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Council property services group manager David Bainbridge, in a statement this afternoon, said the structural strengthening work would begin in November and take about four months.
Three courts would be "out of action'' while this work was carried out, and the MoreFM Arena would be closed, he said.
"The timing has been chosen as this is the quietest time of the year for arena bookings.''
The work would involve installing steel bracing to strengthen the building, while floors would be protected by a temporary covering.
The $2 million project followed revelations last year the entire complex - used by 650,000 people a year - was significantly earthquake-prone, at between 10%-15% of the new building standard (NBS).
The entire complex was also being affected by subsidence, warping floors and creating leaks and other weather-tightness issues.
The upgrade aimed to lift the building above 34% of NBS, meaning it would no longer be considered earthquake-prone.
Work on the complex's Woolstore building and amenities area was expected to be completed by mid-June, Mr Bainbridge said.
Costs remained within the $2 million budget, he said.
"The project has gone well so far and we appreciate people's patience with the disruption.''