Aug 23-24, Kuala Lumpur, Malaysia
International Seminar on Computer Aided Analysis and Design Of Building Structures Institute of Engineers Malaysia
•
Computers and Structures Inc., USA
•
Asian Center for Engineering Computations and Software Asian Institute of Technology, Thailand
•
Building Structures Modeling and Analysis Concepts
Naveed Anwar
Overr al Ove alll D esi gn Pr P r oce oces ss
• Conception • Modeling • Analysis • Design • Detailing • Drafting • Costing
Integrated Design Process
Buil ding 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
The Buil ding Str uctur al System - Physical Building Structure Floor Diaphragm Frame and Shear Walls Lateral Load Resisting System
Floor Slab System Gravity Load Resisting System
Sub-structure and Member Design
Beams, Columns, Two-way Slabs, Flat Slabs, Pile caps Shear Walls, Deep Beams, Isolated Footings, Combined Footings
The Building Str uctur al 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
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 Response To Loads
T h e S im p l i f i ed S tr u c t u r a l Sy s t em
STRUCTURE RESPONSES
EXCITATION Loads Vibrations Settlements Thermal Changes
pv
Displacements Strains Stress Stress Resultants
Analysis of Str uctur es
xx
x
yy y
zz z
pvx 0
pv
Real Structure is governed by “Partial Differential Equations” of various order Direct solution is only possible for: • Simple geometry • Simple Boundary • Simple Loading.
The Need for M odeling
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
The Need for Str uctur al M odel
STRUCTURE RESPONSES
EXCITATION Loads Vibrations Settlements Thermal Changes
Displacements Strains Stress Stress Resultants
pv
Structural Model
F ini te Element M ethod: 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”
Conti nuum to Discr ete M odel
pv
3D-CONTINUM MODEL
(Governed by partial differential equations)
CONTINUOUS MODEL OF STRUCTURE
(Governed by either partial or total differential equations)
DISCRETE MODEL OF STRUCTURE
(Governed by algebraic equations)
F r om Classical to F EM Soluti on
Classical
Equilibrium
Actual Structure xx x
yy y
zz z
FEM
Assumptions
Structural Model
Stress-Strain Law
pvx 0
Kr
Compatibility “Partial Differential Equations”
t
_
dV
p
t v
_
u dV
R
“Algebraic Equations”
p
t s
_
u ds
v
(Principle of Virtual Work)
K = Stiffness r = Response R = Loads
Simplif ied Str uctur al System
Loads (F)
Deformations (D) Fv
D
K
F
F=KD
T h e St r u c t u r a l S y s t e m
STRUCTURE
RESPONSES
EXCITATION pv
• Static • Dynamic
• Elastic • Inelastic
• Linear • Nonlinear
The Equilibr ium Equations 1. Linear-Static
Ku
Elastic OR Inelastic
F
2. Linear-Dynamic Elastic
(t ) C u(t ) Ku(t ) F (t ) M u 3. Nonlinear - Static
Ku F NL
Elastic OR Inelastic
F
4. Nonlinear-Dynamic
Elastic OR Inelastic
(t ) C u(t ) Ku(t ) F (t ) NL F (t ) M u
Basic Steps in F EA
Evaluate Real Structure Create Structural Model Discretize Model in FE Solve FE Model Engineer
Interpret FEA Results
Engineer + Software Software
Physical significance of Results
Discr etization of Conti nuums General Solid ( Orthogonal dimensions) Z
H, B much less than L
Regular Solid Beam Element
X
( T small compared to Lengths ) Y
Solid Element
Plate/ Shell
Membrane/ Panel In-Plane, Only Axial
Plate/ Slab Out of Plane, Only Bending
Shell In-Plane and Bending
Global M odeling of Str uctur al Geometr y
(a) Real Structure
(b) Solid Model
(c) 3D Plate-Frame
(e) 2D Fram e
(d) 3D Fram e
(f) Grid-Plate
Fig. 1 Various Wa ys to Model a Real Struture
Dimensions of Elements • 1 D Elements (Beam type) – Can be used in 1D, 2D and 2D – 2-3 Nodes. A, I etc. Truss and Beam Elements (1D,2D,3D)
• 2 D Elements (Plate type) – Can be used in 2D and 3D Model
– 3-9 nodes. Thickness
Plane Stress, Plane Strain, Axisymmetric, Plate and Shell Elements (2D,3D)
• 3 D Elements (Brick type) – Can be used in 3D Model – 6-20 Nodes. Brick Elements
DOF f or 1D Elements Dy
Dy
Dy Rz
Dz
Dx
2D Truss
Dx
3D Truss
2D Beam
Ry Dy Rz
Dy Dx
Rz
Dy Dz
Rx
Dx
Rx
Rz
2D Frame
2D Grid
3D Frame
DOF f or 2D Elements Ry ?
