Double angle tension member, M18, same side

Assumptions: the two angles are placed back to back (one leg of each touching) with their other legs bolted to the same face of the gusset plate, each angle with its own line of bolts. The bolts are therefore in single shear, and each angle carries half the load, $150$ kN. M18 bolts of grade 4.6, $d_0=20$ mm; gusset plate 10 mm; E250.

1. Bolts

• Single shear, thread in the shear plane: $V_{dsb}=\dfrac{400}{\sqrt3\times1.25}\times192\times10^{-3}=35.47$ kN
• Bearing ($e=35$, $p=50$): $k_b=\min(35/60,\ 50/60-0.25,\ 0.976,\ 1)=0.583$; on the 6 mm angle leg $V_{dpb}=\dfrac{2.5\times0.583\times18\times6\times410}{1.25}\times10^{-3}=51.7$ kN (on the 10 mm gusset 86.1 kN)
• Bolt value $=35.47$ kN → per angle $n=150/35.47=4.2$ → 5 bolts per angle (10 in all), pitch 50 mm (min $2.5d=45$ mm), end distance 35 mm ($\ge1.5d_0=30$ mm); capacity $5\times35.47=177.4$ kN per angle.

2. Section

$A_g\ge\dfrac{300\times1.10}{250}\times10^3=1320$ mm². Try 2 ISA 75×75×6 ($A=866$ mm² each, total 1732 mm²), bolt line 40 mm from the heel.

• Yielding per angle: $T_{dg}=\dfrac{866\times250}{1.10}=196.8$ kN
• Rupture per angle: $A_{nc}=(75-3-20)\times6=312$ mm², $A_{go}=(75-3)\times6=432$ mm², $b_s=75+40-6=109$ mm, $L_c=4\times50=200$ mm, $\beta=1.4-0.076\times\dfrac{75}{6}\times\dfrac{250}{410}\times\dfrac{109}{200}=1.084$

$$T_{dn}=\frac{0.9\times312\times410}{1.25}+\frac{1.084\times432\times250}{1.10}=198.6\ \text{kN per angle}$$

• Block shear per angle ($A_{vg}=1410$, $A_{vn}=870$, $A_{tg}=210$, $A_{tn}=150$ mm²): $\min(229.3,\ 196.0)=196.0$ kN
• Strength of the pair $=2\times\min(196.8,\ 198.6,\ 196.0,\ 177.4)=354.7$ kN $>300$ kN ✓ (bolts govern)

3. Slenderness and tacking

The minimum radius of gyration of the pair (about the axis parallel to the gusset) equals that of one angle, $r\approx23$ mm, so $L/r=2500/23=109<400$ ✓. Tack the two angles together with bolts at intervals of not more than 1000 mm.

Answer: 2 ISA 75×75×6 placed back to back on the same side of the gusset, each connected with 5 M18 bolts (4.6) at 50 mm pitch (10 bolts in all).