OPTIMUM ANGLE OF HEXAGRID

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1 OPTIMUM ANGLE OF HEXAGRID Jaison.P.K 1, Abhilash.P.P 2 1 (Structural Engineering, Sreepathy Institute of Management and Technology, Vavanoor, India, jaisonpk333@gmail.com) 2 (Department of Civil Engg, Sreepathy Institute of Management and Technology, Vavanoor, India, abhiaie@gmail.com) Abstract The creativity of engineers has been reflecting in Structural engineering field and the pace of innovation and accomplishment is already fast but will grow even faster. Load resisting sub-system of a structure is referred as structural system and the load transferring method of each system is different. The invention of new structural system introduces new ideas to structural world as well as architectural world. This paper illustrates a new sub-system called Hexagrid and which is inspired by honeycomb. Moreover, this paper aims to find out the optimum angle of hexagrid and gives a contribution to optimization of hexagrid. This study is a continuation of angle performance study of hexagrid conducted by Jaison.P.K [1]. Investigation initiated with analysis of 3D periphery hexagrid structures and developed the relation connecting hexagrid angle with maximum lateral deflection of the structure. The focus of the study was changed to single hexagrid to find out the reason behind the previous output data. Conclusions obtained from above research were led to develop more practical models and their analysis. Evaluation of results of final phase has developed a relation between angles and deflections as well as the relation showing an optimum angle of Hexagrid. All analyses are as per Indian standards using ETABS software and material chosen is reinforced cement concrete. Keywords Innovation, Load resisting sub-system, Structural system, Hexagrid, 3D periphery hexagrid structure, Hexagrid angle, Single hexagrid, Optimum angle. 1. INTRODUCTION Concept of hexagrid structure is evolved from the brilliant works of honey bees. Honeycomb is a regular arrangement of hexagons. This type of arrangement is fruitful to the honeycomb to get lateral strength as well as material consumption. Hexagrid tries to introduce the above idea to structural engineers. It is not possible to arrange the polygon having more number of sides than hexagon in regular manner and perimeter is decreasing according to increase in number of sides. Which is why, hexagon shape consumes less material than other shapes because material is provided through the perimeter. Hexagrid is arranged in the periphery of structure to get two sides parallel to the ground. Therefore, no vertical members occur in periphery structure and horizontal and inclined members can be occurring. Columns take lateral loads by bending action but inclined members take the lateral loads by axial action. So that, hexagrids are provided with a belief of take lateral loads effectively. Hexagrid contains two types of angles such as angle between inclined members and angle between inclined and horizontal members. This paper aims to study the performance of these angles in structural behavior such as maximum lateral deflection and finally to concludes with an optimum angle. These angles are related to each other to maintain sum of interior angles of hexagon remains constant. This is the reason why, this paper concentrates on one type of angle ie angle between diagonal members. Experiments were treated similar to trial and error method ie changing the angle and taking other parameters are constants such as member properties, material properties, supporting conditions, loading condition and so on. Analysis of different3d structures and cellular units were done using integrated building design software ETABS This study Collected maximum lateral deflection as output data and developed relation connecting angle between diagonal members and maximum lateral deflection of the entire structure. Because Hexagrid structure is a periphery structure intends to take lateral loads effectively. The scope of this study is that to help topological study of hexagrid significantly. Further studies in hexagrid are only possible after the topological study. The parameter angle plays a major role in hexagrid because variation in angle of hexagrid can make a difference to the entire structural dimensions without any change in quantity of material. Moreover the hexagrid angle also influences the structural behavior such as lateral deflection. Optimum angle shows minimum deflection and it will help the study of other parameters and optimization of hexagrid. Honeycomb 2. REVIEW OF LITERATURE This paper is continuation of a study which on Angle performance study of hexagrid conducted by Jaison.P.K [1]. He completed his works with the help of analysis of 2D and 3D hexagrid structures. His study composed of four phases and each phase is a continuation of previous one. He had developed a relation connecting angle between diagonal Volume: 03 Issue:

