Study on equivalent static wind load on long-span roof based on response-related scale

Using several formulas of across-wind aerodynamic forces and aerodynamic damping of rectangular super-high-rise buildings with side ratios smaller than 2 proposed previously by the authors, across-wind equivalent static loads and responses of super-high-rise buildings are evaluated through a proper combination of resonant and background components. The resonant component is computed according to the power spectral density of the base moment and the aerodynamic damping. The background component, whose vertical distribution is derived from background moment responses at different heights and then expressed as a cubic equation of the relative height, is computed using the base moment coefficients. Furthermore, comparisons are made for the equivalent static wind loads and responses of a hypothetical typical building between the present method and the AIJ (1996) method, which indicate the applicability of the present method. Finally, the effects of background component and aerodynamic damping on the equivalent wind loads and responses are also discussed.

Gust response envelope approach to the equivalent static wind load for large-span grandstand roofs

This study aimed to develop an approach to accurately predict the wind models and wind effects of large wind turbines. The wind-induced vibration characteristics of a 5 MW tower-blade coupled wind turbine system have been investigated in this paper. First, the blade-tower integration model was established, which included blades, nacelle, tower and the base of the wind turbine system. The harmonic superposition method and modified blade element momentum theory were then applied to simulate the fluctuating wind field for the rotor blades and tower. Finally, wind-induced responses and equivalent static wind loads (ESWL) of the system were studied based on the modified consistent coupling method, which took into account coupling effects of resonant modes, cross terms of resonant and background responses. Furthermore, useful suggestions were proposed to instruct the wind resistance design of large wind turbines. Based on obtained results, it is shown from the obtained results that wind-induced responses and ESWL were characterized with complicated modal responses, multi-mode coupling effects, and multiple equivalent objectives. Compared with the background component, the resonant component made more contribution to wind-induced responses and equivalent static wind loads at the middle-upper part of the tower and blades, and cross terms between background and resonant components affected the total fluctuation responses, while the background responses were similar with the resonant responses at the bottom of tower.

Investigation on wind-induced aero-elastic effects of tall buildings by wind tunnel test using a bi-axial forced vibration device

Wind-induced response behavior of long-span roof structures is very complicated, showing significant contributions of multiple vibration modes. The largest load effects in a huge number of members should be considered for the sake of the equivalent static wind loads (ESWLs). Studies on essential matters and necessary conditions of the universal ESWLs are discussed. An efficient method for universal ESWLs on long-span roof structures is proposed. The generalized resuming forces including both the external wind loads and inertial forces are defined. Then, the universal ESWLs are given by a combination of eigenmodes calculated by proper orthogonal decomposition (POD) analysis. Firstly, the least squares method is applied to a matrix of eigenmodes by using the influence function. Then, the universal ESWLs distribution is obtained which reproduces the largest load effects simultaneously. Secondly, by choosing the eigenmodes of generalized resuming forces as the basic loading distribution vectors, this method becomes efficient. Meanwhile, by using the constraint equations, the universal ESWLs becomes reasonable. Finally, reproduced largest load effects by load-response-correlation (LRC) ESWLs and universal ESWLs are compared with the actual largest load effects obtained by the time domain response analysis for a long-span roof structure. The results demonstrate the feasibility and usefulness of the proposed universal ESWLs method.

To lightweight the engine connecting rod, and ensure it to meet the performance requirements, static equivalent load method was studied in the paper. Firstly, Connecting rod stress distribution was analyzed. Then, Multi-body dynamics model was established for the transient analysis, and connecting rod maximum stress was gotten when the engine working. Finally, Using equivalent static load method, the dynamic load was converted to an equivalent static load. And as the boundary conditions, it was used to the optimization process to optimize the shape of connecting rod. The weight of lightweight connecting rod was reduced by 9.5%. Under the condition of satisfying the stress, the purpose of the connecting rod optimization was reached.

The tuned liquid damper (TLD) is a proven and an increasingly popular auxiliary device for mitigating the dynamic effects induced by wind loading on tall buildings. As buildings become taller, lighter, and more flexible, there is a greater contribution from the dynamic component. The most reliable tool for assessing the dynamic component is wind tunnel testing. A boundary layer wind tunnel is capable of accurately calculating an equivalent static wind load (ESWL) acting on a building. The current study investigates the reduction in the ESWL of a lateral-torsional coupled building with a TLD system installed. The building is sensitive to torsion in the first two vibration modes. The current investigation uses three unique multi-modal TLD systems designed specifically for a lateral-torsional coupled building. The building ESWL is evaluated with the TLD systems using measurements from tests conducted at the Boundary Layer Wind Tunnel Laboratory at Western University.

Failure analysis and curvature-based failure criterion of super large cooling tower under strong equivalent static wind load

A novel probabilistic approach is presented for estimating the equivalent static wind loads that produce a static response of the structure, which is equivalent in a probabilistic sense, to the extreme dynamic responses due to the unsteady pressure random field induced by the wind. This approach has especially been developed for complex structures (such as stadium roofs) for which the unsteady pressure field is measured in a boundary layer wind tunnel with a turbulent incident flow. The proposed method deals with the non-Gaussian nature of the unsteady pressure random field and presents a model that yields a good representation of both the quasi-static part and the dynamical part of the structural responses. The proposed approach is experimentally validated with a relatively simple application and is then applied to a stadium roof structure for which experimental measurements of unsteady pressures have been performed in boundary layer wind tunnel.

