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Basically, the force supplied by a concrete compression machine is a definite value. For normal concrete strength application, say below 50MPa, the stress produced by a 150mmx150mmx150mm cube is sufficient for the machine to crush the concrete sample. However, if the designed concrete strength is 100MPa, under the same force (about 2,000kN) supplied by the machine, the stress under a 150mmx150mmx150mm cube is not sufficient to crush the concrete cube. Therefore, 100mmx100mmx100mm concrete cubes are used instead to increase the applied stress to crush the concrete cubes. For normal concrete strength, the cube size of 150mmx150mmx150mm is already sufficient for the crushing strength of the machine.
A single observation, such as 50486055535157526145 cannot have a standard deviation cube test compressive result.
The difference in compressive strength is due to the difference between the modulus of elasticity of concrete and that of the steel which is used to apply the compressive force on the concrete. The pressure applies a lateral confinement pressure which is equal to d/3 meaning that for the cylinder, 2d/3 is confined leaving d/3 unconfined whereas for the cylinder 2d/3 is confined means all of the cube is confined. This leads to the cube having a higher compressive strength that the cylinder. For more information, try to read about the triaxial test and the effect of confinement on the compressive strength of soil samples.
fc'=0.87 fck fc'= cylinder strength fck= cube strength
If the cube is uniform ( ie it has uniform density) then the geometric center of the cube is its center of gravity.