belt, girdle, band, strap, zone
帶 centers on a long, flexible strip used to bind, encircle, or define an area: a belt, girdle, band, strap, or zone.
帶 is the traditional form of 帯. It combines 巾 (cloth) with a phonetic element that originally depicted a belt or sash tied around the waist. The modern simplified form 帯 reduces the upper part.
The top 冖 looks like a belt being wrapped around something, and the bottom 巾 is cloth. Picture a long cloth belt cinching a robe: 帶 is a belt or strap.
For タイ, imagine tying a belt around your waist: tie -> タイ, and the belt holds everything together.