Structural Optimization of RC Columns in a Multi-storeyed Building by Tree-Columns Subjected to Lateral Loads

. It has become the agenda to use the bottom storey as the parking area in the multi-storey buildings and it has been quite a disturbance caused by RCC columns occupying more while projecting down to the ground. To get rid of this disturbance and for the aesthetic appearance, the number of columns in the bottom storey has to be reduced so that number of the footing will also get reduced. To achieve this, the five-storey RCC framed structure of plan area 30m X 33m which is assumed to be situated in Chennai with each storey height of 4m is modelled in STAAD Pro software in the way that the loads from the four columns present in the ends of each room will be transferring to the single-column placed in the centre of each room at the bottom storey. Then the necessary loads such as Gravity loads, Seismic loads, Wind loads, and software-generated automatic load combinations were applied to the generated model and the analysis was carried out. Similarly, the conventional model of the same plan was also analyzed by STAAD Pro software with the same set of load cases, and a comparative study of structural parameters such as bending moment, shear force, and deflection was done. Finally, both the models were designed as per IS code and Cost analysis between the two models was carried out.


Introduction
For the past few decades, there has been an increasing trend of high-rise multi-storey buildings due to the vertical development of infrastructure.So evidently the load from the building will also be high resulting in more footings, i.e. it occupies more ground space to transfer the load to Earth effectively.But achieving the same effective load transfer with minimum use of Ground spaces has always been a challenge.In comparison with other buildings, it will reduce the foundation cost and also reduces space.
Analysis of the G+4 multi-storey residential building was done using STAAD.Pro, the limit state method of philosophy was adopted for the computations of shear force, bending moment, and deflections of structural members [1].Also, a multi-storey building was analyzed using different load combinations by commercial software and then designed using IS code of practice [2].The storey height of the G+7 framed structure was analyzed using STAAD.Pro and costs were compared between the type of composite materials used and based on their load combinations [3].The lateral load's Viz.For the analysis and design study, seismic and wind loads were applied to the G+6-storey RC frame of the existing type.The significant increase in the analytical parameters was influenced by seismic zone ranging from I to V [4].The earthquake-resistant structure was analyzed and designed using STAAD.Pro software.The storey drift was increased from bottom to top and other parameters namely shear force, bending moment, and storey displacements were also highly influenced by seismic forces [5].Structural design optimization could be done using many soft computing tools for sustainable construction practice [6].The adoption of BIM software for construction management projects was much more feasible and workable [7].The BIM technology could also be very well adapted for civil infrastructure projects other than framed buildings' structural applications [8].The merits and demerits of BIM technology were studied in terms of planning, analysis, and design of components involved in RC-framed buildings [9].For a G+3 storey building, a single column of 2.5 m square in shape was provided at midlocation to support the entities of slabs, beams, and walls.The complete structure was analyzed and designed using STAAD.Pro software [10].The following section of the review of literature deals with the structural optimization done on the building frame using algorithm codes excluding the graphical user interface approach: The structural optimization could be performed for seismic-resistant buildings using steel or composite columns.The algorithm adopted had potential benefits for materials cost control by ensuring the provisions of Eurocode standards [11].For an RC frame, the expected annual loss approach was adopted for evaluation with limit-state approaches.Further, seismic retrofitting was done by optimization using a genetic algorithm [12].In RC framed structures, the optimization could be performed by plastic analysis.Based on this approach, the number of iterative steps required for the design would be minimized [13].The optimization of the structure was done using a genetic algorithm based on engineering parameters and judgements [14].For a 3-storey building, cost optimization was performed using the Jaya algorithm has shown effective results through the optimization process [15].A global optimization algorithm was adopted for the resistance of four-storey building subjected to progressive collapse.This approach has led to the optimization of materials used [16].The Indian code of practice was followed namely, IS 875 Part 1 [17] for dead loads, IS 875 Part 2 [18] for imposed loads, IS 875 Part 3 [19] for wind loads and, IS 1893 [20] for seismic loads analyses.The ductile design and detailing were carried out using IS 13920 [21] and the RC design was performed according to IS 456 [22] codes of practice.The novelty of the present study is the optimization of columns adopted in the conventional building frame by tree-column/single-column subjected to lateral and gravity load combinations.For modelling, analysis, and design adopted the STAADPRO software which works based on the stiffness approach.In this software, necessary loads like Gravity loads, Seismic loads, and Wind loads were applied and analyzed.A structure supported on a single column provides a better architectural view compared to a structure supported on many columns.The single-column structure can be made either by steel or RCC.Reinforced concrete as a structural material is widely used in many types of structures.It is competitive with steel if economically designed and executed.Reinforced Concrete is a composite material with relatively low tensile strength and ductility, which are counteracted by the inclusion of reinforcement with higher tensile strength and ductility.

