Transverse strength, also known as flexural strength or bending strength, is a measure of a material's ability to resist deformation under load. It represents the highest stress experienced within the material at its moment of failure. This property is particularly important in engineering and materials science, especially when dealing with beams or flat components subjected to bending forces.

The formula for calculating transverse strength (\(\sigma\)) is:

\[ \sigma = \frac{3PL}{2bd^2} \]

Where:

- \( \sigma \) is the transverse strength (in MPa or N/mm²)
- \( P \) is the load at the fracture point (in N)
- \( L \) is the length of the support span (in mm)
- \( b \) is the width of the test specimen (in mm)
- \( d \) is the thickness or depth of the test specimen (in mm)

Let's calculate the transverse strength for a rectangular beam:

- Given:
- Load at fracture (\( P \)) = 1000 N
- Support span length (\( L \)) = 200 mm
- Specimen width (\( b \)) = 50 mm
- Specimen thickness (\( d \)) = 10 mm

- Apply the transverse strength formula: \[ \sigma = \frac{3PL}{2bd^2} \]
- Substitute the known values: \[ \sigma = \frac{3 \times 1000 \text{ N} \times 200 \text{ mm}}{2 \times 50 \text{ mm} \times (10 \text{ mm})^2} \]
- Perform the calculation: \[ \sigma = \frac{600,000 \text{ N} \cdot \text{mm}}{10,000 \text{ mm}^3} = 60 \text{ MPa} \]

Let's visualize a three-point bending test used to measure transverse strength:

This diagram illustrates:

- The rectangular beam specimen (yellow)
- The applied load (\( P \)) at the center (red arrow)
- The support span (\( L \)) (green line)
- The width (\( b \)) and thickness (\( d \)) of the specimen

In this three-point bending test, the load is applied at the center of the beam, causing it to bend. The transverse strength is calculated based on the maximum load the specimen can withstand before failure occurs.

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