In-plane elastic buckling of pin-ended shallow parabolic arches

Effects of approximations on non-linear in-plane elastic buckling and postbuckling analyses of shallow parabolic arches

“…which is also used in the derivation of the non-linear strain of shallow parabolic arches [17,18,[31][32][33][34]. The merit of these assumptions is that they lead to the same differential equations of equilibrium and the same analytical solutions for shallow parabolic arches as those for shallow circular arches.…”

“…However, the disadvantages and limitations of analytical solutions based on the approximation assumptions given by Eqs. (3) and (4) have not been addressed adequately, and the analytical solutions have been used incorrectly for parabolic arches that are not very shallow [31][32][33][34]. Hence, identifying the effects of the approximation assumptions on the accuracy of the solutions is much needed, as well as determining the limits of the rise-to-span ratio within which the analytical solutions can be used for predicting the non-linear in-plane buckling and postbuckling of parabolic arches closely, so that incorrect use of the analytical solutions can be avoided.…”

“…In deference to the case of circular arches [1][2][3][4], it is difficult to formulate the accurate non-linear longitudinal normal strain for parabolic arches and consequently it is also difficult to derive the accurate analytical solutions for the non-linear in-plane buckling of parabolic arches. Hence, approximate analytical solutions were sought by several researchers [17,18,[31][32][33][34] using an approximation assumption that dy dz 2 ( 1 ð3Þ…”

In-plane elastic stability of fixed parabolic shallow arches

“…However, only a few studied on the in-plane stability of shallow parabolic arches. Moon et al [18] investigated the elastic buckling of pin-ended shallow parabolic arches with the equilibrium method. Bradford et al [19] and Wang et al [20] studied the stability of parabolic arches with horizontal spring supports.…”

Equilibria and stability boundaries of shallow arches under static loading in a thermal environment

“…Half-sine, circular and parabolic shapes have been studied [15,16,17] and a variety of loading conditions have been investigated, such as concentrated loads [18,19,20], distributed and end moments loads [21,22,23], and variations in the thermal fields or support conditions [5,24,25]. This paper introduces a semi-analytical procedure to find the exact solution to a half-sine pinned shallow arch under transversal loading.…”