You cannot make a useful transformer out of solid steel. The eddy currents will be a killer. Any energy you are putting in the primary is basically just heating the steel, and that is about it. The higher the frequency the transformer need to operate at, the thinner the leaves of steel have to be, so with a solid steel core, you may be limited to a maximum frequency well below 1 Hz.
Look at the piece of steel going through the center of the primary. If you draw a line around the circumference, you have an unbroken conductor - a shorted turn. If a transformer has a shorted turn, the inductance drops down to near zero, and it is no longer a useable transformer.
Also you need steel with the right magnetic properties. The gaps you have in the joins will very greatly reduce the transformer performance, as well as radiating EMF big time. A single gap of 0.1mm will noticeably reduce the inductance of a steel core transformer which is why leaves are interleaved in a normal transformer.
Is that steel across the middle of the transformer below the primary? If it is, it will stop most of the flux from the primary reaching the secondary winding.
Your best bet may be to find a suitable sized mains transformer which is bolted together rather then welded, pull it apart, and then using that hardware to build your own design.
Richard.