Cost optimization of reinforced concrete chimney

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Cost optimization of reinforced concrete chimney

  1. 1. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 2, March - April (2013), © IAEME402COST OPTIMIZATION OF REINFORCED CONCRETE CHIMNEYProf.Wakchaure M.R.1, Sapate S.V2, Kuwar B.B.3, Kulkarni P.S.41(Assistant Professor, Civil Engineering Department, Amrutvahini college of Engineering,Sangamner, Pune university, India)2(M.E.Structures, Civil Engineering Department, Amrutvahini college of Engineering,Sangamner, Pune university, India)3(M.E.Structures, Civil Engineering Department, K.K.Wagh college of Engineering, Nasik,Pune university, India)4(M.E.Structures, Civil Engineering Department, K.K.Wagh college of Engineering, Nasik,Pune university, India)ABSTRACTThe design of reinforced concrete chimney structure almost always involves decisionmaking with a choice of set of choices along with their associated uncertainties andoutcomes. While designing such a structures, a designer may propose a large number offeasible designs; however, only the most optimal one, with the least cost be chosen forconstruction. For delivering an acceptable design, computer based programmes may helptoday’s design practitioner. A program is developed for analysis and designing a low costRCC chimney in MATLAB. The optimtool module is used to find out the structure havingminimum cost with appropriate safety and stability. Illustrative case of chimney structure ispresented and discussed by using Interior point method from optimtool. The comparisonbetween conventional and optimal design is made and further results are presented. In finalresult, percentages saving in overall cost of construction are presented in this paper.Keywords: RCC chimney, Cost optimization, Interior point method, MATLAB, optimtool.1. INTRODUCTIONDuring the past few years industrial chimneys have undergone considerabledevelopments, not only in the structural conception, modeling and method of analysis, butINTERNATIONAL JOURNAL OF CIVIL ENGINEERING ANDTECHNOLOGY (IJCIET)ISSN 0976 – 6308 (Print)ISSN 0976 – 6316(Online)Volume 4, Issue 2, March - April (2013), pp. 402-414© IAEME: www.iaeme.com/ijciet.aspJournal Impact Factor (2013): 5.3277 (Calculated by GISI)www.jifactor.comIJCIET© IAEME
  2. 2. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 2, March - April (2013), © IAEME403also in the materials employed and the methods of construction. Illustrative case of chimneystructure is presented and discussed by using Interior point Method from optimtool inMATLAB. Interior point method and sequential quadratic programming methods are the twoalternative approaches for handling the inequality constraints.Interior point method provides an alternative to active set method for the treatment ofinequality constraints. Interior point method have been a remerging field in optimizationsince the mid of 1980s. At each iteration, an interior point algorithm computes a direction inwhich to proceed, and then must decide how long of a step to take. The traditional approachto choose a step length is to use a merit function which balances the goals of improving theobjective function and satisfying the constraints. Sequential quadratic programming (SQP)ideas are used to efficiently handle nonlinearities in the constraints. Sequential quadraticprogramming (SQP) methods find an approximate solution of a sequence of quadraticprogramming (QP) sub problems in which a quadratic model of objective function isminimized subject to the linearized constraints. Both interior method and SQP method havean inner or outer iteration structure, with the work for an inner iteration being dominated bycost of solving a large sparse system of symmetric indefinite linear equation, SQP methodprovide a reliable certificate of infeasibility and they have potential of being able to capitalizeon a good initial starting point.In this paper, cost optimization is done for 66 m industrial RCC Chimney (Figure1)which is having constant outer diameter of 4m and thickness is varying from top to bottom inthree steps. Thickness of top segment (24m) shell is 200mm, and that of middle (24m) andbottom segment (18m) it is 300mm and 400mm respectively.Fig.1 Reinforced concrete chimney
