Torsional Reduction Techniques in High Rise Structures

Torsional Reduction Techniques in High Rise Structures

Jitender Sharma 1, Abhinav Singh 2, Reena Sehgal 3

1,2,3Department of Civil Engineering, Ganga Institute of Technology and Management,

Kablana, Jhajjar, Haryana, India

Abstract: This paper studied the reasons behind the four trends in torsional effects in asymmetric-plan buildings observed in the current literature. It was found that the modal eccentricities and the non-proportionality between the modal translations and the modal rotation are key to understanding these trends in torsional effects in asymmetric-plan buildings. These key points were obtained from the three-degree-of- freedom modal systems, which represent the single vibration mode of a two-way asymmetric-plan building. This paper showed that the modal eccentricities, rather than the overall structural eccentricities, are the critical parameters for deciding the trend of the unequal displacement demand on the floor diaphragm. In addition, the non-proportionality between the modal translations and the modal rotation leads to the trend that the torsional effects generally decrease when plastic deformations increase.

I.INTRODUCTION

Centre of mass (CM) is the point where entire mass of the system is concentrated. During an earthquake, acceleration induced inertia forces will be developed at each floor level, where the mass of an entire story may be assumed to be calculated. Hence, the location of a force at a particular level will be determined by the centre of the accelerated mass at that level.

In regular buildings, the portions of the centres of floor masses will differ very little from level to level. However, irregular mass distribution over the height of the building may result in variations in centres of masses, which may need to be evaluated. The summation of all the forces, Fj, above a given story with due allowance for the in-plane position of each, will then locate the position of the resultant force, Vj, within that story.

Centre of rigidity (CR) is the point that locates the position of a story shear force which will cause only relative floor translations. It is also referred as centre of stiffness of a system.

If, as a result of lateral forces, one floor of the building translates horizontally as a rigid body relative to the floor below, a constant inter-story displacement say x will be imposed on all frames and walls in that story. Therefore, the induced forces in these elastic frames and walls, in the relevant planes, will be proportional to the respective stiffness. The resultant total force, Vj=Vx, induced by the translational displacement x, will pass through the centre of rigidity (CR).

The position of CR may be different in each story. It is relevant to story shear forces applied in any direction in a

horizontal plane. Such a force may be resolved into two components, such as Vx & Vy, which will cause simultaneous story translations x & y respectively. The displacement due to story twist are proportional to the distance of the element from the centre of rotation i.e. CR.

Calculation of Centre of Rigidity (Centre of Stiffeness):

X coordinate = (Kyi x Xi)/ Kyi ; Y coordinate = (Kxi x Yi)/ Kxi where, Kxi & Kyi correspond to the lateral stiffness of the n lateral load resisting elements in the x and y directions respectively.

Fig:1 Configurations of the four plans

Note: Displacements due to story twist, when combined with those resulting from floor translations, can result in total element inter-story displacements that may be difficult to accommodate. For this reason the designer should attempt to minimize the magnitude of story torsion (Mt). This may be achieved by a deliberate assignment of stiffness to lateral force resisting components, such as frames or walls, in such a way as to minimize the distance between the CR and the line of action of the story shear force. To achieve this in terms of floor forces, the distance between the CR and CM should be minimized.

1. EVALUATION OF PLAN CONFIGURATION (BASE ISOLATION TECHNIQUE)

   where, KE indicates the kinetic energy, DE is the dissipated energy, SE is the strain energy and IE is the seismic input energy. DE is the sum of VE and HE, which are the viscous and hysteretic energies, respectively.

   In Eq. 1, KE and SE are the portions of the structural energy that are recoverable, whereas VE and HE are the portions that are dissipative. When the input energy cannot be dissipated via the viscous damping of the structure, the residual energy will be dissipated in the form of HE for strong motions. Energy input to a fixed-

   base structure will be dissipated in the form of VE if IE is not too large. In the ductile design of fixed-base structures, plastic deformations may occur in several joints or members when the structure is subjected to strong motion and there is sufficient ductility such that collapse is prevented. The lateral motion of the system is coupled with the torsional motion under horizontal ground excitation when the center of stiffness of the elastomeric bearings does not coincide with the center of mass of the deck. Simplified base-isolated model is introduced to estimate torsional behaviour of seismic isolation with different superstructure plan configuration. Thus, four plans are selected and compared, it is observed that there is considerably more variation in the torsional to lateral frequency ratio in the L-plan (case 4) in comparison with the other cases (Fig. 1). Therefore, this type of plan is suitable for the study of the torsional behaviour of isolated structures.

