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  • D. R. Panchal, N. K. Solanki, S. C. Patodi / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.1656-1662 Towards Optimal Design of Steel - Concrete Composite Plane Frames using a Soft Computing Tool D. R. Panchal *, N. K. Solanki * and S. C. Patodi ** * (Applied Mech. & Str. Engg. Dept., FTE, M. S. University of Baroda, Vadodara 390001,) ** (Civil Engineering Department, Parul Institute of Engineering & Technology, Vadodara 391760,)ABSTRACT The use of steel – concrete composite multi-storey non-swaying steel frames withelements in a multistoried building increases the serviceability and strength constraints has beenspeed of construction and reduces the overall reported by [3]. Minimum cost design of steelcost. The optimum design of composite elements frames with semi-rigid connections and columnsuch as slabs, beams and columns can further bases via genetic algorithm consideringreduce the cost of the building frame. In the displacement, stress and member size constraints haspresent study, therefore, Genetic Algorithm (GA) been studied [4]. The main aim in the above reportedbased design optimization of steel concrete applications has been to find the best solution tocomposite plane frame is addressed with the aim derive the maximum benefit from the availableof minimizing the overall cost of the frame. The limited resources. The best design could be in termsdesign is carried out based on the limit state of minimum cost, minimum weight or maximummethod using recommendations of IS 11834, EC 4 performance or a combination of these.and BS 5950 codes and Indian and UK design Among the various available techniques, Genetictables. The analysis is carried out using computer Algorithm [5] technique, which is based on the- oriented direct stiffness method. A GA based concept of the survival of the fittest, is the mostoptimization software, with pre- and post- adaptive technique to solve search and optimizationprocessing capabilities, has been developed in problems. The availability of various options inVisual Basic.Net environment. To validate the composite structural components makes it lucrativeimplementation, examples of 2 × 3 and 2 × 5 to find the optimum shape and size of steel beam andcomposite plane frames are included here along composite column in steel concrete composite planewith parametric study. frame. This paper is, therefore, devoted to theKeywords - Composite plane frame, Genetic development of GA based optimization software foralgorithm, Optimization, Soft computing finding the optimum size of steel - concrete composite elements of a frame system. VB.NET1. INTRODUCTION environment is selected because it facilitates better The term “composite construction” is user interface over the web, simplified deployment,normally understood in the context of buildings and a variety of language support and an extendableother civil engineering structures to imply the use of platform for the future portability of compiledsteel and concrete formed together into a component application. In the optimum design of the compositein such a way that the resulting arrangement plane frame, composite column section and beamfunctions as a single unit [1]. Such structural section are considered as sizing variables and hencecomponents have an ideal combination of strengths number of design variables equals to number ofwith the concrete being efficient in compression and members in the plane frame geometry. One solutionthe steel being efficient in tension. string of GA, thus contains section properties of all A steel – concrete composite building may the beams and columns. The objective is to find thebe considered as group of plane frames supporting best possible combination of section properties ofcomposite slab with or without profile sheets. In members so as to minimize the cost of the compositecolumns of composite plane frames either Steel frame subjected to moment, shear, lateral torsionalReinforced Concrete (SRC) column, where a steel buckling and axial compression constraints.section is encased in concrete, or a Concrete Filled Concrete encased UK and Indian steel sections andTube (CFT) is generally used. Composite floor may concrete filled hot finished hollow sections are usedconsist of steel beams supporting concrete slab with in the optimum design process in the present study.or without profile sheets. Analysis of composite plane frame has been carried Cheng and Chan [2] have addressed the out by stiffness member approach while the designoptimal lateral stiffness design of composite steel has been carried out according to provisions of Euroand concrete tall frameworks subjected to drift code 4 [6] and IS: 11384 [7] code employing theconstraint and overall member sizing constraint. limit state method of design. To validate theGenetic algorithm based optimum design method for suggested concepts and implementation part of the 1656 | P a g e
