A steel H$-$pile $($HP $250$ X $85)25m$ long was driven into saturated cohesive soil. The undrained cohesive strength of the soil is $90$kPa and the unit weight of soil, $=20k\frac{N}{m^3}.$ If the pile is restrained against rotation, calculate the ultimate lateral resistance of the pile by Brom's method.

$($Use Table $4$ for $M_y=1\mathrm{.}1S{F}_y,$ Section Modulus $(S)=\frac{I_{}}{0\mathrm{.}5}{d}_1,F_y=248M\frac{N}{m^2})$

Table $4$: Properties of H$-$Pile

$\backslash$table$[[\backslash$table$[[$Designation$,],[$size $($mm$)\backslash$times $],[$weight $($kg$/$m$)]],\backslash$table$[[$Depth d$\_(1)],[($mm$)]],\backslash$table$[[$Section area$],[($m$^(2)\backslash$times $10^(-3))]],\backslash$table$[[$Flange and web$],[$thickness w$],[($mm$)]],\backslash$table$[[$Flange width d$\_(2)],[($mm$)]],\backslash$table$[[$Moment of$],[$inertia$],[($m$^(4)\backslash$times $10^(-6))]]],[\backslash$bar $($I$\_(\backslash$times $)),$I$\_($ry$)],[$HP $200\backslash$times $53,204,6\mathrm{.}84,11\mathrm{.}3,207,49\mathrm{.}4,16\mathrm{.}8],[$HP $250\backslash$times $85,254,10\mathrm{.}8,14\mathrm{.}4,260,123,42],[\backslash$times $62,246,8\mathrm{.}0,10\mathrm{.}6,256,87\mathrm{.}5,24],[$HP $310\backslash$times $125,312,15\mathrm{.}9,17\mathrm{.}5,312,271,89],[\backslash$times $110,308,14\mathrm{.}1,15\mathrm{.}49,310,237,77\mathrm{.}5],[\backslash$times $93,303,11\mathrm{.}9,13\mathrm{.}1,308,197,63\mathrm{.}7],[\backslash$times $79,299,10\mathrm{.}0,11\mathrm{.}05,306,164,62\mathrm{.}9],[$HP $330\backslash$times $149,334,19\mathrm{.}0,19\mathrm{.}45,335,370,123],[\backslash$times $129,329,16\mathrm{.}5,16\mathrm{.}9,333,314,104],[\backslash$times $109,324,13\mathrm{.}9,14\mathrm{.}5,330,263,86],[\backslash$times $89,319,11\mathrm{.}3,11\mathrm{.}7,328,210,69],[$HP $360\backslash$times $174,361,22\mathrm{.}2,20\mathrm{.}45,378,508,184],[\backslash$times $152,356,19\mathrm{.}4,17\mathrm{.}91,376,437,158],[\backslash$times $132,351,16\mathrm{.}8,15\mathrm{.}62,373,374,136],[\backslash$times $108,346,13\mathrm{.}8,12\mathrm{.}82,371,303,109]]$