Hybrid precat beam take advantage of the material propertie of both teel and precat concrete without acrificing the performance of the compoite beam. The depth of the beam and lab can alo be reduced when lab are contructed on the edge of precat concrete.

3 Mathematical Problem in Engineering 3 Figure 1: Building contruction with hybrid precat frame. Stud bolt Steel plate Angle and bolt for imple connection (hear tap) Cat-in-place concrete Steel plate Simple connection (hinge) Variable Precat concrete Variable Figure 2: Detailed information on beam-column joint member. Figure 2 how the beam-column joint connection of hybrid precat frame, where joint connection are not filled with concrete (i.e., pin-joint). Typical hybrid precat beam-column connection deigned for pinned condition (Figure 2) enable the gravity load to be tranferred through the joint where the web of teel beam i bolted to the teel ection of the hybrid precat column. Thi type of tructural frame ytem provide impler contruction with tructural tability to upport gravity load. Figure 3 how the generalized teel joint configured for gravity loading that are ued in the hybrid precat frame. Additional hear tap are intalled to provide connection between the teel ection from both column and beam. Steel ection inerted into the hybrid precat beam and column allow hybrid precat frame to be erected in a many a three torie at a time. Conventional teel joint ued in conventional teel contruction are utilized a generalized connection. Figure 4 how the contruction proce ued to produce the hybrid precat frame. Both the hybrid precat column and the beam unit of the hybrid precat frame were manufactured a two-tory or three-tory column unit and were erected in one cycle. The main procee of floor work, which took about four day, conited of marking, core wall reinforcement work and form intallation, intallation of hybrid precat column unit and beam unit, intallation of deck plate or a PC plate and joint form, lab reinforcement work, and pouring.

4 4 Mathematical Problem in Engineering Steel plate Column reinforced rebar Simple connection(hear tap) Beam unit Cat-in-place concrete Variable Shear tap Stud bolt Stud bolt CFT Variable Precat concrete Shear tap Without CFT Shear tap With CFT (a) Detail of the beam-column joint of the hybrid precat frame (b) Detail of the hear tap Shear tap Stud bolt CFT Variable Service condition (c) Contruction detail of the column unit Figure 3: Detail of the hybrid precat frame joint. Precat tructure cannot be erected a fat a teel tructurebecauebeamwithoutlablacktability,ahownin Figure 5.Thehybridprecatframe,however,canbeerected a quickly a teel tructure without lab contruction. The hybrid precat frame uggeted in thi paper are hybrid compoite tructure that have the merit of both teel and precat concrete tructure; in particular, the teel ection function a erection component. Thi hybrid contruction method make it poible to erect precat concrete frame in a time-frame imilar to that of teel frame Structural Stability during Contruction. The propoed hybrid precat frame with teel joint provide tructural tability during contruction. In contrat, the vertical reinforcing teel ued for vertical plicing in conventional precat application i vulnerable to buckling againt unexpected vertical loading before the joint are filled with concrete, which could caue tructural intability of the frame under contruction, a hown in Figure 6.Inthepropoedmethod, teel ection are inerted between the upper and lower precat column and are connected to teel ection located at both end of the precat beam and girder or teel ection running throughout the entire length of the precat beam, allowing eay and table connection. 3. Ue of Convergence of the Hybrid Precat Frame Becaue hybrid precat frame can be deigned uing a wide range of pan and joint deign, bearing wall-type apartment building may be replaced with building with hybrid precat frame. Structural ytem hould be optimized with teel connection, which are required to be a mall a kgf/m 2 (about one-tenth that of reinforcing teel), enabling contructability and aembly time imilar to that of teel frame. Figure 7 how deflection of a compoite frame building ubjected to wind load. The lateral diplacement are within acceptable limit. Diplacement along the x-axi and yaxi wa 20 cm (H/3910) and 29 cm (H/1955), repectively. Acceptable tory drift in repone to eimic loading wa alo oberved in both direction, a hown in Figure 8.Thee reult demontrate that the optimized tructural compoite frame have tructural tability. 4. Dynamic Analyi of a Building with Hybrid Precat Frame Figure 9 howabuildingwith13torieandtwobaement (total floor area of 6741 m 2 ) that wa deigned with

