Understanding Stress in Circular Plates with Holes
When an axial load is applied to a circular plate with a hole, it is crucial to differentiate between nominal stress and maximum stress due to the presence of stress concentration. Here's how to calculate these stresses:

1. Nominal Stress Calculation
- The **nominal stress** (σ_n) is the average stress across the cross-sectional area, calculated as:
σ_n = P / A
- Where:
- **P** = Applied axial load
- **A** = Cross-sectional area of the plate (without considering the hole)
- For a circular plate of radius R and a hole of radius r, the area A can be calculated as:
A = π(R² - r²)

2. Maximum Stress Calculation
- The **maximum stress** (σ_max) occurs at the edge of the hole due to stress concentration. This can be calculated using the stress concentration factor (K_t):
σ_max = K_t × σ_n
- Where:
- **K_t** = Stress concentration factor (a dimensionless value)
- **σ_n** = Nominal stress calculated previously

3. Summary of Stress Calculations
- **Nominal Stress (σ_n)**: Average stress over the effective area.
- **Maximum Stress (σ_max)**: Increased stress at the hole due to geometrical discontinuity.
- **Stress Concentration Factor (K_t)**: A critical parameter to assess how much the stress increases at the hole compared to the nominal stress.
By following these steps, you can effectively analyze the stress distribution in a circular plate with a hole under axial loading. Understanding the relationship between nominal and maximum stress is vital for ensuring the integrity and safety of mechanical components.