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What is Free Body Diagram (FBD) in Structural Analysis ??

Free Body Diagram of A Cable Joint
Fig.1.Free Body Diagram of A Cable Joint

Free body diagram is one of the main aid used for solving static problem in the static analysis of structures.



Free Body Diagram of Structural Elements


The free body diagram is method that can be used in modelling a structure conveniently. FBD in more precise way is a method that we use to conceptualise a structure or its respective elements so that easy analysis of the same can be carried out.

The free body diagram can be defined as a graphical, symbolic and a dematerialised representation of a structure or its elements. This conversion will remove all the connecting pieces.

While drawing a free body diagram, all the physical attributes that are on the structures are removed and symbolised conceptually. 

Features of Free Body Diagram

  1. A simple single line will be used to represent a body or a segment
  2. Connection will be represented by distinct properties.The junction will be conceptualised to a set of forces and moments. These forces are reactions at the connection. 
  3. When comes to nodes, there are internal forces. These are represented by means of external forces. This will include the influence from all the members that is connected to that node.

Consider the figure-2 below. The features explained below can be properly explained with the help of this figure. This is a street lamp. The different stages that are used to evolve the free body diagram of the street lamp is explained below. 



Fig.2.Free Body Diagram of a Street Lamp
1. Initially, the whole system is dematerialised. Here, the lamp is dematerialised into a body that is weighing say 30#. The weight is acting in the direction of gravity from the centre of the body(downwards). Hence a straight line arrow heading downwards is drawn from the centre of the lamp. The system have lamp as the only element, whose weight is known.

2. Next we need to find other forces that will keep this lamp in equilibrium. For this we look at the left end fixed support. Now we identify the forces and moments that will be generated in a fixed support. The fixed support will have a moment, vertical reaction and Horizontal reaction.As here, there is no other horizontal force, the horizontal reaction can be neglected. Hence at the left end fixed support , we have a vertical reaction and a moment.
More about Different Supports & Reaction- Read the article: 
Supports and Reactions in Structural Analysis
3. Next the span distance can be obtained from which the final free body diagram can be drawn.

All those necessary elements of force that is essential to analyse or solve a force system will be included in the free body diagram (FBD).

FBD is not found essential in simple problems. But, when it comes to complex analysis situations, FBD methods is increasingly utilised.

More examples of conversion of load systems in to free body diagrams are explained in the examples below.

Example 1: A Beam Fixed at one end and Free at other end


Fig.3.Free Body Diagram of a Cantilever Beam with a Point load at the end




Example 2: Three Different Structural Systems with same loading and support


Fig.4. Three Different Structural Systems in Real Arrangement
The free body diagram for the above structural systems can be drawn as shown in figure-5 below. Here you can see that the internal structural elements have been removed in the FBD diagram. This is because, the internal arrangement have no influence in determining the support reactions. 
Fig.5.Free Body Diagram of Figure-4


And if the loading geometrics and the supports are the same, the external reaction will also remain the same.







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