Splitting Tensile Test on Concrete

Introduction
A splitting tensile test is a common test performed on concrete to determine its tensile strength. In this test, a cylinder of concrete is subjected to an axial load that is applied diametrically on opposite sides of the cylinder. The load is gradually increased until the cylinder fails by splitting along the applied load line. The ultimate load at failure is denoted as P.

Understanding the Splitting Tensile Strength
The splitting tensile strength of concrete is a measure of its resistance to tensile forces applied perpendicular to the direction of the load. It is an important property to consider in the design of concrete structures, as concrete is generally stronger in compression than in tension.

Calculating the Splitting Tensile Strength
The splitting tensile strength of concrete can be calculated using the formula:

Splitting Tensile Strength (σ) = P / (πDL)

where:
- σ is the splitting tensile strength of concrete
- P is the ultimate load at failure
- D is the diameter of the cylinder
- L is the length of the cylinder

Explanation of the Correct Answer
The correct answer is option C: 2P / (πDL). This is the correct formula to calculate the splitting tensile strength of concrete.

Reasoning behind the Correct Answer
To understand why option C is the correct answer, let's break down the formula:

Splitting Tensile Strength (σ) = P / (πDL)

The denominator of the formula, (πDL), represents the area of the cylinder cross-section. This is because the tensile strength is calculated by dividing the applied load (P) by the cross-sectional area over which the load is applied.

The numerator of the formula, 2P, is derived from the fact that the load is applied on opposite sides of the cylinder, resulting in two equal and opposite forces. Therefore, the total load is twice the applied load (P).

By dividing the total load (2P) by the cross-sectional area (πDL), we get the splitting tensile strength of concrete (σ) as 2P / (πDL).

Therefore, option C, 2P / (πDL), is the correct formula to calculate the splitting tensile strength of concrete.

In conclusion, the splitting tensile strength of concrete is determined by dividing the ultimate load (P) by the product of 2 times the diameter (D) and the length (L) of the cylinder, as given by option C.

T = 2P / πDL