The plan shown below represents a floor system, where an $8-$in$.-$thick slab is supported by a series of beams with a width of $14$ in$.$ and a depth of $20$ in$.($below the slab$).$ The beams are supported by columns with cross section dimensions of $24$ in$.\backslash$times $24$ in$.$ The floor supports a live load of $100$ psf$.$ It is required to estimate the factored load on Beam ABC and calculate the positive and negative moments in Beam ABC according to ACI approximate method as well as under different live load patterns.

Note:

$-$ For dead load calculations, assume concrete self$-$weight of $150$ lb$/$ft$3$

$-$ Beam ABC supports a tributary width of $18$ ft $($center to center of adjacent spans$)$

$-$ The ends A and C are built integrally with the supporting columns.

$-$ For Live load patterns, Assume the cases of: $(1)$ live load over both spans and $(2)$ live

$-$ load is applied on one span only of the beam