Somebody didn't do their structural engineering homeworks... I suppose you're referring to the collapse of 7 World Trade Center. Look it up on Wikipedia if you're curious.
These articles cover most of it, for the more technical stuff look directly at the reports.
Long story short, WTC7 was pelted with concrete. The facade was damaged beyond repair. Burning stuff put the building on fire, and the water pipes had cracked because two skyscrapers had collapsed on top of them. WTC7 was allowed to burn out, with fires raging through the building unhindered. Eventually, a few floors inside collapsed, so a lone pillar held the weight of eight storeys in the east wing with no lateral support. A little crack, and the pillar went down, taking the entire east wing with it. This in turn dragged with it the rest of the tower. You can actually see on the videos how the eastern part of the building is the first to go down, immediately followed by the rest. It's even slightly visible on the image you posted, you can see the V-shape where the first coloumn failed.
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