ANALYSIS OF MULTI CYLINDRICAL SHELLS ADAPTED WITH RETAINING WALLS

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1 IJAS 6 () August 0.arpapress.com/oumes/o6Issue/IJAS_6 5.pdf ANALYSIS OF MULTI CYLINDICAL SHELLS ADATED WITH ETAINING WALLS Ai Majidpourkhoei Technica and ocationa University, Tehran, Iran Emai: majidpour@eittc.ac.ir ABSTACT etaining as are used to retain earth or other materias hich have the tendency to side and repose at a particuar incination. They provide atera support to the embankment or other materias in order to hod them in a vertica position. As against equa forces shes are ess thick in comparison ith fat sabs, their appication is economica regarding consumptive materias, so in this research in order to reduce consumptive materias, muti cyindrica shes are adapted ith retaining as and cacuation and anaysis of one kind of ne ightened retaining a is proposed. To anayze she structures, there are different theories. The appication of these theories depends on geometrica shape, she quaity, she usage, boundary condition and enforced oads. To anayze and cacuate ightened she retaining a, equations are required hich shoud both present the mechanica behavior of the she ith required eactness and aso be sovabe mathematicay. To attain this goa, the method proposed in this research can be appied. In soving the probem formed of muti cyindrica she ith sabs, engineering mechanics combined principes are used and the equations of bending theory of cyindrica she are adapted ith retaining as. Generay, in this paper the anaysis method of ightened retaining as consisted of muti cyindrica shes are presented. Keyords: Muti cyindrica shes, Lightened retaining a, She retaining a.. INTODUCTION etaining as are structures used to provide stabiity for earth or other materia here conditions disao the mass to assume its natura sope and are commony used to hod back or support soi banks coa or ore pies, and ater. etaining as aso have appications in buidings and bridges such as basement, foundation a, bridge abutment etc. etaining as must be of adequate proportions to resist overturning (or ecessive titing) and siding as e as being structuray adequate. The anaysis and computation of a ne kind of structura design of ightened retaining a is presented in this paper based on design factors resuted from theoretica researches about the previous retaining as and their ightening methods. As figure iustrates the retaining as resuted i be consideraby economica regarding consumption of materia. In other ords, for front bearing eement of retaining a, muti cyindrica shes and for base eement (foundation), fat sab are taken into consideration. As mentioned, for front bearing eement against soi pressure, muti cyindrica concrete she is used instead of fat concrete sab because shes are more suitabe than fat sabs since they are thinner than fat sabs hen facing equa pressures, so their use is more economica regarding materia consumption. Using shes instead of fat sabs eads to 5 to 0 percent saving in materia usage [, ]. Anayzing the structure of shes is often based on to distinct theories hich are idey used. First: membrane theory, a membrane either fat or bent is considered as a body that has the same she shape or to-dimension feibe she and can resist pressure too. Second: bending theory incuding feure effects [, 4]. Membrane theory can t present an appropriate soution in a rea and practica conditions of changing shape. This theory can not either predict stress state in borders and aso in other specific regions. By appying bending theory, considering membrane forces, shearing forces, and enforced moments to she structure these eaknesses can be compensated [5, 6]. In this essay e i cacuate and adapt bending theories of cyindrica shes ith retaining as. The materias and resuts of this research i be imited to cyindrica shes the profie of hich is semicirce or circuar arch. 74

structure. Considering the generaities of structure and the reation of main she ith other eements is one of the important considerations in she structure designing.

