Transverse Strength Calculator

Understanding Transverse Strength Calculator

Transverse rupture strength (TRS) measures a material's resistance to bending. Commonly used for testing ceramics, cemented carbides, and hard materials.

How to use this calculator

1. Enter the breaking force value, this is the load at failure.
2. Enter the span length between supports and the specimen dimensions.
3. Make sure all units are consistent, since the calculator uses them directly in the formula.
4. Click calculate to get the transverse rupture strength.

The formula explained

The calculator uses \(\sigma = \frac{3FL}{2bd^2}\) to compute the breaking stress in a three-point bending test. It finds the maximum transverse stress at failure from the force, span, width, and thickness of the sample.

• \(\sigma\) = transverse rupture strength
• \(F\) = breaking force at failure
• \(L\) = support span length
• \(b\) = specimen width
• \(d\) = specimen thickness or depth

Step by step method

1. Start with the force at fracture, the span length, the width, and the thickness.
2. Substitute the values into \(\sigma = \frac{3FL}{2bd^2}\).
3. Square the thickness, then multiply and divide in the correct order.
4. Report the result in the stress unit that matches your input units.

Worked example

Problem. A specimen breaks under a force of 500 N. The support span is 100 mm, the width is 10 mm, and the thickness is 5 mm. Find the transverse rupture strength.

1. Substitute into the formula: \(\sigma = \frac{3(500)(100)}{2(10)(5^2)}\).
2. Compute the denominator: \(5^2 = 25\), so \(2(10)(25) = 500\). Then the numerator is \(150000\).
3. Divide: \(\sigma = \frac{150000}{500} = 300\).

Tips and common mistakes

• Use the same unit system for all inputs, because mixing mm and m will give a wrong result.
• Be careful to square the thickness \(d\), not the width \(b\).

Frequently asked questions