A Method of Shear-Lag Analysis of Box Beams for Axial Stresses, Shear Stresses, and Shear Center Page: 3 of 61

                                
simple, the NACA methods become more difficult to apply.
The computation is very tedious and of dubious accuracy
where there are excessive approximations required of the
designer in idealizing the structure so that it will fit
the method. Furthermore, the NACA methods require two
separate analyses for beam and chord bending, which con-
siderably lengthens the calculations.
From design considerations, it is desirable to have a
simple flexible method of shear-lag analysis that can be
tailored to the individual conditions of any wing beam.
It should require a minimum of idealization of sections so
that irregular beams may be readily analyzed and should, if
possible, enable a simultaneous consideration of beam and
chord bending. It should be possible to check the results
of the analysis in a simple straightforward fashion.
The method of shear-lag analysis herein presented was
developed by the Grumman Aircraft Engineering Corporation
in the course of recent designs and, it is believed, incor-
porates these desirable features.
OUTLINE OF METHOD
Essentially, the method consists in applying a correc-
tion for shear lag to the areas of a beam cross section
and then analyzing the substitute beam by the conventional
bending theory. A check for the shear-lag correction can
be made if desired.
(1) Shear lag reduces the effectiveness of cover sheet and
stringers for carrying bending stresses. Consequently,
stresses in the cap strips will be raised and stresses in
the stringers will be reduced from those computed by the
ordinary beam theory. If the stringer stress at a section
decreases 20 percent and the cap-strip stress increases 10
percent from the theory, the effectiveness factor E' for
the stringer will be  100 - 10 - 20 = 70 percent, referred
to the beam theory cap-strip stress as 100 percent.
Effectiveness curves are drawn in chordwise and span-
wise directions for each stringer and wing section by tak-
ing mathematically ideal curves and altering them arbitrar-
ily to suit local conditions in the structure. Care must
be taken that the location of the centroid of the effective
material, and hence the shear center, varies in a smooth