Volume 19, Issue 1 (2019)
MCEJ 2019, 19(1): 91-103 |
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Haji kazemi H, Sharifian M, Sharifian M. Approximate Method for Seismic Analysis of Double-Layer Grids. MCEJ 2019; 19 (1) :91-103
URL: http://mcej.modares.ac.ir/article-16-14532-en.html
URL: http://mcej.modares.ac.ir/article-16-14532-en.html
1- Civil Engineering Department, Ferdowsi University of Mashhad
2- Civil Engineering Department, Quchan University of Technology , m.sharifian@qiet.ac.ir
3- Civil Engineering Department, Quchan University of Technology
2- Civil Engineering Department, Quchan University of Technology , m.sharifian@qiet.ac.ir
3- Civil Engineering Department, Quchan University of Technology
Abstract: (6178 Views)
The dynamic response of the double-layer girds (a kind of space trusses) can be determined by means of the software based on the finite element method. However, it is always needed the approximate techniques by which one can easily and quickly obtain the suitable estimation of the dynamic behavior of the structures. This need may be caused by: 1- providing an appropriate estimation in the first stage of designing the members, and 2- verification of the results of the computer programs.
In this study, an approximate method is suggested for seismic analyses of the double-layer grids with the spatial square on square layout, the square or rectangular plan and simple supports around the structure. The method is on the basis of the simulation of double-layer grid to the equivalent beam and plate. Here, the smallest circular frequency of the vertical vibration is computed by using Rayleigh’s method. In addition, the seismic forces caused by the vertical acceleration of the earthquake are evaluated by employing the equations of the dynamics of the structures and estimating the shape function of the first mode of the vertical vibration. There are the deflections of the structural nodes in the achieved equation for estimating the circular frequency; therefore, an initial estimation for the sizes of the members of the double-layer gird is required. In fact, since the weight of the structure should be considered in evaluating the applied loads, an approximate design must be performed. For this purpose, a step by step technique is suggested based on the AISC Specification to initially design the structure. In addition, the assessment of the deflection of the double-layer girds is done based on the uniformly distributed loads and non-uniformly distributed loads.
Finally, to assess the suggested approximate method, 21 models of the double-layer grids with the spatial square on square layout are considered. These models have the horizontal and diagonal (web) members with the equal lengths. The supports of the double-layer girds are simple. The bays have 30 to 60 m with the step of 5 m and the number of 10, 12 and 14 horizontal members along the span. In order to analyze and design the models, the members are considered to be connected to each other as bending free connections. The spectrum analysis is done to take into account the seismic effects. Also, SAP2000 is used to analyze and design the models in question, and the results achieved by this software are considered as exact outcomes. On the other hand, the models are analyze by the suggested approximate method and the obtained results including frequencies, seismic vertical forces of the members of the models are compared with the exact outcomes in diagrams. The findings show that the proposed method can be evaluated the dynamic properties of the double-layer girds with a suitable precision which prove the robustness of the derived scheme. In fact, the maximum error in estimating the frequency is about 15%, and 12% if it is considered the variation of the weight of the double-layer girds and if it is not considered, respectively. Furthermore, the comparison of the achieved forces of the members between the exact and approximate results is revealed that the maximum error is about 11%, which is a good estimation for an approximate method.
In this study, an approximate method is suggested for seismic analyses of the double-layer grids with the spatial square on square layout, the square or rectangular plan and simple supports around the structure. The method is on the basis of the simulation of double-layer grid to the equivalent beam and plate. Here, the smallest circular frequency of the vertical vibration is computed by using Rayleigh’s method. In addition, the seismic forces caused by the vertical acceleration of the earthquake are evaluated by employing the equations of the dynamics of the structures and estimating the shape function of the first mode of the vertical vibration. There are the deflections of the structural nodes in the achieved equation for estimating the circular frequency; therefore, an initial estimation for the sizes of the members of the double-layer gird is required. In fact, since the weight of the structure should be considered in evaluating the applied loads, an approximate design must be performed. For this purpose, a step by step technique is suggested based on the AISC Specification to initially design the structure. In addition, the assessment of the deflection of the double-layer girds is done based on the uniformly distributed loads and non-uniformly distributed loads.
Finally, to assess the suggested approximate method, 21 models of the double-layer grids with the spatial square on square layout are considered. These models have the horizontal and diagonal (web) members with the equal lengths. The supports of the double-layer girds are simple. The bays have 30 to 60 m with the step of 5 m and the number of 10, 12 and 14 horizontal members along the span. In order to analyze and design the models, the members are considered to be connected to each other as bending free connections. The spectrum analysis is done to take into account the seismic effects. Also, SAP2000 is used to analyze and design the models in question, and the results achieved by this software are considered as exact outcomes. On the other hand, the models are analyze by the suggested approximate method and the obtained results including frequencies, seismic vertical forces of the members of the models are compared with the exact outcomes in diagrams. The findings show that the proposed method can be evaluated the dynamic properties of the double-layer girds with a suitable precision which prove the robustness of the derived scheme. In fact, the maximum error in estimating the frequency is about 15%, and 12% if it is considered the variation of the weight of the double-layer girds and if it is not considered, respectively. Furthermore, the comparison of the achieved forces of the members between the exact and approximate results is revealed that the maximum error is about 11%, which is a good estimation for an approximate method.
Article Type: Original Research |
Subject:
Earthquake
Received: 2017/10/29 | Accepted: 2019/05/22 | Published: 2019/05/15
Received: 2017/10/29 | Accepted: 2019/05/22 | Published: 2019/05/15
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