A variational problem about maximal stable arches in a hopper is formu
lated. This problem idealizes an industrial problem related to guarant
eering reliable flow of material out of a storage silo. To obtain exis
tence, the generalized function are introduced and studied. Specifical
ly, functions in the spaces can be discontinuous in the interior of th
e domain as well as along the boundaries. For the von Mises type of ma
terial in two dimension, the limit load is estimated and its asymptoti
c behavior is investigated.