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International Journal of Science, Engineering and Technology Research (IJSETR) Volume 1, Issue 1, July 2012 Study On Torsional Response of High-Rise Steel Frame Building Under Eccentricity Changes Nan Yu Thwe, Kyaw Moe Aung Abstract— In this paper, study on torsional response of irregular 12- storyed steel building due to eccentricity changes is presented. The structure is situated in seismic zone 4 and composed of special moment resisting frame. Dead loads, live loads, wind and seismic loadings data are considered based on UBC 97 (Uniform Building Code). Required data for design specification of structural elements are considered according to AISC-LRFD 99. Structural steel used in the building is A572 Grade 50 steel. Torsional behavior of asymmetric building is one of the most frequent cause of structural damage and failure during eccentricity changes. In this work, a study on the influence of the torsion effects on the behavior of structure is carried out. To study torsional response of steel building, three different eccentricity values such as 10%, 15% and 20% are considered and analysis results are also compared. In this paper, torsion in a proposed building is studied by eccentricity changes. And then, analysis results of proposed building are compared .The comparison of storey forces are compared due to eccentricity changes. Index Terms— Dynamic analysis, Response spectrum analysis, Torsional response, Eccentricity changes, Torsion effect of steel structure. I. INTRODUCTION Myanmar is a developing country in South-East Asia. Nowadays, the multi-storeyed buildings are widely used in Myanmar and the potential of its popularity will be greater in future. The proposed building is superstructure of 12- storey steel building. Steel have been used for many years in building construction. Steel structures are stiff; lesser time is required for construction; they are easier for fabrication than reinforced concrete structures; lesser weight will be resulted out for using it. Myanmar is situated in a secondary seismic belt which is in the junction of two major belts called Alps Himalaya and Circum Pacific belts. It is likely to meet destructive damage of earthquake to the buildings in some areas. Therefore, in constructing of high-rise buildings, it should be designed to resist the earthquake effects. The proposed building is 12-storeyed steel building. From a structural engineering standpoint, one of the major distinguishing characteristics of high-rise building is the need to resist large lateral forces due to wind or earthquake. In most Manuscript received Oct 15, 2011. Nan Yu Thwe, Department of Civil Engineering, Mandalay Technological University,(e-mail:[email protected]). Mandalay, Myanmar +95 9 91054737 Kyaw Moe Aung, Associate Professor, Head Department of Civil Engineering, Mandalay Technological University, Mandalay, Myanmar, (e-mail: @gmail.com). of buildings, torsion in buildings during earthquake shaking may be caused from a variety of reasons, the most common of which are non-symmetric distributions of mass and stiffness. Modern codes deal with torsion by placing restrictions on the design of buildings with irregular layouts and also through the introduction of an accidental eccentricity that must be considered in design. Most of the current structural design provisions require to consider the torsional behaviour using the design eccentricities, which take into account both natural and accidental sources of torsion. The natural eccentricity is generally defined as the distance between the center of mass (CM) and the center of rigidity (CR) for a considered floor, while accidental eccentricity generally accounts for factors such as the rotational component of ground motion about the vertical axis, the difference between computed and actual values of the mass and rigidity and an unfavourable distribution of live load mass. Torsional forces also affect the way an L-shaped building reacts during an earthquake. Torsional forces are forces that make an object rotate. If buildings are not designed to resist torsional forces, considerable damage or collapse could occur. II. OVERVIEW OF STRUCTURE Earthquakes generate torsional movements of structures for three reasons(1) an eccentricity can exist at every storey between the storey’s resultant force, which coincides with the mass centre CM of the storey, and the centre of rigidity CR of that storey, (2) ground movement has rotation aspects which affect very long structures, (3) even in a symmetrical building, there is an uncertainty on the exact location of the CM and design codes impose consideration in the analysis of an ‘accidental’ eccentricity equal to 5% of the building length perpendicular to the