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Seismic Res onse of Barrel Vault Structure with3D-Panel Prefabricated S stem Usin DifferentT es of Seismic Anal ses

H. Chavoshi & H. KananipourGraduate M.Sc. Student in Structural Engineering, University of Science & Culture, Tehran,

IranA. MassumiAssistant Professor, Dept. of Civil Engrg., Faculty of Engineering, Tarbiat Moallem

University, Tehran, Iran

SUMMARY:In this study, comparison and surveying between different seismic stability analyses of barrel vault structure with

3D-Panel prefabricated system have been accomplished. For this structural system in addition to prefabricating,

some other structural advantages can be mentioned in two general cases: First, in structure principal modes, the

dome pattern of system has distributed the tension and compression stresses on its surface and maximumefficiency of the system of seismic and gravity load-bearing structure is made. On the other hand, because of

using three dimensional panels for structural shell, the weight and the thickness of the structure was reduced and

distancing of two membrane concretes from the neutral axis of section (-due to the existence of central poly

styrene layer-) created a noticeable stiffness. The present layout gathers all of the advantages above according to

the capability of the 3D-panel system to make various space shapes, whereas the other structural systems do not

have this capability to make simply different architectural sketches like dome and barrel vault. For the supposed

structure statically equivalent analysis, spectral analysis and time-history analysis are carried out by records of

some strong earthquake motions with rather high local magnitudes (i.e., M > 6.5). The results showed that for all

cases due to limiting of maximum compressive stress in thin shell concrete membrane to minimum allowable

tensile stress in concrete, the thickness of concrete membrane as the structural element considered desirable and

the structural situation is suitable for any increasing in the length and the height of special structure that has been

considered in this study as a sample.

Keywords: Barrel-vault structures, 3D-Panel system, Thin membrane concrete, Seismic stability analyses,

Industrial and modern construction technologies

1. INTRODUCTION

In the present industrial building & construction of the world, the usage of 3D-panel prefabricated

systems has been spread swiftly. Three dimensional panels can be used as the load-bearing elements in

box frames or the partition walls in ordinary structures. The buildings with 3D-panel systems have

many privileges such as reducing the human cost of work, waste of stuffs, control of construction

quality and reducing the construction time and dependence of it to the weather conditions. The three-

dimensional panels are light and ease in transportation due to nonentity of concrete membrane beforethe final installation in the site, whereas the difficulties and the expenses of elements transportation in

other prefabricated systems are not existed in this system. One of important advantages in this system

is completion of junctions after installation of panels in the site and before the shotcrete of them, this

processor cause to a uniform structure with confident conjunctions. So, it can be concluded that 3D-

panel system in a moderate manner in compare with on site and complete prefabricated systems has

the all advantages of prefabricated systems and in the other hand it has eliminated some deficiencies of

them.

The first justification of the space sketch of the model is surveyed by chavoshi, sharikian & Massumi.

In this paper the results of various seismic analyses on the sample model are compared. In this model

light 3D-panel shell element is considered as the gravity and lateral load-bearing structural element. It

should be mentioned that the cylindrical vault is a rudimentary pattern for the other available sketches

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and the shell conditions show that usage of the other patterns such as parabolic cross sections or the

different spans in the building is possible.

2. SHELL THEORIES

Shells are three-dimensional bodies bounded by two, relatively close, curved surfaces. The three-

dimensional equations of elasticity are complicated when written in curvilinear or shell coordinates.

Typically, researchers make simplifying assumptions for particular applications. Almost all shell

theories (thin and thick, deep and shallow) reduce the three-dimensional (3D) elasticity equations to

the two-dimensional (2D) representation. This is done usually by eliminating the coordinate normal to

the shell surface in the development of the shell equations. The accuracy of thin and thick shell

theories can be established if these theories are compared to the 3D theory of elasticity.

A summary of equations for laminated composite shells is made in this section. In particular, the

straindisplacement equations, the stressstrain equations and the equations of motion are described.

These equations and the associated boundary conditions constitute a complete set of shell theory

equations.

2.1.Three-dimensional elasticity theoryA shell is a three-dimensional body confined by two parallel (unless the thickness is varying) surfaces.

In general, the distance between those surfaces is small compared with other shell parameters. In this

section, the equations from the theory of 3D elasticity in curvilinear coordinates are presented. The

literature regarding vibrations of laminated shells using 3D elasticity theory will then be reviewed.

