Split Cylinder Tensile Strength

Concrete is roughly ten times weaker in tension than in compression, and measuring that tensile strength directly is far harder than it sounds. Gripping a concrete specimen to pull it apart introduces stress concentrations at the grips, any eccentricity in the pull adds bending, and specimens have an inconvenient habit of failing at the grip rather than in the middle. The split cylinder test sidesteps all of it with a piece of elasticity theory and a testing machine that only knows how to push.

Lay a cylinder on its side and squeeze it across a diameter. The theory of elasticity says that a disc loaded this way develops a nearly uniform tensile stress across the loaded plane, perpendicular to the load, over most of its depth — compression only near the two contact points. So the specimen splits neatly down the diameter, in tension, under a machine that is doing nothing but compressing. The stress at failure is $f_{ct} = 2P/(\pi L D)$, and that relation is the closed-form elastic solution: no fitted constant, no empirical correlation, nothing to belong to anybody. That is the reason it is on this site while the code tables are not.

What is standardised is how the test is run — the bearing strip material and width, the loading rate, the specimen condition — and that lives in ASTM C496 and its EN and CSA equivalents, all of them copyrighted and all of them the authority. This page gives you arithmetic on a result. It does not tell you the result is valid.

The bearing strips deserve an explanation, because they look like an afterthought and are not. Load a cylinder against bare steel platens and the contact stress along the line of contact is enormous — the specimen crushes locally instead of splitting, and the test measures nothing. Thin plywood or hardboard strips spread the load over a narrow band, and the elasticity solution above is the limit as that band goes to zero. A wider strip lowers the peak tensile stress slightly, so the measured strength reads a little high, which is exactly why the strip width is specified rather than left to judgement.

The trap that fails good concrete is that there are three tensile strengths and they are all called "the tensile strength". Direct tension gives the lowest number. Splitting tension sits in the middle. Modulus of rupture, from a beam in flexure, gives the highest — half again above direct tension is typical. They differ because each stresses a different volume of material in a different stress field, and concrete's strength is set by its worst flaw, so the more material you stress the weaker it looks. Quoting a splitting result against a specification written for flexural strength, or the reverse, is a real error and an easy one.

Two things this site deliberately does not compute, and the reasons are worth stating. The first is the core strength correction for length-to-diameter ratio. A drilled core shorter than twice its diameter reads high, because the platen restraint reaches further into the specimen, and the correction factors for that are a table in ASTM C42. A table is copyrighted, it is not a formula, and it cannot be honestly reconstructed by fitting a curve through remembered values. Use the standard. The second is cube-to-cylinder conversion. The familiar rule that a cube reads about 1.25 times a cylinder — or that you multiply a cube strength by 0.8 — is a convention with a long tail of exceptions: the ratio drifts with strength level, and Eurocode simply carries both values side by side rather than converting between them. It is a rule of thumb, not a relation, and a calculator that presented it as arithmetic would be lying about how well it is known.

The same geometry does duty in two other trades, incidentally. The Brazilian test measures the tensile strength of rock in mining and geotechnical work, and the indirect tensile test on asphalt cores is this identical equation with a different material and a controlled specimen temperature.