  • D. R. Panchal, N. K. Solanki, S. C. Patodi / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.1656-1662software, it is used to find optimum cross sectional population. The fittest design among generations isproperties of members by trying varieties of considered to be the near-optimum design.available composite cross – sections stored in the To ensure that the best individual of eachdatabase. The optimum design solutions provided by generation is not destroyed from one design cycle tothe software are compared with the results provided another, an „elitist‟ strategy is followed in the design[8] for a two bay three-storey plane frame. Also, algorithm. At each generation, among theresults of a parametric study carried on a 2 x 5 frame individuals which satisfy all the design constraints,are presented followed by suitable recommendations the one with minimum weight is stored andfor the practicing engineers. compared with a similar individual of the next generation. If the new one is heavier than the old one2. ALGORITHM FOR A COMPOSITE FRAME then there is a loss of good genetic material. This The problem of size optimization of a situation is rectified by replacing the individualcomposite plane frame can be defined as follows: having the lowest fitness of the current generation Find, (x) with the fittest individual of previous generation. In To minimize, CT(x) = CS + CC this way the loss of good individuals during the Subject to, gi(x) ≤ 0 … development of new generations is prevented [3].(1)where, CT(x) is the total cost of composite frame, CS 3. DESIGN VARIABLES AND CONSTRAINSis the cost of steel used in plane frame, CC is the cost A design variable is used for the compositeof concrete slab, x is the vector of design variables beam which contains the details of steel sectionand gi(x) is the ith constraint function. properties such as width of flange, depth of section,Genetic algorithm based optimum design algorithm area of cross section etc. Another design variable is[9] for steel concrete composite frames consists of used for composite columns which representsthe following steps: column size and steel section details. A variable(a) Initial population of trial design solutions is when decoded gives a unique integer number whichconstructed randomly and the solutions are helps in extracting the section properties from SQLgenerated in binary coding form. server database.(b) The binary codes for the design variables of each In structural optimization problems,individual solution are decoded to find the integer constraints are formed by setting relationshipnumber which is assigned as an index to a composite between function of design variables with thesection in the available design table list. The analysis resource values, and constraints in the optimizationby computer – oriented direct stiffness approach is process prevent the search to enter the infeasiblecarried out by extracting section properties of regionmembers of steel concrete composite frame, whichrepresents an individual in the population. The 3.1 Constraints imposed on composite beamanalysis results are used for design and to evaluate (a) Moment constraint: In ultimate limit stateconstraint functions. design the moment capacity of the composite beams(c) The fitness value for each individual is should exceed the total factored applied momentcalculated using (Narayanan et al. 2001) which can be written as F(X) = 1/(1+Op(x))… (2) 𝑀 𝑛 ≤ 𝑀 𝑝𝑛 …(4)with the penalized objective function Op(x) given by Op(x) =(1+K* C) O(x) 𝑀 𝑝 ≤ 𝑀 𝑝𝑝 …(5)… (3)where O(x) is the objective function which is the 𝑀 𝑝𝑛 = 𝑃𝑦 × 𝑍 𝑝𝑥total cost of the frame, K is the penalty factor, and C 𝐴 𝑠 𝑓 𝑠𝑘 𝐷 𝐴 𝑠 𝑓 𝑠𝑘 2is the cumulative value of constraint violation. The + 𝛾𝑠 2 + 𝑎 − 𝛾𝑠 4𝑡 𝑤 𝑓𝑦 𝛾 𝑎 …(6)fitness thus obtained are scaled to get scaled fitness.(d) Depending on scaled fitness, individuals are 𝐴 𝑎 𝑓𝑦 𝐷 𝑋𝑢 𝑀 𝑝𝑝 = + ℎ𝑐 − …(7)copied into the mating pool. 