   There is more eccentricity in case 4 relative to the other cases, so shifting the Center of Mass (CM) toward the CS generates a higher torsional response and the structural torque is reduced to a minimum if the center of stiffness of the isolation system coincides with the center of mass of the structure. Case 1 is a system with a symmetric distribution of mass and identical isolators distributed regularly in the building plan. The torsional to lateral frequency ratio varies when the CM is shifted toward the CS in cases 2, 3 and 4 for the same distributed total mass. As a result, the torsional resistance in asymmetric base- isolated structures will be increased when the elastomeric bearings in the exterior of the plan are stiffer and larger than interior or rubber bearings which are used in the interior and lead rubber bearings in the exterior. The torsional to lateral frequency ratio is computed in four cases of eccentricity in the base and for a rigid diaphragm level. The total distributed mass is constant but relative to the plan geometry characteristics and the rotational mass moment of inertia varies. The results of the computed frequency ratios indicate that case 4 is affected more by the torsional components; therefore the plan configuration of case 4 is a suitable selection for this purpose.

2. EXPERIMENTAL APPROACH USING STAAD PRO

   V8i

   Beams sizes: 300mmx300mm , Column sizes: 450mmx450mm

   Loading : Self Weight + 12KN/m Wall load + 5.2KN/sqm(dead) + 2KN/sqm(live)

3. RESULTS IN VARIOUS MODES:

   Figure-3

   STAGE -2 (L TYPE ASYMMETRIC CONFIGURATION)

   Figure-4

   WITH SAME MEMBER SIZES & LOADING SHAPES

   IN VARIOUS MODES

   Figure-5

   STAGE-3(TORSION CONTROL USING HIGHER COLUMN SIZES ON GEOMETRY DEFICIENT SIDE OF BUILDING)

   Figure-6

   SHAPES IN VARIOUS MODES

   STAGE-1

   Figure-2 (analytical model)

   Building Configuration (symetric)-as per fig-2

   Height = 25m (5 nos storey@5m c/c), Length = 20m (4nosbays@5m c/c), Width=12m (4nos bays@3m c/c)

   Figure-7

4. CONCLUSION

The study of structures of their torsional behavior done above gives us data and points from which we can conclude some points. A uniform shaped structure such as a rectangular shaped does not have torsion behavior in it, where as a structure of L shape (as studied above) have torsional behaviour.

The torsion in the structure can be eliminated by different methods. The base isolation method can be adopted to obtain a structure without torsional forces in the structure. As above shown through experimental approach using STAAD PRO, any structure with torsion in it can be reduced or removed by providing columns of higher sizes in the geometry deficient area.

Any structure with torsion in it becomes expensive as compared to any structure without any torsional forces. As either different methods are adopted to eliminate the torsion such as base isolation, which is an extra added cost to the structure. Or as explained above the column sizes are increased which directly increases the cost of the structure.

REFERENCES

1. Huang, M., Chan, C., Lou, W., and Bao, S. (2015). "Time- domain dynamic drift optimisation of tall buildings subject to stochastic wind excitation." Structure and Infrastructure Engineering, 10.1080/15732479.2013.850729, 97-111. Online publication date: 1-Feb-2015. CrossRef

2. Caracoglia, L. (2014). "A stochastic model for examining along-wind loading uncertainty and intervention costs due to wind-induced damage on tall buildings." Engineering Structures, 10.1016/j.engstruct.2014.07.023, 121-132.

   Online publication date: 1-Nov-2014. CrossRef

3. Bobby, S., Spence, S., Bernardini, E., and Kareem, A. (2014). "Performance-based topology optimization for wind-excited tall buildings: A framework." Engineering Structures, 10.1016/j.engstruct.2014.05.043, 242-255.

   Online publication date: 1-Sep-2014. CrossRef

4. Chen, X., Kwon, D., and Kareem, A. (2014). "High-frequency force balance technique for tall buildings: a critical review and some new insights." Wind and Structures, 10.12989/was.2014.18.4.391, 391-422.

