Question $3[37$ marks $-65$ minutes$]$

A steel framing plan that supports a reinforced concrete floor is shown in Figure $3.$ The reinforced concrete floor is $175mm$ thick; the self weight of the steel beams is equivalent to a uniformly distributed surface load of $0\mathrm{.}3k\frac{N}{m^2}$; the superimposed dead load on the floor is $0\mathrm{.}5k\frac{N}{m^2},$ and the specified live load on the floor is $2\mathrm{.}9k\frac{N}{m^2}.$ Assume the unit weight of reinforced concrete to be $24k\frac{N}{m^3}.$

Figure $3$

$[5$ marks$]$ a$)$ Determine the axial force in Column $C$ under the total factored dead and live loads based on a dead load factor of $1\mathrm{.}25$ and a live load factor of $1\mathrm{.}5.$

$[12$ marks$]$ b$)$ Develop the shear force and bending moment diagrams for Beam AB under the total factored dead and live loads based on a dead load factor of $1\mathrm{.}25$ and a live load factor of $1\mathrm{.}5.$

$[10$ marks$]$ c$)$ An I$-$shaped steel beam is selected for Beam AB$.$ Based on the maximum factored bending moment and shear force determined in b$),$ compute the minimum required section modulus and area of the web of the steel beam to satisfy the limit state design requirements for bending and shear. Assume the tensile and shear yield strengths of the steel beam to equal $350$MPa and $230$ MPa, respectively, and the resistance factor to equal $0\mathrm{.}9.$

$[10$ marks$]$ d$)$ The deflection control criterion requires that the maximum deflection of Beam $AB$ under the specified live load not exceed $40mm.$ Calculate the minimum moment of inertia $(I)$ of the cross section of Beam $AB$ that meets the above deflection control criterion. $E=2\mathrm{.}0{10}^5$ MPa.