From the Spaceflight Meteorology Group:

At 3:10 am, the northern eyewall of Beryl has moved ashore near Matagorda and the center should move ashore by 4AM this morning. So far wind gusts around JSC have been in the 35 to 45 mph range. This will increase in the next couple hours as Beryl continues moving north.

One of the stronger bands should curve into the JSC vicinity between 4 and 5:30 this morning bringing heavy rains and those gustier winds. A few weak tornadoes have occurred along the Gulf coast south of Jamaica Beach with this band but so far nothing reported inland. If the band aligns over Galveston Bay just right the possibility for a brief, weak tornado near JSC will increase particularly between 4 and 5:30.