Providing a Model for Assessment of Horizontal and Vertical Earthquake Effects on the Double-layer Barrel Vaults in Space Structures

In this study, the effect of place soil and seismic vulnerability has not been considered in determining the earthquake force, although all results have been based on scale accelerographs. Moreover, the importance of structures has not been rated based on small or large spans, decorative or structural structure and the effect of these cases is not considered. In this regard, double-layer barrel vaults have been studied and effect of horizontal and vertical seismic force on it reviewed and equations are presented in order to evaluate the equivalent static force of horizontal and vertical earthquake. Presented equations facilitate determining the equivalent static force due to earthquake for space structures, but they also have deficiencies which solving them can be useful for researchers who want to continue the way.


INTRODUCTION
The space structure is the one which has threedimensional behavior, so that, its general behavior can never be approximate by using one or more independent double-dimensional sets (Ishikawa and Kato, 1993).With this definition, a wide range of structures and even some of the previous brick arches and domes are considered as the space structures, but the purpose in this study is the specific threedimensional structures which usually have direct components with rigid or joint connections (Kato et al., 1997).A space structures can be considered as a structural system, which composes of linear components and these are placed in a way that are transferred three-dimensionally for many times (Kawaguchi, 1997).A space structures often has a form of flat or curved surface.Applying the least material, the space structures create the most rigid structures and they have ability to cover large spans without using the middle columns.In today world, the use of space structures for covering the large spans has been also developed (Maalek and Mohyeddin Kermani, 2002).Types of space structures are very various in terms of geometrical structures, type of material and behavior.Barrel vaults are one of the types of latticed space structures which are implemented as one layer or two.Due to the ability to cover the areas with large spans and making beautiful architecture, these structures have wide applications and are considered by architects and designers (Nooshin, 1998).Space barrel vaults are divided into one or multi-layer space barrel vaults (Ogawa et al., 2002).One-layer barrel vaults have rigid joints and the components work as three-dimensional bending beam; the multilayer barrel vaults are jointed and the function of components is in the form of threedimensional truss.In this study modeling of earthquake force exerted on the barrel vault and different types of space structures were surveyed.
Latticed space structures are tantamount to doublelayer barrel vaults based on the shape and position.In this study, the effect of earthquake on space structures has been evaluated.

DIFFERENT TYPES OF SPACE STRUCTURES
Flat lattices: It means the combination of a tetrahedral or polyhedral system with unit layers of lattice.Flat lattice composed of a planar unit which is connected with unit beams.Flat lattices can have one, two, three or even multiple layers, but they are widely used in the form of two layers (Saka and Taniguchi, 1997).Double-layer lattices consist of two parallel plates which are jointed together by elements.When the components in a double-layer lattice are elongated, three-layer lattices are used in order to prevent the risk of buckling and given that half of space structures costs is related to the joints, these type of structures are often non-economical.Another point, which should be considered in designing double-layer lattices and most of space structures, is that it is better for better distribution of force and making it tensile to design the columns inside the lattice and the column be connected to multiple nodes and located around the console for achieving the regular distribution (Sokol and Sumec, 2002).

Barrel vaults:
The barrel vault is a lattice which has curvature in a direction.This structure is used widely for covering the rectangular corridor surfaces and sometimes is without columns and is placed on the ledge of barrel vault which is attached to the fulcrum.Barrel vaults have the axis (Saka and Taniguchi, 1997).If the barrel vault has a layer, the joints are rigid.Barrel vault are often used in a combined form and the back beams play the role of combining the barrel vaults to each other.The point which should be considered in designing this type of structures is that the end of barrel vaults should be strong and this is reinforcement can be achieved by the beam, beam and column and sun-like shape.Appropriate design of each structure requires the correct prediction of forces which are imposed to the structure (Sadeghi, 2003).The force of earthquake is among these forces.Many regulations provide several approximate equations which estimate the equivalent earthquake force for building structures (Shear frames).Using these equations is on the basis of simple hypotheses which are not beneficial for such these structures in terms of geometric structure and structural behavior of space structures.The main objective of this study is to provide a model for evaluating the effects of horizontal and vertical earthquake on double-layer barrel vaults in space structures.

MODELING OF EARTHQUAKE FORCE EXERTED ON THE BARREL VAULT
Equivalent static earthquake forces on double-layer barrel vaults can be calculated horizontally and vertically.For instance, the horizontal effect of earthquake in this method is measured for barrel vault according to Eq. ( 1) by determining the basic shear for the barrel vault: The coefficient of earthquake horizontal force can be calculated by Eq. ( 2): In which, α is the constant factor and depends on the type of barrel vault fulcrum and SA (T 1 ) is the response acceleration of design range for the first mode of barrel vault vibration.In this method, distribution of horizontal seismic forces in height of barrel vaults is also according to triple Eq. ( 6).
In Research Part I, Part II by Sadeghi (2004a, b), various double-layer barrel vaults (with square context on a square) are considered with ratio of rise to span 0.15, 0.30 and 0.45 in order to obtain the base shear force.Two types of fulcrum conditions are considered for each of the barrel vault that is shown in Fig. 1.In this figure mode A and B are presented.Mode A: In this mode, the barrel vaults have the joint fulcrum only on two edges.Mode B: In addition to fulcrums of mode A, this mode has roller fulcrum in sub-nodes of arch in the beginning and at the end.In order extract the equivalent static force of earthquake, 12 accelero graphs with high PGA (Table 1) are exerted in base of

DISCUSSION AND CONCLUSION
Space structures are widely used in covering large spans.Latticed space structures are mainly from similar space structures.In addition, this family is equivalent to double-layer barrel vaults based on the shape and position.Study of dynamic and seismic behavior of these structures has been increased significantly in recent years.In this study, the effect of earthquake on space structures has been evaluated.
This study has used the similar modeling and the modeling by Sadeghi (2004b).Therefore, the results of this research are in line with the study by Sadeghi (2004b).Given the analyses carried out by Pushover method, Sadeghi (2003) has recommended that the coefficient of barrel vault behavior should be considered equal to the unit and based on the effect of earthquake load, the barrel vaults should be designed in the elastic forms.

:
If a lattice has curvature in two directions, it is called the Dome (Specifications for the Design and Construction of Space Trusses, 2001).The covering of a dome is probably part of a sphere or a cone or combined of several coverings.Domes are structures with high rigidity and are used for very large spans up to approximately 250 m.Dome height should be greater than 15% of base diameter of dome.

Fig. 1 :
Fig. 1: Context and fulcrum conditions of barrel vaults Vb = CH 0 ×W t (1) In which, CH 0 : The coefficient of earthquake horizontal force W t : The effective weight of whole barrel vault

FigFig. 3 :
Fig. 2: Leve mentioned nodes resp is extracted of related adding the coefficient determined shear of ea (Fig. 2) Eq CH 0 = In ord seismic fo without ne been linked Mode 1 w different ea CH 0 = In wh acceleratio mode of calculated response s available, the followi

Table 1 :
Selected earthquakes and their overall features