documentclass[a4paper, 12pt, fleqn]{report}
usepackage[left=25mm,right=25mm,top=30mm,bottom=30mm]{geometry}
usepackage[dvipsnames]{xcolor}
usepackage{tikz}
usetikzlibrary{calc,intersections}
usepackage{pgfplots}
pgfplotsset{width=0.95textwidth,compat=1.13}
newcommand{vertLineFromPoint}[1]{
    draw[dashed]
        (#1) -- (#1|-{rel axis cs:0,0})
    }
newcommand{horLineFromPoint}[1]{
    draw[dashed]
        (#1) -- (#1-|{rel axis cs:0,0})
    }

 begin{document}
 begin{center}
    begin{tikzpicture}
    begin{semilogyaxis}[
        extra x ticks={173.819},
        extra x tick labels={$L_e$},
        extra y ticks={8.5,24.033},
        extra y tick labels={$P_c$,$F_{UTS}$},
        extra tick style={grid=none},
        xlabel={Length [mm]},
        ylabel={Load [kN]},
        xmin=0, xmax=300,
        ymax=1000,
        xtick={0,50,100,150,200,250,300},
        legend pos=north east]

        addplot[color=blue, mark=square, thick]
            coordinates{
            (300,2.847)(225,4.416)(175,8.267)(125,16.402)(75,45.56)(50,102.51)(25,410.041)
            };

        addplot[color=BurntOrange, mark=o, thick]
            coordinates{
            (300,2.438)(225,3.898)(175,5.603)(125,8.339)(75,12.261)(50,14.555)(25,16.29)
            };

        addplot[color=Green, mark=x, thick]
            coordinates {
            (250,3.55)(200,5.4)(150,9.45)(100,13.9)(65,15.6)
            };


        vertLineFromPoint{173.819,8.5};
        horLineFromPoint{173.819,8.5};
        horLineFromPoint{300,24.033};
    end{semilogyaxis}
    end{tikzpicture}
    end{center}

end{document}