82273570 international seminar on computer aided analysis and design of building structures

7/28/2019 82273570 International Seminar on Computer Aided Analysis and Design of Building Structures

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International Seminar on

Computer Aided Analysis and Design

Of Building Structures

Aug 23-24, Kuala Lumpur, Malaysia

Institute of Engineers Malaysia

Computers and Structures Inc., USA

Asian Center for Engineering Computations and Software

Asian Institute of Technology, Thailand


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Building Structures

Modeling and Analysis Concepts

Naveed Anwar

Asian Center for Engineering Computations and Software, ACECOMS, AIT


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Modeling, Analysis and Design of Buildings AIT - Thailand ACECOM

Overall Design Process

Conception

Modeling

Analysis

Design

Detailing

Drafting

Costing

Integrated

Design

Process


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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


5/147 Modeling, Analysis and Design of Buildings AIT - Thailand ACECOM

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 SystemGravity 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 floorstiffness



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 LoadsHow 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


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Structural Response

To Loads



The Simpl i f ied Structu ral System

STRUCTURE

pv

EXCITATIONLoads

VibrationsSettlements

Thermal Changes

RESPONSESDisplacements

Strains

Stress

Stress Resultants



Analysis of Structures

pv

Real Structure is governed by PartialDifferential Equations of various order

Direct solution is only possible for:

Simple geometry

Simple Boundary Simple Loading.



The Need for Modeling

A - Real Structure cannot be Analyzed:

It can only be Load Tested to determine response

B - We can only analyze aModel of the Structure

C - We therefore need tools to Model the

Structure and to Analyze the Model


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Structural

Model

The Need for Structural Model

EXCITATIONLoads

VibrationsSettlements

Thermal Changes

RESPONSESDisplacements

Strains

Stress

Stress Resultants

STRUCTURE

pv


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F ini te 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


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Continuum to Discrete Model

pv

(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)

3D-CONTINUM

MODEL


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From Classical to FEM Solution

Assumptions

Equilibrium

Compatibility

Stress-Strain Law

(Principle of Virtual Work)

Partial Differential

Equations

Classical

Actual Structure

Algebraic

Equations

K = Stiffness

r = Response

R = Loads

FEM

Structural Model


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Simpli f ied Structural System

Loads (F) Deformations (D

Fv

F = K D

F

KD


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The Struc tural Sys tem

EXCITATIONRESPONSES

STRUCTURE

pv

Static

Dynamic

Elastic

Inelastic

Linear

Nonlinear


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The Equil ibr ium Equations

1. Linear-Static Elastic OR Inelastic

2. Linear-Dynamic Elastic

3. Nonlinear - Static Elastic OR Inelastic

4. Nonlinear-Dynamic Elastic OR Inelastic


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Di ti ti f C ti


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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 Elemen

Solid Element

H, B much less than L

Gl b l M d li f St t l G t


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Global Modeling of Structural Geometry

(f) Grid-Plate

Di i f El t


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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.

DOF f 1D El t


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DOF for 1D Elements

Dx

Dy

DxDz

Dy

Dx

Dy

Rz

Dy

RxRz DxDz

Dy

Rx

Rz

Ry

2D Truss 2D Beam3D Truss

2D Frame 2D Grid 3D Frame

Dy

Rz

DOF for 2D Elements


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DOF for 2D Elements

Dx

DyDy

Ry ?

RzRx

Dz

Dy

Rx

Rz

Ry ?

