you could successfully secure a framing system to a wall using brown plugs and say 2,1/2" or 3" screws, if the weight of a push bike is all it has to hold.
Most likely it will be stuck on a wall. It will be in a semi-public location, so I would like it securely attached to the wall. I'd then use my D-lock to lock the bike up on the rack.
Ideally the rack would be "n" shape stuck on the floor...
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