5 Mathematical Problem in Engineering 5 Stud bolt Shear tap CFT Steel plate Cat-in-place concrete Shear tap Precat concrete Figure 4: Hybrid precat frame contruction proce. Upward contruction Critical path + Figure 5: Reduction of the hybrid precat frame contruction period. Rebar connection Rebar connection (a) Figure 6: Conventional precat concrete connection. (b)

6 6 Mathematical Problem in Engineering X-direction m (H/3909.9) Mida gen potproceor diplacement reultant e e e e e e e e e e e e Scale factor = E Y-direction m (H/1954.9) Mida gen potproceor diplacement reultant e e e e e e e e e e e e Scale factor = E (a) (b) Figure 7: Wind diplacement Story drift ratio (x-axi) Story drift ratio (y-axi) F 16F 15F 14F 13F 12F 11F 10F 9F 8F 7F 6F 5F 4F 3F 2F 1F 17F 16F 15F 14F 13F 12F 11F 10F 9F 8F 7F 6F 5F 4F 3F 2F 1F Story drift ratio Allowable tory drift ratio Story drift ratio Allowable tory drift ratio (a) (b) Figure 8: Story drift. the propoed compoite frame and elected for dynamic analyi. The floor plan and elevation with framing uing compoitecolumnandbeamarealohown.thebuilding wa deigned uch that the hear wall were reitant to lateral eimic loading, while the frame reited only vertical load. Dynamic analyi wa performed to invetigate the influence of the deign and ize of the compoite frame on the dynamic characteritic of the building. Figure 10 how a computer model of the building with compoite frame and wall in which the teel ection at both end of the beam are connected to teel inerted between two precat column. Figure 10(a) how gravity compoite frame attached to hear wall that are reponible for lateral earthquake loading. Figure 10(b) how cloe connection detail of the frame and wall that contitute the building frame. Figure 10(c) how teel frame and connection betweenbeamandcolumn.thematerial,tructural,and contruction hybrid application were integrated to combine the contructability of teel tructure with the economy of concrete tructure. Table 1 and 2 how modal participation mae and eigenvalue reult, repectively. The fundamental tranlational mode wa found in the third return period; the firt and econd mode were conidered to be mixed tranlational mode with torion. A fundamental tranlational mode of 1.5 econd along with a weak y-axi wa deemed reaonable. The fundamental period and mode hape for the compoite frame were more imilar to thoe of teel tructure than thoe of concrete tructure, indicating that the tructural behavior of a building with compoite frame and teel

7 Mathematical Problem in Engineering 7 Y Y6 X Y3 Y4 Y5 25,928 3,500 3,500 3,500 3,500 X1 X2 X3 14,600 6,300 2,000 6,300 1,300 5,000 5,000 1,300 3,290 41,790 3,500 7,000 7,000 7,000 7,000 7,000 3,500 3,500 3,500 3,500 3,500 3,500 3,500 3,500 3,500 3,500 Hall 2,900 2,900 3,500 3,500 3,500 3,500 2,900 4,100 3,500 3,500 3,000 2,400 39,200 X6 X6 X7 X8 X9 7,400 X10 1,400 4,900 4,900 1,400 6,300 2,000 6,300 14,600 17,750 (a) Figure 9: Continued.

8 8 Mathematical Problem in Engineering 5,382 14,600 6,300 2,000 6,300 2,150 4,150 6,150 7,000 5,100 1,447 1,500 3,600 3,600 3,800 2,900 2,900 2,900 2,900 2,900 2,900 2,900 2,900 2,900 2,900 2,900 2,900 1,400 2,600 1,300 1, , ,000 G.L ,250 2,250 2,250 2,250 2,250 2,250 2,250 2,250 2,250 2,250 2,250 2, ,300 1,600 2,880 2, G.L ,900 1,400 3,600 3,600 3,800 2,900 2,900 2,900 2,900 2,900 2,900 2,900 2,900 2,900 2,900 2,900 1,500 7,200 40,000 5,382 8,300 6,300 6,150 7,000 5,100 1,447 (b) Figure 9: Floor plan and elevation.

