International Conference on
Trends and Challenges in Concrete Structures Ghaziabad, UP, India December 19-21, 2013
EFFECT OF STAIRCASE ON RC FRAME STRUCTURES UNDER SEISMIC LOAD
1
Zaid M.1, M. Danish2, M. Shariq3, A. Masood 4 & A. Baqi 5
M. Tech., Department of Civil Engineering, AMU, Aligarh, India, Email:
[email protected] 2 M. Tech., Department of Civil Engineering, AMU, Aligarh, India, Email:
[email protected] 3 Asst. Professor, CES, University Polytechnic, AMU, Aligarh, India, Email:
[email protected] 4 Professor, Department of Civil Engineering, AMU, Aligarh, India, Email:
[email protected] 5 Professor, Department of Civil Engineering, AMU, Aligarh, India, Email:
[email protected]
ABSTRACT Staircase is the part of secondary system of the structures and it is one of the essential parts of a building because of its functional importance. Staircase when compared to the modern escalators serves not only better in emergency conditions (such as fire escapes, natural disaster etc.) but also provides considerable stiffness to the building. Due to complex modelling of staircase, it is designed separately for non-seismic and seismic forces. The effect of staircase on the RC frame structure found in literature may be summarized as imparting discontinuity in the modelling, variation in failure of allied structural elements, contribution in non-linear performance of buildings, modification in various seismic parameters such as reduction in time period and storey drift of the building. Hence it can be concluded that the effect of staircase in analysis and design of RC frame buildings cannot be ignored. In the present study, the effect of staircase on RC frame structures has been carried out by adopting various building models (a bare frame, a frame having infill panels and a frame having infill except first storey) with and without staircase and number of storeys of the building has been varied from 4 storeys to 10 storeys. The Linear Response Spectrum analysis of the models has been carried out as per IS: 1893 (Part 1) - 2002 and IS: 456 – 2000 with the help of FEM based software. Seismic characteristics in terms of Time period, Mass Participation Factor and Storey Drift have been compared with the seismic characteristics of models without staircase. Further, the effect of changing position of staircase in the building has also been observed. In addition to these, short column effect, variation in moments of beams and columns that are attached to staircase slab, failure and deformation in staircase models and comparison of effects of infill panels have also been studied. Keywords: Staircase, Response spectrum analysis, Infill Panel, Short column effect
INTRODUCTION Earthquake is a spontaneous event and behaves quite differently. The force generated by seismic action of earthquake is different than other types of loads, such as, gravity and wind loads. It strikes the weakest spot in the whole three dimensional building. Ignorance in design and poor quality of construction result many weaknesses in the structure thus cause serious damage to life and property. One of the examples, which shook the country on 26th January 2001, is Bhuj Earthquake that caused thousands of casualties with over 300,000 buildings collapsed. Staircase is the part of secondary system of the structures and it is one of the essential parts of a building because of its functional importance. Staircase when compared to the modern escalators serves not only better in emergency conditions (such as fire escapes, natural disaster etc.) but also provides considerable stiffness to the building. Due to complex modelling of staircase, it is designed separately for non-seismic and seismic forces. The effect of staircase on the RC frame structure found in literature may be summarized as imparting discontinuity in the modelling, variation in failure of allied structural elements, contribution in non-linear performance of buildings, modification in various seismic parameters such as reduction in time period and storey drift of the building. Hence it can be concluded that the effect of staircase in analysis and design of RC frame buildings cannot be ignored. In addition, masonry infills are frequently used to fill voids between the vertical and horizontal resisting elements (as partition wall) of the building frames with the assumption that these infills will not take part in resisting any kind of load either axial or lateral. Hence, its significance in the analysis of frame is generally neglected. As recent studies have shown that a properly designed infilled frames can be superior to a bare frame in terms of stiffness, strength and energy dissipation. From structural point of view, the composite action between infill panels and frames