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National Advisory Committee for Aeronautics, Technical Notes - Stress Concentration Around an Open Circular Holes in a Plate Subjected to Bending Normal to the Plane of the Plate

An aluminum—alloy plate containing an open circular
hole of diameter large compared with the thickness of the
plate was subjected to bending forces normal to the plane
of the plate. Deflection and strain measurements were
taken for two different loads.

Stress concentrations occurred at the edge of the
hole and the maximum stresses were tangential to the hole
at the ends of the transverse diameter. The maximum stress
at the edge of the hole was 1.59 times the computed stress
on the net section and 1.85 times the computed stress in a
solid plate of the same dimensions subjected to the same '
bending forces. The maximum deflections were about 20
percent greater than the corresponding deflection f.or a
solid plate of the same size subjected to the same bending
forces.

The smallest edge distance was equal to 2-1/2 times
the diameter of the hole and the stress concentration on
this side of the hole was the same as on the side where
the edge distance was about 4~l/2 diameters. A theoreti—
cal analysis of the problem shows that. for an aluminum
plate of infinite width, the stress concentration at the
edge of the hole would be 1.87 times the stress in a solid
plate. which is substantially the same relation obtained
for the plate tested.

It is a well-established fact that holes, fillets, and
other discontinuities in force—carrying members give rise
to concentrations of the stresses-in the vicinity of the
discontinuities. Under conditions of repeated loading,
these stress—concentration effects are of great importance
because they materially reduce the fatisure strength of
the members.

In recent years, this problem has received
considerable attention and the stress—concentration fac~
tors for open'holes, notches, and fillets have been deter—
mined by both photoelastic (references 1, 2, and 3) and
analytical (references 4-and 5) methods. "To a large ex—
tent, however, these investigations have been confined to
specimens subjected to forces producing two—dimensional
stress systems. Tuzi (reference 3) and Howland and Steven—
son (reference 5) have studied the distribution of stresses
in a plate containing a centrally located open circular
hole and subjected to bending forces parallel to the plane
of the plate. The problem of a plate containing an open
circular hole and subjected to bending forces normal to the
plane of the plate has been analytically studied by Goodier
(reference 6). No results of any experimental determina—
tion of the stress concentration around an open hole in a
plate subjected to bending forces normal to the plane of
the plate have been found. The lack of experimental infor~
mation regarding this problem is readily explained when it
is realized that the stresses are three~dimensional and
hence have not been.determined by photoelastic methods.