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

Differential equations of bending of an idealized H-section beam
column were derived for a nonlinearly viscoelastic material whose
mechanical properties are analogous to a model consisting of a linear
spring in series with a nonlinear dashpot whose strain rate is propor-
tional to a power of the applied stress. The resulting constant stress
or load creep curve consists of a straight line, the slope of which can
be considered as the secondary creep rate of a real material.

The equations derived were used to obtain the creep-bending deflec-
tions of a beam in pure bending and of a column with initial sinusoidal
deviation from straightness. The results of the analysis of the simple
beam showed that the deflections vary linearly with time. The analysis
of the deflections of the column, accomplished With the assumption that
the original shape of the structure was maintained at all times, showed
the existence of a finite critical time at which the deflections become
indefinitely large. The critical time decreases rapidly with increasing
axial compression and column inaccuracy.

The need for methods predicting the behavior of structural components
at high temperatures is becoming increasingly urgent, particularly in the
fields of aircraft structures and propulsion. During the past he years
considerable attention has been paid to the fundamental constant-stress
and constant-load tensile creep behavior of materials. However, with few
exceptions, it is only recently that results of the investigation of the
creep behavior of beams and columns have been presented (see, e.g.,
refs. 1 to 9). It is the purpose of the present report to apply to the
problem of the creep behavior of beams and columns a stress-strain—time
relation which can be considered as a generalization of the relation
obtained between the strain rate and stress for a Maxwell linearly visco-
elastic model consisting of a spring connected in series with a dashpot
(see fig. 1 and refs. 6 and 8 to 10).