Fillet weld size for bracket plate, 100 kN

Assumptions: the 12 mm bracket plate is welded to the ISMB 350 flange ($t_f=14.2$ mm) by a C-shaped weld: top and bottom 100 mm and vertical 160 mm. The working load of 100 kN acts parallel to the flange at $e=140$ mm from the weld plane, giving direct shear and bending in the weld. Factored load $P_u=1.5\times100=150$ kN. Shop weld, E250.

Weld group (per mm of throat)

• $L=2\times100+160=360$ mm
• $I_{xx}=\dfrac{160^3}{12}+2\times100\times80^2=1621333$ mm³
• $M=150\times10^3\times140=21.0\times10^6$ N·mm

Force per mm at the extreme weld (y = 80 mm)

• Shear: $q_s=\dfrac{150\times10^3}{360}=416.7$ N/mm
• Bending: $q_b=\dfrac{My}{I_{xx}}=\dfrac{21.0\times10^6\times80}{1621333}=1036.2$ N/mm
• Resultant: $q=\sqrt{q_s^2+q_b^2}=1116.8$ N/mm

Size of weld

$$f_{wd}=\frac{410}{\sqrt3\times1.25}=189.4\ \text{N/mm}^2,\qquad t_t=\frac{1116.8}{189.4}=5.90\ \text{mm},\qquad s=\frac{t_t}{0.7}=8.43\ \text{mm}$$

Take $s=9$ mm (capacity $0.7\times9\times189.4=1193$ N/mm $>1116.8$ N/mm; an 8 mm weld gives only 1060 N/mm).

Checks: minimum size for 14.2 mm flange = 5 mm; maximum size = plate thickness $-1.5=10.5$ mm (12 mm plate), so 9 mm is acceptable.

Answer: 9 mm fillet weld (shop) on all three sides.