Performance Based Seismic Evaluation of RC Frames with Floating Columns

    Shah B. A. Associate Professor, Applied Mechanics Department, M. S. University of Baroda, and

    Patodi S. C. Professor, Civil Engg. Department, Parul Institute of Engg. & Tech., Limda, Baroda.

    In the present study, a mathematical model of a G+7 storey space frame having nine columns at all the panel points of a 3m x 3m grid with an overall plan dimension of 6m x 6m is considered. The effect of omitting a column from the first storey to sixth storey on seismic performance of an RC space frame is studied. Rectangular and equivalent square cross sections of columns are considered for comparison under push over analysis using commercially available ETABS software. Base shear, roof displacement, effective time period and effective damping are reported at performance point for all the models developed. The storey drift plots are also compared for square and rectangular column frames having a transfer girder carrying columns up to six floors above it. It is observed that for the frames with transfer girders carrying less than three floors above it do not have a significant effect on the seismic performance. Also, the square shaped columns are found to perform better than the rectangular columns under similar situation of floating columns.

    Introduction

    After the Bhuj earthquake in the year 2001, it was observed that a number of RC framed structures in the city of Ahemdabad got damaged. One of the major discrepancies found in the framing of low to medium rise buildings, G+4 to G+7 structures, was the concept of floating columns. The local building byelaws stipulated that the allowable projection of a building beyond the building periphery should not be considered in the allowable floor space index (FSI) calculations. This fact led to the construction of RC framed buildings where the columns on the corner of building in the ground floor was shifted on the outer edge of the periphery making it float over a beam. Thus, the concept of using a floating column got popular to increase the usable area of the floor. Also, sometimes, the columns are omitted from the framing at a particular level and the load transferred from the column above on to a transfer girder is distributed to the columns of the floor below.
    It is particularly mentioned by Murty [1] in earthquake tip number 6, published after the Bhuj earthquake by BMTPC for general awareness of engineers and architects, that the floating columns are not preferred from seismic performance point of view of a building. Although, the general observations on discouraging the use of floating columns are also mentioned by Lagorio [2] in his book, no specific work has been reported on the exact behavior of frames with floating columns. This fact has prompted the present study for incorporating the floating columns in RC frames and to critically examine their effect on seismic performance.
    In the present work, in order to study the effect of omitting a column in the peripheral framing of a G+7 storey building, one column is omitted at the first floor designated by F1 frame to sixth floor designated by F6 frame. The seismic performance of a frame having all the columns as rectangular is also evaluated vis-à-vis a space frame with all the columns having an equivalent square cross section. Push over analysis is carried out in order to identify the effectiveness of the framing in resisting the seismic forces.

    Mathematical Models Developed

    The problem selected for the performance evaluation of structure having floating columns is a G+7 storey space frame with an overall plan dimension of 6m x 6m having four panels of 3m x 3m each. Columns are considered at each panel points forming a space frame with columns extending to 3m below plinth level up to foundation level. The column height is considered as 3m for all storeys and the cross section is considered as 230mm x 450mm for all columns with the longer side parallel to global Y axis in plan. Another model with equivalent square section of 322mm x 322mm is considered for comparing its performance with the rectangular one. The column section is increased by 50mm in both the lateral directions below plinth level. Typical isometric and plan views of the frame are shown in Fig. 1. The size of all the beams is considered to be 230mm x 450mm. The transfer girder is considered as 300mm x 750mm for frame F1 and 230mm x 600mm for frames F2 to F6.

    Performance Based Seismic Evaluation
    Figure 1: Typical Isometric and Plan Views of the G+7 Frame

    The six space frame models with one of the central columns omitted at the y = 0 face at first floor level to sixth floor level are generated and analyzed for the two variations in column cross sections. The line diagrams of the models designated as F1 to F6 are shown in Fig. 2.

