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National Advisory Committee for Aeronautics, Technical Notes - A Method for Calculating Stresses in Torsion-Box Covers with Cutouts

A theory is presented for-calculating stresses in the covers of
torsion boxes containing large cutouts. Half the symmetrical uncut por-
tion of the cover is represented by three stringers that carry all direct
stresses and the intermediate cover material which is assumed to carry
only shear stress.' Differential equations of equilibrium are derived
and.solved to obtain stresses along each stringer. Illustrative examples
are solved and the results are compared with experimental values. For
one of these examples the results are also compared with a more detailed
solution made by a numerical method of analysis. The agreement between
theory and experiment is satisfactory in all cases except those with very
large cutouts and flexible bulkheads.

An approximate method was developed in reference‘l for the analysis
of stresses in torsion boxes containing large cutouts. This method con-
sists in first idealizing the structure by concentrating all the direct-
stress-carrying material of the box into main flange members and assuming
all the shear to be carried by the webs and cover sheets. Expressions
are then written for shear and direct stress in each of the members in
terms of an unknown distribution of torque between the shear webs and
cover sheets in the Cutout bay. Finally, the principle of least work is
used to find the actual distribution of torque and thus to determine the
shear and direct stresses. The analysis is adequate for the design of
all components of such structures except the cover containing the cutout.

The present paper extends the theory of reference 1 to permit a more
detailed calculation of the stresses in the covers.of such boxes. The
method is based upon an idealization of the cover similar to that just
described.except that the full-width portion adjacent to the cutout is:
made to contain three stringers on each side of the longitudinal center
line instead of only one as in reference 1. Differential equations of
equilibrium are derived and solved to obtain stresses along each stringer.