Let's break down the problem step by step: --- ## **Step 1: Given Data** - **P** (force at C): 295 N (x-direction) - **Q** (force at E): 200 N (y-direction) - **Diameter of bar ABD**: \( d = 10. \) mm = .01 m --- ## **Step 2: Calculate Cross-Sectional Area** \[ A = \frac{\pi}{4} d^2 = \frac{\pi}{4} (.01)^2 = 7.854 \times 10^{-5} \text{ m}^2 \] --- ## **Step 3: Identify the Stresses at Point A (Section AB)** - **Axial Stress (\(\sigma\))**: Due to force **P** in the x-direction (axial). - **Shear Stress (\(\tau\))**: Due to force **Q** in the y-direction (transverse). --- ## **Step 4: Calculate Axial (Normal) Stress** \[ \sigma_{x} = \frac{P}{A} = \frac{295}{7.854 \times 10^{-5}} = 3.76 \times 10^6 \text{ N/m}^2 = 3.76 \text{ MPa} \] --- ## **Step 5: Calculate Shear Stress** \[ \tau_{xy} = \frac{Q}{A} = \frac{200}{7.854 \times 10^{-5}} = 2.55 \times 10^6 \text{ N/m}^2 = 2.55 \text{ MPa} \] --- ## **Step 6: Final Answers** ### **The stresses acting on the critical stress element are:** \[ \boxed{ \sigma_{x} = 3.76\ \text{MPa} } \] \[ \boxed{ \tau_{xy} = 2.55\ \text{MPa} } \] --- ### **Summary Table** | Stress Type | Value | |-------------------|----------------| | Normal (\(\sigma_x\)) | 3.76 MPa | | Shear (\(\tau_{xy}\)) | 2.55 MPa | --- **These are the stresses acting on the critical stress element at section AB.**