give more lateral resistance and in-plane stiffness, resulting in reduction of total and inter storey drift. REVIEW OF LITERATURE Past studies show that the vulnerability of staircase element, when subjected to earthquake as it imparts additional stiffness to the building, for these reasons the elements that constitute the stair are often characterized by a high seismic demand. This develops more shear force at short columns and can lead to a premature brittle failure. J Lavado et al (2004) suggested that under seismic loading, the effect of staircase can be very important in structures, constituted by frames. Study on a three and six storied building with and without staircase has been carried out. Results show development of local rigidity effect, generating a “shear wall effect” in columns surrounding the stairwell, hence increasing axial stresses in surrounding column and beams also, effecting strength and ductility demands which are not taken into account if the stair slabs are not introduced into the structure. E Cosenza et al (2008) investigated seismic performance of existing moment resisting RC frame building and suggested that the stair increases structural strength and stiffness of the structure resulting
into reduction of fundamental time period, also, attracting seismic forces that could fail into short columns due to high shear forces. Further, the structural solutions and design practice of stair slabs in gravity load designed structures are analysed to define their real geometric definition and to understand their performance. Zhang Wang et al (2009) studied dynamic performance of RC building with staircase and found that the existence of staircase greatly affects the lateral stiffness of frame, performance under seismic loads, the peak of internal force and node response spectrum under different earthquakes. 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. E Cosenza et al (2009) concluded that shear failure becomes dominant in the squat column & slabs and precedes the conventional ductile failure. Zhang Cuiqiang et al (2010) described 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. Qiwang Su (2010) reported that staircase arrangement can affect the torsional mode of the structure which can make the torsional mode to be the first mode of vibration, hence designing without the plate staircase in consideration would lead to structural weakness in the structure and cause severe damage under earthquake and affect its functionality. Y Cheng et al (2011) analysed and discussed seismic behaviour of R.C. stairs and their influence on the lateral stiffness of masonry stair well. The results show K-type bracing function of step slabs to main structure, decreasing shear deformation in floor and shear forces in seismic walls. However, there is increase in internal forces of stairs. J J Zhu et al (2011) discussed the active and hazard impacts of staircase on structures under earthquake. Comparison of overall properties, pushover performances, seismic response and internal force of elements are summarized and discussed between two models, with and without staircase. Suggestions on designing process are also given. P C Zhang et al (2011) investigated that in multi-storey framework the stairs members contribute stiffness as K-type brace which effect the deformation of frame, triggering tension or compression to the stairs plate. However, the Ktype brace effecting were neglected in practical design courses. Authors also suggested methods that can be used to repair the existing stair structure or for new building in order to improve the structural function of stairs and over all building. Danish et al (2013) studied the effects of infill in RC frame structure and found that they impart extra stiffness to the structure. The results from their study also compared in this study. Thus, from the past studies it is clear that stair slabs present in the multi-storey RC frame buildings, impart additional stiffness to the structure due to their K-shaped bracing effect, resulting into the reduction of time period of the structure and lateral storey drift. However, in process of this mechanism, the stair slabs induce significance amount of stresses into the supporting columns and beams, making them susceptible to severe damage when subjected to lateral loads. Although, various models have undertaken and analysed in previous studies but performance of RC frame building containing floor system with other lateral load resisting elements like unreinforced infill panels has not been analysed, thus a
