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National Advisory Committee for Aeronautics, Technical Notes - Tables of Stiffness and Carry Over Factor for Structural Members Under Axial Load

Tables of stiffness and carry—over factor are present—
ed for members in which the cross section and axial load do
not vary along the length of the member. These tables are
of use in solving problems in the stability of structural
members under axial load as well as in applications of the
Cross method of moment distribution when the effects of ex-
ial load in the members are considered., The interval boa
tween successive values of the argument is small enough to
make interpolation unnecessary in engineering calculations.

The method of moment/distribution devoloped.by Hardy
Cross (reference 1) can frequently be used to advantage in
the stress analysis of continuous beams, continuous frames,
and rigid joint trusses, some cases of which occur in aero—
nautical structures. In reference 2 James summarized the
principles of the Cross method and extended it to show how
the effects of axial load in the members may be con'Sidered
in a moment— distribution analysis. In reference 3 the
Cross method was further extended to show how the princi—
ples of moment distribution may be used to solve problems
in the stability' of Ltructural members under axial load.

In the stability calculations as well as in a moment—
distribution analysis where the effects of axial load are
considered, it is desirable to have tables giving the stiff-
ness and carry—oVer factor as a function of the axial load
and properties of the member. Such a set of tables isxore-
sented in this paper.

The tables apply to members for which the cross sec—
tion and axial load do not vary along the length of the
member. The interval between successive values of—the ar-
gument was made so small that no: in.terpolation will be
necessary when the tables are used in engineering calcula-
tions.

If a member is on unyielding supports at e-ach end, the
moment at one end necessar;r to produc-e a rotation of one-
fourth radian of that end is called the "stiffness. The
stiffness of a member will depend upon the amount of re—
straint at the far end. In the derivation of the criterion
for stability as given in reference 3, three types of~re~
straint at the far end are considered.