It goes further than that. Young's modulus does indeed determine the elasticity (springiness) of a material but don't go ahead and think it's only relevant for systems with moving parts that deform and go back into their original shape. Young's modulus is literally at the very heart of every structural engineering calculation, static or dynamic.

The stiffness of any structure is determined (among others) by E*I, I being the second moment of area determined by the shape of an object and E being Young's modulus of the material. The tension in any structure is also determined (among others) by (load)/E*I. So Young's is proportionally responsible for an objects ability to resist deformation under force and inversely proportional for the stress inflicted to the material by those forces. Both deflection and stress are potential causes for failure. If your structure loses a significant amount of its structural rigidity, it might fail. If the stress in parts of your structure rises significantly, they might fail.

So steel may only melt at 1400C, but it has already lost half its load bearing capabilities at around 550C. Whether a structure collapses entirely is mostly a question of what factor of safety the engineers have applied when dimensioning the components. If the temperature was 550C (hypothetical, for this example) and the steel beams did indeed lose half of their ability to resist deformation by the loads they were bearing, and the tension in them did double, even a relatively high factor of safety of 2 ( i.e. everything is built twice as strong as it needs to be) would be the tipping point for catastrophic failure. In reality the factor of safety was probably lower, between 1.5 and 2.