Water Retaining Structures

Modeling, Analysis, Design

Asian Center for Engineering

Computations and Software

Asian Institute of Technology

August 25-27

Dr. Naveed Anwar

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Overall Topics

Types of Water Retaining Structures

System Selection and Preliminary Design

Modeling and Analysis Concepts

Special Modeling Considerations

Special Analysis Considerations

Special Design Considerations

Special Detailing Considerations

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Types of Structures Considered

Water Tanks

Water Reservoirs

Sanitary Structures

Swimming Pools

Concrete Dams

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System Selection And

Proportioning

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Total Design Process

Functional Design

Physical Plant Layout

Hydraulic Design

Structural Design

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Why they are special?

Common RequirementsStrength, stability, economy, etc

Special RequirementsVariable pressure type of loads

Serviceability

Limited deflection

Cracking, creep, shrinkage

Durability

Permeability/water tightness

Chemical attacks

Corrosion

Construction

High quality control

Difficult situations

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Main Steps

System selection

Dimensioning

Modeling

Analysis

Design for strength & stability

Check for serviceability

Detailing

Construction

Environmental aspects

Maintenance consideration

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Classification

Based on Usage

Based on Location

Based on Shape

Based on Size

Based on Material

Based on Structural System

Based on Construction Method

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Classification

Based on Usage

Water Storage

Water Containment

Water Treatment

Water Transmission

Waste-water tanks

Manholes, Junction chambers

Pump stations

Swimming pools

Dams

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Classification

Based on location

Under ground

On ground

Elevated

Offshore

Onboard

On vehicle

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Classification

Based on Shape

Rectangular

Circular

Spherical

Spheroids

General Shells and

Curvilinear shapes

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Classification

Based on Material

Reinforced concrete

Prestressed concrete

Steel

Aluminum

Plastic

Fibre-reinforced

Composite

Ferrocement

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Overhead Tanks

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Overhead Tanks

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Overhead Tanks

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Swimming Pools

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Swimming Pools

http://www.aquarianpools.com/pools/commercial-pool-01.jpg

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Dams and Reservoirs

http://creative.gettyimages.com/source/search/ImageEnlarge.aspx?MasterID=200135809-001&s=ImageDetailSearchState|3|5|0|15|2|1|0|0|1|1|60|6|1|0|%22Dams%3ak%22||1|0&pk=6http://creative.gettyimages.com/source/search/ImageEnlarge.aspx?MasterID=200133104-001&s=ImageDetailSearchState|3|5|0|15|2|1|0|0|1|7|60|6|1|0|%22dams%3ak%22||1|0&pk=6http://creative.gettyimages.com/source/search/ImageEnlarge.aspx?MasterID=10072400&s=ImageDetailSearchState|3|5|0|15|2|1|0|0|1|18|60|6|1|0|%22dams%3ak%22||1|0&pk=6

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Dams and Reservoirs

http://creative.gettyimages.com/source/search/ImageEnlarge.aspx?MasterID=10094423&s=ImageDetailSearchState|3|5|0|15|2|1|0|0|1|30|60|6|1|0|%22dams%3ak%22||1|0&pk=6

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Special Tanks

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Major Components

Water Retaining Walls

Base Slabs

Roof/Covers

Framing Systems

Ring Beams

Columns

Braces

Stiffeners

Foundation System

Joints

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Proportioning of Tanks

Un-constrained, optimized proportioning is

extremely difficult

Choice between Circular/ Rectangular

Choice between Tall/ Flat

Often the constrains provided by the

functional requirements help to determine

overall shape and dimensions

The proportioning generally limited to

Selection of wall/ slab thickness

Providing counterforts and stiffeners

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Minimum Requirements

Minimum Wall Thickness

Absolute minimum 150mm

With 50mm cover, minimum 200mm

For walls above 3 m high and in contact with

water, minimum 300 mm

Minimum Slab Thickness

Absolute minimum 150mm

Preferable is 200 mm

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Proportioning of Tank Walls

High Cantilevers should be avoided

Add vertical counterforts

Add cross-walls

Add transverse beams

Add Tie-backs or props

Choice between uniform and variable wall

thickness

Material vs construction and formwork saving

Slip form considerations

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Proportioning of Floor Slabs