    Performance Based Seismic Evaluation
    Figure 2: Space Frame Models with Omitted Columns
    The loading considered for the analysis is an area load applied to the diaphragms at the floor levels. The dead load of 1.5 kN/m2 and a live load of 3 kN/m2 are considered on all typical floors along with a uniformly distributed dead load of 13 kN/m on the peripheral beams to account for the 230mm thick brick walls. The loads considered on terrace are a dead load of 2 kN/m2 with a live load of 1.5 kN/m2 along with a uniform dead load of 6 kN/m on peripheral beams to account for the parapet walls. The self-weight due to slabs and beams is calculated by the program and applied as a dead load. The earthquake loads are defined in the lateral X-and Y-directions as per IS 13920 [3] calculated by the program for zone factor Z = 0.16, medium soil and importance factor of 1 with response reduction factor of 5 with initial damping as 5%. The time period is specified as 0.8132 calculated as per IS 1893, Part 1, 2002 [4]. Thus, in all, there are 4 static load cases which are defined. For carrying out the design of all the elements as per IS 456, 2000 [5], 13 standard load combinations are considered for the four basic static load cases. The push over analysis is considered only after carrying out the design.

    Specified Pushover Parameters

    For carrying out the push over analysis as per ATC 40 [6] and FEMA [7] guidelines, default PMM plastic hinges are defined at the two ends of all columns and also at 5% and 95% span length of all beams. Default M3 hinges are also defined at the mid span of all beams. The first typical push over case defined for the analysis is PUSH1 in the vertical (gravity) direction wherein the full dead load and 50% of live load is applied up to their full magnitude to push the structure in the gravity (global Z) direction. The second push over case defined is PUSH2 which is the lateral push in the global X direction. This is a displacement controlled push in which displacement of the central node at the roof level is monitored up to a target displacement of 4% of the height of the building. The pattern of load to be applied is selected as per the earthquake load in the X direction and geometric nonlinearity due to P-delta effects is considered. The method of unloading adopted in case of a hinge dropping load is considered as local redistribution. This push over case is started with the stresses in the hinges already there due to the gravity push – PUSH1. The conjugate displacement option is selected to adjust the push so that the target displacement is achieved. Since the structure is symmetric about the Y axis, there is only one lateral push defined in the X direction.
    The next push to be applied in order to obtain the performance point for the same structure is the push in the lateral Y direction. Thus, PUSH3 is defined as a push over case in the lateral Y direction where the Y displacement of central node at terrace level is monitored when a push is given as per the load pattern of earthquake load defined in the Y direction. All the parameters applied for PUSH2 are applied to this push over case also. As the column is omitted on one of the faces parallel to the X axis, another push over case termed as PUSH4 is also required to be defined where the push is given in the negative Y direction.

    Results of the Analysis

    The value of base shear, roof displacement, effective time period and effective damping are noted at performance point and are presented here in Table 1.

    Table 1 Values at Performance Point for the Frames under Consideration

    Frame Designation
    Parameter Rectangular columns Square columns
    PUSH X PUSH +Y PUSH -Y PUSH X PUSH +Y PUSH -Y
    Regular V in kN 655 962 - 842 - -
    D in m 0.224 0.168 - 0.194 - -
    Teff in sec 2.382 1.657 - 1.924 - -
    βeff % 9 7.4 - 7.3 - -
    F1 V in kN 638 959 919 793 840 815
    D in m 0.216 0.171 0.176 0.181 0.196 0.202
    Teff in sec 2.348 1.702 1.682 1.898 1.97 1.946
    βeff % 9 6.8 7.9 8.3 6.8 7.6
    F2 V in kN 702 671 673 815 848 826
    D in m 0.205 0.181 0.172 0.186 0.195 0.199
    Teff in sec 2.09 2.288 2.095 1.908 1.95 1.927
    βeff % 7.7 12.3 14.7 7.8 6.9 7.6
    F3 V in kN 644 1063 888 825 847 827
    D in m 0.222 0.187 0.163 0.189 0.195 0.196
    Teff in sec 2.354 1.696 1.639 1.916 1.941 1.924
    βeff % 9.1 5 8.9 7.6 7 7.7
    F4 V in kN 657 967 941 827 871 852
    D in m 0.225 0.17 0.17 0.192 0.192 0.192
    Teff in sec 2.37 1.673 1.656 1.924 1.881 1.865
    βeff % 8.6 7 7.8 7.5 6.8 7.5
    F5 V in kN 661 966 950 844 834 835
    D in m 0.226 0.169 0.169 0.195 0.195 0.193
    Teff in sec 2.372 1.667 1.654 1.926 1.934 1.921
    βeff % 8.5 7.1 7.7 7.4 7.1 7.5
    F6 V in kN 664 964 957 842 839 839
    D in m 0.227 0.169 0.169 0.194 0.195 0.194
    Teff in sec 2.372 1.661 1.655 1.926 1.929 1.922
    βeff % 8.5 7.3 7.5 7.3 7.3 7.4
    V – Base shear, D – Roof displacement, Teff – Effective time period, βeff – Effective damping

    In the push over analysis, the number of hinges develops progressively in various elements like beams and columns. The numbers of hinges developed at performance point with category of hinges in each case are reported in Table 2.

