These are barns I photographed in the Willamette Valley in Oregon in September, 2014. The gambrel is a distinctive and common barn roof shape in this part of the world, as is the curved roof barn (See www.theshelterblog.com/?s=curved+roof posted last month.)
The word gambrel “derives from the hock (bent part) of a horse’s leg, also called a gambrel. The lower part of the roof is a steep slope, the upper part shallower. The break-in roofline allows head room in the loft space, and is useful in barns for hay storage as well as in homes for rooms above plate level.” –From Shelter II, p. 98.
There are also plans for a 24′ × 32′ gambrel-roofed barn on pages 102-103 of Shelter II.