Simplified vibration serviceability evaluation of slender monumental stairs

Slender monumental stairs are major architectural features in many high-end building structures. Architectural requirements for these are usually very aggressive, with long spans and slender stringers being the norm. The resulting low natural frequencies are often within reach of the lower harmonics (which have high amplitudes) of the vertical force caused by a person descending the stair. Also, some configurations with very low frequency lateral vibration modes might allow high lateral accelerations. Because the potential for annoying vibrations is high, it is critical that stair designers have access to evaluation methods. Current evaluation methods rely on finite-element analysis-based response prediction methods that are outside the reach of many structural engineering firms. This paper presents a simplified vertical acceleration 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 calibrate the prediction method for design use. Lateral vibrations are discussed, and an evaluation method is proposed. Finally, a numerical example is provided.