Sheffield Crown Court heard that Mr Mott was moving an overhead travelling crane from an area of the factory where it had been supporting the 8.5m-long girder.
The court was told that as he did this, a clamp attached to the crane hook snagged on the girder causing it to topple and fall, crushing Mr Mott against the floor.
Bespoke Precast Ltd, registered at Bardon Hall, Copt Oak Road, Markfield, Leicestershire, was fined £100,000 and ordered to pay £42,471 costs after pleading guilty breaching the Health and Safety at Work etc Act 1974. The firm no longer operates from the Whaley Road site in Barnsley.
After the hearing HSE inspector Alison Crank said: "John Mott's death was a preventable tragedy and his wife and family continue to struggle to come to terms with their loss.
"The crane was frequently needed elsewhere in the factory to move steelwork around and we believe Mr Mott wanted to use it to move some of his own welding work. As he was moving the crane, a beam clamp used to attach girders to the crane, snagged and caused this horrific incident.
"Working with steel of this size and weight in particular can be dangerous if precautions are not taken to maintain stability and workers are not kept out of danger zones. As this case shows, the risks increase significantly when lifting equipment is in use in the area.
"A suitable risk assessment would have identified the measures that could have been taken to prevent the girder becoming unstable and falling off the support bench. The crane or any other lifting equipment could then have been moved safely."