Tension member with lug angle, 400 kN

Given: axial pull (factored) $T=400$ kN, joint length available 300 mm, gusset 16 mm, M20 bolts of grade 4.6, Fe410/E250 ($f_y=250$, $f_u=410$). A single angle connected by one leg would need 9 bolts ($400/45.26$), i.e. about 480 mm of joint length, which is more than 300 mm, so a lug angle is used at the end (IS 800:2007 cl. 10.12).

Section

Required $A_g\ge\dfrac{400\times10^3\times1.10}{250}=1760$ mm². Try ISA 100×100×12: $A_g=2257$ mm².

• Yielding: $T_{dg}=\dfrac{2257\times250}{1.10}=513.0$ kN $>400$ ✓
• Rupture: with a lug angle both legs are effectively connected, so there is no shear-lag reduction. $A_n=2257-12\times22=1993$ mm²; $T_{dn}=\dfrac{0.9\times1993\times410}{1.25}=588.3$ kN $>400$ ✓

Bolts (M20, 4.6)

• Shear $V_{dsb}=\dfrac{400}{\sqrt3}\times\dfrac{245}{1.25}\times10^{-3}=45.26$ kN
• Bearing ($e=40$, $p=50$, $t=12$ mm): $k_b=0.508$, $V_{dpb}=99.9$ kN → bolt value $45.26$ kN

Forces with lug angle

Outstanding leg force $\approx T\dfrac{A_{out}}{A_g}$ with $A_{out}\approx(100-6)\times12=1128$ mm²: $P_{out}=199.9$ kN.

• Connected leg force $=400-199.9=200.1$ kN → main angle to gusset: $n=200.1/45.26=4.4$ → 5 bolts
• Lug angle to gusset: $1.2\,P_{out}=239.9$ kN → 6 bolts
• Lug angle to main angle: $1.4\,P_{out}=279.9$ kN → 7 bolts

Lug angle

The lug angle itself must develop $1.2P_{out}=239.9$ kN. ISA 65×65×8 ($A=976$ mm², $T_{dg}=221.8$ kN) is not enough. Use ISA 75×75×10 ($A=1402$ mm²): $T_{dg}=318.6$ kN; net section with a hole in each leg $T_{dn}=\dfrac{0.9(1402-2\times10\times22)\times410}{1.25}=284.0$ kN; both $>239.9$ kN ✓.

Layout

   gusset 16
  |==o==o==o==o==o==   main angle  (5 bolts @ 50)
  |==o==o==o==o==o==o  lug angle   (6 bolts @ 50)
        <- 300 mm ->

Pitch 50 mm ($\ge2.5d$), end distance 40 mm; length on the gusset $40+5\times50=290\le300$ mm ✓. The lug angle is bolted to the gusset beyond the main angle and to the outstanding leg of the main angle (7 bolts).

Answer: ISA 100×100×12 with lug angle ISA 75×75×10; 5 M20 bolts for the main angle, 6 for the lug angle to the gusset and 7 for the lug-to-main-angle connection.