2 IJAS 6 () August 0 Majidpourkhoei Anaysis of Muti Cyindrica Shes Figure. Muti cyindrica she retaining a.. ANALYZE AND CALCULATE LIGHTENED SHELL ETAINING WALL One of the main procedures reated to designing of she structure is the seection of geometrica shape and force transfer system design by she structure. Considering the generaities of structure and the reation of main she ith other eements is one of the important considerations in she structure designing. This is important because of behavior, baance and genera stabiity of structure specificay the performance of structure against forces. These points are aso considered in proposed structure for retaining a. According to soi atera force theories, a she i be infuenced by a trianguar oad resuted from soi active pressure (Figure ). Aso genera proportions (Measures) of proposed retaining a is regarded the same as figure. The connection of a she ith base sab is assumed rigid. Aso the base sab is considered far thicker than cyindrica shes. Further the rigidity of base sab feure is considered much. The inkage pace of cyindrica she ith base sab against torsion has much rigidity. Considering a these factors, the inkage pace of base sab ith cyindrica shes is rigid and restrained. Figure. Soi active pressure. 75

3 IJAS 6 () August 0 Majidpourkhoei Anaysis of Muti Cyindrica Shes Figure. Tentative design dimensions for a muti cyindrica she retaining a. Figure 4. arameters of muti cyindrica she retaining a. 76

4 IJAS 6 () August 0 Majidpourkhoei Anaysis of Muti Cyindrica Shes 77 In this section, the suggested cyindrica she retaining a ithout counterfort in cassica ay cacuated, in the net part, both forms, ith and ithout counterfort she retaining as, have been cacuated through finite eement method. Were aso appied for the moment anaysis of cyindrica shes. It is convenient to rite this system of equations in the matri form: L U g () Where: L, U u, Eh g And eements of the differentia matri L are:,, a, a ) ( a Where:, h a We obtain the fooing stress resutant-and stress coupes-dispacements reations for cyindrica shes: ) ( u Eh N, u Eh N ) ( () ) ( D M, ) ( D M () Where: ) ( Eh D Boundary condition is regarded as foos: 0 u 0 0 M M N N 0 0, 0, 0 0, 0, 0 (4) 0

Aso: k H 0, 0, 0 0 0 0 k, 0, 0 0 0 k Therefore the computation of eements of retaining a by appying the fooing differentia equations and considering border and inkage condition is done: 0 (6) a a a a

5 Aso: k H 0, 0, k, 0, k Therefore the computation of eements of retaining a by appying the fooing differentia equations and considering border and inkage condition is done: 0 (6) a a a a ( ) 0 k The soving of main differentia equation of the bending theory of muti cyindrica shes by considering accepted border conditions is seected in the net part through finite eement method. So the probem of combining base sab ith muti cyindrica shes are soved. In the net part, dispacement and interna forces created in cyindrica shes are cacuated through finite eement method by using specific instructions [7, 8, 9, 0, ].. NUMEICAL METHOD OF SOLING OBLEM Numerica eampes of soving probem by choosing numerica vaues for physica and geometrica parameters of cyindrica shes are made. The numerica methods, usuay the finite eement method, discussed in this section (ANSYS computer program as shon in Figure 5). Computations are represented for the fooing figure geometrica quantities (Figure 6). The shes thickness are determined as foos in case cyindrica shes are thin: (5) (7) (8) t= 50 H to 0 H, tmin. = 50 mm Figure 5. Structure eements for the finite eement method (ith and ithout counterfort she retaining as). 78

6 Figure 6. Geometrica parameters of cyindrica she retaining a. Figure 7. Dispacement of cyindrica she retaining a by the method of finite eement(ith and ithout counterfort she retaining as). 79

7 Figure 8. Stress of cyindrica she retaining a by the method of finite eement (ith and ithout counterfort she retaining as). Figure 9. Defection of cyindrica she retaining a by the method of finite eement (ith and ithout counterfort she retaining as). Based on this point the amount of bending moment (M Y ) and norma forces (N Ө ) created in the fooing tabe is presented: Tabe. Norma forces and bending moment of counterfort she retaining a. Y (m) N Ө (Kg/m) M Y (Kg-m/m) In this ay the forces resuted from ightened retaining as are cacuated. The reactions resuted from earth fiing of retaining a is aso cacuated on the base of specific reations resuted from materia strength [,, 4]. Here M is the bending moment resuted from eecuted oads effect on retaining 80

