صفحه 1:
18 متم طع Modeling and
Design of Shear Wall-
۱۵ كلاه دزت
Naveed Anwar
Asian Center for Engineering Computations and Software,
Pe te
صفحه 2:
The Basic Issues
0 CoreC) boot ge ets Bre
~ Transfer of loads to shear walls
- Modeling of shear walls in 2D
- Modeling of shear Walls in 3D
2 - 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
commonest of cellular shear walls
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صفحه 3:
Due to misleading name “Shear Wall”
pi " The dominant mode of failure is shear
" Strength is controlled by shear
= Designed is governed primarily by shear
" Force distribution can be based on relative
stiffness
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صفحه 4:
Shear Wall or Column
صفحه 5:
۱ Shear Wall or Frame
Shear Wall Shear Wall or Frame ?
Ss =>
صفحه 6:
Shear Wall and Frame Behavior
Chea Od Pehaior, Dodebry, له سس 0
صفحه 7:
Shear Wall and Truss Behavior
Chea Od Pehaior, Dodebry, له سس 0
صفحه 8:
Shear Wall and Frame
Shear Wall Behavior ا
صفحه 9:
AIT ۱۳ POCCODE مس0 و 4 رطط ,هه Od و۵
صفحه 10:
Frame and Frame-Shear Wall
صفحه 11:
۰ Frames Deform
- Predominantly in a shear mode
- Source of lateral resistance is the rigidity of beam-
column/slab joints
2 ۶ انعد للع
- Essentially in bending mode
- Shear deformations are rarely significant
- Only very low shear walls with H/W ratio <1 fail
in shear
- Behave mostly like a slender cantilever
- Designed to resist the combined effect of axial,
bending and shear
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صفحه 12:
The Basic Behavior of
‘ar Walls, Frames and Shear Wall-Fri
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صفحه 13:
9۱ ای Only Frame Only Shear +
۳9 a 1 Frame ( Total 3
) 10121300255639 -- - - 2 و وت خ 1 Cases )
a 9 23 00 rr Cases:
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صفحه 14:
۱
0 له سس رف( سم 3 Chea
صفحه 15:
Cl
Interaction
bs SV acc - اام
0
OC ea rete موت 0ل
5
0 له سس رف( مه Chea Dd
صفحه 16:
Interaction
صفحه 17:
00
85. 0
0 له سس رف( مه Chea Dd
صفحه 18:
۱
۱
صفحه 19:
۱
مس 9۵ مت 9 > مس مها
دوت كن" رون كم - COR
Chea Od rhator, Dodebay, له سس 0
صفحه 20:
مس 90 - مس لوط
3-4 ,بط( عم 3 وق
صفحه 21:
مس مت
er UO Bad
Oke Od بط ,وه J
صفحه 22:
7
0 له سس رف( مه Chea Dd
صفحه 23:
الات
eect
صفحه 24:
Qorey Orfevitos (IOGorey Gulkdtog)
Chea Od Pehaior, Dodebry, له سس 0
صفحه 25:
Shear Wall-Frame Interaction
Gorey OeRecitoa (@DGvrey @utldtas)
Chea Dd Brbator, Dodebay, Poder wd Dewi
صفحه 26:
Shear Wall-Frame Interaction
Qorey Orfevitos (DGorey Butldtag)
Chea Od Pehaior, Dodebry, له سس 0
صفحه 27:
Shear Wall-Frame Interaction
A < انا ۳ 6۳۳ | سم = Porve / A
he (poem ee LOE Ep SE
4 مم - 9001006 - .ىسايق
ط نه ند 2002 KO eS
6۸9: 9, یر - 600 / 02.66 -
9.79«
2-0 90*۲0۵ 2 ین دادیم عسخ۵۳
0۵0006 لب
0 له سس رف( سم 3 Chea
صفحه 28:
Change in Shear Wall Moments
slab w/bearn coupling
1 —
ومو و 1000 1600 2006 2500 3000 500.
Shearwall Murent (He kips
مس0 و 4 Ordeby, ,هه Od و۵
صفحه 29:
Coupling Element Moments
مومس
م2 وا وه
Coupling Elements (tekips) ]
مس0 و 4 Ordeby, ,هه Od و۵
صفحه 30:
112641 ١9 62۳ ۸ 6080867 ۸
Di ۳ 7 -
Chea 3 له سس رف( سم 0 AIT ۱۳ POCCODE
صفحه 31:
Distance {rom graund
2
5
9
Uniform Load
= Trangular Load
1 1
0.5 06 07 08
Deflection of structure
] 10۳
AIT ۱۳ POCCODE مس0 و 4 رطط ,هه Od و۵
صفحه 32:
صفحه 33:
Comparison of... : Type A
| tt tt of iing=110 8
3
مس0 و 4 Ordeby, ,هه Od و۵
صفحه 34:
سس ورزد شتسه هلف
aot تم
۱۷۱ ما aa
صفحه 35:
Comparison of... : Type C
مس0 و 4 Ordeby, ,هه Od و۵
صفحه 36:
Comparison of... : Type D
1 il lenghof balding 110 سس
2 wt
اكاب وص ووو
مس0 و 4 00 ,هه Od و۵
صفحه 37:
AIT ۱۳ POCCODE
صفحه 38:
Wall-Frame Interaction: Key Conclusions
The shear wall deform predominantly in bending mode
- The common assumptions to neglect the frames in
lateral load resistance can lead to grossly erroneous
1 ارت
- Consideration of shear wall-frame interaction leads to a
more economic design
- The shear walls should be designed to resist the
combined effect of axial, bending and shear
= نان رو og the alee ee in aot in very important, both
Ghee Od Prkatr, ee cere ert سس
صفحه 39:
Basic Types of Shear Walls _
سيت
صفحه 40:
we Basic Types of Shear Walls __
صفحه 41:
صفحه 42:
Simple Beam 8۰3۳
۱[ عاصهصعاه تن
وون۳۷* with rigid سرت
Model” 5لمع
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صفحه 43:
Frame Model for Planer Walls
۱
0 On ecad
Cee aie tec na
۱ ea
كك 00 Rae oe eae ed
— سم +: 01 0
ke Se eM Rr a
۱ coe cA en ola co
bir Pane
Chea Dd Brbator, Dodebay, Poder wd Dewi
صفحه 44:
Frame Models for Cellular Walls
Difficult to extend the
Coleyitersy el Mm KOM ا
٠ اقا ۱۷۵ مهن 6 eN aK
to “equivalent” column and
كأصعدمعاء “لأيت” عمأمتدمم رمه
* Can be used in 2D analysis
but more complicated for 3D
analysis
ل ا الا كان ا
converted to planer wall, the
simplified procedure cab
used for modeling
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صفحه 45:
Walls are subjected to in-plane deformations so
2D elements that have transnational DOF need
to be used
* Acoarse mesh can be used to capture the
2 overall stiffness and deformation of the wall
ا الا وا yi Alnac minty ey tbat)
bending or curvature
* General Shell Element or Membrane Elements
can be used to model Shear Walls
Chea Od Pehaior, Dodebry, له سس 0
صفحه 46:
A Modeling Walls Using M e
Nodes: 4
DOFs: 2 DOFs /Node Ux and Uy
2-Translation
1 ۱ Dimension: 2 dimension element
eae اا لكت
Properties: Modulus of Elasticity(E),
Poisson ratio(v),
Thickness(t )
صفحه 47:
00611110 Wallis using
pl 061
Nodes: 4
DOFs: 3 DOFs /Node Ux and Uy
and Rz
7 7/۷ ا ال
Shape: Regular / Irregul.