In this study, an efficient topology optimization method under crash loads is proposed by combining the equivalent static loads with a model order reduction method, which is referred as the reduced model–based equivalent static loads method for nonlinear dynamic response topology optimization method. Considering that some parts of the vehicle experience large nonlinear deformations, whereas others exhibit only small linear deformations in a vehicle crash scenario, the linear and nonlinear behavior parts are identified and the whole model of the complete structure is divided into nonlinear and linear sub-models. At each cycle, the model order reduction method is used in the linear sub-model during crash analysis to solve the low-density-elements-induced mesh distortion problem and accelerate this process. In the linear static topology optimization, the nonlinear sub-model that was initially used to describe the nonlinear behavior part is linearized by the equivalent static loads method and then reduced by the Guyan reduction method. Then, the reduced equivalent static load model is assembled into the linear sub-model that is defined as the design space to formulate a reduced topology optimization model of the complete structure and the reduced equivalent static loads that only act on master degrees of freedom are calculated. Finally, the linear static topology optimization is performed based on the reduced topology optimization model with the reduced equivalent static loads to enhance the efficiency and improve the numerical stability. The process is repeated until the convergence criterion is satisfied. The effectiveness of the proposed method is demonstrated by investing a numerical example. The results show that the proposed method provides a feasible strategy for the topology optimization under crash loads, which can effectively improve the numerical stability and convergence.

SummaryHigh‐frequency force balance test is a major technical means to evaluate the wind effect of super high‐rise buildings. Most super high‐rise buildings have the characteristic that the first two‐order modal frequencies are close, and thus, considerable modal coupling effects (MCEs) may occur under wind load. For a balance model system (BMS), MCEs increase the difficulty of correcting aerodynamic distortion signals. For the wind‐induced vibration analysis of a structural system (PSS), the calculation results of the wind‐induced response and the equivalent static wind load (ESWL) may be significantly affected without considering MCE. Based on the above‐mentioned signal distortion of BMS and the modal coupling problem of PSS, this study proposes a wind‐induced vibration calculation method for the two coupled systems (BMS and PSS). The method uses the second‐order blind identification technique based on complex modal theory and the Bayesian spectral density method considering full aerodynamic characteristics to achieve effective correction of the distortion signal in BMS. In addition, it deduces the calculation method of the wind‐induced response and ESWL considering the three‐dimensional coupled vibration of a super high‐rise building. The wind effect calculation results of a 528‐m super high‐rise building confirm the necessity and effectiveness of the proposed method.

joined-wing configuration that was published by Wolkovich in 1986 has been studied by many researchers (Wolkovich, J., The Joined-Wing: An Overview, Journal of Aircraft, Vol. 23, No. 3, 1986, pp. 161―178. doi: 10.2514/3.45285). Thejoined-wing airplane is defined as an airplane that incorporates tandem wings arranged to form diamond shapes from both the top and front views. joined wing can lead to increased aerodynamic performances as well as a reduction in the structural weight. However, the joined wing has high geometric nonlinearity under the gust load. gust load acts as a dynamic load. Therefore, nonlinear dynamic (transient) behavior of the joined wing should be considered in structural optimization. In previous research, linear dynamic response optimization and nonlinear static response optimization were performed. It is well known that conventional nonlinear dynamic response optimization is extremely expensive. Therefore, in this research, nonlinear dynamic response optimization of a joined wing is carried out by using equivalent static loads. concept of equivalent static loads is expanded and newly proposed for nonlinear dynamic response optimization. Equivalent static loads are the load sets that generate the same response field in linear static analysis as that in nonlinear dynamic analysis. Therefore, nonlinear dynamic response optimization can be conducted by repeated use of linear response optimization. For the verification of efficiency of the proposed method, a simple nonlinear dynamic response optimization problem is introduced. problem is solved by using both the equivalent static loads method and the conventional method with sensitivity analysis using the finite difference method. procedure for nonlinear dynamic response optimization of a joined wing using equivalent static loads is explained, and the optimum results are discussed.

With the development of construction technology and material, more and more super high-rise buildings will be constructed in the future. In a specific metropolitan area, super high-rise building with various cross-section and high side ratio have to been designed and constructed due to the size limitation of construction site. This kind of building is also very prone to wind excitations. In this research, wind tunnel tests for a practical case of this kind of building with surrounding buildings were carried out in atmospheric boundary wind tunnel. Equivalent static wind loads (ESWLs), wind-induced responses and wind load distribution on the building were analyzed. In particular, the base overturning moment along the axis with weak lateral stiffness were investigated for bearing capacity limit state design of the building. The results demonstrate that the maximum value of wind-induced base overturning moments and acceleration responses appears at 60° or 330° wind directions instead of the orthogonal wind direction, and the aerodynamic interference of surrounding buildings affects the wind pressure distribution on facades of the building. These results and conclusion may be helpful to wind-resistant design of super high-rise buildings with high side ratio.

Dome structures are known to have good seismic resistance. However, the Indonesian National Standard (SNI) does not extensively discuss the earthquake loading methods that can be used as references in designing dome structure elements. This study aims to identify the most appropriate earthquake loading method for buildings with a dome shape. Several earthquake loading methods are compared, including equivalent static analysis, spectral response, and time history. A case study is used, involving a dome structure with a span of 60 meters, a height of 30 meters, and made of A36 steel. The earthquake source location is taken from Denpasar, Bali. The analysis includes base shear, deformation comparison, and internal forces for all three loading methods. The results show differences in structural responses between the equivalent static, response spectrum, and time history methods. The response spectrum method is considered more suitable for dome structure modeling in terms of safety, while the equivalent static method is more appropriate for practical considerations and ease of design.

Wind resistant size optimization of geometrically nonlinear lattice structures using a modified optimality criterion method