Shear wall design - muros de corte Etabs

Buddhi S. Sharma
ACECO MS, AIT
Design of Shear Walls Using ETABS
O-SCAAD-1
May 21, 2002, AIT, Bangkok

ACECOMS, AIT
Design of Shear Walls
The Basic Issues
• What is a Shear Wall?
• Modeling and analysis issues
– Transfer of loads to shear walls
– Modeling of shear walls in 2D
– Modeling of shear Walls in 3D
– Interaction of shear-walls with frames
• Design and detaining issues
– Determination of rebars for flexure
– Determination of rebars for shear
– Detailing of rebars near openings and corners
– Design and detailing of connection between various components
of cellular shear walls

ACECOMS, AIT
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

ACECOMS, AIT
Shear Wall or Column
Wall Column

ACECOMS, AIT
Shear Wall or Frame
Shear Wall Frame
Shear Wall or Frame ?

ACECOMS, AIT
Shear Wall or Truss?

ACECOMS, AIT
Planner Walls
Planer Stiffened Regular
Openings
Irregular Openings

ACECOMS, AIT
Cellular Walls

Location and
Layout of
Shear Walls

ACECOMS, AIT
Purpose of Shear Walls
• Resist the lateral loads for medium rise buildings
up to 40 floors
– Reduce total deflection and story drift
– Increase lateral stiffness
– Reduce moments in columns and floor members due to
lateral loads
– Reduce the overall cost of the structural system
– Can also serve as elevator shafts, service ducts, etc,

ACECOMS, AIT
Loads Transferred to Shear Walls
• Distribution of lateral loads to individual shear walls, to
moment resisting frames, to wall-frames and to
individual columns depends on:
– Stiffness of each column and wall
– Lateral stiffness of each frame or wall frame
– Location of the the vertical unit with respect to the load building
lateral stiffness center
– Location of the load center with respect to the stiffness center
– The geometry and in-plane stiffness of the floor slab system

ACECOMS, AIT
Load Transferred to Shear Walls
f
Building Plan
D
F
Stiffness
Center
Load Center
?
?

ACECOMS, AIT
How to Locate the Walls
• Reduce the eccentricity between the stiffness center and
the load center
– Consider Eccentricity due to Wind Loads, depending on overall
geometry of the structure
– Consider Eccentricity due to Earthquake Loads, depending on
Mass Distribution
– Consider Eccentricity not only at foundation level but at various
heights
• Reduce the in-plane bending in the slab system and
Evenly distribute the stiffness in both directions
• Use building layout in plan to enhance overall stiffness
and reduce need for shear walls

ACECOMS, AIT
How to Check Eccentricity!
• For Wind Loads
– Apply Wind load in X-Direction and check nodal displacements. If
displacement in Y-Directions are nearly zero or very small, then
there is no eccentricity between wind load and and stiffness center
in Y-direction
– Repeat the same for Y-Direction Load
• Seismic Loads
– Assign the Mass properties to the building and carryout a Modal
Analysis: If the first two modes are Translational, and third mode is
Torsional, then there is no eccentricity between the mass center and
Stiffness Center in Both Directions

ACECOMS, AIT
Eccentric and Concentric Response
F
No Eccentricity
D
F
Eccentric Shear Wall

ACECOMS, AIT
Eccentric and Concentric Response
Mode-1 Mode-2 Mode-3
Symmetrical Mass and
Stiffness
Unsymmetrical Mass and
Stiffness

ACECOMS, AIT
Avoid Eccentricity in Plan
Or

ACECOMS, AIT
Reduce In-plane Bending in Floor

ACECOMS, AIT
Vertical Irregularity
Expansion
Joint
Balanced Shear
Walls at All Levels
No Shear Walls Using Expansion
Joints to eliminate
some walls

ACECOMS, AIT
Using Efficient Building Plan Shape

ACECOMS, AIT
Shear Wall and Frame Behavior
Shear Wall Behavior Frame Behavior

ACECOMS, AIT
2
5
10
Axial Stresses in Planer Walls

ACECOMS, AIT
2
5
10
Axial Stresses in Cellular Walls
Uniaxial Bending

ACECOMS, AIT
2
5
10
Axial Stresses in Cellular Walls
Biaxial Bending

ACECOMS, AIT
Modeling of Planer Walls
Using Beam and Column Using Panels, Plates and Beams
Using Truss

