Limit State Method

The buckling strength of the member is affected by residual stress, initial bow and accidental eccentricities of load.

To account for all these factors, the strength of the members subjected to axial compression is defined by buckling class a, b, c or d as per clause 7.1.2.2 and Table 7 of IS 800:2007.

Imperfection factor, obtained from buckling class, and Euler’s Buckling Stress ultimately govern compressive force capacity of the section as per clause 7.1.2 of IS 800:2007.

The buckling class of a solid rod section is determined per Table 10 of the specification.

Working Stress Method

The actual compressive stress is given by:

f_c = FX/A_e

where:

• A_e = The effective section area as per Clause 7.3.2 of the code. This is equal to the gross cross sectional area, AX, for any non-slender (plastic, compact, or semi-compact) section class. In the case of slender sections, this is limited to value of Ae as described below.

The permissive compressive stress is calculated by first determining the Buckling Class of the section per Table 10 of the code and α_YY & α_ZZ based on Table 7.

F_ac = 0.6·F_cd

where:

• F_cd = the minimum of the values of Fcd calculated for the local Y and Z axis.

F_cd = (FYLD/γ_mo)/ [φ + (φ² + λ²]

• λ = the non-dimensional slenderness factor is evaluated for each local Y and Z axis.

λ = (FYLD/F_cc)^1/2

φ = 0.5[ 1 + a(λ - 0.2) + λ²] 

• F_cc = the Euler Buckling Stress.

F_cc = π²·E/(Kl/r)²

• K = the effective length factor for bending about either the local Y or Z axis, as provided in the KY and KZ parameters, respectively.
• r = radius of gyration about the local Y or Z axis for the section.
• FYLD = The yield strength of steel specified in the FYLD parameter.

Slender Sections

For member with slender section under axial compression, design compressive strength should be calculated on area ignoring depth thickness ratio of web in excess of the class 3 (semi-compact) limit.

Refer to clause 7.3.2 and Table 2 of IS 800:2007, (corresponding to “Internal Element of Compression Flange”)

A_e= A_g - (d/t_w - 42ε) · t_w ²

where:

• A_e = Effective area of section.
• A_g = Gross area of section.
• d = Depth of web.
• t_w = thickness of web.

Flexural-Torsional Buckling for Single Angles

In the case of single angles (ST and RA), a axial compression load does not pass through the member centroid. In practical applications, the load must pass through one of the legs. The deviation between the load and the centroid can be considerable, and thus the effect of flexural-torsional buckling must be considered.

The parameters of ANG, FXTY, and NBL are used to control these calculations.

The calculations for the flexural-torsional buckling strength of a single angle member in compression are performed per section 7.5.1.2 of the code (either limit state method or working stress method are applicable).