Ry ? Dy
Dy
Dy Dz
Rz
Rx
Dx
Membrane
Plate
Dx
Rz
Shell
Rx
DOF f or 3D Elements
Dy Dz
Dx
Solid/ Brick
F r ame and Gr id M odel • The structure represented by rod or bar type elements • Does not model the cross-section dimensions 3D Frame
• 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 2D Frame
2D Grid
M embr mbra ane M odel • 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
Pl an ane e Str ess an and d Pl an ane e
Plain-Strain Assumptions
x 1 unit
x2
x1
x3
3D Problem
x
2D Problem
Plane Strain Problem
Plane Stress Problem
Plate Pl ate B en di din n g M od ode el • Primar Primarily ily 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
Gener al Plate-Shel l M odel • 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
Solid M odel • 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
Soil -Str uctur e I nter action • 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
Connecting Dif f er ent Types of Elements Truss Truss Frame
Membrane
OK
Dz
OK
Rx, Ry, Rz
OK
Rx, Ry, Rz, Dz
Rx ? Dx, Dy
OK
OK
OK
Rx, Rz
OK
Rx, Ry, Rz OK
Plate
Solid
1
2
Shell
Solid
OK
OK
Rx ?
Rx, Ry, Rz
Dx, Dy
OK
OK
Rx, Rz
OK
OK
Rx, Rz
OK
Rx, Ry, Rz, Dz
Dx, Dz
OK
Rx, Rz
OK
Dz
Dx, Dz
OK
OK
Orphan Degrees Of Freedom: 0
Plate
OK
Membrane
Shell
Frame
3
4
What Type of Analysis should be Carried Out?
A n al alys ysii s T yp ype e
T h e typ type e of A n al aly ysi s to be ca carr r i ed ou ou t depe de pen n ds on th the e Str u ctu cturr al Sys yste tem m Ex citation (Loads) – The Type of Excitation – The Type Structure (Material and Geometry) – The Type Response
B as asii c An A n al alys ysii s T ype ypes s Excitation Structure Response
Basic Analysi Analysiss Type
Static
Elastic
Linear
Linear-Elastic-Static Linear -Elastic-Static Analysis
Static
Elastic
Nonlinear
Nonlinear-Elastic-Static Nonlinear -Elastic-Static Analysis
Static
Inelastic
Linear
Linear-Inelastic-Static Linear -Inelastic-Static Analysis
Static
Inelastic
Nonlinear
Nonlinear-Inelastic-Static Nonlinear -Inelastic-Static Analysis
Dynamic
Elastic
Linear
Linear-Elastic-Dynamic Analysis
Dynamic
Elastic
Nonlinear
Nonlinear-Elastic-Dynam Nonlinear -Elastic-Dynamic ic Analysis
Dynamic
Inelastic
Linear
Linear-Inelastic-Dynam Linear -Inelastic-Dynamic ic Analysis
Dynamic
Inelastic
Nonlinear
Nonlinear-Inelastic-Dynam Nonlinear -Inelastic-Dynamic ic Analysis
Some M ore Soluti on 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
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”
Elasti c Vs I nelastic • 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.