earthquake direction being considered, in addition to the computed CM-CR distance. The centre of rigidity CR is the point where the application of a force generates only a translation of the building parallel to that force. The effects of torsion have to be determined based on the CM-CR distance and on the accidental eccentricity in either a + or - sense. In irregular structures, the computation of torsional effects resulting from the non – coincidence of CM and CR can only be done in a 3-D model. The effects of accidental eccentricity can be found applying at every level a torque computed as the product of the storey force by the CM-CR distance. The effects of those two terms of torsion are then “combined”, which means that effects of accidental eccentricity have to be considered with + and – signs. 1 All Rights Reserved © 2012 IJSETR International Journal of Science, Engineering and Technology Research (IJSETR) Volume 1, Issue 1, July 2012 Torsional effects in earthquakes can occur even where the centers of mass and resistance coincide. For example, ground motion waves acting on a skew with respect to the building axis can cause torsion. Cracking or yielding in an usymmetric fashion also can cause torsion. These effects also can magnify the torsion due to eccentricity between the centers of mass and resistance. Torsional irregularities are defined to address this concern. Figure.1 Torsion III. OBJECTIVE OF STUDY The objectives of this study are as follows: [1] To study the torsional response of high rise steel structure due to eccentricity changes. [2] To investigate the effects of torsion by increasing eccentricity 10%, 15% and 20%. [3] To compare analysis results of proposed building due to eccentricity changes. IV. PREPARATION FOR DESIGN CALCULATION A. Structural Framing System This structure is designed based on UBC - 97. It is located in Mandalay area which is UBC seismic zone 4. The structure has not only 169 ft of long axis of periphery line but also 83 ft of short axis. The grandstand has a total building height of 129 ft and total building area of 14027 ft2. STADD-PRO software is used to analyze the superstructure. B. Material Properties of Structure Material properties of structure are as follows: 1) Material Property of Steel i. Analysis property data - Unit weight of steel Modulus of elasticity Poisson ratio Coefficient of thermal expansion Minimum yield strength, Fy Ultimate tensile strength, Fu = 490 pcf = 29 x 106 psi = 0.3 =6.5 x10-6in/in per degree F = 50 ksi = 65 ksi C. Loading Consideration Loads are forces tending to effect and produce deformations, stresses or displacement in structure. They are gravity loads and lateral loads. Gravity loads are caused by the gravitational pull of the earth and act in vertical direction. Gravity loads are further classified as dead loads and live loads. The two primary lateral loads on structure are wind and earthquakes. Design load combinations are also used. 1) Dead Loads: Dead loads consist of the weight of all material and fixed equipments incorporated into the building. -unit weight of concrete = 150 pcf - 9 " thick brick wall weight =100 pcf - 4.5 " thick brick wall weight = 55 pcf - superimposed dead load for finishing = 25 psf - Weight of finishing & ceiling = 25 psf -weight of lift = 3 tons 2) Live loads: Live loads shall be the maximum loads expected by the intended use or occupancy. They may be fully or partially in place or not present at all. - Live load on typical floor = 40 psf - Live load on roof = 20 psf - Live load on lift = 100 psf - Live load on stair case = 100 psf - Live load on lobbies = 100 psf - Live load on platforms = 100 psf - Unit weight of water = 62.4 pcf 3) Wind Load: The determination of wind design force on a structure is basically a dynamic problem because a building will be continually affected by gusts and other aerodynamic force. Required Data in designing for wind load: - Exposure type = Type B - Basic wind velocity = 80 mph - Method used = Normal Force Method - Windward coefficient = 0.8 - Leeward coefficient = 0.5 - Importance Factor = 1.0 4) Earthquake Load: Nowadays, the structures are designed to resist in an earthquake according to lateral force design. Effects on earthquakes on structures are as follows: (i) Seismic importance factor, I (ii)Seismic zone factor, Z (iii)Soil profile types, S (iv)Seismic source type (v)Near - source factors, Na and Nv (vi)Seismic response coefficients, Ca and Cv (vii) Response Modification Factor, R - Seismic zone = zone (4) - Seismic source type =A - Soil profile type = SD - Structural system = SMRF - Seismic zone factor = 0.4 - Seismic importance factor, I = 1.0 - Response modification factor, R = 8.5 -Seismic response coefficient, Ca = 0.44 Na -Seismic response coefficient, Cv =0.64 Nv - CT value = 0.035 5) Load Combinations In dynamic case, the following load combinations are considered according to AISC-LRFD-99 code. (1) 1.4DL (2) 1.2DL+1.6LL 2 All Rights Reserved © 2012 IJSETR International Journal of Science, Engineering and Technology Research (IJSETR) Volume 1, Issue 1, July 2012 (3) 1.2DL+1.6LL+1.3WX (4) 1.2DL+1.6LL-1.3 WX (5) 1.2DL+1.6LL+1.3WZ (6) 1.2DL+1.6LL-1.3 WZ (7) 1.2DL+0.8 WX (8) 1.2DL-0.8 WX (9) 1.2DL+0.8 WZ (10) 1.2DL-0.8 WZ (11) 0.9DL+1.6WX (12) 0.9DL-1.6WX (13) 0.9DL+1.6WZ (14) 0.9DL-1.6WZ (15) 1.4DL+LL+1SPECX (16) 1.4DL+LL-1SPECX (17) 0.7DL+SPECZ (18) 0.7DL-SPECZ Figure 5, 3D view of proposed building IV. ANALYSIS RESULTS OF THE PROPOSED BUILDING B. Design Results for Frame Members Design results for frame members are mentioned below. Beam and column sections of the proposed building are listed in Table I. TABLE I COLUMN AND BEAM SECTIONS OF PROPOSED BUILDING A. Site Location and Profile of structure Type of building Type of occupancy Location Shape of building Typical story height Bottom story height Size of building 12-storeyed steel building Residential Seismic zone 4 Irregular shape (L-shape) = 10 ft = 11 ft Length = 169 ft Width = 83 ft Plan, Elevation and 3D view of proposed building are shown in Figure 1, 2, 3 and 4. Figure 2.Plan view of proposed building Column Section Storey 1 to 3 Storey 4 to 6 C1 W12x136 W12x120 C2 W14x132 C3 W12x152 C4 Storey Level Storey 7 to 9 Storey 10 to 12 W12x106 W12x65 W12x106 W12x96 W12x65 W12x120 W12x106 W12x65 W12x170 W12x136 W12x106 W12x65 B1 W12x35 W12x35 W12x35 W12x35 B2 W12x30 W12x30 W12x30 W12x30 B3 W12x26 W12x26 W12x26 W12x26 Stair Roof W12x65 W12x30 C. Analysis Results for steel structure When the proposed building is dynamically analyzed with eccentricity changes, it is found that some frame members are not satisfied to design criteria. In 10% eccentricity, it has been observed that 8 numbers of beams are failed. In 15% eccentricity, it has been observed that 10 numbers of beams are failed. In 20% eccentricity, it has been observed that 13 numbers of beams are failed. Columns are not failed for the proposed building in all cases of eccentricity. The fail beams are summarized in Table II. TABLE II FAIL MEMBER SECTIONS OF PROPOSED BUILDING Eccentricity 10% Figure 3, Line Plan of proposed building Beam No 231 Eccentricity 15% Section Beam No W12x30 231 234 4483 W12x30 W12x30 4487 4488 4493 4496 4498 Eccentricity 20% Section Beam No Section W12x30 231 W12x30 232 234 W12x30 W12x30 232 234 W12x30 W12x30 W12x35 W12x35 W12x35 4650 4483 4488 W12x30 W12x30 W12x35 4650 4483 4487 W12x30 W12x30 W12x35 W12x35 W12x35 4496 4497 W12x35 W12x35 4493 4496 W12x35 W12x35 4510 4522 W12x35 W12x35 4498 4499 W12x35 W12x35 4510 W12x35 4522 4523 W12x35 W12x35 Figure 4.Elevation view of proposed building 3 All Rights Reserved © 2012 IJSETR International Journal of Science, Engineering and Technology Research (IJSETR) Volume 1, Issue 1, July 2012 V. STABILITY CHECKING OF SUPERSTRUCTURE According to UBC 97, checking for story drift, checking for P- Δ effect, checking for overturning, checking for sliding, checking for torsion are needed to be safe for the structure. There are five portions to check stability of the structure. A. Checking for story drift Story drift is lateral displacement of one level of structure relative to the level below. In UBC-97, for structure having a fundamental period of greater than 0.7 second, the calculated story drift shall not exceed 0.020 times the story height. The story drift shall not exceed 0.025 times the story height for structures having the fundamental period of 0.7 second or lesser. These limitations are to ensure a minimum level of stiffness so as to control inelastic deformation and possible instability. ΔM= 0.7 R Δs Where, ΔM = Maximum displacement R = Response modification factor= 8.5 Δs = Deformation According to analysis results by STADD-Pro software, the value of story drifts for proposed portions are within story drifts limitation. Thus, the superstructure is stable. respectively. In eccentricity 20%, factor of safety in Xdirection is 6.2 and that of Z- direction is 4.92. Thus, the structure will be safe for sliding. E. Checking for torsion Accidental torsion that occurs due to uncertainties in the building’s mass and stiffness distribution must be added to the calculated eccentricity. The torsional effect is checked between the most two distant points in a structure. In this structure, the safety factors for X and Z-directions are 1.07 and 1.239 for eccentricity 10%, and 1.17 and 1.247 for eccentricity 15% and 1.17 and 1.273 for eccentricity 20%. The torsional irregularity cannot be neglected because the safety factors of this structure are not within the limit. The amount of torsion by