Methodology
The methodology adopted for the optimization of structural columns is shown in Fig. 1.

Modelling and Assigning Properties
The plan of 5 storeys commercial building (Hotel) was modelled in AutoCAD software with the area of the building as 30m x 33m as shown in Fig. 2. The rooms in the building plan were modelled as per National Building Code 2016 [23].Each storey has an elevation of 4m where the bottom storey is intended for parking.The columns are embedded up to 2m below the ground level.The elevation was shown in Fig. 3.This plan was imported to STAAD Pro software and the structural elements of the building model were completely drawn in software and ends were assigned with fixed supports.To achieve the objective, the conventional building model is modified so that columns on 4 sides in each room are supported on the cross beams provided at the bottom of 2nd storey so that these columns would act as floating columns.Hence the space occupied by those columns in the 1st storey was made free providing more space for parking.Here, the cross beams provided was made as transfer beam to transfer the loads from floating columns.The circular column was modelled and placed at the intersection of cross beams to carry loads from those beams to the ground.The elevation view of the tree column model and the orientation of cross beams along with the position of circular columns were shown in Fig. 4 & Fig. 5 respectively.For the floating columns that seem to transfer heavy loads to the transfer beams, the diagonal beam was provided connecting the bottom of the floating column and the circular column (at 2m below the topmost fibre).After the completion of the STAAD Pro model, the material was chosen as concrete and the dimension for beams, columns and slabs were assigned to both the tree column model as well as the conventional model.The dimensions of the structural members assigned initially were shown in Table 1 below.

Structural Element Size
Beams 230mm X 230mm (for staircase), 300mm X 300mm, 450mm X 450mm, 300mm X 600mm (for transfer beam) Columns 300mm X 450mm, 450mm X 450mm, Circular Column of Φ 800 mm, Circular Column of Φ 600 mm Slab 150mm for the floor slab,100mm the for staircase After assigning the dimensions to the members, the clear 3D view of the model can be seen and can be cross-checked.The 3D rendered view of the bottom storey for the detailed view of the position of cross beams and diagonal beams were shown in Fig. 8.

Fig.8. 3D view of the bottom storey
After assigning material and dimensions to all the available structural members, the 3D rendered view of both conventional and tree column models were shown in Fig. 9 &10 below.

Seismic Loads
Then the loads acting in the structure are assigned.First of all, the seismic load was assigned to the building.Since our building is considered to be in Chennai which is in Zone III according to IS 1893-2016 [20], the corresponding Zone factor is 0.16 and the importance factor is 1.2 as it was a commercial building (Hotel) which will be having more than 200 occupants.The reduction factor was taken as 5.0 assuming the building to have Special Moment Resisting Frame (SMRF).The building was assumed to be placed on Type II soil.With these parameters, the seismic load was applied to the building in all four directions (+X, -X, +Z and -Z).

Gravity Loads
Then the Dead load have to be assigned.The self-weight of the structure was assigned such that the software automatically calculates the self-weight of the structure with the assigned dimensions of structural members and considers the unit weight of concrete as 25 kN/m 3 .The dead load imposed by brick walls on the horizontal beams are assigned in those beams as UDL.The Uniformly Distributed Load was calculated by considering the unit weight of the brick as 15.7 kN/m 3 as per IS 875 Part 1 [17].Also, the dead load due to floor finish as per IS 875 Part 1 [17] was assigned to the model.The Live load on the floors was also assigned according to IS 875 Part 2 [18].The details on Dead load and Live Load applied to both the tree column model and conventional model was shown in Table 2.