9 Mathematical Problem in Engineering 9 Table 1: Modal participation mae. Mode number TRAN-X TRAN-Y ROTN-Z Ma (%) Sum (%) Ma (%) Sum (%) Ma (%) Sum (%) (a) (b) (c) Figure 10: Computer model of the building. Table 2: Eigenvalue analyi (fundamental period). Mode number Frequency Period (rad/ec) (cycle/ec) (ec) Tolerance e e e e e e 137 joint againt vertical and lateral loading reemble that of teel tructure, even though the building ha an external appearance of a concrete tructure. Figure 11 how the firt tranlational mode (a) and thoe of two mixed mode ((b), (c)). Figure 11(d), 11(e), and11(f) how thee mode from the top view, repectively. 5. Reduction of Structural Quantity and Emiion of Environmentally Hazardou Subtance and Material Thi tudy evaluated chromium VI and carbon dioxide emiion of the building contructed with the propoed frame and conventional wall. Reduction in energy conumption due to reduction in material quantity were etimated baed on comparion of an apartment building contructed with hybrid precat frame and that of a conventional bearing-wall building. Original unit of major building component (Table 3), which were announced in 2008 by the United Kingdom Table 3: Emiion and energy uage of major building component [17]. Building component CO 2 emiion per original unit Energy conumption per original unit Concrete 25 MPa kg-co 2 /m MJ/m 3 Concrete 35 MPa kg-co 2 /m MJ/m 3 Reinforcement kg-co 2 /kn MJ/kN Steel ection kg-co 2 /kn MJ/kN Inventory of Carbon and Energy (ICE), were ued to evaluate carbon dioxide emiion and the energy efficiency of the propoed contruction. The embodied energy E and carbon emiion per kn for the calculated material quantity are obtained from the Univerity of Bath ICE databae [17, 18]. The ICE ha been tructured into 34 main material group. The databae alo provide the embodied energy and carbon coefficient for contruction material. Table 3 preent the converted embodied energy and carbon coefficient for four building component: concrete (25 MPa), concrete (35 MPa), reinforcement, and teel ection. Dometic and foreign cement heavy metal analyi reult (May 2013) publihed by the Korea National Intitute of Environment Reearch (NIER) were utilized to evaluate chromium VI emiion (Table 4). In order to explain how the data that evaluate the gravity ytem preented in thi paper in term of material quantity, analytical approach for the hybrid precat compoite beam deign baed on the train compatibility method wa introduced. Figure 12 and 13 illutrate the ide view and croection of a hybrid compoite beam. In order to determine the

10 10 Mathematical Problem in Engineering Table 4: Heavy metal content tandard in cement [19]. Cr 6+ A Cd Cu Hg Pb Ave. (May, 2013) mg/kg mg/kg 1.02 mg/kg mg/kg 0.61 mg/kg mg/kg (a) Fundamental tranlational mode (b) Mixed mode 1 (c) Mixed mode 2 (d) Fundamental tranlational mode (e) Mixed mode 1 (f) Mixed mode 2 Figure 11: Mode hape. Figure 12: Side view of a hybrid compoite beam. d d d d Figure 13: Cro-ection of a hybrid compoite beam. exact material quantity, the hybrid compoite beam deign wa carried out baed on the train compatibility method. Equation (1) and(2) are the mean tre factor α and the centroid factor γ for any train ε cm at the extreme compreion fiber calculated baed on tre-train relationhip. Equation (3)and(5)repreenttheequilibriumequationof compreive and tenile force at yield limit and maximum load limit tate, repectively. The nominal moment capacitie of a hybrid compoite beam at yield limit and maximum load limit tate are calculated by (4) and(6), repectively. Figure 14 and 15 repreent train and tre diagram at yield limit and maximum load limit tate, repectively. In both figure, black color indicate teel and reinforcement rebar were platicized (yielded) while white color repreent tructural member remained elatic. The tructural quantity required by apartment building with hybrid compoite frame wa obtained from (6) and compared with that of conventional building with bearing wall a hown in Table 5. Thee

