Design of Shear Walls Using ETABS O-SCAAD-1 May 21, 2002, AIT, Bangkok
Buddhi S. Sharma ACECOMS, AIT
The Basic I ssues • 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
Design of Shear Walls
ACECOMS, AIT
Shear Wall Definition
Wh at i s 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
Design of Shear Walls
ACECOMS, AIT
Shear Wall or Column
Wall Design of Shear Walls
Column ACECOMS, AIT
Shear Wall or F r ame Shear Wall
Design of Shear Walls
Shear Wall or Frame ?
Frame
ACECOMS, AIT
Shear Wall or Tr uss?
Design of Shear Walls
ACECOMS, AIT
Plann er Walls
Planer Design of Shear Walls
Stiffened
Regular Openings
Irregular Openings
ACECOMS, AIT
Cellul ar Walls
Design of Shear Walls
ACECOMS, AIT
Location and Layout of Shear Walls
Pur pose 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,
Design of Shear Walls
ACECOMS, AIT
L oads Tr ansf er r ed 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 center the vertical unit with respect to the load building lateral stiffness – Location of the load center with respect to the stiffness center – The geometry and in-plane stiffness of the floor slab system
Design of Shear Walls
ACECOMS, AIT
L oad Tr ansf er r ed to Shear Walls ?
Load Center f
F
D
Stiffness Center
? Building Plan
Design of Shear Walls
ACECOMS, AIT
H ow to L ocate th e 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
Design of Shear Walls
ACECOMS, AIT
H ow to Che ck Eccentr icity! • 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
Design of Shear Walls
ACECOMS, AIT
Eccentr ic and Concentr ic Response F
No Eccentricity
F D
Eccentric Shear Wall
Design of Shear Walls
ACECOMS, AIT
Eccentr ic and Concentr ic Response Unsymmetrical Mass and Stiffness
Symmetrical Mass and Stiffness
Mode-1 Design of Shear Walls
Mode-2
Mode-3 ACECOMS, AIT
Avoid Eccentr icity in Pl an
Or
Design of Shear Walls
ACECOMS, AIT
Reduce I n-pl ane Bending in F loor
Design of Shear Walls
ACECOMS, AIT
Ver ti cal I r r egul ar ity
Expansion Joint
No Shear Walls
Design of Shear Walls
Balanced Shear Walls at All Levels
Using Expansion Joints to eliminate some walls
ACECOMS, AIT
Using Ef f icient B ui lding P lan Shape
Design of Shear Walls
ACECOMS, AIT
Shear Wall Behavior
Shear Wall and F r ame Behavior
Shear Wall Behavior
Design of Shear Walls
Frame Behavior
ACECOMS, AIT
Axial Str esses in Planer Walls 10
5
2
Design of Shear Walls
ACECOMS, AIT
Axial Str esses in Cellular Walls 10
Uniaxial Bending
5
2
Design of Shear Walls
ACECOMS, AIT
Axial Str esses in Cellular Walls 10
Biaxial Bending
5
2
Design of Shear Walls
ACECOMS, AIT
Modeling of Shear Walls
M odeling of Planer Walls
Using Truss
Using B eam and Column Design of Shear Walls
Using Panels, Plates and B eams
ACECOMS, AIT
Modeling of Shear Walls
Using Beam Elements
Design of Shear Walls
ACECOMS, AIT
F r ame M odels 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
Design of Shear Walls
ACECOMS, AIT
M odeling of Walls using 1D Elements Beam elements with rigid ends
Simple beam elements
Beam elements in “Truss Model”
H2
H1
t
t L Design of Shear Walls
L
txh L ACECOMS, AIT
F r ame M odel for Plane r Walls • Specially Suitable when H/B is more than 5
H
• The shear wall is represented by a column of section “B x t” • The beam up to the edge of the B
t
Rigid Zones
Design of Shear Walls
wall is modeled as normal beam • The “column” is connected to beam by rigid zones or very large cross-section
ACECOMS, AIT
F r ame M odels for Cellul ar Walls t
• Difficult to extend the concept to Non-planer walls
H
• Core Wall must be converted to “equivalent” column and appropriate “rigid” elements
B
2t H t B
Design of Shear Walls
