## What are trusses?

In civil engineering, a truss is the most important structure that forms the most fundamental member of any building structure and commercial complexes. Trusses are composed of individual members or links that are interconnected by suitable joints, such as rivets, welds, or bolts, and nuts. In trusses, the interconnection leads to the formation of a series of triangles joined together such that all the triangular members behave as a single rigid body. In a simple truss, three members are connected to form a truss member. In trusses, the force always acts at the joints or the interconnection between the individual members.

In buildings and bridges, trusses are primarily provided to withstand the load of the building and provide stability. The loads that act on the truss members are primarily tensile, compression, and bending moment.

## Plane and space truss

A plane truss or planar truss is basically a two-dimensional network of uniform cross-sectional members. They generally comprise straight members such as bars and links. The members are joined to one another by pin joints. In the plane trusses, the loads applied and reactions induced are only at the joints, and lie in the plane of the truss. Each member of the truss structure is subjected to axial tensile and compressive loads. Hence, plane trusses are also two-force members. A truss member can also be subjected to bending moment, and make the truss member undergo hogging and sagging bending. Under the hogging bending, the top chords of the truss member experience tensile forces, and the bottom chords experience compressive forces. In the case of sagging bending, the reverse happens.

A space truss is a three-dimensional structure that consists of members arranged to form tetrahedrons. These kinds of structures remain under the application of three-dimensional force systems. The simplest space truss structure can be formed by joining six members with four joints to form a tetrahedron. The space trusses are internally stable structural members that do not undergo deformations due to applied forces.

Every member of a space truss is connected by frictionless ball and socket joints due to which the members undergo miniature mobilities that help in better load absorptions.

## Determinacy of trusses

All truss structures are mounted on supports; depending on the support types, specific reactions are induced when these structures are acted by external forces. Under the application of forces, the truss structures undergo deformations and develop internal stresses. To analyze a structure composed of a truss, the primary step is to draw a free-body diagram and determine the support reactions. The ease of reaction estimation depends on the determinacy or indeterminacy of the structure. For analysis of both plane trusses and space trusses, the determinacy should be estimated.

A plane truss or a space truss member can be structurally determinate or indeterminate. For a plane truss, if the reaction developed at the supports can be calculated by applying the equilibrium equations alone, then such plane trusses are termed a statically determinate plane truss. If the reactions cannot be determined by the equilibrium equations alone, such types of plane trusses are statically indeterminate plane trusses.

For a plane truss, there are two equilibrium equations, $\sum _{}{F}_{X}=0$and $\sum _{}{F}_{Y}=0$. Here, ${F}_{X}$ and ${F}_{Y}$ are the forces in the X direction and Y direction, respectively. Similarly, for a space truss to be statically determinate, the reactions must be determined by the equilibrium equations alone. If the reactions cannot be determined by equilibrium equations alone, such trusses are known as statically indeterminate trusses. A plane truss is a three-dimensional structure. Hence, there exist three equilibrium equations: $\sum _{}{F}_{X}=0$, $\sum _{}{F}_{Y}=0$, and $\sum _{}{F}_{Z}=0$. Here, ${F}_{Z}$ is the forces along the Z direction.

## Stability of trusses

Trusses installed for structural applications must be stable and rigid enough to provide stability to the whole building or the structure, apart from checking the determinacy and indeterminacy of trusses and required load calculations, engineers also must ensure the truss is structurally stable. To estimate the stability, the truss must satisfy the stability condition, which is given by

$M+R=2j$, where, $M$ is the number of members, $j$ is the number of joints, and $R$ is the number of support reactions.

This equation is valid for a plane truss that consists of only two-dimensional members.

- if $M+R<2j$, this signifies the truss is unstable and will collapse under load.
- if $M+R=2j$, the truss is stable.
- if $M+R>2j$, the truss is indeterminate.

## Context and Applications

The topic of truss and its related concepts are interdisciplinary and are taught in both civil engineering and mechanical engineering courses.

The topic is primarily taught in various undergraduate and postgraduate degree courses of

- Bachelor of Science (Physics)
- Master of Science (Physics)
- Bachelors of Technology in Civil Engineering
- Masters of Technology in Civil Engineering

## Practice Problems

1. Which of the following is true for planar truss?

- It is a two-dimensional member
- The loads are acted at the joints
- Undergoes twisting
- Both a and b

Correct option- d

Explanation: A plane truss is a two-dimensional member where the loads act at joints.

2. Which of the following is the first step in determining the truss support reactions?

- Applying equilibrium equations
- Check for stability of the truss
- Draw free-body diagrams
- None of these

Correct option- c

Explanation: To determine the support reactions, a free-body diagram of the truss should be drawn.

3. Which of the following is true for a truss member under external loads?

- The loads acts at the truss member periphery.
- The loads acts at the joints.
- Truss members experiences twisting along with bending moment.
- None of these

Correct option- b

Explanation: The external loads always act at joints for a truss member.

4. Which of the following stresses are primarily induced in a plane truss?

- In-plane shear stress
- In-plane maximum shear stress
- Tensile stresses
- All of these

Correct option- c

Explanation: A truss member under external loading conditions undergoes tensile and compressive deformations, which induce both the tensile and compressive stresses.

5. Which of the following is true for a simple truss?

- They are two-force members
- It has straight members
- The members joined together forms a tetrahedron
- Both a and b

Correct option- d

Explanation: The members of a plane truss are straight two-force members.

## Related Concepts

- Girder trusses
- Complex trusses
- Method to form stiffness matrix of a two-dimensional bar member
- Stiffness matrix method in truss analysis

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