The Lateral Buckling of Timber Arches

This paper presents the stability analyses of glulam arches subjected to distributed vertical loading. The present analysis employs a strain-based formulation of a nonlinear geometrically exact three-dimensional beam theory. The influence of the relative height of the arch on the lateral buckling load is studied. The buckling load is determined by bisection method with observing the sign of the determinant of the tangent stiffness matrix. The post-critical load deflection path is traced by a modified arc–length method. Such influences are shown for arches with a constant cross-section or constant volume. After determining the most favorable height of the arch, the influence of the number and position of lateral supports is shown. We also compare the deflections, bending, and radial stresses at the lateral buckling states to the limit values which are recommended by European standards.