Dx

Membrane Plate Shell

DOF for 3D Elements


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DOF for 3D Elements

DxDz

Dy

Solid/ Brick

Frame and Grid Model


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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 Fram

2D Grid

2D Frame

Membrane Model


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Membrane 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

Plane Stress and Plane


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Plane Stress and Plane

Plane Stress ProblemPlane Strain Problem

Plate Bending Model


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Plate Bending Model

Primarily Bending mode

Moment and Shear arepredominant

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 Model


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General Plate Shell Model

Combined Membrane and Plate

Suitable for general applicationto surface structures

Suitable for curved structures

Thick shell and thin shellimplementations available

Membrane thickness and platethickness can be specifiedseparately

Numerous results generated.Difficult to design the section for

combined actions

Solid Model


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Solid 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 I nteraction


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Soil Structure I nteraction

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


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Connecting Different Types of Elements

Truss Frame Membrane Plate Shell Solid

TrussOK 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

PlateRx, Rz OK Rx, Rz OK OK Rx, Rz

ShellRx, Ry, Rz OK

Rx, Ry, Rz,

DzDx, Dz OK Rx, Rz

SolidOK OK Dz Dx, Dz OK OK

0

Orphan Degrees Of Freedom:

1 2 3 4


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What Type of

Analysis should beCarried Out?

Analysis Type


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Analysis Type

The Type of Excitation (Loads) The Type Structure (Material and Geometry)

The Type Response

The type of Analysis to be carr ied outdepends on the Structural System

Basic Analysis Types


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as a ys s yp s

Excitation Structure Response Basic Analysis Type

Static 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


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yp

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


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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 I nelastic


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Elastic Material

Follows the same path during loading and unloading and returns to initialstate 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


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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

Elastici ty and L inear ity


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Action

Deformation

Action

Deformation

Action

Deformation

Action

Deformation

Linear-Elastic Linear-Inelastic

Nonlinear-Elastic Nonlinear-Inelasti


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Physical Object Based

Modeling, Analysis and Design

Continuum Vs Structure


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A continuum extends in all direction, has infinite

particles, with continuous variation of materialproperties, 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 Structures


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Structures can be categorized in many ways.

For modeling and analysis purposes, the overall physicalbehavior 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


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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


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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


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Load Transfer Path For Gravity Loads


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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


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The Load is transferred through amedium 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


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Object

Line

Area

Volume

Point LoadConcentrated Load

Beam Load

Wall Load

Slab Load

Slab Load

Wind Load

Seismic Load

Liquid Load

Node

Beam / Truss

Connection Element

Spring Element

Plate ElementShell Element

Panel/ Plane

Solid Element

Point SupportColumn Support

Line Support

Wall Support

Beam Support

Soil Support

Soil Support

Point

LoadGeometry

Medium

Support

Boundary

ETABS uses graphic object modeling concept

Load Transfer Path is diff icul t to Determine


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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

Mediu

Boundary

Load Transfer Path is diff icul t to Determine


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Transfer of a Point Load to Point Supports Through Various Mediums

Point Line Area Volume

Objects in ETABS


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Building Object Specific Classification

PlankOne way slabs

SlabOne way or Two way slabs DeckSpecial one way slabs

WallShear Walls, Deep Beams, In-Fill Panel

FrameColumn, Beam or Brace

Finite Elements Shell

Plate

Membrane

Beam

Node

The Frame Element


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The Actions Corresponding to Six DOF at Both Ends, in

Local Coordinate System

1

3

2

3

2

+P+V2

+V3

+V3

+V2+P

1

3

2

3

2

+T+M2

+M3

+M3

+M2+T

Shell Element


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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 carryinggeneral loads

Building Specific ApplicationMay be used for modeling of general slabs

systems. But not used generally

Plate Element


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General

Total DOF per Node = 3Total Displacements per Node = 1

Total Rotations per Node = 2

Plates are for flat surfaces

Application

For Modeling surface elements carryingout of plane loads

Building Specific ApplicationFor representing floor slabs for Vertical

Load Analysis

Model slabs

Membrane Element


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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 carryingin-plane loads

Building Specific ApplicationFor representing floor slabs for Lateral

Load Analysis.

Model Shear walls, Floor Diaphragm etc

Meshing Slabs and Walls


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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


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Selection Of Structural Systems

Basic Concepts and Considerations

Knowledge Model for System Selection


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Structural

System Selection

Architecture

Syste

msEng

ineering

Aesth

etics

Value

Engin

eering Econom

ics

Construction

Engineering

Knowledge

Engineering

Artificial Intelligenc

SoftwareEngineering

Build

ing

Serv

ices

Engineering

S

tructural

E

ngineering

Engin

eering

Judgementa

nd

Common

Sens

e

Ergonomic

s

Eng

ineering

Architecture

Building Services

Construction Eng.

