BUILDINGS WITH BASE ISOLATION TECHNIQUES (Report)

2012 BUILDINGS WITH BASE ISOLATION TECHNIQUES

Mahmoud S. Ahmed M.A.Sc., B.Sc. i

BUILDINGS WITH BASE ISOLATION TECHNIQUES

By

Mahmoud SAYED AHMED Ph.D. Candidate, Civil Engineering Department, Ryerson University, Toronto, ON, Canada, [email protected] [email protected]

Project Report Presented to Ryerson University

In partial fulfillment of the Requirement for the Tall Building course

In the program of Civil (Structural) Engineering

Toronto, Ontario, Canada, 2012 © Mahmoud SAYED AHMED, 2012

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BUILDINGS WITH BASE ISOLATION TECHNIQUES Mahmoud SAYED AHMED C.Eng.(Egypt), M.A.Sc., B.Sc.

Abstract Base isolation (BI) system for buildings is introduced to decouple the building structure from potentially damaging induced by earthquake motion, preventing the building superstructures from absorbing the earthquake energy. The mechanism of the base isolator increases the natural period of the overall structure, and decreases its acceleration response to earthquake / seismic motion. A steel building with structural rubber bearing is introduced throughout this study. The study analysis performed to check for the adequacy of the base isolation against building lateral drift and inter-story drift as per allowance in National Building Code of Canada 2010. Two buildings were analyzed using the nonlinear time history response analysis using the dynamic MODAL analysis for fixed base (FB) building, and Isolated base (IB) building with rubber bearing. The analysis represents a case study for symmetric steel building to show the ultimate capacity of the selected structural bearing, and to make a comparison for the difference between the isolated base and the fixed base buildings. Initial results show that the presence of the structural rubber bearing reduces significantly the vertical displacement, moment and shear generated for the same mode.

Keywords: building, base isolation, rubber bearing, earthquake, dynamics, time history response Citation: Sayed-ahmed, Mahmoud. Building with Base Isolation Techniques. Journal of Al-Azhar University Engineering Sector (JAUES), Vol. 7, No. 1, Dec. 2012, pp. 147-159.

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Acknowledgments The author would like to thank Prof. Dr. K.M. Anwar Hossain, P.Eng. for his helpful directions during the course of this research. The author also appreciate the support from Ryerson University, ON, Canada; library for support and making the available database for literature review and civil engineering department for offering the SAP2000 to run the modal analysis.

Disclaimer The proposed information is for research purpose only, in which its presented data may provide guidance for a future detailed design procedure. Furthermore any design or analysis needs a registered professional engineer to design, revise, and stamp for approval. Author claim no liability to anyone.

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Contents Abstract ........................................................................................................................................... iii Acknowledgments ........................................................................................................................... iv Disclaimer ........................................................................................................................................ iv List of tables.................................................................................................................................... vii List of figures .................................................................................................................................. vii List of Abbreviations ........................................................................................................................ ix List of Symbols ................................................................................................................................. ix Chapter I: Introduction .................................................................................................................... 1 1.1 General .................................................................................................................................. 1 1.2 The problem .......................................................................................................................... 1 1.3 The objectives........................................................................................................................ 3 1.4 The scope............................................................................................................................... 3 1.5 The contents and the arrangement of the report ................................................................. 3 Chapter II: Literature review ........................................................................................................... 4 2.1 General .................................................................................................................................. 4 2.2 History of base isolation ........................................................................................................ 5 2.2.1 Base-isolation review ..................................................................................................... 6 2.3 Common types of structural bearing .................................................................................... 9 2.3.1 General ........................................................................................................................... 9 2.3.2 Types of structural bearings ......................................................................................... 10 2.3.3 Design of elastomeric structural bearing ..................................................................... 13 2.3.4 Bearing Motion ............................................................................................................. 17 2.4 Earthquake load .................................................................................................................. 18 2.4.1 General ......................................................................................................................... 18 2.4.2 OBC code requirements for earthquake load .............................................................. 20 2.5 Vibration and basic concept ................................................................................................ 25 2.5.1 General ......................................................................................................................... 25 2.5.2 Vibration ....................................................................................................................... 25 2.5.3 Time-History analysis: basic concept............................................................................ 27 2.5.4 Analysis of dynamics response by mode superposition ............................................... 31 2.6 Base isolation....................................................................................................................... 34

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Chapter III: Parametric Study ........................................................................................................ 44 3.1 General ................................................................................................................................ 44 3.2 Reinforced concrete structure case study........................................................................... 44 3.2.1 Project description ....................................................................................................... 44 3.2.2 Base-Isolated building .................................................................................................. 48 3.2.3 Fixed base building ....................................................................................................... 55 3.2.4 SAP2000 Model Analysis .............................................................................................. 62 Chapter IV: Conclusions................................................................................................................. 67 4.1 General ................................................................................................................................ 67 4.2 Conclusions .......................................................................................................................... 67 4.3 Recommendations............................................................................................................... 68 References ..................................................................................................................................... 69 Bibliography................................................................................................................................... 70 Appendix........................................................................................................................................ 71 A: Earthquake ............................................................................................................................ 71 B: Structural bearing.................................................................................................................. 75 C: Earthquake time history ........................................................................................................ 77

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List of tables Chapter II Table 2. 1 Influential loads on buildings ........................................................................................ 18 Table 2. 2 Importance factor for earthquake load ........................................................................ 22

Chapter III Table 3. 1 High damping bearing Properties ................................................................................. 45 Table 3. 2 Modal participating mass ratio (MPMR) for fixed and isolated base building ............. 62 Table 3. 3 Modal moment and shear values for edge column B.1 ................................................ 63 Table 3. 4 Joint displacement in column B.1 ................................................................................. 64 Table 3. 5 Joint reactions for column B.1 at the base (Joint 13) ................................................... 65

List of figures Chapter I Figure 1. 1 Design procedure for Base Isolation buildings according to NBCC 2005 ...................... 2

Chapter II Figure 2. 1 Three functions of a bearing [cedengineering.com] ..................................................... 4 Figure 2. 2 Building structure with hybrid control system [Pozo et al 2005] ................................. 7 Figure 2. 3 Base-isolated structure founded on shallow soil layer ................................................. 8 Figure 2. 4 Analytical model for base-isolated structure including soil impedances ...................... 8 Figure 2. 5 External forces of isolated system [Li, H.-N & Wu X.-X 2006] ....................................... 9 Figure 2. 6 Elastomeric bearing [pretread.com] ........................................................................... 11 Figure 2. 7 Roller Bearing [rwsh.de] .............................................................................................. 11 Figure 2. 8 Bolt Rocker bearing [bt-bautechnik-gmbh.de] ............................................................ 12 Figure 2. 9 Pot bearing [agom.it] ................................................................................................... 12 Figure 2. 10 Spherical bearing [Dongil Rubber Belt] ..................................................................... 12 Figure 2. 11 Internal forces which act to displace the rubber from the vertical height lost in deflection to the unloaded sides [Farat] ....................................................................................... 15 Figure 2. 12 Load-deflection for one and three layer units reinforced with steel plate [Farat] ... 15 Figure 2. 13 The shape factor [Farat] ............................................................................................ 15 Figure 2. 14 Lift-off: bearing behavior assumed in : “seismic linear model” [NCHRP 596]........... 15 Figure 2. 15 Maximum average pressure on a layer of elastomeric bearing at SLS without rotation [CHBDC] ........................................................................................................................... 16 Figure 2. 16 Building movement ................................................................................................... 17 Figure 2. 17 Principal plates in earth’s crust ................................................................................. 19

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Figure 2. 18 Tectonic plate movement.......................................................................................... 19 Figure 2. 19 Seismic design data for selected locations in Ontario, Canada ................................. 21 Figure 2. 20 Rigid base SDOF system subject to translational component of earthquake ground motion ........................................................................................................................................... 30 Figure 2. 21 Effective load due to horizontal earthquake ground acceleration ........................... 30 Figure 2. 22 Earthquake base shear [Tedesco, J.W.] ..................................................................... 30 Figure 2. 23 Mechanical model representing MDOF building structure subject to ground acceleration ................................................................................................................................... 33 Figure 2. 24 Response spectrum for ground motion recorded on Sep 19, 1985 at SCT site in Mexico City and spectral ordinates for fixed-base and isolated building [] .................................. 36 Figure 2. 25 Natural vibration modes for two buildings [] ............................................................ 37 Figure 2. 26 Friction pendulum sliding (FPS) isolator .................................................................... 39 Figure 2. 27 Relative displacement during chi-chi earthquake [Tsai et al 2003] .......................... 39 Figure 2. 28 Typical Friction Pendulum System............................................................................. 40 Figure 2. 29 Pasadena City Hall ..................................................................................................... 41 Figure 2. 30 Plan view & cross-section [Forell/Eleseer Engineering, Inc.] .................................... 42

