Modulus of Rupture of Rectangular Sample in Three-Point Bending Calculator

Formula Used:

\[ \text{Modulus of Rupture} = \frac{3 \times \text{Load at Fracture Point} \times \text{Length of Section}}{2 \times \text{Width of Section} \times (\text{Average Section Thickness})^2} \]

Load at Fracture Point:

Length of Section:

Width of Section:

Average Section Thickness:

Modulus of Rupture:

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1. What is Modulus of Rupture in Three-Point Bending?

The Modulus of Rupture in Three-Point Bending is a measure of the tensile strength of concrete beams or slabs. It represents the stress at which a material fails or fractures under bending load.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{Modulus of Rupture} = \frac{3 \times F_f \times L}{2 \times B \times T^2} \]

Where:

\( F_f \) — Load at Fracture Point (N)
\( L \) — Length of Section (m)
\( B \) — Width of Section (m)
\( T \) — Average Section Thickness (m)

Explanation: This formula calculates the maximum stress experienced by a rectangular sample during three-point bending test until fracture occurs.

3. Importance of Modulus of Rupture Calculation

Details: Accurate modulus of rupture calculation is crucial for material testing, quality control, and structural design applications where bending strength is a critical parameter.

4. Using the Calculator

Tips: Enter load at fracture point in Newtons, dimensions in meters. All values must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between modulus of rupture and tensile strength?
A: Modulus of rupture is calculated from bending tests and represents the stress at failure, while tensile strength is measured directly from tension tests.

Q2: Why use three-point bending instead of other test methods?
A: Three-point bending is a simple and widely used method for determining the flexural strength of materials, especially for brittle materials like concrete.

Q3: What are typical modulus of rupture values for concrete?
A: Typical values range from 2-7 MPa for normal strength concrete, depending on mix design, curing conditions, and age.

Q4: How does sample preparation affect test results?
A: Proper sample preparation, including smooth surfaces, parallel sides, and appropriate dimensions, is crucial for accurate and reproducible results.

Q5: Can this formula be used for non-rectangular sections?
A: This specific formula is designed for rectangular cross-sections. Different formulas apply for circular or other shaped sections.