Concrete in Tension: Tensile Strength of Concrete
The tensile and compressive strengths of concrete are not proportional. An increase in compressive strength is accompanied by a smaller percentage increase in tensile strength. The tensile strength of ordinary concrete commonly falls between about 8% and 15% of its compressive strength, but the ratio normally decreases as the compressive strength increases.
Concrete is strong in compression but relatively weak and brittle in tension. When tensile stress exceeds its tensile capacity, cracks form approximately perpendicular to the principal tensile stress. This is why reinforcement is placed where tension is expected in reinforced concrete members.
Three Types of Concrete Tensile Strength
The true tensile strength of concrete is difficult to determine. Direct tension, splitting tension, and flexural tests do not produce the same value because the stress distribution and the volume of highly stressed concrete are different in each test.
| Method | What is loaded | Reported result | Important point |
|---|---|---|---|
| Direct tension | A specimen is pulled axially | Direct tensile strength | Difficult to obtain pure tension without eccentricity or grip effects |
| Splitting tension | A cylinder is loaded along its diameter | Splitting tensile strength, fct | Indirect test; generally lower than flexural strength |
| Flexural test | A plain concrete beam is loaded in bending | Modulus of rupture, fr | Used for cracking and pavement applications; normally the highest of the three measures |
Splitting Tensile Strength of Concrete
The split-cylinder test has been widely used to estimate the tensile strength of concrete. A cylinder is placed on its side in a testing machine. A compressive line load is applied along its length, with support along the bottom of the cylinder. The compression produces transverse tensile stress, and the cylinder splits along a vertical diameter when its tensile strength is reached.
The tensile stress at splitting is calculated as:
fct = 2P / (πLD)
where:
- fct = splitting tensile strength
- P = maximum applied load at splitting
- L = length of the cylinder
- D = diameter of the cylinder
The load and dimensions must use a consistent unit system. If P is in newtons and L and D are in millimetres, fct is obtained in N/mm2, which is MPa.
Standards note: ASTM lists C496/C496M-17, the former splitting tensile test standard, as withdrawn in 2026 while revision work item WK92425 remains listed. For contractual testing, check the current project specification and the latest ASTM status before naming the test method.
Flexural Tensile Strength and Modulus of Rupture
Another common approach is the modulus of rupture, fr. It is the maximum tensile bending stress calculated for a plain concrete test beam at failure. ASTM C78/C78M uses a simple beam with third-point loading.
ACI 318 gives the following modulus of rupture for normal structural design calculations:
fr = 0.62λ√f’c MPa
fr = 7.5λ√f’c psi
where f’c is the specified compressive strength and λ is the lightweight-concrete modification factor. For normal-weight concrete, λ = 1.0. Values commonly used for sand-lightweight and all-lightweight concrete are 0.85 and 0.75, with interpolation permitted where applicable.
The cracking moment of a reinforced concrete section is commonly estimated as:
Mcr = frIg / yt
where Ig is the gross moment of inertia and yt is the distance from the centroid to the extreme tension face.
Concrete Tensile Strength Calculator
This calculator gives the ACI modulus-of-rupture value and a textbook mean splitting-strength estimate. These are estimates from compressive strength, not replacements for a specified laboratory test.
| ACI modulus of rupture, fr | 3.40 MPa |
|---|---|
| Mean splitting-strength estimate | 2.90 MPa |
Actual results depend on the mixture, aggregate, curing, age, moisture condition, specimen, and test method.
Example for 30 MPa Concrete
For normal-weight concrete with f’c = 30 MPa:
ACI modulus of rupture = 0.62 × √30 = 3.40 MPa
Mean splitting-strength estimate = 0.53 × √30 = 2.90 MPa
The two values are not interchangeable. The flexural value is used where the modulus of rupture is required, while the splitting value describes the result of an indirect tensile test or an empirical estimate of that result.
What Affects the Tensile Strength of Concrete?
- Compressive strength and water-cementitious materials ratio
- Aggregate type, surface texture, size, and bond with the cement paste
- Age, curing, and moisture condition at testing
- Specimen size, test arrangement, loading rate, and stress distribution
- Existing shrinkage, thermal, handling, or drying cracks
- Concrete density and the type of lightweight aggregate, when used
Concrete made with crushed rock may develop greater tensile strength than similar concrete made with rounded gravel because of the aggregate shape and bond. However, the actual result should be taken from testing when tensile performance is important.
Why Tensile Strength Matters
Tensile strength affects the first cracking of beams and slabs, temperature and shrinkage cracking, shear behaviour, bond, anchorage, serviceability, and pavement performance. After reinforced concrete cracks in flexure, the reinforcing steel carries most of the tension across the crack while concrete between cracks continues to contribute through tension stiffening.
References
- Wight, J. K., Reinforced Concrete: Mechanics and Design, 8th Edition, Section 3-4.
- ACI 318-19, Building Code Requirements for Structural Concrete, Section 19.2.3.
- ASTM C78/C78M-22, Flexural Strength of Concrete Using Simple Beam with Third-Point Loading
- ASTM concrete standards list, including the 2026 status of C496/C496M-17
- ASTM WK92425, revision work item for C496/C496M
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