rigorous study has been presented in this paper involving effect of staircase on RC frame building having URM infill panels. Effect of vertical stiffness irregularity in the form of soft storey has been evaluated. Three types of models with and without staircase have been undertaken into analysis and parametrically varied from 4 storeys to 10 storeys. The results have been discussed in terms of time period of structure, mass participation factor and story drift. OBJECTIVES OF THE PRESENT STUDY The objectives of the present study are as follows: i. To study the effect of staircase on G+3, G+5, G+7 and G+9 storeyed RC frame buildings. ii. To compare the seismic response of the building in terms of base shear, storey drift, mode participation factor and time-period of vibration MATERIALS AND METHODS Modelling of structures To carry out the parametric study, three types of RCC frames without and with staircase have been considered; a bare frame, a frame with infill at all storeys and a frame with no infill at first storey. Number of storeys has been varied as G+3, G+5, G+7 and G+9. The overall plan dimension of the RC frame structures is 14.4m × 24.4m which is measured along the central line of the columns. All the buildings are assumed to be fixed at ground level and storey heights are taken to be 3.35m each. A solid RCC slab of 110mm thickness has been considered and all the members of the structure are assumed to be homogeneous isotropic and having elastic modulus same in compression as well as in tension, details are shown in Table 1. Soil structure interaction effect, P-∆ effect, the effect of openings, out of plane stability and energy dissipation of infill has not been considered in the present study. Table 1 Section details (*along z-direction (width); **along x-direction (length)) MEMBER SIZE (mm) Beams (Transverse*) 500 × 300 Roof Beams (Longitudinal**) 300 × 300 Corridor Beams(Longitudinal) 300 × 300 External Beams (Longitudinal) 350 × 300 Columns 600 × 500 External Walls 250 Internal Walls 150 Slab 110
Building nomenclature Nomenclature of the models adopted for analysis is given in Table 2. Table 2 Building nomenclature S.No. Type of Model Without Staircase With Staircase Bare Frame A1 B1 1 Frame with infill at all storeys A2 B2 2 Frame with no infill at first storey A3 B3 3
A typical plan of A2 is shown in Fig. 1 and three dimensional view of B1 is given in Fig. 2. Side elevation of different types of models are shown in Fig. 3(a) to 3(c) viz. bare frame, frame with infills at all storey and frame with infills without at first storey. The external and internal masonry infills considered in the study are 250 mm and 150 mm respectively.
Fig.1 Plan of the Building
Fig.2 3-D view of Model B1
Fig. 3(a) Side Elevation of A1 Fig. 3(b) Side Elevation of A2 Fig. 3(c) Side Elevation of A3 METHOD OF ANALYSIS Response Spectrum Analysis Modal: Analysis based on response spectrum has been adopted to dynamically analyse the structure with the help of FEM based software. The following Response Spectrum given in IS 1893 (Part 1):2002 for hard soil (for 5% damping) with Square root of sum of squares (SRSS) combination method has been used for the
analysis. Response Spectra Curve for finding base shear is shown in Fig. 4 and gravity and live loads incorporated in the building structure are given in Table 3 and Table 4 respectively. A comparison of the dynamic characteristics all models is observed, wherein the time period, mass participation factor (%), design base shear and storey drift obtained from the analysis results corresponding to mode 1, mode 2 and mode 3 as given by FEM software are observed. Zone factor, Z = 0.16 (Zone III), Importance factor, I = 1.5, Soil site type = hard soil, Response reduction factor, R = 3 and Damping is assumed to be 5 %.
Sa g
½ °1 15T , 0.00 d T d 0.10° ° ° 0.10 d T d 0.40¾ ®2.50, °1 ° ° 0.4 d T d 4.0 ° ¯T ¿
Fig. 4 Spectra Curve for finding Base Shear from Fundamental Time Period Table 3 Dead Loads S. No. Load Type Intensity (kN/m2) 1 Terrace Water Proofing 2.5 2 Floor Finish 1.0 3 Sanitary Blocks including filling 2.5
Table 4 Live Loads S. No. Load Type Intensity (kN/m2) 1 Roof 1.5 2 Library 10 3 Assembly Hall 5 4 Sanitary Blocks 3 5 Office Floors 4 6 Officer’s Chamber 3 7 Stairs 5 8 Corridor 5
Equivalent Diagonal Strut Model The in-fill walls considered without opening in the present study are modelled as equivalent diagonal strut as proposed by Smith. The use of Equivalent Strut Model is attractive from practical point of view. The properties required for defining the strut model depend on type of analysis. For linear type of analysis (as in present study), only the area, length of the strut and modulus of elasticity are required to calculate the
elastic stiffness of in-fill strut. The following expressions have been used to determine the parameters required for modelling the diagonal strut (as shown in Fig. 5). Dh
DL w
S
4
2
S 2
4
4E f I c h E m t sin 2T
