Stress Concentration Factor for a Circular Hole in a Flat Plate under Tensile Force

When a flat plate with a circular hole is subjected to a tensile force, the stress is not uniformly distributed across the plate. The presence of the hole causes stress concentrations around its edges, leading to higher stresses compared to the surrounding material. The stress concentration factor (Kt) quantifies this increase in stress.

Explanation:

The stress concentration factor for a circular hole in a flat plate under tensile force can be calculated using the following formula:

Kt = 1 + 2(d/D) + (d/D)^2

Where:
Kt: Stress Concentration Factor
d: Diameter of the hole
D: Diameter of the plate

Derivation:

To understand how this formula is derived, let's consider a flat plate with a circular hole under tensile force. The plate experiences a uniform stress (σ) in the absence of the hole. However, the presence of the hole causes the stress to increase around its edges.

The stress distribution can be visualized using a stress contour plot. Near the hole edges, the stress is significantly higher, forming a region of stress concentration. As we move away from the hole, the stress gradually decreases and approaches the uniform stress value.

Factors Affecting Stress Concentration:
1. Stress concentration is maximum at the edges of the hole.
2. The stress concentration factor depends on the geometry of the hole and plate.

Calculation:
For a circular hole in a flat plate, the stress concentration factor can be calculated using the formula mentioned earlier:

Kt = 1 + 2(d/D) + (d/D)^2

In this case, the diameter of the hole (d) is a measure of the size of the stress concentration, while the diameter of the plate (D) represents the overall dimensions of the plate.

Conclusion:
Based on the calculation, the theoretical stress concentration factor for a flat plate with a circular hole under tensile force is 3, as given in option B. This means that the stress at the hole edges is three times higher than the uniform stress in the absence of the hole.