ACECOMS, AIT
Modeling of Shear Walls
Using Beam Elements

ACECOMS, AIT
Frame Models for Shear Walls
– 4-Node plane element does not accurately capture the
linear bending, because constant shear distribution is
assumed in formulation but actually shear stress
distribution is parabolic
– Since the basic philosophy of RC design is based on
cracked sections, it is not possible to use the finite
elements results directly for design
– Very simple model (beam-column) which accurately
captures the behavior of the structure, and the results
can be used directly to design the concrete elements

ACECOMS, AIT
Modeling of Walls using 1D Elements
L
t x h
L
t
H2
H1
Simple beam
elements
L
t
Beam elements
with rigid ends
Beam elements
in “Truss Model”

ACECOMS, AIT
Frame 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
B
H
t

ACECOMS, AIT
Frame 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 cab used for modeling
B
H
t
B
H
2t
t

ACECOMS, AIT
Using Plate/Shell Elements
1
2
3
U1, R1
Node 3
U3, R3
U2, R2
U1, R1
Node 1
U3, R3 U2, R2
U1, R1
Node 4
U3, R3
U2, R2
U1, R1
Node 2
U3, R3
U2, R2
Shell

ACECOMS, AIT
Modeling Walls using 2D Elements
• Walls are subjected to in-plane deformations so
2D elements that have transnational DOF need
to be used
• A coarse mesh can be used to capture the
overall stiffness and deformation of the wall
• A fine mesh should be used to capture in-plane
bending or curvature
• General Shell Element or Membrane Elements
can be used to model Shear Walls

ACECOMS, AIT
Modeling Walls Using Membrane
Nodes: 4
DOFs: 2 (or 3) DOFs /Node Ux and Uy
2-Translation, 0 or 1 rotation
Dimension: 2 dimension element
Shape: Regular / Irregular
Properties: Modulus of Elasticity(E),
Poisson ratio(v),
Thickness( t )

ACECOMS, AIT
Modeling Walls using Shell Elements
Nodes: 4
DOFs: 5 or 6 DOFs /Node Ux and Uy
3 Translation, 2 or 3 rotation
Dimension: 2 dimension element
Shape: Regular / Irregular
Properties: Modulus of Elasticity(E),
Poisson ratio(v),
Thickness( t )
1
2
3
U1, R1
Node 3
U3, R3
U2, R2
U1, R1
Node 1
U3, R3 U2, R2
U1, R1
Node 4
U3, R3
U2, R2
U1, R1
Node 2
U3, R3
U2, R2
Shell

ACECOMS, AIT
Using Panel/ Plate Elements
Modeling Shear-Walls
using Panels only
(No Moment continuity
with Beams and Columns unless
6 DOF Shell is used)
Modeling Shear-Walls using Panels,
Beams, Columns
(Full Moment continuity
with Beams and Columns is restored by
using additional beams)

ACECOMS, AIT
Using Plates to Model Walls
Multiple elements greater accuracy in determination of stress distribution
and allow easy modeling of openings
Using Plate Elements only
(No Moment continuity
with Beams and Columns unless
6 DOF Shell is used)
Using Plate Elements with
Beams, Columns
(Full Moment continuity
with Beams and Columns)

ACECOMS, AIT
Connecting Walls to Slab
In general the mesh in the slab
should match with mesh in the wall
to establish connection
Some software automatically
establishes connectivity by using
constraints or “Zipper” elements
“Zipper”

ACECOMS, AIT
Using Truss Models
C
t
B
t x 2t
t x t

ACECOMS, AIT
Using Trusses to Model Shear Walls
• The behavior of shear walls can be closely
approximated by truss models:
– The vertical elements provide the axial-flexural
resistance
– The diagonal elements provide the shear resistance
• Truss models are derived from the “strut-tie”
concepts
• This model represents the “cracked” state of the
wall where all tension is taken by ties and
compression by concrete

ACECOMS, AIT
2
5
10
Truss Model for Shear Walls
Comparing Deformation and
Deflections of Shell Model with
Truss Model