11 Mathematical Problem in Engineering 11 Building component Table 5: Evaluation of tructural ytem. Sytem Gro area Building material CO 2 emiion Energy conumption Cr 6+ emiion Concrete H.P.F m m 3 /m % (H.P.F. = 35 MPa ( 30.9%) kg-co 2/m % ( 22.5%) % MJ/m % mg/m2 ( 21.4%) ( 31.1%) B.W. = 25 MPa) B.W m m 3 /m % kg-co 2 /m % MJ/m % mg/m 2 100% Reinforcement H.P.F m kn/m % ( 27.4%) kg-co 2/m % ( 27.6%) % MJ/m2 ( 28.7%) B.W m kn/m % kg-co 2 /m % MJ/m % H.P.F m kn/m % 20.6 kg-co Steel ection 2 /m % MJ/m % B.W m 2 kn/m 2 % kg-co 2 /m 2 % MJ/m 2 % H.P.F.: hybrid precat frame; B.W.: bearing wall. ε c = f c mm ε t = ε t E = 192 MPa ε t = ε t =ε y = 301 MPa 400 MPa Figure 14: Strain and tre diagram at yield limit tate mm ε t = ε c = ε t E = 286 MPa f c ε t = MPa ε t =ε y = MPa Figure 15: Strain and tre diagram at maximum load limit tate. equation would help engineer etimate precie contruction material and undertand how building with hybrid compoite frame behave. Conider α= ( f c {2ε c ( ε 2 c ) }dε 0 ε co ε c co (ε cm [ f c {2ε c ( ε 2 c ) }dε 0 ε co ε c co f c {1 100 (ε c ε co )} dε c ]) ), (2) f c {1 100 (ε c ε co )} dε c ) (f c ε cm) 1, γ=1 (( ε c f c {2ε c ( ε 2 c ) }dε 0 ε co ε c co ε c f c {1 100 (ε c ε co )} dε c ) (1) αf c bc+a E ε c c (c d )+ 1 2 A w E ε c c (c d ) =A F y +A f E ε c c (d c d t f 2 ) A we ε c c (d c d t f ), where A w =t w(c d ), A w =t w (d c d t f ) M n =αf c bc(c γc)+a E ε c c (c d ) A w E ε c c (c d ) 2 +A F y (d c) (3)

12 12 Mathematical Problem in Engineering Proce Day One floor Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 Marking Rebar work (wall) Wall form intallation Slab form intallation Rebar work (lab) Electrical and mechanical facilitie (lab) Cleaning and pouring Figure 16: Procee for contructing one floor of a conventional wall-type apartment building [20]. +A f E ε c c {(d c d t f )(d c d t f 2 ) + t f 2 (d c d t f 3 )} A we ε c c (d c d t f ) 2, where A w =t w(c d ), A w =t w (d c d t f ) αf c bc+a E ε c c (c d )+ 1 2 A w E ε c c (c d ) =A F y +A f F y +A wp F y A wnye ε y, where A w =t w(c d ), A wp =t w {(d c+d +t f )+(ε y /ε c )c}, A wny =t w (ε y /ε c )c M n =αf c bc(c γc)+a E ε c c (c d ) A w E ε c c (c d ) 2 +A F y (d c) +A f F y (d c d t f 2 ) A wpf y {(d c d t f )+ ε y ε c c} A wnye (ε y ) 2 ε c where A w =t w(c d ), A wp =t w {d (c + d +(ε y /ε c )c)}, A wny =t w (ε y /ε c )c. A completed bearing wall apartment building wa elected for thi comparion. Apartment building with hybrid precat frame and bearing wall frame were evaluated in term of building material, CO 2 emiion, energy conumption, and Cr 6+ emiion hown in Table 5.Contruction c, (4) (5) (6) material per quare meter were calculated baed on (5)and (6) whichwerethenuedtocalculatethequantitieoftable 5. The building material of concrete and reinforcement of apartment building with hybrid precat frame were reducedby31%and27%,repectively,comparedwiththat ofbearingwallframebuilding.theco 2 emiion, energy conumption, and Cr 6+ emiion of apartment building with hybrid precat frame were alo decreaed compared with bearing wall frame building a hown in Table 5, exhibiting theefficiencyofuinggravityhybridprecatframefor apartment building. 6. Reduction in Contruction Schedule Figure 16 and 17 compare the contruction time frame baed on the ue of conventional bearing wall veru the propoed hybrid frame. The contruction time i the um of each critical path, a hown in n i=1 (CA i )=CA 1 + CA 2 + CA 3 + CA 4. (7) The critical path that affect contruction time for a bearing wall apartment are CA 1 (marking, 1 day), CA 2 (rebar work, wall, 1 day), CA 3 (wall form intallation, 2 day), CA 4 (lab form intallation, 1 day), CA 5 (rebar work, lab, 1 day), and CA 6 (cleaning and pouring, 1 day). Intallation of electrical and mechanical facilitie at the lab i performed with rebar work of the lab and take le time than that of rebar work. Electrical and mechanical facilitie at the lab are therefore excluded from the critical path. The contruction time per floor i even day baed on (7). The critical path affecting contruction time for an apartment building uing hybrid frame are CA 1 (rebar work, core wall, 0.5 day), CA 2 (column-beam unit intallation (1 day), beam unit intallation (1.5 day)), CA 3 (rebar work, lab, 0.5 day), and CA 4 (cleaning and pouring, 0.5 day). Column-beam unit intallation and beam unit intallation are carried out alternately. Beam are only intalled at every econd and third floor ince column are erected a a three-tory unit.

