International Seminar onInternational Seminar onComputer Aided Analysis and DesignComputer Aided Analysis and DesignOf Building StructuresOf Building Structures
International Seminar onInternational Seminar onComputer Aided Analysis and DesignComputer Aided Analysis and DesignOf Building StructuresOf Building Structures
Aug 23-24, Kuala Lumpur, MalaysiaAug 23-24, Kuala Lumpur, Malaysia
•Institute of Engineers MalaysiaInstitute of Engineers Malaysia
•Computers and Structures Inc., USA Computers and Structures Inc., USA
•Asian Center for Engineering Computations and SoftwareAsian Center for Engineering Computations and Software Asian Institute of Technology, ThailandAsian Institute of Technology, Thailand
•Institute of Engineers MalaysiaInstitute of Engineers Malaysia
•Computers and Structures Inc., USA Computers and Structures Inc., USA
•Asian Center for Engineering Computations and SoftwareAsian Center for Engineering Computations and Software Asian Institute of Technology, ThailandAsian Institute of Technology, Thailand
Building StructuresModeling and Analysis Concepts
Building StructuresModeling and Analysis Concepts
Naveed AnwarNaveed Anwar
Asian Center for Engineering Computations and Software, ACECOMS, AITAsian Center for Engineering Computations and Software, ACECOMS, AIT
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Overall Design ProcessOverall Design Process
• Conception
• Modeling
• Analysis
• Design
• Detailing
• Drafting
• Costing
Integrated Integrated Design Design ProcessProcess
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Building Systems
• Building is an assemblage of various Systems– Basic Functional System
– Structural System
– HVAC System
– Plumbing and Drainage System
– Electrical, Electronic and Communication System
– Security System
– Other specialized systems
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Beams, Columns, Two-way Slabs, Flat Slabs, Pile caps Shear Walls, Deep Beams, Isolated Footings, Combined Footings
Sub-structure and Member Design
Frame and Shear WallsLateral Load Resisting System Floor Slab System
Gravity Load Resisting System
Building Structure
Floor Diaphragm
The Building Structural System - Physical
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
The Building Structural System - Conceptual
• The Gravity Load Resisting System (GLRS)– The structural system (beams, slab, girders, columns, etc)
that act primarily to support the gravity or vertical loads
• The Lateral Load Resisting System (LLRS)– The structural system (columns, shear walls, bracing, etc)
that primarily acts to resist the lateral loads
• The Floor Diaphragm (FD)– The structural system that transfers lateral loads to the
lateral load resisting system and provides in-plane floor stiffness
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Building Response
• Objective: To determine the load path gravity and lateral loads
• For Gravity Loads - How Gravity Loads are Distributed
– Analysis of Gravity Load Resisting System for:
• Dead Load, Live Live Load, Pattern Loads, temperature, shrinkage
– Important Elements: Floor slabs, beams, openings, Joists, etc.
• For Lateral Loads – How Lateral Loads are Distributed
– Analysis of Lateral Load Resisting System for:
• Wind Loads, Seismic Loads, Structural Un-symmetry
– Important elements: Columns, shear walls, bracing , beams
Structural ResponseStructural ResponseTo LoadsTo Loads
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
The Simplified Structural System
STRUCTURE
pv
EXCITATIONLoads
VibrationsSettlements
Thermal Changes
RESPONSESDisplacements
StrainsStress
Stress Resultants
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Analysis of Structures Analysis of Structures
pv
xx yy zzvxx y z
p 0
Real Structure is governed by “Partial Differential Equations” of various order
Direct solution is only possible for:• Simple geometry• Simple Boundary• Simple Loading.
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
The Need for ModelingThe Need for Modeling
A - Real Structure cannot be Analyzed: It can only be “Load Tested” to determine response
B - We can only analyze a “Model” of the Structure
C - We therefore need tools to Model the Structure and to Analyze the Model
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Structural Model
The Need for Structural Model
EXCITATIONLoads
VibrationsSettlements
Thermal Changes
RESPONSESDisplacements
StrainsStress
Stress Resultants
STRUCTURE
pv
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Finite Element Method: The Analysis Tool Finite Element Method: The Analysis Tool
• Finite Element Analysis (FEA) “A discretized solution to a continuum
problem using FEM”
• Finite Element Method (FEM)“A numerical procedure for solving (partial) differential equations associated with field problems, with an accuracy acceptable to engineers”
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Continuum to Discrete Model
pv
(Governed by partialdifferential equations)
CONTINUOUS MODELOF STRUCTURE
(Governed by eitherpartial or total differential equations)
DISCRETE MODELOF STRUCTURE
(Governed by algebraicequations)
3D-CONTINUM MODEL
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
From Classical to FEM Solution From Classical to FEM Solution
xx yy zzvxx y z
p 0
tvt
st
v
dV p u dV p u ds_ _ _
Assumptions
Equilibrium
Compatibility
Stress-Strain Law
(Principle of Virtual Work)
“Partial Differential Equations”
Classical
Actual Structure
Kr R
“Algebraic Equations”
K = Stiffnessr = Response
R = Loads
FEM
Structural Model
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Simplified Structural System
Loads (F) Deformations (D)Fv
F = K DF = K D
FF
KKDD
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
The Structural SystemThe Structural System
EXCITATION RESPONSES
STRUCTURE
pv
• Static• Dynamic
• Static• Dynamic
• Elastic• Inelastic
• Elastic• Inelastic
• Linear• Nonlinear
• Linear• Nonlinear
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
The Equilibrium Equations
1. Linear-Static Elastic OR Inelastic
2. Linear-Dynamic Elastic
3. Nonlinear - Static Elastic OR Inelastic
4. Nonlinear-Dynamic Elastic OR Inelastic
FKu
)()()()( tFtKutuCtuM
)()()()()( tFtFtKutuCtuM NL
FFKu NL
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Basic Steps in FEABasic Steps in FEA
Evaluate Real Structure
Create Structural Model
Discretize Model in FE
Solve FE Model
Interpret FEA Results
Physical significance of Results
Engineer
Engineer + Software
Software
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
X
Z
Y
Membrane/ PanelIn-Plane, Only Axial
ShellIn-Plane and Bending
Plate/ SlabOut of Plane, Only Bending
General Solid
Regular Solid
Plate/ Shell
( T small compared to Lengths )
( Orthogonal dimensions)
Discretization of Continuums
Beam Element
Solid Element
H, B much less than L
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Global Modeling of Structural Geometry
(b) Solid Model (c) 3D Plate-Frame (d) 3D Frame
(a) Real Structure
(e) 2D Frame
Fig. 1 Various Ways to Model a Real Struture
(f) Grid-Plate
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Dimensions of Elements
• 1 D Elements (Beam type)– Can be used in 1D, 2D and 2D
– 2-3 Nodes. A, I etc.