Different considerations for Elevated, On-

ground and Underground tanks

If elevated then provide small span is

preferable due to heavy loads

Domes or shells can be used to reduced

bending

If underground upward pressure may be

considered

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Modeling and Analysis

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Analysis Methods

Simplified Method

Using coefficients for slabs and walls

Using frame analysis for supporting structure

Using Simplified Equations

Suitable for ordinary and common cases

Detailed Method

Using Finite Element Method

Suitable for all types of structures

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Structural Analysis

The Purpose of Analysis

The Significance of Modeling

Analysis Types

Linearity and Non-Linearity

Static and Dynamic Analysis

Modeling of Foundations

Use of Different Types of Elements

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Structural

Model

EXCITATIONLoads

Vibrations

Settlements

Thermal Changes

RESPONSESDisplacements

Strains

Stress

Stress Resultants

STRUCTURE

pv

Structural System Analysis Model

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Analysis of Structures

pv

xx yy zz

vxx y zp 0

Real Structure is governed by

various order

Direct solution is only possible for:

Simple geometry

Simple Boundary

Simple Loading.

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The Need for Modeling

A - Real Structure cannot be Analyzed:

response

B -

Structure

C - We therefore need tools to Model the

Structure and to Analyze the Model

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Finite Element Method: The Analysis Tool

Finite Element Analysis (FEA)

Finite Element Method (FEM)

numerical procedure for solving

(partial) differential equations

associated with field problems, with

an accuracy acceptable to

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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

xx yy zz

vxx y zp 0

t

v

t

s

t

v

dV p udV p uds_ _ _

Assumptions

Equilibrium

Compatibility

Stress-Strain Law

(Principle of Virtual Work)

Differential

Classical

Actual Structure

Kr R

K = Stiffness

r = Response

R = Loads

FEM

Structural Model

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Simplified Structural System

F = K D

F

KD

Loads (F) Deformations (D)

Fv

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The Analysis System

EXCITATION RESPONSES

STRUCTURE

pv

Static

Dynamic

Elastic

Inelastic

Eight types of equilibrium equations are possible!

Linear

Nonlinear

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The Equilibrium Equations

1. Linear-Static Elastic

2. Linear-Dynamic Elastic

3. Nonlinear - Static Elastic OR Inelastic

4. Nonlinear-Dynamic Elastic OR

Inelastic

FKu

)()()()( tFtKutuCtuM

)()()()()( tFtFtKutuCtuM NL

FFKu NL

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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

Basic Analysis Types

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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

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Analysis Type

The type of Analysis to be carried out depends

on the Structural System

The Type of Excitation (Loads)

The Type Structure (Material and

Geometry)

The Type Response

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Static Vs Dynamic

Static Excitation

When the Excitation (Load) does not vary rapidly with

Time

When the Load can be assumed to be applied

Dynamic Excitation

When the Excitation varies rapidly with Time

Most Real Excitation are Dynamic but are

Most Dynamic Excitation can be converted to

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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.

