Rhys Barker, 18, was killed along with a 36-year-old Bradford man at work on the site in Cheshire, last Wednesday afternoon.
Friend Ryan Norris has set up a JustGiving page to raise money to place a memorial bench at Airedale Academy, where Rhys had studied.
Setting a target of £750, more than three times that amount has been raised so far and cash continues to come in.
Ryan, who is 17 and knew Rhys for more than 10 years having been through school together, said: “Everybody has just been left really shocked, it’s not something you would expect to happen.
“Rhys was irreplaceable and so unique.
“He was a quiet lad and was always there for you.
“He just enjoyed spending time with his mates and he was really into his boxing.
“It was a pleasure to have such a great lad in our lives, on behalf of his friends, family and myself.
“The response on JustGiving has been unbelievable, I wasn’t expecting half as much.
“We’ve even had somebody come froward and say they could make the bench for us, and the rest of the money will be given to Rhys’ family.
“Rhys’ mum is overwhelmed by the support and couldn’t be more grateful.”
Anyone wishing to donate is being urged to log onto www.justgiving.com/crowdfunding/rhysbarker
Meanwhile, Elizabeth Fairhurst, principal at Airedale Academy, said: “We were shocked and saddened to hear of the tragic death of Rhys.
“Rhys joined Airedale Academy in year seven and remained with us into the sixth form to study business.
“He was a friendly young man, extremely well-mannered who was popular with students. His teachers remember him as hardworking, dedicated and quiet.”
Post-mortem examinations showed both Rhys and the second man died from crush injuries at the site in Crewe.
The crane collapsed into a house next to the building site.
An investigation is now being carried out by police in conjunction with the Health and Safety Executive.