EFFECTS OF STAIRCASE ON THE SEISMIC PERFORMANCE …

EFFECTS OF STAIRCASE ON THE SEISMIC PERFORMANCE OF

RCC FRAME BUILDING.

N SHYAMANANDA SINGH Assistant Professor, Department of Civil Engineering,NIT MANIPUR,

Imphal-795001, Manipur, India. [email protected]

CHOUDHURY.S

Professor, Department of Civil Engineering,NIT SILCHAR, Silchar-788010, Assam, India.

Abstract: In the present paper, the effects of staircase on the seismic performance of the RCC frame buildings of different heights and different plans have been studied. In codal design of buildings, the stair model is generally not included in the analysis of RC frame buildings. Due to the rigidity of inclined slab and of short columns around staircase, beams and columns are often characterized by a high seismic demand. The identification of the weakest elements of the structure, the failure type considering the presence of the stairs, and their contribution in the non linear performance of RC frame buildings are some of the areas on which the present paper has presented. For analysis and design, SAP 2000 version 14.0.0 has been used. Performances of both categories of the buildings have been evaluated through push over analyses and nonlinear time history analysis. Keywords: Response Spectrum method, Push over analysis, non linear time history analysis. 1. Introduction In RC frame buildings, the primary structural system to resist lateral load are beams and columns. Besides, primary structural system, some elements also contribute to lateral load resistance. These elements fall in the category of secondary systems. Secondary system can be structural secondary like staircase, structural partition etc and non-structural secondary like storage tanks, machinery etc. A special case of structural secondary members which are normally designed for non seismic force are concrete staircase.

In the present study, the effects of staircase on the seismic performance of the RC frame buildings of different heights and different plans have been studied. In general the presence of a stair creates a discontinuity in a reinforced concrete frame made of beams and columns. From geometrical point of view, a stair is composed by inclined elements (beams and slabs) and by short (squat) columns. These elements contribute to increase the stiffness of the building. For these reasons the elements that constitute the stair are often characterized by a high seismic demand. The short columns are subjected to high shear force that can lead to a premature brittle failure .The inclined beams are subjected by high variation in axial force that can modify the resistance and deformability of all these elements.

The identification of the vulnerable elements of the structure, the failure type with the presence of the stairs, and the contribution of stair in the nonlinear performance of RC frame buildings are some of the area of particular interest and have been considered in this study.

Zhang Wang-Jil et al (2009) results shows that existence of stair greatly affects the lateral stiffness of frame, dynamic performance, the peak of internal force and node response spectrum under different earthquake compactable to Chinese code. Zhang Cuiqiang et al (2010) publish in their paper that by decoupling the stiffness of the stair, the stair stiffness contributions at each node were reported. It was observed from their study that stair can change the order of the mode and the weakness direction of the structure. Jiao Ke et al (2009) reported that for frame structures, corner column in staircase, staircase beams, staircase column and the slab of the staircase are yielded first and damage indicating the weakest point in the structure. Qiwang Su (2010) reported in his paper that staircase arrangement can affect the torsional mode of the structure which can make the torsional mode to be the first mode of vibration.E Cosenza et al (2009) concluded from their study that shear failure becomes dominant in the squat column and slabs and precedes the conventional ductile failure.

N Shyamananda Singh et al. / International Journal of Engineering Science and Technology (IJEST)

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2. Modeling and Analysis Structural modeling of the buildings has been prepared as per the geometrical plans configuration in Fig. 1 and Fig. 2 by SAP 2000 Version 14.0.0. Beams and columns have been modeled as 3-D frame elements. In the modeling process, the properties assigned to the frame elements include geometric dimension, reinforcement detail, and the type of material. For all the models, concrete grade M30 and reinforcement steel of grade FE 500 have been assumed for analyses and design of the structure.

The slab at each floor level and roof level have been assumed to be of thickness 125 mm and modeled as rigid diaphragms. The nonlinearity of frame sections have been modeled as lumped plastic hinges at the column and beam ends. The beams have been assigned with moment (M3) hinges and columns with coupled axial moment (P-M2-M3) hinges at the two ends. In modeling of plastic hinges in the frames, the default hinge properties defined by SAP 2000 as per FEMA 356 have been used. Staircase has been modeled as a series of prismatic 3D beam elements along its axis, inclined to the horizontal. The sectional properties of the staircase elements have been taken as the full width of the solid part beneath the steps. The models have been assumed to be fixed supports at the pedestal top of the foundation at a depth of 1.5 m from the plinth beam. The height of each storey is assumed to be 3.3 m and all the frames have been assumed to be located at Zone V, medium soil, importance factor 1 and 5% material damping ratio as per Indian Code (IS: 1893(Part 1):2002).Dead load and imposed load were calculated as per IS 875:1987.

