STABILITY ANALYSIS OF THE SEISMIC RESPONSE OF HIGH RISE STEEL BUILDINGS INCLUDING P-DELTA EFFECTS

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1 P a g e 353 Available online at APPLIED RESEARCH JOURNAL RESEARCH ARTICLE ISSN: Applied Research Journal Vol.2, Issue, 8, pp , August, 2016 STABILITY ANALYSIS OF THE SEISMIC RESPONSE OF HIGH RISE STEEL BUILDINGS INCLUDING P-DELTA EFFECTS * Rafaa M. Abbas and Anas N. Hassony Department of Civil Engineering, College of Engineering, University of Baghdad, Iraq. ARTICLE INFO Article History: Received: 23, August, 2016 Final Accepted: 04, October, 2016 Published Online: 30, October, 2016 Key words: Dynamic Analysis, High-Rise Building, Finite Element, P-Delta Effect, Stability. ABSTRACT The objective of this study was to investigate the effect of P-Delta analysis on the static and dynamic stability analysis of high rise steel buildings subjected to earthquake excitation. Different building models including ten, twenty, thirty, forty and fifty story composite steel buildings with symmetrical and asymmetrical layouts were analyzed. Finite element approach by using ETABS software was used to conduct this study. Different parameters were investigated including number of stories, structural elements stiffness, and bracing system. The "second-order" analysis, which includes geometric nonlinearity and P-Delta effect, used to check the adequacy of the "amplified first-order" analysis proposed by AISC specification for stability and strength design. Second-order analysis with linear and nonlinear time-history, including P-Delta effects was accounted for. The numerical analysis results presented reveal that the stability coefficient approach introduced in the ASCE 7-10 standard to consider P- effects in the design and analysis of structures appears to be overly conservative. A maximum stability coefficient (θ max ) greater than 0.25 would be necessary to account for P-Delta effects. This depends on the type of loading, number of stories, type of analysis as static or dynamic and shape of the buildings as symmetrical or asymmetrical. Copy Right, ARJ, All rights reserved 1. INTRODUCTION As urbanization increases worldwide, the construction of tall buildings in seismic regions is becoming increasingly common [1]. The advantages of multistory buildings that take limit space with human capacity and relay on the function of the building as residential, office or others. The response of high rise buildings against lateral loading largely depends on the characteristics of the loading. The most important criteria in the design of multistory buildings is the stability and story drifts in all directions within limit due to effects of lateral loadings. Most of engineers design building structures using conventional first order method that do not include lateral sway effect of the building or what is called the "P-Delta" effect. In the seismic design of multi-story structures allowance should be made for P-Delta effects [2]. These are the additional overturning moments applied to the structure resulting from the vertical weights P supported by the structure, acting through the lateral deflection, which directly result from the horizontal seismic inertia forces. They are second order effects which increase the displacements, member forces and alter the dynamic response of the structure. The classical elastic analysis and design methodology may be inadequate if the additional destabilizing moments are not taken into account, which may requires increasing members cross sectional area. P-Delta effect typically involves large external forces upon relatively small displacements. If deformations become sufficiently large as to break from linear compatibility relationships, then Largedisplacement and large-deformation analyses become necessary. The two sources of P-Delta effect are as follows [3]: *Corresponding author: Rafaa M. Abbas, Dr.rafaa@coeng.uobaghdad.edu.iq Department of Civil Engineering, College of Engineering, University of Baghdad, Iraq.

