The primary purpose of this study is to determine stability boundaries (interaction curves) for a three degree of freedom, shallow arch model under multiple dynamic loads. The model consists of four rigid bars connected by frictionless pins, with rotational springs and dashpots at the three interior joints, and a translational spring at the right hand exterior joint. Three independent loads (P₁, P₂, P₃) are applied to the model, one at each of the three interior joints.

The model's equations of motion, which are derived from Lagrange's equations of motion, are numerically integrated, using the Newmark-Beta method (β = 1/4), to determine the buckling loads. The buckling loads are those loads for which the buckling criterion, the end bars simultaneously below the horizontal, is satisfied.

The interaction curves and buckling loads are determined for a parabolic arch with damping under step loads, a parabolic arch without damping under step loads, an eccentric arch without damping under step loads, a parabolic arch without damping under impulse loads, and an