Geometrically unstable structure

A truss is a structural framework composed of straight members connected at joints. It is used to support loads and distribute them evenly throughout the structure. Trusses are commonly used in bridges, roofs, and other load-bearing structures.

Classification of trusses

Trusses can be classified into several categories based on their characteristics. One classification is based on the behavior of the truss under external loads. Trusses can be categorized as determinate or indeterminate structures.

Determinate structures

Determinate structures are those in which the reactions and internal forces can be determined solely using the equations of static equilibrium. These structures have a unique solution for all the unknowns. In other words, the reactions and forces in each member can be determined by solving a set of simultaneous equations.

Statically unstable structures

Statically unstable structures are those that cannot be analyzed using the equations of static equilibrium alone. These structures have more unknowns than the number of equations available, making it impossible to determine the reactions and internal forces without additional information or assumptions.

Structurally unstable structures

Structurally unstable structures are those that fail to maintain their shape or stability when subjected to external loads. They are unable to resist the applied loads and may collapse or deform significantly. These structures generally have insufficient stiffness or strength to support the applied loads.

Geometrically unstable structures

Geometrically unstable structures are those that undergo rigid body translation under an arbitrary load. Rigid body translation refers to the movement of the entire structure as a whole, without any deformation or change in shape of individual members. In such structures, the joints are not rigid enough to maintain the shape of the truss, causing it to move as a unit.

Explanation of the correct answer

Based on the given options, the correct answer is option 'B' - Geometrically unstable structure. This is because a truss that undergoes rigid body translation for an arbitrary load does not maintain its shape and exhibits movement as a whole. The joints in the truss are not rigid enough to resist the translation, resulting in a geometrically unstable structure.