• Journal of Korean Association for Spatial Structures
• /
• v.4 no.4 s.14
• /
• pp.65-76
• /
• 2004

Walking loads are usually considered as nodal loads in the finite element vibration analysis of structures subjected to walking loads. Since most of the walking loads act on elements not nodes, the walking loads applied on the elements should be converted to the equivalent nodal walking loads. This paper begins with measuring walking loads by using a force plate equipped with load cells and investigates the characteristics of the walking loads with various walking rates. It is found that the walking loads are more affected by walking rates than other parameters such as pedestrian weight, type of footwear, surface condition of floor etc. The measured walking loads are used as input loads for a finite element model of walking induced vibration. Finally, this paper proposes the equivalent nodal walking loads that are converted from the walking loads acting on elements based on finite element shape functions. And the proposed equivalent walking loads are proved to be applicable for efficient analysis of floor vibration induced by walking loads.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.24 no.8 s.179
• /
• pp.1949-1957
• /
• 2000

All the loads in the real world act dynamically on structures. Since dynamic loads are extremely difficult to handle in analysis and design, static loads are utilized with dynamic factors. The dyna mic factors are generally determined based on experiences. Therefore, the static loads can cause problems in precise analysis and design. An analytical method based on modal analysis has been proposed for the transformation of dynamic loads into equivalent static load sets. Equivalent static load sets are calculated to generate an identical displacement field in a structure with that from dynamic loads at a certain time. The process is derived and evaluated mathematically. The method is verified through numerical tests. Various characteristics are identified to match the dynamic and the static behaviors. For example, the opposite direction of a dynamic load should be considered due to the vibration response. A dynamic bad is transformed to multiple equivalent static loads according to the number of the critical times. The places of the equivalent static load can be different from those of the dynamic load. An optimization method is defined to use the equivalent static loads. The developed optimization process has the same effect as the dynamic optimization which uses the dynamic loads directly. Standard examples are solved and the results are discussed

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.30 no.1 s.244
• /
• pp.66-75
• /
• 2006

Nonlinear response structural optimization using equivalent static loads (NROESL) has been proposed. Nonlinear response optimization is solved by sequential linear response optimization with equivalent static loads which are generated from the nonlinear responses and linear stiffness matrix. The linear stiffness matrix should be obtained in NROESL, and this process can be fairly difficult for some applications. Proportional transformation of loads (PTL) is proposed to overcome the difficulties. Equivalent static loads are obtained by PTL. It is the same as NROESL except for the process of calculating equivalent static loads. PTL is developed for large-scale probems. First, linear and nonlinear responses are evaluated from linear and nonlinear analyses, respectively. At a DOF of the finite element method, the ratio of the two responses is calculated and an equivalent static load is made by multiplying the ratio and the loads for linear analysis. Therefore, the mumber of the equivalent static loads is as many as that of DOF's and an equivalent static load is used with the reponse for the corresponding DOF in the optimization process. All the equivalent static loads are used as multiple loading conditions during linear response optimization. The process iterates until it converges. Examples are solved by using the proposed method and the results are compared with conventional methods.

• Wind and Structures
• /
• v.20 no.1
• /
• pp.95-115
• /
• 2015

Wind effects on roofs are usually considered by equivalent static wind loads based on the equivalence of displacement or internal force for structural design. However, for large-span spatial structures that are prone to dynamic instability under strong winds, such equivalent static wind loads may be inapplicable. The dynamic stability of spatial structures under unsteady wind forces is therefore studied in this paper. A new concept and its corresponding method for dynamic instability-aimed equivalent static wind loads are proposed for structural engineers. The method is applied in the dynamic stability design of an actual double-layer cylindrical reticulated shell under wind actions. An experimental-numerical method is adopted to study the dynamic stability of the shell and the dynamic instability originating from critical wind velocity. The dynamic instability-aimed equivalent static wind loads of the shell are obtained.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2007.04a
• /
• pp.321-326
• /
• 2007

The joined-wing is a new concept of the airplane wing. The fore-wing and the aft-wing arc joined together in the joined-wing. The range and loiter are longer than those of a conventional wing. The joined-wing can lead to increased aerodynamic performances and reduction of the structural weight. The structural behavior of the joined-wing has a high geometric nonlinearity according to the external loads. The gust loads are the most critical loading conditions in the structural design of the joined-wing. The nonlinear behavior should be considered in the optimization of the joined-wing. It is well known that conventional nonlinear response optimization is extremely expensive: therefore, the conventional method is almost impossible to use in large scale structures such as the joined-wing. In this research, geometric nonlinear response structural optimization is carried out using equivalent loads. Equivalent loads are the load sets which generate the same response field in linear analysis as that from nonlinear analysis. In the equivalent loads method, the external loads are transformed to the equivalent loads (EL) for linear static analysis, and linear response optimization is carried out based on the EL.

