Modeling of Shear Walls for Nonlinear and Pushover Analysis of Tall Buildings

Transcription

1 Asian Center for Engineering Computations and Software, AIT Asian Institute of Technology, Thailand 14th ASEP International Convention, Philippines, May 2009 Modeling of Shear Walls for Nonlinear and Pushover Analysis of Tall Buildings Naveed Anwar, D. Eng

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3 Some of the Questions Related to Shear Walls What is a Shear Wall How does a Shear Wall behave What is the normal role of Shear Wall What role a Shear Wall can play How to Model and Design the Shear Walls for the intended role

4 What is a Shear Wall? How can we tell when a member is a shear wall Is the definition based on? Intended Use Shape in Cross-section Geometry in Elevation Loading Type and Intensity Behavior and Theory Location, Direction, Orientation

5 Shear Wall or Column Wall Column

6 Shear Wall or Frame Shear Wall Shear Wall or Frame? Frame

7 Shear Wall or Truss?

8 Conventional Role of Shear Walls Provide lateral stiffness to buildings Reduce Drift Ratio Reduce wind-induced acceleration Provide strength against lateral loads Shift moment and shear away from frame members Change the deformation and mode of the building Interact with frames to convert shear and moment to axial forces through outriggers etc.

9 Tall Shear Wall Design Primarily governed by Flexural Strength, can be allowed to yield at well defined locations Shear is generally not the critical factor for tall shear walls All walls must and can remain elastic in shear without failure V M W=1 W=1 H=50 m H=100 m (2 times) 833 3,333 (4 times)

10 Seismic Code Development Actual Elastic Demand Vs Code-mandated Design Forces The difference is expected be handled by yielding, ductility, energy dissipation and reduction of demand Typically handled by Response reduction Factor

11 New Design Approaches Current building codes do not adequately address many critical aspects in seismic design of tall buildings Performance based design provides a desirable alternative Reinforced concrete walls are effective to resist lateral loads while providing good performance Various approaches exist to predict the reliable nonlinear and inelastic response of RC walls

12 Performance Based Design in International Context Explicitly stated by local authorities in some countries such as Japan and China UBC, IBC and other codes provide little-to-no specific guidance Eurocode 8 is not performance based Much framework for performance based design is in Vision 2000, ATC40 and FEMA 356 Recently, performance based design of high-rise buildings issued in LATBSDC 2008 and SEAONC 2007

13 Basic Vertical Seismic Systems Moment Resisting Frame Braced Frame Shear Walls

14 Typical Multi-Story Structural Systems

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16 Nonlinear Performance Comparisons Six alternative structural systems compared by pushover plots for specific fourstory building BF Braced Frame SW Shear Wall EBF Eccentric Braced Frame MF Steel Moment Frame MF+Dampers Steel Moment Frame with Passive Dampers BI Base Isolation

17 Nonlinear Performance Comparisons

18 Role of Shear Walls, Outriggers, Dampers.

19 Ductile Core Wall Structural System Offer lower costs, faster construction and flexible architecture Seismic forces are resisted by reinforced core surrounded by elevator banks For buildings 100 m or taller, core has a minimum dimension of 10 m in plan and 50cm 90cm thick Concrete Core Wall Building under Construction, the Washington Mutual/Seattle Art Museum

20 Ductile Core Wall System Projects

21 Ductile Core Wall Structural System 3D View Lateral Force Resisting System Plan View One Rincon Hill in San Francisco, California (57-story, 625 feet)

22 Modeling and Analysis Goals For static push-over analysis, overall strength should be calculated correctly and the stiffness along the curve should be essentially accurate. For a dynamic analysis, the cyclic behavior and energy dissipation should be essentially correct Meaningful deformation demand-capacity values and usage ratios should be calculated for assessing performance The demand-capacity values and deflected shape should show any concentrations of damage The Goal is to get results that can be useful for design, not to get an exact simulation of the behavior

23 Distinct Parts in a Wall Type Vertical cantilever Well-defined vertical and horizontal segments Staggered openings Desirable Yielding of the vertical steel Yielding of longitudinal steel Yielding of vertical ties Undesirable Shear yield or vertical crushing of concrete Shear yield, severe diagonal cracking or concrete crushing Yielding of horizontal ties and crushing of struts Strut and Tie Action in Right Part

24 Openings in Shear Walls Very Small Openings may not alter wall behavior Medium Openings may convert shear wall to Pier and Spandrel System Very Large Openings may convert the Wall to Frame Spandrel Beam Wall Pier Pier Column

25 Main Aspects of behavior for Planner walls In-Plane Behavior : Key Aspects

26 Unsymmetrical Bending Behavior As a cantilever bends and concrete cracks, the neutral axis shifts towards the compression side.