  3. 3. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 2, March - April (2013), © IAEME4042. OBJECTIVE FUNCTIONThe objective function is a function of design variables the value of which providesthe basis for choice between alternate acceptable designs. Here the objective function is costminimization. The cost function f (cost) is:f (cost) = Cs*Wst + Cc*Vc +Cb*VbWhere, Cs, Cc and Cb= Unit cost of steel, concrete and brick lining respectively.Wst is the weight of steel.Vc and Vb= Volume of concrete, and brick lining respectively.Cost calculation for concrete, steel and brick lining are inclusive of centering,shuttering and cutting.3. FORMULATION OF OPTIMIZATION PROBLEM.The general three phases considered in the optimum design of any structure are1) Structural modeling.2) Optimum design modeling.3) Optimization algorithm.In structural modeling, the problem is formulated as the determination of a set ofdesign variables for which the objective of the design is achieved without violating the designconstraints. For the optimum design modeling, Study the problem parameter in depth, so as todecide on design parameter, design variables, constraints, and the objective function. In thesearch for finding optimum design starts from a design or from a set of designs to proceedtowards optimum.3.1 Structural ModelingIn cost optimization of RCC chimney the aim is to minimize the overall construction costunder constraints. This optimization problem can be expressed as follows:Minimize f(X)Subject to the constraintsgi (X) ≤ 0 i=1, 2, . . . . phj (X) = 0 j=1, 2,. . . . mWhere, f(X) is the objective function andgi(X), hj(X) are inequality and equality constraints respectively.3.2 Optimum Design Model3.2.1 Design VariablesIn optimization process, we required decision variables, design constraints, andobjective function. Decision variables are defined by a set of quantities some of which areviewed as variables during the design process. The design variables cannot be chosenarbitrarily, rather they have to satisfy certain specified functional and other requirements.Figure 2 shows the design variables considered for RCC chimney. h = Height of chimneystructure, X1=Thickness of segment, X2=Vertical reinforcement, X3=Horizontalreinforcement, X4 = Thickness of brick lining.
  4. 4. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 2, March - April (2013), © IAEME405Fig.2: Mathematical model used for optimization of R.C.C. Chimney.3.2.2 Design ConstraintsThe restrictions that must be satisfied to produce an acceptable design are collectively calledas design constraint. The following design constraints are imposed on the variables.1. Actual eccentricity (E) should be less than allowable eccentricity (Ea).2. Maximum compressive stress should be less than allowable compressive stress.3. Maximum Tensile stress should be less than allowable tensile stress (0.85Mpa).4. Restriction on maximum and minimum vertical reinforcement percentage as perCICIND Model code for concrete chimney shell.5. Restriction on horizontal reinforcement percentage as CICIND Model code forconcrete chimney shell.6. Stresses due to temperature gradient should be less than permissible stresses.7. Bearing capacity criterion.In design of RCC chimney structure, the objective function is taken for minimizingthe overall cost of construction. Structurally, a chimney is designed for its own weight, windpressure or seismic forces and the temperature stresses. Its own weight cause directcompression in the section which increases towards the base. The wind pressure tends tobend the chimney as a cantilever about its base, causing compression on leeward side andtension on windward side. These stresses should not exceed the permissible values fordifferent grades of concrete and steel. So in this particular optimization, constraint is givenfor stresses in leeward and windward side. The temperature stresses are developed inchimney due to difference of temperature on its outside and inside surfaces. So the constraintis given so that stresses induced due to temperature should be within permissible limit. Otherconstraints are for maximum and minimum reinforcement percentage, Eccentricity whichmust satisfy the standard code requirement. Bearing capacity criterion includes maximumreaction pressure on footing should be less than safe bearing capacity of soil.hX2X1111X3