Wind Loads
Since the height of the building is more than 10m, the wind loads have to be applied.As our building was said to be situated in Chennai, the parameters needed for the calculation of wind load are taken from IS 875 Part 3 [19], and design wind pressure was calculated.From Table 3, values of maximum design wind pressure for different floor levels are fed to the software.Also, STAAD Pro software was provided with an exposure factor of 95% assuming that only 5% of the buildings have openings for windows, etc.Then the pressure coefficients were calculated as follows: As per IS 875 (Part 3): 2015 [19], Internal Pressure Coefficients = +0.2 or -0.2 [For openings less than 5%] External Pressure Coefficients: h/w =20/30 = 0.666; l/w = 33/30 = 1.1 where h, l, and w were the height, length, and width of the building.For the above case, from Table 5 in IS 875(Part 3): 2015 [19] and assuming the wind angle as 0°, a=0.7; b= -0.25; c= -0.6; d= -0.6;By adding the internal and external pressure coefficients, the resultant pressure coefficients are, a=0.9; b= -0.45; c= -0.8; d= -0.8;These resultant pressure coefficients were applied in all four directions where 'a' and 'b' were applied in respective +x and -x directions whereas 'c' and 'd' were applied in +z andz directions respectively.

Load Combinations
After applying all the loads, the predefined load combinations as per IS 456: 2000 [22] are generated and applied to the model.The load combinations generated by STAAD Pro software are tabulated in Table    LC 22 0.9(LC 3) + (-1.5)(LC 2)

Analysis & Design of Model
The model was analyzed and errors or warnings if found were rectified.Then the structural behaviour of the building such as shear force, bending moment, etc. for the applied loads and their combinations were studied.Then the building was designed with a Grade of concrete taken as M25.The grade of steel provided for main reinforcement was Fe500 and the Fe250 grade of steel was provided for shear reinforcement.
As we had provided the diagonal beam connecting the floating column (at the end) and circular column (at 2m from the top fibre), there was a danger of a short column effect due to the seismic forces.This effect was minimized by providing ductile reinforcement throughout the circular column as per IS 13920-2016 [21].So, helical reinforcement was provided in those columns.The software output was studied for any warnings of failures in structural members.If so found, the members are provided with the next available cross-section available in Table 1.
The above analysis with load and design was carried out for the conventional model and a study between the tree column model and conventional model for structural behaviour and cost of the framed structure was made and discussed.

Displacement
The conventional building model has suffered displacement in all three axes from its original position.Horizontal sway is more prominent in the structure as compared to vertical displacement.Only certain nodes have undergone mild rotation from their original position and many nodes have not even rotated from their mean position.Displacement for conventional buildings and their maximum values are presented in Table 5. Tree column structure has undergone displacement in all three axes as shown in Fig. 11.Even though horizontal sway is more prominent as compared to vertical, members have suffered more vertical displacement as compared to a conventional building.The resultant displacement due to displacement in three axes is greater in value in the tree column structure.Maximum rotation is noted in the tree column about the z-axis.Displacement for the tree column model and its maximum values are presented in Table 6.It is evident from the above tables that displacement for tree column structure is lesser when compared to the conventional model in X and Z directions while in Y-axis maximum displacement is greater in tree column structure shown in Fig. 12.In both the models even though resultant displacement value differs from each other the maximum displacement is within the permissible limits.
From the obtained displacements of conventional and tree column structures, it was observed that maximum nodal displacements were attributed along X-direction (one of the lateral directions) than Y-and Z-directions respectively.This was due to the applications of seismic loads along the concerning direction reflecting the highest nodal displacements.The tree column model had the highest vertical displacements of 16.225 mm when compared with the conventional model.The reason was due to the less restraints provided and the span was higher when connected as a diagonal member.

Bending Moment, Shear Force and Axial Force
All the nodes in a conventional building suffer greater torsional moment (Mx) in comparison with the bending moment (My and Mz).In node 1129 it is found that moments about three axes are almost zero and it doesn't undergo a turning moment (or) it undergoes negligible moments about any axis.Node 991 has undergone the maximum bending moment out of all nodes(111.568kNm).The structure has undergone both positive and negative shear forces.Bending and shear corresponding to the conventional building are shown in Table 7. Tree column structure in contrast to the above-mentioned conventional building has undergone maximum bending moment about the z-axis.It has undergone more bending moments rather than the torsional moment.Even though the bending moment is maximum about the z-axis, the bending moment about the y-axis for all the below-mentioned nodes is negligible.Even the tree column has undergone both positive and negative shear force.The bending moment and shear force for the tree column structure are represented in Table 8.From the SFD results obtained, it was inferred that shear force (Fy) was increased by 1.35 times in the tree column model than in the conventional model.In BMD results, the bending moment 'Mz' obtained for the tree column model has increased 5.61 times than the conventional model.The reason was due to the influence of seismic forces has caused such attributions of shear forces and bending moments in the tree column structure is similar to the results reported by Supraja et al. [5].When comparing the torsional moment 'Mx', the tree column structure has shown a 1.45 times increase than the conventional structure.The reason was more than 3 members were meeting at the beam-column joints has caused a higher degree of static indeterminacy.

