When an area receives less than 3  hours of direct, uninterrupted sunlight daily, growing even shade-tolerant grasses is a tall order. Remember that dappled sunlight doesn't count towards this 3-hour requirement as lawn grasses have not evolved to photosynthesize in this highly variable environment. Fine fescue and a number of cultivars of bluegrass are better at growing in areas receiving 3 hours of sunlight but even then their wear tolerance goes down considerably with any kind of foot traffic.  Plan to overseed the space on a yearly basis to have a thicker stand as dieback will be significant.  Other options include going with a groundcover that is well adapted to dry shade, such as Vinca minor, or you can mulch the space with a 2-4 inch layer of wood chips.