Are theoretically calculated periods of vibration for skeletal structures error-free?

Simplified equations for fundamental period of vibration of skeletal structures provided by most seismic design provisions suffer from the absence of any associated confidence levels and of any reference to their empirical basis. Therefore, such equations may typically give a sector of designers the false impression of yielding a fairly accurate value of the period of vibration. This paper, although not addressing simplified codes equations, introduces a set of mathematical equations utilizing the theory of error propagation and First-Order Second-Moment (FOSM) techniques to determine bounds on the relative error in theoretically calculated fundamental period of vibration of skeletal structures. In a complementary step, and for verification purposes, Monte Carlo simulation technique has been also applied. The latter, despite involving larger computational effort, is expected to provide more precise estimates than FOSM methods. Studies of parametric uncertainties applied to reinforced concrete frame bents – potentially idealized as SDOF systems – are conducted demonstrating the effect of randomness and uncertainty of various relevant properties, shaping both mass and stiffness, on the variance (i.e. relative error) in the estimated period of vibration. Correlation between mass and stiffness parameters – regarded as random variables – is also thoroughly discussed. According to achieved results, a relative error in the period of vibration in the order of 19% for new designs/constructions and of about 25% for existing structures for assessment purposes – and even climbing up to about 36% in some special applications and/or circumstances – is acknowledged when adopting estimates gathered from the literature for relative errors in the relevant random input variables.