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STUDY ON THE PERFORMANCE OF WAFFLE SLAB STRUCTURE WITH SQUARE GRIDSAND RECTANGULAR GRIDS WITH THE HELP OF N2 METHOD Karunesh Mishra1, Amit Richariya2
1Research Scholar, Dept. of Civil Engineering, SVN University, Sagar (M.P)
2Assistant Professor, Dept. of Civil Engineering, SVN University, Sagar (M.P)
Abstract- Whenever large spaces within a building need to be enclosed without obstructions and supports, architects often deploy waffle slabs to construct floors and ceilings. As a result of the development in architectural design and new building management concepts, waffle slabs are becoming on demand for structural designers.
Therefore, it becomes important to know more about its structural behavior.
In the present work, the pushover analysis of a waffle slab structure is performed both in x and y directions. The structure is G+1 storey building. Two cases are studied in the present work i.e. Case A: waffle slab structure with square grids and Case B: waffle slab structure with rectangular grids. The structure is designed as per IS: 456-2000 using limit state method of design and the method of analysis and design of waffle slab is done by using approximate method of analysis. The software used in the analysis is ETABS. The results obtained from the analysis such as capacity curves, deflection, stresses, displacement and base shear are compared. Based on the above results, one of the cases is considered for conversion from multi degree of freedom system to single degree of freedom system.
Keywords: Waffle slab, square grids, rectangular grids, IS: 456-2000, ETABS, deflection, stresses.
1. INTRODUCTION 1.1 Waffle Slab
Whenever huge spaces within the edifice need to be enclosed without obstacle and supports, architects often deploy waffle slabs to construct floors and ceilings. As a result of the development in architectural design and new structure management concepts, waffle slabs are fetching on demand for structural engineers.
Therefore, it becomes vital to know more about its structural behavior.
The slab with an arrangement of intersecting beams placed at regular interval and interconnected to a slab of nominal thickness is known as Waffle slab. Waffle slab is also known as two- way ribbed slab. These slabs are used when a huge column free area is the main requirement. They are used for heavy loads and large span structures as they exhibit higher stiffness and smaller deflection. Void formed in the ceiling leads to reduction in dead load and is beneficially utilized for concealed architectural lighting.
Waffle slab holds a greater amount of loads as compared to the conventional concrete slabs. Waffle slabs are light weight, therefore less foundation cost and longer spans are economical. Waffle slabs have fairly slim floor depths. These slabs
have good fire resistance, durable finishing and excellent vibration control.
The top of the waffle slab is generally smooth, like a traditional building surface, but the underside has a shape reminiscent of a waffle.
1.2 Nonlinear Static Analysis
The nonlinear static analysis has turn out to be a popular method for estimating seismic deformation demands in building structures as well as their local and global capacities for the evaluation of the safety of structures against an earthquake- induced collapse. The existing building can become seismically deficient since seismic design code requirements are constantly upgraded and developed in engineering knowledge. Further, Indian buildings built over past two decades are seismically deficient because of lack of awareness regarding seismic behavior of structures. The widespread damage particularly to RC buildings during earthquakes exposed the construction practices being adopted around the world, and generated a great demand for seismic evaluation and retrofitting of existing building stocks.
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1.3 N2 MethodN2 method was developed in the mid 1980‟s by Peter Fajfar. N2 method is a non-linear method for the siesmic analysis of the structures where N stands for Non-linear analysis and 2 stands for two mathematical models as single degree of freedom system and multi degree of freedom system. It combines the pushover analysis of a multi-degree-of-freedom (MDOF) system with the response spectrum analysis of equivalent single- degree-of-freedom (SDOF) system.
The N2 method is in fact a variant of the spectrum method based on inelastic spectra. Inelastic demand spectra are determined from a characteristic smooth elastic design spectrum. The reduction factors, which relate inelastic spectra to the basic elastic spectrum, are consistent with the elastic spectrum. The lateral load pattern in nonlinear static analysis related to the assumed displacement shape. This feature leads to a transparent conversion from a MDOF system to an equivalent SDOF system and response of the structure is evaluated in terms of performance point.
2 Methodology and Modeling 2.1 Methodology
The seismic analysis of waffle slab structure is performed in the current project with the help of Pushover analysis using ETABS software. For this, the proposed methodology is as follows:
1. Step by step procedure of pushover analysis and N2 method is done.
2. Modeling and pushover analysis in both x and y direction of waffle slab structure with square grids and rectangular grids is performed using ETABS software.
3. The results of analysis such as capacity curves, stresses,
deflections, hinge mechanism, performance point and base shear has been compared for the waffle slab structure with square grids and rectangular grids.
4. Based on the study, a problem of waffle slab structure is taken and converted the multi degree of freedom system into single degree of freedom system using N2 method.
2.2 Description of the Structure and Selection of Parameters
A typical waffle slab structure is considered in the present study. The structure is G+1 Storey building and two cases are considered in the study-
Case A- Waffle slab structure with square Grids (1m x 1m)
Case B- Waffle slab structure with rectangular Grids (1.5m x 1m)
The overall plan dimension is 21 m x 15 m and the height of the each storey is 3.5m and overall height of the structure 7m. For the purpose of design, linear structural analysis of the structure is carried out by the computer program ETABS. The slab of the structure is defined as Shell type. The structure is designed as per IS: 456-2000 using limit state method of design and the method of analysis and design of waffle slab is by using approximate method of analysis.
