The options show frames consisting of rigid bars connected by pin joints. Which one of the frames is non-rigid?

The correct option is the third option (Option 3), which shows a three-panel rectangular frame where the middle panel lacks a diagonal bracing member.

To determine which frame is non-rigid, we can analyze the structural stability and triangulation of each option:

1. Definition of Rigidity in Pin-Jointed Frames:
A frame consisting of rigid bars connected by pin joints is rigid if it cannot undergo any continuous deformation (change in shape) without changing the lengths of its members. In two dimensions, the basic rigid unit is a triangle. A structure built entirely of connected, fully-braced triangles is stable and rigid.

2. Analysis of the Options:
• Option 1: This frame consists of four joints forming a quadrilateral divided by a single diagonal member. This division forms two triangles sharing a common side. Since both parts are triangulated, the frame is rigid.
• Option 2: This frame has five outer joints and an internal joint connected to the vertices. It consists of multiple triangular sub-structures sharing vertices. Because it is completely triangulated, it is rigid.
• Option 4: This is a three-panel truss where every single rectangular panel contains a diagonal bracing member. The diagonal members turn each panel into rigid triangles, making the entire frame rigid.

• Option 3 (The Correct Answer):
Let us analyze the distribution of members in this frame. It consists of three panels:
- The leftmost panel has a diagonal member.
- The rightmost panel has crossing diagonal members meeting at a central pin joint.
- The middle panel has four joints forming a rectangle with only vertical and horizontal members, but no diagonal member.

Without a diagonal bracing member in the middle panel, that section behaves like a four-bar linkage mechanism with one degree of freedom. Under an external load, such as a vertical force

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applied at the right end, the middle rectangular panel will readily undergo shear deformation (changing from a rectangle to a parallelogram) without stretching or compressing any of the bars. This allows the rightmost panel to translate and rotate relative to the leftmost panel, resulting in a large deformation of the overall structure. Therefore, this frame is non-rigid.