# D1.L.1.1.3 Compression

The allowable compressive stress for columns shall be as required by clause XVII-2213 of NF-3000 1974.

1. Gross Sections of Columns:

1. On gross section of axially loaded compression members, when (Kl/r) < Cc ,

$F a = F y [ 1 - ( K L / r ) 2 2 C c 2 ] 5 / 3 + 3 ( K L / r ) 8 C c - ( K L / r ) 3 8 C c 3$

Where:

$C c = 2 π 2 E F y$
2. When (Kl/r) > Cc ,

$F a = 12 π 2 E 23 ( K L / r ) 2$
3. When (Kl/r) > 120,

2. Member elements other than columns:

1. For Plate Girder Stiffeners, Fa = 0.60·Fy
2. For webs of rolled shapes, Fa = 0.75·Fy

The above clauses are applicable only when the width-thickness ratio of the element satisfies all the sub-sections of clause XVII-2224 of NF-3000 1974.

If the above-mentioned clauses are not satisfied,

1. For un-stiffened compression element, a reduction factor, Qs, is introduced. Detailed values of Qs for different shapes are given in the clause XVII-2225.2 of NF-3000 1974.

2. For stiffened compression element, a reduced effective width, be, is introduced.

1. For the flanges of square and rectangular sections of uniform thickness:

$b e = 253 t f [ 1 - ( 50.3 ( b / t ) f ) ] ≤ b$
2. For other uniformly compressed elements:

$b e = 253 t f [ 1 - ( 44.3 ( b / t ) f ) ] ≤ b$

Consequently, a reduction factor, Qa, equal to the effective area divided by the actual area is introduced.

Combining both these factors, allowable stress for axially loaded compression members containing stiffened or un-stiffened elements shall not exceed

$F a = F y Q s Q a [ 1 - ( K L / r ) 2 2 C ' c 2 ] 5 / 3 + 3 ( K L / r ) 8 C ' c - ( K L / r ) 3 8 C ' c 3$

Where:

$C ' c = 2 π 2 E Q s Q a F y$
The section is also checked that the stress is less than 2/3× the critical buckling stress, which is taken as the Euler critical buckling load divided by the cross sectional area:
$F = 2 3 P cr A$
where
 Pcr = the Euler critical buckling load of the column: $π 2 E I ( K L ) 2$