13 Mathematical Problem in Engineering 13 Proce Day Firt floor Second floor Third floor Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 Day 8 Day 9 Day 10 Rebar work (core wall) Core wall form intallation Column-beam unit intallation Beam unit intallation Deck plate intallation Joint form intallation Rebar work (lab) Electrical and mechanical facilitie (lab) Cleaning and pouring Figure 17: Procee for contructing three floor of an apartment building uing hybrid frame [20]. Table 6: Comparative analyi of the contruction period [20]. Structural type Typical floor Contruction period 30-tory apartment building Comparion Bearing wall 7 day/1 floor 210 Day 100.0% Hybrid precat frame 10 day/3 floor 100 Day 47.6% A a reult of the critical path analyi, the contruction timeperfloorifourdayforthefirtfloorandthree day for the next two floor, requiring ten day for the contruction of three floor utilizing column of a threetory unit. The time for frame erection wa reduced by 52% when uing hybrid frame, highlighting their economic and contruction benefit. Erection of tructural frame for one floor uing conventional bearing wall involve rebar work andconcretepouringandrequireaboutevenday,a hown in Figure 16. In contrat, only three day were required to intall wall and lab form, indicating that the overall contruction wa influenced by form work, which i highly dependent on work kill. However, erection of three floor with hybrid precat frame required only ten day when three-tory hybrid precat column were erected at one lift. The ignificant reduction in form work contributed to the decreae in overall contruction time obtained when uing thehybridprecatframe,ahowninfigure 17.Ahownin Table 6, frame erection of a 30-tory building required even day per floor or 210 day for the entire building when uing conventional bearing wall. However, only ten day per three floor (or 100 day for the entire building) were required for frame erection of the building with hybrid precat frame, which correpond to a 52.4% reduction in frame erection time. 7. Concluion Thi tudy decribed and characterized an optimized hybrid precat compoite tructural ytem for gravity ytem. Major contribution are ummarized below. (1) Gravity hybrid precat frame were preented. Thee hybrid frame conit of precat concrete and teel whichcanbeerectedatapeedimilartothatofteel frame. Steel ection inerted in precat column and beam are ued a erection teel component. (2)Mathematicalmodelofgravityhybridprecatbeam wa preented at yield limit tate and maximum load limit tate. Neutral axi of potyield tate found from equilibrium equation wa ued to calculate nominal moment capacitie of a hybrid compoite beam at both limit tate. (3) The new building frame ytem for gravity loading fabricated with hybrid precat compoite frame coniting of imple connection between column and beam were propoed in thi paper. The dual frame ytem of moment connection with much more complicated contruction detail required ignificanttimeandcotthanthatofbuildingframe ytem of gravity loading. However, the gravity hybrid precat compoite tructure will provide implified contruction method, while enhancing economy during contruction. The reduction of contruction reource including concrete and reinforcement (31% reduction of concrete and 27% reduction of reinforcement) were achieved when apartment were to be built with hybrid precat frame. (4) The gravity hybrid precat frame ue le contruction material than conventional frame and therefore reduce carbon dioxide and hazardou ubtance emiion compared to conventional frame. It wa

