What kind of earthquake waves does the most damage to buildings and structures?

P waves or pressure waves are the fastest traveling, and tend to be the primary waves to hit after an earthquake has begun. As such they tend to not be as destructive as the waves that follow. The most destructive waves tend to be the aftershock waves of an earthquake because the structural integrity of a building becomes comprimised by the main event of the earthquake causing it to not be able to withstand the after shocks despite the diminished seismic magnitude of the aftershock waves.

The energy of all land based earthquakes are transmitted through the Earth's crust by seismic waves, (oceanic earth quakes tend to create oceanic tidal waves or tsunamis which can be very destructive as well) the force of which can be measured by a seismometer and recorded using the Richter magnitude scale which ranges from 2.0 (micro) to 10+ (epic). The amount of damage done to buildings, cities, and infrastructures depends entirely on the magnitude of the earthquake, their location relative to the epicenter of that earthquake, and the overall stability, structural integrity, and earthquake preparedness of that building, city or infrastructure. As an example, the recent tragic catastrophy in Haiti was devistating due not only to the fact that the earthquake was a magnitude 7 (major) on the Richtor magnitude scale but the structural integrity of many of the buildings was deteriorating and the infrastructure to respond to the damage caused by a major earthquake was not as well established and prepared as it could have been because of the level of poverty that the whole country suffers from. Because of those factors, the earthquake in Haiti was very destructive and catastrophic not only to the indevidual buidlings but to the national infrastructure as well, (meaning that the sea ports and airports were destroyed and are having a hard time receiving aid, and the first responders to the earthquake are not as prepared for a catastrophe of this magnitude as they could have been.) An earthquake of the same magnitude in a city like Las Angeles would probably not cause the same severity of trauma and destruction to the buildings and infrastructure of the city itself due to the earthquake preparedness of that region and the well established financial infrastructure and supporting networks of the region and surrounding states. For more information, please see the related links section of this answer page.