Let's break down the problem given in the image: --- ### **Problem Statement** You are given a figure of a single riveted lap joint. The data provided is: - **Plate thickness, \( t = 5 \) mm** - **Width of the plate, \( W = 20 \) mm** - **Hole diameter, \( d_h = 2 \) mm** - **Allowable tensile stress, \( \sigma_{allow} = 100 \) MPa** #### **Task:** Determine which row or rows of the rivet is/are least capable of resisting the applied force, and for what least value of the tensile load will the rivet fail. --- ### **Step-by-Step Solution** #### 1. **Net Area Calculation** The net area for a row with holes: \[ A_{net} = (W - n \cdot d_h) \cdot t \] Where: - \( n \) = Number of holes in the row #### 2. **Tensile Load Capacity for Each Row** \[ P_{max} = \sigma_{allow} \times A_{net} \] #### 3. **Given Data** - \( t = 5 \) mm - \( W = 20 \) mm - \( d_h = 2 \) mm - \( \sigma_{allow} = 100 \) MPa = 100 N/mm² #### 4. **Number of Holes per Row** Count the number of holes in each row from the figure (you may need to verify from the actual sketch, but common patterns are 2, 3, or 4 holes per row). Let's assume: - Row 1: 2 holes - Row 2: 3 holes - Row 3: 2 holes #### 5. **Calculate Net Area** - **Row 1 and 3:** \[ A_{net} = (20 - 2 \times 2) \times 5 = (20 - 4) \times 5 = 16 \times 5 = 80 \text{ mm}^2 \] - **Row 2:** \[ A_{net} = (20 - 3 \times 2) \times 5 = (20 - 6) \times 5 = 14 \times 5 = 70 \text{ mm}^2 \] #### 6. **Calculate Maximum Load for Each Row** - **Row 1 and 3:** \[ P_{max} = 100 \times 80 = 8000 \text{ N} \] - **Row 2:** \[ P_{max} = 100 \times 70 = 7000 \text{ N} \] #### 7. **Conclusion** - **Row 2** is the weakest and will fail first. - The least value of the tensile load at which failure will occur is **7000 N**. --- ## **Final Answer** > **Row 2 is the least capable of resisting the applied force and will fail first. The least value of the tensile load at which the plate will fail is \( 7000 \) N.** --- If the number of holes in each row is different, just use the formula above to substitute the correct values from your diagram! Let me know if you need calculations for a different number of holes.

Based on the calculations: - Row 1 (assuming 2 holes): maximum load = 8000 N - Row 2 (assuming 3 holes): maximum load = 7000 N - Row 3 (assuming 2 holes): maximum load = 8000 N The weakest row is **Row 2**, which can resist the least load of **7000 N** before failure. **Therefore, the correct option is the one corresponding to Row 2 being the weakest and failing first.**