Fig. 1 Plan A


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Fig. 2 Plan B

A force-displacement (moment- rotation) curve has been defined which gives the yield value and the plastic

deformation following yield. This is done in terms of a curve with value at five points, A-B-C-D-E, as shown in Fig.3. Point A represents the origin. At point B yielding starts and hence no plastic deformation occurs in the hinge up to this point .Point C represents the ultimate capacity, Point D represents a residual strength and point E represents total failure. Deformation points IO (immediate occupancy), LS (life safety), and CP (collapse Prevention) have been also specified.

E

Fig.3 Force –Displacement curve.

In the present study, all the buildings has been designed by Response Spectrum method of IS Code. The design lateral force ( ) at floor i in mode k is given by,

(1) Where, =design horizontal acceleration spectrum value using natural period of vibration ( of mode k.

= Mode shape coefficient at floor i in mode k

= Modal Participation factor of mode k.

= Seismic weight of floor i.

The design horizontal seismic coefficient for various modes are worked out using the equation

Deformation

For

ce

A

B

C

D IO

LS

CP


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(2)

Where, Z= Zone factor of the different seismic zones of India I= Importance factor, depending on the functional use of structures, characterized by hazardous consequences of its failure, post earthquake functional needs. R= Response reduction factor which represent the structure ductility, damping as well past earthquake performance of the structure.

= Average response acceleration coeffeiceint for rock and soil sites as given by IS 1893(Part 2):2002.

Performance evaluation of all the buildings by Nonlinear static procedure ( NSP) has been performed by the applications of lateral loads to the model in proportion to the distribution of inertia forces in the plane of each floor diaphragm. For NSP, two vertical distributions of lateral load i.e mode proportional loading and uniform load pattern of loading has been applied. In the present study, for nonlinear dynamic analysis (time history analysis) (NLTHA), five Spectrum compactable Ground Motion (SCGM) were generated from real earthquake data recorded. The SCGM were generated by software developed by A.Kumar (2004).

Table 1 Details of five SCGMs used for NLTHA Sl. No

Designation Original Earthquake Duration

(sec)

1 SCGM-1 San Fernando (1971) 41.64

2 SCGM-2 Duzce,Turkey (1999) 25.58

3 SCGM-3 Imperial Valley (1979) 28.36

4 SCGM-4 Mammoth Lakes (1980) 25.95

5 SCGM-5 N. Palm Springs (1986) 20.03

Fig. 4 Comparison of the Response Spectra of SCGMs and IS Spectrum


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3. Sample buildings and nomenclature A sample of sixteen buildings with heights of 3, 6, 8 and 12 storeys has been studied. All the sixteen buildings has been designed and analysed as per the Indian codes.

Table 2 Nomenclature of the buildings Building Nomenclature

Without Stair Model With Stair Model

Plan - A A-3, A-6 AS-3, AS-6

A-9, A-12 AS-9, AS-12

Plan - B B-3, B-6 BS-3, BS-6

B-9, B-12 BS-9, BS-12

Fig.4 Typical building without stair model Fig.5 Typical building with stair model

4. Methodology In the first stage, initially buildings without stair model has been analyzed and designed as per IS code by Response Spectrum method.Stair dead load and live load have been provided as line loads on the connecting or landing beam. Member Sizes of the buildings have been adjusted until all the structure members are safe.Base Shear correction has been applied to all the structure.Capacity Design has been performed to all the buildings.Performance of the buildings has been analyzed by NSP and NLTHA. In the second stage, stair model has been incorporated in the models and the buildings has been redesigned with the same member sizes.Identification of the vulnerable elements of the structure near staircase, the failure type with the presence of the stairs has been done.Evaluation of the extra inner forces on these vulnerable elements has been done.Iterative and adjustment of the failed members has been done till all the members are safe.Base Shear and Capacity Design has also been done for these sets of buildings also.Performance evaluation through NSP and NLTHA has been done. In third stage, comparison of performances of the two sets of buildings has been done.Performance level comparision has been done by NSP through Push over curve and from the results of NLTHA, comparison of IDR (%) has been done. 5. Results and discussions 5.1 Performance of buildings without staircase model In engineering practice, the modeling of staircase is not considered in the modeling of the structure. The staircase has been assumed to be simply supported and the dead load and live load reactions on the landing


