why does beowulf hang grendel’s arm from the rafters of herot?

Beowulf hangs Grendel's arm from the rafters of Herot as a symbol of victory and a trophy to show that he has defeated the monster. This act serves multiple purposes: it is a boastful display to all who gather in Herot that Grendel can no longer harm them, a sign of Beowulf's strength and bravery, and a warning to other monsters. It also taunts Grendel's mother, provoking her retaliation. The hanging of the arm reassures the people of Herot and marks the restoration of safety and order in the hall after Grendel's terror.