ACECOMS, AIT
Truss Model for Shear Walls
2
5
10
Comparing Deformation and
Deflections of Shell Model
with Truss Model

ACECOMS, AIT
2
5
10
Truss Models for Shear Walls
Comparing Axial Stress and Axial
Force Patterns

ACECOMS, AIT
2
5
10
Truss Models for Shear Walls
Uniaxial Biaxial

ACECOMS, AIT
How to Construct Truss Models
• For the purpose of analysis, assume the
main truss layout based on wall width
and floor levels
• Initial member sizes can be estimated as
t x 2t for main axial members and t x t for
diagonal members
• Use frame elements to model the truss.
It is not necessary to use truss
elements
• Generally single diagonal is sufficient for
modeling but double diagonal may be
used for easier interpretation of results
• The floor beams and slabs can be
connected directly to truss elements
C
t
B
t x 2t
t x t

ACECOMS, AIT
Openings in Shear Walls

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

ACECOMS, AIT
Openings in Shear Walls - Cellular
2
5

ACECOMS, AIT
Openings in Shear Walls - Planer

ACECOMS, AIT
Modeling Walls with Opening
Plate-Shell Model Rigid Frame Model Truss Model

ACECOMS, AIT
Frame Model of Shear Walls
3 DOF
per rigid zone
Rigid Zones
Beams
Columns
A: Shear Wall with Line Loads B: Finite Element Model
C: Define Beams & Columns D: Beam-Column Model
Based on Concept proposed by E.L. Wilson

ACECOMS, AIT
Basic Design Considerations
• Main Shear Wall
– Flexural Design
– Shear Design
• Spandrels and Links
– Flexural Design
– Shear Design
• Ductility Considerations
• Anchorage with Footings
• Connection with Floor Slab/ Beams

ACECOMS, AIT
Flexural Design

ACECOMS, AIT
Flexural Design
As Single Flexural Member

ACECOMS, AIT
Designing as A Flexural Member
• Approach
– Design the Wall as “Big Column”
– Follow the normal axial-flexural
concept and provisions
• Input Needed
– P, Mx , (and My)
– Wall Dimensions
• Problems
– Does not consider the non-linear
strain distribution
– In efficient rebar distribution

ACECOMS, AIT
Design Procedure
1. Obtain Design Actions from Analysis
2. Assume rebar sizes, amount and distribution
3. Determine Cross-section capacity as column in
form of Interaction Surfaces and Curves
4. Check if all action sets (P, Mx, My) fall within
the interaction surface. The extreme values
should be near the surface
5. If required, revise cross-section and repeat

ACECOMS, AIT
Getting Result from Frame Model
Design actions (P, Mx, My and V) are obtained directly
Vx
Vy
P
Mx
My
V
P
M

ACECOMS, AIT
Getting Results from Truss Model
C
T
D
Tension
Member
Compression
Member
V
P
M
)
cos(
)
sin(
)
sin(



D
V
x
D
Cx
Tx
M
D
C
T
P
d
c
t







xc
xt
xd

ACECOMS, AIT
Getting Results From Shell Model
f1, f2, …..fn are the nodal stresses at
section A-A , obtained from analysis
CL of wall
A
A










n
i
i
i
i
n
i
i
n
i
i
i
i
i
v
A
V
x
F
M
F
P
f
A
F
1
1
1
f1
f2
f3
f4
f5
C
T
1
x
x1
t
V
P
M

ACECOMS, AIT
Assuming Reinforcement
• Assume larger bars on the corners
• Assume more bars on predominant tension
direction/ location
• Assume uniform reinforcement on wall sides
• Total Rebars ratio should preferably be more
than 0.8% and less than 3% for economical
design

ACECOMS, AIT
Obtaining Section Capacity Curves
• Can be done manually by using linear strain
distribution and equilibrium conditions
– Generate few control points on the curve
– Difficult to apply for Cellular and non rectangular walls
• Can be obtained in more complete form using
Software
– CSI-Section Builder
– GEAR – Column Section Module
– PCA Column

