He was given first aid by staff and other gym members before paramedics rushed him to Lady Cilento Children’s Hospital.
According to PCYC gym and fitness centre policy and procedures, children under the age of 16 must complete an induction with a parent or guardian and must be supervised while at the gym.
Mr Shaw’s family issued a statement after the teenager died at the Lady Cilento Children’s Hospital.
“Ben passed away yesterday afternoon with his family and friends around him,” the statement said.
“Ben was able to leave a legacy and donate his organs and tissue, giving life to others.
“We’d like to thank everyone who has been involved in Ben’s care, including all friends and family.”
A spokesman said prosecution had commenced over a “Category 2 offence under the Work Health and Safety Act 2011 for failing to comply with a health and safety duty and exposing individuals to a risk of death or serious injury”.
The complaint was set to be mentioned in the Pine Rivers Magistrates Court on November 8.