• 2 D Elements (Plate type)– Can be used in 2D and 3D Model
– 3-9 nodes. Thickness
• 3 D Elements (Brick type)– Can be used in 3D Model– 6-20 Nodes.
Truss and Beam Elements (1D,2D,3D)
Plane Stress, Plane Strain, Axisymmetric, Plate and Shell Elements (2D,3D)
Brick Elements
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
DOF for 1D Elements
DxDx
DyDy
DxDxDzDz
DyDy
DxDx
DyDy
RzRz
DyDy
RxRxRzRz DxDxDzDz
DyDy
RxRxRzRz
RyRy
2D Truss2D Truss 2D Beam2D Beam 3D Truss3D Truss
2D Frame2D Frame 2D Grid2D Grid 3D Frame3D Frame
DyDy
RzRz
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
DOF for 2D Elements
DxDx
DyDyDyDy
Ry ?Ry ?
RzRzRxRx
DzDz
DyDy
RxRxRzRz
Ry ?Ry ?
DxDx
MembraneMembrane PlatePlate ShellShell
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
DOF for 3D Elements
DxDxDzDz
DyDy
Solid/ BrickSolid/ Brick
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Frame and Grid Model
• The structure represented by rod or bar type elements
• Does not model the cross-section dimensions
• Suitable for skeletal structures
• Sometimes surface type structures can also be represented by frame model
• The simplest and easiest model to construct, analyze and interpret
• Can be in 2D or in 3D space
3D Frame
2D Grid
2D Frame
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Membrane ModelMembrane Model
• Ignore bending stiffness
• Tension / Compression
• In- plane Shear
• For in plane loads
• Principle Stresses
• suitable for very thin structures / members
• Thin Walled Shells,
• Specially Suitable for Ferro Cement Structure
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
1 unit
x 1
x 3
x 2
3D Problem
2D Problem
Plain-StrainAssumptions
Plane Stress and PlanePlane Stress and Plane
x
x
Plane Stress Problem Plane Strain Problem
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Plate Bending ModelPlate Bending Model
• Primarily Bending mode
• Moment and Shear are predominant
• Suitable for moderately thick slabs and plates
• For Out-of-plane loads only
• Can be used in 3D or 2D models
• Suitable for planks and relatively flat structures
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
General Plate-Shell ModelGeneral Plate-Shell Model
• Combined Membrane and Plate• Suitable for general application
to surface structures• Suitable for curved structures• Thick shell and thin shell
implementations available • Membrane thickness and plate
thickness can be specified separately
• Numerous results generated. Difficult to design the section for combined actions
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Solid ModelSolid Model
• Shear Axial deformation mode in 3D
• Suitable for micro-models
• Suitable for very thick plates / solids
• May not be applicable much to ferocement structures
• Use 6 to 20 node elements
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Soil-Structure Interaction
• Simple Supports• Fix, Pin, Roller etc.
• Support Settlement
• Elastic Supports• Spring to represent soil
• Using Modulus of Sub-grade reaction
• Full Structure-Soil Model• Use 2D plane stress elements
• Use 3D Solid Elements
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Connecting Different Types of Elements
Truss Frame Membrane Plate Shell Solid
Truss OK OK Dz OK OK OK
FrameRx, Ry, Rz OK
Rx, Ry, Rz, Dz
Rx ?
Dx, DyRx ? Rx, Ry, Rz
MembraneOK OK OK Dx, Dy OK OK
Plate Rx, Rz OK Rx, Rz OK OK Rx, Rz
ShellRx, Ry, Rz OK
Rx, Ry, Rz, Dz
Dx, Dz OK Rx, Rz
Solid OK OK Dz Dx, Dz OK OK
0
Orphan Degrees Of Freedom:1 2 3 4
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
What Type of Analysis should be
Carried Out?
What Type of Analysis should be
Carried Out?
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Analysis Type
– The Type of Excitation (Loads)
– The Type Structure (Material and Geometry)
– The Type Response
The type of Analysis to be carried out depends on the Structural System
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Basic Analysis Types
Excitation Structure Response Basic Analysis TypeStatic Elastic Linear Linear-Elastic-Static Analysis
Static Elastic Nonlinear Nonlinear-Elastic-Static Analysis
Static Inelastic Linear Linear-Inelastic-Static Analysis
Static Inelastic Nonlinear Nonlinear-Inelastic-Static Analysis
Dynamic Elastic Linear Linear-Elastic-Dynamic Analysis
Dynamic Elastic Nonlinear Nonlinear-Elastic-Dynamic Analysis
Dynamic Inelastic Linear Linear-Inelastic-Dynamic Analysis
Dynamic Inelastic Nonlinear Nonlinear-Inelastic-Dynamic Analysis
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Some More Solution Types
• Non-linear Analysis– P-Delta Analysis
– Buckling Analysis
– Static Pushover Analysis
– Fast Non-Linear Analysis (FNA)
– Large Displacement Analysis
• Dynamic Analysis– Free Vibration and Modal Analysis
– Response Spectrum Analysis
– Steady State Dynamic Analysis
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Static Vs Dynamic
• Static Excitation– When the Excitation (Load) does not vary rapidly with Time
– When the Load can be assumed to be applied “Slowly”
• Dynamic Excitation– When the Excitation varies rapidly with Time
– When the “Inertial Force” becomes significant
• Most Real Excitation are Dynamic but are considered “Quasi Static”
• Most Dynamic Excitation can be converted to “Equivalent Static Loads”
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Elastic Vs Inelastic
• Elastic Material– Follows the same path during loading and unloading and returns to initial
state of deformation, stress, strain etc. after removal of load/ excitation
• Inelastic Material– Does not follow the same path during loading and unloading and may not
returns to initial state of deformation, stress, strain etc. after removal of load/ excitation
• Most materials exhibit both, elastic and inelastic behavior depending upon level of loading.
