D1.L.4.1.3 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:

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}}}

(Eq. A1)

Where:

C_{c} = \sqrt{\frac{2 π^{2} E}{F_{y}}}

When (Kl/r) > C_c ,

F_{a} = \frac{12 π^{2} E}{23 {(K L / r)}^{2}}

(Eq. A2)

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 - (Kl/r)/444]
2. When (Kl/r) > 120,
  
  F_a = F_y[0.40 - (Kl/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/(F_y/kc)^1/2 < b/t < 195/(F_y/kc)^1/2 , Q_s = 1.293 - 0.00309·(b/t)·(F_y/kc)^1/2

When b/t > 195/(F_y/kc)^1/2 , Q_s = 26,200·kc/[F_y(b/t)²)]

Where:
- kc = 4.05/[(h/t)^0.46] if 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 is introduced and is equal to the effective area divided by the actual area. Combining both these factors, allowable stress for axially loaded compression members containing stiffened or unstiffened 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}}