Why compressive strength is always greater than tensile strength in a beam?

Compressive strength is greater than tensile strength not just in beams, but in metals, concrete, ceramics, ice, and many other materials.

Consider a uniaxial test of tension or compression. Because the cross-sectional area of the sample increases with the load, the stress is actually lower than what we would expect from dividing the load by the area of an unloaded sample. The opposite is true for a tension test. The cross section gets smaller with increasing load. Remember this is true regardless of whether the deformations are reversible and elastic or irreversible and plastic. Therefore the nominal compressive strength is greater than the nominal tensile strength even in a perfectly isotropic material.