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Linear Vs Nonlinear
• Linearity– The response is directly proportional to excitation– (Deflection doubles if load is doubled)
• Non-Linearity– The response is not directly proportional to excitation– (deflection may become 4 times if load is doubled)
• Non-linear response may be produced by:– Geometric Effects (Geometric non-linearity)
– Material Effects (Material non-linearity)
– Both
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Elasticity and LinearityElasticity and LinearityA
ctio
n
Deformation
Act
ion
Deformation
Act
ion
DeformationA
ctio
nDeformation
Linear-Elastic Linear-Inelastic
Nonlinear-Elastic Nonlinear-Inelastic
Physical Object Based Modeling, Analysis and Design
Physical Object Based Modeling, Analysis and Design
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Continuum Vs Structure
• A continuum extends in all direction, has infinite particles, with continuous variation of material properties, deformation characteristics and stress state
• A Structure is of finite size and is made up of an assemblage of substructures, components and members
• Dicretization process is used to convert Structure to Finite Element Models for determining response
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Physical Categorization of Structures
• Structures can be categorized in many ways.
• For modeling and analysis purposes, the overall physical behavior can be used as basis of categorization
– Cable or Tension Structures
– Skeletal or Framed Structures
– Surface or Spatial Structures
– Solid Structures
– Mixed Structures
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Structure Types
• Cable Structures• Cable Nets• Cable Stayed
• Bar Structures• 2D/3D Trusses• 2D/3D Frames, Grids
• Surface Structures• Plate, Shell• In-Plane, Plane Stress
• Solid Structures
• Cable Structures• Cable Nets• Cable Stayed
• Bar Structures• 2D/3D Trusses• 2D/3D Frames, Grids
• Surface Structures• Plate, Shell• In-Plane, Plane Stress
• Solid Structures
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Structure, Member, Element
• Structure can considered as an assemblage of “Physical Components” called Members– Slabs, Beams, Columns, Footings, etc.
• Physical Members can be modeled by using one or more “Conceptual Components” called Elements– 1D elements, 2D element, 3D elements
– Frame element, plate element, shell element, solid element, etc.
• Modeling in terms Graphical Objects to represent Physical Components relieves the engineers from intricacies and idiosyncrasy of finite element discretization
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Structural Members
Dimensional Hierarchy of Structural Members
Continuum
Regular Solid(3D)
Beam (1D)b h
L>>(b,h)
b
htz
Plate/Shell (2D)x z
t<<(x,z) x
z
y
x L
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Load Transfer Path For Gravity Loads
• Most loads are basically “Volume Loads” generated due to mass contained in a volume
• Mechanism and path must be found to transfer these loads to the “Supports” through a Medium
• All types of Static Loads can be represented as:– Point Loads
– Line Loads– Area Loads
– Volume Loads
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
The Load Transfer Path
• The Load is transferred through a medium which may be:– A Point– A Line– An Area– A Volume – A system consisting of combination of
several mediums
• The supports may be represented as:– Point Supports– Line Supports– Area Supports– Volume Supports
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Graphic Object Representation
Object
Line
Area
Volume
Point LoadConcentrated Load
Beam LoadWall LoadSlab Load
Slab LoadWind Load
Seismic LoadLiquid Load
Node
Beam / TrussConnection Element
Spring Element
Plate ElementShell ElementPanel/ Plane
Solid Element
Point SupportColumn Support
Line SupportWall Support
Beam Support
Soil Support
Soil Support
Point
LoadGeometryMedium
SupportBoundary
ETABS uses graphic object modeling concept
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Load Transfer Path is difficult to Determine
• Complexity of Load Transfer Mechanism depend on:
– Complexity of Load
– Complexity of Medium
– Complexity of Boundary
Point Line Area Volume
Line
Area
Vol.
Line
Area
Volume
Load
Medium
Boundary
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Load Transfer Path is difficult to Determine
Transfer of a Point Load to Point Supports Through Various Mediums
Point Line Area Volume
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Objects in ETABS
• Building Object Specific Classification– Plank – One way slabs
– Slab – One way or Two way slabs
– Deck – Special one way slabs
– Wall – Shear Walls, Deep Beams, In-Fill Panel
– Frame – Column, Beam or Brace
• Finite Elements– Shell
– Plate
– Membrane
– Beam
– Node
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
The Frame Element
• The Actions Corresponding to Six DOF at Both Ends, in Local Coordinate System
• The Actions Corresponding to Six DOF at Both Ends, in Local Coordinate System
11
33
22
33
22
+P+P+V2+V2
+V3+V3
+V3+V3
+V2+V2+P+P
11
33
22
33
22
+T+T+M2+M2
+M3+M3
+M3+M3
+M2+M2+T+T
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Shell Element
General•Total DOF per Node = 6 (or 5)•Total Displacements per Node = 3•Total Rotations per Node = 3•Used for curved surfaces
Application•For Modeling surface elements carrying general loads
Building Specific Application•May be used for modeling of general slabs systems. But not used generally
1
23
U1, R1Node 3
U3, R3
U2, R2
U1, R1
Node 1
U3, R3 U2, R2
U1, R1
Node 4
U3, R3
U2, R2
U1, R1
Node 2
U3, R3
U2, R2
Shell
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Plate Element
General•Total DOF per Node = 3•Total Displacements per Node = 1•Total Rotations per Node = 2•Plates are for flat surfaces
Application•For Modeling surface elements carrying
out of plane loads
Building Specific Application•For representing floor slabs for Vertical Load Analysis•Model slabs
R1
Node 1
U3R2
1
23
R1
Node 2
U3R2
R1
Node 3
U3R2
R1
Node 4
U3R2
Plate
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Membrane Element
General•Total DOF per Node = 3 (or 2)•Total Displacements per Node = 2•Total Rotations per Node = 1 (or 0)•Membranes are modeled for flat surfaces
Application•For Modeling surface elements carrying in-plane loads
Building Specific Application•For representing floor slabs for Lateral Load Analysis. • Model Shear walls, Floor Diaphragm etc
Membrane
U1Node 1
R3U2
U1Node 3
R3U2
U1
Node 4
R3
U2
U1
Node 2
U2
3 2
1
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Meshing Slabs and Walls
In general the mesh in the slab should match with mesh in the wall to establish connection
Some software automatically establishes connectivity by using constraints or “Zipper” elements
“Zipper”“Zipper”
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Selection Of Structural Systems Selection Of Structural Systems
Basic Concepts and Considerations Basic Concepts and Considerations
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Knowledge Model for System Selection
StructuralSystem Selection
ConstructionEngineering
Artificial Intelligence
Str
uct
ura
lE
ng
ine
eri
ng
• Architecture
• Building Services
• Construction Eng.