𝛾𝑎 2 2(e) The individuals are coupled randomly and thereproduction operator is applied. Using one- or two- where Mpn and are negative and positivepoint crossover, off springs are generated and the plastic moment of resistance of the section of thenew population is obtained. composite beam respectively, Mn is factored design(f) Mutation is applied to the new population with a negative moment and Mp is factored design positiveprobability value between 0.01 and 0.07. moment. Corresponding functions for this constraint(g) vii. The initial population is replaced by the new are:population and steps (i) to (vi) are repeated until a g1(x) = Max ((Mn / MPn – 1), 0) …(8)pre-determined number of generations are reached or g2(x) = Max ((Mp / MPp – 1), 0)until the same individual dominates the new … (9) 1657 | P a g e
  • D. R. Panchal, N. K. Solanki, S. C. Patodi / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.1656-1662(b) Shear force constraint: This constraint ensures 4. DESIGN EXAMPLE OF A 2 X 3 STOREYthat the shear capacity of the frame member is more COMPOSITE FRAMEthan the actual load induced in the member. The A problem of two-bay, three-storeyconstraint for member is considered as, composite portal frame with fixed support is under taken. The gravity loads at construction stage andV < VP … (10) composite stage are as shown in Figs. 1 and 2 𝑓𝑦𝑉𝑝 = 0.6 × 𝐷 × 𝑡 × 𝛾𝑎 … (11) respectively. The design and GA data are listed below followed by the output given by GA basedwhere V is the factored shear force and Vp is the optimization program.plastic shear capacity of beam. The associated Geometry dataconstraint function is given by, • Number of bays in horizontal direction = 2 • Number of Storeys = 3 g3(x) = Max ((V / Vp – 1), 0) … (12) • Storey height = 3 m(c) Lateral torsional buckling constraint: This • Span of beam = 6.6 mconstraint ensures that the capacity of frame member • Slab thickness = 130 mmis more than the actual torsion moment induced in Material datathe member and is written as, • Grade of concrete = M 30 • Grade of steel = Fe 275 M < Mb … (13) 𝑓𝑦 • Grade of reinforcement = Fe 415 𝑀 𝑏 = 𝑥 𝐿𝑇 𝛽 𝑊 𝑍 𝑝𝑥 𝛾 … (14) Load data at serviceability limit state 𝑚where M is the negative moment at construction • Dead load on the beam = 35.16 kN/mstage and Mb is the design buckling resistance • Live load on the beam = 14.84 kN /mmoment of a laterally unrestrained beam. The Load data at ultimate limit stateassociated constraint function is has the form, • Dead load on the beam = 49.224 kN /m g4(x) = Max ((M / Mb – 1), 0) …(15) • Live load on the beam = 23.744 kN /m Unit cost data3.2 • C Unit cost of steel = 32 Rs./ kg.onstraints imposed on composite column • Unit cost of concrete = 3000 Rs./ cum.(a) Axial compression constraint: In ultimate GA datalimit state design the compression capacity of a • String Length = 9composite column should exceed the total factored • Population size = 50applied axial compression force. The corresponding • Generation = 50constraint function is written as, • Type of crossover = Single Point CrossoverP <  Pp … (16) • Crossover probability = 0.90Pp = Aa*fy /a +c *Ac *(fck)cy /c • Selection scheme = Roulette Wheel Scheme + As * fsk / s …(17) • Mutation Probability = 0.07 with variablewhere P is the axial force,  is a reduction factor for mutation.column buckling and Pp is a plastic resistance to Objective Functioncompression of the cross section. The constraint Total cost of composite frame = Cost of beamfunction can be written as, + Cost of connector + Cost of column. g1(x) = Max ((P / ( Pp) – 1), 0) …(18) Output(b) Moment constraint: In ultimate limit state Figure 3 shows the optimum design results obtaineddesign the moment capacity of the composite through GA based program.column should exceed the total factored appliedmoment and thus the constraint is written as follows:M < 0.9 µ Mp …(19)Mp = py ( Zpa-Zpan) + 0.5 pck (Zpc-Zpcn ) + psk ( Zps- Zpsn) …(20)where  = moment resistance ratio, M is the designbending moment and Mp is a plastic momentresistance of composite column. The design againstcombined compression and uni-axial bending isadequate if Eq. (19) is satisfied.The constraint function for GA based search can bewritten as follows:g2(x) = Max ((M / (0.9 µ Mp) – 1), 0) …(21) Fig. 1 Composite frame loading at construction stage 1658 | P a g e
