Let's break down the given problem and the details visible in the image: --- ### **Given Data:** - **Plate thickness (t) = 10 mm** - **Width of the plate (w) = 120 mm** - **Hole diameter (d) = 12 mm** - **Allowable tensile stress (σ_allow) = 100 MPa** --- ### **Question:** Determine which row (or rows) of the rivet is or are least capable of resisting the applied force and will fail under what value of the tensile load? --- ### **Step 1: Calculate Net Area in Each Row** For a riveted joint, the weakest (least capable) row is the one with the minimum net cross-sectional area after accounting for holes. #### **Net Area Formula:** \[ A_{net} = (w - n \cdot d) \cdot t \] Where: - \(n\) = number of holes in the row (along the width) - \(d\) = diameter of each hole - \(w\) = width of plate - \(t\) = thickness of plate --- ### **Step 2: Find Maximum Load Each Row Can Withstand** \[ P_{max} = A_{net} \cdot \sigma_{allow} \] --- ### **Step 3: Apply the Data to Each Row** From the diagram, let's assume (since not all details are visible) that: - **Row 1:** 2 holes - **Row 2:** 3 holes - **Row 3:** 4 holes (as an example) Let's calculate for each case. --- #### **Row 1:** \[ A_{net,1} = (120 - 2 \times 12) \times 10 = (120 - 24) \times 10 = 96 \times 10 = 960 \text{ mm}^2 \] \[ P_{max,1} = 960 \times 100 = 96,000 \text{ N} = 96 \text{ kN} \] #### **Row 2:** \[ A_{net,2} = (120 - 3 \times 12) \times 10 = (120 - 36) \times 10 = 84 \times 10 = 840 \text{ mm}^2 \] \[ P_{max,2} = 840 \times 100 = 84,000 \text{ N} = 84 \text{ kN} \] #### **Row 3:** \[ A_{net,3} = (120 - 4 \times 12) \times 10 = (120 - 48) \times 10 = 72 \times 10 = 720 \text{ mm}^2 \] \[ P_{max,3} = 720 \times 100 = 72,000 \text{ N} = 72 \text{ kN} \] --- ### **Step 4: Identify the Weakest Row** The weakest row is the one with the **least value of \(P_{max}\)**, which is **Row 3** in this case. --- ## **Summary Table** | Row | Number of Holes | Net Area (\(mm^2\)) | Max Tensile Load (\(kN\)) | |-------|-----------------|---------------------|---------------------------| | 1 | 2 | 960 | 96 | | 2 | 3 | 840 | 84 | | 3 | 4 | 720 | 72 | --- ## **Final Answer** - **Row 3 (with 4 holes) is the least capable of resisting the applied force and will fail first.** - **Row 3 will fail under a tensile load of \( 72 \) kN.** --- If you want the calculation for specific rows as per your diagram, please let me know the exact number of holes in each row!