27 Connecting a Beam to a Shear Wall If a beam element is connected to a shear wall, a beam element must be imbedded in the wall

28 Coupling Beam Behavior - Bending Elastic Behavior Curvature varies linearly along length There may be significant local deformation in the pier Actual Behavior Plastic zone may form near end Crack may open because of bond slip

29 Coupling Beam Behavior - Shear Elastic Behavior Compression diagonal shortens Tension diagonal extends Beam as a whole does not extend Actual Behavior with Conventional Reinforcement Vertical steel yields Horizontal steel does not yield Beam as a whole does not extend Actual Behavior with Diagonal Reinforcement Tension diagonal yields Compression diagonal has a much smaller deformation Beam as a whole must increase in length

30 Handling Nonlinearity in Shear Walls Hinging is expected in shear walls near the base Difficult to convert a large shear wall core into an equivalent column and beam system The question remains on how to effectively models Another major question is the length of the hinge zone

31 Hinge Length for a Wall Paulay and Priestly ( Seismic Design of Reinforced Concrete and Masonry Buildings, Wiley, 1992) L p = hinge length D w = depth of wall cross section L p = 0.2 D w h e h e = effective wall height (height of cantilever wall with a single load at the top and the same moment and shear at the hinge as in the actual wall A larger shear (i.e., a larger bending moment gradient) gives a smaller hinge length FEMA 356 recommends a hinge length equal to smaller of (a) one half the cross section depth (b) the story height.

32 Nonlinear Modeling of Shear Walls For Elastic Model Shell or Membrane model is common Normal shell model can not handle Nonlinearity or hinging A Study carried out to compare various methods in an attempt to answer the questions 1. Single Column model 2. Fiber or Frame model 3. Strut and Tie model 4. Nonlinear Layered Shell model

33 The Main Comparative Parameter The Moment Curvature of the Wall Section is used as the reference for comparison of the wall model response This is reasonable, as the wall is tall enough to deform in flexure

34 Single Column Model Simplest model Equivalent column at the center line of wall section Rigid links are required to make deformation compatibility Non-linear axial-flexural hinges at the top and bottom Optional shear hinges at the mid height Requires predefined hinge length Suitable for walls of small proportions Difficult to handle cellular core walls or walls with openings Disregards the wall rocking and effect of neutral axis shift Used as reference model and quick assessment of performance

35 Column Model for Planer Walls H B tt Rigid Zones Specially Suitable when H/B is more than 5 The shear wall is represented by a column of section B x t The beam up to the edge of the wall is modeled as normal beam The column is connected to beam by rigid zones or very large cross-section

36 Column Models for Cellular Walls tt Difficult to extend the concept to Non-planer walls H B Core Wall must be converted to equivalent column and appropriate rigid elements Can be used in 2D analysis but more complicated for 3D analysis H 2t tt After the core wall is converted to planer wall, the simplified procedure can used for modeling B

37 Single Column Model Disregards the neutral axis shift on vertical displacements Disregards the rocking of wall Computes Response assuming plane -Section remain plane Not suitable for short/squat walls Can not capture geometric changes, openings, Single Column Model Behavior Experimentally Observed Behavior

38 Single Column Model Moment Hinge, directly using the Moment Curvature of the Wall Section, multiplied by Hinge Length Shear Wall Frame Element

39 Axial Load-Deformation Hinge Property

40 Fiber or Frame Model Wall section is discretized by closely spaced columns Nonlinear axial load-deformation hinges are used Different ductility shall be used for unconfined and confined portion of the wall Eliminate the predefined hinge length which is needed in single element models

41 Fiber or Frame Model Shear Wall Section Discretizedinto Frame Elements. Each column acts as a Fiber representing part of the wall

42 Fiber or Frame Model Shear link element is used to provide shear stiffness Diaphragm constraint and Beam constraint Axial hinge Diaphragm constraint and Beam constraint Shear link Diaphragm constraint and Beam constraint Release moment in both ends of fiber element Fiber or Frame Model

43 Axial Hinges

44 Hinges for Nonlinear Modeling Upper Portion is assumed or designed to be Elastic Axial Hinges for Column Fibers Moment Hinges for the Spandrel

