As shown in the figure, we will use a simple beam structure using H$-$beam. From the left point A $($x$=0)$ in the horizontal direction x$=5,10,$ and $15$m$,$ a force of $1000$ kN is applied in the vertical downward direction. For the distribution of bending moment caused by external force, refer to the figure$\mathrm{.}1.$ If the width of the H$-$beam cross$-$section is b$=600$mm and the plate thickness is t$=60$mm and the depth is h$,$ express the cross$-$sectional secondary moment $($lb$)$ as a formula for h$\mathrm{.}2)$Based on the bending moment distribution diagram provided in Figure, find the distribution diagram by position in the horizontal direction of the maximum axial stress acting on the tensile edge of the cross section of h$-$beam$\mathrm{.}3.$ It is intended to be designed so that the maximum axial stress of the tensile node is $200$ Mpa or less. Find the required depth $($hb$)$ and cross$-$sectional area $($Ab$)$ of the h$-$beam cross$-$section$\mathrm{.}4.$ When the depth of all cross sections is unified to the required depth obtained above $($i$.$e$.,$ using a pristine beam$),$ calculate the total volume of term materials $($volume Vb$)$ required for the construction of h$-$beam bridges.Fig. $2$ H$-$beam $$