I can help
Can you get me the depth of the beam, the width of the beam and the flange thickness of the beam to the nearest 1/8"?
With this information, I can look up the actual beam size in the AISC tables
So you want to slide a beam at the midspan of your 18' span floor joists, so you will be making two 9' spans more or less to help support the sagging existing 18' span floor joists?
Are these floor joists in a bedroom area or a general occupancy area in your home?
Sorry to say the shallowest Wide Flange beam or Structural Tube are both 8" deep. A 4" deep member will not span 22.5'.
I’d like to point out that a Professional Engineer’s standard of care typically includes a site visit to assess field conditions and get an overall understanding of the structure. This can obviously not be accomplished through the internet. The information provided here is meant for planning purposes only (general sizing and budgeting) and is based on the information provided by you. All loading cases considered are for vertical loads only, no lateral analysis has been completed. The information should be verified by a professional engineer who can visit the site to ensure that potentially important information has not been overlooked or omitted.
With a post in the middle of the 22.5' span, you could make two spans of 11.25'.
You could use a W4x13 (50 ksi) steel beam. This beam is 4" wide and 4.125" deep. The beam weighs 13 pounds per foot of beam.
If you feel you have received a satisfactory answer to your question, click the Rating button that is appropriate. Experts are credited for each adequately Rated answer they provide. If you have additional questions, please let me know. Thanks
Let me know if you have any more questions