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National Advisory Committee for Aeronautics, Technical Notes - Creep Bending and Buckling of Linearly Viscoelastic Columns

The general dynamic equation of creep bending of a beam loaded lat-
erally and axially was derived for a linearly viscoelastic material whose
mechanical properties can be characterized by four parameters. The mate-
rial can exhibit instantaneous and retarded elasticity as well as pure
flow.

The equation derived was used to obtain the creep bending deflection
of a beam in pure bending and of a column with initial sinusoidal devia-
tion from straightness. As expected, the ratio of the creep deflections
of the beam in pure bending and the deflections of a corresponding purely
elastic structure is identical to the ratio of the creep strain and the
corresponding elastic strain of a bar under simple tension or compression.

The results of the analysis of the creep deflection of the column
showed that the deflections increase continuously with time and become
infinitely large only when the loading time is correspondingly large.
However, large deflections are obtained in reasonably short periods of
time if the applied load is near to the Euler load of the column. The
deflection-time curves obtained from a numerical example are of the same
type as those determined by experiment with aluminum columns.

The problem of the determination of the behavior of beams and columns
under conditions conducive to creep deformation has been given attention
only in the past several years (see, for example, refs. 1 to 8). This
problem is becoming increasingly important because of the high tempera—
tures at which high-speed missiles and aircraft as well as modern power
plants operate. It is the purpose of the present report to investigate
analytically the nature of the creep deformation of beams formed from
materials which can be assumed to exhibit linearly viscoelastic properties
either at room or elevated temperatures.