• Value Eng.
• Aesthetics
• Ergonomics Eng.
• Structural Eng.
• Knowledge Eng.
• Economics
• Artificial Intelligence
• System Eng.
• Common Sense
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Determining System Suitability
ijk
p
kijklij
n
jiji
m
iil SCSBSAV
111
The Analytical Hierarchy ApproachA weighted importance and suitability value analysis to determine the comparative value of a system or option
Value of an Option
Global Importance
Weights and Scores
Sub Importance
Weights and Scores
Suitability Value and
Score
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Evaluating System Suitability
Slab Systems Criteria Weights and Scores System Value
(V)Main Criteria Ai Am
Sub Criteria Bij Sub Criteria Bin Bmn
Item k Item p Item k Item p Item p
Wt Score Wt Score Wt Score Wt Score Score
System – 1
System – l Cijkl Sijkl Cijnl Sijpl Cinkl Sinkl Cinnl Sinpl Smnpl
System - q
ijk
p
kijklij
n
jiji
m
iil SCSBSAV
111
The Suitability Equation
Using the Suitability Equation
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Assigning Suitability Values
10 Most important, most suitable, most desirable, essential
8,9 Very important, very suitable, very desirable
6,7 Important, suitable or desirable
5 May be or could be important, suitable or desirable
4,3 May not be important, suitable or desirable
1,2 Not important, not suitable, not desirable
Score or Weight Representation of Suitability
0 Definitely not required, definitely not suitable, ignore
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Selection of Structural System
Function has considerable effect on the selection of structural system
Based on Function/Occupancy of Tall Buildings:
• Residential Buildings– Apartments
– Hotels
– Dormitories
• Office and Commercial Buildings
• Mixed Occupancy – Commercial + Residential
• Industrial Buildings and Parking Garages
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Typical Characteristics of Residential Bldg
• Known location of partitions and their load
• Column lines generally matches architectural layout
• Typical spans 15-22 ft
• Tall buildings economy in achieved using the thinnest slab
• One way pre-cast or flat slab – popular
• Lateral load resistance provided by frame or shear walls
• More or less fixed M/E system layouts
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Typical Characteristics of Office and Commercial Bldg
• Unknown location of partitions and their load• Typical spans 20-35 ft• Need for flexible M/E layouts• Post-tension or ribbed and flat slab with drop panel –
popular
• Ideal balance between vertical and lateral load resisting systems: sufficient shear walls to limit the resultant tension under gravity plus wind
• Lateral load resistance varies significantly
Vertical Load Vertical Load Resisting SystemsResisting Systems
The Components Needed to The Components Needed to Complete the Load-Transfer Path for Complete the Load-Transfer Path for
Vertical Gravity LoadsVertical Gravity Loads
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Gravity Load Resisting Systems
Purpose
“ To Transfer Gravity Loads Applied at the Floor Levelsdown to the Foundation Level”
• Direct Path Systems• Slab Supported on Load Bearing Walls
• Slab Supported on Columns
• Indirect Multi Path Systems• Slab Supported on Beams
• Beams Supported on Other Beams
• Beams Supported on Walls or Columns
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Vertical Load Resisting Systems
1. Slabs supported on Long Rigid Supports– Supported on stiff Beams or Walls
– One-way and Two-way Slabs
– Main consideration is flexural reinforcement
2. Slab-System supported on Small Rigid Supports– Supported on Columns directly
– Flat Slab Floor systems
– Main consideration is shear transfer, moment distribution in various parts, lateral load resistance
3. Slabs supported on soil– Slabs on Grade: Light, uniformly distributed loads
– Footings, Mat etc. Heavy concentrated loads
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Vertical LoadVertical Load Behavior and Response Behavior and Response
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Popular Gravity Load Resting Systems
• Direct Load Transfer Systems (Single load transfer path)
– Flat Slab and Flat Plate
– Beam-Slab
– Waffle Slab
– Wall Joist
• Indirect Load Transfer System (Multi step load transfer path)
– Beam, Slab
– Girder, Beam, Slab
– Girder, Joist
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Conventional Approach
• For Wall Supported Slabs– Assume load transfer in One-Way or Two-Way manner
– Uniform, Triangular or Trapezoidal Load on Walls
• For Beam Supported Slabs– Assume beams to support the slabs in similar ways as walls
– Design slabs as edge supported on beams
– Transfer load to beams and design beams for slab load
• For Flat-Slabs or Columns Supported Slabs– Assume load transfer in strips directly to columns
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Popular Gravity Load Resting Systems
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Gravity Load Transfer Paths
Single PathSlab On Walls
Single PathSlab on Columns
Dual PathSlab On Beams,
Beams on Columns
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Gravity Load Transfer Paths
Mixed PathSlab On WallsSlab On BeamsBeams on Walls
Complex PathSlab on BeamsSlab on Walls
Beams on BeamsBeams on Columns
Three Step PathSlab On Ribs
Ribs On BeamsBeams on Columns
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Simplified Load Transfer
Transfer of Area Load
To Lines To Points To Lines and Points
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Load Transfer Through Slab and Beam
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Slab Deformation and Beams
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Slab System Behavior
5.0 m
Slab T = 200 mmBeam Width, B = 300 mmBeam Depth, Da) 300 mmb) 500 mmc) 1000 mm
D
B
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Moment Distribution in Beam-Slab
Effect of Beam Size on Moment Distribution
a) Beam Depth = 300 mm
b) Beam Depth = 500 mmc) Beam Depth = 1000 mm
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Moment Distribution in Slabs Only
Effect of Beam Size on Moment Distribution
a) Beam Depth = 300 mm b) Beam Depth = 500 mm c) Beam Depth = 1000 mm
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Modeling and Analysis for Modeling and Analysis for Vertical LoadsVertical Loads
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Modeling for Gravity Loads
• Must be carried out for several load cases/ patterns
• Does not change much for different floors
1. Use “Direct Design” Methods– Model, analyze and design “Floor by Floor, Without columns”
– Slab analysis and design by using Coefficients
– Beam analysis as continuous beams
2. Use Sub-Frame Concept– Model slab/ beam for in-plane loads
– Model, analyze and design “Floor by Floor, With columns”
3. Use Grid, Plate Model for the Floor– Model slab and beams for out-of plane loads
– Analyze un-symmetrical loads, geometry, openings etc.