—
Properties: Modulus of Elasticity(E)
Poisson ratio(v),
Thickness(t )
Dimension: 2 dimension element
Chea Od Pehaior, Dodebry, له سس 0
صفحه 48:
Using Incomplete Membrane Using with Beams and or
00۲ Columns are Required
(No Moment continuity with (Full Moment continuity
(كمتدو8 with Beams and Columns)
Chea Od Pehaior, Dodebry, له سس 0
صفحه 49:
ter accuracy in determination of و
easy modeling of openings
Using Complete Membrane Using with Beams,
00۲ عصصبامن
is NOT Required
(Moment continuity
"الدع سمغبة مصدع8 طاغتيور
اللي (Car MB UC rtontmelystaretttin
with Beams and Column:
Okra (9 Pekar, Dodetoy, Badyer cod Devi
صفحه 50:
ing Walls to Slab
Some software automatically
establishes connectivity by
using constraints or “Zipper”
اك ان
Conne
/
In general the mesh in the
slab should match with mesh
طعتاطهؤدة مغ 1لهت1 قط صذ
connection
صفحه 51:
* The behavior of shear walls can be closely
EV Hectic m maar omc OH
- The vertical elements provide the axial-flexural
ةا eLc)
2 - The diagonal elements provide the shear resistance
Ce Bat ا ل ال لان ا ا ا ا
concepts
* This model represents the “cracked” state of
صرح عهنا بط مها 6 صمتعصها له عتمطای الق انا
compression by concrete
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صفحه 52:
Truss Model for Shear Walls
Comparing Deformation
and Deflections of Shell
Model with Truss Model
Ghew Ord Debate, Oodet
صفحه 53:
Truss Model for Shear Walls
Comparing
Deformation and
Deflections of Shell
Model with Truss
Model
Ohea Dd مه ۵
صفحه 54:
Truss Models for Shear Walls
Comparing Axial Stress and
Axial Force Patterns
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صفحه 55:
صفحه 56:
How to Construct Truss Models
For the purpose of analysis, assume
لل ل ا ال نا
width and floor levels
L} ا 1لا
estimated as t x 2t for main axial
Sutil ل لل
members
ay ا ا كا
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
COA Kemal MRO RAT
Cnty
tx2t
AIT - Teak POCCODE
Chea Od Pehaior, Dodebry, له سس 0
صفحه 57:
_Openings in Shear Walls.
Very Large
Openings may
lena TCM
to Frame
86207
er) Vala)
Medium
Openings may
convert shear
wall to Pier and
Spandrel System
iia
—
—
5207
۱6۲
Very Small
]9( ering
not alter wall
و۱۱
=
=
صفحه 58:
Openings in Shear Wa.
Chea Od Pehaior, Dodebry, له سس 0
صفحه 59:
Openings in Shear Walls - Planer
1
0 له سس رف( سم 3 Chea
صفحه 60:
; Modeling Walls with Opening
01 ۲:۵ لأزونه ل mC انا
0 له سس رف( مه Chea Dd
صفحه 61:
۱
صفحه 62:
- 4-Node plane element may not accurately capture the
linear bending, because constant shear distribution is
assumed in formulation but actually shear stress
2 distribution is parabolic
- Since the basic philosophy of RC design is based on
cracked sections, it is not possible to use the finite
اون عملباوع! عاصمصواه ۶0۲ 1
- Very simple model (beam-column) which can also
captures the behavior of the structure, The results
can be used directly to design the concrete elements.
Chea Dd Brbator, Dodebay, Poder wd Dewi
صفحه 63:
Shear Wall Design -Meshing
Shell Deformations:
- همعط eed oe La ee RT
وعمءترو يت فلنام أمعسرعكء افطع
- A single shell element in the program
تترم1ع0 لهتكه قصة “تمعطاى عع سساحرده 205
1 Eola
Ba
ولسءط ارده
b) Shear Deformation c} Bending
صفحه 64:
0 له سس رف( مه Chea Dd
صفحه 65:
0 له سس رف( مه Chea Dd
صفحه 66:
Comparison of Behavior
صفحه 67:
+4 44014 aT?
صفحه 68:
صفحه 69:
صفحه 70:
ect of Shear Wall L
Chea Od Pehaior, Dodebry, له سس 0
صفحه 71:
۳
ty of Shear Walls
In ETABS
صفحه 72:
- Zoning
Ce
ON لب لس
۱
- Labeling
. سرهم
| ۰ ی
- Section Types
0 Cn od (OM aoe)
أ eee ncaa
۱
صفحه 73:
Shear Wall Design -Meshing
Appropriate Meshing and labeling of Shear
Walls is the key to proper modeling and
design of walls
No automatic meshing is available for walls
(only manual)
Loads are only transferred to walls at the
corner points of the area objects that make up
ات
Generally the Membrane or Shell type
Elements should be used to model walls
* Wall Meshing a
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صفحه 74:
Wall Meshing:
- Piers and spandrels where bending
deformations are significant (slender piers
and spandrels), need to mesh the pier or
spandrel into several elements
- If the aspect ratio of a pier or spandrel one
shell element is worse than 3 to 1, consider
additional puoshing of the element to
0017
صفحه 75:
Shear Wall Design - Pier Zones __
Pier Zone Labeling (Naming/Grouping)
ree a Mec Ne cae Re ee coe
02000 ل
7 eed Regen AO ae enone ae
Coe NE Rad ae aaa
ed edt a Reel Ra coe as
EER Dol a Rie hoor ed
yet pulput Porces Por the elewedt or bePore pou
coo desiqa the elewet.
©0000 بو - ۸۱۲ مس0 و 4 Ordeby, ,هه Od و۵
صفحه 76:
Shear Wall Design - Pier Zones
Se لي ا 7 mh ce ace a
۱ cae ase
ot stativar اا
booted at he top aed botiear oP ual pier elewents.
Draked _POCOODE
Chea Od Pehaior, Dodebry, له سس 0
صفحه 77:
۱) 6ستاعطهة]آ
Examples
صفحه 78:
eneral Comments ۴ Cased
TR aE a ل
Pd
SSE ae aR e LA caida a ee
00
00 ا م
ne Re Beane a aoe
Oe han marae ease oR De 9۳
CAN La a el ead
(عسام
566100 ۲6۴ و85
at Il Floor Top
صفحه 79:
2 General Pa Case a:
9 cee
Cental ie eek ne a
0
موم
0
0ك
em neta eee R coed
موی با مسا موجه )و
00
وه
ا 0ك
00000000
bower bevel.
صفحه 80:
Genera comment Case a (Common Way):
ek eel i Nek ane cae]
De ا
Cee een hte feet dood ca oe
سول
eT ae ره
رت
ره
|
ره
ار و بات بل لو ول با بط
Ce eee ed coe
a
صفحه 81:
Sections
يدير
و
یوت
tive
Unite: Kinin و ما
يدير
‘orn
va
uo
a0
om
ama
STORY® PotD: عماج اليم
رمس عنام
Flew ل
ato
۱9۵2 4
ee i
)0 عوام جنوج -©
۱۱۱ عونم 46
ععذم طاعوع 06] غنام أن 0
ow
1
pa
صفحه 82:
Shear Wall Design - Spandrel Zones
Spandrel Zone Labeling (Naming/Grouping)
05 aE aa sR cao
Wo) Nea ar ee cl (acd)
1 5 ce rca aN cae RENE a Ba cB Cacao
Sn Oa ec cad ea ioe concede cca
vce
REE aoe CA RR cca ei oI
OA Carico Ce ca Rc cee eR ANN ci
Dee al
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صفحه 83:
Shear Wall Design - Pier Zones
Example of Possibly Incomplete Wall Pier Labeling
مس0 و 4 Ordeby, ,هه Od و۵
صفحه 84:
Shear Wall Design - Spandrel Zones
Spandrels or ۳
- Wall spandrel forces are output at the left and
right ends of wall spandrel Elements
- Wall spandrel design is only performed at
stations located at the left and right ends of wall
spandrel elements
- Multiple wall spandrel labels cannot be assigned
to a single area object.