2 members and maximum lateral deflection of the structure in each phase. First phase deals with analysis of 2D structures and other phases examines with analysis of 3D structures. Second last phase included effective application of lateral loads and structural properties had got more priority in last phase. All phases mention same relationship between hexagrid angle and maximum lateral deflection ie an inversely proportionality. In other words, higher angles show minimum lateral deflections. This paper, Optimum angle of hexagrid aims to find out reason behind the result obtained in his study and to determine the optimum angle of hexagrid. The latest grid structural system is diagrid structural system and studies about diagrids is more fruitful to strengthening the ideas in path of investigation. There are some literatures in which they investigated about diagrids. The paper on Optimum Angle of Diagrid Structural System prepared by Nishith B. Panchal [2] examines the comparison study of 24- storey, 36-storey, 48-storey and 60-storey of diagrid structural system with a diagrid angle 50.2, 67.4, 74.5 and The comparison of analysis of results is in terms of top storey displacement, storey drift, time period, angle of diagrid and steel and concrete consumption. His works mention that diagrid angle in the region of 65 to 75 provides more stiffness to the diagrid structural system which reflects the less top storey displacement. The storey drift and storey shear show less values in the region of diagrid angle 65 to 75. Diagrid angle in the region 65 to 75 provides less cost in terms of consumption of steel and concrete as compared to different angles of diagrid. Diagrid angle in the region 65 to 75 gives better results in terms of top storey displacement, storey drift, storey shear, time period and material consumptions when height of building increases. Khushbu Jani [3] implemented a study on analysis and design of diagrid structural system for high rise steel buildings. She has conducted analysis and design of 36 storey diagrid steel building in detail. In which, a regular floor plan of 36 m 36 m size is considered and ETABS software was used for modeling and analysis of structure. All structural members are designed as per IS 800:2007 considering all load combinations. Study in load distribution in diagrid system is further continued for 36 storey building. Moreover, the analysis and design results of 50, 60, 70 and 80 storey diagrid structures are presented. From the study she had observed that most of the lateral load is resisted by diagrid columns on the periphery, while gravity load is resisted by both the internal columns and peripheral diagonal columns. Such that, internal columns need to be designed for vertical load only. System is more effective because of lateral and gravity load are resisted by axial force in diagonal members on periphery of structure. She concludes that diagrid structural system provides more flexibility in planning interior space and façade of the building. Another study conducted on diagrid structural system such as strategies to reduce lateral forces on high-rise buildings was by Nishith B. Panchal [4]. He had examined the comparison of 20-storey simple frame building and diagrid structural system building. In which, the comparison of analysis of results in terms of top storey displacement, storey drift, steel and concrete consumption. His work revealed that as the lateral loads are resisted by diagonal columns, the top storey displacement is very much less in diagrid structure as compared to the simple frame building. Furthermore, Diagrids provide more resistance in the building which makes system more effective. The design of both structures were done by using same member size but that member sizes are not satisfied to design criteria in case of simple frame structure and failure occurs with excessive top storey displacement. Therefore the higher sizes of members are selected to prevent the failure criteria. Also in this study, Diagrid structure system provides more economy in terms of consumption of steel and concrete as compared to simple frame building and diagrid structural system provides more flexibility in planning interior space and facade of the building. Diagrid as an innovative technique for high rise Structure was conducted by Nikesh Ganesh Rathod [5] in The intention of his work is to present diagrid structures, comparison of different diagrid structure with conventional structures. Effect of the change in the angle of twist, angle of tilt, tampered shaped structure, freeform etc. are also examined in his paper. The Optimal angle of diagrid increases with the increase in height of entire structure. These structures can be seen in different forms as twisted, tilted, tapered, freeform, etc. Lateral stiffness of the twisted tower is smaller than that of the straight tower if structures considered are of many framed members and the structural performance of a tilted tall building is dependent upon its structural system and angle of tilt. What s more, If the angle of tilt is ranging from 0 to 13 degrees, it do not influence lateral stiffness of tilted diagrid. Tapered tall buildings are less susceptible to severe across-wind direction vibrations caused by vortex-shedding. In the case of freeform diagrid, the rate of reduction in lateral stiffness increases with increase of degree of fluctuation. Steel diagrid proves more economic than concrete. His work revealed that, in diagrid 33% less steel is required than conventional building and architecturally diagrid structures give more aesthetic than conventional building. 3. METHODOLOGY This research work is composed of four phases and each of them is continuation of previous one. First phase deals with angle performance study in hexagrid with the help of 3D analysis. Generation of ideas in each phase is based on the result obtained in the previous phase. Phase 2 is for find out the reason behind the output data of previous phases and it contains analyses of single hexagrids. Third phase is the study of variation in lateral deflection along the direction of load acting with respect to hexagrid angle. The last phase deals with study with 3D structures contain periphery hexagrid structure with inner framed structure. The main output data of all phases is maximum lateral deflection of the structure. Relation connecting deflection and hexagrid angle by means of graph and study is based on these graphs. Final stage of the study aims to detect depression in graphs which will show the optimum angle. Volume: 03 Issue:

