Jeffrey Plevey had been working in the Citadel building in the Splott area on Tuesday afternoon when the structure gave way.
Mr Plevey's family said: "We are saddened to announce the passing of Jeff, a much-loved and treasured member of our family.
"A hard-working man who was always life and soul of any gathering, of which there were many. He will be greatly missed by all his family and friends."
Two other people escaped with minor injuries in the incident, which has prompted a joint investigation by police and the Health and Safety Executive (HSE).
Detective Inspector Ian Bourne said: "I would like to pay tribute to my emergency and rescue service colleagues who worked in difficult and challenging circumstances yesterday.
"I would also like to offer my condolences to the family of the man who sadly lost his life.
"Our aim now, together with the Health and Safety Executive, is to carry out a robust investigation and establish the cause of this tragic incident."
The area remained cordoned off on Wednesday while engineers work to make the structure safe.