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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

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Elasticity and LinearityA

ctio

n

Deformation

Actio

n

Deformation

Actio

n

Deformation

Actio

n

Deformation

Linear-Elastic Linear-Inelastic

Nonlinear-Elastic Nonlinear-Inelastic

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Linear and Nonlinear

u

F

Non Linear Equilibrium

Ku = F

Ku - FNL = FFNL

FKu

)()()()( tFtKutuCtuM

)()()()()( tFtFtKutuCtuM NL

FFKu NL

Nonlinear, Static and Dynamic

Linear, Static and Dynamic

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The Modal Analysis

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The Modal Analysis

The modal analysis determines the inherent natural

frequencies of vibration

Each natural frequency is related to a time period

and a mode shape

Time Period is the time it takes to complete one

cycle of vibration

The Mode Shape is normalized deformation pattern

The number of Modes is typically equal to the

number of Degrees of Freedom

The Time Period and Mode Shapes are inherent

properties of the structure and do not depend on the

applied loads

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Free Vibration Analysis

Definition

Natural vibration of a structure released from initial condition and

subjected to no external load or damping

Main governing equation -Eigenvalue Problem

Solution gives

Natural Frequencies

Associated mode shapes

An insight into the dynamic behavior and response of the structure

tt

tt

PuKucuM

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The Modal Analysis

The Modal Analysis should be run before

applying loads any other analysis to check

the model and to understand the response of

the structure

Modal analysis is precursor to most types of

analysis including Response Spectrum, Time

History, Push-over analysis etc.

Modal analysis is a useful tool even if full

Dynamic Analysis is not performed

Modal analysis easy to run and is a fun to

watch the animations

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Application of Modal Analysis

The Time Period and Mode Shapes, together

with animation immediately exhibit the

strengths and weaknesses of the structure

Modal analysis can be used to check the

accuracy of the structural model

The Time Period should be within reasonable

range, (Ex: 0.1 x number of stories seconds)

The disconnected members are identified

Local modes are identified that may need

suppression

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Application of Modal Analysis

The symmetry of the structure can be

determined

For doubly symmetrical buildings, generally the

first two modes are translational and third mode

is rotational

If first mode is rotational, the structural is un-

symmetrical

The resonance with the applied loads or

excitation can be avoided

The natural frequency of the structure should not

be close to excitation frequency

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Eccentric and Concentric Response

Mode-1 Mode-2 Mode-3

Symmetrical Mass and

Stiffness

Unsymmetrical Mass

and Stiffness

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Special Modeling Problems

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Base Isolation

Isolators

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Building Impact

Building Impact

Analysis

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Dampers

Friction device

Concentrated damper

Nonlinear element

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Gaps and Joints

Bridge Deck

ABUTMENT

Gap Element

Tension only element

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Hinges

2 Rotational DOF

Degrading Stiffness?

PLASTIC HINGES

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Dampers

Mathematical Model

F= ku

F= CvN

F= f(u,v,umax

)

Mechanical Damper

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Linear Viscous Damping

Does not Exist in Normal Structures and

Foundations

5 or 10 Percent modal Damping Values are

Often Used to Justify Energy Dissipation Due

to Non-Linear Effects

If Energy Dissipation Devices are Used Then

1 Percent Modal Damping should be Used for

the Elastic Part of the Structure

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Uplift

Uplifting

Allowed

FRAME WITH UPLIFTING ALLOWED

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Structural Modeling

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Structural Members

Dimensional Hierarchy of Structural Members

Continuum

Regular Solid

(3D)

Beam (1D)

b h

L>>(b,h)

b

ht

z

Plate/Shell (2D)

x z

t

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Structure Types

Cable StructuresCable Nets

Cable Stayed

Bar Structures2D/3D Trusses

2D/3D Frames, Grids

Surface StructuresPlate, Shell

In-Plane, Plane Stress

Solid Structures

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Global Modeling of Structural Geometry

(b) Solid Model (c) 3D Plate-Frame (d) 3D Frame

(a) Real Structure

(e) 2D Frame

Fig. 1 Various Ways to Model a Real Struture

(f) Grid-Plate

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Some Sample Finite Elements

Truss and Beam Elements (1D,2D,3D)

Plane Stress, Plane Strain, Axisymmetric, Plate and Shell Elements (2D,3D)

Brick Elements

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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

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DOF for 2D Elements

Dx

DyDy

Ry ?

RzRx

Dz

Dy

Rx

Rz

Ry ?

