D1.L.3.2.3 Compression

The allowable compressive stress for columns, except those fabricated from austenitic stainless steel shall be as required by NF-3322.1(c)(1). The allowable compressive stress for columns fabricated from austenitic stainless steel shall be as required by NF-3322.1(c)(2). The allowable compressive stress for member elements other than columns constructed by any material, including austenitic stainless steel, shall be as required by NF-3322.1(c)(3).

Gross Sections of Columns, except those fabricated of austenitic stainless steel:
1. On gross section of axially loaded compression members, when (Kl/r) < C_c ,
  
  $F_{a} = F_{y} \frac{[1 - \frac{{(K L / r)}^{2}}{2 C_{c}^{2}}]}{5 / 3 + \frac{3 (K L / r)}{8 C_{c}} - \frac{{(K L / r)}^{3}}{8 C_{c}^{3}}}$
  
  Where:
  
  $C_{c} = \sqrt{\frac{2 π^{2} E}{F_{y}}}$
2. When (Kl/r) > C_c ,
  
  $F_{a} = \frac{12 π^{2} E}{23 {(K L / r)}^{2}}$
3. When (Kl/r) > 120,
  
  $F_{a s} = \frac{F_{a} [E q . (a 1) or E q . (a 2)]}{1.6 - (\frac{l}{200 r})}$
Gross sections of columns fabricated from Austenitic Stainless steel:
1. When (Kl/r) ≤ 120,
  
  $F_{a} = F_{y} (0.47 - \frac{K L / r}{444})$
2. When (Kl/r) > 120,
  
  $F_{a} = F_{y} (0.40 - \frac{K L / r}{600})$
Member elements other than columns:
1. For Plate Girder Stiffeners, F_a = 0.60·F_y
2. For webs of rolled shapes, F_a = 0.75·F_y

The above clauses are applicable only when the width-thickness ratio of the element satisfies all the sub-sections of NF-3322.2(d).

If the above-mentioned clauses are not satisfied,

For un-stiffened compression element, a reduction factor, Q_s, is introduced. Detailed values of Q_s for different shapes are given in NF-3322.2(e)(2)(a) to NF-3322.2(e)(2)(d).

In the case for angles or plates projecting from compression members and for projecting elements of compression flanges of girder,

When $95 / \sqrt{F_{y} / k c} < b / t < 195 / \sqrt{F_{y} / k c}$ , $Q_{s} = 1.293 - 0.00309 (b / t) \sqrt{F_{y} / k c}$

When $b / t > 195 / \sqrt{F_{y} / k c}$ ,

$Q_{s} = \frac{26, 200 k c}{F_{y} {(b / t)}^{2}}$

Where:
- $k c = \frac{4.05}{{(h / t)}^{0.46}}$ when h/t > 70, otherwise, kc = 1.0.
For stiffened compression element, a reduced effective width, b_e, is introduced.
1. For the flanges of square and rectangular sections of uniform thickness:
  
  $b_{e} = \frac{253 t}{\sqrt{f}} [1 - (\frac{50.3}{(b / t) \sqrt{f}})] \leq b$
2. For other uniformly compressed elements:
  
  $b_{e} = \frac{253 t}{\sqrt{f}} [1 - (\frac{44.3}{(b / t) \sqrt{f}})] \leq b$
Consequently, a reduction factor, Q_a, 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

$F_{a} = F_{y} \frac{Q_{s} Q_{a} [1 - \frac{{(K L / r)}^{2}}{2 {C'}_{c}^{2}}]}{5 / 3 + \frac{3 (K L / r)}{8 {C'}_{c}} - \frac{{(K L / r)}^{3}}{8 {C'}_{c}^{3}}}$

Where:

${C'}_{c} = \sqrt{\frac{2 π^{2} E}{{Q_{s} Q_{a} F}_{y}}}$

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 = \frac{2}{3} \frac{P_{cr}}{A}

where

P_cr

the Euler critical buckling load of the column:

\frac{π^{2} E I}{{(K L)}^{2}}