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صفحه 85:
Wa
صفحه 86:
Fully integrated wall pier
and spandrel design
ACI, UBC and Canadian
Codes
Design for static and
dynamic loads
Automatic integration of
صوصو 0صه عرمنص 101 وع©01] 1
صفحه 87:
* Design based on :
- Equilibrium Conditions
— Strain Compatibility Principle
~ Linear Strain Variation
|
|
|
|
1 . Stress Diagrah
۳ |
|
Linear Strain nde
صفحه 88:
صفحه 89:
Concrete Shear Wall Design
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
2 location
* Graphical display of reinforcement and stress
۵105
* Interactive design and review
* Summary and detailed reports including database
formats
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صفحه 90:
Shear Wall - Typical Design Process
تس تال بل زیر
2. Choose the Shear Wall design code and review other
فطع عوأالاعء عصة دععمعمعقعمم لعغواعء Cet La
ترا اعلمهمك لصة ععأم موأوكهة .3 2
درز ایا یار ات لیا .3
5ع الالزء لاه لاوأدكه8 .4
5. Select Design Combos
اه راو ۱۳
0 له سس رف( مه Chea Dd
صفحه 91:
Shear Wall - Typical Design Process
7. View Design Input and Output Information
8. Design the Member Interactively
2 9. Print Design Report
BRM elt Tile (mers etal lel
تا رات ایا وت pe
12. Repeat the Above Cycle
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صفحه 92:
Shear Wall Design - Output
Tablo 1 Shoar Wall Dosign Output Summary
COLUNN HEADING DESCRIPTION
‘Simplified Pier Section Desian’
Sony Labo Labol of the story level aesooited with the pier
Pier Label abel 7
‘Salion Location This § ether Top or Bottom to designate the lop or ha bation
tthe pier.
ge Memb Len ‘The long oF ie userstetmed ede member, DBA, oF tie
length ofthe program-detormined edge membor at tho kf sido
tthe ples
Memo Rink | Thelenoti of the user-defined edge mombsr, DBT, or the دولك
length ofthe program-determined edge member atthe igh
‘se of he ple
‘Tho roared area of sted altho cantor ofthe edge moniber at
tie lel se ofthe pk. Note thal the area of steel reported here
|s the maximum of the required tension sleet andthe requirad
compression steel
AS Right ‘The filed area oT Stes al Ne center ofthe edges member al
tho right sido f the pior. Noie that the area of stool rapartod
here isthe maximum cf the recuied tension steel and the =
quired compression steel
Av Shear The required area per unitiength (heigh) cf harizorial shear
‘eiorcina steel nthe pet
B Zone Length This om opplins only lo codes thal sonsidor boundary zone.
This isa teauited lena, sucha 22.762 incies, otis "Not
[Necdod\" ori "Net Checkad)" Not Needed! nc.eates thet
boundary oloments are not required. Noi Chooked mocns that
ny chock fos boundary elements is performed by the program
صفحه 93:
i
maximum requires rao
caus othe etal arsa of vera &
te Seaton Designer
ion. Tsai is prodded asa benchmark to hes you un
The mavirum area pat jot honaonia re
Node" ort "Not Ch od dl
under elarant chee
5 ا
0
Ege
صفحه 94:
Label سس
[Piertabel [|
|[ #قعوس]
mum area per unit length (height
shear in the s
inches, ort is "Not
Needex cked.” Not Needed indicates that
boundan eked means that
th
صفحه 95:
Shear Wall Design - Output
Spandrel Design
Slory Label Label ofthe sory fovel assodated withthe spandrel
Label Label assigned to the spare اه هرک
Station Location This is eer Left or Right to designate the left end or the ight
end ofthe spandre
[107 “The length of he spancrel ۹1/۱32۹ the اع
Shear Vo “The conorete shear capacity used in the spandrel design, See
in Technical
etermine the e Shear Capach
in Technical. Note
8-99, of "Determine the C
‘Shear Canacitv’ in Technical Note Soandrel Shear Desian
S81 10-89 for more information.
Fleguired Feinforcing 5621
andrei
2
10 “The required area of flexural reinforcing steel at the top of the
spandrel
“The required area of flexural reinforcing sted al the betlom of لصالا
the spandrel
3 “The required area per unit engin of vettioal shear reinforcing
stool in ho spandal
An ‘The required area per unit length (height) of horizontal shear
feinforcing steel in the spandrel,
Ave ‘The required area of diagonal shear reinforcing sieal in the
spandrel This tem is only calculated for selsmic piers.
ماه 9 حواق. Doriobas, سب سوت eens: ۳۳۳۳۱
صفحه 96:
The Basic Issues
- Transfer of loads to shear walls
- Modeling of shear walls in 2D
- Modeling of shear Walls in 3D
4 - 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
ل فلن meter
0 له سس رف( مه Chea Dd
صفحه 97:
A ~~ Eccentricity in 8
1 : :
ayy
Chea Od Pehaior, Dodebry, له سس 0 AIT - Teak POCCODE
صفحه 98:
0 له سس رف( سم 3 Chea
صفحه 99:
Expansio
Joint
۷ ايد
FE
۳
s 2
م د ذه 5
ie] د 3
2
۳
8 بم
ae ©
AS 75
ean
q ee
a 3 ظ ۵
a oe
> 5-5
Wa
شنم(
No Shear Walls
صفحه 100:
0 له سس رف( مه Chea Dd
صفحه 101:
صفحه 102:
0 له سس رف( مه Chea Dd
صفحه 103:
Axial Stresses in Cellular Walls
Uniaxial Bendin:
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صفحه 104:
Axial Stresses in Cellular Walls
Biaxial Bending
Chea Dd Brbator, Dodebay, Poder wd Dewi
صفحه 105:
0 له سس رف( مه Chea Dd
صفحه 106:
"+ C+ Dsin@)
x. + Dsin@)x,
Compression عمتعهع1
Member Member
©0000 بو - ۸۱۲ مس0 و 4 Ordeby, ,هه Od و۵
صفحه 107:
11 fn are the nodal
stresses at section A-A , obtained
from analysis
0۵0000 لمرلا مس0 و 4 Ordeby, ,هه Od و۵
صفحه 108:
The curve is generated by
Dela sii maw Lied eb
طامرع0
بق
Nx= | paceraar 3 Bi
ia
بل
مه 3° f(e)dadzt مره
il
صفحه 109:
تا لا
ات تابن ۱
changing Angle
and Depth of
Neutral Axis
0 هد ره مرصده جر عد امآ
12 1
dxdy: y..+ — ۴ 3 )م ] —|,$= M,
| مدرم ی ey سرا 5 وه - با
x.| 9 مه برچ ومد جز دام لش |ممت رم
Chea Od Pehaior, Dodebry, له سس 0
صفحه 110:
Interaction Surface and Curves
=
صفحه 111:
3 و
The capacity is almost —
completely un-axial ۹
Moment capacity can be
increased by providing Rebars
at the corners
صفحه 112:
The capacity is
212051:
completely
العاف ها
صفحه 113:
+ ~ عع
2
<2
صفحه 114:
صفحه 115:
صفحه 116:
Axial Zone Model - Planer Wall
Chea Od Pehaior, Dodebry, له سس 0
صفحه 117:
صفحه 118:
صفحه 119:
Shear Design of Pier
“7 1
* Determine Concrete
shear capacity, Vc
¢ Check if Vc exceeds the
limit, if it does, section
7 | needs to be revised
_ * Determine steel Rebars
by 115-17-1
¢ Check additional steel
101 عتسدكلعءك
requirements
Chea Od Pehaior, Dodebry, له سس 0
صفحه 120:
ACI Equations for Pier Design دح
Basic Concrete a 5
صفحه 121:
۱
shear capaci
* Check if Vc exceeds the
limit, if it does, section
2 needs to be revised
* Determine steel Rebars
for Vs=V-Vc
* Check additional steel
for seismic
requirements
Chea Dd Brbator, Dodebay, Poder wd Dewi
صفحه 122:
4
Check for minimum steel and spacing etc.