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beams on both ends have been calculated. Beams and columns sizes of the buildings have been tabulated in Table 3

Table 3 Member sizes for buildings without staircase model

Building Nomenclature Column Sizes (mm) Beam sizes (mm)

A-3 400×400 350 ×350 300×400

A-6 600×600,550 ×550,450×450,400×400,350×350 300×400

A-9 600×600,550 ×550,450×450,400×400,350×350 300×400

A-12 600×600,550 ×550,450×450,400×400,350×350 300×400

B-3 350 ×350 300×400, 300×500

B-6 400×400,350×350 300×400,300×550

B-9 450×450,400 ×400,350×350 300×400,300×550

B-12 500×500,450×450,400 ×400,350×350 300×400,300×550

The general trend of the performance of the buildings without staircase model designed as per codal provision and analysed by NSP has been observed to be at LS in both the direction. The performance point (PP) of the buildings at Maximum Considered Earthquake ( MCE) is given in Fig.6.

(a) Short Direction (b) Long Direction




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Fig.6 PP of buildings without staircase model at MCE level.

From NLTHA analyses, for buildings of Plan –A, the inter-storey drift ratio (IDR %) has been observed to have an average of 1.83% in short direction and 1.69% in long direction. For buildings of Plan-B, IDR% has an average value of 1.27% in short direction and 1.09% in long direction. Maximum IDR (%) at MCE has been tabulated in Table 4.


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Table 4 Maximum Inter Storey Drift (%) at MCE

Building Nomenclature

Maximum Inter Storey Drift (%)

Short Direction Long Direction

A-3 1.45 1.28

A-6 2.29 2.1

A-9 1.61 1.62

A-12 1.97 1.75

B-3 1.23 0.69

B-6 1.65 1.57

B-9 0.93 0.98

B-12 1.29 1.14

5.2 Performance of buildings with staircase model Stair model has been incorporated in all the building models and has been redesigned incorporating the extra inner forces on the vulnerable elements near the staircase core. Beams and columns sizes of the redesigned buildings have been tabulated in Table 5.

Table 5 Member sizes for buildings with staircase model

Building Nomenclature Column Sizes (mm) Beam sizes (mm)

AS-3 500×500,400×400,350 ×350 300×400,300×550

AS-6 600×600,550×550,450×450,400×400,350×350

300×400,300×550, 350×550,350×750

AS-9 600×600,550×550,500×500,450×450, 400×400,350×350

300×400,300×550, 350×550,300×650, 350×750

AS-12 600×600,550×550,450×450,400×400, 350×350

300×400,300×500,300×550, 300×650,350×750, 450×750

BS-3 350 ×350 300×400,300×550

BS-6 400×400,350×350 300×400,300×550, 350×550,350×750

BS-9 450×450,400 ×400,350×350 300×400,300x500, 300×550,300×600, 300×650

BS-12 500×500,450×450,400×400,350×350 300×400,300×550, 300×600,300×650, 350 x750,450×750

The general trend of the performance of the buildings with staircase model analysed by NSP has been observed to be at LS in both the direction expect for a few cases in the long direction where it has been observed to be in IO level.



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Fig.7 PP of buildings with staircase model at MCE level.

From NLTHA analyses, for buildings of Plan –A with staircase model, the inter-storey drift ratio (IDR %) has been observed to have an average of 1.15% in short direction and 1.23% in long direction. For buildings of Plan-B, IDR% has an average value of 1.27% in short direction and 0.95% in long direction. Maximum Inter Storey Drift (%) at MCE has been tabulated in Table 10.

Table 10 Maximum Inter Storey Drift (%) at MCE Building Nomenclature

Maximum Inter Storey Drift (%)

Short Direction Long Direction

AS-3 1.95 1.92

AS-6 0.83 0.94

AS-9 0.91 1.12

AS-12 0.90 0.95

BS-3 2.10 0.80

BS-6 0.88 0.97

BS-9 0.98 1.00

BS-12 1.11 1.05

5.3 Comparision of results The performance of buildings designed without stair model as discussed in 5.1 and with stair model in 5.2 have been compared .The effect of stair model on time period , effects on landing beams and columns adjacent to the landing beams and the dynamic performance of the buildings has also been discussed.

5.3.1 .Effects on time period of the Buildings

The effect on the time period of the building has been highlighted in Fig.8


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Fig.8 Comparisons of time period of buildings with and without staircase model.

It has been observed that incorporation of stair model in the building reduces the dynamically analysed time period of the structure by about 22.31%.