eccentricity 10%, 15% and 20% are as follow. Figure 6, Checking of Torsion for proposed building B. Checking for P- Δ Effect According to UBC-97, the resulting member forces and moments and story drifts included by P- Δ effects shall be considered in the evaluation of overall structural frame stability. In seismic zone 3 and 4, P- Δ effects need not be considered when the story drift (Δ) is less than or equal to 0.02 hx/R. So, the proposed building is located in seismic zone 4. The maximum drift ratio of stadium is satisfied with the limitation, we can neglect P- Δ effect. C. Checking for Overturning Moment Every structure shall be designed to resist the overturning effects caused by earthquake forces. The distributed of earthquake forces over the height of a structure causes to experience overturning moment. The UBC-97 requires that every designed structure be able to resist overturning effect included by earthquake forces. Based on analysis result of structure, the safety factor is not only 49.47 for X- direction but also 25.38 for Z- direction for eccentricity 10%. In eccentricity 15%, the safety factor of X- direction is 47.86 and that of Z- direction is 24.47. For eccentricity 20%, factor of safety for both X and Z-directions are 47.78and 24.35 respectively. So, the proposed building is able to resist overturning effect as the safety factors for X and Z directions are greater than 1.5. D. Checking for Sliding Factor of safety for sliding is the ratio of the resistance due to friction to sliding force. From UBC-97, the safety factor of sliding must be greater than 1.5. For the proposed building, the factors of safety for sliding in both X and Z- directions are 5.69 and 5.89in eccentricity 10%. For eccentricity 15%, safety factor for both X and Z directions are 5.7 and 5.37 VI. COMPARISON OF STABILITY RESULTS In this study, the design results for members are carried out load combinations based on AISC-LRFD (99) code. The comparison of structural performance results of response spectrum analysis are graphically described. A. Comparison of Storey Drift in X direction This section discusses the relative story drift value for response spectrum analysis and all these values are graphically represented in Figure 7. Figure 7.Comparison of Story Drift in X- direction It can be found that, storey drift value in X-direction between 10% and 15% is increased about 1.2 times and between 15% and 20% is increased about 1.1 times due to SPECTRUM X. B. Comparison of Storey Drift in Z-direction This section discusses the relative story drift value for response spectrum analysis and all these values are graphically represented in Figure 8. 4 All Rights Reserved © 2012 IJSETR International Journal of Science, Engineering and Technology Research (IJSETR) Volume 1, Issue 1, July 2012 Figure 11.Comparison of Story Moment in X- direction Figure 8.Comparison of Story Drift in Z- direction It can be found that, storey drift value in X-direction between 10% and 15% is increased about 1.4 times and between 15% and 20% is increased about 1.1 times due to SPECTRUM Z. C. Comparison of Storey Shear in X-direction This section shows story shear for eccentricity changes in each story level and shown in figure 9. This figure shows storey moment values in X-direction are slightly decreased from 1 to 12.Maximum value of storey moment is 39700 kips-inches in storey 1 at 20% eccentricity due to SPECTRUM X. F. Comparison of Storey Moment in Z- direction This section discusses the storey moment value for eccentricity changes and it is represented on figure 12. Figure 12.Comparison of Story Moment in X- direction Figure 9.Comparison of Story Shear in X- direction In comparison of storey shear in X- direction, between 10% and 15% is increased about 1.06 times and between 15% and 20% is increased about 1.2 times due to SPECTRUM X. D. Comparison of Storey Shear in Z-direction This section shows story shear for eccentricity changes in each story level and shown in figure 10. This figure shows storey moment values in X-direction are slightly decreased from 1 to 12.Maximum value of storey moment is 79600 kips-inches in storey 1 at 20% eccentricity due to SPECTRUM Z. G. Comparison of Point Displacement in X- direction This section discusses the point displacement value for eccentricity changes and it is represented on figure 13. Figure 10.Comparison of Story Shear in Z- direction In comparison of storey shear in Z- direction, maximum value of 7356 kips is occurred at storey 2 in SPEC Z. E. Comparison of Storey Moment in X- direction This section discusses the storey moment value for eccentricity changes and it is represented on figure 11. Figure 13.Comparison of Point Displacement in X- direction This figure shows point displacement values in X-direction are