Chapter III Figure 3. 1 3D Finite element model ............................................................................................. 45 Figure 3. 2 Plan and elevation view ............................................................................................... 46 Figure 3. 3 Combo (Dead plus live) effect on the N-S for Grid A.1 or A.4 ..................................... 47 Figure 3. 4 Response histories (a) displacement of column (joint 15, 13), (b) displacement of column w.r.t. base, (c) displacement of base shear ...................................................................... 49 Figure 3. 5 Isolated-base – Mode 1 – Period 2.81065 ................................................................... 50 Figure 3. 6 Isolated-base – Mode 2 – Period 2.7975 ..................................................................... 51 Figure 3. 7 Isolated-base – Mode 3 – Period 2.42139 ................................................................... 52 Figure 3. 8 Isolated-base – Mode 4 – Period 0.32664 ................................................................... 53 Figure 3. 9 Isolated-base – Mode 5 – Period 0.24728 ................................................................... 54 Figure 3. 10 Methods to transfer force from column to foundation [Honeck, W.C., Westphal, D.] ....................................................................................................................................................... 55 Figure 3. 11 Response histories (a) displacement of column (joint 15, 13), (b) displacement of column w.r.t. base, (c) displacement of base shear ...................................................................... 56 Figure 3. 12 Fixed-base – Mode 1 – Period 0.49310 ..................................................................... 57 Figure 3. 13 Fixed-base – Mode 2 – Period 0.35973 ..................................................................... 58 Figure 3. 14 Fixed-base – Mode 3 – Period 0.35117 ..................................................................... 59 Figure 3. 15 Fixed-base – Mode 4 – Period 0.19916 ..................................................................... 60 Figure 3. 16 Fixed-base – Mode 5 – Period 0.14006 ..................................................................... 61 Figure 3. 17 Base Isolation joint reactions in joint local coordinate system (MODAL) – Mode 1 . 66

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List of Abbreviations BI CHBDC CSI CQC FEM FPS HDR IBC in kip LBR MDOF NBCC OBC PGA

Base isolation Canadian Highway Bridge Design Code control-structure interaction complete quadratic combination finite element method friction pendulum system high damping rubber International Building Code Inch 1000 pounds-force (4.4482216 kN) lead rubber bearing Multi-degree-of-freedom National Building Code of Canada Ontario Building Code Peak ground acceleration

PTFE SFRS SDOF SRSS

polytetrafluoroethylene seismic force resisting system Single-degree-of-freedom square root of sum of squares

S S(Ta) Ta u V W W X,Y,Z ω Θ ζ Δ σ

shape factor spectral response acceleration fundamental lateral period displacement shear force width weight directions natural circular frequency rotation damping deflection stress

List of Symbols A A Bx c E f F g G h H I Ie J k L m M M Mv Rd Ro

area pseudo-acceleration Torsional sensitivity damping constant modulus of elasticity cyclic frequency force acceleration due to gravity shear modulus height of floor / layer total height moment of inertia earthquake importance factor base overturning moment reduction factor stiffness length mass moment total weight factor for higher mode ductility-related force modification factor overstrength-related force modification factor

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Chapter I: Introduction 1.1 General Base isolation (BI) is a mechanism that provides earthquake resistance to the new structure. The BI system decouple the building from the horizontal ground motion induced by earthquake, and offer a very stiff vertical components to the base level of the superstructure in connection to substructure (foundation). It shifts the fundamental lateral period, Ta, dissipates the energy in damping, and reduces the amount of the lateral forces that transferred to the inter-story drift, and the floor acceleration. The Structural Engineers Association of Northern California (SEONC) published a simple regulation titled “Tentative Isolation Design Requirements” in 1986, which later was added as provisions in the Uniform Building Code 1997, FEMA 273 with exception of permit to pushover, and IBC2000. The structural bearing criteria include vertical and horizontal loads, lateral motion, and lateral rotation that transferred from the superstructure into the bearing and from the bearing to the substructure. Bearing allows for stress-free support of the structure in terms of (1) they can rotate in all directions, (2) they deform in all directions, (3) they take horizontal forces (wind, earthquake).

1.2 The problem Reducing the effect of the horizontal forces generated from wind pressure or earthquake load is of great concern to designers. The structural bearing technique is one of those tools to reduce the lateral displacement of the building, to increase the structural safety, and to increase the human comfort during the occurrence of such event. This study tries of

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clarify the advantage of the base isolation technique with respect to buildings since only few researches were done into this area. Figure 1 shows the schematic diagram for the design process for building against earthquake loading as governed by the National Building Code of Canada 2010 part 4. Clause 4.1.1.4 in NBCC 2010 specifies that buildings and their structural members shall be designed by one of the following methods (i) analysis based on generally established theory, (ii) evaluation of a given full-scale structure or a prototype by loading tester or (iii) studies of model analogues. Throughout this model analogue study the selected building height will be less than 60 m for regular shape building.

Figure 1. 1 Design procedure for Base Isolation buildings according to NBCC 2005

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1.3 The objectives The main objectives of this study work can be stated as follow: 1- To contribute to the efficient design of structural base isolated techniques for buildings 2- To model and investigate a behavior of building with base isolation.

1.4 The scope The scope of this study includes: 1- Conducting literature review on previous work, and codes of practice to structural behavior of Base Isolated Buildings 2- Carrying out finite element modeling (FEM) study on two identical building with different base conditions

1.5 The contents and the arrangement of the report Chapter II of this report summarizes the literature review on the structural bearing, and application for buildings with related codes and standards. Chapter III present a case study conducted on two identical steel buildings, one with base isolation, and other was fixed base for comparison of the results. Chapter V presents the conclusions of this research, and the recommendation for future study.

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Chapter II: Literature review 2.1 General Base isolation (BI) system for buildings is introduced to decouple the building structure from potentially damaging induced by earthquake motion, preventing the building superstructures from absorbing the earthquake energy. The mechanism of the base isolator increases the natural period of the overall structure, and decreases its acceleration response to earthquake / seismic motion. Base-isolation relies on the structural bearing, which is the connection element between the superstructure and substructure to dissipate the horizontal displacement, rotation or translation, as shown in Figure 2.1. The bearing that prevents translation is called a fixed bearing or fix point bearing if it is fixed in all directions; it is called a unidirectional movable bearing or a guided bearing. Base shear introduced due to seismic ground acceleration for fixed base building or base-isolated building is investigated throughout this chapter.

Figure 2. 1 Three functions of a bearing [cedengineering.com]

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2.2 History of base isolation The first base isolation was registered as a patent in 1800’s, and the one of the first few buildings that used the base isolation was in early 1900’s in Tokoyo Imperial Hotel, in which after that structural bearing commercially used in bridge construction. The first material used for BI was made of lead rubber bearing (LBR) providing high flexibility and damping. In early 1980’s the high damping rubber (HDR) was used in US, but the drawback was that these products have no restoring force where they dislocate after the shaking force. The developed friction pendulum system (FPS) in shape of spherical surface overcomes this demerit of sliding bearing, and providing a restoring force. Since 1840’s the natural rubber has been used for base isolation,

through

the

process

of

material

development

synthetic

rubber

or

polytetrafluoroethylene (PTFE) which is developed by DuPont was used, and designed for 50 years or more. About 40 years ago, the elastomeric (layered rubber and steel) was used in bridges, providing an increase of 7% in stiffness after 37 years from installation, with oxidation restriction to 10 mm to 20 mm. Few design equations were developed for base isolation and bearing by codes committees like UBC, IBC2000, FEMA273, NZS4203, CHBDC S6, AISI and AASHTO LRFD for bridges. According to the CHBDC, clause 11.6.11, it states “Bearing shall support and transfer all loads while accommodating translations and rotations in the structure”, also added in clause 1.8.3.3 that “Bridges with superstructures supported on bearings shall be designed to permit the jacking of the superstructure. Jack and shimming locations shall be shown on the drawings. The design shall allow for movement at the permanent bearing locations sufficient to permit bearing replacement”. Building should have the same provisions for bearing and its replacement as per CHBDC as well. Nevertheless more provision must be added for building since it is more complex structure than that of bridges. Due to the presence of the base isolation, the superstructure of the building above ground needs a transfer slab

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acting as upper part of the foundation slab, to carry loads from column/frame system. A normal practice is to locate a bearing at the reaction points at the transfer slab, sometimes lateral movement is restrained at selected bearing. Design procedures of BI building can be listed as: (1) response spectrum method, (2) time history analysis, (3) ultimate capacity of isolator, where a study for the restoring system must be considered.

2.2.1 Base-isolation review For earthquake resistant construction using base isolation [Noel J, R. 1992] it was found that more attention should be paid to four points: 1. preparation of guidelines for evaluation and approval of base isolation structures; 2. preparation of guidelines related to the performance of base isolation devices; 3. facilities to encourage exchange, collection and dissemination of technical information on the response-control structure; and 4. study of methods of evaluation of performance of response-control structures. A study run by Murat & Senol for the active-passive base-isolation systems used for the seismic response control of structures appears to be effective for small to medium strength earthquakes. Hybrid base isolation systems, as shown in Figure 2.2, which use an active system together with the passive base isolation system, may be used to control the response of structures subjected to larger ground motions created by larger magnitude earthquakes. The hybrid base isolation system using passive base isolation pads together with hydraulic type actuators is proposed. The system, placed between the foundation of the building and its superstructure, is used to minimize the forces imposed on the superstructure by the earthquake induced ground motion [Murat, S & Senol, U. 1995] [Pozo et al 2005]. In application for the base-isolation system, the Historical buildings have relatively low height, are usually massive and their natural vibration period is rather low.