ACECOMS, AIT
Interaction Curves - Uniaxial
The curve is generated by varying
the neutral axis depth






















zi
N
i
si
z A
c
ny
N
i
si
A
c
nx
d
A
f
dz
da
f
M
A
f
da
f
N
si
b
si
b
1
1
.
)
(
)
(




Safe
Un-safe

ACECOMS, AIT
Interaction Surface - Biaxial
The surface is
generated by
changing Angle and
Depth of Neutral
Axis
+ Mz
- My
+P
+ My
- Mz
Pu
A cross-section of
interaction surface at P u
Safe
Un-safe
 
 
 































 

 
  



...
)
,
(
1
...
.
,
1
...
)
,
(
1
...
.
,
1
...
)
,
(
1
...
,
1
1
2
1
3
1
2
1
2
1
2
1
1
i
n
i
i
i
x y
y
i
n
i
i
i
x y
x
x y
n
i
i
i
z
x
y
x
A
x
dy
dx
y
x
M
y
y
x
A
y
dy
dx
y
x
M
y
x
A
dy
dx
y
x
N
















ACECOMS, AIT
Interaction Surface and Curves

ACECOMS, AIT
Narrow Planner Walls
The capacity is almost completely un-
axial
Moment capacity can be increased by
providing Rebars at the corners

ACECOMS, AIT
Cellular Wall – No Opening
The capacity is
almost completely
biaxial

ACECOMS, AIT
Single Cell Walls

ACECOMS, AIT
Double Cell Walls

ACECOMS, AIT
Flexural Design
Using Axial Zones

ACECOMS, AIT
Design Walls in Zones
• Basic Concept
– Design the wall to resist the external actions by
compression, tension and shear zones
– More intuitive and more economical
– Zone of high tension designed as tension member
with concentrated rebars
– Zone of high compression designed as compression
member with appropriate rebar limits
– Zone of low stress design as wall with nominal wall
rebars

ACECOMS, AIT
Designing as Axial Zones

ACECOMS, AIT
Design Procedure
1. Obtain Design Actions from Analysis
2. Compute Axial Forces
3. For each axial force, assume section, assume
rebars and check capacity
4. If capacity not enough, revise section, re-
compute Axial Forces, and continue until
required section for each force is designed
5. Provide nominal wall reinforcement in between
the axial zones

ACECOMS, AIT
Getting Result from Frame Model
Compute Forces from Actions
P
Mx
My
P
M
2
2
1
1
/
5
.
0
/
5
.
0
x
M
P
F
x
M
P
F




i
y
i
x
i
x
M
y
M
P
F 


4
x1 x2 yi
F1 F2
Fi

ACECOMS, AIT
Getting Results from Truss Model
C
T
D
Tension
Member
Compression
Member
xc
xt
xd
Results obtained from truss
analysis can be used Directly
F1 = T
F2 = C

ACECOMS, AIT
Getting Results From Shell Model
f1, f2, …..fn are the nodal stresses at
section A-A , obtained from analysis
CL of wall
A
A
i
i
i
i
i
f
A
F
t
x
A


f1
f2
f3
f4
f5
C
T
1
x
x1
t
F1=T F2=C

ACECOMS, AIT
Axial Zone Model – Planer Wall

ACECOMS, AIT
Axial Zones for Box Wall

ACECOMS, AIT
Design as Truss: Strut and Tie
• Directly design the
tension members for
reinforcement
• Directly design the
compression members
as columns
• The design is similar to
the “Axial Zones”
concept

ACECOMS, AIT
Concrete Shear Wall Design in ETABS
• 2D wall pier design and boundary-member checks
• 2D wall spandrel design
• 3D wall pier check for provided reinforcement
• Graphical Section Designer for concrete rebar location
• Graphical display of reinforcement and stress ratios
• Interactive design and review
• Summary and detailed reports including database
formats

ACECOMS, AIT
Shear Design
Spandrel
Pier

ACECOMS, AIT
Shear Design Procedure
• For Walls without Openings
– Design the wall as piers
• For Walls with Openings
– Design the Piers, the vertical part
– Design the Spandrels, the horizontal part