4E f I b L E m t sin 2T
1 D h2 D L2 2
[a] [b] [c] Fig.5. Equivalent Strut Model
where, ‘Em’ is Elastic Modulus of masonry wall, ‘Ef’ is Elastic Modulus of masonry of frame material, t is thickness of the in-fill wall, ‘h’ is Height of the in-fill wall, L is Length of the infill wall, ‘Ic’ is Moment of Inertia of the column of the frame, ‘Ib’ is Moment of Inertia of the beam of the frame, ‘θ’ is tan-1 (h/L) and ‘w’ is width of the Equivalent Strut. The values for width of equivalent diagonal struts using above expressions are given in Table 5. Table 5 Width of equivalent diagonal strut for both external and internal masonry infill (*the equivalent strut shall have the same thickness and modulus of elasticity as the in-fill panel it represent) H (m) L (m) αh αl w (m) 3.35 6.2 1.51 2.7 1.55 3.35 6.2 1.71 3.07 1.76 3.35 6.0 1.51 2.67 1.54 3.35 6.0 1.71 3.03 1.74 3.35 2.2 1.47 2.04 1.28 3.35 2.2 1.44 1.66 1.10 3.35 3.05 1.64 1.68 1.20 1.675 3.05 1.27 2.40 1.00
RESULTS AND DISSCUSSION Dynamic Response of buildings without and with staircase models Dynamic characteristics of the models are obtained from Response Spectrum Method of analysis and compared in terms of seismic parameters viz. Time period, Mass Participation Factor, and Storey Drift have been compared with the seismic characteristics of models
without staircase. The Linear Response Spectrum analysis of the models has been carried out as per IS: 1893 (Part 1) - 2002 and IS: 456 – 2000 with the help of FEM based software. Further, the effect of changing position of staircase in the building has also been observed. In addition to these, short column effects, variation in moments of beams and columns that are attached to staircase slab have also been studied. Time Period When a building is subjected to dynamic action it develops a vibratory motion in the building due to its elastic properties and mass. The vibration is similar to the vibration of a violin string, which consists of a fundamental tone and the additional contribution of various harmonics. Similarly, the vibration of a building consists of a fundamental mode of vibration and the additional contribution of various modes, which vibrates at higher frequencies. On the basis of time period the building may be classified as Rigid (T < 0.3 sec), Semi-Rigid (0.3 sec < T < 1 sec), and Flexible Structure (T > 1). Fundamental period of vibration can be determined by code base empirical formula. The time periods obtained from dynamic analysis of G+3, G+5, G+7 and G+9 buildings in z-direction of seismic force for first mode are given in Table 6. The fundamental time periods for G+3, G+5, G+7 and G+9 buildings, estimated by using the empirical expression given in IS 1893 (Part 1): 2002 are given in Table 7, which shows decrease in time periods with the inclusion of in-fill and further due to staircase and similar trend is followed by increasing the number of storeys.
No. of storeys
4
8
Table 6 Time periods obtained from dynamic analysis in z- direction Time Time period(sec) period(sec) Frame No. of Frame Configuration Mode 1 Configuration Mode 1 storeys A B A B Bare frame 0.404 0.388 Bare frame 0.632 0.605 With infill at all With infill at all 0.172 0.149 0.257 0.236 6 storey storey With no infill at With no infill at 0.250 0.248 0.341 0.340 first storey first storey Bare frame 0.868 0.829 Bare frame 1.111 1.061 With infill at all With infill at all 0.353 0.334 0.464 0.448 10 storey storey With no infill at With no infill at 0.438 0.437 0.546 0.546 first storey first storey
Modal Mass Participation Factor The effective modal mass provides a means for judging the significance of a particular mode of vibration in the dynamic analysis. It has been observed during this study that for G+3,
G+5, G+7 and G+9 with the different frame configurations (i.e. bare frames, frames with infill at all storeys and frames with no in-fill at first storey) with and without staircase, the mass participation factors (in Z-direction) for the first mode gets increased when effect of infill is considered as shown in Table 8. But in the case of models with staircase, reduction in the value of mass participation factor is obtained within their respective mode shapes. However the reason behind this behaviour is unknown. Table 7 Fundamental Time periods (sec) for RC Buildings Number of storeys Frame configuration Fundamental time period (sec) Bare frame 0.525 G+3 With in-fill 0.318 Bare frame 0.712 G+5 With in-fill 0.477 Bare frame 0.883 G+7 With in-fill 0.635 Bare frame 1.044 G+9 With in-fill 0.795
No. of storeys
4
8