slightly increased from 1 to 12.Maximum value of point displacement is 3.97inches in storey 12 at 20% eccentricity due to SPECTRUM X. 5 All Rights Reserved © 2012 IJSETR International Journal of Science, Engineering and Technology Research (IJSETR) Volume 1, Issue 1, July 2012 H .Comparison of Point Displacement in Z- direction This section discusses the point displacement value for eccentricity changes and it is represented on figure 14. Figure 14.Comparison of Point Displacement in Z- direction This figure shows point displacement values in Z-direction are slightly increased from 1 to 12.Maximum value of point displacement is 7.96inches in storey 12 at 20% eccentricity due to SPECTRUM Z. VII. CONCLUSIONS In this study, 12-storeyed steel building with L shaped in plan is selected as a proposed building. The main aim is to study torsional response of proposed building. The building is analyzed for eccentricity changes 10%, 15% and 20% respectively and then story responses are also compared as a analytical result. The structure is analyzed and designed according to STADD-Pro software, UBC-97 and AISC-LRFD 1999 specifications. Structural steels used in the building are A572 Grade-50.Wide flanges W-sections are used for frame members. Torsional irregularity may exist in structures, which are symmetric regarding to both plan geometry and stiffness distribution of structural elements. Firstly, the proposed model is analyzed with static analysis. If the static condition is satisfied, the model is also analyzed with response spectrum analysis for dynamic approach. And then, three eccentricity changes (10%, 15% and 20%) are considered and analyzed to compare the analysis results. After the analysis with three eccentricity changes10%, 15% and 20%, 8 numbers, 10 numbers and 13 numbers of beams are not satisfied for torsion criteria. Most of beams are failed in Z direction. Columns are not failed in this structure although three different eccentricity changes are considered. Checking for storey drift, P- Δ effect, overturning and sliding are satisfied and checking for torsion are not satisfied in stability checking. Checking for torsion are satisfied in X-direction and not satisfied in Z-direction for eccentric 10%, 15% and 20%.And then, the amount of torsion are slightly increased 1.239, 1.247 and 1.273 by changing 10%, 15% and 20%. In comparison of analysis results, storey drift, storey shear, storey moment and point displacement during eccentricity changes are compared due to Spectrum X an Z. The storey drift and shear are maximum values at 2nd floor and minimum values at 12th floor in X direction and Z direction. The storey moments are slightly decreased from 1 to 12 storey in X-direction and Z-direction due to Spectrum X and Z-direction. From this study, all analysis results are slightly increased due to eccentricity changes. VIII. ACKNOWLEDGMENT First of all, the author wishes to express her deep gratitude to Excellency Minister Dr. Ko Ko Oo, Ministry of Science and Technology for opening the Master of Engineering course at Mandalay Technological University.The author's deep thanks are due to Dr. Myint Thein, Rector of Mandalay Technological University, for his invaluable directions, managements and helps. The author deeply thanks to her supervisor, Dr. Kyaw Moe Aung, Associate Professor and Head, Department of Civil Engineering, Mandalay Technological University, for his supervision, for his valuable advices, true – line guidance and encouragement during the preparation of this study. The author is indebted to all of her teachers from Civil Engineering department for their patient guidance, suggestion and encouragement for completion of this study. The author wishes to convey her special thanks to all her friends and all persons who helped directly or indirectly towards the successful completion during the preparation of this study. Finally, the author is deeply grateful to her beloved parents for their supports, advice and encouragement to attain her destination. REFERENCES [1] De La Llera, J.C., and Chopra, A.K. 1994. Accidental and natural torsion in earthquake response and design of buildings. Report 94/07, Earthquake Engineering Research Centre,University of California, Berkeley, Calif. [2] Akbar RTamboli: Handbook of Structural Steel Connection Design and Details, McGraw-Hill Co.Inc.(1997). [3] Bungale S.Taranath: Steel, Concrete and Composite Design of Tall Building,2nd Edition, Mc Graw Hill Co.Inc., (1997). [4] Uniform Building Code, Volume 2. Structural Engineering Design Provisions1997,8th International conference of Building Officials. (1997). [5] Charles G. Salmon, John E.Johnson: Steel structure (Design and Behavior), 3rd Edition, Harper Collins Publishers, (1986). 6 All Rights Reserved © 2012 IJSETR