Formulation for Reliable Analysis of Structural Frames

Structural engineers use design codes formulated to consider uncertainty for both reinforced concrete and structural steel design. For a simple one-bay structural steel frame, we survey typical uncertainties and compute an interval solution for displacements and forces. The naive solutions have large over-estimations, so we explore the Mullen-Muhanna element-by-element strategy, scaling, and constraint propagation to achieve tight enclosures of the true ranges for displacements and forces in a fraction of the CPU time typically used for simulations. That we compute tight enclosures, even for large parameter uncertainties used in practice, suggests the promise of interval methods for much larger structures.