5.3.2 Effects on the landing beams and columns It has been observed that the presence of staircase tremendously influence the peak value of response quantities of beams and columns around staircase. The landing beams and columns adjacent to staircase have been found to fail due to excessive demand imposed owing to the presence of staircase.

Fig.9 Comparisions of Shear force on landing beams of buildings


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Fig.10 Comparisions of Axial force on columns adjacent to landing beams


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Fig.11 Comparisions of Bending Moment (M2) on columns

It has been observed that with incorporation of stair model, columns touching landing beam have been found to be subjected to an increase in axial force by an average of 19%. The lateral moment in such columns increased on average by 32%. Shear force in landing beam increased by 36% on average. The torsional moment in landing beam increased enormously.

5.3.3 Effects on IDR % The effects on IDR% after the incorporation of stair model has been discussed in the section. The maximum IDR % from the five NLTHA of buildings of particular height has been found out and comparision has been shown in Fig.12





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Fig.12 Comparisons of IDR% of buildings with staircase model and without staircase model


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It has been observed from the buildings considered that the interstorey drift ratio has been found to reduce by 33% in short direction and 23% in long direction on average on incorporation of stair model in a general trend expect in few cases.

6 CONCLUSIONS

From the study made and from the results presented in the previous sections, the following important conclusions have been drawn within the purview of the buildings considered.

(1) It has been observed that the presence of staircase tremendously influence the peak value of response quantities of beams and columns around staircase. The landing beams and columns adjacent to staircase have been found to fail due to excessive demand imposed owing to the presence of staircase.

(2) Incorporating only weight of staircase and not stair element in computer model shall lead to under-design as the Codal design is inadequate to cater the additional demand imposed due to presence of staircase on landing beams and columns adjacent to staircase.

(3) With incorporation of stair model, columns touching landing beam have been found to be subjected to an increase in axial force by an average of 19%. The lateral moment in such columns increased on average by 32%. Shear force in landing beam increased by 36% on average. The torsional moment in landing beam increased enormously.

(4) The interstorey drift ratio has been found to reduce by 33% in short direction and 23% in long direction on average on incorporation of stair model.

(5) Dynamically analyzed time period got reduced by about 22.31% on incorporation of stair model. (6) Non-incorporation of stair element in computer model may lead to failure of staircase under major

earthquakes.

References [1] Cao Wanlin (1998), Experimental Study on Story Stiffness and Its Degeneration of Staircase FrameStructure with Special Shape

Columns, Journal of Building Structures. [2] Chopra,A.K,Goel R.K (2004), A modal pushover analysis procedure to estimate seismic demands for unsymmetric-plan buildings,

Earthquake Engineering And Structural Dynamics, 33, pp 903-927. [3] Dai Hongjun,QI Ai (2009), Analysis of performance of reinforced concrete frame structure with staircase based on ETABS, Journal of

Earthquake Engineering and Engineering Vibration. [4] E Cosenza, G. Monti (2009), The state of Earthquake Engineering Research in Italy: the ReLUIS-DPC 2005-2008 Project, 51-110,

Doppiavoce, Napoli, Italy. [5] Fajfar,P (2005), Torsional effects in the pushover-based seismic analysis of buildings, Journal of Earthquake Engineering, 9(6), pp

831-854. [6] Qiwang Su (2010), Finite Element Analysis of Staircase under Earthquake Action, Advanced Materials Research, 163-167 (2011), pp

2964-2968. [7] Kumar,A(2004), Software for generation of spectrum compatible time history, Proceedings of 13th World Conference on Earthquake

Engineering, August 1-6, 2004, Paper No. 2096. [8] __ATC 40 (1986) Seismic evaluation and retrofit of concrete buildings , Report No.SSC 96- 01, Seismic Safety Commission , State of

California, Proposition 122 Program, prepared by Applied Technology Council. [9] __Computers and Structures (2000), SAP 2000: Three Dimensional Static and Dynamic Finite Element Analysis and Design of

Structures, Computers and Structures Inc, Berkeley, California, USA. [10] __FEMA 356(2000) Pre Standard and commentary on the seismic rehabilitation of buildings, Federal Emergency Management

Agency, Washington, DC. [11] __IS 1893:2002, Criteria for Earthquake Resistance Design of Structures: Part 1 General Provisions and Building (fifth revision),

Bureau of Indian Standards, New Delhi, 2002.


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EFFECTS OF STAIRCASE ON THE SEISMIC PERFORMANCE …