• 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
ACECOMS, AIT
Modeling of Shear Walls
Using Plate/Shell Elements U3, R3
U3, R3 U2, R2
Node 3
U2, R2 Node 4
U1, R1 3
U1, R1
2
U3, R3 1
U3, R3
U2, R2
Node 1
U2, R2 Node 2
U1, R1
U1, R1
Shell
Design of Shear Walls
ACECOMS, AIT
M odeling Walls using 2D E lements • 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
Design of Shear Walls
ACECOMS, AIT
M odeling Wall s Using M embr ane
Nodes:
4
D O F s:
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 )
Design of Shear Walls
ACECOMS, AIT
M odeling 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 Thickness( t ) ratio(v),
U3, R3
U3, R3 U2, R2
Node 3
U2, R2 Node 4
U1, R1 3
U1, R1
2
U3, R3 1
U3, R3
U2, R2
Node 1
U2, R2 Node 2
U1, R1
U1, R1
Shell Design of Shear Walls
ACECOMS, AIT
Using Panel/ Pl ate Elements
Modeling Shear-Walls using Panels only
Modeling Shear-Walls using Panels, Beams, Columns
(No Moment continuity with Beams and Columns unless 6 DOF Shell is used)
(Full Moment continuity with Beams and Columns is restored by using additional beams)
Design of Shear Walls
ACECOMS, AIT
Using Plates to M odel 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)
Design of Shear Walls
Using Plate Elements with Beams, Columns (Full Moment continuity with Beams and Columns)
ACECOMS, AIT
Conn ecti ng Walls to Slab
“Zipper”
In general the mesh in the slab should match with mesh in the wall to establish connection
Design of Shear Walls
Some software automatically establishes connectivity by using constraints or “Zipper” elements
ACECOMS, AIT
Modeling of Shear Walls
Using Truss Models
txt
C t x 2t B Design of Shear Walls
t
ACECOMS, AIT
Using Tr usses to M odel 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 Design of Shear Walls
ACECOMS, AIT
Tr uss M odel f or Shear Walls 10
Comparing Deformation and Deflections of Shell Model with Truss Model
5
2
Design of Shear Walls
ACECOMS, AIT
Tr uss M odel f or Shear Walls 10
Comparing Deformation and Deflections of Shell Model with Truss Model
5
2
Design of Shear Walls
ACECOMS, AIT
Tr uss M odels f or Shear Walls 10
Comparing Axial Stress and Axial Force Patterns
5
2
Design of Shear Walls
ACECOMS, AIT
Tr uss M odels f or Shear Walls 10
5
2
Uniaxial Design of Shear Walls
Biaxial
ACECOMS, AIT
H ow to Constr uct Tr uss M odels
txt
•
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 x 2t t B Design of Shear Walls
ACECOMS, AIT
Modeling of Shear Walls
Openings in Shear Walls
Design of Shear Walls
ACECOMS, AIT
Openings in Shear Walls Very Small Openings may not alter wall behavior
Medium Openings may convert shear wall to Pier and Spandrel System
Beam
Spandrel
Column
Wall Pier
Design of Shear Walls
Very Large Openings may convert the Wall to Frame
Pier
ACECOMS, AIT
Openi ngs in Shear Walls - Cellul ar 5
2
Design of Shear Walls
ACECOMS, AIT
Openi ngs in Shear Wall s - Pl aner
Design of Shear Walls
ACECOMS, AIT
M odeling Wall s wi th Opening
Plate-ShellModel
Design of Shear Walls
RigidFrameModel
TrussModel
ACECOMS, AIT
F r ame M odel of Shear Walls
A : S h e ar Wa ll w ith L in e L o a d s
B : F in ite E le m en t M o d e l
Rigid Zones Beams 3 DOF per rigid zone
Columns
C: Define Beams & Columns
D: Beam-Column Model
Based on Con cept proposed by E.L . Wil son
Design of Shear Walls
ACECOMS, AIT
Design of Shear Walls
Basic Design Con sider ati ons • Main Shear Wall – Flexural Design – Shear Design
• Spandrels and Links – Flexural Design – Shear Design
• Ductility Considerations • Anchorage with Footings • Connection with Floor Slab/ Beams
Design of Shear Walls
ACECOMS, AIT
Flexural Design
Design of Shear Walls
