Simplified vibration response prediction for slender monumental stairs

Slender monumental stairs are major architectural features in hotels, condominiums, hospitals, and other high-end building structures. Architectural requirements for these are usually very aggressive, with long spans and slender stringers being the norm. Slender stairs often have fairly massive treads and guardrails which, combined with slender stringers, results in natural frequencies within reach of the very large lower harmonics of the force caused by a person descending the stair. Stair designers must be able to predict the vertical vibration response of a stair during the design phase. Current prediction methods rely on finite element analysis-based response prediction methods which are outside the reach of many structural engineering firms. This paper presents a simplified response prediction method based on the fundamental natural mode of the stair, which is suitable for manual calculations. Response predictions are compared to experimental measurements to show that the predictions are accurate enough for design use.