The writ said: "The entire framework was so unstable that bracing had to be put up around it before it could be demolished."
QPC is suing Willis & Partners for breach of contract and negligence.
Willis & Partners had been engaged as M&E engineer by developer Crosby Homes, which also appointed QPC as design-and-build contractor.
The writ said that work on the building had begun on 9 April 2001, using the foundations inherited from the previous building. It said the steelwork was put up by 3 October.
However, within days workmen realised the building was swaying as they installed the second of the concrete floors.
The writ says: "Investigations revealed the steelwork was wholly inadequate to support the load and Willis admitted the frame it designed was inadequate even for the roof steelwork."
The writ says loss adjusters agreed that the structure ought to be demolished and rebuilt and that Willis & Partners' insurers accepted liability.
The project was completed one year behind schedule.
Neither Willis nor QPC were available for comment this week.