8 a that is from center of gravity of retaining a; G is the soi gravity, q 0 the effect of effective active soi on retaining a, b the height of retaining a, b the idth of base sab, A the area of base sab to the ith of meter, W resistant moment [,, 4]. G The genera stabiity of ightened she retaining as are studied. M ma (9) A W min q0b G. b M (0) 6 6. b A. b, W () 6 5. CONCLUSION The resuts of this research are:. Studying the amounts resuted for consumptive concrete voume of gravity retaining as and ightened she retaining a sho that the use of counterfort she retaining as are consideraby economica in consumption of concrete and ead to about 70-75% in comparison ith concrete gravity retaining as. Aso, the use of counterfort she retaining as are consideraby economica in consumption of concrete and ead to about 7-0% in comparison ith concrete cantiever retaining as. Aso, the use of counterfort she retaining as are consideraby economica in consumption of concrete and ead to about 4-6% in comparison ith concrete counterfort retaining as. So it is more economica to use cyindrica she retaining as.. The research the resuts of hich are presented in this paper, for the first time brings about a method to cacuate and anayze ightened she retaining a. Aso, for the first time cyindrica shes are adapted ith retaining as in the proposed shape and form and numerica eampe is stated as e.. The resuted equations for she retaining a ith required eactness represent the mechanica behavior of the she, and it i sho itsef in the resuts of stresses, defections functions, and aso in forces and bending moments cacuation. 4. The use of shes in front bearing eement of ightened retaining a instead of eve sabs i be more economica from consumptive point of vie, as the she curve increases bearing rigidity and capacity of the she and some of materias i go far aay from neutra ae, so the feura rigidity of she i increase a ot. Aso through increasing base sab thickness, the computation about it i be considered the same as compete rigid sab hich is competey obvious in the eary computations. 6. ACKNOWLEDGEMENTS I oud ike to appreciate professor X.Q. Seyfuayev, the advisor of my research, and the head of Civi Engineering Department of Azerbaijan University of Architecture and Construction. 7. EFEENCES []. aju N.K., Advanced reinforced concrete design. Ne Dehi: CBS yvkuagea and distributors (988). []. Seyfuayev X.Q., Mühəndis dəmirbeton konstruksiyaarı dərsik. Bakı: TI-MEDIA şirkətinin mətbəəsi (00). []. Timoshenko S, oinosky Krieger S., Theory of pates and shes. nd Edition. NeYork: McGra Hi Book company (959). [4]. asov.z., Genera theory of shes and its appication to engineering. Moskva: NASA Technica Transation TTF-99 (949). [5]. Seyfuayev X.Q., Konstruktiv qeyribircins ortotrop dəmirbeton yatıq qabıqarın hesabanma üsusiyyətərinin tədqiqi. Azərbaycan təhsi cəmiyyəti Tenika J, : 47-5 (00). [6]. Seyfuayev X.Q., Cəbrayıova G X. Nazikdivarı dəmirbeton fəza konstruksiyaarı dərsik. Bakı: TI-MEDIA şirkətinin mətbəəsi (009). [7]. Kave A., Finite eement method. Tehran: Iranian science and technoogy university pubications (00). [8]. Moaveni S., Finite eement anaysis theory and appication ith ANSYS. Tehran: Nagos pubications (00). [9]. aki K.C, Nederkut D.A., Finite eement method. Kardiyef: University coege pubications (974). [0]. Segrind L., Appied finite eement anaysis. Ne York: John iey and sons pubications (984). []. Zienkieicz O.C, Cheung Y.K., The finite eement method in structura mechanics. London: McGra-Hi Book company (967). []. Boes J.E., Foundation Anaysis and design. nd Edition. NeYork: McGra-Hi Book company (977). []. Das B.M., rincipes of foundation Engineering. nd Edition. Boston: WS-KENT company (990). [4]. Barnes G.E., Soi mechanics-princips & practice. Second edition. Itay: agrave pubications (000). 8

SECTION A. Question 1

SECTION A. Question 1 SECTION A Question 1 (a) In the usua notation derive the governing differentia equation of motion in free vibration for the singe degree of freedom system shown in Figure Q1(a) by using Newton's second