Explain from a visual perspective why this structure is unst

Explain from a visual perspective why this structure is unstable. DO NOT simply just state an equation and leave it at that. Assuming that roller cannot move left or right I do not understand visually how the right member can rotate around that pin. That roller can only move up and down so how could it possibly do so without that member changing its length? Am I supposed to assume that it does? Note that the left member is fixed to the ground so it cannot move.

Solution

Your argument seems quite valid, and you don\'t want equation, but it is necessary here. Note that the middle pin cannot hold a moment. Any load that is applied transversely onto the right member will create the bending moment about this pin, that it can not support, so the bar will rotate indefinitely, and thus it is unstable.

In other words, it is better to assume that the roller support provides a reaction only to the right (horizontally.) That means when a transverse load is applied to the right bar, its right end(roller) will get detached from the roller support, just like a person falling off the skates when his body creates the moment about the skate wheels.

This is the only valid explanation for it. I hope it satisfies your query.