Value Eng.

Aesthetics

Ergonomics Eng.

Structural Eng.

Knowledge Eng.

Economics

Artificial Intelligence

System Eng.

Common Sense

Determining System Suitabi l i ty


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The Analytical Hierarchy Approach

A weighted importance and sui tabil i ty 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 Suitabil i ty


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Slab Systems Criteria Weights and Scores System

Value(V)

Main Criteria Ai Am

Sub Criteria Bij Sub Criteria B

in B

mn

Item k Item p Item k Item p Item p

Wt Score Wt Score Wt Score Wt Score Score

System1

System l Cijkl Sijkl Cijnl Sijpl Cinkl Sinkl Cinnl Sinpl Smnpl

System - q

The Suitability Equation

Using the Suitability Equation

Assigning Suitabil i ty Values


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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


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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 OccupancyCommercial + Residential

Industrial Buildings and Parking Garages

Typical Character istics of Residential Bldg


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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 slabpopular

Lateral load resistance provided by frame or shear walls

More or less fixed M/E system layouts

Typical Character istics of Off ice and Commercial Bldg


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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 resultanttension under gravity plus wind

Lateral load resistance varies significantly


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Vertical Load

Resisting Systems

The Components Needed to

Complete the Load-Transfer Path

for Vertical Gravity Loads

Gravity Load Resisting Systems

P


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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

Vertical Load Resisting Systems

1 Sl b t d L Ri id S t


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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


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Vertical Load

Behavior and Response

Popular Gravity Load Resting Systems


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Direct Load Transfer Systems (Single load transfer path)

Flat Slab and Flat Plate Beam-Slab

Waffle Slab

Wall Joist

Indirect Load Transfer System (Mul ti step load transfer path)

Beam, Slab

Girder, Beam, Slab

Girder, Joist

Conventional Approach


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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


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Gravity Load Transfer Paths


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Single PathSlab On Walls

Single PathSlab on Columns

Dual PathSlab On Beams,

Beams on Columns

Gravity Load Transfer Paths


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Mixed PathSlab On Walls

Slab On Beams

Beams on Walls

Complex PathSlab on Beams

Slab on Walls

Beams on Beams

Beams on Columns

Three Step PathSlab On Ribs

Ribs On Beams

Beams on Columns

Simpli f ied Load Transfer


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Transfer of Area Load

To Lines To Points To Lines and Points

Load Transfer Through Slab and Beam


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Slab Deformation and Beams


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Slab System Behavior


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Slab T = 200 mm

Beam Width, B = 300 mm

Beam Depth, D

a) 300 mm

b) 500 mmc) 1000 mm

D

B

Moment Distr ibution in Beam-Slab

Effect of Beam Size on


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Effect of Beam Size on

Moment Distribution

a) Beam Depth = 300 mm

b) Beam Depth = 500 mmc) Beam Depth = 1000 mm

Moment Distr ibution in Slabs Only

Effect of Beam Size on Moment Distribution


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a) Beam Depth = 300 mm b) Beam Depth = 500 mm c) Beam Depth = 1000 mm


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Modeling and Analysis for

Vertical Loads

Modeling for Gravity Loads

Must be carried out for several load cases/ patterns


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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


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Column Strip

Middle Strip

DesignStrip

Middle Strip

DesignStrip

Using Equivalent F rame MethodDesign Str ip


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Column Strip

Middle Strip

Middle Strip

Design Strip

L

L

L1

Longitudinal Beams

Transverse Beams

Drop Panels

L t l L d


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Lateral Load

Resisting Systems

The Components Needed toComplete the Load-Transfer Path

for Lateral Loads

Purpose

Lateral Load Bearing Systems


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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 Loads


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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-symmetricalstructures

