Seismic Torsion Behaviour and Rigidity Analysis of Multistory Plan Asymmetric RC Building

Abstract

Due to the client demand on architectural drawings and land structure of Nepal, it is very difficult to make the structure with regular plan shapes, and thus, horizontal or vertical irregularity may be developed. These irregularities of the structure are more responsible for the collapse of building under the dynamic loads action during strong ground motions of earthquake and cause a significant torsional reaction in the structure. The main objectives of this paper are to study the torsional behaviour of reinforced concrete building with plan asymmetry which is located in zone V subjected to earthquake load and its parameters reflect the torsion effect and recommending the practical solution in order to reduce torsional effect. To carry out the study, both symmetric and asymmetric (L-SHAPE, + shape and T shape) plan buildings of eleven storey were modelled and ETABS software is used for analysis. The result proves that asymmetrical plan buildings are more vulnerable than symmetrical plan buildings. To reduce the torsional irregularity effect of asymmetrical plan structure curtailed shear wall system is recommended as practical solution with considering the stiffness. It was concluded that curtailed shear wall system improves the seismic performance of the structure reducing the cost criteria. After additional of shear wall, the torsional irregularity ratio of asymmetrical plan structure comes with in permissible limit as per IS 1893. Torsion creates damage or complete structures collapse, to control torsion, irregular structures should be carefully analysed.

1 Introduction

Due to irregular shapes of the structure, there is a more chance of damage of building under the dynamic loads action during strong ground motions of earthquake. In additional of lateral oscillations, mostly the structure undergoes on torsional vibration. In the symmetrical building, CM (centre of mass) and the CR (centre of rigidity or resistance) harmonize with one another due to which there is no torsion occur in the building but in asymmetrical building the CM (centre of mass) and the CR (centre of rigidity or resistance) in the building do not harmonize which create a torsion in the building-the distance between these two points is known as torsion eccentricity. At the additional of horizontal opposing components like shear walls, bracings, the focal point position of rigidity will change and which cause a critical change in eccentricity of total structure. This research focuses mainly on torsional behaviour of irregular plan structure and the method to avoid or minimize such problems during the design of structures. The structural irregularity can be broadly classified as plan horizontal and vertical irregularities as per IS code 1893:2002. To reduce the torsional irregularity effect of asymmetrical plan structure shear wall system is recommended as practical solution.For reduce the structure torsion and stiffness in steps catering to the seismic performance in between two adjacent storeys, a shear wall may be introduced at corners, reducing the size at every floor level with error and trial method which improves the structure seismic performance, reducing the cost criteria.

The scope of the study mainly focuses on torsional behaviour of irregular plan structure and the method to avoid or minimize such problems during the design of structures. To know the torsional behaviour of irregular plan building the analysis of 11 storey building is carried out with the help of ETABS 15.2.2 software situated in zone v.

2 Literature Review

Adarsh and Rajeeva [1], In this paper, author analysed both symmetrical and asymmetrical structures with plan irregularity to study the torsion irregularity of the reinforced concrete structures for that they have considered 5 models with different cases The analyses of fifteen storeys were done by ETABS software. In this study, they compared torsional irregularity, modal participating ratio, lateral displacement, storey drift, and storey shear. The main finding was in model-1 and model-2 torsional value exceeded the code limit value, lateral displacement and storey drift is maximum for model 3 and 4 storey. They concluded that by the addition of shear walls at proper places the displacement caused by earth quake and wind forces will be minimized and in the building the displacement due to seismic action is influenced by position of shear wall.

Kusanale1 et al. [2] concluded that the torsional behaviour of asymmetrical building subjected to seismic forces. In this study, they have modelled three type of structure with symmetric plan, L-shaped plan, T-shaped plan. Two models of each case with G + 3 and G + 6 floors are analysed. The modelling and analysis are done by using SAP2000 software. In this study, they did the comparison of all models on the basis of time period, torsion moment and base shear and found that torsional moment in asymmetrical building is more than symmetrical building.

Hussain and Tengli [3] studied the torsion effect of irregular building under the seismic loads. For this study, they have modelled and analysed a regular (G + 14) and irregular building (L-shaped + 14) using three-dimensional dynamic analysis (response spectrum method). The analysis of is carried out by using ETABS software. In this study, they compared maximum storey drifts, storey displacements, time periods and modes of frequencies. They found that with increasing in number of mode time period decrease. The frequency of irregular building is great than the frequency of regular building, and storey drift is irregular building is greater than regular structure. They concluded that structures which have irregularities plan have significant impact on the response of seismic of the structure, especially in terms of seismic base shear and base displacement. Due to torsion in irregular structure forces in columns increase.

