Absolutely! Let's break down the problem step by step: --- ## **Problem Recap** - **Force applied at pedal:** \( F = 700\, \text{N} \) - **Crank arm length:** \( L_{\text{crank}} = 170\, \text{mm} \) - **Crank arm diameter:** \( d_{\text{arm}} = 15.\, \text{mm} \) - **Pedal spindle diameter:** \( d_{\text{spindle}} = 11.\, \text{mm} \) - **Distance from pedal to crank arm:** \( L_{\text{pedal}} = 60\, \text{mm} \) --- # **Part A: Maximum Principal Stress in the Crank Arm** ## **Step 1: Type of Stress** The crank arm is subjected to a **bending moment** due to the force applied at the pedal. ### **Bending Moment:** \[ M = F \cdot L_{\text{crank}} \] \[ M = 700\, \text{N} \times .170\, \text{m} = 119\, \text{Nm} = 119,000\, \text{Nmm} \] ## **Step 2: Maximum Bending Stress** The maximum bending stress in a circular cross-section: \[ \sigma_{\text{max}} = \frac{M c}{I} \] Where: - \( c \) = outer radius = \( \frac{d}{2} \) - \( I \) = moment of inertia for a solid circle = \( \frac{\pi}{64} d^4 \) Plug in the numbers: **Find \( c \):** \[ c = \frac{15.}{2} = 7.5\, \text{mm} \] **Calculate \( I \):** \[ I = \frac{\pi}{64} d^4 = \frac{\pi}{64} (15.)^4 = \frac{\pi}{64} \times 50625 \approx 2485.6\, \text{mm}^4 \] **Plug values into the stress formula:** \[ \sigma_{\text{max}} = \frac{119,000 \times 7.5}{2485.6} \approx \frac{892,500}{2485.6} \approx 359\, \text{MPa} \] --- # **Part B: Maximum Principal Stress in the Pedal Spindle** ## **Step 1: Type of Stress** The spindle experiences a **bending moment** due to the force at a distance. ### **Bending Moment:** \[ M_{\text{spindle}} = F \cdot L_{\text{pedal}} \] \[ M_{\text{spindle}} = 700\, \text{N} \times .060\, \text{m} = 42\, \text{Nm} = 42,000\, \text{Nmm} \] ## **Step 2: Maximum Bending Stress** \[ c = \frac{11.}{2} = 5.5\, \text{mm} \] \[ I = \frac{\pi}{64} (11.)^4 = \frac{\pi}{64} \times 14641 \approx 719.2\, \text{mm}^4 \] \[ \sigma_{\text{max}} = \frac{42,000 \times 5.5}{719.2} \approx \frac{231,000}{719.2} \approx 321\, \text{MPa} \] --- # **Summary Table** | Part | Stress Formula | Value (MPa) | |---------------|----------------------------------------|-------------| | Crank Arm | \( \sigma = \frac{Mc}{I} \) | 359 | | Pedal Spindle | \( \sigma = \frac{Mc}{I} \) | 321 | --- ## **Key Concepts** - **Bending Moment:** Product of force and perpendicular distance. - **Bending Stress:** \( \sigma = \frac{Mc}{I} \) - **Moment of Inertia (solid circle):** \( \frac{\pi}{64} d^4 \) --- **Let me know if you want to see the calculations in more detail or have questions about bending stress!**