Table 8 Mass Participation factor for G+3 buildings in Z- direction Mass Mass Participation Participation Frame No. of Frame Factor (%) Factor (%) Configuration storeys Configuration Mode 1 Mode 1 A B A B Bare frame 82.38 81.96 Bare frame 80.72 80.50 With infill at With infill at 92.55 84.10 87.84 80.35 6 all storey all storey With no infill With no infill 98.28 97.60 96.29 95.68 at first storey at first storey Bare frame 79.84 79.70 Bare frame 79.27 79.15 With infill at With infill at 83.64 77.57 80.12 75.31 10 all storey all storey With no infill With no infill 93.46 92.86 90.08 89.48 at first storey at first storey
Storey Drift The inter storey drift is restricted so that the minimum damage would take place during earthquake and posing less psychological effect in the mind of people. The Indian Seismic Code IS 1893 (Part 1): 2002 recommends that “The storey drift in any storey due to the minimum specified designed lateral force, with partial load factor of 1.0, shall not exceed
0.004 times the storey height.” The variation of storey drift with height observed during space frame analysis is shown in Fig. 6 (for different frame configurations as mentioned above). It has been observed that the storey drifts are considerably reduced when the effect of infills are considered. After incorporation of staircase the values of drifts are further get reduced. All the drifts are found to be within permissible limit i.e. 1.34 cm. The case in which in-fills are not present at bottom storey, a peak of maximum drift is obtained which shows the presence of soft storey at that level. As the height of building is increased there is increase in the story drift is seen. 13.4
G+3 STOREY DRIFT vs HEIGHT
Height (m)
10.05 6.7
3.35 0 0
0.1 0.2 G+3 bare frame Drift (cm)
0.3
Fig. 6 Height v/s Storey Drift for frames G+3 to G+9 Effect of staircase on the supporting columns and beams When a RC frame building is subjected to seismic loading it is observed that there is a significant amount of reduction in time period of structure due to staircases. They provide extra stiffness to withstand lateral loads. This effect is more profound when there more no. of staircases present in the building. Dog-legged staircase shows more stiffness to the lateral deformation of structure by acting as K-type braces in the stair well. However, in addition to that, these staircases in buildings also cause the secondary effect of formation of short columns at intermediate landing by dividing supporting columns into two parts. This results into the enhanced shear demand (see Fig.7) in the short columns. There is also increase in the
Fig. 7 Shear force pattern of frame building with staircase axial load in these columns due to increased rigidity in the particular bay. Thus, shear force and axial force together can cause brittle failure of these columns. Effect of position of staircase in the building In addition to the shear column effect, the position of staircase in building also affects its seismic performance when subjected to lateral loads. This is due to development of torsional moments caused by stiffness irregularity in the plan, when these secondary structural are not provided symmetrically to the plan. Thus increasing torsional demand of the structural elements and there is change in the fundamental mode of the structure, from shear or flexure mode to torsional mode. Hence, structural members adjoining to the stairwell may be subjected to torsional failure due to formation of high torsional moments in the structure. The model of G+5 storey building with Mode shape 1 is shown in 8(a) and 8(b), respectively.
Fig. 8(a) G+5 building with staircase at corner
Fig. 8 (b) First mode shape of G+5 building
CONCLUSIONS The following conclusions are drawn from the present study: x The natural period of vibration of the building frame depends upon its mass and lateral stiffness. Presence of staircase and in-fill panels increases both the mass and stiffness of the building, though the contribution of the latter is more significant. x Fundamental time periods as estimated by using empirical expression given in IS: 1893 (Part 1): 2002 has been found to be decreasing with the inclusion of in-fills and staircase. x It has been observed that the storey drifts are considerably reduced when the effect of staircase are considered. All the drifts are found to be within permissible limit. x When there are no in-fills at the first storey, the storey drift is found to be considerably greater than that observed when the effect of in-fill at all storeys is considered. Hence, stilt buildings are more vulnerable to collapse due to soft storey formation. x The position of staircase in building severely affects the seismic behaviour of building by changing mode shape configuration. x Dog-legged staircase on mid landing imparts additional shear demand in the supporting column leading to short column effect, result into the brittle failure. REFERENCES 1.