  5. 5. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 2, March - April (2013), © IAEME4064. RESULTS OF OPTIMIZATIONThe programs developed were applied to obtained optimal solution for 66 m heightRCC chimney. Optimal values are obtained for three cases which include segments ofdifferent heights as mentioned below and compared with conventional values. CASE (I) 3segments of 24m, 24m, and 18m. CASE (II) 6 segments of 12m, 12m, 12m, 12m, 9m, and9m. CASE (III) 11 segments of 6m each. The design parameters considered in above casesthat are related to wind pressure on chimney, code specifications, unit cost and othercharacteristics of construction materials. Optimal solution changes with the variation of theseparameters which is an important issue as far as practical design is concerned. This isconstrained nonlinear programming problem for the numerical solution of the RCC chimneystructure using MATLAB, optimtool. A constrained equation and objective function has beenprepared for various height segments. Following are the input parameters of chimney whichis used in the optimtool for making constrained equations.Table 1: Input parametersInput parameter Unit Symbol Design ValueHeight m h 66Yield strength of steel kN/m2fy 500*103Characteristic strength of concrete kN/m2fck 25*103Unit wt of concrete kN/m3dc 25Density of steel kg/m3ds 7894.09% minimum steel for vertical steel % ρmin 0.3% maximum steel for vertical steel % ρmax 4% minimum steel for horizontal steel % ρhmin 0.2spacing for horizontal steel mm s 250Cost of steel Rs/kg Cs 60Cost of concrete Rs/m3Cc 8000Cost of concrete Rs/m3Cb 2500S.B.C. kN/m2b 180Table 2: CASE (I) Optimal values for three (3) segmentsSr.NohmSeg-mentSegmentLengthmX1mmX2mm2X3mm2TotalX2mm2WeightedAvg.ThicknessmmVolume ofconcretem31 24 0-24 24 196 23462 393 23462276.45 213.442 48 24-48 24 289 33666 578 571283 66 48-66 18 367 41888 734 99016
  6. 6. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 2, March - April (2013), © IAEME407Table 3: CASE(I) Conventional values for three (3) segmentsSr.NohmSeg-ment X1mmX2mm2TotalX2mm2X3mm2WeightedAvg.ThicknessmmVolume ofconcretem31 24 0-24 200 24127 24127 400290.09 223.152 48 24-48 300 37699 61826 6003 66 48-66 400 58904 120730 800Table 4: CASE (I) Cost comparison.Sr.NohmSeg-mentSegmentLength(m)Co(Rs)Ct(Rs)TotalOptimumCost (Rs)TotalConventionalcost (Rs)%saving1 24 0-24 24 466063 474396 466063 474396 1.762 48 24-48 24 696700 748876 1162763 1223272 4.953 66 48-66 18 670284 727159 1833047 1950431 6.02Table 5: CASE (II) Optimal values by taking six (6) segments.Sr.NohmSeg-mentSegmentLengthmX1mmX2mm2TotalX2mm2X3mm2WeightedAvg.ThicknessmmVolume ofconcretem31 12 0-12 12 160 9667 9667 321252.68 196.332 24 12-24 12 195 11676 21343 3913 36 24-36 12 237 13985 35328 4734 48 36-48 12 287 16720 52048 5735 57 48-57 9 317 18323 70371 6336 66 57-66 9 364 20770 91141 727
  7. 7. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 2, MarchGraph1: CASE (I) comparison ofGraph2: CASE (I) comparison of02000004000006000008000001000000120000014000001600000180000020000000TotalCostinRs01500030000450006000075000900001050001200001350001500000steelinmm2rnational Journal of Civil Engineering and Technology (IJCIET), ISSN 09766316(Online) Volume 4, Issue 2, March - April (2013), © IAEME408CASE (I) comparison of optimum and conventional costCASE (I) comparison of optimum and conventional steel.0 24 48 72Optimal Costconventional CostHeight in m12 24 36 48 60 72Optimal steelconventional steelHeight in mrnational Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308April (2013), © IAEMEoptimum and conventional steel.
  8. 8. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 2, MarchGraph3: CASE (II) comparison of optimum andGraph4: CASE (I02000004000006000008000001000000120000014000001600000180000020000000CostinRs01500030000450006000075000900001050001200001350001500000steelinmm2rnational Journal of Civil Engineering and Technology (IJCIET), ISSN 09766316(Online) Volume 4, Issue 2, March - April (2013), © IAEME409) comparison of optimum and of conventional costII) comparison optimum and conventional steel12 24 36 48 60 72Optimal Costconventional CostHeight in m12 24 36 48 60 72Optimal steelconventional steelHeight in mrnational Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308April (2013), © IAEMEconventional cost
