What is goal of your Question ? do you mean fatigue in related to fatigue life of structural under cyclic loading or detect fatigue cracks or growth of cracks ? please describe your question more and clearly .
Question is not clear. Generally, fatigue studies include determination of residual stiffness, residual strength, life and remaining life of the structure.
can anyone help me to know that is the fatigue life depends on the structure design or it is just material dependent?
if it does depends on design please suggest some reading material to the related topics if available, also i want to know is it possible to improve the fatigue life of the structure by making some changes in it, for example like changing support condition, or by providing some extra support on the structure
To the best of my knowledge, fatigue life depends on material, design, manufacturing type, environmental conditions and environmental loads. Fatigue life depends also on which risk you accept for failure.
You have a How To description on fatigue analysis below which outlines some of these concepts