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Figure 2. 2 Building structure with hybrid control system [Pozo et al 2005] Hence if such buildings are located in a seismically active region, using base isolation systems will be a very effective way for improving their dynamic response. In some cases the displacements at the base isolation level are rather big and exceed the allowed limits. In such cases it is recommended to add dampers to the base isolation system [Iskhakov, I. & Ribakov, Y. 2007]. Analytical seismic responses of structures retrofitted using base isolation devices are investigated by Vasant & Jangid and the retrofitting of various important structures as historical buildings, bridges, and liquid storage tanks are selected to investigate the effectiveness of the base isolation in seismic retrofitting. It is observed that the seismic response of the retrofitted structures reduces significantly in comparison with the conventional structures depicting effectiveness of the retrofitting done through the base isolation technique [Vasant A & Jangid, R.S. 2008]. Chia-Ming and Billie F. presented development and experimental verification of an active base isolation system for a seismically excited building and modeling the complex nature of control-structure interaction (CSI) [Chia-Ming & Billie F. 2010]. Hyung-Jo et al investigated a smart base-isolation system using magnetorheological (MR) elastomers, which are a new class of smart materials whose elastic modulus or stiffness can be adjusted depending on the

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magnitude of the applied magnetic field. The results further suggest that the feasibility of using MR elastomers as variable stiffness elements for enhancing the performance of conventional base-isolation systems [Hyung-Jo et al 2011]. Yannian et al studied the influence of the action of coupling earthquake to sliding base-isolation structure for 6 story building. The results by exemplification show that the peak values of relative acceleration, relative displacement and inter-storey shear force of sliding base-isolation structure increase in different degree under the action of coupling earthquake [Yannian et al 2011]. Regarding the slide-limited friction base isolation technology, Gui-Feng & Yu-Hong studied the total restoring force model of isolation device. They analyzed the influential factors such as friction coefficient, elastic stiffness and yield displacement of displacement-constraint device on base isolation system [Gui-Feng & Yu-Hong 2011]. Spyrakos et al investigated and developed 2-DOF (degree-of-freedom) for the effect of soil-structure interaction (SSI) on the response of the base isolated multistory building founded on elastic soil layer overlaying rigid bedrock and subjected to harmonic ground motion [Spyrakos et al 2009].

Figure 2. 3 Base-isolated structure founded on shallow soil layer

Figure 2. 4 Analytical model for base-isolated structure including soil impedances

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Figure 2. 5 External forces of isolated system [Li, H.-N & Wu X.-X 2006] Li & Wu investigated the limitation of height-to-width ration (HWR) for base-isolated building with elastomeric rubber bearing. It was found that the isolated building with longer period may have a relatively HWR value: and the stiffness of the superstructure affects HWR limit value little [Li, H.-N & Wu X.-X 2006]. The main two key conditions, which determine the HWR limit for an isolated structure, are: (1) the outermost rubber pads of the isolated layer cannot bear tensile force; (2) the compressive force that the outermost rubber pads bear cannot exceed their ultimate antipressure strength.

2.3 Common types of structural bearing 2.3.1 General Base-isolation may be referred to its function, main material, or may receive a combined terms. The main functions maybe listed as: Point rocker bearing, Sliding bearing, Pot bearing, Spherical bearing, Deformation bearing, Fixed bearing, Movable bearing, Restraints, and Guide bearing. The Base-Isolation can be referred to the main material: Steel bearing, PTFE bearing (polytetrafluoroethylene), and Elastomeric bearing (reinforced/not reinforced). The Base

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Isolation can also be referred as of combined terms: point rocker sliding bearing, pot sliding bearing, spherical sliding bearing, and deformation sliding bearing.

2.3.2 Types of structural bearings In revision to the CHBDC clause 11, the code requires that the bearings (1) carry high permanent compression load with minimum compression deflection; (2) to accommodate horizontal movement by shear deflection with low shear stiffness to prevent excessive loads on the buildings footings due to thermal expansion and contraction; (3) to accommodate rotational deflections due to the transfer slab hogging and sagging; (4) to accommodate live loads with minimal additional compressive deflection; (5) to have a natural frequency particular to the application. The standards recognized the bearing as follows: -

Plain elastomeric o

Natural Rubber (polyisoprene)

o

Neoprene (polychloroprene)

-

Steel reinforced elastomeric

-

Roller bearing

-

Rocker bearing

-

Pot bearing

-

Disc bearing

-

Spherical and cylindrical bearing

-

Other (require approval)

Where factors affecting the selection criterion include: dead load, total load, lateral load, uplift, rotations, translations, cost and durability.

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Pot bearings are designed to carry combinations of vertical loads, horizontal loads, longitudinal and transversal movements, and rotations. This type of bearing can carry very high loads of over 50,000 kN. A completely encased natural rubber pad is positioned in a steel pot. Under high pressure the pad behaves like a liquid. The elasticity of the rubber allows tilting movement (rotation) of the piston in the horizontal axis [agom.it]. Rolling bearing is a bearing which carries a load by placing round elements between the two pieces. The relative motion of the pieces causes the round elements to roll with very little rolling resistance and with little sliding [wikipedia.org]. Elastomeric bearing developed in 1936 and consists from circular or rectangular laminated pads, layers made of reinforced rubber, and layers made of steel plates, the horizontal displacement is resisted by the friction forces F which depends on the compressive force C of these bearing, and its coefficient of friction p, with F = Cp. Spherical bearing consists from three main parts; the pan, the sphere part, and the upper plate made of constructional steel. The horizontal displacement causes friction resistance, and moment due to rotation.

Figure 2. 6 Elastomeric bearing [pretread.com]

Figure 2. 7 Roller Bearing [rwsh.de]

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Figure 2. 8 Bolt Rocker bearing [bt-bautechnikgmbh.de]

Figure 2. 9 Pot bearing [agom.it]

Figure 2. 10 Spherical bearing [Dongil Rubber Belt] Rocker bearing consist of one or more rollers of steel along with a rocker arrangement which permits a longitudinal and rotational movement. There are three types of Linear Rocker Bearings: fixed, guided-sliding and free-sliding Linear Rocker Bearings. Disc Bearing accommodates rotation by deformation of a single elastomeric disc, molded from a urethane compound. It may contain a device for partially confining the disc against lateral expansion.

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2.3.3 Design of elastomeric structural bearing Rubber bearings is displaced around the edge of the bearing resulting in a bulging when it is subjected to vertical loading, as shown in Figure 2.11, since rubber itself is incompressible. Figure 2.12 shows the amount of compressive deflection per unit compressive load (kN/mm) depends on the bulge of the rubber i.e. shape factor and the shear modulus of the rubber compound. To achieve an appropriate natural frequency to achieve the required deflection, elastomeric layer should not be more than 25 mm, in which after that a need to add horizontal reinforcing plates are moulded into the rubber bearing to reduce the shape factor relative to the overall height of the bearing and to increase the compressive stiffness of such bearing. The elastomeric bearing design procedures was adopted for AASHTO LRFD bridge design specification by the NCHRP Report 596 “Rotation limits for elastomeric bearing”, and by the American Iron and Steel Institute (AISI), “Steel bridge bearing selection and design guide”. [1] Where S is the shape factor, L is the length of the bearing parallel to the span of the bay, W is width of the bearing, measured perpendicular to the length, as per Figure 2.13. Rubber is not complete incompressible, and the effect of compressibility index, λ, developed in Stanton and Lund [2006] [2]

√

Where K is the bulk modulus of the rubber, and G is the shear modulus of the rubber. In designing for rubber bearing the AASHTO LRFD Bridge Design Specification introduced two methods; Method A that specifies that shear modulus of the elastomer should be between 0.080 ksi and 0.250 ksi, and nominal hardness should be between 50 and 70 on the Shore A

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scale, and all other physical properties should conform to ASTM D 4014. The service level axial stress is limited by [3]

ksi

Where σa = the average axial stress, and G = the shear modulus of the elastomer. This stress can be increased by 10% if the bearing is fixed against shear displacement. The shear deflection is governed by [4] Where hrt is the total thickness of the elastomer. To ensure the lift-off as shown in Figure 2.14 is prevented, the rotation and axial stress must satisfy [5]

(

)

Where θx is the rotation applied to the bearing about x-axis, hrt is the thickness of one rubber layer, and n is the number of internal rubber layers. Finally the length and the width of the bearing must be greater than three times the total thickness to prevent instability. Method B specifies that the shear modulus of the elastomer should be between 0.080 – 0.175 ksi, and the nominal hardness should be between 50 – 60 on Shore A scale, and all other properties to conform ASTM D 4014. The bearing that is subjected to shear deformation, total axial stress is governed by: [6]

ksi

Live load stress is required to less than 0.66 GS, and the total stress can be increased to 2.0 GS and 1.75 ksi if the shear displacement is prevented. The combination of the axial load and rotation are governed by the need to prevent the lift-off and to avoid excessive shear strain in the compressive side of the bearing. The governing equation to prevent lift-off [7]

(

)

14

Figure 2. 11 Internal forces which act to displace the rubber from the vertical height lost in deflection to the unloaded sides [Farat]

Figure 2. 12 Load-deflection for one and three layer units reinforced with steel plate [Farat]

Figure 2. 13 The shape factor [Farat]

Figure 2. 14 Lift-off: bearing behavior assumed in : “seismic linear model” [NCHRP 596]

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Figure 2. 15 Maximum average pressure on a layer of elastomeric bearing at SLS without rotation [CHBDC]

And for preventing excessive shear strain on the compressive side [8]

[

(

)

]

These two equations bound the axial stress, rotation pair lying between them will neither lift off nor cause excessive local compression. In the Canadian Standards CHBDC a set of limitation for bearing stresses are plotted in Figure 2.15.