Consider a shell element of thickness h, radii of curvature Rand R(a radius of twist Ris not shown

here) (Fig. 2.1.). Assume that the deformation of the shell is small compared to the shell dimensions.

This assumption allows us to neglect non-linear terms in the subsequent derivation. It will also allow

us to refer the analysis to the original configuration of the shell. The strain displacement relations can

be written as:

Where , , z are the normal strains, R, Rare the radii of curvature and Ris the radius of twist. u,

v, w are the displacements at a point in the , and z directions, respectively and A, B are the Lame

parameters. , z, z are the in-plane and transverse shear strains, respectively and finally t is the

time parameter.

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Figure 2.1.Stresses in shell coordinates (free outer surfaces).

For the development of the constitutive relations, the laminated composite thin shells are assumed to

be composed of plies of unidirectional long fibers embedded in a matrix material such as epoxy resin.

On a macroscopic level, each layer may be regarded as being homogeneous and orthotropic. However,

the fibers of a typical layer may not be parallel to the coordinates in which the shell equations are

expressed. The stressstrain relationship for a typical nth lamina (typically called monoclinic) in a

laminated composite shell made of N laminas, is shown in Fig. 2.2, and given by Eqn. 2.2.:

Figure 2.2.Lamination parameters in shells.

(2.2)

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Where , ,z are the normal stresses in the , and z directions and , z,zare the in-plane and

transverse shear stresses, respectively. are the stiffness parameters for layer k and the otherparameters were explained in Eqn. 2.1.

The positive notations of the stresses are shown in Fig. 2.1. In order to develop a consistent set of

equations, the boundary conditions and the equations of motion will be derived using Hamiltonsprinciple. Substituting the equations for potential energy (U), external work (W) and kinetic energy

(T), performing the integration by parts, and setting the coefficients of the displacement variations

equal to zero, in a normal manner, yields the equations of motion:

(2.3)

Where q, q, qz are the body forces in the , and z directions, respectively and is the density per

unit volume. The other parameters were explained in Eqn. 2.1. and Eqn. 2.2.

The above equations do not depend on the shell material. Hamiltons principle will also yield

boundary terms that are consistent with the other equations (straindisplacement and equilibrium

relations). The boundary terms for z = constant are:

(2.4)where 0z, 0z and 0z are surface tractions and u

0, v

0 and w

0 are displacement functions at z =

constant. Similar results are obtained for the boundaries = constant and = constant. A three-

dimensional shell element has six surfaces. With three equations at each surface, a total of 18

equations can be obtained for a single-layered shell.

The above equations are valid for single-layered shells. To use 3D elasticity theory for multilayered

shells, each layer must be treated as an individual shell. Both displacements and stresses must be

continuous between each layer.

2.2.Thin-shell theoryIf the shell thickness is less than 1/20th of the wavelength of the deformation mode and/or radii of

curvature, a thin-shell theory, where shear deformation and rotary inertia are negligible, is generally

acceptable. Depending on various assumptions made during the derivation of the straindisplacement

relations, stressstrain relations, and the equilibrium equations, various thin shell theories can be

derived. Among the most common of these are Loves, Reissners, Naghdys, Sanders and Flugges

shell theories. All these theories were initially derived for isotropic shells and expanded later for

laminated composite shells by applying the appropriate integration through laminas, and stressstrain

relations. For very thin shells, the following additional assumptions simplify the shell equations and

their order.

The shell is thin such that the ratio of the thickness compared to any of the shells radii orany other shell parameter, i.e., width or length, is negligible when compared to unity.

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The normals to the middle surface remain straight and normal when the shell undergoesdeformation.

The first assumption assures that certain parameters in the shell equations (including the z/R) term

mentioned earlier in the thick shell theory can be neglected. Due to the second assumption, the shear

deformation can be neglected in the kinematic equations and this allows the in-plane displacement to

vary linearly through the shells thickness as given by:

(2.5)

Applying Kirchhoff hypothesis of neglecting shear deformation and the assumption that ez is

negligible, the stressstrain equations for an element of material in the kth lamina may be written as:

(2.6)where Qij are the elastic stiffness coefficients for the material. After calculating some mathematical

configurations, force and moment resultants will be obtained. Using Hamiltons principle and applying

boundary conditions affiliate to thin shells yield the equations of motion.

