In my opinion, the wire must expand due to the magnetic force acting radially outwards on two diametrically opposite ends of the loop as a result of the equation:
F = I(dl × B)
Where B is the magnetic field due to the loop which is perpendicular to the plane of the loop.
Yes, magnetic force on wire elements of the loop acts to expand it. But this is usually very weak force, so no expansion is observed. Similarly for a current-carrying solenoid.
If magnetic field is very strong (like in P. Kapitza's super quick experiments, around 100 Tesla), these expansion forces are strong and he had to bandage the wires very well to a solid body that is well attached to the ground (during increases/decreases of magnetic field, the solenoid also wants to rotate).