   Online publication date: 25-Apr-2014. CrossRef

5. Spence, S. and Kareem, A. (2013). "Data-Enabled Design and Optimization (DEDOpt): Tall steel building frameworks." Computers & Structures,

   10.1016/j.compstruc.2013.04.023, 134-147.

   Online publication date: 1-Dec-2013. CrossRef

6. Ruo-qiang, F., Jihong, Y., Yan, G., Qing-xiang, L., and Bin,

   Y. (2013). "Wind-induced torsion vibration of the super high- rise building of Shenzhen Energy Center." The Structural Design of Tall and Special Buildings, 10.1002/tal.749, 802- 815.

   Online publication date: 1-Jul-2013. CrossRef

7. Bernardini, E., Spence, S., and Gioffrè, M. (2012). "Effects of the aerodynamic uncertainties in HFFB loading schemes on the response of tall buildings with coupled dynamic modes." Engineering Structures,

   10.1016/j.engstruct.2012.04.030, 329-341.

   Online publication date: 1-Sep-2012. CrossRef

8. Steenbergen, R., Vrouwenvelder, A., and Geurts, C. (2012). "The use of Eurocode EN 1991-1-4 procedures 1 and 2 for building dynamics, a comparative study." Journal of Wind Engineering and Industrial Aerodynamics, 10.1016/j.jweia.2012.03.025, 299-306.

   Online publication date: 1-Aug-2012. CrossRef

9. Bernardini, E., Spence, S., and Gioffrè, M. (2012). "Dynamic response estimation of tall buildings with 3D modes: A probabilistic approach to the high frequency force balance method." Journal of Wind Engineering and Industrial Aerodynamics, 10.1016/j.jweia.2012.03.014, 56-64.

   Online publication date: 1-May-2012. CrossRef

10. Li, Q., Zou, X., Wu, J., and Wang, Q. (2011). "Integrated wind-induced response analysis and design optimization of tall steel buildings using Micro-GA." The Structural Design of Tall and Special Buildings, 10.1002/tal.569, 951-971.

    Online publication date: 1-Dec-2011. CrossRef

11. Huang, M., Chan, C., and Kwok, K. (2011). "Occupant comfort evaluation and wind-induced serviceability design optimization of tall buildings." Wind and Structures An International Journal, 10.12989/was.2011.14.6.559, 559-582. Online publication date: 25-Nov-2011. CrossRef

12. Kim, Y., Kanda, J., and Tamura, Y. (2011). "Wind-induced coupled motion of tall buildings with varying square plan with height." Journal of Wind Engineering and Industrial Aerodynamics, 10.1016/j.jweia.2011.03.004, 638-650.

    Online publication date: 1-May-2011. CrossRef

13. Lou, W., Huang, M., Jin, H., Shen, G., and Chan, C. (2010). "Three-dimensional wind load effects and wind-induced dynamic responses of a tall building with X-shape." The Structural Design of Tall and Special Buildings, 10.1002/tal.514, 885-900.

    Online publication date: 1-Dec-2010. CrossRef

14. 2013. References. Wind Loads147-152. Citation | PDF (159 KB) | Permissions

15. Chan, C., Huang, M., and Kwok, K. (2010). "Integrated wind load analysis and stiffness optimization of tall buildings with 3D modes." Engineering Structures,

    10.1016/j.engstruct.2010.01.001, 1252-1261.

    Online publication date: 1-May-2010. CrossRef

16. Chan, C., Huang, M., and Kwok, K. (2009). "Stiffness Optimization for Wind-Induced Dynamic Serviceability Design of Tall Buildings." Journal of Structural Engineering, 10.1061/(ASCE)ST.1943-541X.0000036, 985-997.

    Online publication date: 1-Aug-2009. Abstract | Full Text HTML | PDF (481 KB) | Permissions

17. Huang, M., Chan, C., Kwok, K., and Hitchcock, P. (2009). "Cross Correlations of Modal Responses of Tall Buildings in Wind-Induced Lateral-Torsional Motion." Journal of Engineering Mechanics, 10.1061/(ASCE)0733- 9399(2009)135:8(802), 802-812.