3. THE SEMI CYLINDRICAL SAMPLE ANALYSIS PROCESSOR

In this section a barrel vault structure sample with 3D-Panel system in a semi cylindrical form has

been conducted using the computer program SAP 2000. Gravity loads are applied to the structureregard to Iranian National Building Code for Structural Loadings: Part6 and seismic loads by

different methods are applied to the model that the details of these analyses will explained in part 3.2.

Figure 3.1.Finite elements model in the barrel vault sample

The model characteristics are mentioned as below:

According to the architectural plan the diameter of cylinder is seven meters and the length of itis 15 meters.

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The doorway and windows of building are voided in the finite elements model as thearchitectural plan.

The poly-styrene layer thickness of panel is about eight centimetres and a concrete layer withthree centimetres thickness is considered in both sides of it. The steel mesh are wires in square

shapes with eight centimetres lengths and three millimetres diameters that they are related to

each other by shear connectors through the central foam.(Fig. 3.2.)

Figure 3.2.Exhibition of different elements in 3D-Panel

3.1. Materials and elementcharacteristics in modelThe modulus of elasticity, compressive strength, Poissons ratio and unit weight of concrete are taken

as 8.58 GPa, 21.4 MPa, 0.2 and 2400 kg/m3, respectively. It should be mentioned that modulus of

elasticity for concrete is reduced to 40% of normal concrete as it circumstances during shotcrete, Also

the modulus of elasticity, compressive strength, Poissons ratio and unit weight of the central

polystyrene foam are taken as 3.0 MPa, 0.11 MPa, 0.37 and 15 kg/m3, respectively. For the steel mesh

ultimate tensile strength, yield stress, minimum reducing in area section, the modulus of elasticity,

compressive strength, Poissons ratio and unit weight are taken as 515 MPa, 450 MPa, 30%, 200GPa,

0.3 and 7850 kg/m3, respectively.

3.2. Gravity loading

The unit area weight of panel is about 173 kg/m2, so it conservatively considered 200 kg/m

2 in the

model, also the snow loading for buildings in the assumed city should be taken 150 kg/m2butas the

dome shape of sketch it is assumed in three phase with three reduction coefficient equal to 1, 0.66,

0.25:

1/3 top of barrel vault: 150 kg/m2 1/3 middle of barrel vault: 100 kg/m2 1/3 bottom of barrel vault: 40 kg/m2

3.3. Seismic loading

For the supposed structure statically equivalent, spectral and time-history analyses are carried out to

compare shell conditions after various analyses. First, statically equivalent analysis is carried out with

calculated earthquake factor equal to 0.22. Iranian Seismic Code is used to compute this factor designaccording to the sample circumstances. Then modal analysis is carried out and the fundamental

periods of structure are extracted as follows: 0.093s, 0.083s, 0.054s. Spectral analysis is accomplished

according to the fundamental periods of main modes and standard design spectrum at Iranian Seismic

Code. As the last analysis, five selected strong ground motion records are used for input excitation as

listed in Table 3.1. All of these excitations are recorded in a low to moderate distance from the

epicenter (less than 45 km) with rather high local magnitudes (i.e. M > 6). Due to the high intensities

demonstrated in the records, they are used directly without being normalized.

The stiffness proportional damping is applied on the structure in which the damping ratio for the

fundamental mode is selected as 2%.The fundamental frequency of the structure system and therefore,

the coefficient of the stiffness matrix of the model are 10.7251Hz and 0.0037,respectively.The

integration parameters of , and are taken -0.2, 0.36 and 0.7, respectively.

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Table 3.

Ea

1 Ch

2 Im

3 Ta

4 K

5 N

As sho

lateral d

the Iran

Percents

records

As sho

staticall

analyses

the door

mechani

.Strong gro

rthquake

i-Chi,Taiwan

perial Valley

bas 1978

be 1995

rthridge 199

n in results

rifts are neg

ian Seismic

, so the stru

Fig. 3.3).

Figur

n in Fig. 3.

equivalent

do not exc

way and wi

sms.

