ESTATICA VECTORIAL - EJERCICIOS, Ejercicios de Estática

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Analysis of Statically Determinate Trusses

THEORY OF STRUCTURESAsst. Prof. Dr. Cenk Üstünda

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Common Types of Trusses

^

A truss is one of the major types of engineering structures whichprovides a practical and economical solution for many engineeringconstructions, especially in the design of bridges and buildings thatdemand large spans. ^

A truss is a structure composed of slender members joined together attheir end points ^

The joint connections are usually formed by bolting or welding the endsof the members to a common plate called gusset ^

Planar trusses lie in a single plane & is often used to support roof orbridges

Common Types of Trusses

Roof Trusses

Common Types of Trusses

Bridge Trusses^ ^

The main structural elements of a typicalbridge truss are shown in figure. Here itis seen that a load on the deck is firsttransmitted

to

stringers,

then

to

floor

beams, and finally to the joints of thetwo supporting side trusses. ^

The top and bottom cords of these sidetrusses are connected by top and bottomlateral bracing, which serves to resist thelateral forces caused by wind and thesidesway caused by moving vehicles onthe bridge. ^

Additional stability is provided by theportal and sway bracing. As in the caseof many long-span trusses, a roller isprovided at one end of a bridge truss toallow for thermal expansion.

Common Types of Trusses

Bridge Trusses^ ^

The greatest economy of

material is

obtained if the diagonals have a slopebetween

45

°

and

60

°

with

the

horizontal.

If

this

rule

is

maintained,

then for spans greater than 91 m, thedepth of the truss must increase andconsequently the panels will get longer. ^

This results in a heavy deck system and,to keep the weight of the deck withintolerable limits, subdivided trusses havebeen

developed.

Typical

examples

include the

Baltimore

and

subdivided

Warren

trusses.

^

The

K-truss

shown can also be used in

place of

a subdivided truss, since it

accomplishes the same purpose.

Common Types of Trusses

^

Assumptions for Design^ 

The members are joined together by smooth pins  All loadings are applied at the joints ^

Due to the 2 assumptions, each truss member acts as anaxial force member

Classification of Coplanar Trusses

Simple Truss^ 

The basic

“stable

”^ triangle element is ABC

^

The remainder of the joints D, E & F are established inalphabetical sequence ^

Simple trusses do not have to consist entirely of triangles

Classification of Coplanar Trusses

Compound Truss^ 

It is formed by connecting 2 or more simple truss together  Often, this type of truss is used to support loads acting over alarger span as it is cheaper to construct a lighter compoundtruss than a heavier simple truss

Classification of Coplanar Trusses

Compound Truss

Classification of Coplanar Trusses

Complex Truss^ 

A complex truss is one that cannot be classified as being eithersimple or compound

Classification of Coplanar Trusses

Determinacy^ 

Therefore only  By comparing the total unknowns with the total number ofavailable equilibrium equations, we have:

ate

indetermin

statically 2

e

determinat

statically 2^ j r b

j

r b

^

^

and 0

y

x^

F

F

Classification of Coplanar Trusses

Stability^ 

If b + r < 2j => collapse  A truss can be unstable if it is statically determinate orstatically indeterminate  Stability will have to be determined either through inspectionor by force analysis

Classification of Coplanar Trusses

^

Internal Stability^ ^

The internal stability can be checked by careful inspection of thearrangement of its members  If it can be determined that each joint is held fixed so that it cannotmove in a

“rigid body

”^ sense with respect to the other joints, then the

truss will be stable  A simple truss will always be internally stable  If a truss is constructed so that it does not hold its joints in a fixedposition, it will be unstable or have a

“critical form

”

Classification of Coplanar Trusses

^

Internal Stability^ ^

To determine the internal stability of a compound truss, it isnecessary to identify the way in which the simple truss are connectedtogether  The truss shown is unstable since the inner simple truss ABC isconnected to DEF using 3 bars which are concurrent at point O