  • D. R. Panchal, N. K. Solanki, S. C. Patodi / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.1656-1662 Fig. 2 Composite frame under loading at composite stage Fig. 5 Generation versus cost graph The obtained results are compared in Table 1 with Summary of the results obtained is as follows: those provided by [10]. i. Type of beam: Structural steel beam with headed Table 1 Comparison of Results for A 2 × 3 Storey stud shear connector. Frame ii. Size of beam : All beam are of size 305 (depth) x % Composite Composi 102 (flange width) mm x 33 kg/m. Savin Frame te Frameiii. Type of shear connector– Headed stud of 12 mm Store Membe g Section Section diameter x 100 mm height. y r in (Wang and Li (Presentiv. Type of column: Partial encased composite Weig 2000) Work) column. ht 305 x HN300x150x6. Size of column: All columns are of size 203 x 203 102 Beam 5x9 8.89 mm concrete casing with 203 × 203 mm × 33 kg/m @ 32.8 @ 36 kg/m rolled steel I section. kg/m 3rd 203 x HW Colu 203 34.7 250x250x9x14 mn @ 46.1 3 @70.63 kg/m kg/m 305 x HN300x150x6. 102 Beam 5x9 8.89 @ 32.8 @ 36 kg/m kg/m 2nd 203 x HW Colu 203 34.7 250x250x9x14 mn @ 46.1 3 @ 70.63 kg/m kg/m 305 x HN300x150x6. 102 Fig. 3 Final results for a 2 bay × 3 storey frame Beam 5x9 8.89 @ 32.8 The final solution is obtained after 9 GA runs. The @ 36 kg/m kg/m convergence of GA towards optimum solution is 1st 203 x indicated by the graphs of generation versus fitness HW Colu 203 34.7 and generation versus cost as shown in Figs. 4 and 5 250x250x9x14 mn @ 46.1 3 respectively @ 70.63 kg/m kg/m 5. DESIGN EXAMPLE OF A 2 X 5 STOREY COMPOSITE FRAME A two-bay five-storey, fixed footed composite portal frame is selected here. Gravity loads acting on the frame at construction stage and composite stage are as shown in Figs. 6 and 7 respectively. The optimum design of this frame is carried out five times by selecting different type of section every time. The following five sections are considered for Fig. 4 Generation versus fitness grpah optimum design: 1659 | P a g e
  • D. R. Panchal, N. K. Solanki, S. C. Patodi / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.1656-1662• Fully encased Indian steel column section.• Partially encased Indian steel column section.• Square tubular section filled with concrete.• Rectangular tubular section filled with concrete.• Circular tubular section filled with concrete.Geometry data• Number of bays in horizontal direction = 2• Number of storeys = 5• Storey height = 3 m• Span of beam = 7 m• Slab thickness = 130 mm• c/c distance between beams = 7 mLoad data• Imposed load = 3.5 kN/m2• Partition load = 1.0 kN/m2• Floor finishing load = 0.5 kN/m2• Construction load = 0. 5 kN/m2 Fig. 7 Composite frame under loading at compositeUnit cost data stage• Unit cost of steel = 32 Rs./kg Output• Unit cost of concrete = 3000 Rs./cum Figure 8 shows the output obtained by selecting fullyGA data encased Indian sections. The results derived from the• String length = 9 program by selecting partially encased Indian• Population size = 50 sections are depicted in Fig. 9. The optimum• Generation = 50 concrete infilled hollow square, circular and• Type of crossover = Single point crossover rectangular sections obtained through the program• Crossover probability = 0.90 are displayed in Figs. 10, 11 and 12 respectively.• Selection scheme = Roulette wheel scheme• Mutation probability = 0.07 with variablemutationMaterial data• Grade of concrete = M 30• Grade of steel = Fe 250• Grade of reinforcement = Fe 415 Fig. 8 Output for Fully Encased SectionsFig. 6 Composite frame under loading atconstruction stage Fig. 9 Output for partially encased sections 1660 | P a g e
  • D. R. Panchal, N. K. Solanki, S. C. Patodi / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.1656-1662 Results of the parametric study are summarized here in TABLE 2 wherein total structural weight and overall cost (in Indian currency) for each type of section are mentioned. Table 2 Weight and Cost Comparison of Composite Frame Steel Cost Case Type (Kg) (Rs.) Square concrete filled Case 1 7912 272035 tubular column and beam sectionFig. 11 Output for concrete filled hollow circularsections Circular concrete filled Case 2 7619 259500 tubular column and beam section Rectangular concrete filled Case 3 8132 280915 tubular column and beam section Fully encased Case 4 Indian column 8025 281530 and beam section Partially encased IndianFig. 