4. Use full 3D Modeling
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Column StripColumn Strip
Middle StripMiddle Strip
De
sig
n S
trip
Middle StripMiddle StripD
esi
gn
Str
ip
The Design Strip ConceptThe Design Strip Concept
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Using Equivalent Frame Method – Design StripUsing Equivalent Frame Method – Design Strip
Column Strip
½ Middle Strip
½ Middle Strip
Design Strip
L2
L2
L1
Longitudinal Beams
Transverse Beams
Drop Panels
Lateral LoadLateral LoadResisting SystemsResisting Systems
The Components Needed to The Components Needed to Complete the Load-Transfer Path for Complete the Load-Transfer Path for
Lateral LoadsLateral Loads
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Purpose
“ To Transfer Lateral Loads Applied at any location in the structure down to the Foundation Level”
• Single System• Moment Resisting Frames
• Braced Frames
• Shear Walls
• Tubular Systems
• Dual System• Shear Wall - Frames
• Tube + Frame + Shear Wall
Lateral Load Bearing Systems
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Lateral Loads
• Primary Lateral Loads– Load generated by Wind Pressure
– Load generated due to Seismic Excitation
• Other Lateral Loads– Load generated due to horizontal component of Gravity
Loads in Inclined Systems and in Un-symmetrical structures
– Load due to lateral soil pressure, liquid and material retention
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Sample Lateral Load Resistance Systems
• Bearing wall system– Light frames with shear panels– Load bearing shear walls
• Fully Braced System (FBS)– Shear Walls (SW)– Diagonal Bracing (DB)
• Moment Resisting Frames (MRF)– Special Moment-Resisting Frames (SMRF)– Concrete Intermediate Moment-Resisting Frame (IMRF)– Ordinary Moment-Resisting Frame (OMRF)
• Dual Systems (DS)– Shear Walls + Frames (SWF)– Ordinary Braced Frame (OBF)– Special Braced Frame (SBF)
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Moment Resisting Frame
• The Load is transferred by shear in columns, that produces moment in columns and in beams
• The Beam-Column connection is crucial for the system to work
• The moments and shear from later loads must be added to those from gravity loads
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Shear Wall and Frame
• The lateral loads is primarily resisted by the shear in the walls, in turn producing bending moment
• The openings in wall become areas of high stress concentration and need to be handled carefully
• Partial loads is resisted by the frames
• Traditionally 75/25 distribution haws been used
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Shear Wall - Frame
• The Walls are part of the frame and act together with the frame members
• The lateral loads is primarily resisted by the shear in the walls, in turn producing bending moment.
• Partial loads is resisted by the frame members in moment and shear
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Braced Frame
• The lateral loads is primarily resisted by the Axial Force in the braces, columns and beams in the braced zone.
• The frame away from the braced zone does not have significant moments
• Bracing does not have to be provided in every bay, but should be provided in every story
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Tubular Structure
• The system is formed by using closely spaced columns and deep spandrel beams
• The lateral loads is primarily resisted by the entire building acting as a big cantilever with a tubular/ box cross-section
• There is a “shear lag” problem between opposite faces of the tube due to in-efficiency of column beam connection
• The height to width ratio should be more than 5
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Braced Tube Systems
• Diagonal Braces are added to the basic tubular structure
• This modification of the Tubular System reduces shear lag between opposite faces
Lateral Load Lateral Load Resisting Resisting SystemSystem
Behavior, Response and Behavior, Response and ModelingModeling
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Modeling for Lateral Loads
1. 2D Frame Models– Convert building in to several 2D frames in each direction
– Suitable for symmetrical loads and geometry
2. 3D Frame Model– Make a 3D frame model of entire building structure
– Can be “open floor” model or “braced floor” model
3. Full 3D Finite Element Model– A full 3D Finite Element Model using plate and beam elements
4. Rigid Diaphragm Model– A special model suitable for buildings that uses the concept of Rigid
Floor Diaphragm
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Modeling as 2D Frame(s)
• Convert 3D Building to an assemblage of 2D Frames– Using Independent Frames
– Using Linked Frames
– Using Sub-Structuring Concept
• Advantages– Easier to model, analyze and interpret
– Fairly accurate for Gravity Load Analysis
• Main Problems:– Center of Stiffness and Center of Forces my not coincide
– Difficult to consider building torsional effects
– Several Frames may need to be modeled in each direction
– Difficult to model non-rectangular framing system
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Create a Simple 2D ModelCreate a Simple 2D Model
1. Consider the Structure Plan and 3D View
2. Select and isolate Typical 2D Structure
4. Obtain results
3. Discretize the Model, apply loads
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Using Linked FramesUsing Linked Frames
PlanModeling
Shear Wall
Typical Frame Elevation
Linked Elements
Link Element can allow only to transmit the shear and axial force from one end to other end. It has moment discontinuity at both ends
Link Element act as a member which links the forces of one frame to another frame, representing the effect of Rigid Floor.
