# What is a Perfect, Imperfect, Deficient and Redundant Truss?

## Efficient or Perfect Truss

A truss is considered perfect when the number of its members is just enough to maintain its shape under external loads without any distortion. Such a truss can withstand the applied load without collapsing or undergoing any deformation. In other words, perfect trusses are **statically determinate structures** that possess enough members to resist external loads.

A perfect truss can be determined by checking if it satisfies the equation m = 2j-3, where m is the number of members and j is the number of joints. With the perfect number of members, a truss can effectively resist external loads without excess material, resulting in a structurally efficient design.

## Imperfect Truss

An imperfect truss is a type that fails to satisfy the relation between the number of members and the number of joints, as described by the equation m = 2j – 3. It may be a deficient truss or a redundant truss. In other words, an imperfect truss has an excess or insufficient number of members compared to the ideal number required to maintain the structural integrity of the truss. Such a truss is considered an inefficient structure.

## Deficient or Collapsible Truss

A deficient truss is characterized by a structural design in which one or more members are fewer than the required number, as indicated by the equation m < 2j-3. This type of truss is also known as a collapsible truss since it tends to collapse under the influence of collapsible forces.

🔗Assumptions in Truss Analysis

## Redundant Truss

If a truss has an excess number of members beyond what is required for structural stability (m > 2j-3), it is known as a redundant truss. This type of truss is structurally inefficient but can withstand load without collapsing. Redundant trusses have the advantage of being able to resist the failure of one or more members, making them a fail-safe structure. If one member fails, the load can be redistributed among the remaining members, ensuring that the structure remains intact. Redundant trusses are commonly used in bridges and other structures where public safety is of primary concern.