3 Analysis

3.1 Modelling

To know the torsional behaviour of irregular plan building, the analysis of 11-storey building is carried out with the help of ETABS 15.2.2 software situated in zone v. Eccentricity, maximum storey drift, maximum joint displacement, torsional irregularity ratio, storey stiffness, modal participation mass ratio and natural time period is compared for all models.

3.2 Model Types

To know the torsional behaviour of the structure model are categorized into various types: Model-I—Regular Plan Building, Model-II—Asymmetrical +-shaped Plan Building, Model-III—Asymmetrical L-shaped Plan Building, Model-IV—Asymmetrical T-shaped Plan Building, Model-V Asymmetrical +-shaped Plan Building with shear wall and Model-VI—Asymmetrical L-shaped Plan Building with shear wall.

3.3 Model Data

See Table 1 and Figs. 1, 2, 3, 4, 5 and 6.

Table 1 Details of base model

Fig. 1

Plan view of Model-I

Fig. 2

Plan view of Model-II

Fig. 3

Plan view of Model-III

Fig. 4

Plan view of Model-IV

Fig. 5

Plan and elevation of Model-V (up to four storey the length of shear wall is 3 m and with increase in height its length reduced up to 1.5)

Fig. 6

Plan and elevation of Model-VI (up to Fifth storey the length of shear wall is 3 m and with increase in height its length reduced up to 1.5)

4 Results and Discussion

The parameters which were studied to know the torsional behaviour of regular and irregular plan buildings are maximum joint displacement, maximum storey drift, eccentricity, torsional irregularity ratio, base shear, model participating mass ratio and natural time period. To avoid the torsion of plus and L-shaped irregular plan structure, the shear wall is introduced in Model-II and Model-III which is known has Models-V and VI, respectively after that their results value are compare with each other, i.e. before applying shear wall and after applied of shear wall.

4.1 Model Participating Mass Ratio

IS 1893: 2002 clause 7.8.4.2 states that number of modes to be used in the analysis should be such that the sum total of modal masses of all modes considered is at least 90% of the total seismic mass of the structure.

The first mode and second mode should be translation vibration mode as recommended by the IS Code. From Table 2, it was observed that the first two modes of Model-I gave a pure translation vibration mode shape that means no rotation and torsion in Model-I as per code recommendation. But, first mode of Model-II, Model-III and Model-IV has rotational vibration in first mode which indicated there is torsion in those models.

Table 2 Modal participating mass ratios (%) of Model-I, II, III and IV

Table 3 shows the modal participating mass ratios (%) of Models-V and VI. A comparison of the first two modes of Model-II with Model-V and Model-III with Model-V I was done. After the application of shear wall on Model-II, i.e. Model-V, and Model-III, i.e. VI, the first mode and second mode gave a translation vibration mode shape that means no rotation which was as per code recommendation which indicated that there is no torsional effect in Model-V and Model-VI.

Table 3 Modal participating mass ratios (%) of Models-V and VI

4.2 Time Period for the Modes of Vibration

From Fig. 7, it is observed that the Model-I has maximum time period and Model-V has minimum time period. After the additional of shear wall on Model-II, i.e. Model-V and Model-III, i.e. Model-VII, time period is reduced by 20.47% and 25.4%, respectively, this is because additional of shear wall make the structure more rigid under strong ground motion of earthquake.

Fig. 7

Comparison of Model time period for the Modes of Vibration of different Models

4.3 Story Drift

As per Cl. no. 7.11.1 of IS 1893-2002, the storey drift in any storey due to specified design lateral force with partial load factor of 1.0, shall not exceed 0.004 times the storey height.

From Fig. 8, it is observed that Model-III has maximum story drift among Model-I, Model-II and Model-IV. The storey drift of Model-V and Model-VI is reduced by 7% and 36.4% after addition of shear wall in Models-II and III, respectively.

Fig. 8

Comparison of maximum storey drift

4.4 Maximum Joint Displacement

From Fig. 9, it is observed that Model-III has maximum deflection.The joint deflection of Model-II and Model-III is decreased by 22.4% and 43.08%, respectively, after introduced of shear wall.

Fig. 9

Comparison of maximum Joint displacement

4.5 Eccentricity

From Tables 4 and 5 and Figs. 10 and 11, it is observed that the centre of mass and centre of rigidity of Model-I (regular plan building) are coincide with each other which means there is no eccentricity in Model-I. It was also observed that model-III has maximum eccentricity value in both directions. The maximum eccentricity of value Model-II of storey 1 and storey 2 decreased by 50% and 45% in Y-direction, respectively, after introduced of shear wall. The eccentricities of the model-VII with equivalent shear wall are reduced by 67.28% when compared with the eccentricities of torsionally irregular model-III.