Load due to lateral soil pressure, liquid and material

retention

Sample Lateral Load Resistance Systems

Bearing wall system

Light frames with shear panels


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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


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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 shearfrom later loads must be

added to those from gravity

loads

Shear Wall and Frame

The lateral loads is


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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 rame

The Walls are part of the


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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 bythe frame members in

moment and shear

Braced Frame

The lateral loads is primarily

i d b h A i l F i


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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 beprovided in every bay, but

should be provided in every

story

Tubular Structure

The system is formed by using

l l d l d d


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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 problembetween opposite faces of the tub

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

th b i t b l t t


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the basic tubular structure

This modification of theTubular System reduces shear

lag between opposite faces

Lateral Load


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ResistingSystem

Behavior, Response

and Modeling

Modeling for Lateral Loads

1 2D Frame Models


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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 F rame(s)

Convert 3D Building to an assemblage of 2D Frames

U i I d d t F


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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 Model

2. Select and

isolate Typica


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1. Consider the Structure

Plan and 3D View

isolate Typica

2D Structure

4. Obtain results

3. Discretize

the Model,

apply loads

Using Linked Frames

Linked Elements

F1


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Plan

Modeling

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 ofRigid Floor.

F3

F2

F1 F2 F3

Ful l 3D F ini te Element Model

The columns and beams are modeled by using

beam elements


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beam elements

The slabs and shear walls are modeled by usingplate 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

Ful l 3D F ini te Element Model

Example:

U th 4000


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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

Modeling of F loor Diaphragm

U Di l

Use Plate Elements

P l Pl St


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Use Plate

Elements

Use Diagonal

Bracing 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


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p y g

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)


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p ( p )

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 eachother

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


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UL

UL1

UL2

UL3

X

Y

F3 , 2

F1 , 1

F3 , 3

Building d.o.f.s

F2 , 1

r x

r qrY

Local Frame DOF

When Single Rigid Floor Cannot be Used


107/147



108/147


Automatic Floor Meshingand Auto Load Transfer

(In ETABS)

Area Objects: Slab

By default uses two-way load transfer

mechanism


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Simple RC solid slabCan also be used to model one way slabs

Area Object: Deck

Use one-way load transfer mechanism

lli C i Sl b


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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


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Generally used to model pre-cast slabs

Can also be simple RC solid slab


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Automatic Floor MeshingFirst step to Auto Load Transfer

Basic F loor M odeling Object

Points

Columns


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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


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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


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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

Piece 1 Piece 2 Piece 3

Beam 1 Beam 2


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Girder B

Beam1

Beam2

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


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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 columnsare 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 tocreate a mesh of four-sided elements

Girder A Girder A



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Girder B

Beam1

Beam2

Beam3

Girder B

Beam1

Beam2

Beam3

c) ETABS Automatic Floor Meshingb) ETABS Imaginary Beams Shown Dasheda) Floor Plan

Example of ETABS automatically generated mesh for floor-type area objects


Example of ETABS

automatically generated mesh

f fl bj


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d) ETABS Automatic Floor Meshing

b) ETABS Imaginary Beams Connecting

Columns Shown Dashed

a) Floor Plan (No Beams)

c) ETABS Imaginary Beams Extended to

Edge of Floor Shown Dashed

for floor-type area objects


For floors that are automatically meshed by ETABS it is

d d h d l b ( l ll li bj )


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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 ObjectsC3C4 C3C4 C3C4

Illustration of how ETABS

creates the distribution of

imaginary beams


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c)b)a)

f)e)d)

i)h)g)

C1 C2 C1 C2

C1 C2

C3C4

C1 C2

C1 C2

C3C4

C1 C2

C3C4

C1 C2

C3C4

C1 C2

C3C4

C1 C2

C3C4

imaginary beams


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Automatic Transformation andTransfer of Floor Loads toAppropriate Elements

(Using the Auto Meshed Geometry)

Load Transformation

The main issue:

How point loads line loads and area loads that lie on an area


123/147


How point loads, line loads and area loads that lie on an area

object in your object-based ETABS model are represented inthe analysis model

There are four distinct types of load transformation inETABS 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 anyautomatic meshing into the analysis Edge1 dge

4

12

Edge1d

ge4

12

r

s


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automatic meshing into the analysis

model

ETABS normalizes the coordinates ofthe four corner points of the area object

The normalization is the key

assumption in this method

It is a perfectly valid assumption if thequadrilateral is a square, rectangular or

a parallelogram

a) Quadrilateral Element

Ed

4

3

Ed

ge2

Edge3

b) The r and s Axes

Ed

4

3

r

Ed

ge2

Edge3

(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


125/147


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 andthose 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

If the supporting membert th d i t f


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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 Element

of 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

at the end point of animaginary beam is itselfimaginary, then the load

from the imaginary beamtributary to that end pointis lost, that is, it isignored 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)


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If the beams along edges are real beams ETABS transfers the load ontoadjacent beams

Edge 1

Edge 3

Edge2

Edge4

x1 x2

Point load, P


a) Rectangular Interior Element

of Meshed Floor

b)Distribution of Point Load

x1 x2Edge 4 Edge 2

P

P * x2

x1 + x2

P * x1

x1 + x2

c) Loading on Edge 2

P * x1

x1 + x2

d) Loading on Edge 4

P * x2

x1 + x2

If the supportingmember at the end pointof an imaginary beam is

itself imaginary, then theload from the imaginarybeam tributary to thatend 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


128/147


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 thesurrounding 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

Edge3

Edge2

Ed

ge4

Uniform load

Di ti f d k

Edge3

Edge2

Ed

ge4

Edge3

Edge2

Ed

ge4 Midpoint

Midpoint


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d)

Edge1

Edge3

Edge2

Ed

ge4

Edge1

Edge3

Edge2

Ed

ge4

e) Transformation of Uniform Load

Edge1


a) General Interior Element of

Meshed Floor Deck

b)

Edge1 Edge1

c)

g) Loading on Edge 2

f) Loading on Edge 1

h) Loading on Edge 3 i) Loading on Edge 4

Midpoint

Example of general interior meshed element with a

uniform load

a) General Interior Element ofMeshed Floor Deck

Edge1

Edge3

Edge2

Ed

ge4

P1

P2

P3

b)

Edge1

Edge3

Edge2

Ed

ge4

P1

P2

P3

Line 1

Line 2

Line 3

Example of general interior meshed

element with a point load

Exterior Meshed Element

Beam 1a

E FD

Beam 1b Beam 1

Beam2

b

Beam2

bExample of exterior meshed

elements with real beams on all sides


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Edge of deck is atcenter of spandrelbeam, typical in thisexample

B CA

a) Floor Plan b) Deck Meshing

Beam2

a

Beam2

a

Beam 3a

B CA

ED


Beam

Beam1

a

Bea

m1

b

Bea

m2

b

Beam 3a Beam 3b

Beam1

a

Bea

m1

b

Beam2

a

Bea

m2

b

Beam 4a Beam

Imag

inaryNo beam at

edge of deck

No beam at

edge of deck

Example of exterior meshed elements

with cantilever beams extending to

edge of deck


ED inaryBeam6

b2

b ba

m2

bImagin

aryBeam7

ImaginaryB

eam8

No beam at

d f d k


131/147


ImaginaryBe

am8


B CA

ED

ImaginaryBeam5

Im

agi

Beam 3a Beam 3b

Beam1

a

Bea

m1

Beam2

a

Bea

m2

Beam 3a Beam 3b

Beam1

a

Bea

m1

Beam2

a

Bea

E1ImaginaryBeam6

Beam 3b

Beam2

b

E2

c) Condition at Skewed Deck

Edge (Areas D and E)

ImaginaryB

eam7

D

D

Beam 3aBeam1

b

edge of deck

No beam at

edge of deck

Example of exterior

meshed elements

with cantilever

beams extending to

edge of a skewed

deck


Beam 1

EDBeam 1

Edge of deck


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B CA


Beam2

Beam2

Column 1 Column 1

Example of exterior meshed elements with overhanging slab


Beam 1a Beam 1a

E FD

Beam 1b Beam 1b

Beam2

b

Beam2

b

G H I

J

Beam3

b


133/147


B CA


Beam2

a

Beam2

aK

Beam3

a

Example of exterior meshed elements with overhanging slab

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.