ACECOMS, AIT
Shear Design of Pier
• Determine Concrete
shear capacity, Vc
• Check if Vc exceeds the
limit, if it does, section
needs to be revised
• Determine steel Rebars
for Vs=V-Vc
• Check additional steel for
seismic requirements
p
L
p
t

ACECOMS, AIT
ACI Equations for Pier Design
   
p
p
u
p
p
c
LW
c
L
L
.
P
L
.
t
f
R
.
V
4
8
0
8
0
3
3 


 
p
p
p
u
u
p
p
u
c
LW
p
c
LW
c L
.
t
L
V
M
Abs
t
L
P
.
f
R
.
L
f
R
.
V 8
0
2
2
0
25
1
6
0




































 
 
p
ys
c
u
v
L
.
f
V
V
Abs
A
8
0



   
p
p
c
LW
u
L
.
t
f
R
V
Abs
8
0
10 


Basic Concrete Shear Capacity
Concrete not to Exceed the limit
Area of Steel Computed as

ACECOMS, AIT
Shear Design for Spandrel
top
r
d 
bot
r
d 
a
c
s
h
s
t
s
h
s
L
Elevation
Section
• Determine Concrete
shear capacity, Vc
• Check if Vc exceeds the
limit, if it does, section
needs to be revised
• Determine steel Rebars
for Vs=V-Vc
• Check additional steel for
seismic requirements

ACECOMS, AIT
ACI Equations for Spandrel Design
s
s
c
LW
c d
t
f
R
V

 2
c
u
c
n
s V
V
V
V
V 




s
s
c
LW
s d
t
f
R
V 
 8
s
ys
s
v
d
f
V
A 
Basic Concrete Shear Capacity
Concrete not to Exceed the limit
Area of Steel Computed as
Check for minimum steel and spacing etc.

ACECOMS, AIT
ACI Equations for Spandrel Design
5

s
s
d
L
When and c
u
V
.
V
5
0


0
50


min
h
ys
s
min
v
A
f
t
A
When 5

s
s
d
L
and c
u
V
.
V
5
0


0

 min
h
min
v A
A
When 5
2 

s
s
d
L
Check
s
s
c
LW
s
s
u
d
t
f
R
d
L
V










 10
3
2
 s
min
h
s
min
v
t
.
A
t
.
A
0025
0
0015
0



ACECOMS, AIT
Notations for Shear Design
top
r
d 
bot
r
d 
s
h
s
t = Thickness of Spandrel
= Distance from top of spandrel to the centroid of top reinforcing
= Distance from bottom of spandrel to the centroid of bottom reinforcing
= Total depth of spandrel
LW
R = Shear reduction factor as specified in the concrete material properties for
light weight concrete.
s
d = Effective depth of spandrel
s
V = Portion of Shear force in spandrel carried by reinforcing steel
c
V = Portion of Shear force in spandrel carried by concrete
s
L = Length of Spandrel

ACECOMS, AIT
Notations for Shear Design
p
t = Thickness of Pier
p
L = Length of Pier
min
v
A = Minimum vertical required area of distributed shear reinforcing
min
h
A = Minimum horizontal required area of distributed shear reinforcing
n
V = Nominal Shear strength
ys
f = Shear yield strength of steel
c
f  = Concrete Compressive Strength

ACECOMS, AIT
Wall Section
• Place more reinforcement at the ends and distribute the
remaining in the middle portion
• Confine the Rebars at the end for improved ductility and
increased moment capacity
Option -1
Option -2
Option -3

ACECOMS, AIT
Effect of Rebar Layout
Moment Capacity for 1% Rebars
a) Uniform Distribution
b) Concentrated Bars
Max M= 380
Max M= 475
Nearly 25% increase for same steel

ACECOMS, AIT
Wall Section
• Place more reinforcement at
the corners and distribute the
remaining in the middle
portion
• Confine the Rebars at the
corners for improved
ductility and increased
moment capacity
• Provide U-Bars at the
corners for easier
construction and improved
laps

ACECOMS, AIT
Effect of Rebar Layout
Moment Capacity for 1% Rebars
a) Uniform Distribution
b) Concentrated Bars
Nearly 20% increase for same steel
Max M= 16500
Max M= 19600

ACECOMS, AIT
Rebar Detailing For Openings

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