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
Chea Dd Brbator, Dodebay, Poder wd Dewi
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:
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Axial Zone Model - Planer Wall
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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
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ACI Equations for Pier Design دح
Basic Concrete a 5
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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
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4
Check for minimum steel and spacing etc.
۲۲89۳9 مس0 و 4 Ordeby, ,هه Od و۵
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5 quations tor Spanare
3 — 05
and
AIT ۱۳ POCCODE مس0 و 4 Ordeby, ,هه Od و۵
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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
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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
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Moment a for 1% Rebars
Nearly 25% increase for same steel
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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
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Moment Capacity for 1% Rebar:
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Rebar Detailing For Openings __
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ی
0-5-2
ess of
۱1 ۱۱۱۱۱۱۱
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Complexity
7
|
۰
Te ۳۳ ل
2
Slenderness:
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a ۱۵۵۸
مشک فایلا تاد
۱
Short Column LongColumn Column Capacity (P-M
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* “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
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137ل ااا
ee للش
Larger Non- Sway Moment اانا
Larger Sway از ات
Momen t
3
C,, =0.6+ له 204
M2
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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)
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۱ What is Sway
SNe
جد
* Appreciable rel. 3 ioment of two ends of column
A
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. More on Sway
2
* Unbraced Column (Sway)
1
:
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Calculation of 6,,, (Non-Sway)
0ل
9
ccc لك
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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
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re about C,, Factor
we
i |
3
3
5
ّ
> ۵
1
2
كل
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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
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... 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,
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Determination of K. ... سا
* Isolated Memb
Bottom
AIT - Teak POCCODE
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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.
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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,,
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Slenderness procedure for Buildings سا
Vur Vor || Vor
©0000 بو - ۸۱۲ 0 و 3 طط ,موه Ohew Od
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۲۲89۳9 0 له سس رف( سم 3 Chea
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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
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Some Special Cases
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