An Approximate Method of Shear-Lag Analysis for Beams Loaded at Right Angles to the Plane of Symmetry of the Cross Section Page: 5 of 14

                                
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In a stringer located at a distance   y  from the
dividing line, the stress is obtained by adding to the
stress 0Ic/I calculated by the ordinary bending theory,
a correction that is given by the formula
A0 = Ay - 4 -   y  1 +0-            1 +  A?.F       (3)
= F             1 +                      ()
h /
Formula (3) is an approximation (reference 2) to another
formula whica is derived on the assumption that the camber
is negligible.  If the carber is appreciable, the formula
should be used only for the region near the flange
(y/b -->).  ) ortunately, only this region is of importance
in design.
TEST SPECIMENS AND TEST PROCEDURE
The dimensions of of two of the three beams are shown in
figure 3.  The third beam was made by cutting the D-section
shown in figure 3(b) along the line B-B.   The material was
24S-T aluminum alloy.   The value of Young's modulus was
taken as 10,500 kips per square inch.
Each beam was supported at the center.   Two equal loads
were applied, one to each half of the beam, to produce the
bending moments.   The structure as well as the loading being
symmetrical about the root, eacb half of the beam could be
considered as a cantilever with a perfectly fixed root.    On
the beam with triangular cross section, each load was an-
plied close to the tip of the beam.   On the other beams,
the loads were aonlied at the middle of the semisoan in
order to increase the shear-lag effect. The loads were ap-
plied to each beam at the experimentally determined shear
center.
Strain measurements were made rith Tuckerman optical
strain gages with a gage length of 2 incnese. The load was
applied in three equal increments.   Check runs were made
if the load-stress diagram indicated a zero error of more
than 0.2 kip per square inch.