Geodesic
Stability of pinned--rotationally restrained arches
Theoretical and applied mechanics, Tome 48 (2021) no. 1.

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The article aims to find the buckling loads for pinned--rotationally restrained shallow circular arches in terms of the rotational end stiffness, geometry and material distribution. The loading is a concentrated vertical force placed at the crown. A geometrically nonlinear model is presented which relates not only the axial force but also the bending moment to the membrane strain. The nonlinear load-strain relationship is established between the strain and load parameters. This equation is then solved and evaluated analytically. It turns out that the stiffness of the end-restraint has, in general, a significant effect on the lowest buckling load. At the same time, some geometries are not affected by this. As the stiffness becomes zero, the arch is pinned-pinned and as the stiffness tends to infinity, the arch behaves as if it were pinned-fixed and has the best load-bearing abilities.
Keywords: arch, buckling, stiffness, snap-through 
@article{TAM_2021_48_1_a2,
     author = {L\'aszl\'o P\'eter Kiss},
     title = {Stability of pinned--rotationally restrained arches},
     journal = {Theoretical and applied mechanics},
     pages = {39 - 51},
     publisher = {mathdoc},
     volume = {48},
     number = {1},
     year = {2021},
     url = {http://geodesic.mathdoc.fr/item/TAM_2021_48_1_a2/}
}
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László Péter Kiss. Stability of pinned--rotationally restrained arches. Theoretical and applied mechanics, Tome 48 (2021) no. 1. http://geodesic.mathdoc.fr/item/TAM_2021_48_1_a2/