Dynamic analysis of a concrete chimney considering the aerodynamic damping

Abstract

Usually, the analysis of structures under wind loading is performed using an equivalent static analysis, where the influence of floating response is taken into account by the gust factor. This methodology can be used in case of rigid structures for not presenting a considerable dynamic response. More flexible structures, in particular those lightly damped, may show an important resonant response and their dynamic properties must be considered in the analysis. The aim of this paper is to present a methodology for dynamic analysis of structures under wind loading considering the geometric nonlinearity, the vibration caused by the kinetic energy of wind gusts and the aerodynamic damping due to the relative movement between this structure and the wind. The formulation proposed is applied to a 180-meter-high concrete chimney and the results were compared with those obtained through the recommendation given in the standard ABNT NBR 6123:1988 [2] for the dynamic structural analysis.

Assessment of buildings non-deterministic dynamic structural response when subjected to wind actions

“…The building is made of reinforced concrete elements and presents a modulus of elasticity equal to 32 GPa (E = 32 GPa), Poisson's ratio of 0.2 (ν = 0.2), specific weight equal to 25 kN/m 3 (ρ = 25 kN/m 3 ) and damping ratio of 0.02 (ξ = 2% [5]). On the other hand, the aerodynamic damping effect [12] was not considered, due to the high computational cost and the minimum impact on the results [13]. It is worth highlighting that the building structural model attends all requirements related to the ultimate and serviceability limit states recommended by the Brazilian design standard NBR 6118 [14].…”

“…𝑉𝑉 �( 𝑧𝑧, 𝑡𝑡) = ∑ � 2𝑆𝑆 𝑣𝑣 (𝑓𝑓 𝑖𝑖 )∆𝑓𝑓 𝑐𝑐𝑐𝑐𝑐𝑐(2𝜋𝜋𝑓𝑓 𝑖𝑖 𝑡𝑡 + 𝜃𝜃 𝑖𝑖 ) 𝑁𝑁 𝑖𝑖=1 (12) The fluctuating part of the wind velocity V � (t) is generated with random phase angles, and the amplitude of each harmonic is calculated based on the spectral density determined using the Kaimal spectrum [Equation 13], where fS(f) corresponds to the spectral density associated with the longitudinal component of the turbulence with frequency f. The term X is the dimensionless frequency and can be represented by Equation 14, and the term u * is the friction velocity, represented by Equation 15, where V � (Z) is the static part of the wind velocity at height Z, and K is the Karman constant. It should be emphasised that, according to the Kaimal power density spectrum, the building fundamental frequency determined by the modal analysis (see section 4) is in the range of higher energy transfer peaks associated with low natural frequencies (see Figure 13).…”

A method for along-wind vibration control of chimneys by tuning liners

“…(1). A damping ratio ξ of 0.01 is considered for the first two mode frequencies of the concrete cylinder [26]. The damping of the liners is ignored due to their low value and on the safe side.…”