    Online publication date: 1-Aug-2009. Abstract | Full Text HTML | PDF (356 KB) | Permissions

18. Chen, X. and Huang, G. (2009). "Evaluation of peak resultant response for wind-excited tall buildings." Engineering Structures, 10.1016/j.engstruct.2008.11.021, 858-868.

    Online publication date: 1-Apr-2009. CrossRef

19. Chan, C., Chui, J., and Huang, M. (2009). "Integrated aerodynamic load determination and stiffness design optimization of tall buildings." The Structural Design of Tall and Special Buildings, 10.1002/tal.397, 59-80.

    Online publication date: 1-Feb-2009. CrossRef

20. Swaddiwudhipong, S., Anh, T., Liu, Z., and Hua, J. (2007). "Modelling of wind load on single and staggered dual buildings." Engineering with Computers, 10.1007/s00366-007- 0061-2, 215-227.

    Online	publication	date:	24-Jul-2007.	Online	publication	date:	25-Sep-1999.
    CrossRef				CrossRef

21. Chen, X. and Kareem, A. (2005). "Dynamic Wind Effects on Buildings with 3D Coupled Modes: Application of High Frequency Force Balance Measurements." Journal of Engineering Mechanics, 10.1061/(ASCE)0733- 9399(2005)131:11(1115), 1115-1125.

    Online publication date: 1-Nov-2005. Abstract | Full Text HTML | PDF (249 KB) | Permissions

22. Tamura, Y., Kareem, A., Solari, G., Kwok, K., Holmes, J., and Melbourne, W. (2005). "Aspects of the dynamic wind- induced response of structures and codification." Wind and Structures, 10.12989/was.2005.8.4.251, 251-268.

    Online publication date: 25-Aug-2005. CrossRef

23. Chen, X. and Kareem, A. (2005). "Coupled Dynamic Analysis and Equivalent Static Wind Loads on Buildings with Three- Dimensional Modes." Journal of Structural Engineering, 10.1061/(ASCE)0733-9445(2005)131:7(1071), 1071-1082.

    Online publication date: 1-Jul-2005. Abstract | Full Text HTML | PDF (180 KB) | Permissions

24. Liang, S., Li, Q., Zou, L., and Wu, J. (2005). "Simplified formulas for evaluation of across-wind dynamic responses of rectangular tall buildings." Wind and Structures, 10.12989/was.2005.8.3.197, 197-212.

    Online publication date: 25-Jun-2005. CrossRef

25. Lin, N., Letchford, C., Tamura, Y., Liang, B., and Nakamura,

    O. (2005). "Characteristics of wind forces acting on tall buildings." Journal of Wind Engineering and Industrial Aerodynamics, 10.1016/j.jweia.2004.12.001, 217-242.

    Online publication date: 1-Mar-2005. CrossRef

26. Kareem, A. and Zhou, Y. (2003). "Gust loading factorpast, present and future." Journal of Wind Engineering and Industrial Aerodynamics, 10.1016/j.jweia.2003.09.003, 1301- 1328.

    Online publication date: 1-Dec-2003. CrossRef

27. 2013. References. Guide to the Use of the Wind Load Provisions of ASCE 7-02119-122.

    Citation | PDF (104 KB) | Permissions

28. Zhou, Y., Kijewski, T., and Kareem, A. (2003). "Aerodynamic Loads on Tall Buildings: Interactive Database." Journal of Structural Engineering, 10.1061/(ASCE)0733- 9445(2003)129:3(394), 394-404.

    Online publication date: 1-Mar-2003. Abstract | PDF (1237 KB) | Permissions

29. Thepmongkorn, S. and Kwok, K. (2002). "Wind-induced responses of tall buildings experiencing complex motion." Journal of Wind Engineering and Industrial Aerodynamics, 10.1016/S0167-6105(01)00214-8, 515-526.

    Online publication date: 1-May-2002. CrossRef

30. Thepmongkorn, S. and Kwok, K. (2002). "Effects of coupled translational-torsional motion and eccentricity between centre of mass and centre of stiffness on wind-excited tall buildings." Wind and Structures, 10.12989/was.2002.5.1.061, 61-80.

    Online publication date: 25-Feb-2002. CrossRef

31. 2013. References. Guide to the Use of Wind Load Provisions of ASCE 7-98125-130.

