The only horizontal steel rod that I can find is the one that I mentioned.
That part is called the pin hinge.
If you want or need further assistance, go to http://www.PartSelect.com
. type in the search box K45SS or K5SS. Depending on the model that you might have.
Click on either one of the three parts pics to zoom in on one of them, and you might be able to identify the part in question.
The newer models of K'Aid Stand Mixers except the Pro 500 and Pro 600 series all pretty much use the same identical parts, and you might find the part in question there. The main difference is the power in the motor. Good luck!!