3 A. Phase 1 Hexagrids are provided along the periphery of structure. This phase deals with modeling and analysis of 3D periphery structures. Study starts with modeling and analysis of angled hexagrid structure. Seven structures representing seven different angles such as 90 0, 100 0, 110 0, 130 0, 140 0, and were modeled and analyzed. M 25 grade concrete and HYSD 415 steel bars were selected as materials and A cross section of 200mm 200mm and length of 1m were selected as member properties which taken uniformly for beam as well as brace. Supporting condition was assigned as pinned join and dead load, wind load, earthquake load applied as per Indian standards such as IS 875 and IS hexagrids provided in vertical direction and 21 hexagrids provided in both horizontal and lateral directions. Moreover, total quantity of reinforced cement concrete limited to m 3 for all 3D structures. Single Hexagrid C. Phase 3 This phase aims to develop relation connecting maximum lateral deflection along the direction of load applied with hexagrid angle. Loads were applied in X direction only to take the load along width of hexagrid. 33.2kN nodal load was applied along X direction which was selected from Phase 3. Modeled a couple of hexagrids and they were connected by beams in Y direction to prevent deflection along Y direction. Hexagrid 3D structure B. Phase 2 This is an investigational study to find out the reason behind output data of previous studies. Proper understanding of structures is become easier by study concentrates on unit element. Hence single hexagrids in and angles were used in this phase. M 30 grade concrete and HYSD 415 steel bars were selected as materials and A cross section of 300mm 300mm and length of 1m were selected as member properties which taken uniformly for beam as well as brace. Supporting condition was assigned as pinned join and dead load, earthquake load applied as per Indian standards such as IS 875 and IS Single hexagrid is 2D structure and modeled in XZ plane. Moreover, loads were applied in X direction only to take the load along width of hexagrid. 33.2kN nodal load was applied along X direction which was selected from Phase 3. Couple of Hexagrids connected by beams Seven structures representing seven different angles such as 80 0, 85 0, 90 0, 105 0, 120 0, and were modeled and analyzed. M 30 grade concrete and HYSD 415 steel bars were selected as materials and A cross section of 300mm 300mm and length of 1m were selected as member properties which taken uniformly for beam as well as brace. Supporting condition was assigned as pinned join and dead Volume: 03 Issue:

4 load, wind load, earthquake load applied as per Indian standards such as IS 875 and IS D. Phase 4 Hexagrids providing in the periphery of a structure and it is bounded a convention framed structure. This phase tries to introduce this practical situation to the angle performance study. Nine hexagrid periphery structures with inner frame were modeled and analyzed in this phase. The nine structures representing nine different angles such as 90 0, 100 0, 105 0, 110 0, 120 0, 130 0, 135 0, and M 30 grade concrete and HYSD 415 steel bars were selected as materials and A cross section of 300mm 400mm was selected as member properties which taken uniformly for beam as well as brace. Furthermore, a cross section of 400mm 400mm was selected for columns. Supporting condition was assigned as pinned join and dead load, wind load, earthquake load applied as per Indian standards such as IS 875 and IS a table was prepared which recorded maximum lateral deflection. HEXAGRID ANGLE(degree) Maximum deflection in mm MAXIMUM LATERAL DEFLECTION(mm) Output data of Phase Hexagrid angle in degree Angle-Deflection graph-1 The graph shows that maximum lateral deflection inversely proportional to hexagrid angle. As a result, higher angles shows minimum deflections and optimum angle lies in the higher angles. This phase of investigation indicates that the maximum lateral deflection of the hexagrid structure will be minimum in higher angles. Hexagrid walls are provided with a belief of taking the lateral loads through its thickness. Therefore Phase 2 is for find out the reason behind result obtained in Phase 1. Hexagrid periphery structure with inner frame 4. RESULTS AND DISCUSSIONS Angle performance study intends to analyze the variation in an important structural behavior maximum lateral deflection of entire structure according to variation in hexagrid angle. Moreover, this also aims to find out optimum hexagrid angle. Development of graph with help of output data from a number of structures gives a correct idea about relation of deflection with angle and optimum hexagrid angle. Optimum hexagrid angle is the hexagrid angle at which the maximum lateral deflection has minimum value. Result of each phase is the reason of initiation of next phase. Study was conducted in 3D hexagrid structure in Phase 1 and Story response plot of single hexagrid Volume: 03 Issue:

