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The nonlinear in-plane stability of shallow arches with cross-sectional inhomogeneity is investigated. It is assumed that a central concentrated load is exerted at the crown of the arch and the supports are uniform rotationally restrained pins at the endpoints with constant stiffness. The effects of the springs on the stability is investigated. It is found that such arches may buckle in an antisymmetric bifurcation mode with no strain increment at the moment of the stability loss, and in a symmetric snap-through mode with an increased strain. The effects of the springs are notable on the bucking ranges and also on the critical (buckling) loads. If the spring stiffness is zero we get back the results valid for pinned-pinned arches and as the stiffness of the rotational restraints tends to infinity the results become consistent with those for fixed-fixed arches. The results computed are compared with finite element calculations.

In-plane buckling of rotationally restrained heterogeneous shallow arches subjected to a concentrated force at the crown point