    Table 2 Plastic Hinges Developed at Performance Point of the Frames
    Frame Designation Hinge Category A-B B-IO IO-LS LS-CP TOTAL
    Column Rect Sq Rect Sq Rect Sq Rect Sq
    Regular PUSH X 414 397 54 71 16 16 0 0 484
    PUSH Y 388 397 64 71 32 16 0 0 484
    F1 PUSH X 418 398 50 66 13 17 0 0 481
    PUSH Y 388 387 74 73 19 21 0 0 481
    PUSH -Y 382 381 76 79 23 21 0 0 481
    F2 PUSH X 414 397 49 66 18 18 0 0 481
    PUSH Y 382* 391 78 70 10 20 8 0 481
    PUSH -Y 379 386 87 82 11 13 4 0 481
    F3 PUSH X 382 393 71 69 26 19 2 0 481
    PUSH Y 358 388 80 75 41 18 2 0 481
    PUSH -Y 364 383 90 81 25 17 2 0 481
    F4 PUSH X 410 395 51 66 20 20 0 0 481
    PUSH Y 389 391 71 72 21 18 0 0 481
    PUSH -Y 379 385 73 78 29 18 0 0 481
    F5 PUSH X 411 389 53 76 16 16 1 0 481
    PUSH Y 386 387 65 77 30 17 0 0 481
    PUSH -Y 379 394 70 67 32 20 0 0 481
    F6 PUSH X 408 387 57 77 15 17 1 0 481
    PUSH Y 383 387 65 77 33 17 0 0 481
    PUSH -Y 382 392 70 70 29 19 0 0 481
    * For rectangular column model, 3 hinges develop in the category D-E.

    It is difficult to compare these parameters especially when there is no marked difference between the two compared categories. One of the criteria to judge the seismic performance of a frame is to identify the location of the plastic hinges. As the plastic hinges forming in column elements of the frame are indicative of a general failure of a structure, the number of hinges developing in the columns is particularly noted in the present study. The plastic hinges developed along with the stress level indicated by their category in column elements are presented as Table 3. It is worthwhile to note here that as the columns are omitted on only one of the faces, the push in the +ve and –ve Y direction yield different results which are also included in the present study.
    In order to judge the variation in base shear and roof displace- ment at performance point for all the models presented in Table 1, the results are also presented graphically in Figs. 3 to 6.
    The storey drift variation for regular frames with square and rectangular columns is presented in Fig. 7 whereas Figs. 8 and 9 represent the drift variation in G+7 storey space frames with square and rectangular columns respectively subjected to push in the lateral X direction. The variation in storey drift for frame F1 under the three lateral push PUSHX, PUSHY and PUSH –Y with square and rectangular columns is shown in Fig. 10. Similar graphs are presented for G+7 storey frames with floating columns designated as F2 to F6 in Figs. 11 to 15. All the storey drifts are presented to compare the behavior of a particular frame having rectangular columns and equivalent square columns under lateral push up to the performance point.

    Discussion of Results

    1. It is clear from Table 1 that the frame with square columns shows a better performance as it resists more base shear at a lower roof displacement at performance point compared to that having rectangular columns.

    2. Figures 3 and 4 show that the minimum base shear resisted by all G+7 frames with square columns is 793 kN and the highest value is 871 kN. Thus, there is a variation of 9.8% in the base shear value resisted at performance point. The same variation in case of frames with rectangular columns is from 638 kN to 1063 kN which is as huge as 66.6%. The lowest value of base shear resisted by F1 frame under PUSH in the X direction is 24.29% less for rectangular columns as compared to square columns under same PUSH.

