Step |
Parameter |
Equation |
1 |
Radius of gyration [k] |
$$k=\sqrt { \frac { I }{ A } } $$ |
2 |
Eccentricity ratio [er] |
$$er=\frac { ec }{ { k }^{ 2 } } $$ |
3 |
Slenderness ratio [S] |
$$S=\frac { L }{ k } $$ |
4 |
Effective slenderness ratio [S_{eff}] |
$${ S }_{ eff }=\frac { LC }{ k } $$ |
5 |
If er=0 and Seff > (2π^{2}E/S_{y})^0.5 then go to step 6 |
6 |
Force (according to Euler column formula) [P_{cr}] |
$${ P }_{ cr }=\frac { { \pi }^{ 2 }EI }{ { L }^{ 2 }{ C }^{ 2 } } $$ |
7 |
If er=0 and S_{eff} ≤(2π^{2}E/S_{y})^0.5 then go to step 8 |
8 |
Force (according to Parabolic/J.B. Johnson formula) [P_{cr}] |
$${ P }_{ cr }=[{ S }_{ y }-({ \frac { { S }_{ y }L }{ 2\pi k } ) }^{ 2 }\frac {
{ C }^{ 2 } }{ E } ]A$$ |
9 |
If er≠0 and S>0.282(AE/P)^0.5 then go to step 10 |
10 |
Force (according to secant formula) [P_{cr}]* |
$${ P }_{ cr }=\frac { { S }_{ yc }A }{ 1+(\frac { ec }{ { k }^{ 2 } }
)sec[(\frac { LC }{ 2k } )\sqrt { { P }_{ cr }/AE } ] } $$ |
11 |
If er≠0 and S≤0.282(AE/P)^0.5 then go to step 12 |
12 |
Force (according to stress formulas) [P_{cr}]* |
$${ P }_{ cr }=\frac { { S }_{ yc }A }{ 1+\frac { ec }{ { k }^{ 2 } } } $$ |