The only one I know is the three point bending test for flexural strength.
There are two methods to test flexural strength, three point and four point method.
The maximum flexural stress happens to concentrate only in a point in three point test, if you are testing a non-homogeouse material as it's always so in reality, it's not handy at all, brittle materials in three point test are prone to premature fracture, however the stresses in four point test, extended across the beam (construction ...), it means in case of not-homogenous material béton armé (Eng. Reinforcement concrete), we can have more accurate map of material behaviour.
Usually these two methodes are considered as destructive test.
Another destructive test is splitting tensile strength test, here, you can find more about this test.
Pure axial (tensile, compression) tests (destructive tests) are quite popular. Universal testing machines or hydraulic presses are two familiar examples of instrument testing machines.
Besides hardness tests (semi-destructive) such as Brinell, Rockwel and Vickers are among the most popular tests these days in Europe.