Design of Frames in Superstructure
After the study of the results acquired from the analysis report, both the building models were designed by software for checking the suitability of the cross-section assigned initially.Here, the building models were designed till the cross-section provided to structural members seems adequate to handle the loads applied.

Support Reactions and Design of Footings
After the proper analysis and design of structural members in the superstructure, the foundation of both building models was designed by STAAD Foundation software with support reactions obtained from the STAAD Pro software.The overall maximum and minimum support reactions obtained for whole building models are tabulated in Table 9 and Table 10.The obtained forces and moments in columns exerted support reactions were similar to the results obtained in axial force, shear force and bending moments of the respective structural models.
For both models, the support reactions of all individual footings were automatically imported to the STAAD Foundation software and designed accordingly.
Here, the design results of footings found under a single room of both models were discussed.Fig. 17 depicts the positions of footings in a single room for both models together.

Fig.17. Position of footings in a single room
In the above figure, blocks 1A, 1B, 1C, and 1D were footings of a single room in a conventional building whereas block 2 is the single footing of a single room in a tree column building and these footings were designed individually.The cross-section and depth of each footing obtained from the STAAD foundation for maximum support reactions were as follows: There is a considerable difference in space occupied by footings as per the above example but for some cases, the differences were negligible.It was because of the same set of applied loadings in the superstructure.Hence, the footing depths were checked against one-way and two-way shear.The design of reinforcements was made based on the bending moments and shear criterion.

Cost Comparison
The cost of the substructure could be almost the same as the loads to be transferred to the foundation are the same in both cases.So, here the cost of the superstructure is only discussed.The take-off of both models for the only framed structure alone is shown in Table 12.= 55,21,980.00Since the non-structural members are the same in size and material, their costs are the same.So, with the cost of structural members alone, it is found that the cost of our model is slightly higher than the cost of the conventional model.The difference in the percentage of cost between both models was found to be about 7.57%.

Conclusions
The maximum resultant displacement of the Tree column structure (our tree column model) is greater in comparison with the conventionally framed structure but is within the permissible limit.The structural members and nodes are analyzed for Shear Force and Bending moment and are designed to resist them.The tree column structure (our tree column model) suffers more bending moments in comparison with the torsional moment acting on it.The transfer beam acts as a cantilever beam and it is evident from the structural response diagrams of the building.The inclined diagonal members receive more loads from the columns of above storeys and help in keeping the stability of the building Material take off for substructure for both tree column and conventional structure are almost of the same value as there is no difference in the loading.Material take-off for structural elements in the superstructure is more in the case of tree column building than conventional framed structure and there is a cost difference of about 7.57%.

Fig. 4 . 5 . 4 )Fig. 6 .
Fig.4.Elevation view of the Tree column model Fig.5.Plan of Tree column model (concerning Y-Y in Fig.4) The model was drawn carefully and to be checked for dimension errors.The final STAAD Pro diagram of the conventional model and tree column model of the building were shown in Fig.6 & Fig.7 respectively.

Table 2 .
Dead Load and Live Load Calculations.

Table 3 .
Wind Pressure Calculation

Table 4 .
Definition of Load Cases

Table 5 .
Displacement in Conventional building model 2023

Table 6 .
Displacement in Tree Column Building model

Table 7 .
SF and BM Values of Conventional Building model (Hor-Horizontal, Ver-Vertical) The maximum Torsional Bending Moment (Mx) corresponds to -218.466 kNm.Maximum Bending moments in My and Mz are -8.341kNm and 110.75 kNm respectively.

Table 8 .
SF and BM Values of Tree Column Building model (Hor-Horizontal, Ver-Vertical)

Table 9 .
Support reactions of Conventional model

Table 10 .
Support reactions of Tree column model

Table 11 .
Footing design of a single roomFrom Table11, the space occupied by footings of the conventional model was found to be approximately 19 m 3 whereas, for the tree column model, it was approximately 16 m 3 .

Table 12 .
Quantity take-off of both models Assuming the nominal cost of M25 grade concrete 4,100 per m 3 and the nominal cost of reinforcing steel 40 per kg, the cost of both types of structural framing is calculated & shown below.Total Cost of framed structure for conventional model = (4100 x 636.6) + (40 x 63077) = 51,33,140.00Total Cost of framed structure for tree column model = (4100 x 736) + (40 x 62609.50)