A folding chair is two crossed frames, a sheet of fabric or a thin board stretched between them, and a handful of rivets. There is usually no catch, no pin to insert and nothing to tighten. Yet once it is open it carries a person's entire weight without any tendency to fold back up. The explanation is not in the strength of the parts but in the angle of the pivot.
Open the chair slowly and you can feel a small moment of resistance, then a distinct give, after which the frame seems to settle into place by itself. That give is the crossed arms passing their dead centre. A few degrees of geometry, not a lock, is what makes the chair safe to sit on.
What past dead centre means
Imagine the line along which the sitter's weight travels down through the seat. If the central pivot of the crossed frame sat exactly on that line, the joint would be in an indifferent position: the tiniest looseness, a nudge, or an uneven floor would decide which way it went. A chair built that way would gradually sink under anyone who sat in it, because nothing in the geometry prefers being open.
Push the pivot slightly past the line and the preference appears. Now a downward load on the seat produces a force that rotates the frame further open rather than folding it. The weight is not fighting the mechanism, it is holding it in place. The chair is stable for the same reason a leaning ladder is caught by the wall: the load has been arranged so that its own direction closes the escape route.
The limit is a small steel stop, usually hidden under the seat or beside one of the lower joints. It does not look like much, but it takes the entire load once the frame has gone over centre. That is why it is a stamped or folded piece of metal and rarely a plastic trim: the geometry decides where the force goes, and every bit of it arrives at this one small part. Designers put it out of sight, not out of the load path.
The seat is a tie, not just a platform
The fabric or board across the top has a second job. It connects the two crossed frames so they cannot splay sideways independently; in effect it is a tension member completing a structure that would otherwise be two loose scissors. A woven or fabric seat works in tension, while a rigid panel works with its own stiffness, but both prevent the left and right frames from drifting apart under load.
This is the same reasoning as the ribs inside a plastic box. Stiffness is not added everywhere; a thin member placed along the line where the force actually travels does most of the work. A chair seat that is heavier than it needs to be does not make the frame more secure, because the security comes from the crossed geometry and the tie between the two sides.
An umbrella uses a version of the same arrangement. Its ribs are pushed past a point where the spring-loaded runner holds them open, so the canopy resists being turned inside out until a force large enough to pull the runner back arrives. In the chair the stop is a fixed piece of steel and the load comes from above; in the umbrella the stop is a sliding runner and the load comes from the wind.
Why the rivet loosens first
The part that eventually fails is almost always a pivot. Each opening and closing rubs the same rivet against the same hole, and over thousands of cycles the round hole wears into a slight oval. That extra clearance eats the few degrees of over-centre travel. Once the geometry loses them, the chair no longer pushes itself open under load; it begins to creep downwards, and the sitter feels the seat settle a little further each time.
This is the same pattern as a power strip switch: the shell, the fabric and the tubes all outlive the one part that moves. The repair is usually not a new seat but a washer, a new pin or a tightened joint — anything that restores the small angular margin the design depends on. Replacing the worn pivot brings back a chair that nobody otherwise thought was broken.
There is a simple test. With the chair empty, open it a little at a time and rest a fingertip beside the central joint. Just before it reaches its final position there is a moment when the resistance changes sign and the frame seems to finish opening on its own. Those two or three degrees are the entire lock. No catch was left out of the design; the angle is the catch.