12 Output for concrete filled hollow rect. Case 5 8385 287454 column and beamsections section In optimization process, genetic parameterssuch as population size, number of generations,crossover probability and mutation probability playan important role. The final solutions are obtainedafter 4 to 8 GA runs for various composite sections.The relation between number of generations andtime taken in optimization process is depicted in Fig.13. Fig. 14 Comparison of weight between types of sections The comparison of structural steel weight versus type of section is shown in Fig. 14. It can be observed that the fully encased Indian steel section performs better than the partially encased one. In case of concrete filled tubular sections, concrete filled hollow circular section performed the bestFig. 13 Time taken in optimization process graph 1661 | P a g e
  • D. R. Panchal, N. K. Solanki, S. C. Patodi / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.1656-1662with steel weight of 7619 kg which is the minimum International Journal of Computers andamong the five types of sections considered here. Structures, 79, 2001, 1593–1604. [4] M. Hayalioglu, and S. Degertekin,6. CONCLUSIONS Minimum cost design of steel frames with Most classical methods do not have the global semi-rigid connections and column basesperspective and often get converged to a locally via genetic optimization, Internationaloptimal solution whereas GA based soft computing Journal of Computers and Structures, 83,tool is a global optimization method which can find 2005, 1849–1863.new innovative designs instead of traditional designs [5] D.E. Goldberg, Genetic algorithms incorresponding to local minima. In the present work search, optimization and machine learningthis soft computing tool has been used in (Pearson Education Asia Limited, 2000).conjunction with computer-oriented direct stiffness [6] Eurocode 4, Design of composite steel andmethod for the development of GUI based software concrete structure, European Committeewhich is found to be quite attractive and effective. Report, 2004.The first example of 2 x 3 frame has clearly [7] IS: 11384, Code of Practice for Compositeindicated the benefits of using the present GA based Construction in structural steel andoptimization software in the design of composite concrete, Bureau of Indian Standards, Newbuilding frames. Delhi, 1985. Suitable selection of crossover and mutation [8] R. Narayanan, V. Kalyanaraman, , A. R.probabilities in optimization problem is necessary to Santhakumar, and S. Seetharaman,obtain new generation with better solution. After a Teaching resource of structural steelnumber of trials, it is found that the crossover design, (Kolkata: Institute for Steelprobability of 0.72 to 0.90 and mutation probability Development and Growth, 2001.)of 0.03 to 0.07 give quite satisfactory results. [9] K. Deb, Optimization for engineering The developed menu-driven software is capable design: algorithms and examples, (Newof finding the optimum solution for various types of Delhi: Prentice-Hall of India Privatecomposite plane frame problems and provides the Limited, 2005).generation history report automatically along with [10] J Wang and, G. Li , A practical designthe optimum section details including the overall method for semi-rigid composite framescost of structure. The software can be used for both under vertical loads, Journal ofsymmetrical as well as unsymmetrical composite Construction Steel, 64, 2008, 176-189.frames. From the parametric study, it is clear that thecircular concrete filled tubular column section ismore economical compared to other type of columnshapes such as square concrete filled tubular section,rectangular concrete filled tubular section and fullyas well as partially concrete encased sections. It isalso found that the circular concrete filled in tubularcolumn section is 4.60% more economical comparedto the concrete filled square tubular column section.The circular concrete filled in tubular columnsection is found 7.62%, 7.82% and 9.72% moreeconomical than the concrete filled in rectangulartubular column section, fully concrete encasedsection and partially concrete encased sectionrespectively.REFERENCES [1] D.A. Nethercot, Composite construction, (London: Spon Press of the Taylor & Francis Group, 2004). [2] L. Cheng and C. Chan, Optimal lateral stiffness design of composite steel and concrete tall frameworks, International Journal of Engineering Structures, 31, 2009, 523-533. [3] E. Kameshki, and M. Saka, Optimum design of non linear steel frames with semi- rigid connections using a genetic algorithm, 1662 | P a g e