Determine the load carrying capacity:

Determine the load carrying capacity of an ISMB-500 section encased in concrete with 50 mm cover all round. The length of the column is 3 m and it is effectively held in position and restrained against rotation at one end, and at the other end restricted against rotation but not held in position

(f_y = 250 MPa and M 15 of concrete) is used.

Solution

Effective length of the column (case (d) of Table 1) is given by

l_eff = 1.20 L  = 1.20 × 3 m = 3.6 m

Properties of the Steel section are : Sectional area (A) = 110.74 cm²

r_xx = 20.21 cm;           r_yy = 3.52 cm; Flange width b₀ = 180 mm

Slenderness ratio for uncased column about y-y axis

= 3600/35.2 = 102.3 (< 250 ∴ OK)

Slenderness ratio for encased column = 3600/(0.2 (180 + 100)) = 64.3

∴  σ_ac for uncased column = 78.2 MPa

σ_ac for cased column = 117.7 MPa

σc for concrete Mix M 15 = 4 MPa

Area of concrete = 280 × 600 - 11074 mm² = 156926 mm²

∴ Land carrying capacity of cased column = 117.7 × 11074 + 4 × 156925

= 1931114 N ≈ 1931 kN.

Load carrying capacity of uncased column = 11074 × 78.2 = 865987 N

≈ 866 kN.

The holding capacity of encased column cannot be greater than 2 × 866 = 1732 kN by Design Considerations (b) above, hence the value of 1732 kN (instead of 1931) is to be taken.