Problem $1$: Floor joists having a cross$-$sectional dimensions of $1-\frac{1}{2^{\text{'}\text{'}}}9-\frac{1}{2^{\text{'}\text{'}}}$ are simply supported, span $12ft.$ and carry a floor load of $50l\frac{b}{f}{t}^2.$ Compute the center$-$to$-$center spacing between joists to develop a maximum bending stress of $1200l\frac{b}{i}{n}^2.$ Compute what safe floor load could be carried if the centerline spacing was $16$ in$.$ Neglect dead loads. $($Hint: substitute for force per unit length in the moment calculation force per unit area $x$ joist spacing and solve for joist spacing.$)$