      Performance Based Seismic Evaluation Performance Based Seismic Evaluation
      Figure 3: Variation in Base Shear for Frames with SquareColumns Figure 4: Base Shear for Frames with Rectangular Columns
    3. Figure 3 further indicates that the base shear resisted at performance point by frames with square columns drops by 49 kN for PUSH in the X direction when a column is removed from the first storey which is a variation of only 5.8% compared to a regular frame with square columns. This variation further decreases as the omitted column is shifted towards upper storey designated by F2, F3, F4, etc.

    4. It can also be seen from Fig. 3 that the omission of column in the fifth and sixth storey has no effect on the base shear resisted at performance point for frames with square columns. The same is observed for frames with rectangular columns (Fig. 4).

    5. The maximum base shear variation at performance point is in case of frames with rectangular columns under Y PUSH, which reduces considerably for frame F2 to 671 kN as compared to 962 kN for a regular frame without floating columns.

    6. From Figs. 5 and 6 it is clear that for frames F4, F5 and F6, the roof displacement values are almost same for square as well as rectangular columns. It is also observed that the roof displacement at performance point is more for frames F1, F2 and F3 under PUSH in –ve Y direction for square columns and for + Y PUSH for rectangular columns.

      Performance Based Seismic Evaluation Performance Based Seismic Evaluation
      Figure 5: Variation in Roof Displacement - Square Columns Figure 6: Variation in Roof Displacement - Rectangular Columns
    7. It can be seen from Table 1 that the value of effective damping which is a measure of damage in the frame due to PUSH ranges between 6.9% and 8.3% for frames with square columns. The same value ranges from 5% to 14.7% for models with rectangular columns. This indicates a more consistent performance of square shaped columns compared to rectangular columns under seismic effects.

    8. The effective time period at performance point for all frames with square columns is around 1.9 sec as indicated in Table 1, whereas the same varies between 1.65 and 2.38 sec for rectangular columns. The constant time period at performance point indicates the consistency of seismic performance of square shaped columns.

    9. The number of plastic hinges developed in various categories at performance point is definitely an indication of seismic performance of a structure. From Table 2 it can be seen that for the frames with square columns, no hinges are developed in the category beyond life safety (LS) stage. As against this, in case of frame F2 with rectangular columns under PUSH Y, 3 plastic hinges develop stress beyond collapse stage. This indicates a better performance of square columns in general.

      Table 3 Hinges Developed in Columns at Performance Point of the Frames
      Frame Designation Hinge Category A-B B-IO IO-LS D-E TOTAL
      Column Rect Sq Rect Sq Rect Sq Rect Sq Rect Sq
      Regular PUSH X 4 1 3 0 0 0 0 0 7 1
      PUSH Y 1 1 0 0 0 0 0 0 1 1
      F1 PUSH X 1 0 3 0 0 0 0 0 4 0
      PUSH Y 0 3 0 0 0 0 0 0 0 3
      PUSH -Y 0 1 0 0 0 0 0 0 0 1
      F2 PUSH X 0 2 0 0 0 0 0 0 0 2
      PUSH Y 6 1 0 0 0 0 3 0 9 1
      PUSH -Y 0 2 6 0 3 0 0 0 9 2
      F3 PUSH X 6 1 3 0 0 0 0 0 9 1
      PUSH Y 4 1 0 0 0 0 0 0 4 1
      PUSH -Y 2 2 0 0 0 0 0 0 2 2
      F4 PUSH X 1 1 6 0 3 0 0 0 10 1
      PUSH Y 0 1 0 0 0 0 0 0 0 1
      PUSH -Y 2 1 0 0 0 0 0 0 2 1
      F5 PUSH X 1 1 5 0 4 0 0 0 10 1
      PUSH Y 2 2 0 0 0 0 0 0 2 2
      PUSH -Y 2 2 0 0 0 0 0 0 2 2
      F6 PUSH X 1 1 5 0 3 0 0 0 9 1
      PUSH Y 2 1 0 0 0 0 0 0 2 1
      PUSH -Y 2 1 0 0 0 0 0 0 2 1
    10. The development of hinges in columns is more serious as compared to beams in a frame. This data of number and category of hinges developed only in the column elements out of the totally developed hinges is presented in Table 3. This table once again shows better performance of square shaped columns as against rectangular columns for the same frame. Further, for square columns, the category of hinges is in the lowest stress level i.e. up to the immediate occupancy (IO) stage. If the performance of the frames with floating columns is compared to that of one without floating columns, there is not much difference in the hinges developed in the column elements for square columns.