16

2.3.4 Bearing Motion Bearings are allowed to move and rotate with respect to the support plane, rotation and displacement should be considered in three directions at a right angle to each other. Type of bearing must be selected prior to the calculation of the bearing movement. The selection criterion of the bearing depends on a preliminary estimation for the displacement as listed in below table, and based on the next fix-point: (1) Steel structure: ±0.50 mm/m, (2) Concrete structures: +0.30 mm/m, -0.60 mm/m, (3) Prestressed concrete structures: +0.30 mm/m, -1.20 mm/m [Eggert, H & Kauschke, W. 2002].

Figure 2. 16 Building movement Since by code provisions, it is required to make an access to the bearing elements underneath the superstructure for replacement after their service life. Small columns are likely to be constructed above the foundation slab to carry the load bearing. Above the bearing, there is a transfer slab that carries all gravity loads. The bearing deformation at the top of the carrying base or columns can be expressed as follow: [9] Where T is the bearing net thickness, A is the bearing area, G is the shear modulus, L,E,I are the carrying structural element data, FH is the horizontal force, and f is the displacement between substructure and superstructure.

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Table 2. 1 Influential loads on buildings

Superstructure

Outer loads

Restraints

Substructure

Outer loads

restraints

Dead loads

In Z direction

Wind & Earthquake

Horizontal

Temperature

In all directions

Shrinkage

In all directions

Prestressing

In prestressing direction

Creep

In prestressing direction

Support settlement

In Z direction

Dead loads

In Z direction

Wind & Earthquake

Horizontal

Shock

Horizontal

Temperature

In all directions

Subsoil motion

Z (settlement) direction and rotation about horizontal axis (rotation of the foundation)

2.4 Earthquake load 2.4.1 General Earthquake is the sudden release of accumulated energy in the tectonic plates of the earth crust and resulting in propagation of seismic waves; P waves, S waves and surface waves. Earthquake occurs at the faults at boundaries the tectonic plates, causing colliding, separation, sliding, or subducting between the adjacent plates. Epicenter is the ground surface point that intersects vertically in a line to the depth of the hypocenter, which considered being a significant factor of seismic hazard. Earthquake magnitude was first introduced with Richter [Richter 1935] for local magnitude (ML). Richter magnitude can measure the amount of seismic released energy up to ML 6.5. The surface-wave magnitude (Ms) was developed to solve the saturation problem of Richter magnitude above ML of 6.5 [Gutenberg 1945]. However this scale was also saturated at Ms > 8. The short-period body-wave magnitude (Mblg) developed by [Kanamori 1983] for

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Figure 2. 17 Principal plates in earth’s crust

(a) Plate collide

(b) Plate separate

(c) Plate slide

(d) Plate subduct

Figure 2. 18 Tectonic plate movement

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North America and Canada tectonic plate, however this scale also get saturated at magnitude levels less than that of Ms. The moment magnitude (Mw or M) was developed by [Kanamori 1977; Hanks and Kanamori 1979] where it relies on the seismic moment with the following equation [10] Where D is the average displacement over the entire fault surface, A is the area of the fault surface, and μ is the average shear rigidity of the faulted rock. The seismic moment represents the amount of energy released at the source. [11] Where Mw is the moment magnitude and Mo is the seismic moment.

Duration (Ta) of the ground motion, the peak ground acceleration (PGA), and the seismic maps are parameters of great interest to assess the seismic hazardous for the given location. Based on past seismic events, the Annual Maxima Series (AMS) and the annual probability of occurrence of earthquakes data for their magnitude, period and location would assess the acceptable risk for design loads. Codes allow using the static push-off analysis for regular building less than 60 m of height as in NBCC 2005, and to use the response spectrum method for other types of buildings.

2.4.2 NBCC code requirements for earthquake load The static base shear load for structural elements due to earthquake motion shall be determined according to the procedure given in the following equations [NBCC 2010] [12]

20

[13] And for and the seismic force resisting system (SFRS) with an Rd equal to or greater than 1.5, V need not to be greater than [14] Where S(Ta) is the 5% damped spectral response acceleration, expressed as a ratio to gravitational acceleration, for a period of T; Mv is the factor for higher mode effect on base shear [Humar & Mahgoub 2003]; IE is the earthquake importance factor; W is the dead load plus 25% of the design snow load plus 60% of the storage load for area used for storage; R d is the ductility-related force modification factor; Ro is the overstrength-related force modification factor [Mitchell et al 2003]; and V is the lateral earthquake design force at the base of the structure. 0.8

Spectral Response Acceleration,S

0.7 0.6 0.5 Toronto 0.4 Alexandria 0.3 White River 0.2 0.1 0 0

0.5

1

1.5

2

2.5

Period, T

Figure 2. 19 Seismic design data without PGA for selected locations in Ontario, Canada

21

Figure 2.15 shows the parameters used to represent seismic hazard for specific geographical locations are the 5%-damped horizontal spectral acceleration values for 0.2, 0.5, 1.0 and 2.0 seconds periods that have the 2% probability of being exceeded in 50 years. The four spectral parameters are deemed sufficient to define spectra closely matching the shape of the Uniform Hazardous Spectra (UHS). Hazardous values are the 50th percentile (median) value based on statistical analysis of the earthquake that have been experienced in Canada. The median was chosen over the mean because the mean is affected by the amount of epistemic uncertainty incorporated into the analysis. It is the view of the Geological Survey of Canada and the members of the Canadian National Committee on Earthquake Engineering that the estimation of the epistemic uncertainty is still too incomplete to adopt into the Code [NBCC 2010]. Buildings are classified by one of the major occupancy and classified in more than one Importance Category. Table 2.2 shows the importance factor for earthquake loads and effects, IE, forming part of sentence 4.1.8.5(1) in NBCC 2010. Low Importance Category buildings are defined as building with low human-occupancy farm buildings as having an occupant load of 1 person or less per 40 m2 of floor area. Normal Importance Category building is used for residential buildings, High Importance Category building is used for petrochemical facilities, and Post-disaster Importance Category building is used for hospitals and special buildings.

Table 2. 2 Importance factor for earthquake load Importance category

Ultimate limit state

Low

0.8

Normal

1.0

High

1.3

Post-disaster

1.5

22

The fundamental lateral period, Ta, in the direction under consideration for steel moment frame [15] The weight, W, of the building shall be calculated using the formula [16]

∑

The total lateral seismic force, V, shall be distributed such that a portion, Ft, shall be assumed to be concentrated ath the top of the building, where Ft, is equal to 0.07 Ta V but need not exceed 0.25V and may be considered as Zero, where the fundamental lateral period, Ta, doesn’t exceed 0.7 s; the reminder V-Ft, shall be distributed along the height of the building, including the top level, in accordance with the formula [17]

∑

The structure shall be designed to resist overturning effects caused by the earthquake forces determined in the below formula, and the overturning moment at level x, Mx, shall be determined using the below equation [18]

∑

Where

for hx ≥ 0.6hn, and

for hx < 0.6hn

Where J is the base overturning moment reduction factor

Torsional effect are considered by applying torsional moments about a vertical axis at distance ±0.10Dnx from the centers of mass at each floor derived for each of the following load cases considered separately [Humar et al 2003] to avoid torsional moment due to accidental eccentricities:

[19]

23

Where Fx is the lateral force at each level and Dnx is the plan dimension of the building at level x perpendicular to the direction of seismic loading being considered. Torsional sensitivity will be considered then by calculating the ration Bx for each level x for each orthogonal direction ⁄

[20]

Where B is the maximum of all values of Bx in both orthogonal directions, δmax is the maximum story displacement at the extreme points of the structure, at level x in the direction of the earthquake induced by equivalent static force at distance ±0.10Dnx from the center of mass at each floor, and δave is the average displacement at the extreme point of the structure at level x by the above mentioned forces. Based on the lateral deflection calculated for base shear, the largest interstory deflection at any level shall be limited to 0.01hx for post-disaster buildings, 0.02 hx for schools, and 0.025 hx for all other buildings.

2.4.2.1. Method of analysis The Equivalent static force per NBCC 2010, article 4.1.8.7 for the superstructure conditioned to (a) (b) Regular structure where h < 60m, and Ta < 2 sec in each of its two orthogonal directions. In NBCC 2010, article 4.1.8.16 for foundations required that the foundations shall be capable to transfer earthquake loads and effects between the building and the ground without exceeding the capacities of the soil. In case at site where

, foundations or basement

walls shall be designed to resist earthquake lateral pressure from backfill or natural ground.