L inear Vs Nonl inear • 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
Elasticity and L inear ity n o i t c A
Linear-Elastic
n o i t c A
Deformation
Linear-Inelastic
Deformation
n o i t c A
n o i t c A
Nonlinear-Elastic Deformation
Nonlinear-Inelastic Deformation
Physical Object Based Modeling, Analysis and Design
Conti nuum Vs Str uctur e • 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
Physical Categor ization of Str uctur es • 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
Str uctur e 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
Str uctur e, M ember , 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
Str uctur al M ember s Continuum
Regular Solid (3D)
y Plate/Shell (2D) x z t<<(x,z)
z x
Beam (1D) b h L>>(b,h) h
t
z x
L b
Dimensional Hierarchy of Structural Members
L oad Tr ansfer Path F or Gr avity L oads • 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
The L oad Tr ansfer 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
Gr aphic Object Representati on Object
Load
Geometry Medium
Support Boundary
Point
Point Load Concentrated Load
Node
Point Support Column Support
Line
Beam Load Wall Load Slab Load
Beam / Truss Connection Element Spring Element
Line Support Wall Support Beam Support
Area
Slab Load Wind Load
Plate Element Shell Element Panel/ Plane
Soil Support
Volume
Seismic Load Liquid Load
Solid Element
Soil Support
ETA BS uses graphi c object modeling concept
L oad Tr ansfer Path i s diff i cul t to Deter mine • Complexity of Load Transfer Mechanism depend on:
Load
Vol.
– Complexity of Load – Complexity of Medium
Area
– Complexity of Boundary
Line Point Line Line Area Volume
Boundary
Area
Volume
Medium
L oad Tr ansfer Path i s diff i cul t to Deter mine
Point
Line
Area
Volume
Transfer of a Point Load to Point Supports Through Various Mediums
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
The F r ame Element • The Actions Corresponding to Six DOF at Both Ends, in Local Coordinate System 2
2
1
1
+V2
+M2 +P 2
2
3
3
+V3
3
+V3 +P
+V2
+T
+M3
3
+M3
+T
+M2
Shell Element General •Total DOF per Node = 6 (or 5) •Total Displacements per Node = 3 •Total Rotations per Node = 3 •Used for curved surfaces
U3, R3
U3, R3 U2, R2
Node 3
U2, R2 Node 4
U1, R1
Application •For Modeling surface elements carrying general loads
3
U3, R3 1
U3, R3
U2, R2
Node 1
Building Specific Application •May be used for modeling of general slabs systems. But not used generally
U1, R1
2
U2, R2 Node 2
U1, R1
Shell
U1, R1
Plate Element General •Total DOF per Node = 3 •Total Displacements per Node = 1 •Total Rotations per Node = 2 •Plates are for flat surfaces
U3
U3
R2
Node 3
Node 4
R1
Application •For Modeling surface elements carrying out of plane loads
3
R2
Node 1
Building Specific Application •For representing floor slabs for Vertical Load Analysis •Model slabs
R1 2
1
U3
R2
U3
R2
Node 2
R1
R1
Plate
M embrane 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
R3
U2
U2 Node 4
Node 3
U1 3
U1 2
1
R3
U2
Node 1
R3
U2
Node 2
U1
Membrane
U1
M eshing Slabs and Walls
“Zipper”
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
Selection Of Structural Systems Basic Concepts and Considerations
Knowledge M odel for System Sel ection •
Architecture
•
Building Services
•
Construction Eng.
•
Value Eng.
•
Aesthetics
•
Ergonomics Eng.
•
Structural Eng.
•
Knowledge Eng.
•
Economics
•
Artificial Intelligence
•
System Eng.
