# Truss Analysis Methods: An Introduction

*Truss* can be defined as a structure which is formed by joining its members end to end. The joint at which two or more members are joined is called a node. The beauty of a truss structure lies in its sturdiness; since the external forces lead to tensile or compressive reactive internal forces, the structure is very stable and is very commonly used to make bridges. The construction and nuances of bridges and their construction is an extensive topic in Civil Engineering. To know about career in engineering take up a course from the website.

Trusses can be of two types: a planar truss and a space truss. The planar truss has all its members in a two dimensional plane whereas a space truss has its members and nodes extended to a 3D space. The top members in a truss are called top chords and the bottom members of the truss are called bottom chords. The top chords are associated with compression whereas the bottom chords offer tension. The web is the area of the interior section of the members and the panels are the areas inside the web.

**Analysis of Trusses**

While analyzing a truss structure, a person needs to assume some things to keep things simple:

- The joint is where the entire load is applied, and all other forces on the member are to be neglected.
- The weight of a member is very insignificant to the amount of load that has been applied to it. Hence, it will not be considered in further calculations. However, some methods may take in account half of the weight of the member as acting on each individual joint of the member.

To further on the discussion about trusses you need to be very familiar to geometry. The lesson on geometry from Udemy.com could prove to be really beneficial for you. The analysis of trusses can be carried on by the following methods: direct stiffness, flexibility (force), and finite element.

**Direct Stiffness Method**

The method is suited for computer analysis of complex structures. It is also known as the *Matrix Stiffness Method*. The method uses the stiffness values of the individual members for calculating the forces that are acting on the members. The system is reduced to a simpler connection of members that are interconnected at the nodes. The members are studied by disconnecting them from the whole structure and looking at their stiffness values individually. The individual stiffness values of the members are then put into a matrix equation which helps find the behavior of the whole structure.

Using the matrix equation, many unknown variables can be found, which is not otherwise possible. Learning matrix algebra is quite easy and once you get a hang of it, solving matrix equations is a piece of cake.

The direct stiffness method is the building block of many computer aided structure analysis software. The method has its roots when scientists used the method to find out various characteristics about air plane structures. Further, the method is widely used in studying the stability of civil structures such as bridges.

**The Flexibility or Force Method of Truss Analysis**

The *Flexibility Method* of truss analysis helps us analyze the relationship between the forces and the displacement that exist within the structure. The main goal of the force method is to find the value of redundant forces. The number of redundant forces is equivalent to the degree of indeterminacy of the structure. The force method can be used to find the unknowns by following the procedures mentioned below:

- Determine the static degree of indeterminacy. The number of releases is equal to the degree of indeterminacy. Then the number of releases is equated to the degree of static determinacy. The release structure or the primary structure must be chosen such that it is statically determinable. The redundant forces should be chosen in a way so that the structure becomes easy to analyze.
- Calculate the displacement errors in the primary structure due to the redundant forces using the virtual forces method.
- Calculate the displacement in the primary structure due to the unit value of the redundant forces using the virtual forces method. Find the displacements in the same directions as the displacements found in step number two.
- Calculate the value of the redundant forces to eliminate displacement errors. Using displacement superposition you will get n number of linear equations where n is the same as the number of releases. This guarantees that there is zero relative displacement in the structure.
- The compatibility equations help us determine that the structure is stable.
- Finally, we find the forces that are present in the original structure which is the sum of the redundant forces and the external forces on the released structure.

## The Finite Element Method

In this method the solution to the problem is found by finding solutions to sub problems which then combine to form the whole solution.

The fundamentals underlying Finite Element Method are:

- The individual structure is divided into individual parts. Truss can be the simplest finite element since the stress in the structure is equally distributed throughout the structure. Hence, truss could be treated as a single element.
- Write equations for each element.Represent elongation in terms of displacement of the nodes.Represent forces in terms of the displacement of the nodes.
- Combine the equations and solve them using linear algebra principles.
- Equate the sum of the forces to zero as the nodes are stationary.
- Add up all the nodal displacements and equate it to zero, since the structure is stationary.

Some of the words of wisdom about the finite element method are as follows:

- With more and more powerful functions being built into the FEA packages, the analyzer should never think that the packages are suitable for every modeling situation. The packages cannot always be assumed to provide accurate results. A user should always be wary of the easy way out, since the easy way is not always necessarily the correct way.
- Since computers are getting faster and faster, you cannot always assume that the answer which can be computed at a faster rate is always right. A fast reached result is of no use if it is inaccurate.
- An engineer should not always rely solely on the FEA results. Since a lot of civil engineering tools have come into the market, the engineers have a tendency to rely heavily on them which could be dangerous.

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