    Citation | PDF (388 KB) | Permissions

32. Piccardo, G. and Solari, G. (2000). "3D Wind-Excited Response of Slender Structures: Closed-Form Solution." Journal of Structural Engineering, 10.1061/(ASCE)0733-9445(2000)126:8(936), 936-943.

    Online publication date: 1-Aug-2000. Abstract | PDF (138 KB) | Permissions

33. Kareem, A., Kijewski, T., and Tamura, Y. (1999). "Mitigation of motions of tall buildings with specific examples of recent

34. Thepmongkorn, S. and Kwok, K. (1998). "Wind-induced coupled translational-torsional motion of tall buildings." Wind and Structures, 10.12989/was.1998.1.1.043, 43-57. Online publication date: 25-Mar-1998. CrossRef

35. Zhang, W., Xu, Y., and Kwok, K. (1995). "Interference effects on aeroelastic torsional response of structurally asymmetric tall buildings." Journal of Wind Engineering and Industrial Aerodynamics, 10.1016/0167-6105(94)00098-X, 41-61. Online publication date: 1-Jun-1995. CrossRef

36. Bose, P. and Datta, T. (1994). "Lateral-torsional motion of tall buildings to along-wind forces." Computers & Structures, 10.1016/0045-7949(94)90377-8, 897-905.

    Online publication date: 1-Nov-1994. CrossRef

37. Beneke, D. and Kwok, K. (1993). "Aerodynamic effect of wind induced torsion on tall buildings." Journal of Wind Engineering and Industrial Aerodynamics, 10.1016/0167- 6105(93)90082-Y, 271-280.

    Online publication date: 1-Dec-1993. CrossRef

38. Kareem, A. (1992). "Dynamic response of high-rise buildings to stochastic wind loads." Journal of Wind Engineering and Industrial Aerodynamics, 10.1016/0167-6105(92)90117-S, 1101-1112.

    Online publication date: 1-Oct-1992. CrossRef

39. Saiful Islam, M., Ellingwood, B., and Corotis, R. (1992). "WindInduced Response of Structurally Asymmetric HighRise Buildings." Journal of Structural Engineering, 10.1061/(ASCE)0733-9445(1992)118:1(207), 207-222.

    Online publication date: 1-Jan-1992. Abstract | PDF (821 KB) | Permissions

40. Xu, Y., Kwok, K., and Samali, B. (1992). "Torsion response and vibration suppression of wind-excited buildings." Journal of Wind Engineering and Industrial Aerodynamics, 10.1016/0167-6105(92)90623-I, 1997-2008. Online publication date: 1-Jan-1992. CrossRef

41. Li, Y. and Kareem, A. (1990). "Recursive Modeling of Dynamic Systems." Journal of Engineering Mechanics, 10.1061/(ASCE)0733-9399(1990)116:3(660), 660-679.

    Online publication date: 1-Mar-1990. Abstract | PDF (1025 KB) | Permissions

42. Kareem, A. (1990). "Reduction of wind induced motion utilizing a tuned sloshing damper." Journal of Wind Engineering and Industrial Aerodynamics, 10.1016/0167- 6105(90)90070-S, 725-737.

    Online publication date: 1-Jan-1990. CrossRef

43. Kareem, A. (1988). "Aerodynamic response of structures with parametric uncertainties." Structural Safety, 10.1016/0167- 4730(88)90010-0, 205-225.

    Online publication date: 1-Sep-1988. CrossRef

44. Thoroddsen, S., Peterka, J., and Cermak, J. (1988). "Correlation of the components of wind-loading on tall buildings." Journal of Wind Engineering and Industrial Aerodynamics, 10.1016/0167-6105(88)90131-6, 351-360.

    Online publication date: 1-Aug-1988. CrossRef

45. THORODDSEN, S., PETERKA, J., and CERMAK, J.. 1988. CORRELATION OF THE COMPONENTS OF WIND- LOADING ON TALL BUILDINGS. Advances in Wind Engineering351-360.

    CrossRef

46. Kareem, A. (1987). "Wind effects on structures: a probabilistic viewpoint." Probabilistic Engineering Mechanics, 10.1016/0266-8920(87)90009-9, 166-200.