What were the major construction challenges that the medieval Europeans faced?

The major construction challenges faced by medieval Europeans were war disease and economic status.

Explanation:

The disease spread on the time of the medieval Europeans constructing period is black death which is also known as plague disease.  There was an outbreak of many wars based on religion and pope was threatened and there happened to be loss of many lives. And on the side, the Europeans were threatened by the Mongolians.There exist a very cold climate that had affected the crop pattern and made the crops froze.