2 P a g e 354 Applied Research Journal Vol.2, Issue, 8, pp , August, P-effect, or P-"small-delta", is associated with local deformation relative to the element chord between end nodes. Typically, "P-δ" only becomes significant at unreasonably large displacement values, or in especially slender columns. So long as a structure adheres to the slenderness requirements it is not advisable to model P-δ since it may significantly increase computational time without providing the benefit of useful information. 2. P-delta effect, or P-"big-delta" is associated with displacements relative to member ends. Unlike P-δ, this type of P- effect is critical to nonlinear modeling and analysis. Gravity loading will influence structural response under significant lateral displacement. P-Δ may contribute to loss of lateral resistance, ratcheting residual deformations and dynamic instability. Effective lateral stiffness decreases, reducing strength capacity in all phases of the force-deformation relationship. The subject of stability and P-delta effect in high rise buildings was an area of extensive study. Recently, Donald et al. [4], Shamshinar [5], Mallikarjuna and Ranjith [6], Maheswerappa et al. [7] amongst others investigated the influence of P-Delta on the strength and stability of tall buildings. The aim of this research is to study the stability of tall steel-frame buildings under seismic loading taking into account the second-order effect due to building drift and to compare the outcomes with the current international building standards and specified limits on the drift and stability requirements. 2. BUILDING MODELS The building models adopted in the present study consist of multi-story braced steel frame structure square in plane divided into 10 by 10 bays for each story. Each story height is fixed at four meters and the number of stories for the building models considered rang is 10, 20, 30, 40, and 50 story. Dead load and live load for residential building is assumed to act on the building structure in addition to lateral forces due to earthquake base excitation. The structure of the buildings composed of steel columns with framing beams and girders. The floor system for the building models is assumed to be composite concrete deck slab of 150mm thick with shear stud connectors to connect the deck slab to the girder flanges and simulate full composite action. Lateral stability for the building frame structure is provided by x-type bracing system. 3. FINITE ELEMENT MODELING The finite element code ETABS "Extended 3D Analysis of Building Systems", is used throughout this study to determine the structural behavior of the modeled steel building prototypes. The finite element model includes the composite deck slab, main girders, steel bracings, secondary beams, and steel columns. Three-dimensional finite element models are used to discretize the proposed building models. The composite slab is divided into four shell elements for each panel, and the structural frame beams are divided into the same numbers of slab elements in the "xy" plane. Four-node shell elements with six degrees of freedom at each node are used to model the concrete deck slab. Frame elements are used to model the main girders, cross bracings, secondary beams, and steel columns. Fig. 1 shows the finite element discretization for each building model with different number of stories for symmetrical and asymmetrical building layouts. Fig. 2 shows the bracing system and elevations for the different building models used in the analysis. Table.1 listed steel column, beam, and cross bracing elements section properties used for building structure models adopted in the present study. Building frame element section properties listed in Table.1 and bracing configurations shown in Fig. 2 were selected based on comprehensive design process by using ETABS for the different building layouts to satisfy the minimum requirement for strength design limit according to LRFD load combinations [8], [9]. Table 1 Structural member's cross-section profile adopted for the buildings models. Building Model label Columns section Bracing Main girders Secondary beams BL10 HP12x84 W14x99 W14x22 W10x100 BL20 HP14x117 W14x99 W16x26 W10x100 BL30 HP16x121 W14x99 W16x36 W10x100 BL40 HP18x204 W14x99 W21x44 W10x100 BL50 HP18x204 W14x99 W21x44 W10x100

3 P a g e 355 Rafaa M. Abbas and Anas N. Hassony Typical Symmetrical Building Layout Figure 1 Three-dimensional FE building models. Typical Asymmetrical Building Layout Ten story building Twenty story building Thirty story building Forty story building Fifty story building 4. STABILITY AND P-DELTA EEFECT Figure 2 Elevation and bracing system for the building models.

4 P a g e 356 Applied Research Journal Vol.2, Issue, 8, pp , August, 2016 P-delta effects on story shears and moments, the resulting member forces and moments, and the story drifts induced by these effects are not required to be considered where the stability coefficient (θ) as determined by the following equation is equal to or less than (0.10) [9]: Px Ie V h C x Where sx d P x = the total vertical design load at and above level x; when computing P x, no individual load factor need exceed 1.0 Δ = the design story drift occurring simultaneously with V x. I e = the importance factor determined in accordance with ASCE 7-10 [9]. V x = the seismic shear force acting between levels x and x 1. h sx = the story height below Level x. C d = the deflection amplification factor in Table of ASCE 7-10 [9] (2) The stability coefficient (θ) shall not exceed θ max determined as follows: 0.5 max 0.25 C d (3) Where (β), is the ratio of shear demand to shear capacity for the story between levels (x) and (x 1). Practically, the shear capacity of the different stories in the building models is greater than the shear demand due to lateral forces. Therefore, in the present study the maximum value for the stability coefficient is taken as θ max = Where the stability coefficient (θ) is greater than 0.10 but less than or equal to θ max, the incremental factor related to P-delta effects on displacements and member forces shall be determined by rational analysis. Alternatively, it is permitted to multiply displacements and member forces by [1.0/ (1 θ)]. Where θ is greater than θ max, the structure is potentially unstable and shall be redesigned. Where the P-delta effect is included in an automated analysis, Eq. 2 shall still be satisfied, however, the value of computed from Eq. 1 using the results of the P-delta analysis is permitted to be divided by (1+ ) before checking Eq. 2. The design story drift Δ in Eq. 1 is computed according to the difference of the deflections at the centers of mass at the top and bottom of the story under consideration [9]. The deflection at Level x "δx" used to compute the design stories drift, "Δ", shall be determined in accordance with the following equation: Cd xe x (4) I e The design story drift (Δ) as determined in above shall not exceed the allowable story drift (Δ a ) as obtained from Table of ASCE 7-10 for any story. 5. METHOD OF ANALYSIS An analysis approach defines how the loads are to be applied to the structure statically or dynamically and how the structure responds linearly or nonlinearly, and how the analysis is to be performed [10]. In order to fully investigate stability problem of tall buildings due to seismic excitation different analysis approaches are adopted in this study including amplified first-order analysis, second-order analysis, and linear and nonlinear time history analysis. The simplest procedure in any static or dynamic analysis is the first-order analysis in which the equations of equilibrium are written with respect to the un-deformed "original" geometry of the structure. To account for the secondary effects in this analysis, i.e. P-Delta, an amplification for the first-order analysis results is recommended by design specifications. The Amplified First-Order Elastic Analysis Method defined in AISC [8] is an accepted method for second-order elastic analysis of braced, moment, and combined framing systems is used her. The Second-Order analysis always necessary for stability consideration of structures. The analysis by this method proceeds in a step by step incremental manner. The deformed geometry of the structure obtained from a preceding cycle of calculations is used as the basis for formulating the equilibrium and kinematic relationships for the current cycle of calculations. Geometrical nonlinearity is particularly important for tall