14 14 Mathematical Problem in Engineering obervedtheefficiencyofuinggravityhybridprecat frame for apartment building which decreaed the CO 2 emiion (23% reduction of concrete and 28% reduction of reinforcement), energy conumption (21% reduction of concrete and 29% reduction of reinforcement), and Cr 6+ emiion compared with bearing wall frame building. The ue of gravity hybrid precat frame wa demontrated to provide better olution for environment and economy than that of conventional building. (5) Dynamic analyi of a 15-tory building deigned with the propoed compoite gravity frame wa performed to characterize frequencie and mode hape of the building for eimic deign purpoe. Conflict of Interet The author declare that there i no conflict of interet regarding the publication of thi paper. Acknowledgment Thi work wa upported by Grant from the Kyung Hee Univerity in 2013 (KHU ). Reference [1] J. F. Hajjar, Compoite teel and concrete tructural ytem for eimic engineering, Contructional Steel Reearch, vol.58,no.5 8,pp ,2002. [2] G. Fabbrocino, G. Manfredi, and E. Coenza, Ductility of compoite beam under negative bending: an equivalence index for reinforcing teel claification, Contructional Steel Reearch,vol.58,no.2,pp ,2001. [3] B. Yang and K. Tan, Behaviour of compoite beam-column joint under a middle-column-removal cenario: experimental tet, Structural Engineering, vol. 140, no. 2, Article ID , [4] L. Teer and R. Scotta, Flexural and hear capacity of compoite teel tru and concrete beam with inferior precat concrete bae, Engineering Structure,vol.49,pp ,2013. [5]H.J.Hwang,H.G.Park,C.H.Leeetal., Seimicreitance of concrete-filled U-haped teel beam-to-rc column connection, JournalofKoreanSocietyofSteelContruction,vol.23,pp , [6] J. Haan and B. Khorow, Nonlinear eimic behavior evaluation of ductile beam-column connection in precat concrete, International Civil and Structural Engineering, vol.1, pp ,2011. [7] A. M. Ioani and E. Tripa, Structural behavior of an innovative all-precat concrete dual ytem for reidential building, PCI Journal,vol.57,no.1,pp ,2012. [8] C. Chou and C. Uang, Effect of continuity plate and tranvere reinforcement on cyclic behavior of SRC moment connection, Structural Engineering,vol.133,no.1,pp ,2007. [9] Y. K. Ju and S. D. Kim, Structural behavior of alternative low floor height ytem uing tructural tee, half precat concrete, and horizontal tud, Canadian Civil Engineering, vol. 32, no. 2, pp , [10] X. Wang, M. Truijen, L. Hou, Y. Wang, and Y. Zhou, Integrating augmented reality with building information modeling: onite contruction proce controlling for liquefied natural ga indutry, Automation in Contruction,vol.40,pp ,2014. [11] L. Hou, Y. Wang, X. Wang et al., Combining photogrammetry and augmented reality toward an integrated facility management ytem for the oil indutry, Proceeding of the IEEE, vol. 102, no. 2, pp , [12] L. Hou, X. Wang, L. Bernold, and P. E. D. Love, Uing animated augmented reality to cognitively guide aembly, Computing in Civil Engineering,vol.27,no.5,pp ,2013. [13] Y.Wang,X.Wang,J.Wang,P.Yung,andG.Jun, Engagementof facilitie management in deign tage through BIM: framework and a cae tudy, Advance in Civil Engineering, vol. 2013, Article ID , 8 page, [14] W. K. Hong, J. M. Kim, S. C. Park et al., A new apartment contruction technology with effective CO 2 emiion reduction capabilitie, Energy,vol.35,no.6,pp ,2010. [15]W.Hong,S.Park,J.Kimetal., Developmentoftructural compoite hybrid ytem and their application with regard to the reduction of CO 2 emiion, Indoor and Built Environment, vol.19,no.1,pp ,2010. [16]W.Hong,S.Jeong,S.Park,andJ.T.Kim, Experimental invetigation of an energy-efficient hybrid compoite beam during the contruction phae, Energy and Building, vol. 46, pp , [17] G. P. Hammond and C. I. Jone, Inventory of Carbon & Energy (ICE), Department of Mechanical Engineering, Univerity of Bath,Bath,UK,2008. [18] G. P. Hammond and C. I. Jone, Embodied energy and carbon in contruction material, Proceeding of Intitution of Civil Engineer: Energy,vol.161,no.2,pp.87 98,2008. [19] National Intitute of Environment Reearch (NIER): Dometic and foreign cement heavy metal analyi reult (May 2013), NIER, 2013, 02.page. [20] S. Kim, W. Hong, J. Kim, and J. T. Kim, The development of modularized contruction of enhanced precat compoite tructural ytem (Smart Green frame) and it embedded energy efficiency, Energy and Building,vol.66,pp.16 21,2013.

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