Let's break down your problem step by step, including **spacing/edge checks** and the **strength capacity (shear and bearing) of the connection** for both **LRFD** and **ASD**. --- ## **Given Data** - **Member:** 2L 150x150x12 (Double angle, back-to-back) - **Gusset Plate Thickness (t):** 20 mm - **Bolt:** M22 (8.8) (Diameter = 22 mm, \( f_{ub} = 800 \) MPa) - **Steel Grades:** - Tension Member (S275): \( f_y = 275 \) MPa, \( f_u = 430 \) MPa - Gusset Plate (S235): \( f_y = 235 \) MPa, \( f_u = 360 \) MPa --- ## **A) Check All Spacing and Edge Distances** ### **Bolt Hole Diameter** - Standard hole diameter for M22 bolt: \( d_0 = 22 + 2 = 24 \) mm (assuming 2 mm clearance) ### **Minimum Edge Distance (Eurocode EN 1993-1-8, Table 3.3)** - **Edge distance, \( e_1 \):** Min = \( 1.2 \times d_0 = 1.2 \times 24 = 28.8 \) mm - **Spacing, \( p \):** Min = \( 2.2 \times d_0 = 2.2 \times 24 = 52.8 \) mm ### **Given in Drawing** - Edge distances = 50 mm - Spacings (pitch) = 75 mm #### **Conclusion:** - **Edge distance (50 mm) > min (28.8 mm): OK** - **Pitch (75 mm) > min (52.8 mm): OK** --- ## **B) Strength Capacity of the Connection** ### **1. Shear Capacity of Bolts** #### **Shear Area of Bolt, \( A_s \)** - For M22, \( A_s = \) tensile stress area ≈ 303 mm² #### **Shear Strength per Bolt** - \( V_{b,Rd} = \frac{f_{ub}}{\sqrt{3} \cdot \gamma_{M2}} \cdot A_s \) - \( f_{ub} = 800 \) MPa - \( \gamma_{M2} = 1.25 \) (Eurocode) \[ V_{b,Rd} = \frac{800}{\sqrt{3} \times 1.25} \times 303 = \frac{800}{2.165} \times 303 \approx 369.5 \times 303 \approx 111,948 \text{ N} = 111.95 \text{ kN (per bolt, LRFD)} \] #### **ASD Factor** - ASD safety factor ≈ 2.0 \[ V_{b,ASD} = \frac{800}{\sqrt{3} \times 2.0} \times 303 = \frac{800}{3.464} \times 303 \approx 231 \times 303 \approx 69,993 \text{ N} = 69.99 \text{ kN (per bolt, ASD)} \] #### **Total Bolts** - 4 bolts per line × 2 lines = 8 bolts total \[ \text{Total Shear Capacity (LRFD)} = 8 \times 111.95 = \boxed{895.6\ \text{kN}} \] \[ \text{Total Shear Capacity (ASD)} = 8 \times 69.99 = \boxed{559.9\ \text{kN}} \] --- ### **2. Bearing Capacity (Gusset Plate Governs)** #### **Bearing strength per bolt (Eurocode):** \[ F_{b,Rd} = k_1 \cdot d \cdot t \cdot f_u / \gamma_{M2} \] Where: - \( d \) = bolt diameter = 22 mm - \( t \) = plate thickness = 20 mm - \( f_u \) = lower of member and plate = 360 MPa (gusset) - \( \gamma_{M2} = 1.25 \) - \( k_1 \) = 2.5 (unless end distance or spacing is less; here, all distances are ample) \[ F_{b,Rd} = 2.5 \times 22 \times 20 \times 360 / 1.25 = 2.5 \times 22 \times 20 \times 288 = 2.5 \times 22 \times 5760 = 2.5 \times 126,720 = 316,800 \text{ N} = 316.8 \text{ kN (per bolt, LRFD)} \] #### **ASD:** \[ F_{b,ASD} = \frac{2.5 \times 22 \times 20 \times 360}{2.0} = 2.5 \times 22 \times 20 \times 180 = 2.5 \times 22 \times 3600 = 2.5 \times 79,200 = 198,000 \text{ N} = 198.0 \text{ kN (per bolt, ASD)} \] #### **Total Bearing Capacity:** \[ \text{Total Bearing (LRFD)} = 8 \times 316.8 = 2,534.4\ \text{kN} \] \[ \text{Total Bearing (ASD)} = 8 \times 198.0 = 1,584.0\ \text{kN} \] --- ### **3. Governing Strength** - **Shear governs** (since it's much less than bearing): | Method | Shear (kN) | Bearing (kN) | Capacity (governing) | |--------|------------|--------------|----------------------| | LRFD | 895.6 | 2,534.4 | **895.6 kN** | | ASD | 559.9 | 1,584.0 | **559.9 kN** | --- ## **Summary Table** | Check | Result | |-------------------------|-----------------| | Min Edge Distance | **50 mm > 28.8 mm: OK** | | Min Bolt Spacing | **75 mm > 52.8 mm: OK** | | Shear Capacity (LRFD) | **895.6 kN** | | Shear Capacity (ASD) | **559.9 kN** | | Bearing Capacity (LRFD) | 2,534.4 kN | | Bearing Capacity (ASD) | 1,584.0 kN | | **Governing** | **Shear** | --- ## **Final Answers** ### **A) All spacings and edge distances are adequate.** ### **B) Strength capacity of the connection:** - **LRFD:** \( \boxed{895.6\ \text{kN}} \) (**governing by shear**) - **ASD:** \( \boxed{559.9\ \text{kN}} \) (**governing by shear**) --- If you need **block shear** or **net section checks** for the member itself, let me know!