24

2.5 Vibration and basic concept 2.5.1 General The seismic base isolation is limited by uncoupling the structure from the ground induced motion in the horizontal directions. By arranging the horizontally active elements (bearings) between the superstructure (the building and the secondary foundation slab) and the substructure (base foundation), which may reach to ±300 mm, and reduce the dangerous horizontal acceleration transmitted into the structure to a permissible level and the natural frequency down to 1.4 Hz. Ground motion has magnitude, fault mechanism, and fault distance consistent with site and represented by the maximum considered ground motion, which is known as earthquakeinduced load. Seismic load performs orthogonal horizontal loading on the building, where it uses the model response history analysis to capture 90% of the mass structural in each of the two orthogonal directions [ASCE 7-05]. By the presence of the base isolation systems, the structuralborne noise must be considered, for example the rail traffic generates a soil-bound vibration signals ranges 10-80 Hz when building is less than 25 m away from the track beds, while the average range is approximately 60-250 Hz. The necessary spring compression z to provide a certain vertical natural frequency can be determined by

with fz in Hz and z in mm.

2.5.2 Vibration The structure undergoes vibration when it is disturbed from its static equilibrium position and to allow it to vibrate. The vibration analysis is resulting in describing the natural frequency and damping ratio. This motion that vibrates the building could be resulted from the wind or earthquake-induced force. The time for the undamped system to complete one cycle of

25

vibration is the natural period of vibration donated as Tn, in units of seconds, which is related to the natural circular frequency of vibration, ωn, in radians per seconds.

[21]

The natural cyclic frequency of vibration is donated by fn for a system executes 1/Tn cycles in 1 second. The cyclic frequency fn its units is (Hz) [cycles per seconds (cps)]

[22]

The natural circular frequency ωn, natural cyclic frequency fn, and natural period Tn can be expressed differently as follow

[23]

√

√

√

(rad/sec),

(Hz),

√

(sec)

Where δst = mg/k, δst is the lateral displacement of the mass due to lateral force mg, g is the acceleration due to gravity, m is the mass, k is the stiffness

[24]

√

and

Where ζ is the damping ratio, c is the damping constant measured by the energy dissipated in a cycle of free vibration or in a cycle of forced harmonic vibration, and ccr is the critical damping coefficient. With decaying of motion after vibration the ζ becomes small, √ gives an approximate equation of

and this

.

26

2.5.3 Time-History analysis: basic concept The earthquake response is a base excitation, subjected to an arbitrary ground displacement xg(t). Newton’s second law sets forth the equilibrium condition [Tedesco, J.W. 1998]. [25] Where

F1 = inertia force = FD = damping force =

̈ , ̇,

Fs = elastic restoring force = ks, F(t) = externally applied force = 0. And x(t) is the relative displacement of the mass and xt(t) is the total (absolute) displacement of the mass. Thus, the equilibrium condition may be expressed ̈

[26]

̇

The effective load that induces the dynamic response of this system is defined in recognition of the fact that the inertia form term (Ft) is proportional to the total motion of the system, while the damping force (FD) and elastic restoring force (Fs) are proportional to the relative motion of the system. Therefore, [27] It follows that [28]

̈

̈

̈

Hence it may be written as

27

̈

̈

[29]

̇

Or ̈

[30]

̇

Where Feff(t) is the effective load, attributed to the horizontal ground acceleration, applied to the mass m and is given by ̈

[31] Since ω2 = k/m and [32]

̈

√ ̇

̈

Thus, for any arbitrary acceleration of the support ̈

, the relative displacement of the mass

x(t) can be computed from the Duhamel integral expression, for zero initial conditions, as

[33]

√

∫ ̈

√

It is noted that the relative response of the structure is characterized by its natural frequency ω, the damping factor ζ, and the nature of the base excitation ̈

. Generally, the undamped

natural frequency is used in place of the damped frequency, and the negative sign is ignored.

[34]

Where

[35]

∫ ̈

28

And R(t) is called the earthquake response integral. The relative displacement x(t) is important in the earthquake analysis of structures because of strains

(and stresses) in the structural

members are directly proportional to the relative displacement. For example, the total shear force, or base shear, V transferred to the foundation by elastic constraints [36] Notice that the base shear is equivalent to the elastic restoring force in the system, Fs(t). The exact relative velocity ̇

of the mass is obtained by differentiating the relative displacement

x(t), with respect to time, resulting in ̇

∫ ̈

[37]

√

√

∫ ̈

√

The absolute acceleration of the mass, ̈ to time and noting that ̈

[38]

̈

̈ (

)

√

∫ ̈

̈

, is obtained by differentiation of ̇

, with respect

this yields

∫ ̈

√

√

These equations represent the earthquake time-history response for a SDOF structure, where the effective earthquake force and the elastic restoring force are equivalent at any instant of time. [39]

29

Figure 2. 20 Rigid base SDOF system subject to translational component of earthquake ground motion

Figure 2. 21 Effective load due to horizontal earthquake ground acceleration

Figure 2. 22 Earthquake base shear [Tedesco et al 1998]

30

Finally, if the stiffness term k is expressed in terms of the natural circular frequency of the system ω, then the effective earthquake force is equivalent to

. Notice here that the

effective earthquake force is expressed as the product of the mass m and the pseudo, but not the absolute acceleration ̈

acceleration

.

2.5.4 Analysis of dynamics response by mode superposition In many cases, designers are interest in study the response of the support motions rather than the applied actions by earthquake. For the base isolation, a typical multi-degree-of-freedom MDOF system is selected to study the vibration of the tall building. In this mode the mass mi are lumped (localized) at the floor levels and are interconnected with massless columns that have the equivalent spring constant Ki. Dashpots represented by the damping constant ci model the energy dissipation in the system. The shear force at every level is denoted by Vi, and Vn corresponding to the base shear acting between the structure and the soil, or acting at the base isolation; ̈

is the ground acceleration, and xi represents the relative displacement of the

building at story level i. The other parameters assess the dynamic response of the structure subjected to base excitation are the relative velocities ̇ and total acceleration xti at each story. [ ]{ ̈ }

[40] Where ̈

[ ]{ } ̈

[ ]{ ̇ }

[ ]{ }

is the ground acceleration and {I} is the unit vector of dimension n. At any floor I

the effective load acting on the mass can be expressed as ̈

[41]

The complete effective load vector is given by the product of the mass matrix and the ground acceleration ̈ [42]

as follow: {

}

[ ]{ } ̈

31

Thus the first equation can be written as [43]

[ ]{ ̈ }

[ ]{ ̇ }

[ ]{ }

[ ]{ } ̈

{

}

The model equations of motion can be expressed as following [44]

[ ]{ ̈ }

[ ]{ ̇ }

[ ]{ }

{

}

Where [M] and [K] are the model mass and stiffness matrices respectively, [C] is the model damping matrix, and the effective model force vector { [45]

{

[ ] [ ]{ } ̈

}

[ ] {

} is given by }

Where the term ω is called the natural circular frequency of the system, with units of radians per second, k is the stiffness and is given by √

[46]

rad/sec

The motion is periodic and repeats itself every T seconds, where [47] (

[48]

[49]

[ ]

)

[ ] [ ][ ]

[

]

Since the model mass, model stiffness, and modal damping matrices are diagonal, the n uncoupled equation can be written as follows [50]

̈

̇

r = 1,2,…..,n

Where [51]

{ } [ ]{ } ̈

The response of the rth mode in normal coordinates at any time t may be obtained by evaluation of the Duhamel integral expression for the given ground motion

32

(

[52]

)∫

For undamped system, the above equation can be reduced to (

[53]

)∫

The system response in physical coordinate, for relative displacement is then given as [54]

{

}

∑

{ }

Figure 2. 23 Mechanical model representing MDOF building structure subject to ground acceleration [Tedesco et al 1998]

33

2.6 Base isolation The concept of base isolation systems is quite simple by interposing structural elements with low horizontal stiffness between the structure and the foundation to decouple the structure from the horizontal components of the ground motion which gives the structure a very low frequency than both its fixed base and the ground motion [Naeim, F & Kelly, J.M. 1999]. The deformation of first dynamic mode happens in base isolation while the structure above is rigid; the deformation of higher modes happens in the structure which is orthogonal to the first mode and to the ground motion, these higher modes do not participate in the motion; therefore, the high energy in the ground motion cannot be transmitted to the structure. The base isolation system does not absorb the energy from the earthquakes but it deflects it through the system dynamics which is not depending on the damping level, but dampers are important to suppress resonance at the isolation frequency [Naeim, F & Kelly, J.M. 1999]. For the structural building with fixed base: lumped mass m, lateral stiffness k, and the lateral damping c, for single-degree-of-freedom SDF system with natural frequency ωn, natural period Tn, and damping ratio ζ. The subscript f instead of n to emphasize for fixed base (without isolation system). The base shear Vb for fixed base building is function of the mass and the pseudo-acceleration response

[55]

.

