STRUCTURAL ANALYSIS

DefinitionsDefinitions

Concepts of Stability of Concepts of Stability of StructuresStructures1

Statically Determinate / Statically Determinate / Indeterminate StructuresIndeterminate Structures2

Advantages & Advantages & disadvantages ofdisadvantages of3 disadvantages of disadvantages of indeterminate structuresindeterminate structures

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STRUCTURES

■■ DefinitionDefinitionStructure is defined as an assembly of connected parts (members) used to support loads.

Buildings, bridges, tunnels, tanks and chimneys are example

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g , g , , y pstructures commonly encountered in practice.

Civil Structures

■■ BUILDINGSBUILDINGS

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Civil Structures

■■ BRIDGESBRIDGES

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Civil Structures

■■ LARGE HALLSLARGE HALLS

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Civil Structures

■■ STADIUMSSTADIUMS

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Civil Structures

■■WATER STRUCTURESWATER STRUCTURES

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Support Types

■■ Fixed SupportFixed Supportpppp

R MRx

RyRy

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Support Types

■■ Hinged SupportHinged Supportg ppg pp

Rx

Ry

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Support Types

■■ Roller SupportRoller Supportpppp

R

R

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R

Statically Determinate / Indeterminate Structures

■■ CONDITIONS OF DETERMINATE STRUCTURECONDITIONS OF DETERMINATE STRUCTURE

No. of Equilibrium Equations = No. of unknownsDeterminate ifDeterminate if

No. of Equilibrium Equations No. of unknowns

2D Beams 3 + c2D Frames 3j + c2D Trusses 2j

rr + 3mr + m

3D Beams 6 + c3D F 6j

r63D Frames 6j + c

3D Trusses 3jr + 6mr + m

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Statically Determinate / Indeterminate Structures

■■ BEAM STRUCTUREBEAM STRUCTURE2D Beams2D Beams

3 + c > r3 + c > rUnstable

3 + c = rDeterminate

3 + c < rIndeterminate

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Indeterminate

Statically Determinate / Indeterminate Structures

■■ FRAME STRUCTUREFRAME STRUCTURE2D Frames2D Frames

3j + c > 3m + r3j + c > 3m + rUnstable

3j + c = 3m + rDeterminate

3j + c < 3m + rIndeterminate

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Indeterminate

Statically Determinate / Indeterminate Structures

■■ TRUSS STRUCTURETRUSS STRUCTURE2D Trusses2D Trusses

2j > m + r2j > m + rUnstable

2j = m + rDeterminate

2j < m + rIndeterminate

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Indeterminate

Statically Determinate / Indeterminate Structures

■■ EXAMPLE FRAMESEXAMPLE FRAMES

Class.3J+C

3M+R

CJRMFrame

Class.3J+C

3M+R

CJRM

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3Indet.1215-463A 1Indet1516-544B

Statically Determinate / Indeterminate Structures

■■ EXAMPLE FRAMESEXAMPLE FRAMES

Class.3J+C

3M+R

CJRM Class.3J+C

3M+R

CJRM

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C+R

12Indet2739-9910D

+C+R

Unst.22214636E

Statically Determinate / Indeterminate Structures

■■ EXAMPLE FRAMESEXAMPLE FRAMES

Class.3J+C

3M+R

CJRMFrame

Class.3J+C

3M+R

CJRMFrame

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Det.30303968F 6Indet.2127-767G

Statically Determinate / Indeterminate Structures

■■ TRUSSESTRUSSES

Class.2JM+RJRM

Det.282814325

Class.2JM+R

JRM

Unst (Parallel363618333

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Unst. (Parallel reactons)

363618333

Statically Determinate / Indeterminate Structures

■■ TRUSSESTRUSSES

Class.2JM+R

JRM

Unstable201910316

Class.2JM+R

JRM

1Indeterminate303115427

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Unstable2019103161Indeterminate 303115427

Advantages / Disadvantages of Indeterminate Structures

■■ FORCES (ECONOMY)FORCES (ECONOMY)( )( )DeterminateDeterminate IndeterminateIndeterminate

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Advantages / Disadvantages of Indeterminate Structures

■■ DEFLECTIONSDEFLECTIONSDeterminateDeterminate IndeterminateIndeterminate

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Advantages / Disadvantages of Indeterminate Structures

■■ REDUNDANCYREDUNDANCYDeterminateDeterminate IndeterminateIndeterminate

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Advantages / Disadvantages of Indeterminate Structures

■■ TEMPERATURE EFFECTTEMPERATURE EFFECTDeterminateDeterminate IndeterminateIndeterminate

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Advantages / Disadvantages of Indeterminate Structures

■■ SUPPORT MOVEMENTSSUPPORT MOVEMENTSDeterminateDeterminate IndeterminateIndeterminate

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Problems

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