۲۲89۳9 مس0 و 4 Ordeby, ,هه Od و۵
صفحه 123:
5 quations tor Spanare
3 — 05
and
AIT ۱۳ POCCODE مس0 و 4 Ordeby, ,هه Od و۵
صفحه 124:
Notations for Shear Design
EMA e ال MRC ROM Restores
fistance from bottom of spandrel to the centroid of bottom reinforcing
0 امتفصدوه ۶ه
= Shear reduction factor as specified in the concrete material
properties for light weight concrete.
5 Te Mod eters ot
ortion of Shear force in spandrel carried by reinforcing steel
Joan Morac) rvs occ BU Ms cetera eres Neon ec122
Chea Dd Brbator, Dodebay, Poder wd Dewi
صفحه 125:
Wall Sec
7 6 ا لا
ااي اانا he middle portion
* Confine the Rebars at the end for improved ductility
and increased moment capacity
Option -1
Option -2
Option -3
Chea Od Pehaior, Dodebry, له سس 0
صفحه 126:
Moment a for 1% Rebars
Nearly 25% increase for same steel
صفحه 127:
9
تا اس سس ۱
عاناطساكتل مسد كع صرم
the remaining in the
سییر ۱۱
Confine the Rebars at
1ط 101 ستعصرمه عط
ductility and increased
moment capacity
Provide U-Bars at the
لتعأكدة 101 كتزاع ترون
ا ال اننا
improved laps
Chea Od Pehaior, Dodebry, له سس 0 ۲۲89۳9
صفحه 128:
Moment Capacity for 1% Rebar:
صفحه 129:
Rebar Detailing For Openings __
Chea Od Pehaior, Dodebry, له سس 0
صفحه 130:
ی
0-5-2
ess of
۱1 ۱۱۱۱۱۱۱
صفحه 131:
Complexity
7
|
۰
Te ۳۳ ل
2
Slenderness:
Chea Od Pehaior, Dodebry, له سس 0
صفحه 132:
a ۱۵۵۸
مشک فایلا تاد
۱
Short Column LongColumn Column Capacity (P-M
صفحه 133:
* “Effective” Length
- Actual Length ۱
- End Framing and Boundary Conditions
- Lateral Bracing Conditions
* “Effective” Stiffness
- Cross-sections Dimensions and Proportions
- Reinforcement amount and Distribution
- Modulus of Elasticity of Concrete and Steel
- Creep and Sustained Loads
* Loads
- Axial Load
- End Moments and Moments along the Length
Chea Dd Brbator, Dodebay, Poder wd Dewi
صفحه 134:
137ل ااا
ee للش
Larger Non- Sway Moment اانا
Larger Sway از ات
Momen t
3
C,, =0.6+ له 204
M2
صفحه 135:
What is Sway
Sway is dependent upot ructural configuration
as well as type of loadin
RRS
May be Sway ۷۵ 12 ناماع
مس مس تسف 9
غك
seers)
Chea Od Pehaior, Dodebry, له سس 0
صفحه 136:
۱ What is Sway
SNe
جد
* Appreciable rel. 3 ioment of two ends of column
A
Chea Od Pehaior, Dodebry, له سس 0
صفحه 137:
. More on Sway
2
* Unbraced Column (Sway)
1
:
Chea Dd Brbator, Dodebay, Poder wd Dewi
صفحه 138:
Calculation of 6,,, (Non-Sway)
0ل
9
ccc لك
صفحه 139:
The C,, Factor
The Moment and Stress
Amplification Factors are
derived on the basis of
pin-ended columns with
(C,, = 1.0)
For other Moment
i Oe 60 مط رصمتاطنتعنط
correction factor C,, ۱ 121112 ۱۷/۹/۸
needs to be computed to ۱ | Negative
modify the stress i 5
amplification. 111 15 26 55221167 0
بر
مممهههه ی ۸۱7 مسب ییوس 0
صفحه 140:
re about C,, Factor
we
i |
3
3
5
ّ
> ۵
1
2
كل
صفحه 141:
Effective Length Factor, K.
* To account for “Axial-Flexural Buckling”
1۱ cne CM boas ta Romeo ttt ty
inflection points
۱ ارچ ROBT
* Most common range 0.75 to 2.0
صفحه 142:
... Determination of K
* Members Part 1 ‘ramed Structure
geet Go 1+ G, forG,<2
Odraed 20
حدد K=09/(+G,) 105 ي© <2
Orv K=0.7+0.0%G,+G,) <1.0
(oie) | K=0.85+0.05G, <1.0
_S(El/ Ie) Columns G, =TopEnd
S(El/ D Beams G, =BottonEnd
KaG G IncreasK Increas: G, = Minimum G, and G,
مس0 و 4 Ordeby, ,هه Od و۵
صفحه 143:
Determination of K. ... سا
* Isolated Memb
Bottom
AIT - Teak POCCODE
Chea Dd Brbator, Dodebay, Poder wd Dewi
صفحه 144:
More about Factor K
S(EI/I,) Columns
2) Beams
Kay 1 0
0 ا Raa Toe سا 52
1 ۱ ا لي Or ied
۱۳ C1
Le
83 . 4
Exampley , oe
BL B.
صفحه 145:
of Stiffness ET
,۱06ص ۲۵ احرحصها
Cracking, Variable E, Creep effect -
Geometric and material non linearity -
* I, = Gross Moment of Inertia
* I,, = Moment of Inertia of rebars
V 8, = Effect of creep for sustained loads. = P,,,/P,,
Chea Od Pehaior, Dodebry, له سس 0 ۲۲89۳9
صفحه 146:
Slenderness procedure for Buildings سا
Vur Vor || Vor
©0000 بو - ۸۱۲ 0 و 3 طط ,موه Ohew Od
صفحه 147:
۲۲89۳9 0 له سس رف( سم 3 Chea
صفحه 148:
ل TOT
هت
et Cae kn
یساس تسا
يي ee نك
سجن
ا ل اك
(©6.6 لم امه د eed ed Meee
مد مج
©0000 بو - ۸۱۲ مس0 و 4 رطط ,هه Od و۵
صفحه 149:
Some Special Cases
صفحه 150:
Behavior, Modeling and
Design of Shear WallFrame Systems
Naveed Anwar
Asian Center for Engineering Computations and Software,
The Basic Issues
• 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
commonest of cellular shear walls
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Shear Wall – Common
Misconceptions
Due to misleading name “Shear Wall”
The dominant mode of failure is shear
Strength is controlled by shear
Designed is governed primarily by shear
Force distribution can be based on relative
stiffness
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Shear Wall or Column
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Shear Wall or Frame
Shear Wall
Shear Wall or Frame ?