The materials used are M 25 grade concrete and HYSD Fe 415 grade steel.
The thickness of the slab is 120 mm, and cross-sections of columns and beams are 500 x 500 mm and 750 x 350 mm respectively for both the cases of waffle slab structure.
2.3 Particulars for Case A: Waffle slab Structure with Square Grids
The details and particulars of the waffle slab structure with square grids (1 x 1 m) along with figures is shown below- Table 1 Particulars and details of the waffle slab structure with square grids
PARTICULARS DETAILS
Span in x Direction 21m
Span in y Direction 15m
Number of Lines in x Direction 4
Number of Lines in y Direction 4
Division Width in x Direction 7m
Division Width in y Direction 5m
Thickness of Slab 120mm
Column Length 3.5m
Column Section 500mm x 500mm
Column Longitudinal Reinforcement 20mm ɸ, 8#
Column Transverse Reinforcement 8mm ɸ @ 100mm c/c
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Beam Section 750mm x 350mm
Beam Spacing in x Direction 1m
Beam Spacing in y Direction 1m
Beam Reinforcement 0.0125 m2 at top and bottom
Live Load 4 KN/m
Fig. 1 Proposed waffle slab structure with square grids (wire mesh view)
Fig. 2 Proposed waffle slab structure with square grids (extrude view) 2.4 Development of the Model
To reach the ultimate model for performing the analysis, various models of different dimensions were taken and according to the step by step procedure were analyzed. The modeling has been done in ETABS software with the help of default waffle slab wizard (template) available in it. After the modeling, pushover analysis has been performed.
The pushover analysis is carried out in both x and y directions. Default hinge properties, available in programs based on the Applied Technology Council (ATC- 40) guidelines are used for frame member.
Plastic hinge is used to represent the failure mode in the beams and columns when the member yields. An effort has also been done to convert the MDOF model of waffle slab structure to SDOF model with the help of N2 method.
3 RESULTS AND DISCUSSION 3.1 General
The step by step procedure of Pushover analysis and N2 method discussed in the previous chapter has been implemented on the waffle slab structure and for both the cases of the waffle slab structure.
3.2 Results
The results are divided into two different categories:
1. Results of Pushover Analysis: These are further categorized as:
a) Modal Characteristics
b) Response of Waffle Slab by Pushover Analysis
c) Deflections in Waffle Slab structure
2. Results of N2 Method
3.3 Results of Pushover Analysis
The pushover analysis is carried out for the modal load pattern in both x and y directions on the waffle slab structure for both the cases.
3.4 Modal Characteristics
The dominating mode for the waffle slab structure along with their time period, frequency, modal participation factor and modal participation mass ratio is shown in tables.
3.5 Case A: Waffle slab structure with square grids
Table 2 Modal characteristics of waffle slab structure with square grids in x direction
Mode Period Frequency Modal
Participation Factors
Modal Participation Mass Ratios
Unitless Sec. Cyc/sec. KN-s2 Unitless
1 0.35512 2.815 10.97 92.88
4 0.13668 7.316 3.03 7.11
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Table 3 Modal characteristics of waffle slab structure with square grids in y directionMode Period Frequency Modal
Participation Factors
Modal Participation Mass Ratios
Unitless Sec. Cyc/sec. KN-s2 Unitless
2 0.34698 2.882 10.99 93.22
5 0.13609 7.348 2.96 6.77
4 CONCLUSIONS
Following conclusions are made from the study:
i. Pushover analysis is carried out separately in the x and y directions.
The slope of the pushover curves is gradually changed with increase of the lateral displacement of the building.
Hinges have developed in the beams and columns showing the three stages immediate occupancy, Life safety, Collapse prevention.
ii. On the basis of pushover curves, the waffle slab structure with square grids has higher base shear for the modal load patterns in x and y directions as compared to waffle slab structure with rectangular grids.
iii. The maximum permissible limit of deflection as per IS 456:2000 i.e.
span/250 is 84 mm and 60 mm in x and y directions respectively. The stresses for both the cases are within the permissible limits.
iv. The Maximum permissible stresses in concrete is 0.446*fck i.e. 11.15 N/mm² and for steel is 361.05 N/mm². The stresses for both the cases are within the permissible limits.
v. From results and discussions it can be concluded that both the cases gives better results on the basis of maximum permissible limit of deflection and stresses. Thus one of the case i.e. waffle slab structure with square grids for the modal load pattern in x direction is considered for conversion of MDOF system into SDOF system.
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21. Figure 1.3. Single-degree-of-freedom
(SDOF) system
“http://www.efunda.com/formulae/
vibrations/sdof images/SDOF plot.gif.”
22. Figure 1.4. Multi-degree-of-freedom
(MDOF) system.
“https://image.slidesharecdn .com /chapter4-02/95/dynamics-of-multiple- degree-of-freedom-linear-systems-3-638.”
23. Gagan, C., Golnal, A., Karthik, S., and Kumar, N.G., (2017) “Application of N2 method for performance evaluation of RC framed Asymmetric Edifices.” Journal of Scientific Research and Reports, 15(1), 1-6.
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“Optimum design of RC Waffle slabs,”
Journal of Civil and Structural Engineering.