ACECOMS, AIT
Flexural Design
As Single Flexural Member
Design of Shear Walls
ACECOMS, AIT
Designi ng as A F lexur al M ember • 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
Design of Shear Walls
ACECOMS, AIT
Design Pr ocedur e 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) fallvalues within the interaction surface. The extreme should be near the surface 5. If required, revise cross-section and repeat
Design of Shear Walls
ACECOMS, AIT
Getti ng Result f r om F r ame M odel Design actions (P, Mx, My and V) are obtained directly
P
M
Design of Shear Walls
P Vy
V
Vx
Mx
My
ACECOMS, AIT
Getti ng Results fr om Tr uss M odel P T
C D sin( ) M Txt Cxc D sin( ) xd V D cos( )
D
M
xd xt
Tension Member
Design of Shear Walls
P
C
T
V
xc
Compression Member
ACECOMS, AIT
Getti ng Results F r om Shell M odel CL of wall
Fi Ai f i n
P Fi i 1
P
A
A
M
n
M Fi xi i 1
V
n
V Ai vi i 1
t f5
x1
f4 f3
f2
T
f1
C x1
Design of Shear Walls
f1, f2, …..fn are the nodal stresses at section A-A , obtained from analysis
ACECOMS, AIT
Assumi ng Reinf or cement • Assume larger bars on the corners • Assume more bars on predominant tension direction/ location • Assume uniform reinforcement on wall sides • Total Rebars ratio preferably be more than 0.8% and lessshould than 3% for economical design
Design of Shear Walls
ACECOMS, AIT
Obtaining Secti on Capacity Cur ves • 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
Design of Shear Walls
ACECOMS, AIT
I nter action C ur ves - Uni axi al The cur ve is gener ated by var ying th e neutr al axi s depth
Un-safe N Nnx fc ( ) da fsi A i 1 A N Mny fc ( ) da.dz fsi A dzi i 1 z A b
Safe
si
b
si
Design of Shear Walls
ACECOMS, AIT
I nter action S ur f ace - Bi axi al +P
The surface is generated by changing Angle and Depth of Neutral Axis
A cross-section of interaction surface at P u
Un-safe
- My
Pu
Safe
- Mz
+ Mz
+ My
1
N z 1
1
1
i
x y
Mx
1 2 1
My
1 3 1
2
n
x, y dx dy ... A
i
( x, y ) ...
i 1
1
n
x, y dx dy . y ... A i
i
( x, y ) yi ...
1 Ai i ( x, y ) xi ... x y x, y dx dy . x ... 2 i 1
Design of Shear Walls
x y
2
i 1
n
ACECOMS, AIT
I nter acti on Sur f ace and Cur ves
Design of Shear Walls
ACECOMS, AIT
Nar r ow Plann er Walls The capacity is almost completely unaxial Moment capacity can be increased by providing Rebars at the corners
Design of Shear Walls
ACECOMS, AIT
Cellul ar Wall – No Opening The capacity is almost completely biaxial
Design of Shear Walls
ACECOMS, AIT
Single Cell Walls
Design of Shear Walls
ACECOMS, AIT
Double Cell Walls
Design of Shear Walls
ACECOMS, AIT
Flexural Design
Using Axial Zones
Design of Shear Walls
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 t ension 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
Design of Shear Walls
ACECOMS, AIT
Designi ng as Axial Zones
Design of Shear Walls
ACECOMS, AIT
Design Pr ocedur e 1. Obtain Design Actions from Analysis 2. Compute Axial Forces 3. For each axial force, assume section, assume rebars and check capacity 4. If capacityAxial not enough, revise section, recompute Forces, and continue until required section for each force is designed 5. Provide nominal wall reinforcement in between the axial zones
Design of Shear Walls
ACECOMS, AIT
Getti ng Result f r om F r ame M odel Compute Forces from Actions
P
P
My
Mx
M
F1
F2
Fi x1
x2
0.5 P M / x1 F2 0.5 P M / x 2 F1
Design of Shear Walls
yi
Fi
P 4
Mx yi
My xi
ACECOMS, AIT
Getti ng Results fr om Tr uss M odel
Results obtained from truss analysis can be used Directly
D
C
T xd xt
Tension Member
Design of Shear Walls
F1 = T F2 = C
xc
Compression Member
ACECOMS, AIT
Getti ng Results F r om Shell M odel CL of wall
A
A
F1=T
F2=C