Shear Wall Behavior, Modeling, Analysis and Design
Frame
AIT - Thailand
ACECOMS
Shear Wall and Frame Behavior
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Shear Wall and Truss Behavior
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Shear Wall and Frame
Shear Wall Behavior
Shear Wall Behavior, Modeling, Analysis and Design
Frame Behavior
AIT - Thailand
ACECOMS
Shear Wall and Frame
Interaction
Interaction
forces
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Frame and Frame-Shear Wall
A-1
A-2
A-3
B-4
Shear Wall Behavior, Modeling, Analysis and Design
B-1
B-2
B-3
B-4
AIT - Thailand
ACECOMS
Shear Wall and Frame
Interaction
• Frames Deform
– Predominantly in a shear mode
– Source of lateral resistance is the rigidity of beamcolumn/slab joints
• Shear Wall Deform
– Essentially in bending mode
– Shear deformations are rarely significant
– Only very low shear walls with H/W ratio <1 fail
in shear
– Behave mostly like a slender cantilever
– Designed to resist the combined effect of axial,
bending and shear
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
The Basic Behavior of
ear Walls, Frames and Shear Wall-Fra
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Case Studies: Shear Wall–Frame
Interaction
For each 10, 20 and 30 story
buildings
Only Shear Wall
( Total 3 Cases )
Only Frame
( Total 3 Cases )
Only Shear +
Frame ( Total 3
Cases )
Total 3x3 = 9 Cases
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Case 1: Shear Wall–Frame
Interaction
10 Story Wall
cm
Wall Thickness = 15 cm
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Case 2: Shear Wall–Frame
Interaction
10 Story
Frame
cm
Beam Section = 60 cm x 30 cm
Column Section = 50 cm x 50 cm
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Case 3: Shear Wall–Frame
Interaction
10 Story Wall and
Frame
cm
Wall Thickness = 15 cm
Beam Section = 60 cm x 30 cm
Column Section = 50 cm x 50 cm
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Case 4: Shear Wall–Frame
Interaction
20 Story Wall
cm
Wall Thickness = 20 cm
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Case 5: Shear Wall–Frame
Interaction
20 Story Frame
cm
Beam Section = 60 cm x 30 cm
Column Section = 75 cm x 75 cm
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Case 6: Shear Wall–Frame
Interaction
20 Story Wall and
Frame
cm
Wall Thickness = 20 cm
Beam Section = 60 cm x 30 cm
Column Section = 75 cm x 75 cm
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Case 7: Shear Wall–Frame
Interaction
30 Story Wall
cm
Wall Thickness = 30 cm
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Case 8: Shear Wall–Frame
Interaction
30 Story Frame
cm
Beam Section = 60 cm x 30 cm
Column Section = 100 cm x 100 cm
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Case 9: Shear Wall–Frame
Interaction
30 Story Wall and
Frame
cm
Wall Thickness = 30 cm
Beam Section = 60 cm x 30 cm
Column Section = 100 cm x 100 cm
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Shear Wall–Frame Interaction
To p Fl oor Defl ect i on Com p ari son
400
355.04
350
De fl e ct i o n a t To p Fl o o r (cm)
300
250
Frame+ Wall
200
Frame
158.18
150
Wall
100
50
26.73
15.97
5.14
0
0
10
Shear Wall Behavior, Modeling, Analysis and Design
27.35
12.66
20
Nu mb e r o f St o ry
40.79
20.87
30
40
AIT - Thailand
ACECOMS
Shear Wall–Frame Interaction
St o re y De fl e ct i o n (1 0 St o re y Bu i l d i n g )
30
De fo rm a t i o n (cm )
25
20
W all
Frame
Frame +W all
15
10
5
0
0
2
4
6
8
10
12
St o ry
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Shear Wall–Frame Interaction
St o re y De fl e ct i o n (20 St o re y Bu i l d i n g )
1 80
1 60
De fl e ct i o n (cm )
1 40
1 20
Wall
Fra m e
Fra m e + W a l l
1 00
80
60
40
20
0
0
5
10
15
20
25
St o re y
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Shear Wall–Frame Interaction
St o re y De fl e ct i o n (30 St o re y Bu i l d i n g )
400
350
De fl e ct i o n (cm )
300
250
Wall
Fra m e
Fra m e + W a l l
200
1 50
1 00
50
0
0
5
10
15
20
25
30
35
St o re y
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Shear Wall–Frame Interaction
Force / Stiffness
Stiffness Force /
For the cases considered here (30 story example):
Stiffness Frame 200 / 40.79 =
04.90
Stiffness 200 / 355.04 =
Force=200
Deflection = 40.79
Wall
00.56
Stiffness
Frame + Wall 200 / 12.66 =
15.79
Stiffness Frame +Stiffness Wall 4.90 + 0.56 = 5.46
Stiffness Frame +Stiffness Wall Stiffness Frame + Wall
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Change in Shear Wall Moments
Shear Wall Moments for
the Coupled System
Interaction
forces
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Coupling Element Moments
Interaction
forces
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Shear Wall-Frame Load
Distribution Curves
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Deflected Shape of Shear Wall-Frame
Interactive System
KhanSbarounis
Curves
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Comparison of Shears and Moments in the
Core wall
4 Different Layouts for Same Function Requirements
1 total length of building =110 ft
2
10 ft
5 @ 20 = 100 ft
7
1
2
1 total length of building =110 ft
2
in. thick
flat plate
10 ft
5 @ 20 = 100 ft
7
Column
line
1
2
3
4
5
30 @ 20 = 60 ft
in. thick
flat plate
corewall
corewall
12 in
10 in
6 ft
26 ft
6 ft
20 ft
12 in
1
2
26 ft
30 @ 20 = 60 ft
corewall
corewall
6
CL
Column
line
1
2
3
4
5
6
CL
Type A
Type B
1 total length of building =110 ft
2
7
1
2
20 ft
corewall
corewall
7
in. thick
flat plate
6 ft
26 ft
6 ft
12 in
10 in
20 ft
20 ft
Column
line
1
2
corewall
corewall
12 in
10 in
10 ft
5 @ 20 = 100 ft
in. thick
flat plate
26 ft
20 ft
1 total length of building =110 ft
2
10 ft
5 @ 20 = 100 ft
1
2
3
4
5
Column
line
6
18-story high
shear walls
CL
Type C
Shear Wall Behavior, Modeling, Analysis and Design
1
2
3
4
18-story high
shear walls
5
6
CL
Type D
AIT - Thailand
ACECOMS
Comparison of… : Type A
CL
1 total length of building =110 ft
2
36
10 ft
5 @ 20 = 100 ft
7
1
2
35
in. thick
flat plate
34
33
32
30 @ 20 = 60 ft
corewall
corewall
31
30
12 in
Transverse
section
26 ft
6 ft
29
28
8
7.5” thick
floor slabs
7
6
8' clear height
between floors
5
4
10 ft
Column
line
1
2
3
4
5
Corewall
3
2
6
1
CL
22 ft
Typical Floor Plan- Structure Type A
Shear Wall Behavior, Modeling, Analysis and Design
20 ft
30 ft
30 ft
AIT - Thailand
ACECOMS
Comparison of… : Type B
CL
1 total length of building =110 ft
2
36
35
10 ft
5 @ 20 = 100 ft
1
7
2
34
in. thick
flat plate
33
32
31
29
corewall
corewall
Transverse
section
28
8
7.5” thick
floor slabs
7
12 in
6
10 in
8' clear height
between floors
26 ft
6 ft
5
4
10 ft
3
Corewall
30 @ 20 = 60 ft
20 ft
30
2
1
22 ft
20 ft
30 ft
Column
Column
line
line
1
1
2
3
4
5
30 ft
6
CL
Typical Floor Plan- Structure Type B
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Comparison of… : Type C
CL
1 total length of building =110 ft
2
36
10 ft
5 @ 20 = 100 ft
7
1
2
35
in. thick
flat plate
34
20 ft
30 @ 20 = 60 ft 20 ft
33
32
corewall
corewall
31
30
12 in
29
Transverse
section
10 in
26 ft
6 ft
10 in
28
8
7.5” thick
floor slabs
7
20 ft
6
8' clear height
between floors
5
4
10 ft
Column
Column
line
line
1
1
2
3
4
5
18-story high
shear walls
Corewall
3
2
6
1
CL
22 ft
Typical Floor Plan- Structure Type C
Shear Wall Behavior, Modeling, Analysis and Design
20 ft
30 ft
30 ft
AIT - Thailand
ACECOMS
Comparison of… : Type D
CL
1 total length of building =110 ft
2
36
10 ft
5 @ 20 = 100 ft
7
1
2
35
in. thick
flat plate
34
20 ft
33
32
corewall
corewall
31
30
12 in
Transverse
section
10 in
26 ft
6 ft
29
28
8
7.5” thick
floor slabs
7
20 ft
6
8' clear height
between floors
5
4
10 ft
Column
line
1
2
3
4
5
18-story high
shear walls
Corewall
3
2
6
1
CL
22 ft
Typical Floor Plan- Structure Type D
Shear Wall Behavior, Modeling, Analysis and Design
20 ft
30 ft
30 ft
AIT - Thailand
ACECOMS
Comparison of Shears and Moments in the
Core wall
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Wall-Frame Interaction: Key Conclusions
–
The shear wall deform predominantly in bending mode
–
The common assumptions to neglect the frames in
lateral load resistance can lead to grossly erroneous
results
–
Consideration of shear wall-frame interaction leads to a
more economic design
–
The shear walls should be designed to resist the
combined effect of axial, bending and shear
–
Layout of the shear walls in plan in very important, both
for vertical as well as gravity load
ACECOMS
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
Basic Types of Shear Walls
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Basic Types of Shear Walls
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Basic Modeling
