Eccentric bolted bracket, ISMB 300, 220 kN

Assumptions: bracket plate (12 mm) is lapped on the flange of ISMB 300 ($b_f=140$ mm, $t_f=12.4$ mm); the 220 kN factored load acts in the plane of the bolts at $e=90$ mm from the centroid of the bolt group. M20 bolts of grade 4.6 (shop bolting), $d_0=22$ mm, in two vertical lines.

Bolt value (IS 800:2007 cl. 10.3)

• Shear (single, thread in plane): $V_{dsb}=\dfrac{400}{\sqrt3}\times\dfrac{245}{1.25}\times10^{-3}=45.26$ kN
• Bearing (12 mm plate, $e=40$, $p=60$): $k_b=\min(0.606,0.659,0.976,1)=0.606$; $V_{dpb}=119.3$ kN
• Bolt value $=45.26$ kN

Trial layout

Two vertical lines of 5 bolts: gauge $g=70$ mm (edge distance $(140-70)/2=35\ge1.5d_0=33$ mm), pitch $p=60$ mm (≥ $2.5d=50$), end distance 40 mm. Total 10 bolts.

   e = 90      o   o   y=+120
   <------     o   o   y=+60
 P  |          o   o   y=0
 220 kN        o   o   y=-60
               o   o   y=-120

Forces

• $\Sigma(x^2+y^2)=10(35^2)+2\times2(60^2+120^2)=84250$ mm²
• Moment $T=220\times90=19800$ kN·mm
• Direct shear per bolt $=220/10=22.0$ kN (vertical)
• Critical corner bolt ($x=35,y=120$): torsional components $F_x=\dfrac{Ty}{\Sigma r^2}=28.20$ kN, $F_y=\dfrac{Tx}{\Sigma r^2}=8.23$ kN
• Resultant: $R=\sqrt{28.20^2+(22.0+8.23)^2}=41.34$ kN

$R=41.34\ \text{kN}<V_{db}=45.26$ kN. Safe.

Answer: 10 bolts M20 (4.6), 2 lines of 5, pitch 60 mm, gauge 70 mm, end distance 40 mm.