•
Common Sense
S o f t w a r e E n g i n e e r i n g
A r c h i t e c t u r e
d g a n s e n i r t e n e e n S g e r i n i n e m o n e g g e m n g i n E u d m n E J o C m s
s t e S y
Structural System Selection
Construction Engineering
g e r i n e n n g i e E u l V a
E S B n e u g r i i v l d n i i c e e n e s g r i n g
s c i t e h t s e A
s g c n i r m i o e n e o n g i g r n E E
g n l i a r r e u e t n c i u g r t n S E
Artificial Intelligence
K E n n o g w i n l e e e d g r i n e g
E c o n o m i c s
Deter mi ning System Suitability The Analytical Hierarchy Approach A weighted importance and suitability value anal ysis to deter mi ne the compar ative value of a system or option
n p V l Ai S i Bij S ij C ijkl S ijk i 1 k 1 j 1 m
Value of an Option
Global Importance Weights and Scores
Sub Importance Weights and Scores
Suitability Value and Score
Evaluating System Suitability The Suitability Equation n p V l Ai S i Bij S ij C ijkl S ijk i 1 k 1 j 1 m
Using the Suitability Equation Slab Systems
Criteria Weights and Scores Main Criteria A i Sub Criteria B ij Item k
A m
Sub Criteria B in
Item p
Item k
B mn
Item p
Item p
Wt
Score
Wt
Score
Wt
Score
Wt
Score
Score
C ijkl
S ijkl
C ijnl
S ijpl
C inkl
S inkl
C innl
S inpl
S mnpl
System – 1 System – l System - q
System Value (V)
Assigni ng Suitabili ty Values Score or Weight
Representation of Suitability
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
0
Definitely not required, definitely not suitable, ignore
Selection of Str uctur al System F unction has consider able effect on the sel ection of str uctur al 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
Typical Char acter isti cs 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
Typical Characteristics of Office and Commer cial 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 Resisting Systems The Components Needed to Complete the Load-Transfer Path for Vertical Gravity Loads
Gr avity L oad Resisti ng Systems Purpose “ To Transfer Gravity Loads Applied at the Floor Levels down 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
Ver ti cal L oad Resisti ng 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
Vertical Load Behavior and Response
Popular Gr avity L oad Resti ng Systems • Direct Load Transfer Systems
(Singl e load tr ansfer path)
– Flat Slab and Flat Plate
– Beam-Slab – Waffle Slab – Wall Joist
• Indirect Load Transfer System – Beam, Slab – Girder, Beam, Slab – Girder, Joist
(M ul ti step load transfer path)
Conventi onal Appr oach • 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
Popular Gr avity L oad Resti ng Systems
Gr avity L oad Tr ansf er Paths
Single Path
Single Path
Slab On Walls
Slab on Columns
Dual Path Slab On Beams, Beams on Columns
Gr avity L oad Tr ansf er Paths
Mixed Path
Complex Path
Slab On Walls Slab On Beams Beams on Walls
Slab on Beams Slab on Walls Beams on Beams Beams on Columns
Three Step Path Slab On Ribs Ribs On Beams Beams on Columns
Simplif ied L oad Tr ansf er
To Lines
To Points
Transfer of Area Load
To Lines and Points
L oad Tr ans nsff er T hr oug ough h Sl ab and and Be B eam
Sl ab D ef or ormati mation on and Be B eams
Sl ab Sys Syste tem m B eh avi avior or
D B
Slab T = 200 mm Beam Width, B = 300 mm Beam Depth, D a) 300 mm b) 500 mm c) 1000 mm
M oment Distr ibuti on in Beam-Slab Effect of Beam Size on Moment Distribution
a) Beam Depth = 300 mm
c) Beam Depth = 1000 mm
b) Beam Depth = 500 mm
M oment D istr ibuti on in Slabs Onl y Effect of Beam Size on Moment Distribution
a) Beam Depth = 300 mm
b) Beam Depth = 500 mm
c) Beam Depth = 1000 mm
Modeling and Analysis for Vertical Loads
M odel ing f or Gravity L oads •
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
The Design Str ip Concept
Middle Strip p i r t S n g i s e D p i r t S n g i s e D
Column Strip Middle Strip
Usi ng Equi val ent F r ame M ethod – D esign Str ip
Design Strip ½ Middle Strip
L2
Column Strip ½ Middle Strip Drop Panels Longitudinal Beams
Transverse Beams
L1
L2
Lateral Load Resisting Systems The Components Needed to Complete the Load-Transfer Path for Lateral Loads
L ater al L oad Bearing Systems 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
L ater al L oads • 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
Sampl e L ater al L oad Resistan ce 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)
M oment Resisti ng F r ame • 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
Shear Wall and F r ame • 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
Shear Wall - F r ame • 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
Br aced F r ame • 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
Tubul ar Str uctur e • 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
Br aced 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 Resisting System Behavior, Response and Modeling
M odeling for L ater al L oads 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
M odel ing as 2D F r ame(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
Cr eate a Simple 2D M odel 2. Select and isolate Typical 2D Structure
1. Consider the Structure Plan and 3D View
4. Obtain results
3. Discretize the Model, apply loads
Using L inked F r ames F1
Linked Elements Shear Wall
F2
F3
Modeling
Plan F1
F2
F3
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
Typical Frame Elevation
Link Element act as a member which links the forces of one frame to another frame, representing the effect of Rigid Floor.
F ul l 3D F ini te El ement M odel • 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
F ul l 3D F ini te El ement M odel 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
M odel ing of F l oor Diaphr agm • Use Plate Elements – Panels, Plane Stress
Use Diagonal Bracing
• Use Diagonals – In 3D Frame Models
• Use Conceptual Rigid Diaphragm – Link Frames in 2D – Master DOF in 3D – Use Approximately
Use Plate Elements
The Rigid F loor Diaphr agm • 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
Rigid F loor Diaphr agm 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
H ow RF D Concept Wor ks
Y
uilding d.o.f.’s
F1 , 1
UL
r
UL3
rY X F3 , 3
UL2
r x UL1
F3 , 2 F2 , 1
Local Frame DOF
When Single Rigid F loor Cannot be Used
Ar ea Objects: Slab By
default uses two-way load transfer mechanism
Simple Can
RC solid slab
also be used to model one way slabs
Ar ea 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
Ar ea Object: Plank By
default use one-way load transfer mechanism
Generally Can
used to model pre-cast slabs
also be simple RC solid slab
Basic F loor M odeling 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
Automatic M eshi ng • 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
Automatic M eshi ng •
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.
Automatic Meshing of Line Objects Beam 1
Girder A Piece 1 1 m a e B
2 m a e B
Piece 2
Beam 2 Piece 3
b) Girders A and B As Modeled in the ETABS Analysis Model
Girder B
a) Floor Plan
Example showing how beams are automatically divided (meshed) where they support other beams for the ETABS analysis model
Automatic Meshing of Area Objects –
–
–
–
–
ETABS automatically meshes a floor-type area object up into foursided (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
Automatic Meshing of Area Objects Girder A
1 m a e B
2 m a e B
Girder B
a) Floor Plan
Girder A
3
1
m a e B
m a e B
2 m a e B
3 m a e B
Girder B
b) ETABS Imaginary Beams Shown Dashed c) ETABS Automatic Floor Meshing
Example of ETABS automatically generated mesh for floor-type area objects
Automatic Meshing of Area Objects Example of ETABS automatically generated mesh for floor-type area objects
a) Floor Plan (No Beams)
b) ETABS Imaginary Beams Connecting Columns Shown Dashed
c) ETABS Imaginary Beams Extended to Edge of Floor Shown Dashed
d) ETABS Automatic Floor Meshing
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
Automatic Meshing of Area Objects C4
C3
C4
C3
C4
C3
C1
C2
C1
C2
C1
C2
Illustration of how ETABS creates the distribution of imaginary beams a)
b)
c)
C4
C3
C4
C3
C4
C3
C1
C2
C1
C2
C1
C2
d)
e)
f)
C4
C3
C4
C3
C4
C3
C1 g)
C2
C1
C2
C1
C2
h)
i)
(Using the Auto Meshed Geometry)
L oad Transf or mation 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
L oad Transf or mation 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
E d g e 1
2 e g d E
E d g e 3
3
a) Quadrilateral Element
b) The r and s Axes
(-1, -1)
(-1, 1)
1
2
r
4 (1, -1)
c) Corner Point r-s Coordinates
3 (-1, -1)
r
4
s
(1, 1)
2
3
It is a perfectly valid assumption if the quadrilateral is a square, rectangular or a parallelogram
E d g e 3
3
The normalization is the key assumption in this method
1 4 e g d E
E d g e 1
2 e g d E
4
(-1, 1)
–
2
4 e g d E
s
–
s
1
2
(1, 1)
(r, s)
1 r
P 4 (1, -1)
d) Point Load, P
Example of transfer of out-of-plane loads for other area objects
L oad Transf or mation •
•
•
•
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.
L oad Transf or mation Rectangular Interior Meshed Element with 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
x
x/2
Edge 3
x/2 wx / 2
Edge 3
Direction of deck span 4 e g d E
2 e g d E
4 e g d E
2 e g d E
c) Loading on Edges 2 and 4
Uniform load = w Edge 1 a) Rectangular Interior Element of Meshed Floor
Edge 1 b)Distribution of Uniform Load
Example of rectangular interior meshed element with a uniform load
L oad Transf or mation Rectangular 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
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
x1
x2
P
P * x1 x1 + x2
Edge 3 Direction of deck span 4 e g d E
Point load, P
Edge 1 a) Rectangular Interior Element of Meshed Floor
2 e g d E
Edge 4 x1
Edge 2 x2
c) Loading on Edge 2 P * x2
P * x2
P * x1
x1 + x2
x1 + x2
b)Distribution of Point Load
x1 + x2
d) Loading on Edge 4
L oad Transf or mation 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.
General Interior Meshed Element 3 E d g e 4 e g d E
Uniform load
3 E d g e 2 e g d E
3 E d g e 2 e g d E
4 e g d E
4 e g d E
Direction of deck span
3 E d g e
3 E d g e Line 3 P3
P3 4 e g d E
2 e g d E
P2
4 e g d E
P2
Line 2
P1
P1
E dg e 1
E d ge 1
a) General Interior Element of Meshed Floor Deck
Line 1
E d ge 1
E dg e 1
a) General Interior Element of Meshed Floor Deck 2 e g d E
c)
3 E d g e 2 e g d E
E d ge 1
b) d)
Midpoint
E dg e 1
b)
3 E d g e 4 e g d E
Midpoint
2 e g d E
4 e g d E
E dg e 1 e) Transformation of Uniform Load
f) Loading on Edge 1
Example of general interior meshed element with a point load g) Loading on Edge 2
h) Loading on Edge 3
i) Loading on Edge 4
Example of general interior meshed element with a uniform load
2 e g d E
Exterior Meshed Element Beam 1b
Example of exterior meshed elements with real beams on all sides
Edge of deck is at center of spandrel beam, typical in this example
D
a 2 m a e B
A
b 1 m a e B
No beam at edge of deck Beam 3a
Beam 1b
E
b 2 m a e
F
a 2 m a e B
C
B
a) Floor Plan
Example of exterior meshed elements with cantilever beams extending to edge of deck
Beam 1a
b 2 m a e B
B
b) Deck Meshing
b 2 m a e B
Beam 3b
b 1 m a e B
b 2 m a e B
D Beam 3a
E
y r a 6 n m i g a a e B m I
Beam 3b
a 1 m a e B
a 2 m a e B
a 1 m a e B
A
B
No beam at edge of deck Beam 4a
a) Floor Plan
b) Deck Meshing
C
5 m a e B y r a n i g a m I
Beam 4b
Exterior Meshed Element a m 8 a r y B e I m a g i n 6
e a m 7 n a r y B I m a g i b 1 m a e B
No beam at edge of deck Beam 3a
a 1 m a e B
b 2
b 1
m a e B
m a e B
Beam 3b
a 2 m a e B
a 1 m a e B
m a e B
D Beam 3a
A
m a e B y r a n i g a m I
b 2
E
Beam 3b
B
a 2 m a e B
5 m a e B y r a n i g a m I
C
No beam at edge of deck
a) Floor Plan
b) Deck Meshing D
Example of exterior meshed elements with cantilever beams extending to edge of a skewed deck
e a m 7 n a r y B I m a g i b 1 m a e B
D
a m 8 E2 a r y B e I m a g i n 6 b 2 m a e B
Beam 3a
c) Condition at Skewed Deck Edge (Areas D and E)
E1 Beam 3b
m a e B y r a n i g a m I
Exterior Meshed Element Edge of deck
E
D Beam 1
Beam 1 Column 1
2 m a e B
a) Floor Plan
Column 1
A
B
2 m a e B
C
b) Deck Meshing
Example of exterior meshed elements with overhanging slab
Exterior Meshed Element G Beam 1a
b 2 m a e B
a 2 m a e B
a) Floor Plan
Beam 1b
H
Beam 1a
D
A
E
b 2 m a e B
B
a 2 m a e B
I
Beam 1b
F
C
b) Deck Meshing
Example of exterior meshed elements with overhanging slab
b 3
J
m a e B
a 3 m a e B
K
Effect of Deck Openings 4'
6'
14'
Note: Assume floor loading is 100 psf. Opening is either loaded or unloaded as noted in c, d, e and f which are loading diagrams for Beam 1.