Options for Shear
Walls
Modeling of Walls using 1D
Elements
Beam
elements
with rigid
ends
Simple
beam
elements
Beam
elements in
“Truss
Model”
H2
H1
t
t
L
Shear Wall Behavior, Modeling, Analysis and Design
txh
L
L
AIT - Thailand
ACECOMS
Frame Model for Planer Walls
H
t
B
• 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 crosssection
Rigid Zones
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Frame Models for Cellular Walls
t
H
B
2t
H
t
B
Shear Wall Behavior, Modeling, Analysis and Design
• 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
AIT - Thailand
ACECOMS
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
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Modeling Walls Using Membrane
The Incomplete Membrane Element
Nodes:
DOFs:
4
2 DOFs /Node Ux and Uy
2-Translation
Dimension: 2 dimension element
Shape:
Regular / Irregular
Properties: Modulus of Elasticity(E),
Poisson ratio(v),
Thickness( t )
This “Incomplete” Panel or Membrane
Element does not connect with Beams
completely and rotation DOF of beams
and the ends are “Orphaned”
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Modeling Walls using Shell
Elements
The Complete Membrane Element
Nodes:
DOFs:
and Rz
4
3 DOFs /Node Ux and Uy
2 Translation, 1 rotation
R3
Dimension: 2 dimension element
Shape:
U2
No d e 4
No d e 3
U1
Regular / Irregular
3
Properties: Modulus of Elasticity(E),
Poisson ratio(v),
Thickness( t )
U2
U1
2
1
R3
U2
No d e 1
R3
U2
No d e 2
U1
U1
Memb ra n e
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Using Incomplete Membrane
Elements
Multiple elements greater accuracy in determination of stress
distribution and allow easy modeling of openings
Using Incomplete Membrane
only
Using with Beams and or
Columns are Required
(No Moment continuity with
Beams)
(Full Moment continuity
with Beams and Columns)
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Using Complete Membrane
Elements
Multiple elements greater accuracy in determination of stress
distribution and allow easy modeling of openings
Using Complete Membrane
only
(Moment continuity
with Beams automatically
provided)
Shear Wall Behavior, Modeling, Analysis and Design
Using with Beams,
Columns
is NOT Required
(Full Moment continuity
with Beams and Columns)
AIT - Thailand
ACECOMS
Connecting Walls to Slab
“Zipper”
In general the mesh in the
slab should match with mesh
in the wall to establish
connection
Shear Wall Behavior, Modeling, Analysis and Design
Some software automatically
establishes connectivity by
using constraints or “Zipper”
elements
AIT - Thailand
ACECOMS
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
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Truss Model for Shear Walls
10
Comparing Deformation
and Deflections of Shell
Model with Truss Model
5
2
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Truss Model for Shear Walls
10
Comparing
Deformation and
Deflections of Shell
Model with Truss
Model
5
2
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Truss Models for Shear Walls
10
Comparing Axial Stress and
Axial Force Patterns
5
2
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Truss Models for Shear Walls
10
5
2
Uniaxial
Shear Wall Behavior, Modeling, Analysis and Design
Biaxial
AIT - Thailand
ACECOMS
How to Construct Truss Models
txt
C
t x 2t
B
• 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
t
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
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
Wall
Shear Wall Behavior, Modeling, Analysis and Design
Very Large
Openings may
convert the Wall
to Frame
Column
Pier
Pier
AIT - Thailand
ACECOMS
Openings in Shear Walls Cellular
5
2
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Openings in Shear Walls - Planer
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Modeling Walls with Opening
Plate-Shell Model
Shear Wall Behavior, Modeling, Analysis and Design
Rigid Frame Model
Truss Model
AIT - Thailand
ACECOMS
Frame Model of Shear Walls
A: Shear Wall withLineLoads
B: FiniteElementModel
Ri g i d Zo n es
Bea ms
3DOF
pe r rigi d zon e
Co l u mn s
C: DefineBeams &Columns
D: Beam-ColumnModel
Based on Concept proposed by E.L. Wilson
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Using Beam-Column to Model Shear
Walls
– 4-Node plane element may 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 can also captures
the behavior of the structure, The results can be used
directly to design the concrete elements.
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Shear Wall Design –Meshing
•
Shell Deformations:
– Three types of deformation that a single
shell element could experience
– A single shell element in the program
captures shear and axial deformations
well.
– But a single shell element is unable to
capture bending deformation.
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Modeling Shear Walls Using
Shell Elements
A-1
Plates with Columns and
Beams
A-2
Plates with Beams
Shear Wall Behavior, Modeling, Analysis and Design
A-3
Plates with
Columns
A-4
Plates Only
AIT - Thailand
ACECOMS
Modeling Shear Walls Using
Beam Elements
B-1
Single Bracing
B-2
Double Bracing
Shear Wall Behavior, Modeling, Analysis and Design
B-3
Column with Rigid
Zones
B-4
Columns with
Flexible Zones
AIT - Thailand
ACECOMS
Comparison of Behavior
A-1
A-2
A-3
B-4
Shear Wall Behavior, Modeling, Analysis and Design
B-1
B-2
B-3
B-4
AIT - Thailand
ACECOMS
Comparison of Behavior (5
Floors)
B4
A1
B1
A1
B1
B4
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Comparison of Behavior (15
Floors)
B4
A1
B1
A1
B1
B4
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Comparison of Behavior (25
Floors)
B4
A
1
B1
A1
B1
B4
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Effect of Shear Wall Location
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Modeling of Shear Walls
In ETABS
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Shear Wall Design – Using ETABS
Special Considerations/Concepts:
–
Zoning
•
•
•
–
Pier
Spandrel and
Boundary Zone
Labeling
•
•
–
Pier
Spandrel
Section Types
•
•
•
Simplified Section (C, T or Linear)
Uniform reinforcing section
General Sections
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Shear Wall Design –Meshing
• Wall Meshing and Load Transfer:
–
–
–
–
Appropriate Meshing and labeling of Shear
Walls is the key to proper modeling and
design of walls
No automatic meshing is available for walls
(only manual)
Loads are only transferred to walls at the
corner points of the area objects that make up
the wall
Generally the Membrane or Shell type
Elements should be used to model walls
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Shear Wall Design –Meshing
Wall Meshing:
– Piers and spandrels where bending deformations are
significant (slender piers and spandrels), need to mesh the
pier or spandrel into several elements
– If the aspect ratio of a pier or spandrel one shell element
is worse than 3 to 1, consider additional meshing of the
element to adequately capture the bending deformation
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Shear Wall Design – Pier Zones
Pier Zone Labeling (Naming/Grouping)
– Pier labels are assigned to vertical area objects
(walls) and to vertical line objects (columns)
–
Objects that are associated with the same story
level and have the same pier label are considered
to be part of the same pier.
–
Must assign a pier element a label before you can
get output forces for the element or before you
can design the element.
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Shear Wall Design – Pier Zones
–
A single wall pier cannot extend over multiple
stories
–
Wall pier forces are output at the top and bottom of
wall pier elements
–
Wall pier design is only performed at stations
located at the top and bottom of wall pier elements.
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Shear Wall Design – Pier Zones
Piers Labeling
Examples
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Shear Wall Design – Pier Zones
General Comments on Case d:
–
–
–
–
All of the area objects given the same label
P1
Design is performed across the entire wall
at each story level
Wall forces would be provided for the entire
wall at each story level
Combined reinforcement is reported at the
top and bottom of each floor (3-5 area
objects)
Section for Design
at II Floor Top
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Shear Wall Design – Pier Zones
General Comments on Case a:
–
–
–
–
–
–
–
Common way to label piers
At the upper level, Pier P1 is defined to
extend all the way across the wall above the
openings.
