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Statically Indeterminate Plane Truss

STRUCTURAL ANALYSISBFC23102

www.uthm.edu.my With Wisdom, We Explore

Introduction

What is statistical indeterminate structure?

Also known as redundant structures

Independent reaction/or internal force can be obtained using the equilibrium equation

Number of unknown exceeds the number of equilibrium

Advantage

Economical material usage

Reducing deflection

Enhancing stiffness

Beautifying


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Introductionwww.uthm.edu.my With Wisdom, We Explore

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Bridge truss


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Airport Building (Abu Dhabi)


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Dome truss

Types of Statically Inderterminate

1) External Indeterminate

Related with reaction

Number of reactions exceed than determinate structure by using static equation

m = 2j - 3 and r > 3

Reaction known as external redundant


6

...1011)5(247

25);3(4;7

jrm

jrrm Statistical Indeterminate with 1th degree of indeterminate

332...77

3)5(27

32

randjm

jm

External statistically indeterminate


2) Internal Indeterminate

Related with framework construction

If inadequate member detected, structure is classified as unstable

m > 2j - 3 and r = 3

Internal force known as internal redundant


7

...1213)6(2310

26310

jrm

;j ;rmStatistical Indeterminate with 1th degree of indeterminate

332...910

3)6(210

32

randjm

jm Internal statistically indeterminate


3) External and Internal indeterminate

External and Internal indeterminate m > 2j - 3 and r > 3

If (i) is degree of determination of truss so:i = (m + r) - 2j


8

...1214

)6(2410

2

6;4;10

jrm

jrm Statistical Indeterminate with 2 degree of indeterminate

332...910

3)6(210

32

randjm

jm External and Internal statistically indeterminate

Analysis of Plane Truss (External Redundant)

Analysis using Virtual Work Method/ Unit Load Method


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RA RB RC

HA

P1

A

BC

Support reaction ?

Number of members ?

Determinacy of system


Hint to reduce the system:

If the truss is external statically indeterminate, reduced the support reaction, r to 3

If the truss is internal statically indeterminate, reduced the members to the same number degree of indeterminacy. (e.g: if 1st degree, reduced one member)

If the truss is external and internal statically indeterminate, reduced the support reaction, r=3 and member truss for the balance of degree.


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Analysis of Plane Truss (External Redundant)www.uthm.edu.my With Wisdom, We Explore

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RA RB RC

HA

P1

A

BC

If support at joint B is removed, calculate reaction RB :

BRFF '

Ultimate internal force

0 bbBB R bb

BBR

AE

LFB

'

AE

L

AE

Lbb

2

AEL

AELFRB

/

/

2

'


Example 3.1


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Example 3.1


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Example 3.2


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Example 3.3


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25


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27


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Tutorial 1


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Tutorial 2

Determine the real/ultimate internal force for all members onthe truss system. Take cross-section of top chord members =400mm2, bottom chord members = 600mm2, vertical members= 300mm2 and diagonal members = 250mm2. E = 210GPa.


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Tutorial 3

Determine the real/ultimate internal force for all members on the truss system. Take E=200kN/mm2 and A for AB=CD=HG=FE=500mm2 ; BC=GF=600mm2 ; AH=BG=CF=DE=450mm2 ; BH=BF=DF=300mm2

statically indeterminate plane trussauthor.uthm.edu.my/uthm/www/content/lessons/601/slides...types...

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