$1.$ Calculate the dead load for a concrete beam with dimensions $300$ mm x $500$ mm and a length of $6$ m$.$

$2.$ What is the maximum bending moment for a simply supported beam with a central load of $20$ kN and a span of $4$ m$?$

$3.$ Determine the deflection of a cantilever beam subjected to a point load of $10$ kN at its free end. The beam is $3$ m long, with a moment of inertia of $5000$ cm$^4$ and a modulus of elasticity of $200$ GPa.

$4.$ A steel beam has a section modulus of $300$ cm$^3.$ What is the maximum bending stress if the bending moment is $15$ kNm$?$

$5.$ For a reinforced concrete column, if the axial load is $500$ kN and the effective height is $3$ m$,$ what is the required area of the steel reinforcement if the allowable stress in concrete is $20$ MPa?