In the first case, which happened Sunday morning, the arm of the crane also collapsed, falling onto the top level of the building.
But Alfonso said the city was doing far better than expected when Irma was forecast to slam straight into Miami.
"We have no reported injuries", Alfonso said.
A Florida man riding out Hurricane Irma in a nearby high-rise caught images of a massive construction crane that's collapsed.
MAPPED: Where tsunamis set to strike after killer mega quake
The area is seismically active, and has experienced eight other earthquakes measuring between 7.0 and 7.5 over the past 100 years. A similar quake in 1985 killed thousands of people in Mexico , however, the impact of the latest one is said to be greater.
Maurice Pons, deputy director of the Miami building department, warned last week that roughly two dozen cranes were a serious threat to residents living next door. Miami is seeing 100 miles per hour wind gusts as the storm moves over Florida.
As Irma's outer bands barreled into South Florida Saturday, a high-rise hazard materialized in Downtown Miami.
The boom of the crane snapped off and is now still connected to the tower, but is hanging off the side of the building.
"The luffing crane can not rotate like a weather vane", Whiteman said.
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Suu Kyi blamed "terrorists" for "a huge iceberg of misinformation" and said authorities were trying to "take care of everybody". According to the latest estimates issued by United Nations workers operating there, arrivals in just 12 days stood at 146,000.
Only a few contractors are certified to remove those cranes, and they would not have had enough time to move them out of harm's way even if they all were working at the same time in Miami to prepare for Irma, he said.
City officials said they were using geo-fencing, a 911 communication system, as well as social media, to contact residents in the area.
"All we care about is the safety of everyone right now", the building's developer, PMG, said in a statement.
Premier League Transfer window to close before start of season
At issue is an earlier shutting of transfer windows , as was approved by the 20 Premier League clubs in a vote conducted Thursday. The announcement came after a proposal to change the transfer window was considered in a shareholders' meeting on September 7.