Check for Deflection

Assuming a maximum permissible deflection of L/325, we must have a L/D ratio of 17.9.

Here L = 8000 mm and D = 550 ∴ L/D = 14.5 < 17.9   ∴ OK.

Check for Shear

Maximum SF = wl/2= 45 × 8/2 = 180 kN

Permissible shear stress τ_av = 0.4 × 250 = 100 MPa

Effective web depth (d₁)     = Total depth - 2 × Fillet depth

= 550 - 2 × 19.3 = 511.4 mm

Web thickness = 11.2 mm

∴          Shear stress (calc) =  180, 000/511.4 × 11.2 = 31.4 MPa < 100 MPa ∴ OK.

Web Crippling

Checking the crippling at support; reaction (R) = 8 × 45/2 = 180 kN. Assume support width = 300 mm, fillet depth (t_f) = 19.3 mm = h₂

∴ Effective support width (B) = b + √3 . h2 = 300 +√3 ×19.3 = 333 mm.

Allowable bearing stress (σ_p) = 0.75 f_y = 0.75 × 250 = 187.5 MPa.

Web crippling stress, R/B . t_ω =    180000/333 × 11.2

= 48.3 MPa < 187.5 MPa ∴ OK.

Web Buckling

Slenderness ratio for web = l/r = (0.8 D/t_w )√3 = (0.8 × 550/11.2 )√3 =68

Corresponding σ_ac (from Table 1) is 141 MPa

Buckling stress = 180000/(333 × 11.2)= 48.3 < 141 MPa ∴ OK.