William shakespeare’s plays contributed to renaissance culture by

They didn't. Shakespeare's heyday was the early 1600s- the Renaissance was from the 1400s- to the 1500s. While his plays would have added to a pseudo-Renaissance culture, it would not have contributed to the true Renaissance.

Shakespeare lived concurrent with the period of European history known as the Renaissance, and it could be said that he did influence that period of time through his writings. While the Renaissance included important development in the sciences, as Leonardo da Vinci's contributions suggest, in religion, and in political thought, that period of time, which ran from the 14th through 17th centuries, was defined as much as anything by the arts and literature. And, in that, Shakespeare was an important figure. His depictions of human relations were characteristic of the period in their rejection of the blatantly artificial and simplistic portraits of individuals characteristics of earlier periods, and the interactions between individuals in his plays were considerably more complex than in the occasional work of literature produced during the Middle Ages.  Shakespeare's works certainly elevated the importance of a humanistic approach to literature, but this was Shakespeare's contribution to the period, not the period's contribution to Shakespeare.