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One of the major challenges of constructing any high rise building for civil engineers is to make it earthquake resistant. This resistance largely depends on the building’s shape and structural system. A comparative study has been done in this paper about the seismic behavior and response of buildings having a regular plan and plan irregularity (re-entrant corners). The 5 building models considered in this study are 15 stories each, the same area and identical weight. Among the 5 building models, 2 are with a regular plan (square, rectangle) and the other 3 building models are with plan irregularity (re-entrant corners). All of them are modeled using ETABS 2015 program for Dhaka, Bangladesh (seismic zone 2). Static loads, wind loads and seismic loads are considered for each model and dynamic response under Bangladesh National Building Code (BNBC) 2006 response spectrum has been meticulously analyzed. A comparison for story displacement, base shear, story drift and time period has been established and explored for dynamic response spectrum among the models. The results show that buildings with irregularity have a greater value of time period, drift and displacement and hereby are more susceptible to damage during an earthquake or disaster.

Bangladesh, a South Asian country is located at the junction point of three tectonically active regions [^{th} of April, 2020 originating in Myanmar [

In a study, Ravikumar, C. et al. (2012) showed the structural performances of different irregular buildings in rocky soil in India [

The shape of a building and its regularity both vertically and plan wise plays a vital role in the response of the structure under static and dynamic loading which affects the damages the building would be subjected to during an earthquake. Considering all these factors, 5 building models situated in Dhaka, Bangladesh, 2 of them are regular in shape and the other 3 (L shape, T shape and + shape) having plan irregularity (re-entrant corners) are subjected to static and dynamic loading and are studied. All five models are of the same area and identical weight. Difference in response of each model is observed.

Two kinds of irregularities may exist in a building—Plan irregularity and vertical irregularity [

Re-entrant corner irregularity is one of the most common phenomena seen in a structure due to shape of the land of the owner, aesthetical point of view and less consciousness by professionals during designing. That is why, in this paper, building plans with Re-entrant corners are taken into account for comparison with regular building plans.

Type | Definition | BNBC 2006 reference section |
---|---|---|

1) Tortinal irregularity | Torsional irregularity shall be considered to exist when the maximum story drift, computed including accidental torsion, at one end of the structure transverse to an axis is more than 1.2 times the average of the story drifts of the two ends of the structure. | 1.5.4.2, 2.5.6.5, 1.5.4.3, 1.7.2.9(d) |

2) Re-entrant corners | Plan configuration of a structure and its lateral force resisting system contains re-entrant corners, where both projections of a structure beyond a re-entrant corner are greater than 15% of the plan dimension in the given direction. | 1.7.2.9(d) |

3) Diaphragm discontinuity | Diaphragms with abrupt discontinuities or variations in stiffness, including those having cutout or open areas greater than 50% of the gross enclosed area of the diaphragm or changes in effective diaphragm stiffness of more than 50% from one story to the next. | 1.7.2.9(d) |

4) Out-of-plane offsets | Discontinuities in a lateral force path, such as out-of-plane offsets of the vertical element. | 1.5.5 1.7.2.9(d) |

5) Nonparallel systems | The vertical lateral load-resisting elements are no parallel to or symmetric about the major orthogonal axes of the lateral force-resisting system. | 1.5.4.2 |

The analysis has been done by using two methods—Equivalent static method and response spectrum analysis.

Equivalent static analysis is also known as linear static analysis and can be used only for regular structures with a limited height. It is the simplest form of analysis as it assumes that the building responds in its fundamental mode following the respective code of practice. The design base shear is determined and is then distributed to the height of the building. The lateral forces at each story are also computed and then distributed to the force resisting elements.

It is also known as linear dynamic analysis. According to Section 2.5.7.2, Bangladesh National Building Code 2006, when this procedure is used, an elastic dynamic analysis of a structure shall be performed based on a criterion with a mathematical model and using a response spectrum. The analysis shall include peak dynamic response of all modes having a significant contribution to total structural response. Peak modal response shall be calculated using the ordinates of the appropriate response spectrum curve which corresponds to the modal periods. The number of modes is satisfactory when at least 90% of the participating mass is included in the response for each principal horizontal direction. The analysis should be performed using a mathematical model either by using site-specific response spectra or normalized response spectra. In absence of a site specific response spectrum, normalized response spectra should be used. In this paper, the normalized response spectra for 5% damping ratio (Zone 2) mentioned in BNBC 2006 is used for analysis (

In the present study, 5 building models situated in Dhaka (Seismic Zone 2) are taken. Model 1 and model 2 are of regular shapes (square and rectangular) and models 3, 4 and 5 are of irregular shapes (T shape, L shape and + shape) having re–entrant corner irregularity. Each model has 15 stories. The area and mass of each building are kept identical to have a similar influence. Span lengths along X and Y direction may vary to keep the area and mass same. Dead load, Live load, Partition wall load, Earthquake load, Wind load have been applied following the regulations of BNBC 2006. Material properties and structural parameters are given in

The plans of models 1, 2, 3, 4 and 5 are shown in Figures 3-7 respectively.

