Final answer:
Roofs of gymnasiums and churches tend to fail more during earthquakes due to their large span roofs supported by open web joists prone to buckling, alongside the increased forces imposed on larger structures as opposed to the smaller, more rigid family homes.
Step-by-step explanation:
The question of why roofs of gymnasiums and churches fail more frequently during earthquakes than those of family homes is related to engineering and more specifically, the structural design of buildings. Large buildings like gymnasiums and churches often have wide-span roofs supported by open web joists, which are prone to buckling during seismic events. Buckling occurs when the structural members, which are under compression due to forces such as those from an earthquake, become unstable and deform or collapse. These larger buildings also have more mass and are subject to higher forces during quakes, making them more susceptible to damage. In contrast, family homes typically have smaller, more rigid structures that can better endure the lateral forces of an earthquake without significant damage.