Dismantling work follows the discovery of piling problems on the £65m project.
BAM will have to pull down 50% of the frame then re-pile under the north elevation.
It is understood the remedial work will add between 10 and 15 months to the construction timetable with the project now expected to be completed in the summer of 2022.
Main construction work started on the site last May after BAM replaced Kier who had signed a pre-construction deal for the project but failed to agree a final price with the university.
BAM said in a statement: “Remedial works have commenced on the scheme to deliver the Faculty of Social Sciences (FoSS) building for the University of Sheffield. The scheme is currently under construction.
“BAM identified that there was settlement occurring in excess of that which would normally be expected in a structure of this nature, prompting us to conduct detailed investigations.
“These confirm a problem involving the piling of the structure, which are unusually complicated.
“We therefore conducted a review together with our client and the expert subcontractors involved: Mott Macdonald – structural engineers – and Cementation Skanska – piling contractor.
“This concluded the best course of action would be to partly dismantle some of the current structural frame – to the north elevation then rebuild it. Those works are now underway.
“BAM is working closely with the University to determine the consequent delay to the completion of the new building which it is now anticipated would be in 2022.
“At all times the building has been safe to all those around it.
“BAM has an excellent track record in Sheffield over many years and many building, and is committed to operating responsibly and openly with its clients.”