45 Moment Hinges

46 Strut and Tie Model Extensively used for deep beams and shear walls Nonlinear axial load-deformation hinges are used Difficult to determine the size and reinforcement in diagonal elements Hinges in diagonal struts should be force control to detect shear failure or may or the diagonals may be forced to remain elastic

47 Strut and Tie Model t x t C B t x 2t t

48 Strut and Tie Model Opening Opening Displacement controlled Axial Hinges Force Controlled Axial Hinges matching shear capacity Full Wall Wall with Opening

49 Nonlinear Layered Shell This element is not available in many software yet Nonlinear stress-strain relationship is sampled at Gauss points Integration is performed by standard 2x2 Gauss points Equivalent to having two fibers in each local 1 & 2 directions Stresses at locations other than Gauss points are interpolated or extrapolated

50 Nonlinear Layered Shell Layered Shell Nonlinear stress-strain curve of concrete Nonlinear stress-strain curve of steel

51 Practical Shear Wall Model Membrane behavior of vertical stress in concrete S22 and rebar stress S11 is taken to be nonlinear Horizontal rebar is neglected Out of plane behavior is assumed liner, single concrete plate layer is used

52 Shear Wall Model using Shell Elements Nonlinear behavior in vertical rebar Nonlinear behavior in S22 component of concrete N = Nonlinear, L = Linear S22 S12 S11

53 Comparative Study Two walls are selected to compare the non linear pushover curves generated by various modeling technique Pushover analysis is performed by displacement control (top displacement of 5% drift) Inverted triangular loading is used Axial hinges are assigned in the mid length of the member for fiber or frame model and strut and tie models For the cracked section models, 50% bending stiffness and 40% shear stiffness of gross section are used

54 Comparative Study m = 64 m Wall -01: Planner Wall

55 Comparative Study m = 64 m Wall -02: Core Wall with Opening

56 Time Period Comparison Planner Wall Mode Single Column (Cracked) sec Full Shell (Gross) sec Full Shell (Cracked) sec Fiber/ Frame sec Strut and Tie sec Core Wall Mode Single Column (Cracked) sec Full Shell (Gross) sec Full Shell (Cracked) sec Fiber or Frame sec Strut and Tie sec

57 Time Period Comparison The Elastic stiffness should be represented realistically. This can be checked through time period comparison. It is difficult to estimate the level of cracking or the size of members for Fiber or Strut-Tie models. Shell Models tend to stiffer than others due to shear strain contribution and higher in-plane stiffness Loss of mass in Fiber and Strut and Tie model and overlapping mass in Column model should be considered Time is effected by nonlinear response due to reduction in stiffness

58 Moment-Curvature Relationship Planner Wall 4000 Moment-Curvature (Planner Wall) Moment (Ton-m) Single Column Strut and Tie Fiber or Frame Nonlinear Shell Curvature

59 Moment-Curvature Relationship Core Wall Moment-Curvature (Core Wall) Moment (Ton-m) Single Column Fiber or Frame Strut and Tie Curvature

60 Base Shear Vs. Top Displacement (Ton, m) Fiber or Frame Model Strut and Tie Model Planner Wall Core Wall

61 Hinge Formation Fiber/Frame Strut and Tie Fiber/Frame Strut and Tie

62 Limitations of Pushover Analysis Static pushover analysis is typically unidirectional, single pattern load analysis, in which most hinges will deform monotonically Higher mode contributions are not considered Material and section hysterics can not be considered directly The hinge properties typically will be based on the envelop curve from the expected hysteresis curves The material or section degradation due to cyclic response is not explicitly considered The Dynamic effects are not considered

63 Nonlinear Time History Analysis For a detailed nonlinear time history analysis, the effective of material as well as section level hysterics and degradation for cyclic response needs to be considered Although the basic modeling approaches presented for the static pushover analysis are also suitable for the NLTH, the hinge properties as well as modeling should represent the hysteric behavior The NLTH takes considerably more effort and understanding, specially for selection and scaling of Time

64 Conclusions The objective of this study was to investigate the various approaches of nonlinear modeling of shear walls to predict their nonlinear response by Pushover Analysis Refined fiber or frame model has the capability to represent the nonlinear flexural behavior more reliable than strut and tie model The fiber model can be used to estimate the extent of yielding in the shear walls and can be used to determine the hinge length more realistically than based on single or double story concept Both models lack the proper representation nonlinear shear behavior and shear flexural interaction behavior