Shop welded bracket, 5 mm fillet, safe load

Assumptions: the bracket is shop-welded to the column flange by a C-shaped weld lying on the face of the flange: two horizontal welds of 150 mm and one vertical weld of 400 mm. The load $P$ acts parallel to the flange at $e=120$ mm out from the weld plane, so the weld group carries direct shear $P$ plus bending $M=Pe$. Steel E250 ($f_u=410$ N/mm²), fillet size $s=5$ mm, throat $t_t=0.7\times5=3.5$ mm.

Weld strength (IS 800:2007 cl. 10.5.7)

$$f_{wd}=\frac{f_u}{\sqrt3\gamma_{mw}}=\frac{410}{\sqrt3\times1.25}=189.37\ \text{N/mm}^2,\qquad q_{allow}=f_{wd}t_t=662.80\ \text{N/mm}$$

Weld group properties (per mm of throat)

• Total length $L=2\times150+400=700$ mm
• Neutral axis at mid-depth (symmetrical about the horizontal axis).
• $I_{xx}=\dfrac{400^3}{12}+2\times150\times200^2=17333333$ mm³ (the weld thickness itself is neglected)

Forces per unit factored load $P$ at the extreme weld (y = 200 mm)

• Shear: $q_s=\dfrac{P}{L}=0.001429P$ N/mm
• Bending: $q_b=\dfrac{M y}{I_{xx}}=\dfrac{120P\times200}{17333333}=0.001385P$ N/mm
• Resultant: $q=\sqrt{q_s^2+q_b^2}=0.001989P$ N/mm

Safe load

$$0.001989P\le662.80\Rightarrow P_u=333.2\ \text{kN}$$

Answer: design (factored) load $P_u\approx333.2$ kN, i.e. working load $P\approx222.1$ kN. (If the load instead acted in the plane of the weld group, the weld would be checked for direct shear plus torsion rather than bending.)