F3
F2
F1
F1
F2 F3
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Full 3D Finite Element Model
• The columns and beams are modeled by using beam elements
• The slabs and shear walls are modeled by using plate elements– At least 9 or 16 elements in each slab panel must be
used if gravity loads are applied to the slabs
– If the model is only for lateral analysis, one element per slab panel may be sufficient to model the in-plane stiffness
– Shear walls may be modeled by plate or panel or plane stress element. The out of plane bending is not significant
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Full 3D Finite Element Model
Example:– Uses more than 4000
beam and plate elements
– Suitable for analysis for gravity and lateral loads
– Results can be used for design of columns and beams
– Slab reinforcement difficult to determine from plate results
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Use Plate Elements
Modeling of Floor Diaphragm
Use Diagonal Bracing
• Use Plate Elements– Panels, Plane Stress
• Use Diagonals– In 3D Frame Models
• Use Conceptual Rigid Diaphragm– Link Frames in 2D
– Master DOF in 3D
– Use Approximately
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The Rigid Floor Diaphragm
• Combines the simplicity and advantages of the 2D Frame models with the accuracy of the 3D models
• Basic Concept:– The building structure is represented by vertical units (2D Frames,
3D Frames and Shear Walls), connected by the invisible rigid diaphragm
– The lateral movement of all vertical units are connected to three master degree of freedom
– This takes into account the building rotation and its effect on the vertical units.
– The modeling and analysis is greatly simplified and made efficient
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Rigid Floor Diaphragm Concept
• Modeled as Rigid Horizontal Plane of infinite
in-plane stiffness (in X-Y plane)• Assumed to have a hinge connection with
frame member or shear wall, so flexural
influence of all floors to lateral stiff ness is
neglected• All column lines of all frames at particular
level can not deform independent of each
other• The floor levels of all frames must be at the
same elevation and base line, but they need
not have same number of stories
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How RFD Concept Works
UL
UL1
UL2
UL3
X
Y
F3 , 2
F1 , 1
F3 , 3
uilding d.o.f.’s
F2 , 1
r x
r
rY
Local Frame DOF
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When Single Rigid Floor Cannot be Used
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Automatic Floor Meshing and Auto Load Transfer
(In ETABS)
Automatic Floor Meshing and Auto Load Transfer
(In ETABS)
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Area Objects: Slab
By default uses two-way load transfer mechanism
Simple RC solid slab
Can also be used to model one way slabs
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Area Object: Deck
Use one-way load transfer mechanism
Metallic Composite Slabs
Includes shear studs
Generally used in association with composite beams
Deck slabs may be
o Filled Deck
o Unfilled Deck
o Solid Slab Deck
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Area Object: Plank
By default use one-way load transfer mechanism
Generally used to model pre-cast slabs
Can also be simple RC solid slab
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Automatic Floor Meshing
First step to Auto Load Transfer
Automatic Floor Meshing
First step to Auto Load Transfer
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Basic Floor Modeling Object
• Points– Columns
– Load Points
– Boundary Point
• Lines– Beams
• Areas– Deck: Represents a Steel Metal Deck, One way Load Transfer
– Plank : Represents clearly on-way slab portion
– Slab: Represents one-way or two-way slab portion
– Opening: Represents Openings in Floor
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Automatic Meshing
• ETABS automatically meshes all line objects with frame section properties into the analysis model
• ETABS meshes all floor type (horizontal) area objects (deck or slab) into the analysis model
• Meshing does not change the number of objects in the model
• To mesh line objects with section properties use Edit menu > Divide Lines
• To mesh area objects with section properties use Edit menu > Mesh Areas
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Automatic Meshing
• Automatic Meshing of Line Objects – Frame elements are meshed at locations where other frame
elements attach to or cross them and at locations where point objects lie on them.
– Line objects assigned link properties are never automatically meshed into the analysis model by ETABS
– ETABS automatically meshes (divides) the braces at the point where they cross in the analysis model
– No end releases are introduced.
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Automatic Meshing of Line Objects
Girder A
Girder B
Beam
1
Beam
2
Piece 1 Piece 2 Piece 3
Beam 1 Beam 2
b) Girders A and B As Modeled inthe ETABS Analysis Model
a) Floor Plan
Example showing how beams are automatically divided (meshed) where they support other beams for the ETABS analysis model
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Automatic Meshing of Area Objects
– ETABS automatically meshes a floor-type area object up into four-sided (quadrilateral) elements
– Each side of each element of the mesh has a beam (Real or Imaginary) or wall running along it
– ETABS treats a wall like two columns and a beam where the columns are located at the ends of the wall and the beam connects the columns.