    11. One fact which has been observed for frames with floating columns is that the plastic hinges develop under the gravity push itself when the transfer girder is not stiff enough, which is otherwise not observed in regular frames. Thus, floating columns are not advisable even from the point of view of resisting gravity loads which may not be reflected effectively in the seismic performance criteria. Also, the hinges developed due to gravity loads may further deteriorate the performance of the frame under vertical component of earthquake motion which is not considered in the current analysis.

    12. From Fig. 7 which is included for regular frames without floating columns under the lateral push in X and Y directions, it is clear that the square columns show less storey drift as compared to the rectangular columns pushed along their weaker axis.

      Performance Based Seismic Evaluation Performance Based Seismic Evaluation
      Figure 7: Frames Without Floating Columns Figure 8: Frame with Square Columns - PUSHX
    13. Figures 8 and 9 show the plots of storey drift for G+7 frames with square and rectangular columns respectively under PUSH in the lateral X direction. These plots indicate that the storey drifts for all the frames closely match the basic curve of regular frame without floating column accept for the fact that there are local peaks in the drift values at the specific storey level where a column is omitted. This fact is observed in both square as well as rectangular columns.

      Performance Based Seismic Evaluation Performance Based Seismic Evaluation
      Figure 9: Frames with Rect. Columns – PUSHX Figure 10: Storey Drift for Frame F1
    14. Figures 10 to 12 indicate that in case of frames F1, F2 and F3, the variation in drift is significant between frames with square and rectangular columns. It is obs- erved that the storey drift curves for frame with square columns for all the three lateral push are close to each other indicating consistent performance. The curves for frames with rectangular columns are wide spread and on either side of those for frames with square columns.

      Performance Based Seismic Evaluation Performance Based Seismic Evaluation
      Figure 11: Storey Drift for Frame F2 Figure 12: Storey Drift for Frame F3

      Performance Based Seismic Evaluation Performance Based Seismic Evaluation
      Figure 13: Storey Drift for Frame F4 Figure 14: Storey Drift for Frame F5
    15. Figures 13 to 15 depicting the storey drift for frames F4, F5 and F6 show very less variation which indicates that the floating columns in the upper storey of G+7 frame do not have any significant effect on the seismic performance for both the column shapes.

    Conclusion

    Performance Based Seismic Evaluation
    Figure 15: Storey Drift for Frame F6
    It can be concluded that when a column is omitted in the fifth or sixth storey of a G+7 storey space frame, there is hardly any difference in the base shear resisted at performance point under push over analysis. By comparing the values of effective damping and plastic hinges developed at performance point for a G+7 storey floating column frame having rectangular columns with that having equivalent square columns, it can be concluded that the frames having square columns exhibit a better seismic performance.
    The push over analysis of a G+7 storey frame with floating columns indicates a local increase in storey drift for a particular level where the column is omitted. This observation is true for both square as well as rectangular columns. However, comparison of storey drift curves indicates a more consistent performance of frames with square columns.

    References

    • Murty C. V. R., IITK-BMTPC Earthquake Tip 06, Learning Earthquake Design and Construction, Indian Institute of Technology Kanpur, www.nicee.org, Sep. 2002.

    • Lagorio H. J., Earthquakes an Architect’s Guide to Non Structural Seismic Hazard, John Wiley & Sons Inc., USA, 1990.
    • IS 13920: 1993, Indian Standard Code of Practice for Ductile Detailing of Reinforced Structures subjected to Seismic Forces, Bureau of Indian Standards, New Delhi, 1993.

    • IS 1893: 2002, Indian Standard Criteria for Earthquake Resistant Design of Structures, Part 1: General Provisions and Buildings, Bureau of Indian Standards, New Delhi, 2002.

    • IS 456: 2000, Indian Standard Code of Practice for Plain and Reinforced Concrete, Bureau of Indian Standards, New Delhi, 2000.

    • ATC-40, "Seismic Evaluation and Retrofit of Concrete Buildings, Volume 1 and 2, Report No. SSC 96-01, Seismic Safety Commi- ssion, Redwood City, CA, 1996.

    • FEMA-273/274, NEHRP Guidelines and Commentary on the Guidelines for the Seismic Rehabilitation of Buildings, Washington DC, USA, 1997.

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