What I have just found:
S4x9.5
Elastic properties Sx 3.39 in³
Plastic modul Zx 4.04 in³
I guess, elastic will mean it will bend back and plastic will mean the bend will be permanent.
Strengthness of steal: 50 ksi = 344 N/mm²
Shape S4x9.5: Sx 3.39 in³ * 25.4³ -> Wx = 55552 mm³
Fmax=([Steeltyp]*4*Wx)/l
Fmax= (344(N/mm²)*4*55552(mm³))/3600(mm)/9,81(m/s²) = 2164 kg (4770lbs)
Maximum weight in the middle!
[Weight of the beam would be 51 kg (112lbs)]
Your poles can support 2x 2000lbs = 4000lbs -> 1814 kg
There is a problem of 350 kg. Don't damage your barn.
If you take the next smaller I-beam S3x7.5 the Sx is 1.95 in³ and the maximum weight will be 1244kg (2742lbs) and it's weight will be 40kg (89lbs)
The W-shape I-beams are all to strong.(
Book of Steel)
Barn 4000lbs
S4x9.5 4770 lbs
S3x7.5 2742 lbs
'Life is like a box of chocolates you never know what you're gonna get'
der carl
ps
I have just checked your answer regarding what you want to do. If you put the load not in the middel but at the end next to the rafter, it shall not be more than the 2000lbs of the supporting point!!