The Great Depression of the 1930s are not really as well known for cultural changes as the 1920s were. However, there were changes because of the economic collapse that the US experienced.
The major change was that American families collapsed to some extent. As men lost their jobs, it was harder for families to form or to stay together. Fewer women got married during the Depression and fewer women had children. As the link below tells us,
In 1929 the marriage rate was 10.14 marriages per 1,000 persons but dropped to 7.87 per 1,000 persons by 1932.
Within families that did exist, women's roles became more important economically. Women were expected to do more to make family funds go farther. This meant that they needed to do more things like making clothes and canning food for the family.
In these ways, women's lives did change to some extent during the Depression.