Damage Threshold in the D&D 5e SRD is described as:

"Big objects such as castle walls often have extra resilience represented by a damage threshold. An object with a damage threshold has immunity to all damage unless it takes an amount of damage from a single attack or effect equal to or greater than its damage threshold, in which case it takes damage as normal."

For example: A warship with a Damage Threshold of 20 takes 50 hit points of damage from an attack. Does the warship take the full 50 hit points of damage? Or does the warship take 30 hit points of damage after adjusting for the Threshold?