Modeling of Shear Walls for Nonlinear and

Pushover Analysis of Tall Buildings

Naveed Anwar, D. EngNaveed Anwar, D. EngNaveed Anwar, D. EngNaveed Anwar, D. Eng

Asian Center for Engineering Computations and Software, AIT

Asian Institute of Technology, Thailand

14th ASEP International Convention, Philippines, May 2009

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

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

Shear Wall or Column

Wall Column

Shear Wall or Frame

Shear Wall FrameShear Wall or Frame ?

Shear Wall or Truss?

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.

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

H=100 m

H=50 m

W=1

W=1

V

M

25 50 (2 times)

833 3,333 (4 times)

Seismic Code Development

Actual Elastic Demand Vs Code-mandated Design ForcesThe difference is expected be handled by

yielding, ductility, energy dissipation and reduction of demand

Typically handled by “Response reduction Factor”

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

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

Basic Vertical Seismic Systems

Moment Resisting Frame

Braced Frame Shear Walls

Typical Multi-Story Structural Systems

Nonlinear Performance Comparisons

� Six alternative structural systems compared by pushover plots for specific four-story 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

Nonlinear Performance Comparisons

Role of Shear Walls, Outriggers, Dampers.

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

Ductile Core Wall System Projects

Ductile Core Wall Structural System

One Rincon Hill in San Francisco, California (57-story, 625 feet)

3D View Lateral Force Resisting System

Plan View

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

Distinct Parts in a Wall

Yielding of horizontal ties and crushing of struts

Shear yield, severe diagonal cracking or concrete crushing

Shear yield or vertical crushing of concreteUndesirable

Yielding of vertical tiesYielding of longitudinal steelYielding of the vertical steelDesirable

Staggered openingsWell-defined vertical and horizontal segments

Vertical cantileverType

Strut and Tie Action in Right Part

Very Large Openings

may convert the Wall

to Frame

Very Small Openings

may not alter wall

behavior

Medium Openings

may convert shear

wall to Pier and

Spandrel System

Pier Pier

Spandrel

Column

Beam

Wall

Openings in Shear Walls

Main Aspects of behavior for Planner walls

In-Plane Behavior : Key Aspects

Unsymmetrical Bending Behavior

� As a cantilever bends and concrete cracks, the neutral axis shifts towards the compression side.

� If a beam element is connected to a shear wall, a beam element must be imbedded in the wall

Connecting a Beam to a Shear Wall

� 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

Coupling Beam Behavior - Bending

� 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

Coupling Beam Behavior - Shear

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

� Paulay and Priestly (“Seismic Design of Reinforced Concrete and Masonry Buildings”, Wiley, 1992)

Lp = 0.2 Dw + 0.044 he

Lp = hinge length

Dw = depth of wall cross section

he = 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.

Hinge Length for a Wall

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

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

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

Column Model for Planer Walls

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

BB

HH

tt

Column Models for Cellular Walls

� Difficult to extend the concept to

Non-planer walls

� Core Wall must be converted to

“equivalent” column and

appropriate “rigid” elements

� Can be used in 2D analysis but

more complicated for 3D analysis

� After the core wall is converted to

planer wall, the simplified procedure can used for modeling

BB

HH

tt

BB

HH

2t2t

tt

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

Single Column Model

Frame ElementShear Wall

Moment Hinge, directly using the Moment Curvature

of the Wall Section, multiplied by Hinge Length

Axial Load-Deformation Hinge Property

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

Fiber or Frame Model

Discretized into Frame Elements. Each

column acts as a “Fiber” representing

part of the wall

Shear Wall Section

Diaphragm constraint and

Beam constraint

Diaphragm constraint and

Beam constraint

Diaphragm constraint and

Beam constraint

Axial hinge

Shear link

Release moment in both ends of fiber

element

Fiber or Frame Model

� Shear link

element is

used to provide shear

stiffness

Fiber or Frame Model

Axial Hinges

Hinges for Nonlinear Modeling

� Upper Portion is assumed or designed to be Elastic

� Axial Hinges for Column Fibers

� Moment Hinges for the Spandrel

Moment Hinges

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

Strut and Tie Model

C

tB

t x 2t

t x t

Strut and Tie Model

Full WallWall with Opening

Opening

OpeningDisplacement controlled Axial Hinges

Force Controlled Axial Hinges

matching shear capacity

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

Nonlinear Layered Shell

Layered Shell Nonlinear stress-strain curve of concrete

Nonlinear stress-strain curve of steel

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

Shear Wall Model using Shell Elements

Nonlinear behavior

in vertical rebar

Nonlinear behavior in S22

component of concrete

S22

S11S12

N = Nonlinear, L = Linear

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

Comparative Study

Wall -01: Planner Wall

20 Stories @ 3.2 m = 64 m

Comparative Study

20 Stories @ 3.2 m = 64 m

Wall -02: Core Wall with Opening

Time Period Comparison

ModeSingle Column

(Cracked)

sec

Full Shell(Gross)

sec

Full Shell (Cracked)

sec

Fiber/ Framesec

Strut and Tiesec

1 2.24 1.58 1.59 1.49 1.42

2 0.37 0.26 0.27 0.25 0.25

3 0.14 0.10 0.10 0.09 0.12

4 0.08 0.08 0.08 0.08 0.10

Planner Wall

ModeSingle Column

(Cracked)sec

Full Shell(Gross)

sec

Full Shell (Cracked)

sec

Fiber or Framesec

Strut and Tiesec

1 2.85 1.85 1.87 1.83 2.16

2 2.06 1.43 1.45 1.41 1.61

3 0.47 0.31 0.32 0.30 0.38

4 0.35 0.25 0.27 0.24 0.31

Core Wall

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

Moment-Curvature Relationship

Planner Wall

Moment-Curvature (Planner Wall)

0

500

1000

1500

2000

2500

3000

3500

4000

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

Curvature

Mo

me

nt

(To

n-m

)

Single Column

Strut and Tie

Fiber or Frame

Nonlinear Shell

Moment-Curvature Relationship

Core Wall

Moment-Curvature (Core Wall)

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045

Curvature

Mo

me

nt

(To

n-m

)

Single Column

Fiber or Frame

Strut and Tie

Base Shear Vs. Top Displacement (Ton, m)

Planner Wall

Core Wall

Fiber or Frame Model Strut and Tie Model

Hinge Formation

Fiber/Frame Strut and Tie Fiber/Frame Strut and Tie

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

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

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