The 3D views of models 1, 2, 3, 4 and 5 are shown in Figures 8-12 respectively.

Materials | Values used (unit) |
---|---|

Compressive strength of concrete Modulus of elasticity of concrete Shear modulus of concrete Poisson’s ratio Unit weight of concrete Yield stress of steel | 4000 psi 3600 ksi 1500 ksi 0.2 150 pcf 60 ksi |

Parameters | Value/Type for all models |
---|---|

Structure type Number of stories Elevation Bottom story height Area Grade Beam | RCC building structure 15 165 ft 10 ft 6400 square ft 12 in × 12 in |

Column | Variable to adjust mass 27 in × 24 in square mode 24 in × 21 in rectangular model 24 in × 24 in T shaped model 24 in × 24 in L shaped model 24 in × 24 in + shaped model |

Floor Beam Slab thickness Floor finish (Dead load) Partition wall load Live load Seismic Zone Soil type Importance factor Response Reduction factor Ct Wind Speed | 15 in × 15 in 6 in 30 psf 15 psf 42 psf 2 (Z = 0.15) S₃ (S = 1.5) 1 5 0.03 131 mph |

The mass comparison among the 5 building models has been shown in

Graphical representations showing comparison among story displacement of the 5 building models for Seismic load (EQ), Wind load (WL) and dynamic response spectrum (RS) for both X and Y axis are discussed below.

Displacement of stories for earthquake loads in X and Y direction has been shown using equivalent static analysis in

Displacement of stories for wind load in X and Y direction has been shown using equivalent static analysis in

Displacement of stories using response spectrum analysis has been shown in

A comparison of base shear for RS along X and Y direction among the 5 building models is shown in

Irregularly shaped buildings have a higher base shear value in X direction for RS than compared to regular shapes. The maximum value is 1729 kip obtained for model 4 on the other hand the minimum value is 1406 kip for model 1. Whereas for Y direction, Base shear value for a regular shaped building is higher than irregular T, L and + shaped building. The maximum value is 1677 kip obtained for model 2 which is 1.18 times the minimum value obtained for T shaped model 3. M. A. Farhan and J. Bomisetty (2019) also found out the maximum base shear for regular building which was 1.53 times more than the minimum base share value for T shaped building [

Story-wise drift value for RS max along X and Y direction have been shown in

value is 0.007952 for model 5 and in Y direction, maximum value is 0.007447 obtained for model 3. Rectangular model has the least value in both directions which is 0.00466 in X direction and 0.004197 in Y direction.

models. The comparison is done taking 3 modes. For mode 1, maximum value is 3.485 seconds obtained for model 4 and the minimum value is 2.923 seconds obtained for model 2. For mode 2, model 3 shows the maximum value of 3.267 seconds and model 2 shows the minimum value of 2.573 seconds. For mode 3, model 4 shows the maximum value of 2.692 seconds and model 2 shows the minimum value of 2.109 seconds. Time period for T, L and + shaped irregular buildings are almost the same.

The overall results of data can be summarized as follows:

● Building plans with re-entrant corner irregularity has a larger value of story displacement in comparison to regular building plans and thus are more vulnerable.

● Maximum displacement is obtained for response spectrum among all loads.

● Wind load has been a major concern for high rise buildings. Irregular buildings are more susceptible to wind loads than regular buildings.

● Rectangular model has the least value of displacement, story drift and time period and hence has the most chance of survival during a disaster.

● Rectangular building has a greater value of displacement for wind load along its smaller direction (Y direction is the model) than its larger dimension.

● + shaped building model has a greater value of displacement for seismic load and dynamic response spectrum.

● Base shear values are maximum in regular-shaped buildings in Y direction for dynamic response spectrum whereas irregular buildings show greater value in X direction. The most is seen for L shaped.

● Time period decreases preliminarily as the number of modes increases for all shapes.

● Irregular shaped buildings have a greater time period value compared to regular types.

● Story drifts for + shaped building has the maximum value in X direction and T shaped in Y direction. Rectangular building has the minimum in its larger direction.

● Story drift reaches the maximum value at story 4 and then it starts decreasing

The author declares no conflicts of interest regarding the publication of this paper.

Ankon, S.B. (2020) A Comparative Study of Behavior of Multi-Storied Regular and Irregular Buildings under Static and Dynamic Loading. Open Journal of Civil Engineering, 10, 337-352. https://doi.org/10.4236/ojce.2020.104026