5 P a g e 357 Rafaa M. Abbas and Anas N. Hassony and slender frames subjected to high gravity loading. Geometric nonlinearity in the form of both P-Delta effects and large displacement / rotation effects are taken into account by the second-order analysis. Time-history analysis is a step-by-step analysis of the dynamical response of structure to a specified loading that may vary with time. In this research, time-history analysis is adopted to simulate the dynamic response of the building models due to real base excitation. In order to conduct time history dynamic analysis to simulate seismic base excitation, the building models were analyzed for ground acceleration time history of the 1940 EL Centro California earthquake ground motion [11]. The EL Centro earthquake time history in terms of ground acceleration and time is shown in Fig. 3. In the process of numerical integration for the time-history analysis the differential equation of motions are solved step-by-step, starting at zero time, when the displacement and velocity are presumably known. The time duration of earthquake of interest is divided into discrete intervals and analysis progress by successively extrapolating the displacement from one time station to the next. The aforementioned analysis approaches are accounted for by ETABS software which is used throughout this study to determine the structural dynamic behavior of the modeled steel building prototypes. Figure 3 El Centro earthquake ground acceleration-time history, N-S component. 6. RESULTS AND DISSCUSSION According to the procedure mentioned, stability calculations for all buildings models are performed according to the number of stories, story drift, columns axial and shear forces and methods of analysis. The results for stability coefficient (θ) are presented in the following, moreover, story displacement in terms of drift ratios are also presented. Figs. 4 to 8 present the variation of the stability coefficient and story drift ratios versus the number of building stories due to seismic loading by using amplified first-order analysis and second-order analysis, whereas variation of the stability coefficient and story drift versus the number of building stories due to real earthquake time-history analysis for symmetrical and asymmetrical buildings is show in Figs. 9 to 13. To better evaluate the significance of the stability coefficient (θ), comparison between peak values of (θ) and maximum story drift for each building model is investigated in these figures. The results for the story drift for the different building heights under different analysis approaches, including nonlinear static analysis (second-order analysis) and nonlinear dynamic analysis (time-history analysis), indicate that maximum story drift values are well below allowable story drift limit ( ) of the ASCE 7-10 [9], which stipulate that for structural systems with risk category III the design story drift shall not exceed the allowable story drift ratio h = 0.015, where h is the story height. Investigating stability coefficient values presented in figures 4 to 13 revealed that most of the values are greater than 0.05 and the majority of the building stories having values less than Moreover, the most important is to observe that building stories having stability coefficient greater than 0.25 as shown in figures 8 and 10, where theta (θ) would reach 0.35, the drift ratios for such stories are less than 0.008, which is about half the allowable story drift ratio This result show that the maximum limit imposed on stability coefficient has little importance on the assessment of the dynamic behavior of long-period tall building structures well designed to satisfy strength design limit requirements, especially columns slenderness or members instability P-δ effect, and impose inconsistency with the limitation on the allowable story drift limit which reflects the efficiency of the building lateral stiffness against lateral loading.