• Proceedings of the Korea Concrete Institute Conference
• /
• 2006.11a
• /
• pp.369-372
• /
• 2006

Flat plate slab systems have been commonly used as a gravity force resisting systems, which should be constructed with lateral force resisting systems such as shear walls and moment resisting frame. ACI 318(2005) allows the Direct design method, the equivalent frame method (ACI-EFM) under gravity loads and the finite-element models, effective beam width models and equivalent frame models under lateral loads. ACI-EFM can be used for gravity loads as well as lateral loads analysis. But the method may not predict the behavior of flat plate slabs under lateral loads. Thus Previous study developed a Modified equivalent frame method(Modified-EFM) which could give more precise answer for flat plate slab under lateral loads. This study is to verified the accuracy of a Modified-EFM under combined lateral and gravity loads. The accuracy of this model is verified by comparing the results using the Modified-EFM with the results of finite element analysis. For this purpose, 7 story building is considered. The analysis results of other existing models are included. The analysis results show that Modified-EFM produces comparable drift and slab internal moments with those obtained from finite element analysis.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.31 no.11
• /
• pp.1059-1068
• /
• 2007

Nonlinear response structural optimization is performed using equivalent loads (NROEL). Nonlinear response optimization is extremely cost because many nonlinear analyses are required. In NROEL, the external loads are transformed to the equivalent loads (EL) for linear static analysis and linear response optimization is carried out based on the EL in a cyclic manner until the convergence criteria are satisfied. EL is the load set which generates the same response field of linear analysis as that of nonlinear analysis. The primitive from of theory has been published. In this research, the theory is investigated with large scale example problems. Four examples are solved by using NROEL. Conventional optimization with sensitivity analysis using the finite difference method (FDM) is also applied to the same examples. Moreover, response surface optimization method is applied to the last two examples. The results of the optimizations are compared. In nonlinear response optimization of large scale problems, hundreds (or even thousands) of nonlinear analyses are expected to satisfy the convergence criteria. However, in nonlinear response optimization using equivalent loads, only tens of nonlinear analyses are required. The results are discussed and the usefulness of NROEL is presented.

• Structural Engineering and Mechanics
• /
• v.9 no.3
• /
• pp.305-321
• /
• 2000

This paper develops a simplified, but effective, algorithm in obtaining critical slab design moments for parking garages. Maintaining the uniformly distributed load concept generally adopted in the design of building structures, this paper also introduces the equivalent vehicle load factors, which can simulate the vehicle load effects without taking additional sophisticated numerical analyses. After choosing a standard design vehicle of 2.4 tons through the investigation of small to medium vehicles made in Korea, finite element analyses for concentrated wheel loads were conducted by referring to the influence surfaces. Based on the obtained member forces, we determined the equivalent vehicle load factors for slabs, which represent the ratios for forces under vehicle loads to these under uniformly distributed loads. In addition, the relationships between the equivalent vehicle load factors and sectional dimensions were also established by regression, and then used to obtain the proper design moments by vehicle loads. The member forces calculated by the proposed method are compared with the results of four different approaches mentioned in current design codes, with the objective to establish the relative efficiencies of the proposed method.

• Wind and Structures
• /
• v.19 no.5
• /
• pp.565-583
• /
• 2014

Using synchronous surface pressures from the wind tunnel test, the three dimensional wind load models of high-rise buildings are established. Furthermore, the internal force responses of symmetric high-rise buildings in along-wind, across-wind and torsional directions are evaluated based on mode acceleration method, which expresses the restoring force as the summation of quasi-static force and inertia force components. Accordingly the calculation methods of equivalent static wind loads, in which the contributions of the higher modes can be considered, of symmetric high-rise buildings in along-wind, across-wind and torsional directions are deduced based on internal forces equivalence. Finally the equivalent static wind loads of an actual symmetric high-rise building are obtained by this method, and compared with the along-wind equivalent static wind loads obtained by China National Standard.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.29 no.8 s.239
• /
• pp.1051-1060
• /
• 2005

Nonlinear Response Optimization using Equivalent Static Loads (NROESL) method/algorithm is proposed to perform optimization of non-linear response structures. The conventional method spends most of the total design time on nonlinear analysis. The NROESL algorithm makes the equivalent static load cases for each response and repeatedly performs linear response optimization and uses them as multiple loading conditions. The equivalent static loads are defined as the loads in the linear analysis, which generates the same response field as those in non-linear analysis. The algorithm is validated for the convergence and the optimality. The proposed algorithm is applied to a simple mathematical problem to verify the convergence and the optimality.