– Each column is assumed to have four beams connecting to it – The floor is broken up at all walls and all real and imaginary beams to
create a mesh of four-sided elements
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Girder A
Girder B
Beam
1
Beam
2
Beam
3
Girder A
Girder BBe
am 1
Beam
2
Beam
3
c) ETABS Automatic Floor Meshingb) ETABS Imaginary Beams Shown Dasheda) Floor Plan
Example of ETABS automatically generated mesh for floor-type area objects
Automatic Meshing of Area Objects
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Automatic Meshing of Area Objects
d) ETABS Automatic Floor Meshing
b) ETABS Imaginary Beams ConnectingColumns Shown Dashed
a) Floor Plan (No Beams)
c) ETABS Imaginary Beams Extended toEdge of Floor Shown Dashed
Example of ETABS automatically generated mesh for floor-type area objects
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Automatic Meshing of Area Objects
– For floors that are automatically meshed by ETABS it is recommended that model beams (or at least null-type line objects) are connecting columns rather than no beams (or line objects)
– This makes the automatic meshing for the analysis model cleaner, faster and more predictable
– Including beams and/or null-type line objects between all columns in your model makes automatic floor meshing more predictable
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Automatic Meshing of Area Objects
c) b) a)
f) e) d)
i) h) g)
C1 C2
C3C4
C1 C2
C3C4
C1 C2
C3C4
C1 C2
C3C4
C1 C2
C3C4
C1 C2
C3C4
C1 C2
C3C4
C1 C2
C3C4
C1 C2
C3C4
Illustration of how ETABS creates the distribution of imaginary beams
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Automatic Transformation and Transfer of Floor Loads to
Appropriate Elements
(Using the Auto Meshed Geometry)
Automatic Transformation and Transfer of Floor Loads to
Appropriate Elements
(Using the Auto Meshed Geometry)
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Load Transformation
The main issue:How point loads, line loads and area loads that lie on an area object in your object-based ETABS model are represented in the analysis model
There are four distinct types of load transformation in ETABS for out-of-plane load transformation for floor-type area objects
• with deck section properties • with slab section properties that have membrane behavior only• all other types of area objects • In-plane load transformation for all types of area objects
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Load Transformation
Area Objects – load transformation occurs after any
automatic meshing into the analysis model
– ETABS normalizes the coordinates of the four corner points of the area object
– The normalization is the key assumption in this method
– It is a perfectly valid assumption if the quadrilateral is a square, rectangular or a parallelogram
a) Quadrilateral Element
12
43
b) The r and s Axes
12
43
r
s
(1, 1)(-1, 1)
(1, -1)(-1, -1)
c) Corner Point r-s Coordinates
12
43
r
s
(r, s)
P
(1, 1)(-1, 1)
(1, -1)(-1, -1)
d) Point Load, P
12
43
r
s
Example of transfer of out-of-plane loads for other area objects
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Load Transformation
• The load distribution for deck sections is one way, in contrast to slab sections which are assumed to span in two directions
• ETABS first automatically meshes the deck into quadrilateral elements
• Once the meshing is complete ETABS determines the meshed shell elements that have real beams along them and those that have imaginary beams
• It also determines which edges of the meshed shell elements are also edges of the deck.
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Load Transformation
Rectangular Interior Meshed Element with Uniform Load
Edge 1
Edge 3
Edge
2
Edge
4
x
Edge 1
Edge 3
Edge
2
Edge
4
x / 2 x / 2
Uniform load = w
Direction of deck span
a) Rectangular Interior Elementof Meshed Floor
b) Distribution of Uniform Load
wx / 2
c) Loading on Edges 2 and 4
Example of rectangular interior meshed
element with a uniform load
If the supporting member at the end point of an imaginary beam is itself imaginary, then the load from the imaginary beam tributary to that end point is lost, that is, it is ignored by ETABS
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Load TransformationRectangular Interior Meshed Element with Point Load
– ETABS distributes the point load to the appropriate edge beams (based on the direction of the deck span)
– If the beams along edges are real beams ETABS transfers the load onto adjacent beams
Edge 1
Edge 3
Edge
2
Edge
4
x1 x2
Point load, P
Direction of deck span
a) Rectangular Interior Elementof Meshed Floor
b) Distribution of Point Load
x1 x2Edge 4 Edge 2
P
P * x2x1 + x2
P * x1x1 + x2
c) Loading on Edge 2
P * x1x1 + x2
d) Loading on Edge 4
P * x2x1 + x2
If the supporting member at the end point of an imaginary beam is itself imaginary, then the load from the imaginary beam tributary to that end point is lost, that is, it is ignored by ETABS
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Load Transformation
Rectangular Interior Meshed Element with Line Load
– A line load is transformed in a similar fashion to that for a point load using a numerical integration technique
– The line load is discredited as a series of point loads which are transformed to surrounding beams
– The series of point loads is then converted back to a line load on the surrounding beams
– An area load that does not cover the entire element is also transformed in a similar fashion to that for a point load using a numerical integration technique.
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General Interior Meshed Element
d)
Edge 1
Edge 3
Edge
2
Edge
4
Edge 1
Edge 3
Edge
2
Edge
4
e) Transformation of Uniform Load
Edge 1
Edge 3
Edge
2
Edge
4
Uniform load
Direction of deck span
a) General Interior Element ofMeshed Floor Deck
b)
Edge 1
Edge 3
Edge
2
Edge
4
Edge 1
Edge 3
Edge
2
Edge
4
c)
g) Loading on Edge 2
f) Loading on Edge 1
h) Loading on Edge 3 i) Loading on Edge 4
Midpoint
Midpoint
Example of general interior meshed element with a
uniform load
a) General Interior Element ofMeshed Floor Deck
P1
P2P3
b)
P1
P2P3
Line 1
Line 2
Line 3
Example of general interior meshed
element with a point load
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Exterior Meshed Element
Edge of deck is atcenter of spandrelbeam, typical in thisexample
Beam 1a
B CA
E FD
a) Floor Plan b) Deck Meshing
Beam 1b Beam 1b
Bea
m 2
aB
eam
2b
Bea
m 2
aB
eam
2bExample of exterior meshed
elements with real beams on all sides
Beam 3a
B CA
ED
a) Floor Plan b) Deck Meshing
Beam 3b
Beam
1a
Beam
1b
Imag
inar
y Be
am 5
Beam
2b
Beam 3a Beam 3b
Beam
1a
Beam
1b
Beam
2a
Beam
2b
Beam 4a Beam 4b
Imag
inar
yBe
am 6No beam at
edge of deck
No beam atedge of deck
Example of exterior meshed elements with cantilever beams extending to edge of deck
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Exterior Meshed Element
Imaginary Beam 8
a) Floor Plan b) Deck Meshing
B CA
ED
Imag
inar
y Be
am 5
Imag
inar
yBea
m 6
Beam 3a Beam 3b
Beam
1a
Beam
1b
Beam
2a
Beam
2b
Beam 3a Beam 3b
Beam
1a
Beam
1b
Beam
2a
Beam
2bImaginary Beam 7
Imaginary Beam 8
E1
Imag
inar
yBea
m 6
Beam 3b
Beam
2b
E2
c) Condition at Skewed DeckEdge (Areas D and E)
Imaginary Beam 7
D
DBeam 3aBe
am 1
b
No beam atedge of deck
No beam atedge of deck
Example of exterior meshed elements with cantilever beams extending to edge of a skewed deck
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Exterior Meshed Element
Beam 1
B CA
ED
a) Floor Plan b) Deck Meshing
Beam
2
Beam 1
Beam
2
Column 1 Column 1
Edge of deck
Example of exterior meshed elements with overhanging slab
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Exterior Meshed Element
Beam 1a Beam 1a
B CA
E FD
a) Floor Plan b) Deck Meshing
Beam 1b Beam 1b
Beam
2a
Beam
2b
Beam
2a
Beam
2b
G H I
J
K
Beam
3a
Beam
3b
Example of exterior meshed elements with overhanging slab
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Effect of Deck Openings
a) Floor Plan with Unframed Opening
Beam 1
4' 6' 14'
6'4'
2'
b) Floor Plan with Framed Opening(Beams on all Sides)
Beam 1
4' 6' 14'
6'4'
2'
c) Unframed, unloaded opening
4' 6' 14'
Note: Assume floor loading is 100psf. Opening is either loaded orunloaded as noted in c, d, e and fwhich are loading diagrams forBeam 1.