6 P a g e 358 Applied Research Journal Vol.2, Issue, 8, pp , August, 2016 At this stage, it is worth to mention that the ASCE 7-10 design standard impose limits on the stability coefficient (θ) and response modification factor (R), which appear to have been set to assure a minimum stiffness during cyclic response and with due consideration for the likely ductility demands imposed on structures [12], with highly ductile systems being afforded greater factors than systems with low ductility. However, Sullivan et al. [12] pointed out that because long-period spectral displacements for real earthquakes reach a magnitude and distance-dependent plateau, the ductility demands that are typically imposed on tall frame systems will be low. Therefore, the current use of high response modification factor in the standard is non-conservative and lower typical values is required as such that the seismic shear force (V x ) is increased and the stability coefficient (θ) obtained by Eq. 1 thus decreased. Figure 4 Stability Coefficient and story drift for the 10-story building due to first and second order seismic analysis. Figure 5 Stability Coefficient and story drift for the 20-story building due to first and second order seismic analysis. Figure 6 Stability Coefficient and story drift for the 30-story building due to first and second order seismic analysis.

7 P a g e 359 Rafaa M. Abbas and Anas N. Hassony Figure 7 Stability Coefficient and story drift for the 40-story building due to first and second order seismic analysis. Figure 8 Stability Coefficient and story drift for the 50-story building due to first and second order seismic analysis. Figure 9 Stability Coefficient and story drift for the 10-story building due to time-history analysis. Figure 10 Stability Coefficient and story drift for the 20-story building due to time-history analysis.

8 P a g e 360 Applied Research Journal Vol.2, Issue, 8, pp , August, 2016 Figure 11 Stability Coefficient and story drift for the 30-story building due to time-history analysis. Figure 12 Stability Coefficient and story drift for the 40-story building due to time-history analysis. Figure 13 Stability Coefficient and story drift for the 50-story building due to time-history analysis. 7. CONCLISIONS Current building design standards and specifications suggest limits on the allowable sway or story drift due to lateral loading and P-delta effect to assure building lateral stability and satisfy ductility demand during cyclic response. In this paper, an attempt was carried out to investigate the effect of P-delta on the static and dynamic stability analysis of high rise composite steel buildings. Different building models with different heights and layouts were analyzed by using different finite element analysis approaches under seismic loading to investigate the significance of the stability coefficient impose by ASCE 7-10 for the analysis and design of tall buildings. The results demonstrated that the maximum limit imposed on stability coefficient has little importance on the assessment of the dynamic behavior of long-period tall building structures when the structural framing system of the building satisfies the strength design requirements imposed by the strength design limit of the building codes. A maximum stability coefficient (θ max ) greater than 0.25 is recommended to encompass P- Delta effects in the stability analysis of high rise building. Moreover, it is argued to impose limits on the

9 P a g e 361 Rafaa M. Abbas and Anas N. Hassony minimum and maximum stability coefficient and it is proposed to include P-delta effect in any automated nonlinear geometric dynamic analysis approach for the seismic analysis and design especially when building columns slenderness or member's instability P-δ effect is accounted for in the design requirements. 8. REFERENCES [1] Konapure, C.G. and Dhanshetti, P.V Effect of p-delta action on multi-story buildings. IJERT. 4(01): [2] Davidson, B.J., Fenwick, R.C. and Chung, B.T P-delta effect in multi-story structural design. Earthquake Engineering, Tenth world conference, Rotterdam: [3] Chen, W. F. and Lui, E. M Stability design of steel frames. First Edition, CRC Press. [4] Donald, W.W., Andrea, E.S., Bulent, N.A., Ching-Jen, C., Yoon, D.K. and Garret, H.K Stability analysis and design of steel building frames using the 2005 AISC specification. Steel structures. 6: [5] Shamshinar, B.S Stability of a six story steel frame structures. UniversitiTeknologiMalasiya. [6] Mallikarjuna, B.N. and Ranjith, A Stability analysis of steel frame structures: P-delta analysis. 3(8): [7] Maheswerappa, S.M., Dinni, S.B. and Kulkarni, N Study of p-delta effect on tall structures. Golden Research Thoughts. 4(11): [8] AISC Specification for Structural Steel Buildings. American Institute of Steel Construction, Inc., Chicago, Illinois. [9] ASCE/SEI Minimum design loads for building and other structure", American Society of Civil Engineers. [10] ETABS manual Integrated Building Design Software. CSI, Ver [11] Chopra, A.K Dynamics of structures, theory and applications to earthquake engineering. Third edition, Prentice-Hall of India. [12] Sullivan, T.J., Pham, T.H. and Calvi, G.M P-delta effects on tall RC frame-wall buildings. The 14 th World conference on earthquake Engineering, Beijing, China.