V. IS 800 2007 LSD - I Section - with LTB

Constants

• γ_m0 = 1.1
• γ_m1 = 1.25

Section Classification

Since the section is symmetric about both axes, the neutral axis is at mid-depth.

Hence, from Table 2 of IS 800:2007, both the flange and web are plastic.

Therefore, the overall classification of the section is “plastic”.

h / b_f = 2 > 1.2 and t_f = 10 mm < 40 mm

Hence, from Table 10 of IS 800:2007, the buckling class about the major axis is “a” and the same about the minor axis is “b”.

Check Slenderness Ratio

k_y = k_z = 1

The maximum allowable slenderness ratio is 180.

Slenderness ratio about the major axis, k_zL / r_z = 36.20 < 180

Slenderness ratio about the minor axis, k_yL / r_y = 142.2 < 180

So the slenderness is within the limit.

Axial Tension Capacity

Check for yielding of gross section:

Check for rupture of critical section:

Block shear areas are not specified and therefore not checked.

No tension in the member, so critical ratio is 0.

Check Axial Compression

Axial compression capacity of major axis:

The non-dimensional slenderness ratio,

For buckling class “a”, the imperfection factor, α = 0.21

So, as per Cl. 7.1.2.1 of IS 800:2007,

Therefore, axial compression capacity in the major axis: P_dz = A_xf_cdz = 666.5 kN

The critical ratio for axial compression in major axis = 10 / 666.5 = 0.015

Axial compression capacity of minor axis:

The non-dimensional slenderness ratio,

For buckling class “b”, the imperfection factor, α = 0.34

So, as per Cl. 7.1.2.1 of IS 800:2007,

Therefore, axial compression capacity in the minor axis: P_dy = A_xf_cdy = 219.8 kN, which governs.

The critical ratio for axial compression in minor axis = 10 / 219.8 = 0.045

Check Shear Capacity

Major Axis

As per Cl. 8.4.1.1 of IS 800:2007, the shear area, A_vz = 2×b_ft_f = 2,000 mm²

So, as per Cl. 8.4.1,

Hence, shear capacity along major axis:

Minor Axis

As per Cl. 8.4.1.1 of IS 800:2007, the shear area, A_vy = h×t_w = 1,140 mm²

So, as per Cl. 8.4.1,

Hence, shear capacity along major axis:

As per Cl. 8.4.2, d_w / t_w = 27.72 < 67ε, so resistance to shear buckling need not be checked.

Shear force along both axes = 3 kN.

Critical shear ratio along major axis: 3 / 149.6 = 0.020

Critical shear ratio along minor axis: 3 / 262.4 = 0.011

Check Bending Capacity

Since the section has been classified as “plastic”, β_b = 1.

Major Axis Bending

The elastic lateral-torsional buckling moment:

where

G

=

shear modulus,

I_t

=

torsional constant, I_x = 10.6 cm⁴

d'

=

h - t_f = 190 mm

I_w

=

warping constant, as taken from the CISC document “Torsional Section Properties of Steel Shapes” (see reference),

So, the bending strength with respect to the major axis is M_dz = β_bZ_pzf_bd = 36.35 kN·m

Actual bending moment about the major axis is M_z = 4.5 kN·m.

The critical bending ratio in the major axis is 4.5 / 36.35 = 0.124

Minor Axis Bending

Actual shear force in both axes, V = 3 kN < 0.6V_d = 89.75 kN. Hence, the section is subjected to low shear.

So, the governing bending strength with respect to the minor axis is M_dy = 9.341 kN·m

Actual bending moment about the minor axis is M_z = 4.5 kN·m.

The critical bending ratio in the minor axis is 4.5 / 9.341 = 0.482

Check Combined Interaction of Axial Compression and Bending

Section strength calculation as per Cl. 9.3.1:

Hence, from Table 17:

M_ndy = M_dy = 9.341 kN·m

(Cl. 9.3.1.2(c) )

Overall member strength in bending and axial compression