Pier P2 makes up the wall pier to the left of
the door opening.
Pier P3 occurs between the door and
window openings.
Pier P4 occurs between the window
opening and the edge of the wall.
Pier P5 occurs below the window opening
between the door and the edge of the wall. A
similar labeling of piers occurs at the
lower level.
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Shear Wall Design – Pier Zones
General Comments on Case a (Common Way):
–
–
–
–
–
–
At the upper level, Pier P1 is defined to extend all
the way across the wall above the openings.
Pier P2 makes up the wall pier to the left of the
door opening.
Pier P3 occurs between the door and window
openings.
Pier P4 occurs between the window opening
and the edge of the wall.
Pier P5 occurs below the window opening
between the door and the edge of the wall.
A similar labeling of piers occurs at the lower
level.
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Shear Wall Design – Pier Zones
General Comments on Case a (Common Way):
Design pier –1
Design pier –2
Design pier –3
Sections
Design pier –4
Output for Each Pier
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Shear Wall Design – Spandrel Zones
Spandrel Zone Labeling (Naming/Grouping)
– Spandrel labels are assigned to vertical area objects
(walls) and to horizontal line objects (beams)
– Unlike pier elements, a single wall spandrel element can be
made up of objects from two (or more) adjacent story
levels
– Must assign a spandrel element a label before you can get
output forces for the element or before you can design
the element
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Shear Wall Design – Pier Zones
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Shear Wall Design – Spandrel Zones
Spandrels or Headers
– Wall spandrel forces are output at the left and
right ends of wall spandrel Elements
– Wall spandrel design is only performed at
stations located at the left and right ends of wall
spandrel elements
– Multiple wall spandrel labels cannot be assigned
to a single area object.
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Shear Wall Design – Spandrel Zones
Examples: Spandrel Labeling
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Concrete Shear Wall Design
• Fully integrated wall pier
and spandrel design
• ACI, UBC and Canadian
Codes
• Design for static and
dynamic loads
• Automatic integration of
forces for piers and spandrel
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Shear Wall Design
• Design based on :
– Equilibrium Conditions
– Strain Compatibility Principle
– Linear Strain Variation
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Interaction Surface for Shear
Walls
P
My
Mx
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Concrete Shear Wall Design
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
•
•
•
•
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Shear Wall - Typical Design Process
1. While modeling define Shear Wall elements
2. Choose the Shear Wall design code and review other
related preferences and revise them if necessary
3. Assign pier and spandrel labels
3. Run the building analysis
4. Assign overwrites
5. Select Design Combos
6. Start Designing Walls
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Shear Wall - Typical Design Process
7. View Design Input and Output Information
8. Design the Member Interactively
9. Print Design Report
10.Change Design Section if Required
11. Re-run Design and Re-analyze if needed
12. Repeat the Above Cycle
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Shear Wall Design – Output
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Shear Wall Design – Output
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Shear Wall Design – Output
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Shear Wall Design – Output
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
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
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Avoid Eccentricity in Plan
Or
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Reduce In-plane Bending in
Floor
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Vertical Irregularity
Expansio
n Joint
No Shear Walls
Shear Wall Behavior, Modeling, Analysis and Design
Balanced Shear
Walls at All
Levels
Using
Expansion
Joints to
eliminate some
walls
AIT - Thailand
ACECOMS
Using Efficient Building Plan
Shape
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Design of Shear
Walls
Axial Stresses in Planer Walls
10
5
2
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Axial Stresses in Cellular Walls
10
Uniaxial Bending
5
2
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Axial Stresses in Cellular Walls
10
Biaxial Bending
5
2
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Getting Result from Frame
Model
Design actions (P, Mx, My and V) are obtained directly
P
M
P
V
Shear Wall Behavior, Modeling, Analysis and Design
Vy
Vx
Mx
My
AIT - Thailand
ACECOMS
Getting Results from Truss
Model
P T C D sin( )
M Txt Cxc D sin( )xd
V D cos( )
D
T
M
xd
xt
Tension
Member
P
C
V
xc
Compression
Member
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Getting Results From Shell
Model
CL of wall
Fi Ai fi
n
P Fi
i 1
n
P
A
A
M
V
M Fi xi
i 1
n
V Ai vi
i 1
t
f5
x1
f4
T
f3
f2
C
f1
x1
Shear Wall Behavior, Modeling, Analysis and Design
f1, f2, …..fn are the nodal
stresses at section A-A , obtained
from analysis
AIT - Thailand
ACECOMS
Interaction Curves - Uniaxial
The curve is generated by
varying the neutral axis
depth
Un-safe
Nb
Nnx fc( )da fsiAsi
i 1
A
Nb
Mny fc( )da.dz fsiAsidzi
i 1
zA
Shear Wall Behavior, Modeling, Analysis and Design
Safe
AIT - Thailand
ACECOMS
Interaction Surface - Biaxial
The surface is
generated by
changing Angle
and Depth of
Neutral Axis
Un-safe
Safe
1
Nz 1
1
x, ydxdy...
x y
1
Mx 2
1
1
My 3
1
1
2
n
i
Ai i (x, y) ...
1
n
1
x, ydxdy. y ...
i
x y
2
x, ydxdy. x ...
x y
Shear Wall Behavior, Modeling, Analysis and Design
1
2
1
n
i
1
Ai i (x, y) yi ...
Ai i (x, y) xi ...
AIT - Thailand
ACECOMS
Interaction Surface and Curves
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Narrow Planner Walls
The capacity is almost
completely un-axial
Moment capacity can be
increased by providing Rebars
at the corners
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Cellular Wall – No Opening
The capacity is
almost
completely
biaxial
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Single Cell Walls
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Double Cell Walls
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Designing as Axial Zones
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Axial Zone Model – Planer Wall
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Axial Zones for Box Wall
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Shear Design
Spandre
l
Pier
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
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
Shear Wall Behavior, Modeling, Analysis and Design
Lp
tp
AIT - Thailand
ACECOMS
ACI Equations for Pier Design
Basic Concrete Shear Capacity
Vc 3.3RLW
Pu 0.8Lp
fctp 0.8Lp
4Lp
Concrete not to Exceed the limit
Vc 0.6RLW
fc
Lp 1.25RLW
fc 0.2
M L
Abs u p
2
Vu
Pu
Lptp
tp 0.8Lp
Area of Steel Computed as
AbsVu
Vc
Av
fys0.8Lp
Shear Wall Behavior, Modeling, Analysis and Design
AbsVu
10RLW fctp 0.8Lp
AIT - Thailand
ACECOMS
Shear Design for Spandrel
• 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
hs
Ls
Elevation
ts
dr top
c
a
hs
dr bot
Section
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
ACI Equations for Spandrel
Design
Basic Concrete Shear Capacity
Vc 2RLW
fctsds
Concrete not to Exceed the limit
V
Vs Vn Vc u V c
Area of Steel Computed as
Av
Vs
f ysds
Vs 8RLW
fctsds
Check for minimum steel and spacing etc.