Figur

MaxDrift(Percent%)

MaxNormalStress(Kgf/cm2)

nd motion ch

Stat

1999 TC

1979 Bon

Tab

KJ

San

graphs, du

ligible and t

Code the

ture lateral

3.3.Maxim

. the maxim

loadings.

ed 25 kg/c

ndows area

3.4.Maxim

hi-Chi I

hi-Chi I

aracteristics

ion

-074

ds Corner

as-9101

A

ta Monica

to the do

he allowabl

maximum l

drifts are li

um nodal late

um normal

s can be s2

, also it s

and this de

m normal str

perial Ta

perial Ta

M PG

7.6

6.5

7.4

6.9

6.7

e geometry

limitations

teral drift

ited to allo

ral drifts of s

tresses in t

en in the g

hould be no

ficiency ca

esses in the s

bas Ko

Anal

bas Ko

Anal

(g)-L P

.35

.59

.84

.60

.37

of building

of Seismic

or this mo

able values

ell for differ

e shell are c

raph, the m

ted that thes

be improv

ell for differ

e Northri

sis

e Northri

sis

A(g)-T P

0.60

0.78

0.85

0.82

0.88

and lightne

odes are re

el is calcu

in all of an

nt analyses

ompared fo

ximum stre

e maximum

d by some

nt analyses

ge spectura

ge spectura

A(g)-V U

0.29

0.43

0.69

0.34

0.23

ss of 3D-pa

garded. Acc

lated equal

lyses and e

ethods

different d

sses among

values are

special perf

ethods

l Statically

equivalent

l Statically

equivalent

GS soil

C

C

C

B

B

nel shell,

ording to

to 0.875

rthquake

namic &

different

elated to

rmances

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As the concrete compressive strength () is considered equal to 210 kg/cm2 and also according to theequation 8.6.1 at (ACI 318-08) , the concrete tensile strength (fct) is calculatedequal to 25.7 kg/cm

2.Now, it can be concluded that for all analyses due to limiting of maximum

compressive stress in thin shell concrete membrane to minimum allowable tensile stress in concrete,

the thickness of concrete membrane as the structural element considered desirable (Chapter 19. ACI

318-08) and the structural situation is suitable for any increasing in the length and the height of specialstructure that has been considered in this study as a sample.

4. CONCLUSIONS

In this study, comparison and surveying between different seismic stability analyses of a barrel vault

structure (semi cylindrical) with 3D-Panel prefabricated load-bearing system have been accomplished.

Finite elements method is employed to simulate the shell sketch. To simplify the model, the effect of

foundation wasnt involved in the simulation but in other way to design tie beam (foundation) the

constraint reactions can be extracted from the program results.

As shown in final graphs, nodal lateral drifts of shells and various in plane stresses for differentanalyses method had sure safety factors and the structural situation is suitable for any modifying in

semi cylindrical architecture scheme .It should be mentioned that the semi cylindrical skeleton

construction is a rudimentary sketch for many various other plans, such as different parabolic cross

sections. Also to improve the inner space of building, some flat 3D-panels can be used from the

foundation level to arbitrary height of periphery walls and then the main arch structure will be stood

on it and it is obvious that every little modification in these designs need more observation about it.

REFERENCES

Chavoshi, H., Sharikian, K. and Massumi, A. (2012). Barrel vault structure with 3D-panel prefabricated

modern System. 9th

International Congress on Civil Engineering, Isfahan University of Technology,Isfahan, Iran.Code:11304.

Qatu, M.S. (2004). Vibration of laminated shells and plates. San Diego, CA: Elsevier.

Qatu, M.S., Sullivan, R.W. and Wang, W. (2010). Recent research advances on dynamic analysis of

composite shell. Composite Structures Journal,93, 14-31.

Ray, M.C. and Reddy, J.N. (2004). Optimal control of thin circular cylindrical laminated composite shells

using active constrained layer damping treatment. Smart Mater Struct,13, 64-72.

Librescu, L. and Hause, T. (2000). Recent developments in the modeling and behavior of advanced sandwich

constructions. a survey, Compos Struct,48, 1-17.

Iranian Code for Seismic Resistant Design of Buildings. (2005). Third ed., Building and Housing Research

Center, Tehran, Iran.Iranian National Building Code for Structural Loadings: Part6. (2006). Iranian office of collection and

development of building code, Tehran, Iran.

Building Code Requirements for Structural Concrete (ACI 318-08) and Commentary, an ACI standard

reported by American Concrete Institute committee 318, January 2008.