√

[56]

[57]

[58]

34

For the structural building with base isolation; the base slab – transfer slab – has mass mb with lateral stiffness kb and linear viscous damping cb. Two parameters, Tb the natural vibration period and ζb the damping ratio, are introduced to represent the base isolation for one story building. The base isolation system reduces the base shear because of the natural period of the first mode, the isolation mode, thus increase in the response period, leading to a smaller spectral ordinate. The design spectrum gives the pseudo-acceleration

and deformation

as expressed below

[59]

[60]

√

[61]

[62] [63]

Base-Isolation Building [Lu et al 2012]

35

Effectiveness of base isolation The main function of the base isolation is to reduce the base shear, for this purpose the Tb/Tf period ratio should be as large as practical, otherwise it will be harmful. Case study 1; for example during 1985 in Mexico City and for one-story building the recorded earthquake with pseudo-acceleration value

= 0.25g associated with Tf = 0.4 sec and ζf = 2% for the fixed-

base structure, and

= 0.63g associated with Tb = 2.0 sec and ζb = 10% for the isolated

structure. The ratio

/

= 0.63g/0.25g = 2.52. This means that the base shear in

the base-isolated building is 2.52 times the base shear in the fixed-base building as Tb>>Tf, where it is appropriate to select system with the studied factors [Chopra, A.K. 2001].

Figure 2. 24 Response spectrum for ground motion recorded on Sep 19, 1985 at SCT site in Mexico City and spectral ordinates for fixed-base and isolated building [Chopra 2001]

36

(a) fixed-base building; (b) isolated building Figure 2. 25 Natural vibration modes for two buildings [Chopra 2001]

An example for multi-degree-of-freedom (MDOF) system, case study 2; is a five-story shear frame building with lumped mass m = 100 kips/g at each floor, and stiffness k for each floor, the fundamental period Tf = 0.4 sec, the classical damping matrix cf = a1kf with 2% of damping a1 for the fundamental mode. The base slab mb = m. The isolation system has a fundamental period of Tb = 2.0 sec and ζb = 10%. The modal damping ratios for both systems are shown in Figure 2.25. The first mode for both systems of damping ζb = 10% shows that earthquake-induced force for the first mode is increasing non-linearly for the fixed-base, and almost increased in constant rate for the base-isolated structure all-over its height. For the other modes, the base mass is acting as a fixed base afterward. In calculating of the square root of the sum of the squares (SRSS) base

37

shear Vb with respect to the building weight W for the fixed-based building Vb/W = 1.613, and the Vb/W = 0.361 for the isolated building. This means that the base shear in the base-isolated building is 3.49 times less than the base shear for the fixed-base building, where Tf>>Tb. For moderate-to-high-rise building, the effect of higher modes can be approximately distributed using the general modal relationship shown in Table 2.3, where the fundamental period of vibration may be calculated using the code formulas, and the periods for the second through the fifth modes can be estimated by using tabular values.

Table 2. 3 General modal relationship Mode

1

2

3

4

5

Ratio of period to 1st mode period

1.000

0.327

0.186

0.121

0.083

Participation factor at roof

1.31

-0.47

0.24

-0.11

0.05

Base shear participation factor

0.828

0.120

0.038

0.010

0.000

Case study 3: Seismic Rehabilitation of Pasadena City Hall The friction pendulum sliding FPS isolator, as shown in Figure 2.26 has a great impact in reducing the base shear effect as shown in Figure 2.27. Figure 2.28 show structural detailing for the proposed system, which was successfully used in In California, U.S., for the historical Pasadena City Hall, as shown Figures 2.29 & 2.30. The building was rehabilitated with the seismic isolation that consists of removal of the original basement floor slab, excavation and installation of new foundation, placement of a new basement transfer system, and installation of 240 friction pendulum sliding (FPS) isolators between the foundation and basement level.

38

Figure 2. 26 Friction pendulum sliding (FPS) isolator

Figure 2. 27 Relative displacement during chi-chi earthquake [Tsai et al 2003]

39

Figure 2. 28 Typical Friction Pendulum System

40

(a) Main entrance

(b) Top view Figure 2. 29 Pasadena City Hall

41

Figure 2. 30 Plan view & cross-section [Forell/Eleseer Engineering, Inc.]

42

Table 2. 4 List of major retrofitting buildings projects completed using base isolations [Matsagar & Jangid 2008]

43

Chapter III: Parametric Study 3.1 General This chapter is a study analysis for a steel structure building subjected to earthquakeinduced load, with two scenarios; (a) fixed base building and (b) base-isolated building with rubber bearing. Both buildings are identical expect in the base fixation, and were modeled by SAP2000 (ver. V14.1.0 Advanced) for nonlinear time history analysis.

3.2 Reinforced concrete structure case study 3.2.1 Project description A two story building made of steel structure, Figure 3.1, with 3 bays of 30 feet in each direction, the story height is 12 feet, as shown in Figure 3.1. The structural steel has the following spec; the modulus of elasticity E = 29000 ksi (A992Fy50), Poisson ratio equals to 0.3, the beam section is W24x55, the column section is W14x90. The horizontal slabs are reinforced concrete of 4000 psi and 6 in, 10 in of thickness for the roof and the floor respectively. The vertical loads for roof is 75 psf for the dead load (DL) and 20 psf for live load (LL), while for the floor is 125 psf for DL, and 100 psf for LL. Diaphragm constraints at each level is assigned to make all diaphragm rigid. This project was subjected to nonlinear time history analysis, where seismic load is applied by SAP2000 for lacc_nor-1 file data in the X-direction and lacc_nor-2 file data in the Y-direction simultaneously. Each time history is given in units of cm/sec2, where there are 3000 time steps, at equal spacing of 0.02 sec, for total of 60 sec. There are 8 acceleration points per line. This building is analyzed under two cases; case 1 with fixed base, and case 2 with isolated base. The rubber isolator has specification listed in table 3.1.

44

Table 3. 1 High damping bearing Properties Vertical (axial) stiffness

10,000 k/in (linear)

Initial shear stiffness in each direction

10 K/in

Shear yield force in each direction

5 kips

Ratio of post yield shear stiffness to initial shear stiffness

0.2

Figure 3. 1 3D Finite element model

45

(a) Plan view

(b) Elevation view Figure 3. 2 Plan and elevation view

46

(a) Moment 3-3 Diagram

(b) Axial Force Diagram Figure 3. 3 Combo (Dead plus live load) effect on the N-S for Grid A.1 or A.4

Figure 3.2 shows the plan and elevation views for the 2story 3 bays building. Further in this chapter will focus on column at axis B.1, second column from the left, where the base joint is called as Joint 13, and the first floor joint is called Joint 14, and the roof joint is called Joint 15. Figure 3.3.a shows the bending moment for columns and beams for the structural frame for the gravity load (dead + live load), the bending moment for column B.1 is -52.402, 54.384, -29.742 and 42.203 kip-in at Joints 13, 14, 14, and 15 respectively. Figure 3.3 depict the axial force for

47

columns on axis 1 and 4. It was observed that axial load due gravity load is -76.917 and -220.477 kip for the second and first floor respectively.

3.2.2 Base-Isolated building The base isolation extends the fundamental lateral period resulting in reducing the base shear forces, enhancing the total building drift to the total height and the inter-story drift if compared with the conventional foundations. Figure 3.4.a depicts the time response history for column B.1 with its three joints; Joint 13-15, the figure shows that the column from the base to the roof level moves laterally in a same rate, thus no deflection occurs at the joint 14, Figure 3.4.b depicts the B.1 column movement with respect to the base, and shows that to great extent the column move with base. Figure 3.4.c depicts the displacement of the base shear to the earthquake with respect to time. It is worth mention that the change in the fundamental period changes the moment, and consequently changes the building deformation. Figures 3.5 through 3.9 depict the moment 3-3 diagram and the deformation shape for five different MODAL with different periods -. It was observed that with the decrease of the period, the structure laterally deforms more. Lateral deformation for building is usually assessed by the shear rigidity index (SRI), bending rigidity index (BRI), the drift index (DI) and the inter-story drift (ISD). The last two criterions can be expressed as following: [64] [65]

⁄ ⁄

Where Δi is the deflection at the roof; Hi is the total height of the building, hi is the floor height.

48

Figure 3. 4 Response histories (a) displacement of column (joint 15, 13), (b) displacement of column w.r.t. base, (c) displacement of base shear

49

(a) Moment 3-3 Diagram (MODAL) Model 1 – Period 2.81065

(b) Deformation shape (MODAL) – Mode 1 – Period 2.81065 Figure 3. 5 Isolated-base – Mode 1 – Period 2.81065

50



51



52



53



54

3.2.3 Fixed base building The fixed base for the steel columns, as shown in Figure 3.10 which relies on the steel plate and anchored bolts, reduce the fundamental lateral period resulting in increasing the base shear forces, increasing the total building drift to the total height and the inter-story drift if compared with the base-isolated foundations. Figure 3.11.a depicts the time response history for column B.1 with its three joints; Joint 13-15, the figure shows that the column from the base to the roof level moves laterally in an independent rate, thus deflection occurs at the joint 14, Figure 3.11.b depicts the B.1 column movement with respect to the base, and shows that Joint 13 move the base while joint 14, and 15 move independently. Figure 3.11.c depicts the condensed wave displacement of the base shear in response to the earthquake-induced load. It is worth mention that the change in the fundamental period changes the moment, and consequently changes the building deformation. Figures 3.12 through 3.15 depict the moment 3-3 diagram and the deformation shape for five different MODAL with different periods -. It was observed that with the decrease of the period, the structure laterally deforms more.

Figure 3. 10 Methods to transfer force from column to foundation [Honeck, W.C., Westphal, D.]