5 Whereas, investigation was diverted to single hexagrid and the relation connecting deflection and angle was analyzed. Moreover disclose the actual reason behind it. To this end, 120 angled and 150 angled hexagrids were selected and analyzed the models by assigning lateral loads along X direction only. Red line and blue line in story response plot are the representations of deflection along Y and X directions respectively. Story response plot reveals that maximum lateral deflection recorded in Y direction although lateral loads were only applied along X direction. This mentions that hexagrid is week in one direction and there is a chance to deflect in that direction more independent the direction of load application. Furthermore, maximum lateral deflection recorded in all previous phases is the deflection normal to the hexagrid wall. In phase 3, hexagrid constrained in Y direction and repeated the experiment. That is to say, provided a couple of hexagrids and connected them with beams. Maximum lateral deflection(mm) Angle(degree) Angle-Deflection graph of Phase 3 Observed results are entirely different from the previous phases angle gives the minimum lateral deflection and smaller angles as well as greater angles show more deflection than This reveals that hexagrid wall with proper support in its least stable direction gives a different relation connecting angles and deflections.there is a possibility to get optimum hexagrid angle whether the hexagrid wall is contrained by inner frame. Therefore more experiments which consisting analysis of periphery hexagrid structure contain inner framed system are needed for find out the optimum angle and those implemented in Phase 4. HEXAGRID ANGLE(degree) MAXIMUM LATERAL DEFLECTION(mm) Story response plot of hexagrid constrained in Y direction Red line and blue line in story response plot are the representations of deflection along Y and X directions respectively. This story response plot says that this method can plot deflection along the direction of load application alone. Phase 3 aims to develop relation connecting maximum lateral deflection along the direction of load applied with hexagrid angle. HEXAGRID ANGLE(degree) Output data of Phase 3 MAXIMUM LATERAL DEFLECTION(mm) Maximum lateral deflection(mm) Output data of Phase Angle(degree) Angle-Deflection graph of Phase 4 Volume: 03 Issue:

6 The graph shows a depression in its curvature. Hence it is reveals that hexagrid periphery with inner frame has an optimum angle. Furthermore, angle exhibit minimum lateral deflection. As a result, optimum angle either lies near to or itself as the optimum hexagrid angle. [4] Nishith B. Panchal, Vinubhai R. Patel. Strategies to reduce lateral forces on high-rise buildings, International Journal of Engineering and Technical Research, Vol 3 ( 2014 ) [5] Nikesh Ganesh Rathod, Vinubhai R. Patel. Diagrid as an innovative technique for high rise Structure, Journal of Civil Engineering and Environmental Technology, Vol 2 ( 2015 ) 5. SUMMARY AND CONCLUSIONS Determination of optimum angle of hexagrid is only possible by developing the relation linking angle and deflection. The prime intention of hexagrid is to take lateral load effectively. Hence optimum angle is the angle which shows minimum value for maximum lateral deflection of entire structure. Analyses of 3D periphery hexagrid structures disclose an inversely proportionality between angle and deflection. Research in single hexagrid was revealed that relationship which gets from Phase 1 cannot be accepted because hexagrid wall is weak in one direction and deflection recorded in Phase 1 is the deflection in this direction. Hexagrid wall is similar to 2D structure and it is less stable in one direction which normal to the hexagrid wall. Hexagrid walls are provided with a belief of taking lateral loads along width or its stable direction. Nevertheless, high value of deflection occurs in unstable direction even if load acts in stable direction only. Analysis of couple of hexagrid in third phase is giving a relation of deflection along the direction load applied. Above relation is entirely different from previous relationships and the curvature contain a depression which indicate minimum value of deflection. Phase 3 reaches to a conclusion ie the practical model is a form of hexagrid periphery with inner frame in which the inner frame may prevent the deflection of hexagrid in less stable direction. To put it in another way, it may give another relationship between deflection and angle. Phase 4 deals with periphery hexagrid with inner frame models and this phase strengthened the conclusion of third phase. Relation shows a minimum value for lateral deflection at angle. Therefore, either optimum angle lies near to or itself as the optimum hexagrid angle. 6. FUTURE SCOPE OF THE STUDY The parameter angle plays a major role in hexagrid because variation in angle of hexagrid can make a difference to the entire structural dimensions without any change in quantity of material. Therefore this study is fruitful to topological study. This paper acts as an essential part for optimization of hexagrid and giving guidance to the determination of optimum angle in other grid structures. Moreover, this paper present a new type of structural system and it takes a fine step forward to new inventions related to hexagrid. REFERENCES [1] Jaison.P.K, Abhilash.P.P, Angle Performance Study of Hexagrid, International Journal of Modern Trends in Engineering and Science, Vol 3 (2016) [2] Nishith B. Panchal, Dr. V. R. Patel, Dr. I. I. Pandya, Optimum Angle of Diagrid Structural System, International Journal of Engineering and Technical Research, Vol 2 ( 2014 ) [3] Khushbu Jani. Analysis and design of diagrid structural system for high rise steel buildings, Published by Elesevier Ltd ( 2012 ) Volume: 03 Issue: