basic modeling and analysis concepts kl aug 2002

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


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


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


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


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


The Simplified Structural System

STRUCTURE

pv

EXCITATIONLoads

VibrationsSettlements

Thermal Changes

RESPONSESDisplacements

StrainsStress

Stress Resultants


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.


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


Structural Model

The Need for Structural Model

EXCITATIONLoads

VibrationsSettlements

Thermal Changes

RESPONSESDisplacements

StrainsStress

Stress Resultants

STRUCTURE

pv


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”


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


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


Simplified Structural System

Loads (F) Deformations (D)Fv

F = K DF = K D

FF

KKDD


The Structural SystemThe Structural System

EXCITATION RESPONSES

STRUCTURE

pv

• Static• Dynamic

• Static• Dynamic

• Elastic• Inelastic

• Elastic• Inelastic

• Linear• Nonlinear

• Linear• Nonlinear


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


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


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


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


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


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


DOF for 2D Elements

DxDx

DyDyDyDy

Ry ?Ry ?

RzRzRxRx

DzDz

DyDy

RxRxRzRz

Ry ?Ry ?

DxDx

MembraneMembrane PlatePlate ShellShell


DOF for 3D Elements

DxDxDzDz

DyDy

Solid/ BrickSolid/ Brick


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


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


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


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


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


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


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


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


What Type of Analysis should be

Carried Out?

What Type of Analysis should be

Carried Out?


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


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


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


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”


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.


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


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


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


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


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


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


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


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


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


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


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


Load Transfer Path is difficult to Determine

Transfer of a Point Load to Point Supports Through Various Mediums

Point Line Area Volume


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 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


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


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


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


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”


Selection Of Structural Systems Selection Of Structural Systems

Basic Concepts and Considerations Basic Concepts and Considerations


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


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


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


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


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


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


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


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


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


Vertical LoadVertical Load Behavior and Response Behavior and Response


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


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


Popular Gravity Load Resting Systems


Gravity Load Transfer Paths

Single PathSlab On Walls

Single PathSlab on Columns

Dual PathSlab On Beams,

Beams on Columns


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


Simplified Load Transfer

Transfer of Area Load

To Lines To Points To Lines and Points


Load Transfer Through Slab and Beam


Slab Deformation and Beams


Slab System Behavior

5.0 m

Slab T = 200 mmBeam Width, B = 300 mmBeam Depth, Da) 300 mmb) 500 mmc) 1000 mm

D

B


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


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


Modeling and Analysis for Modeling and Analysis for Vertical LoadsVertical Loads


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


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


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


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


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


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)


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


When Single Rigid Floor Cannot be Used


Automatic Floor Meshing and Auto Load Transfer

(In ETABS)

Automatic Floor Meshing and Auto Load Transfer

(In ETABS)


Area Objects: Slab

By default uses two-way load transfer mechanism

Simple RC solid slab

Can also be used to model one way slabs


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


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


Automatic Floor Meshing

First step to Auto Load Transfer

Automatic Floor Meshing

First step to Auto Load Transfer


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


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


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.


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


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


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




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



– 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



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


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)


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


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


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.


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


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


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


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.


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


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


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


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



Imaginary Beam 8


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



Example of exterior meshed elements with cantilever beams extending to edge of a skewed deck



Beam 1

B CA

ED


Beam

2

Beam 1

Beam

2

Column 1 Column 1

Edge of deck

Example of exterior meshed elements with overhanging slab



Beam 1a Beam 1a

B CA

E FD


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


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


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


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


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


Type of Slab Systems in SAFE


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



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



12356 4

3.0

3.0

3.0

3.0

3.5

2.0

Section


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)



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



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



1245 3

2 @ 5.0

2 @ 2.8

32 @ 3.5

Section atC and D



1245 3

2 @ 5.0

2 @ 2.8

32 @ 3.5

Section atB and E



1245 3

2 @ 5.0

2 @ 2.8

32 @ 3.5

Section atA and G

basic modeling and analysis concepts kl aug 2002

Documents

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structural system columns

lateral loads

gravity loads

computer aided analysis

member design beams

drainage system electrical

inelastic modeling