55

Figure 3. 11 Response histories (a) displacement of column (joint 15, 13), (b) displacement of column w.r.t. base, (c) displacement of base shear

56


(b) Deformation shape (MODAL) – Mode 1 – Period 0.49310 Figure 3. 12 Fixed-base – Mode 1 – Period 0.49310

57



58



59



60



61

3.2.4 SAP2000 Model Analysis The fundamental lateral period was solved using the finite element analysis (FEA) software, SAP2000. Table 3.3 shows that the fundamental period (T) and the corresponding frequency (ƒ=1/T) for the Modal participating mass ratio (MPMR) solved for Ritz Vector Analysis, for the steel building under investigation in this study which has two scenarios; (a) fixed base, and (b) the isolated base. It was found that the isolated base is 5.699, 6.337, 6.895, 1.64, 1.766 times for Modal 1 through 5 respectively. The first three modes were significantly higher, where they absorb more than 95% of the earthquake-induced load. Table 3. 2 Modal participating mass ratio (MPMR) for fixed and isolated base building Modal Mode 1 2 3 4 5

Period, T [seconds] Frequency, ƒ [Hz] Fixed Base Isolated Base Fixed Base Isolated Base 0.49310 2.81065 2.0279 0.35578 0.35973 2.79750 2.7799 0.35746 0.35117 2.42137 2.8476 0.41298 0.19916 0.32664 5.0211 3.06147 0.14006 0.24728 7.1397 4.04399 Where ƒ ≥ 1 Hz for rigid building, ƒ < 1 Hz for flexible building

Moment and shear forces generated from each mode are of great concern to designers, to predict the failure modes, progressive collapse of the building, or to add extra bracing to resist such lateral loading. Table 3.4 analyze the moment and shear values for column B.1 and its 3 joints under five different MODAL periods (modes) for minor (V3, M2) and major (V2, M3). Selection the moment and shear values for the roof, it was found that the moment for the fixed base building is higher than that of the isolated base building by 51.38, 20455, 0.31, 2.34 and 2.23 for mode 1 through 5 respectively for the minor (M2), and 70, 106, 66, 13.7, and 2.289 for mode 1 through 5 respectively for the major (M3). Hence the base isolation enhances the building capacity to resist the earthquake-induced load, and that reduction in moment could be used towards reducing the selection members sizes, reducing the total building weight and cost.

62

Table 3. 3 Modal moment and shear values for edge column B.1 Modal 4 Moment Shear

Modal 5 Moment

Shear

Minor (V3 , M2)

Modal 3 Moment Shear

288 144 144 0

10.95 -10.06 29.27 -29.27

-0.146 -0.146 -0.411 -0.411

-0.012 0.022 -0.035 0.040

2.4E-4 2.4E-4 5.2E-4 5.2E-4

-3.452 3.375 -8.186 8.403

0.047 0.047 0.115 0.115

1104.155 -1110.116 1431.488 -1502.657

-15.399 -15.399 -20.376 -20.376

-423.458 437.875 -536.685 561.644

5.990 5.990 7.627 7.627

Major (V2, M3)


288 144 144 0

4.5E-3 0.038 -0.086 0.112

2.3E-4 2.3E-4 1.4E-3 1.4E-3

14.804 -12.55 32.193 -33.644

-0.19 -0.19 -0.457 -0.457

22.168 -18.120 49.083 -51.388

-0.28 -0.28 -0.698 -0.698

-0.246 2.864 -4.993 5.389

0.022 0.022 0.072 0.072

2765.094 -2588.261 3107.763 -3413.022

-37.176 -37.176 -45.283 -45.283

Minor (V3 , M2)


288 144 144 0

562.661 -538.23 1133.21 -1245.9

-7.645 -7.645 -16.52 -16.52

245.464 -249.23 403.782 -438.537

-3.435 -3.435 -5.849 -5.849

1.067 -2.209 2.217 -1.082

-0.023 -0.023 -0.023 -0.023

-2586.53 2921.005 1862.977 -1791.469

38.47 38.47 -25.378 -25.378

944.549 -1068.03 -691.367 669.645

-13.976 -13.976 9.451 9.451

Major (V2, M3)

Fixed-Base

Isolated-Base

H

288 144 144 0

-0.315 2.776 -3.192 1.321

0.021 0.021 0.031 0.031

-1569.76 1404.129 -2430.91 2904.872

20.652 20.652 37.054 37.054

-1477.367 1353.073 -2251.606 2655.291

19.656 19.656 34.076 34.076

3.372 -2.092 0.841 -0.348

-0.038 -0.038 -8.2E-3 -8.2E-3

-6329.895 7225.272 4966.383 -4667.693

94.133 94.133 -66.903 -66.903

H is the building height in [in], M is the moment in [kip-in], V is the shear force in [kip]

63

Table 3. 4 Joint displacement in column B.1 Modal Mode 1

Joint [Height] 15 [288] 14 [144] 13 [0.00]

Fixed Base U1 U2 -9.2E-14 -0.7459 -5.4E-14 -0.4597 0.00 0.00

U3 -0.0032 -0.0025 0.00

Isolated Base U1 U2 U3 -2.2E-11 -0.4699 -0.0001 -2.2E-11 -0.4642 -0.0001 -2.2E-11 -0.4518 -4.8E-5

2

15 [288] 14 [144] 13 [0.00]

0.8412 0.4806 0.00

-0.2804 -0.1602 0.00

-0.0026 0.0021 0.00

-0.4659 -0.4625 -0.456

1.9E-11 1.8E-11 1.8E-11

2.3E-5 2.1E-5 1.1E-5

3

15 [288] 14 [144] 13 [0.00]

0.7684 0.4362 0.00

1.6E-13 9.0E-14 0.00

-0.0013 -0.001 0.00

-0.5141 -0.5088 -0.4987

0.1714 0.1696 0.1662

6.7E-5 6.0E-5 2.9E-5

4

15 [288] 14 [144] 13 [0.00]

1.19E-14 -1.03E-14 0.00

0.5858 0.5853 0.00

0.0073 0.0043 0.00

-3.3E-14 -1.8E-15 2.6E-14

-0.6543 -0.1044 0.5306

-0.0086 -0.0073 -0.0031

5

15 [288] 14 [144] 13 [0.00]

0.6114 -0.6612 0.00

-0.2038 0.2204 0.00

-0.0062 -0.0034 0.00

-0.727 -0.1064 0.0025

0.2423 0.0355 -0.1926

0.0066 0.0056 0.5778

Where U1, U2, U3 are displacement in x, y, z directions respectively in [in]; Height in [in]

Drift is another point of interest to designers and must conform to code requirements. Table 3.5 shows the deflections in x, y, z directions for the edge column B.1 under the different 5 MODAL (periods) for the fixed base and the isolated base building. The major observation to this table is that the deflection for the base isolated building doesn’t start from zero, thus reduces significantly the drift index for the building. For example in studying the drift index (DI) for MODAL mode 1, the drift index for the isolated base = (0.46999 – 0.4518)/288 = 0.063159E-3 in, while for the fixed base building DI = (0.7459 – 0)/288 = 2.589E-3 mm, which means that the deflection in base isolated building is less by 40.99 times than that of the conventional fixed structure. The joint reactions in Table 3.5 are obtained using modal combination applied

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individually to each joint. The joint reactions are represented as Ri,m where is (i) is for the direction, and (m) for mode. The total reaction follows this equation

√∑

[66]

Table 3. 5 Joint reactions for column B.1 at the base (Joint 13) Joint reaction [kip] 1 2 3 Modal1 0.000 0.678 0.480 Modal 2 0.684 0.000 -0.108 Modal 3 0.748 -0.249 -0.291 Isolated Base Modal 4 0.000 -0.796 31.454 Modal 5 -0.867 0.289 -24.722 Gravity 0.000 0.000 361.487 Modal 1 -3.134E-2 16.522 13.514 Modal 2 37.054 5.849 10.948 Modal 3 -34.076 2.291E-2 5.603 Fixed Base Modal 4 8.258E-3 25.378 -22.900 Modal 5 66.903 -9.451 18.251 Gravity 0.179 0.404 360.799 Directions 1, 2, 3 represent X, Y, Z axis respectively; Gravity load equals to dead and live load Structure Type

Type

For example the joint reaction , Figure 3.17, for the isolated base building in X-direction equals to SQRT (0.6842+0.7482+0.8672) = 1.33 kips, while for the fixed base building it is equal to SQRT (3.134E-22+37.0542+34.0762+8.258E-32+66.9032) = 83.727 kips. Apparently, the joint reaction in fixed base building for column B.1 in X-direction is higher by 62.95 times than that of the base isolated building. While the base reactions for response spectrum are computed for each mode and then the modes are combined using CQC or SRSS modal combination rule:

[67]

[68]

∑

√∑

Where for the base reaction, all join reactions from all columns must be computed [CSI 2012].

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Figure 3. 17 Base Isolation joint reactions in joint local coordinate system (MODAL) – Mode 1

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Chapter IV: Conclusions 4.1 General This study presents both theoretical investigation and modeling for building subjected to earthquake-induced load with fixed base and with base-isolated method using rubber bearing. The objective of this work is to contribute to the efficient design of base-isolated structure subjected to seismic ground motion. The following sections summarize the conclusions resulting from this research work as well as recommendations for future research.