  9. 9. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 2, MarchTable 6: CASE (II) ConventionalSr.NohmSeg-mentX1mm1 12 0-12 2002 24 12-24 2003 36 24-36 3004 48 36-48 3005 60 48-57 4006 66 57-66 400Table 7Sr.NohmSeg-mentSeg-mentLengthm1 12 0-12 122 24 12-24 123 36 24-36 124 48 36-48 125 57 48-57 96 66 57-66 9Graph5: CASE (III) comparison of optimum and0200000400000600000800000100000012000001400000160000018000002000000TotalCostinRsrnational Journal of Civil Engineering and Technology (IJCIET), ISSN 09766316(Online) Volume 4, Issue 2, March - April (2013), © IAEME410) Conventional values by taking six (6) segmentsX2mm2TotalX2mm2X3mm2WeightedAvg.Thicknessmm12063 12063 400290.0912063 24127 40018849 42976 60018849 61826 60029452 91278 80029452 120730 800Table 7: CASE (II) Cost comparison.Co(Rs)Ct(Rs)TotalOptimumCost(Rs)TotalConventionalcost(Rs)192016 237198 192016 237198231931 237198 423947 474396291723 374438 715670 848834346096 374438 1061766 1223272295728 363579 1357494 1586851332517 363579 1690011 1950431) comparison of optimum and of conventional cost0 6 12 18 24 30 36 42 48 54 60 66 72Optimal Costconventional CostHeight in mrnational Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308April (2013), © IAEMEvalues by taking six (6) segments.Volumeofconcretem3223.15Conventional%saving237198 19.05474396 10.63848834 15.691223272 13.201586851 14.451950431 13.35conventional cost
  10. 10. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 2, MarchGraph6: CASE (IITable 8: CASE (III) Optimal values by taking eleven (11) segmentsSr.NohmSeg-mentSegmentLengthm1 6 0-6 62 12 6-12 63 18 12-18 64 24 18-24 65 30 24-30 66 36 30-36 67 42 36-42 68 48 42-48 69 54 48-54 610 60 54-60 611 66 60-66 6150003000045000600007500090000105000120000135000150000steelinmm2rnational Journal of Civil Engineering and Technology (IJCIET), ISSN 09766316(Online) Volume 4, Issue 2, March - April (2013), © IAEME411II) comparison optimum and conventional steel(III) Optimal values by taking eleven (11) segmentsX1mmX2mm2TotalX2mm2X3mm2WeightedAvg.Thicknessmm141 4266 4266 281241.09159 4796 9062 318175 5244 14306 349194 5811 20117 389207 6158 26275 413234 6914 33189 467260 7639 40828 520285 8304 49132 569307 11865 60997 614330 12683 73680 660360 13732 87412 72001500030000450006000075000900001050001200001350001500000 6 12 18 24 30 36 42 48 54 60 66 72Optimal steelconventional steelHeight in mrnational Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308April (2013), © IAEME(III) Optimal values by taking eleven (11) segmentsWeightedThicknessVolumeofconcretem3187.90
  11. 11. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 2, March - April (2013), © IAEME412Table 9: CASE (III) Conventional values by taking eleven (11) segmentsSr.NohmSeg-mentX1mmX2mm2TotalX2mm2X3mm2WeightedAvg.ThicknessmmVolumeofconcretem31 6 0-6 200 6032 6032 400290.09 233.152 12 6-12 200 6032 12063 4003 18 12-18 200 6032 18095 4004 24 18-24 200 6032 24127 4005 30 24-30 300 9425 33552 6006 36 30-36 300 9425 42976 6007 42 36-42 300 9425 52401 6008 48 42-48 300 9425 61826 6009 54 48-54 400 19635 81461 80010 60 54-60 400 19635 101095 80011 66 60-66 400 19635 120730 800Table 10: CASE (III) Cost comparisonSr.NohmSeg-mentSegmentLengthmCo(Rs)Ct(Rs)TotalOptimumCost(Rs)TotalConventionalcost(Rs)%saving1 6 0-6 6 84733 118599 84733 118599 28.562 12 6-12 6 95263 118599 179996 237198 24.123 18 12-18 6 104158 118599 284154 355797 20.144 24 18-24 6 115421 118599 399575 474396 15.775 30 24-30 6 129269 187219 528844 661615 20.076 36 30-36 6 144309 187219 673153 848834 20.707 42 36-42 6 158716 187219 831869 1036053 19.718 48 42-48 6 171936 187219 1003805 1223272 17.949 54 48-54 6 191891 242386 1195696 1465658 18.4210 60 54-60 6 204178 242386 1399874 1708045 18.0411 66 60-66 6 219957 242386 1619831 1950431 16.955. TOTAL COST COMPARISONSGraph is plotted which shows total cost of chimney obtained by optimization. In eachcase i.e. by taking 3, 6, and 11 segments, total cost is plotted and compare it withconventional cost. As numbers of segment goes on increasing, more optimum values we get.