Dx

Membrane PlateShell

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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

Membrane

U1

Node 1

R3U2

U1

Node 3

R3U2

U1

Node 4

R3

U2

U1

Node 2

U2

3 2

1

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Variation of Membrane Elements

1 unit

x1

x3

x2

3D Problem

2D Problem

Plain-Strain

Assumptions x

x

Plane Stress ProblemPlane Strain Problem

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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

R1

Node 1

U3R2

1

23

R1

Node 2

U3R2

R1

Node 3

U3R2

R1

Node 4

U3R2

Plate

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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

1

23

U1, R1

Node 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

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Shell Elements in SAP2000

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Local Cords for Shell Element

Each Shell element has

its own local coordinate

system used to define

Material properties,

loads and output.

The axes of this local

system are denoted 1, 2

and 3. The first two

axes lie in the plane of

the element the third

axis is normal

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DOF for 3D Elements

DxDz

Dy

Solid/ Brick

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Brick Element in SAP2000

8-Node Brick

Bricks can be added by

using Text Generation

in V7. New version 8

will have graphical

interface for Bricks

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The Stress Strain Components

xx

yy

zz

xy

zx

yx

zy

xz

yz

x

y

z

At any point in a continuum, or solid,

the stress state can be completely

defined in terms of six stress

components and six corresponding

strains.

xx

yy

zz

xy

zx

yx

zy

xz

yz

x

y

z

At any point in a continuum, or solid,

the stress state can be completely

defined in terms of six stress

components and six corresponding

strains.

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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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Connecting Dissimilar Elements

When elements with different degree of freedom at ends

connect with each other, special measures may need to

be taken to provide proper connectivity depending on

Software Capability

Beams to Plates Beam to Brick Plates to Brick

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Graphic Object Modeling

Use basic Geometric Entities to create FE

Models

Simple Graphic Objects

Point Object Represents Node

Line Object Represents 1D Elements

Area Object Represents 2D Elements

Brick Object Represents 3D Elements

Graphic Objects can be used to represent

geometry, boundary and loads

SAP2000, ETABS and SAFE use the concept

of Graphic Objects

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Modeling Objects and Finite Elements

Structural Members are representation of actual structural components

Finite Elements are discretized representation of Structural Members

The concept of Graphic Objects can be used to represent both, the Structural Members as well as Finite Elements

In ETABS, the Graphic Objects representing the Structural Members are automatically divided into Finite Elements for analysis and then back to structural members for result interpretation

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Model Creation Tools

Defining Individual Nodes and Elements

Using Graphical Modeling Tools

Using Numerical Generation

Using Mathematical Generation

Using Copy and Replication

Using Subdivision and Meshing

Using Geometric Extrusions

Using Parametric Structures

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Analysis of

Water Retaining Structures

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Basic Analysis Issues

generally in-adequate

Membrane/ Plate or Shell analysis is often

required

Special Structural Forms may have to be

handled

Special Loads and Load Combinations may

need to be handled

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Design Loads

Fluid pressure (internal and external)

Earth pressure

Wind loads

Dead loads

Live loads

Earthquake loads

Temperature

Relative Settlement

Hydrodynamic loads (vibration, etc)

