A simply supported rectangular reinforced concrete beam has a span of $6m,$

width of $250mm,$ effective depth of $500mm$ and a total depth of $600mm.$ The

beam is reinforced with $25mm$ diameter bars. The $f{c}^{\text{'}}=28$MPa and the steel

yield strength $fy=415$MPa. In addition to the live load and its own weight, the

beam carries a $150mm$ thick concrete slab that is $5m$ wide. The unit weight of

concrete is $24k\frac{N}{c}u.m.$

Required:

a$.)$ What is the total service $($unfactored$)$ uniform dead load acting on the

beam in $k\frac{N}{m}?$

b$.)$ What is the nominal moment capacity of the beam in $kN-m$

c$.)$ What is the maximum uniform service $($factored$)$ live load acting over the

entire span that can be supported by the beam in $k\frac{N}{m}?$