What is perfect simple plane truss? A detailed introduction..

Truss is structure usually fabricated from straight slender members of metal or timber arranged in a triangles and connected only at pin joints or nodes. 

Trusses are rigid structures made up of two-force members (Tension member ~ tie and Compression member ~ strut). 

Types of truss

There are two basic model of the truss structure.
  • Plane truss this is a truss type where all members and joints(nodes) are present in same single plane. It’s a two-dimensional model truss structure. An example this is roof truss
Click here to see examples
  • Space truss this is a truss type where members and joints act in different plane. It’s a three-dimensional model truss structure. An example of this is a telephone tower or electrical transmission tower
Click here to see examples

What are the parts of truss?

Any truss you see around have the following parts
  • Joints, truss joints are point where members are connected together and the load of truss normal assumed to act at this connections and often labelled with a letter
  • Members, are the metal/wooden straight elements that are labelled with the connection between joints
  • External force (applied and reaction forces), this come from support reactions and applied external force introduced during truss performance in carrying out it’s designed.

What is truss used for?

1. Trusses are mainly used in the construction of roofs and bridges. Basically, there are truss to be used specific as a roof truss and bridge truss.

According to Hibbeler, 2012 below are trusses which are used as a roof truss:

  • Scissors truss
  • Cambered fink truss
  • Howe truss
  • Warren truss
  • Pratt truss
  • Sawtooth truss
  • Fan truss
  • Bowstring truss
  • Fink truss
  • Three-hinged arch truss

And for bridge truss the following trusses are used:

  • Pratt truss
  • Howe truss
  • Warren truss
  • Parker truss
  • Baltimore truss
  • Subdivided warren truss
  • K-truss

2. Trusses also used in other civil construction aspects such as the construction of telephone tower, scaffold, power pylons or transmission towers, railway platforms, sport stadium etc.

What is the classification of truss system?

Before beginning analysis of a truss member forces, it is important to classify the truss so as to be able to specify its determinacy and stability.

According to Hibbeler, 2012 truss is classified as:

1. Simple truss is constructed by starting with a basic triangular element.

Members of the truss systems are connected to form a triangles in such a way that the truss system cannot be separated into several simple trusses.     

2. Compound truss is formed by connecting two or more simple trusses together.

Quite often this type of truss is used to support loads acting over a large span which may be lighter one than a single heavier simple truss.

There are three ways in which simple trusses are joined together to form a compound truss.

  • Common joint and bar click here to see example
  • Three bars,
  • Large simple truss, called the main truss, substituted by simple trusses, called secondary trusses
3. Complex truss is one that cannot be classified as being either simple or compound

As per Bansal, 2009 a simple truss can further more be classified as perfect or imperfect truss based on this equation m = 2n - 3, 

m= Number of members in the truss

n=Number of joints in the truss

If number of members in the simple truss ( m=2n-3 ), this a perfect truss unless otherwise It’s imperfect truss.

( m < 2n-3 ) Imperfect truss (Deficient truss)

( m > 2n-3 ) Imperfect truss (Redundancy truss)  

How to do truss analysis?

Truss analysis mainly involves the following procedures first checking the stability and determinacy of the truss second determination of the reaction at the supports and last determination of the forces in the members of the truss.

Assumption made during truss analysis

  • All members have negligible weight
  • All members have uniform cross section
  • Members are connected at the joints through pin connections.
  • All the members have only axial force i.e. either tensile or compressive
  • All the external forces are applied only at the joint

Zero-force member

As defined early “Trusses are rigid structures made up of two-force members”, in truss system there a member which introduce for the purpose of providing stability these members are called zero-force member

  • A zero-force member is a member in truss which carries zero force in it and it classified as neither tie nor struts.

Rules for identifying the zero force members

  • If only two non-collinear members are connected to a joint that has no external loads or reactions applied to it, then the force in both members is zero.
  • If three members, two of which are collinear, are connected to a joint that has no external loads or reactions applied to it, then the force in the member that is not collinear is zero.
  • If there are only two members at a joint and the external force is along one of the member, then the other member is a zero-force member.

Methods of analysis for perfect plane simple truss

Analysis of a perfect truss is carried out by the following methods

  1. Graphical method 
  2. Method of joint
  3. Method of section
  4. Northing - Easting method
Check out this video below on how to do Truss analysis using Method of Joint


That's all for this post in conclusion hope you have a clear understanding of the whole concept regarding to perfect plane simple truss, uses, and analysis and if you have any question post it on a comment section below.

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