== "\\[\n\\begin{aligned}\nF_{e_{x}} &= \\frac{ \\operatorname{euler\\ buckling\\ load} \\left( E ,\\ I_{x} ,\\ k_{x} ,\\ L \\right) }{ \\mathrm{area} } = \\frac{ \\operatorname{euler\\ buckling\\ load} \\left( 200000.000 ,\\ 300000000.000 ,\\ 1.000 ,\\ 3500 \\right) }{ 1000 } &= 4.500 \n\\\\[10pt]\nF_{e_{y}} &= \\frac{ \\operatorname{euler\\ buckling\\ load} \\left( E ,\\ I_{y} ,\\ k_{y} ,\\ L \\right) }{ \\mathrm{area} } = \\frac{ \\operatorname{euler\\ buckling\\ load} \\left( 200000.000 ,\\ 150000000.000 ,\\ 1.000 ,\\ 3500 \\right) }{ 1000 } &= 4.500 \n\\\\[10pt]\nF_{e} &= \\operatorname{min} \\left( F_{e_{x}} ,\\ F_{e_{y}} \\right) = \\operatorname{min} \\left( 4.500 ,\\ 4.500 \\right) &= 4.500 \n\\\\[10pt]\n\\lambda &= \\sqrt { \\frac{ f_{y} }{ F_{e} } } = \\sqrt { \\frac{ 350 }{ 4.500 } } &= 8.819 \n\\\\[10pt]\nP_{r} &= \\phi \\cdot \\mathrm{area} \\cdot f_{y} \\cdot \\left( 1 + \\left( \\lambda \\right) ^{ \\left( 2 \\cdot n \\right) } \\right) ^{ \\left( \\frac{ \\left( - 1 \\right) }{ n } \\right) } \\\\&= 0.900 \\cdot 1000 \\cdot 350 \\cdot \\left( 1 + \\left( 8.819 \\right) ^{ \\left( 2 \\cdot 1.340 \\right) } \\right) ^{ \\left( \\frac{ \\left( - 1 \\right) }{ 1.340 } \\right) } \\\\&= 4041.179 \\\\[10pt]\n\\end{aligned}\n\\]"
0 commit comments