Example of effect of openings

on distribution of load over

deck sections


134/147


a) Floor Plan with Unframed Opening

Beam 1

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'

d) Unframed, loaded opening

e) Framed, unloaded opening

f) Framed, loaded opening

0.7k

0.6 klf0.2 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

Load TransformationVertical Load Transformation for Floors with Membrane

Slab Properties

only applies to floor-type area objects with slab section


135/147


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

1

1

33

34

2

2

4

1 2

12

3

1

1 2

1

3

24

1

3

24

123

1

231

2

3

1

2

3


136/147


l) Vertical support

elements at two

adjacent corner point

(no real beams)

j) Vertical support

elements at all corner

points (no real beams)

1

k) Vertical support

elements at three

corner points (no real

beams)

2 1 2 1

m)Vertical supportelements at two

opposite corner points

(no real beams)

1

1

Legend

Real beam at shell edge

No beam at shell edge

Tributary area dividing

Vertical support elemen

n) Vertical supportelements at one

corner point (no

real beams)

1

1

2

2

f) Real beam on one sidee) Real beams on two

opposite sides

d)Real beams on two

adjacent sides

c) Case 2 of real beams onthree sides

b) Case 1 of real beams onthree sides

a) Real beams on all sides

1 1 1

1

2

1

2

1

1

1

1

2

2

i) Real beam on one side

plus two vertical

support elements at

corner points

h) Real beams on two

adjacent sides plus

one vertical support

element at corner point

g)Real beam on one side

plus one vertical

support element at

corner point

11

1

1

1

3

1

3

2

2

2

2midpoint

2

2

3

3

midpoints

Tributary areas for various

conditions of a membrane slab

Floors with Membrane Slab Properties

3

24

3

24

3

24

3

24

Example of load distribution on a

membrane slab


137/147


a) Full uniform load

transformation

b) Partial uniform load

transformation

c) Line load transformation d)Point load transformation

1

1

1

1

1

3

24

3

24

1

1

3

24

3

24

1

Type of Slab Systems in SAFE


138/147


The 5-Story Walkup F lats

5

6

A CB D E F G


139/147


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

4


5

6

A CB D E F G

C1= 0.3 x 0.8C1C2


140/147


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

4

C2 = 0.3 x 0.4

B1 = 0.25 x 0.4

B2 = 0.25 x 0.5

S1 = 0.15

B1

B2


3.0


141/147


12356 4

3.0

3.0

3.0

3.5

2.0

Section

35 Story Off ice Bui lding5

7.0


142/147

Modeling, Analysis and Design of Buildings AIT - Thailand ACECOM6.0 6.0 8.0 8.0 6.0 6.0

8.0

8.0

1

2

4

A CB D E F G

3

7.0 Plan

Typical Floor

(B1, B2, 4-35)

35 Story Off ice Bui lding5

7.0


143/147


8.0

8.0

1

2

4

A CB D E F G

3

7.0 Plan

Floor 1-2

35 Story Off ice Bui lding

4

5

7.0


144/147


8.0

8.0

1

2

4

A CB D E F G

3

7.0 Plan

Floor 3


32 @ 3 5


145/147

Modeling, Analysis and Design of Buildings AIT - Thailand ACECOM1245 3

2 @ 5.0

2 @ 2.8

32 @ 3.5

Section at

C and D


32 @ 3 5


146/147


2 @ 5.0

2 @ 2.8

32 @ 3.5

Section at

B and E


32 @ 3 5


147/147


2 @ 5.0

2 @ 2.8

32 @ 3.5

Section at

A and G

82273570 international seminar on computer aided analysis and design of building structures

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