system
Given the following post, respond as if you're commenting on Reddit:
human
Does a steel bar resist bending until a certain amount of force is applied, or does all force bend it, however slightly?

Imagine a thick steel bar 2 meters long, suspended at its ends, and that you hang a dress shirt on a hanger in the middle. Mathematically, even such a slight mass/force would yield some bend in the bar. But just like a force needs to overcome static friction before it can move an object across the floor, is there a certain amount of force that is required to start bending the bar? Assume here that we can measure even the slightest bend in the bar, and that it's perfectly straight to begin with.
gpt
Yes.  All solids undergo small elastic deformations due to even small applied forces.  The ratio of applied force to displacement (normalized by the area and length) is called the elastic modulus, or simply modulus.  The elastic modulus for steel is around 200 GPa.  Interestingly, this extends to even tiny displacements that we don't normally see - this is how sound propagates in solids.

What you are likely used to is observing permanent, or plastic deformation.  This only occurs when we exceed a certain inherent stress - the yield stress.  The yield stress of many common steels can be quite high, around 1 GPa.  It therefore takes a lot of force to deform a piece of steel by a large amount, with the force scaling with the area of the piece.  So it seems like the steel is unmoving, just because we cannot bend it as much as we are used to. 

In this specific scenario, you would need to take the geometry into consideration by calculating the bending moment of the beam (wikipedia "Bending").