Table 4 Eccentricity in X-direction, Ex (m)

Table 5 Eccentricity in Y-direction, Ey (m)

Fig. 10

Comparison of eccentricity in X-direction

Fig. 11

Comparison of eccentricity in Y-direction

4.6 Torsional Irregularity

For torsional irregularity check, the permissible limit is ΔMax/ΔAvg < 1.2 as per IS 1893 (part-1):2002.

From Figs. 12 and 13 and Tables 6 and 7, it is observed that the torsional irregularity ratio of model-II, III and model-IV has exceeded the code value. In model-I the torsional irregularity ratio in each floor is less than 1.2 which indicate there is no torsional irregularity in model-I. From the results, it is observed that torsional irregularity grows up with the increase of eccentricity. In Model-V and Model-VII, it is observed that, there is no torsional irregularity at each floor.

Fig. 12

Comparison of Max/Avg. drift ratio in X-dir

Fig. 13

Comparison of Max/Avg. drift ratio in Y-dir

Table 6 Torsional irregularity ratio in X-direction

Table 7 Torsional irregularity ratio in Y-direction

4.7 Base Shear

From Table 8, it can be observed that the Model-I which is symmetrical in plan has the biggest value of base shear, whereas the model-III (L-shaped building) has the lowest value of base shear when compared with Model-I, Model-II and Model-IV. The biggest value of base shear in the building denotes the building is stiff under the motion of earthquake, due to this reason the building with higher base shear give better seismic in compared to building with low base shear. After introduced of shear wall the base shear of Model-II and Model-III increased by 1.96% and 2.35%, respectively.

Table 8 Base shear

4.8 Storey Stiffness

From Tables 9 and 10, it is observed that, model-II has maximum value of storey stiffness value at storey 1. With increase in height the value of storey stiffness goes on decreasing and vice versa. Figure 14 and Table 11 represent the stiffness comparison of Model type—II and V with percentage increase of stiffness after additional of shear wall. From this graph, it is observed that maximum increase percentage of stiffness is 67.16% due to X-direction seismic load and 46.63% due to Y-direction seismic load.

Table 9 Story stiffness-X (kN/m)

Table 10 Story Stiffness-Y (KN/m)

Fig. 14

Increase percentage of stiffness from Model-II to Model-V

Table 11 Increase percentage of stiffness

Figure 15 and Table 11 represents the stiffness comparison of Model type—III and VI with percentage increase of stiffness after additional of shear wall. From this graph, it is observed that maximum increase percentage of stiffness is 136.04% due to X-direction seismic load and 142.35% due to Y-direction seismic load.

Fig. 15

Increase percentage of stiffness from Model-III to Model-VI

4.9 First Vibration Mode Shape of Models

Figure 16 represents the first vibration mode shape of different models, and from this table, it is observed that the first mode of Model-I, Model-V, Model-VI have pure translation but Model-II, Model-III, Model-IV have rotation.

Fig. 16

First vibration mode shape of models

5 Conclusion

The present study demonstrates that plan asymmetry has a compelling effect on the reaction of buildings correlated to the symmetric plan building. Based on numerical analysis results for a building model with the symmetrical plan, asymmetrical plan and asymmetrical plan with shear wall following conclusions may be drawn.

• The structures with asymmetrical plan have more seismic impact than structures with symmetrical plan in terms of seismic base shear, displacement and eccentricity.

• For torsional irregularity, the permissible limit is as per IS 1893 (part-1) has been checked.

• Structures with asymmetrical plan have more torsion than the structure with symmetrical plan during strong ground motion of earthquake if it is located in high seismic zones. Since torsion is more critical aspect for main damage or complete structures collapse, therefore, it is very necessary that irregular structures should be carefully analysed for control the torsion. To reduce torsional irregularity effect, shear wall system had been provided.

• To reduce the torsion of the structure for better seismic performance, a shear wall may be introduced at all corners, reducing the size at every floor level by trial and error method. This improves seismic performance of building. Gradual reduction in the stiffness of the structure with reduced sections of the shear walls improves the seismic performance of the structure and also reduces the cost of structure.

• The concept of curtailed shear walls may be an effective method of seismic retrofitting of an existing structure and also for the new structures. Size, position/location, shape, orientation of shear walls, grade of concrete and steel, etc., are project dependents and are need to be decided based on the trial-and-error method.