t f5
x1
f4 f3
Ai Fi
f2
T
f1
C x1
Design of Shear Walls
xi t Ai f i
f1, f2, …..fn are the nodal stresses at section A-A , obtained from analysis
ACECOMS, AIT
Axi al Zone M odel – Pl aner Wall
Design of Shear Walls
ACECOMS, AIT
Axi al Zones for Box Wall
Design of Shear Walls
ACECOMS, AIT
Design as Tr uss: Str ut and Ti e • Directly design the tension members for reinforcement • Directly design the compression members as columns • The design is similar to the “Axial Zones” concept
Design of Shear Walls
ACECOMS, AIT
Concr ete Shear Wall Design i n ETAB S • 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
Design of Shear Walls
ACECOMS, AIT
Shear Design
Spandrel Pier
Design of Shear Walls
ACECOMS, AIT
Shear Design Pr ocedur e • 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
Design of Shear Walls
ACECOMS, AIT
Shear Design of Pi er • 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
Design of Shear Walls
Lp tp
ACECOMS, AIT
ACI Equations for Pier Design Basic Concrete Shear Capacity Vc 3.3RLW
f ct p 0.8L p
Pu 0.8L p 4 Lp
Concrete not to Exceed the limit Vc 0.6 RLW
L p 1.25RLW f c
f c 0.2
Abs M u L p Vu 2
Pu Lpt p
t 0.8L p p
Area of Steel Computed as AbsVu Vc Av f ys 0.8L p
Design of Shear Walls
AbsVu 10RLW
f ct p 0.8L p
ACECOMS, AIT
Shear Design f or Spandr el • 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
hs Ls Elevation
ts d r top
a c
hs
• Check additional steel for seismic requirements d r bo t
Section
Design of Shear Walls
ACECOMS, AIT
ACI Equati ons for Spandr el Design Basic Concrete Shear Capacity Vc
2 RLW
f c ts d s
Concrete not to Exceed the limit Vs Vn Vc
Vu
V c
Area of Steel Computed as
Av
Vs f ys d s
Vs 8RLW
f ct s d s
Check for minimum steel and spacing etc.
Design of Shear Walls
ACECOMS, AIT
ACI Equati ons for Spandr el Design When
When
When Vu
Ls ds
5
and
Ls
Vu 0.5Vc
5 and ds
2
Ls ds
5
Av min
50t s
Av min
Ah min
0
f ys
Ah min 0
Check
L 2 10 s RLW f ct s d s 3 ds
Design of Shear Walls
Vu 0.5Vc
Av min 0.0015t s Ah min 0.0025t s
ACECOMS, AIT
Notati ons for Shear Design Ls
= Length of Spandrel
ts
= Thickness of Spandrel
d r top = Distance from top of spandrel to the centroid of top reinforcing d r bo t = Distance from bottom of spandrel to the centroid of bottom reinforcing
hs
R
= Total depth of spandrel
LW
= Shear reduction factor as specified in the concrete material properties for light weight concrete.
ds
= Effective depth of spandrel
Vs
= Portion of Shear force in spandrel carried by reinforcing steel
Vc
= Portion of Shear force in spandrel carried by concrete
Design of Shear Walls
ACECOMS, AIT
Notati ons for Shear Design Vn
= Nominal Shear strength
f ys
= Shear yield strength of steel
f c
= Concrete Compressive Strength
Lp
= Length of Pier
tp
= Thickness of Pier
Av min
= Minimum vertical required area of distributed shear reinforcing
Ah min = Minimum horizontal required area of distributed shear reinforcing
Design of Shear Walls
ACECOMS, AIT
Detailing of Shear Walls
Wall Secti on • 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
Design of Shear Walls
ACECOMS, AIT
Effect of Rebar L ayout Moment Capacity for 1% Rebars a) Uniform Distribution
Max M= 380
b) Concentrated Bars
Near ly 25% i ncrease for same steel
Design of Shear Walls
Max M= 475
ACECOMS, AIT
Wall Secti on • 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
Design of Shear Walls
ACECOMS, AIT
Effect of Rebar L ayout Moment Capacity for 1% Rebars a) Uniform Distribution
Max M= 16500
b) Concentrated Bars
Max M= 19600
Near ly 20% i ncrease for same steel Design of Shear Walls
ACECOMS, AIT
Rebar Detailing F or Openi ngs
Design of Shear Walls
ACECOMS, AIT