Impact load

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Load Factors

Load Factors for Ultimate Strength Design

Dead load (D) additive effect 1.4

Dead load (D) subtractive effect 0.9

Fluid load, weight (Fv) 1.4

Lateral soil pressure (H) 1.7

Hydrostatic pressure (Fh) 1.7

Live load (L) 1.7

Effects due to Temperature 1.4

Effects due to Shrinkage, Creep (T) 1.4

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Load Combinations

Similar to ACI 318 with following adjustments

Load factors

Lateral earth pressure H =1.7

Lateral liquid pressure F =1.7

Reinforcement in flexure = 1.3 U

Direct tension/hoop reinforcement = 1.6 U

Excess shear = 1.3 U

Compression + Flexure = 1.0 U

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Sample Load Combinations

Load Cases

U1 U2 U3 U4 U5 U6 U7

D+L D+L+H D+H D+L+F D+F D+L+T D+T

1 Dead Load D 1.4 1.4 0.9 1.4 0.9 1.05 1.4

2 Live Load-1 L 1.7 1.7 0 1.7 0 1.28 0

3 Earth Pressure H 0 1.7 1.7 0 0 0 0

4 Fluid Weight Fv 0 0 0 1.4 1.4 0 0

5 Fluid Pressure Fh 0 0 0 1.7 1.7 1.28 0

6 Temperature etc. T 0 0 0 0 0 1.28 1.4

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Factors of Safety

Factors of Safety for Stability

Cohesive heave at temporary state 1.2

Soil bearing at temporary state 1.5

Soil bearing at permanent state 1.2

Buoyancy at temporary state 1.3

Buoyancy at permanent state 1.5

Overturning of structures 1.5

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Live Loads

Not a governing load case for WRS

Main Sources

American National Standard Institute

ANSI A58.1

American Concrete Institute

Local Regulations Codes

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Wind Loads

Factors to be considered:Wind speed

Typically 70-110 miles/hr

Location of the structure

City area

Sub-urban area

Flat open terrain

Offshore

Shape of the structure

Cylindrical

Rectangular

etc

Height of the structure

Area resisting the wind

Dynamic effects (vortex shedding)

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Wind Loads-UBC97 Approach

Wind Loads on Rigid tile Roof covering

Where

b = exposure width

CL = Lift Coefficient

Gcp = Roof Pressure Coefficient

L = Length of Roof

La = Moment arm from axis of rotation

qh = Wind velocity pressure

Ma = Aerodynamic uplift

paLha GcbLLCqM 0.1

Also see Tables provided

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Special Loads

Impact

Vibration

Torque

Seismic

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Special Loads

Impact

Impact loads are occasional

Conservative design approach is recommended

Complete Shock Analysis may be performed

using Dynamic Analysis options

Impact forces should be used in design

Impact allowance can be made by factoring the

static loads by Impact Factors

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Special Loads

VibrationMost environmental machinery is slow moving and does not require separate dynamic analysis

Some other equipments, pumps, fans, etc., may require special consideration for design

Natural frequency of support is significantly different from the machinery

Preferable to maintain Frequency Ratio above 1.5

Use Isolators to reduce vibration transfer

Use dampers to reduce dynamic effects

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Special Loads

Torque

Usually caused by clarifiers and other rotating

equipment (may have diameter up to of 150 m)

Foundation and central column are designed for

torque of 50% in access of the stalling torque

Concrete center column may be keyed and

doweled into the clarifier base slab to resist

torque

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Special Loads

Seismic Loads

Hydrodynamics (sloshing) of fluid in the structure

should be considered

Should include both impulsive and convective

components

Also designed to resist earth-fill pressure and

dead load

Seismic action can induce large horizontal and

overturning forces

Joints on the base may be required to resist large

shear forces

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Pressure Loads

Fluid Pressure

Empty

Partially Filled

Full

Uplifts

Soil Pressures

Adverse

Beneficial

Active

Passive

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Behavior of

Water Retaining

Structures

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Simple Wall Behavior

Fixed Base, Top Free

Fixed Base, Top Hinged

Fixed Base, Top Fixed

Fixed Base, Top Elastic

Pinned Base, Top Pinned

Elastic Base, Top Elastic

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Simple Wall Response

Fixed Base Top Hinged

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Rectangular Panel Behavior

Moment and shear distribution depends

The aspect ratio

The continuity conditions

The supporting condition

The load variation

The average size to thickness ratio

The corner fixity conditions

For single panels, response can be

determined by partial differential equations

of from coefficients

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Circular Panel Behavior

The moment and shear distribution in

circular panel depends on

The Continuity conditions at the perimeter

The load variation on the panel

For single panels, response can be

determined by partial differential equations

of from coefficients

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Stress State in Rectangular Tanks