d) Unframed, loaded opening
e) Framed, unloaded opening
f) Framed, loaded opening
0.7k
0.6 klf 0.2 klf
0.6 klf 0.6 klf
0.6 klf 0.6 klf
0.1 klf
0.1 klf
0.7k
1.5k 1.5k
Example of effect of openings on distribution of load over deck sections
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Load TransformationVertical Load Transformation for Floors with Membrane Slab Properties
– only applies to floor-type area objects with slab section properties that have membrane behavior only
– The load distribution for membrane slab sections is two way
– The actual distribution of loads on these elements is quite complex
– ETABS uses the concept of tributary loads as a simplifying assumption for transforming the loads
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Floors with Membrane Slab Properties
f) Real beam on one sidee) Real beams on twoopposite sides
d) Real beams on twoadjacent sides
c) Case 2 of real beams onthree sides
b) Case 1 of real beams onthree sides
a) Real beams on all sides
1
324
1
3
24
123
1
231
23
1
2
3
1
2
1
2
1
1
1
1
2
2
i) Real beam on one sideplus two verticalsupport elements atcorner points
h) Real beams on twoadjacent sides plusone vertical supportelement at corner point
g) Real beam on one sideplus one verticalsupport element atcorner point
11
1
1
1
3
1
3
2
2
2
2midpoint
2
2
3
3
l) Vertical supportelements at twoadjacent corner points(no real beams)
j) Vertical supportelements at all cornerpoints (no real beams)
1
1
33
3
k) Vertical supportelements at threecorner points (no realbeams)
4
2
2
4
1 2
12
3
1 2
1 2
m)Vertical supportelements at twoopposite corner points(no real beams)
1
1
Legend
Real beam at shell edge
No beam at shell edge
Tributary area dividing line
Vertical support element
midpoints
n) Vertical supportelements at onecorner point (noreal beams)
1
1
2
2
f) Real beam on one sidee) Real beams on twoopposite sides
d) Real beams on twoadjacent sides
c) Case 2 of real beams onthree sides
b) Case 1 of real beams onthree sides
a) Real beams on all sides
1
324
1
3
24
123
1
231
23
1
2
3
1
2
1
2
1
1
1
1
2
2
i) Real beam on one sideplus two verticalsupport elements atcorner points
h) Real beams on twoadjacent sides plusone vertical supportelement at corner point
g) Real beam on one sideplus one verticalsupport element atcorner point
11
1
1
1
3
1
3
2
2
2
2midpoint
2
2
3
3
l) Vertical supportelements at twoadjacent corner points(no real beams)
j) Vertical supportelements at all cornerpoints (no real beams)
1
1
33
3
k) Vertical supportelements at threecorner points (no realbeams)
4
2
2
4
1 2
12
3
1 2
1 2
m)Vertical supportelements at twoopposite corner points(no real beams)
1
1
Legend
Real beam at shell edge
No beam at shell edge
Tributary area dividing line
Vertical support element
midpoints
n) Vertical supportelements at onecorner point (noreal beams)
1
1
2
2
Tributary areas for various conditions of a membrane slab
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Floors with Membrane Slab Properties
a) Full uniform loadtransformation
b) Partial uniform loadtransformation
c) Line load transformation d) Point load transformation
1
324
3
24
1
1
324
3
24
1
1
324
3
24
1
1
324
3
24
1
Example of load distribution on a membrane slab
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
Type of Slab Systems in SAFE
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
The 5-Story Walkup Flats
4.0 4.0 5.5 5.5 4.0 4.0
6.0
6.0
2.8
2.8
Column Layout Plan
1
2
3
5
6A CB D E F G
4
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
The 5-Story Walkup Flats
4.0 4.0 5.5 5.5 4.0 4.0
6.0
6.0
2.8
2.8
Slab and Beam Layout
1
2
3
5
6A CB D E F G
4
C1= 0.3 x 0.8C2 = 0.3 x 0.4
B1 = 0.25 x 0.4B2 = 0.25 x 0.5
S1 = 0.15
B1
B2
C1C2
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
The 5-Story Walkup Flats
12356 4
3.0
3.0
3.0
3.0
3.5
2.0
Section
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
35 Story Office Building
6.0 6.0 8.0 8.0 6.0 6.0
8.0
8.0
1
2
4
5
A CB D E F G
3
7.0
7.0 PlanTypical Floor(B1, B2, 4-35)
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
35 Story Office Building
6.0 6.0 8.0 8.0 6.0 6.0
8.0
8.0
1
2
4
5
A CB D E F G
3
7.0
7.0 PlanFloor 1-2
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
35 Story Office Building
6.0 6.0 8.0 8.0 6.0 6.0
8.0
8.0
1
2
4
5
A CB D E F G
3
7.0
7.0 PlanFloor 3
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
35 Story Office Building
1245 3
2 @ 5.0
2 @ 2.8
32 @ 3.5
Section atC and D
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
35 Story Office Building
1245 3
2 @ 5.0
2 @ 2.8
32 @ 3.5
Section atB and E
Modeling, Analysis and Design of Buildings AIT AIT - Thailand- Thailand ACECOMS
35 Story Office Building
1245 3
2 @ 5.0
2 @ 2.8
32 @ 3.5
Section atA and G