A nonlinear solution to the Brazier problem of cross-sectional flatten
ing for infinitely long tubes under bending is formulated using classi
cal nonlinear shell theory along with semimembrane constitutive relati
ons. It is shown that traditional cylindrical shell equations are not
sufficient to accurately model the nonlinearity of the Brazier effect,
and the suitable corrections to the shell equations are derived. This
approach gives greater physical insight into the problem than traditi
onal variational methods, and it yields a highly nonlinear ordinary di
fferential equation for infinite length cylinders with orthotropic mat
erial properties. This resulting equation is solved numerically using
finite difference techniques, and an approximate analytical solution i
s also obtained, which corresponds to Brazier's original solution. Col
lapse loads as a result of limit points and local instability are comp
ared with classical failure estimates, and the influences of laminate
stacking sequence and internal pressure are explored, Also, a collapse
parameter is introduced that gives a relative measure of the buckling
load to that of the limit load for orthotropic structures, and it is
shown that, for low values of this parameter, the limit moment is not
a suitable estimate for the collapse load of long cylinders.