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
ACI Equations for Spandrel
Design
Ls
5
When
ds
When
When
and
Ls
5 and
ds
2
Ls
5
ds
Vu
0.5Vc
Vu
0.5Vc
50ts
fys
Ahmin 0
Avmin Ahmin 0
Check
Vu 2
Ls
10 RLW fctsds
3
ds
Shear Wall Behavior, Modeling, Analysis and Design
Avmin
Avmin 0.0015
ts
Ahmin 0.0025
ts
AIT - Thailand
ACECOMS
Notations for Shear Design
Ls
= Length of Spandrel
ts
= Thickness of Spandrel
dr= topDistance from top of spandrel to the centroid of top reinforcing
d=
Distance from bottom of spandrel to the centroid of bottom reinforcing
r bot
hs
RLW
= Total depth of spandrel
= 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
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
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
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Effect of Rebar Layout
Moment Capacity for 1% Rebars
a) Uniform Distribution
Max M= 380
b) Concentrated Bars
Nearly 25% increase for same steel
Shear Wall Behavior, Modeling, Analysis and Design
Max M= 475
AIT - Thailand
ACECOMS
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
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Effect of Rebar Layout
Moment Capacity for 1% Rebars
a) Uniform Distribution
Max M= 16500
b) Concentrated Bars
Max M= 19600
Nearly 20% increase for same steel
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Rebar Detailing For Openings
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Slendern
ess of
Columns
Complexity in the Column Design
Loading
Load Complexity
PMx My
PMx
P
S
rt
ho
ng
Lo
L
V.
on
Shape
Shape
Complexity
Most Simple
Problem
g
SlendernessLength
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
What is Slenderness Effect
Moment
Amplification
e
P
P
Capacity
Reductio
n
I
e
C
P
f(Mc)
II
C
M
I. Mc = P.e
II : Mc = P(e +
Short Column
Long Column
Shear Wall Behavior, Modeling, Analysis and Design
Column Capacity (P-M)
AIT - Thailand
ACECOMS
Factors Effecting Slenderness
Effect
• “Effective” Length
– Actual Length
– End Framing and Boundary Conditions
– Lateral Bracing Conditions
• “Effective” Stiffness
–
–
–
–
Cross-sections Dimensions and Proportions
Reinforcement amount and Distribution
Modulus of Elasticity of Concrete and Steel
Creep and Sustained Loads
• Loads
– Axial Load
– End Moments and Moments along the Length
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
ACI Moment Magnification
Summary
Final
Design
Momen
t
Larger Non- Sway Moment
Larger Sway
Moment
Mm Mns ns Ms s
Cm
Pu
ns
1
Cm 0.6 0.4
M1
0.4
M2
0.75PC
(EI)
PC
(KlU )2
Shear Wall Behavior, Modeling, Analysis and Design
2
a) s
1
1
1.0
Pu 0
Vulc
If s 1.5 then
1
1
Pu
1
0.75 Pc
b) s
AIT - Thailand
ACECOMS
What is Sway …
–
Sway is dependent upon the structural configuration
as well as type of loading
Non Sway
Sway
May be Sway
For Non-sway Frames (Very rigid or braced)
–
–
For Sway Frames (Open frames, not braced,
Depends on loads also)
s 1.0
ns 1.0
s 1.0
ns 1.0
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
… What is Sway
• Appreciable relative moment of two ends of column
Sway
0
•
T B
T
lc
Sway Limits
lc
B
a) EIBracingwalls 6EIColumns
PU 0
b) E
0.05
VU lC
Mm
c)
1.05
M
Shear Wall Behavior, Modeling, Analysis and Design
Frame considered
as “Non-Sway”
AIT - Thailand
ACECOMS
… More on Sway
• Braced Column (Non-Sway)
Most building columns may be considered “Non-Sway” for gravity loads
•
More than 40% of columns in buildings are “Non-Sway” for
lateral loads
•
Moment Magnification for “Sway” case is more significant, more complicated and more important
•
• Unbraced Column (Sway)
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Calculation of ns (Non-Sway)
ns
1
Cm
Pu
0.75PC
Moment curvature
Coefficient
Applied column load
Critical buckling load
(EI)
PC
2
(KlU )
2
Flexural Stiffness
Effective Length Factor
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
The Cm Factor
The Moment and Stress
Amplification Factors are
derived on the basis of
pin-ended columns with
single moment
curvature.
(Cm = 1.0)
For other Moment
Distribution, the
correction factor Cm
needs to be computed to
modify the stress
amplification.
Shear
Behavior,
Analysis and Design
CWall
0.4 Modeling,
to 1.0
m =
M1
Cm 0.6 0.4
0.4
M2
M1
M1
M2
M2
M1/M2
Positive
M1/M2
Negative
M1 is the smaller End
Moment
M2 is the larger End
AIT - Thailand
ACECOMS
More about Cm Factor
M1
M2
M2
M1
M1= -M
M2 = M
M1
1
M2
Cm = 1.0
M1 = 0
M2 = M
M1
0
M2
Cm = 0.6
Shear Wall Behavior, Modeling, Analysis and Design
M2
M1
M1 =M
M2 = M
M1
1
M2
Cm = 0.2
M1
M2
M1 =0
M2 = M
M1
0
M2
Cm = 0.6
AIT - Thailand
ACECOMS
Effective Length Factor, K
•
•
•
•
0.5
To account for “Axial-Flexural Buckling”
Indicates the “total bent” length of column between
inflection points
Can vary from 0.5 to Infinity
Most common range 0.75 to 2.0
1.0
Shear Wall Behavior, Modeling, Analysis and Design
0.5 - 1.0
2.0
1.0 -
AIT - Thailand
ACECOMS
… Determination of K
• Members Part of Framed Structure
Unbraced
Frames
20 Gm
K
1 Gm
20
K 0.9 (1Gm)
for Gm 2
K 0.7 0.05(GT GB ) 1.0
k 0.85 0.05Gm 1.0
Braced
Frames
(smaller of)
(EI / LC )
G
(EI / L)
K G
for Gm 2
Columns
Beams
G Increase
, K Increases
Shear Wall Behavior, Modeling, Analysis and Design
GT Top End
GB BottomEnd
Gm Minimum
of GT and GB
AIT - Thailand
ACECOMS
… Determination of K
• Isolated Members
Bottom
End
Top End
Fix
Pin
Free
Fix
0.5
0.8
2.0
Pin
0.8
1.0
Un s t a b l e
Free
2.0
Un s t a b l e
Un s t a b l e
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
… More about Factor K
(EI / lC )
(EI / l)
K
Columns
Beams
Increase
, K Increases
•How about “I” Gross? Cracked? Effective?
•ACI Rules
B1
C2
B2
Beams I = 0.35 Ig, Column I =
0.7Ig
C1
B3
E(IC1 I C2)
Example
T
E(IB1 IB2 )
Lc
B4
C3
E for column and beams may be different
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Determination of Stiffness EI
EI
Ab
0.2EC I g EsIse
or
1 d
0.4EC I g
h
yb
1 d
• Attempt to include,
– Cracking, Variable E, Creep effect
b
– Geometric and material non linearity
• Ig = Gross Moment of Inertia
• Ise = Moment of Inertia of rebars
= Effect of creep for sustained loads. = P /P
d
ud
u
Shear Wall Behavior, Modeling, Analysis and Design
Ig
bh3
12
Ise Ab. yb2
AIT - Thailand
ACECOMS
Slenderness procedure for Buildings
Q
PU 0
VU lC
PU PU1 PU 2 PU 3......
T
PU1
PU2
PU3
PU4
lC
VU1
VU1
VU1
0 T B
VU1
B
VU VU1 VU 2 VU 3.......
average
lC Clearstoreyheight
If Q 0.05 : Non swaycase
Q 0.05 : Sway
Case
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
BS Moment Magnification
• Basic Equation for Slender Columns
Mm Mi Nau
Initial Moment form elastic
analysis
Shear Wall Behavior, Modeling, Analysis and Design
Madd, Additional
moment due to
deflection
AIT - Thailand
ACECOMS
Calculation of Deflection au
Load correction factor
au a Kh
Column Dimension along
deflection
Length Correction Factor
Applied column load
Nuz N
K
1
Nuz Nbal
Axial capacity at balanced
conditions
Axial Capacity for M = 0 Nuz 0.45fcuAc 0.95Asc fy
a
1 le
2000 b
2
Effective Length = lo
(From Table 3.21 and 3.22)
Smaller dimension
Shear Wall Behavior, Modeling, Analysis and Design
AIT - Thailand
ACECOMS
Some Special Cases
M
V
Shear Wall Behavior, Modeling, Analysis and Design
P
M
AIT - Thailand
ACECOMS
Some Special Cases
P
V
Soft
Hard
(e)
P
L1
d
L
L1
h1
L1
h1
Le = ?
h2
L2
(a)
L
2
(b)
Shear Wall Behavior, Modeling, Analysis and Design
(c)
(d)
AIT - Thailand
ACECOMS