Bending in Walls, often

in two directions

Axial tension/

compression in Walls

Bending in Base Slab

Axial Tension/

Compression in Base

Slab

High stress

concentration in

Corners

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Stress State in Rectangular Tanks

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Stress State in Rectangular Tanks

Plan

Moment In Long Wall

Moment In

Short Wall

Tension

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Stress State in Rectangular Tanks

Elevation Short Side

M2

Variation of M2 Along

width of Wall

Variation of M1 Along

width of Wall

A

A M1 along

section A-A

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Stress State in Rectangular Tanks

Base Slab

Uplift Moment in Base Slab

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Effect of Side Walls

Free

No effect of Stiffness of

Side Walls

W

B

W/B very high

The Stiffness Effect of side walls

Increases as W/B ratio DecreasesPLAN

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Stress State

in

Rectangular

Tanks

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Stress State in Circular Tanks

Direct

Tension/Compression

in Walls

Bending in Walls

Bending in Floor Slab

Direct Tension/

Compression in Floor

Slab

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Stress State in Circular Tanks

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Stress State in Circular Tanks

Typical Section of an Open Circular Water Tank M T

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Stress State in Circular Tanks

Typical Section of a Close Circular Water Tank M T

Tension in Wall

w/o Ring Beam

Tension in Wall

with Ring Beam

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Modeling of

Water Retaining Structures

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Modeling Issues

Modeling of Walls

Modeling of Floor Slab

Modeling of Roof structures

Modeling of Supporting Frames

Modeling of Supporting Shafts

Modeling of Soil Supports

Modeling of Pile Supports

Modeling of Water ?

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Modeling of Walls and Slabs

Use Shell Elements as the walls and slabs

are subjected to out-of plane moments as

well as in plane tension and compression

Membrane or Plate elements may not give

adequate response

For domes or for shafts not subjected to

water or soil pressure, membrane elements

can be used

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Elevated Tank Models

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Modeling of Supporting Frames

For elevated tanks, the supporting structure

can be using frame or line elements

Non-linear links or tension only bracing may

be needed for steel frame or wire braced

structures

Haunches are often used in water tank

structures and should be included in the

model

Connection of frame element to shell/ plate/

membrane should be considered properly

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Modeling the Soil Supports

Very critical for determining

the response correctly

Pin or fixed support will

interfere with the free

expansion of floor slab and of

walls

Use springs to model the

supports, both in vertical and

in lateral direction

software

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Modeling Of Soil

Simple Supports: Constraints

Fix, Pin, Roller etc.

Support Settlement

Elastic SupportsSpring to represent soil

Using Modulus of Sub-grade reaction

Full Structure-Soil Model

Use 2D plane stress elements

Use 3D Solid Elements

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Modeling Options

Beam Plate Brick

ConstraintYes Yes Yes

Spring Yes Yes Yes

Brick No Yes Yes

Modeling of Mat

So

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Computing Spring Stiffness

A = Spacing of

Springs in X

B = Spacing of

Springs in Y

Ks = Modulus of

sub-grade reaction

(t/cu m etc.)

K = Spring

constant (t/m etc)A

K= ks*A*B

B

A

B

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Modulus of Sub-grade Reaction

It is defined as the ratio between the

pressure against the footing or the mat and

the settlement at a given point

Where k = Coefficient of Sub-grade reaction

q = Load per unit area

= Settlement

qk

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What is Modulus of Sub-grade Reaction

Ks = P/(L*W*H)

Units = T/m3

How to Obtain

Plate Load Test

Theory of Soil

Mechanics

Bearing Capacity

Related , N, qc etc

1m

1m

1m

P

Load required to produce unit settlement in a unit area

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Soil as Brick