The main contributions to the strength of a steel come from:

Effect of grain size
Effect of microstructure
Effect of solid solution strengthening
Effect of precipitates
Effect of dislocations

These factors are controlled by the chemistry of the steel and the processing route used to produce the final component. All of these aspects need to be taken into account when selecting or designing a steel for a given application.

For ferrite and pearlite steels relationships between yield /tensile strength and various compositional and microstructural factors have been developed. These are useful in that they show general characteristics, although they are unable to incorporate all factors that influence strength in modern steels, for example precipitation strengthening. Examples of these relationships are given below:

YS (MPa) = 53.9 + 32.3 Mn + 83.2 Si + 354 N_f + 17.4 d^-1/2

UTS (MPa) = 294 + 27.7 Mn + 83.2 Si + 3.85 pearlite % + 7.7 d^-1/2

Alloying addition in wt%, d is the ferrite grain size in mm, N_f is the free nitrogen content 

(Equations taken from Steels: Metallurgy and Applications by D.T. Llewellyn, published by Butterworth Heinemann)