Plain and Space Trusses

8/9/2019 Plain and Space Trusses

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PLAIN AND SPACETRUSSES


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TRUSS

It is an assemblage of straightmembers connected at their ends

by flexible connections to form a

rigid configration!


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Plane Truss

It is a trss "here all members of atrss and the a##lied loads lie in the

same #lane!

Space TrussThese are three$dimensional bodies

sb%ected to three$dimensional force

system!


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Plane Trusses Common BridgeTrusses


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Types of Plane Trusses

A! Sim#le Trss

These are formed connecting its member from

ti# to tail in a trianglar form and enlarging by

adding a ne" %oint that connects from the othert"o #re&ios %oint!

'! Com#ond trss

These are formed by connecting t"o or more

sim#le trss to form a single rigid body!

Connections mst be ca#able of transmitting at

least three force com#onents!


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C! Com#lex trss

These are trsses "hich is neither a

sim#le trss nor com#ond trss!


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Determining Internal Stability of

Plane Truss

Conditions are(

If m ) *+% , -./ the Trss is Internally

Unstable

If m 0 *+% , -./ the Trss is Internally

Stable

m 1 total nmber of members

% 1 total nmber of %oints


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Example of Internally Stable andUnstable Truss


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Static Determinacy, Indeterminacy

and Instability of Plane Truss

The Conditions of Static Instability/

determinacy/ and Indeterminacy of Plane Trss

are as follo"s(If/

*m 2 r. ) +%/ statically Unstable Truss

*m 2 r. 1 +%/ statically Determinate Truss

*m 2 r. 3 +%/ statically Indeterminate Truss

degree of static indeterminacy

i = (m + r) 2j


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Analysis of Member Forces on Plane Truss

by Method of oints and Method of

Section

A! "y Method of oints

Using this method/ the forces *member/

reactions/ and a##lied loads. shold be in formof co#lanar concrrent force system/ "hich

mst satisfy t"o e4ation of e4ilibrim 5671

8 and 5691 8!

'y this method/ there shold be selectingof %oint "ith no more than t"o n:no"n

forces *"hich mst not be collinear. acting on

it *%oint.!


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SPA#% TRUSS

S#ace Trssis analysed by as three$dimensionalstrctre sb%ected to three$dimensional force

system!


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Reactions on Space Truss


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The Conditions for determinacy externally of s#ace

strctre are as follo"s(

If r ) ?/ the s#ace strctre is statically unstable

e'ternally

If r 1 ?/ the s#ace strctre is statically determinate

e'ternally

If r 3 ?/ the s#ace strctre is statically indeterminate

e'ternally


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Static Determinacy, Indeterminacy

and Instability of Space Truss

StructureConditions are as follo"s(

If *m 2 r. ) -%/ statically unstable space

truss

If *m 2 r. 1 -%/ statically determinate

space truss

If *m 2 r. 3 -%/ statically indeterminate

space truss


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Analysis of Member ForcesA! Determining forces 'y ;ethod of @oint

LA' 1

67A' 16A'*.

67A' 16A'*.

67A' 16A'*.

6A' 1


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C! Identification of ! If all bt one of the members connected to a

%oint lie in a single #lane and no external loads

or reactions are a##lied to the %oint/ then the

force in the member that is not co#lanar is

=ero!

+! If all bt t"o of the members connected to a

%oint ha&e =ero force and no external loads or

reactions are a##lied to the %oint/ then nless

the t"o remaining members are collinear/ the

force in each of them is also =ero!


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End of Re#ort!

Documents

Plain and Space Trusses