  12. 12. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 2, March6. COMPARISON OF OPTIMUM CONCRETEWeighted thickness in each case iscalculated and is compared with conventional one. Following graph shows amount ofconcrete saving in each case.Graph7Graph8: Comparison of optimum and100000012000001400000160000018000002000000TotalCostinRs150170190210230Volumeofconcreteinm3rnational Journal of Civil Engineering and Technology (IJCIET), ISSN 09766316(Online) Volume 4, Issue 2, March - April (2013), © IAEME413TIMUM CONCRETE AND CONVENTIONAL CONCRETEWeighted thickness in each case is calculated, from which volume of concrete iscalculated and is compared with conventional one. Following graph shows amount ofGraph7: Numbers of segment Vs Total costComparison of optimum and conventional concrete1000000120000014000001600000180000020000000 3 6 9 12 15 18 21 24OptimalCostNumber of segments3 6 11 22Optimal Concreteconventional concreteNo of segmentsrnational Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308April (2013), © IAEMECONCRETEcalculated, from which volume of concrete iscalculated and is compared with conventional one. Following graph shows amount of
  13. 13. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 2, March - April (2013), © IAEME4147. CONCLUSIONS• Optimum values for cost, steel and concrete are then compared with the conventionalvalues. It is revealed from the graphs plotted for each case that the optimum valuesare getting more precise as number of segments goes on increasing. Optimal designshows total percentage cost saving of 6% in case (I), 13% in case (II) and 16% in case(III). This shows that optimization is more cost effective as numbers of segment go onincreasing. From graph, for conventional and optimal design consideration; it showsthat overall cost of structure can be reduced by using optimization technique withstability.• In optimtool, interior point method is more iterative method. So the results are moreelaborated by using interior point method.• The solver is giving optimum solution based on initial guess. If solver has beenchanged that case optimum values of design problem also changed according to initialguess. From above results, it is indicated that initial guess in solver is important forgetting more precise optimum values of respective height of chimney.REFERENCES1. Johannes C. Kloppers and Detlev G. Kroger, “Cost Optimization of Cooling TowerGeometry”, Engineering Optimization, Vol.36, No.5, Year 2004, pp.575-584.2. F.W. Yu and K.T. Chan, “Economic Benefits of Optimal Control for water-cooled ChillerSystems Serving Hotels in a Subtropical Climate”, Energy and Buildings, Vol. 42, No.02,Year 2010. pp. 203-209.3. Izuru Takewaki, “Semi-explicit optimal frequency design of chimneys with geometricalconstraints”, Department of Architectural Engineering, Kyoto University, Sakyo, Kyoto606, Japan Available online 3 May 1999.4. Eusiel Rubio-Castro, Medardo Serna-González and José María Ponce-Ortega, “OptimalDesign of effluent-cooling Systems Using a Mathematical Programming Model”,International Journal of Refrigeration, Vol.34, No.1, Year 2011. pp. 243-256.5. Shravya Donkonda and Dr.Devdas Menon, “Optimal design of reinforced concreteretaining walls”, The Indian Concrete Journal, Vol.86, No.04, pp. 9-18.6. A Model code for concrete chimneys, Part-A-The shell (1984)-CICIND, 136 North street,Brighton, England.7. Geoffrey.M.Pinfold, “Reinforced concrete chimneys and Towers”, A viewpointPublication limited.8. B.C.Punmia, Ashok K Jain and Arun K Jain, “Reinforced concrete structures- Vol.II”,Laxmi Publication (P) Ltd. New Delhi-110002.9. Mohammed S. Al-Ansari, “Flexural Safety Cost of Optimized Reinforced ConcreteBeams”, International Journal of Civil Engineering & Technology (IJCIET), Volume 4,Issue 2, 2013, pp. 15 - 35, ISSN Print: 0976 – 6308, ISSN Online: 0976 – 6316.10. H.Taibi Zinai, A. Plumier and D. Kerdal, “Computation of Buckling Strength ofReinforced Concrete Columns by the Transfer-Matrix Method”, International Journal ofCivil Engineering & Technology (IJCIET), Volume 3, Issue 1, 2012, pp. 111 - 127,ISSN Print: 0976 – 6308, ISSN Online: 0976 – 6316.

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