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National Advisory Committee for Aeronautics, Wartime Report - Stresses Around Rectangular Cut-Outs in Skin-Stringer Panels Under Axial Loads

Cut-outs in wings or fuselages produce stress con-
centrations that present a serious problem to the stress
analyst. As a partial solution of the general problem,
this paper presents formulas for calculating the stress
distribution around rectangular cut-outs in axially loaded
panels. The formulas are derived by means of the substitute-
stringer method of shear-lag analysis.

In a previous paper published under the same title as
the present one, the analysis had been based on a substitute
structure containing only two stringers. The present
solution is based on a substitute structure containing three
stringers and is more complete as well as more accurate than
the previous one. It was found that the results could be
used to improve the accuracy of the previous solution
without appreciably reducing the speed of calculation.
Details are given of the three-stringer solution as well as

of the modified two-stringer solution.
In order to check the theory against experimental
results, stringer stresses and shear stresses were meas-
ured around a systematic series of cut-outs. In addi-
tion, the stringer stresses measured in the previous in-
vestigation were reanalyzed by the new formulas. 'The
three-stringer method was found to give very good accuracy
in predicting the stringer stresses. The shear stresses
cannot be predicted with a comparable degree of accuracy;
the discrepancies are believed to be caused by local
deformations taking place around the most highly loaded
rivets and relieving the maximum shear stresses.

Gut-outs in wings or fuselages constitute one of the
most troublesome problems confronting the aircraft designer.
Because the stress concentrations caused by cut—outs are
localized, a number of valuable partial solutions of the
problem can be obtained by analyzing the behavior, under
load, of simple skin—stringer panels. A method for
finding the stresses in axially loaded panels without cut-
outs was given in reference 1, which also contained sug-
gestions for estimating the stresses around cut-outs. In
reference 2, these suggestions were put into more definite
form as a set of formulas for analyzing an axially loaded
panel with a cut-out.