When (or ) Fcr = (4.4) Where, Fe = (4.5) Ag = gross member area; K = effective length factor L = unbraced length of the member; r = radius of gyration Note that the original Euler buckling equation is Pcr = Note that the AISC equation for is = 0.877Fe Fcr The 0.877 factor tries to account for initial crookedness. For a given column section: Calculate I, Ag, r Determine effective length based on end boundary conditions. K L Calculate Fe, Fyor If (KL/r) greater than , occurs and use Equation (4.4) elastic buckling If (KL/r) is less than or equal to , occurs and use Equation (4.3) inelastic buckling Note that the column can develop its yield strength Fy as (KL/r) approaches zero. 4.5 COLUMN STRENGTH In order to simplify calculations, the AISC specification includes Tables. Table 4-22 on page 4-3 shows KL/r vs. cFcr for various steels. You can calculate KL/r for the column, then read the value of from this table cFcr The column strength will be equal to x Ag cFcr
When (or ) Fcr = (4.4) Where, Fe = (4.5) Ag = gross member area; K = effective length factor L = unbraced length of the member; r = radius of gyration Note that the original Euler buckling equation is Pcr = Note that the AISC equation for is Fcr = 0.877Fe The 0.877 factor tries to account for initial crookedness. For a given column section: Calculate I, Ag, r Determine effective length K L based on end boundary conditions. Calculate Fe, Fyor If (KL/r) greater than , elastic buckling occurs and use Equation (4.4) If (KL/r) is less than or equal to , inelastic buckling occurs and use Equation (4.3) Note that the column can develop its yield strength Fy as (KL/r) approaches zero. 4.5 COLUMN STRENGTH In order to simplify calculations, the AISC specification includes Tables. Table 4-22 on page 4-3 shows KL/r vs. cFcr for various steels. You can calculate KL/r for the column, then read the value of cFcr from this table The column strength will be equal to cFcr x Ag