Smith, B. S. (1962), “Lateral stiffness of infilled frames, Journal of Structural division”, ASCE, 88 (ST6), 183-199. 2. Smith, B. S. (1966), “Behaviour of square infilled frames, Journal of Structural division”, ASCE, 92 (ST1), 381-403. 3. Smith, B. S. (1966), “The Composite Behaviour of Infilled Frames. In Proceedings of a Symposium on Tall Buildings with Particular Reference to Shear Wall Structures”, University of Southampton, Department of Civil Engineering. (Oxford: Pergamon Press). 4. Singh, H. (1995), “Response of Reinforced Concrete Frames with Infilled Panels under Earthquake Excitation”, PhD Thesis, Department of Civil Engineering, Thapar Institute of Engineering & Technology. 5. Bell, D. K. and Davidson, B. J. (2001), “Evaluation of Earthquake Risk Buildings with Masonry Infill Panels”, NZSEE Conference. 6. Das, D. and Murty, C. V. R. (2004), “Brick Masonry Infills in Seismic Design of RC Frame Buildings: Part 2- Behaviour”, The Indian Concrete Journal. 7. Lavado, J. and Gonzalez, M.L. (2004), “Influence of Stair Slabs in Reinforced Concrete Buildings under Seismic Loads”, Proceedings of the Seventh International Conference on Computational Structures Technology, Stirlingshire, UK, 273. 8. Amato, G., Cavaleri, L., Fossetti, M. and Papia, M. (2008), “Infilled Frames: Influence of Vertical Load on The Equivalent Diagonal Strut Model”, The 14th World Conference on Earthquake Engineering, Beijing, China. 9. Cosenza, E., Vederame, G.M., and Zambrano, A. (2008), “Seismic Performance of Stairs in the Existing Reinforced Concrete Building”, 14th WCEE, Beijing, China. 10. Hongjun, D., Ai, Q.I. (2009), “Analysis of performance of reinforced concrete frame structure with staircase based on ETABS”, Journal of Earthquake Engineering and Engineering Vibration.
11. Qiwang Su (2010), “Finite Element Analysis of Staircase under Earthquake Action”, Advanced Material Research, 163-167 (2011), 2964-2968. 12. Baran, M. and Sevi, T. (2010), “Analytical and experimental studies on infilled RC frames”, International Journal of the Physical Sciences, 5(13), 1981-1998. 13. Zhang, P.C. and Yuan, Q. (2011), “The Seismic Design of Staircase in Frame Structure”, Advanced Material Research, 368-373 (2012), 865-868. 14. Zhu, J.J., Wang, C.X. and Lee, Y. (2011), “Analysis of impacts of Staircase upon Seismic Responses of Structure”, Applied Mechanics and Materials, 94-96 (2011), 469-475. 15. Cheng, Y., Du, H., Zhang, S. and Xu, L. (2011), “Seismic Design of R.C. Stairs in Masonry Structures”, advance Material Research 163-167, 4133-4137. 16. Singh, N.S. and Chaudhary, S. (2012), “Effects of Staircase on the Seismic Performance Of RCC Frame Building”. International Journal of Engineering Science and Technology (IJEST). 17. Danish, M., Masood, S., Masood, A. and Shariq, M. (2013), “Seismic Behaviour of Masonry Infills Reinforced Concrete Building”, International Conference on Innovation in Concrete Construction, UKERI Concrete congress, 2169-2191. 18. IS 1893 (Part 1) (2002), “Indian Standard: Criteria for Earthquake Resistance Design of Structures”, New Delhi. 19. IS 456 (2000), “Indian Standard: Plain and Reinforced Concrete- Code of Practice”, New Delhi.
