Solid Shaft Deflection and Journal Stress

Hello

I have a solid shaft roller 4" OD and 48" LG. with journals on either sides with OD of 2" and length 2.5". There is a concentrated load of 5500 lbs over a width of 10" symmetric from the center of the roller. Can someone help me derive or direct me to an equation to calculate the deflection of the roller at the center and the journal stress.

It can be assumed that the journals are fixed at both ends.

Thanks in advance.

Take a look at the following:

[U][I][URL="https://www.engineersedge.com/beam_calc_menu.shtml"]Beam, Structural Deflections Calculators[/URL][/I][/U]

Specifically,

[I][U][URL="https://www.engineersedge.com/beam_bending/beam_bending2e.htm"]Beam Stress Equations / Calculation Supported on Both Ends Single Load at Center[/URL][/U][/I]