4.2 Conclusions Based on the theoretical and modeling findings, the following conclusions can be drawn: 

The main observation from the modeling study on the accuracy of seismic effect and lateral load patterns utilized in the Multi-Modal Pushover analysis (MPA) in predicting earthquake effect showed that the accuracy of the pushover results depends strongly on the load path, properties of the structure and the characteristics of the ground motion.



The lateral deflection for MDOF for multi-story building can be represented as SDOF once the equivalent mass and stiffness is obtained.



The plastic hinge location varies by the type of loading, and the change in MODAL period. It can be located at any point along the span of member as well as the end of the member.



Drift index and inter-story drift should be predicted using the multi-modal (SRSS) and the elastic first mode with long period for the lateral load pattern which corresponds to the average in most cases.

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

Base-isolated structure exhibit less lateral deflection, as the lateral displacement at the base never equals to zero, and less moment values than the fixed base structure.



The base isolation decouples the building from the earthquake-induced load, and maintain longer fundamental lateral period than that of the fixed base.

4.3 Recommendations 1. Study the influence of the structural bearing properties and the stresses generated from tilting of the superstructure due to lateral loading. 2. Study the potential for liquefaction of the soil and its consequences on base-isolated buildings. 3. Establish design procedures and guidelines for Base-Isolation structure.

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References Al-Hussaini, T.M., Zayas, V.A., Constantinou, M.C., "Seismic Upgrade of Multi-Story Buildings Using the Friction Pendulum Isolation System," Proc., Tall Buildings in Developing Countries, International Conference on Tall Buildings, Dhaka, Bangladesh, June, 1993. C. Chia-Ming and B. F. Spencer, Jr., "An Experimental Study of Active Base Isolation Control for Seismic Protection," in Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems 2010, 8-11 March 2010, USA, 2010, p. 76473V (12 pp.). Chopra, A.R., “Dynamics of structures,” Prentice-Hall, New Jersy, USA, 2001. C.-M. Chang and B. F. Spencer, "Active base isolation of buildings subjected to seismic excitations," Earthquake Engineering and Structural Dynamics, vol. 39, pp. 1493-1512, 2010. C.-M. Chang and B. F. Spencer Jr, "An experimental study of active base isolation control for seismic protection," in Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems 2010, March 8, 2010 - March 11, 2010, San Diego, CA, United states, 2010, pp. The Society of Photo-Optical Instrumentation Engineers (SPIE); American Society of Mechanical Engineers; KAIST. CSI, “base reactions for response spectrum,” website: https://wiki.csiberkeley.com/display/kb/ Base+reactions+for+response+spectrum+analysis, accessed March 2012. Eggert, H., Kauschke, W., “Structural Bearings,” Ernst & Sohn, Germany, 2002. G.-F. Zhao and Y.-H. Ma, "Parameters study of rural buildings structures supported on slidelimited friction base isolation system," Zhendong yu Chongji/Journal of Vibration and Shock, vol. 30, pp. 148-152, 2011. G. Sun and A. Li, "Dynamic reliability analysis and parameter optimization of base isolation structure," Journal of Southeast University (Natural Science Edition), vol. 39, pp. 320-7, 2009. H.-J. Jung, et al., "Seismic performance analysis of a smart base-isolation system considering dynamics of MR elastomers," 55 City Road, London, EC1Y 1SP, United Kingdom, 2011, pp. 1439-1450. Honeck, W.C. and Westphal, D., “Practical design and detailing of steel column base plates,” Forell Elsesser Engineers, Inc, July 1999. Humar, J., Yavari, S., and Saatcioglu, M., “Design for forces induced by seismic Torsion”. Can. J. Civ. Eng., vol. 30, pp. 328-337, 2003. Humar, J., and Mahgoub, M.A., “Determination of seismic design forces by equivalent static load method,” Can. J. Civ. Eng., vol. 30, pp. 287-307, 2003. I. Iskhakov and Y. Ribakov, "Modern trends in base isolation applications for seismic protection of historic buildings," in 10th International Conference on Studies, Repairs and Maintenance of Heritage Architecture, STREMAH 2007, June 4, 2007 - June 6, 2007, Prague, Czech republic, pp. 623-632, 2007. J.-g. Sun, et al., "Experimental research on rubber base-isolation tank," Journal of the Harbin Institute of Technology, vol. 37, pp. 806-9, 2005. Li, H.-N, Wu, X.-X., “Limitation of height-to-width ration for base-isolated buildings under earthquake”, Structural Design of Tall Special Building, vol. 15, pp. 277-287, 2006. Lu, L., Chu, S., Yeh, S., Chung, L, “Seismic test of least-input-energy control with ground velocity feedback for variable-stiffness isolation systems”, Journal of sound and vibration, vol. 331, Oct., pp. 767-784, 2012.

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Mitchell, D., Tremblay, R. Karacebeyli, E., Paultre, P., Saatcioglu, M., and Anderson, D., “Seismic force modification factors for the proposed 2005 edition of the National Building Code of Canada,” Can. J. of Civ. Eng., vol. 30, pp. 308-327, 2003. Matsagar, V.A.,and Jangid, R.S. “Base isolation for seismic retrofitting of structures,” Practice Periodical on Structural Design and Construction, vol. 13, No. 4, pp. 175-185, Nov 1, 2008. M. Sener and S. Utku, "Active-passive base isolation system for seismic response controlled structures," in Proceedings of the 36th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference and AIAA/ASME Adaptive Structures Forum. Part 1 (of 5), April 10, 1995 - April 13, 1995, New Orleans, LA, USA, 1995, pp. 2350-2359. M. Sener and S. Utku, "Control of torsional modes in buildings under seismic excitation by adaptive base isolation," in Smart Structures and Materials 1996: Passive Damping and Isolation, Febrary 26, 1996 – Feb. 27, 1996, San Diego, CA, USA, 1996, pp. 145-156. M. Sener and S. Utku, "Adaptive base isolation system for the control of seismic energy flow into buildings," Journal of Intelligent Material Systems and Structures, vol. 9, pp. 104-15, 1998. Naeim, F & Kelly, J.M. 1999 N. J. Raufaste, "Earthquake resistant construction using base isolation," Publ by Natl Inst of Standards & Technology, Gaithersburg, MD, United States, 1992. NRCC, “National Building Code of Canada,” Associate Committee on the National Building Code, National Research Council of Canada, Ottawa, ON, 2005. Pozo, F., Ikhouane, F., and Pujol, G., “Adaptive backstepping control of hysteretic based-isolated structures,” Journal of Vibration and Control, vol. 12, issue 4, pp. 373-394, 2006. R. S. Jangid, "Optimum damping in a non-linear base isolation system," Journal of Sound and Vibration, vol. 189, pp. 477-87, 1996. Tedesco, J.W., McDougal, W.G., and Ross C.A., “Structural dynamics: Theory and applications,” Prentice Hall, USA, 1998. Tsai, C.S., Chiang,T.,-C, & Chen, B.-J., “Finite element formulations and theoretical study for variable curvature friction pendulum system”, Engineering structures, vol. 25, pp. 17191730, 2003. Y. Zhang, et al., "Parameters optimization of sliding base-isolation structure under the action of coupling earthquake," in 1st International Conference on Civil Engineering, Architecture and Building Materials, CEABM 2011, June 18, 2011 - June 20, 2011, Haikou, China, 2011, pp. 4021-4027. V. A. Matsagar and R. S. Jangid, "Base isolation for seismic retrofitting of structures," Practice Periodical on Structural Design and Construction, vol. 13, pp. 175-185, 2008.

Bibliography Mahmoud has more than 12 years of experience in the field of civil engineering. He has worked as civil (structural) engineer for 9 years in The Engineers Brothers Company, Cairo, Egypt. He also worked as Research & Graduate Assistant in Ryerson University, ON, Canada. He worked in EPCM (Engineering, Procurement, and Construction Management) industry for ICI (industrial, commercial & institutional) Buildings. He conducted research in the field of sandwich structure, glass fibre reinforced polymers (GFRP), post-tensioning, and bridges. Mahmoud has published 3 technical papers.

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Appendix A: Earthquake

A.1 Canadian seismic hazard map

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A.2 Seismic acceleration in Canada

A.3 Spectral response acceleration map Sa(0.2)

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2010 National Building Code of Canada seismic hazard maps [Source: www.earthquakescanada.nrcan.gc.ca]

The four spectral acceleration seismic hazard maps show levels of ground shaking at periods of 0.2, 0.5, 1.0 and 2.0 seconds (equivalent to frequencies of 5, 2, 1, and 0.5 Hertz). A high-rise of ten stories or more may sway with a natural period of 1 or 2 seconds, whereas in response to the same earthquake a brick bungalow across the street may vibrate at nearly 10 Hertz.

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B: Structural bearing

B.1 Selection guide for small rotation [AISI]

B.2 Selection guide for moderate rotation [AISI]

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B.3 Selection guide for large rotation [AISI]

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C: Earthquake time history

C.1 Time history function – LACC0

C.2 Time history function – LACC1

Citation: Sayed-ahmed, Mahmoud. Building with Base Isolation Techniques. Journal of Al-Azhar University Engineering Sector (JAUES), Vol. 7, No. 1, Dec. 2012, pp. 147-159.

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BUILDINGS WITH BASE ISOLATION TECHNIQUES (Report)

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