' 6
4'
6'
14'
' 4 ' 2
0.6 klf
0.2 klf Beam 1
c) Unframed, unloaded opening a) Floor Plan with Unframed Opening
4'
6'
14'
d) Unframed, loaded opening 0.7k 0.6 klf
0.7k 0.6 klf
0.1 klf
' 6 ' 4
e) Framed, unloaded opening
' 2
Beam 1
b) Floor Plan with Framed Opening (Beams on all Sides)
0.6 klf
1.5k
1.5k
0.1 klf
f) Framed, loaded opening
0.6 klf
Example of effect of openings on distribution of load over deck sections
L oad Transf or mation Vertical 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
Floors with Membrane Slab Properties 3
2
3
4
2
4 4
2 2 1
1 a) Real beams on all sides
3 3
2 2
1
1 b)Case 1 of real beams on three sides
3 4
3 3 1
2
1 2 j) Vertical support elements at all corner points (no real beams) 2
2 2
1
2
1
1
1
2
2 1
3
3
1
1 c) Case 2 of real beams on three sides
3
2
1 2 k) Vertical support elements at three corner points (no real beams)
1 e) Real beams on two opposite sides 2
midpoint 1
1
2
2 2
3
2 3
2
1 m)Vertical support elements at two opposite corner points (no real beams)
Real beam at shell edge 1 n) Vertical support elements at one corner point (no real beams)
No beam at shell edge Tributary area dividing line Vertical support element Legend
3 3 1
g)Real beam on one side plus one vertical support element at corner point
1 f) Real beam on one side
1 2 l) Vertical support elements at two adjacent corner points (no real beams)
1
1
1 d)Real beams on two adjacent sides
1 h)Real beams on two adjacent sides plus one vertical support element at corner point
1
midpoints
1 i) Real beam on one side plus two vertical support elements at corner points
2
Tributary areas for various conditions of a membrane slab
Floors with Membrane Slab Properties 3
3
3
3
4 4
2 2
4 4
1
2 2 1
1 a) Full uniform load transformation
1 b) Partial uniform load transformation
3
3
3
3
4 4
Example of load distribution on a membrane slab
2 2
4 4
2 2
1
1
1 c) Line load transformation
1 d)Point load transformation
Type of Slab Systems in SAF E
The 5-Story Walku p F lats A
B
C
D
E
F
G
6 5
6.0 4
6.0 3
2.8 2
2.8 1
4.0
4.0
5.5
5.5
4.0
Column Layout Plan
4.0
The 5-Story Walku p F lats A
B
C
D
E
F
G
6 5
C2
C1
C1= 0.3 x 0.8 C2 = 0.3 x 0.4
6.0 4
B1 = 0.25 x 0.4 B2 = 0.25 x 0.5
B1 6.0
B2
S1 = 0.15
3 2
1
2.8 2.8
4.0
4.0
5.5
5.5
4.0
Slab and Beam Layout
4.0
The 5-Story Walku p F lats
3.0 3.0 3.0 3.0 3.5 2.0
6
5
3
4
Section
2
1
35 Stor y Of f ice Bui lding 5
7.0 4
8.0 3
8.0 2
Plan Typical Floor (B1, B2, 4-35)
7.0 1 A
6.0
B
6.0
C
8.0
D
8.0
E
6.0
F
6.0
G
35 Stor y Of f ice Bui lding 5
7.0 4
8.0 3
8.0 2
Plan Floor 1-2
7.0 1 A
6.0
B
6.0
C
8.0
D
8.0
E
6.0
F
6.0
G
35 Stor y Of f ice Bui lding 5
7.0 4
8.0 3
8.0 2
Plan Floor 3
7.0 1 A
6.0
B
6.0
C
8.0
D
8.0
E
6.0
F
6.0
G
35 Stor y Of f ice Bui lding
32 @ 3.5
2 @ 5.0
2 @ 2.8
Section at C and D 5
4
3
2
1
35 Stor y Of f ice Bui lding
32 @ 3.5
2 @ 5.0
2 @ 2.8
Section at B and E 5
4
3
2
1
