Ultimate load of 2 ISA 100x100x8, M16 5.6

Data: 2 ISA 100×100×8 ($A_g=1539$ mm² each) on both faces of a 12 mm gusset; M16 bolts class 5.6 ($f_{ub}=500$) in one line, one shear plane through the shank and the other through the threads (double shear). Number of bolts not given: assumed 4, pitch 50 mm, end distance 40 mm, gauge 55 mm; $d_0=18$ mm; $f_y=250$, $f_u=410$.

1. Bolts

• $V_{dsb}=\dfrac{500}{\sqrt3\times1.25}(A_{nb}+A_{sb})=\dfrac{500}{\sqrt3\times1.25}(157+201)\times10^{-3}=82.7$ kN
• Bearing on gusset 12 mm ($e=40,\ p=50$): $k_b=0.676$; $V_{dpb}=106.4$ kN
• Bolt value $82.7$ kN; four bolts: $330.7$ kN

2. One angle

• $T_{dg}=\dfrac{1539\times250}{1.10}\times10^{-3}=349.8$ kN
• Rupture: $A_{nc}=(100-4-18)\times8=624$ mm², $A_{go}=(100-4)\times8=768$ mm², $b_s=w+w_1-t=100+55-8=147$ mm, $L_c=150$ mm, $\beta=0.832$

$$T_{dn}=\frac{0.9\times624\times410}{1.25}+\frac{0.832\times768\times250}{1.10}=329.5\ \text{kN}$$

• Block shear: $\min(284.5,\ 255.0)=255.0$ kN
• One angle: $\min=255.0$ kN; two angles $=510.0$ kN

3. Result

Ultimate (design) load capacity $=\min(510.0\ \text{kN (angles)},\ 330.7\ \text{kN (bolts)})=330.7$ kN, governed by shear of the bolts. (More bolts raise the capacity until the angle strength is reached.)