Compression capacity of double angle ISA 150x75x12

Data and assumptions: 2 ISA 150×75×12 on opposite faces of a gusset plate (taken as 10 mm thick), long legs (150 mm) against the gusset, length $L=3.5$ m, steel E250 ($f_y=250$). The angles are connected at each end by at least two bolts (or welds), so (IS 800:2007 cl. 7.5.2) the effective length is taken as $KL=0.85L$ (between 0.7L and 1.0L depending on end restraint). Buckling class c for angles (Table 10).

Section properties (from the leg-thickness rectangles)

• Area of one angle $A_a=2556$ mm² (SP 6: about 2540 mm²), $c_x=17.1$ mm (from the back of the 150 mm leg)
• One angle: $I_{xx}=591.9\times10^4$ mm⁴ (axis parallel to the 75 mm leg), $I_{yy}=102.0\times10^4$ mm⁴ (axis parallel to the 150 mm leg)
• Pair: $A=2A_a=5112$ mm²
• About the axis parallel to the gusset: $I_y=2[I_{yy}+A_a(t_g/2+c_x)^2]=453.5\times10^4$ mm⁴, $r_y=29.8$ mm
• About the axis perpendicular to the gusset: $I_x=2I_{xx}=1183.8\times10^4$ mm⁴, $r_x=48.1$ mm
• $r_{min}=29.8$ mm

Slenderness and design stress

$$KL=0.85\times3500=2975\ \text{mm},\qquad \lambda=\frac{KL}{r_{min}}=\frac{2975}{29.8}=99.9\ (<180)$$

Using curve c ($\alpha=0.49$): $f_{cc}=\dfrac{\pi^2E}{\lambda^2}$, $\lambda_n=\sqrt{f_y/f_{cc}}$, $\phi=0.5[1+0.49(\lambda_n-0.2)+\lambda_n^2]$,

$$f_{cd}=\frac{f_y/\gamma_{m0}}{\phi+\sqrt{\phi^2-\lambda_n^2}}=107.2\ \text{N/mm}^2$$

Capacity

$$P_d=A\,f_{cd}=5112\times107.2\times10^{-3}=548\ \text{kN}$$

Tack bolts (stitching) must be provided along the length so that the pair acts together: the slenderness of a single angle between them must not exceed 40 or $0.6\lambda$ of the whole strut, whichever is less (cl. 7.8), with at least two tack connections along the length.

Answer: design axial compressive capacity $\approx548$ kN.