Some Aspects of Computer Aided Design of Underground Water Tanks

Transcription

1 nd IASME / WSEAS Interntionl Conference on GEOLOGY nd SEISMOLOGY (GES '08), Cridge, UK, Ferury 3-5, 008 Soe Aspects of Coputer Aided Design of Underground Wter Tnks DR. H. K. SHARMA, V. P. SINGH, SATPAL SHARMA Deprtent of Civil Engg. Ntionl Institute of Technology (Deeed University), Kurukshetr INDIA Astrct: - Underground tnks re coonly used for storge of wter for doestic use, swiing pool, sedienttion tnk, etc. The verticl wll of such tnks is sujected to hydro-sttic pressure nd soil pressure, nd is designed y using working stress or liit stte ethod for different edge conditions using IS: However, the wlls re norlly cst onolithic with cover sl creting condition, where oth top nd otto ends re fixed. IS: 3370 do not provide design tles for evluting ending oent coefficients for such condition. Present investigtions re therefore ied t developing design tles for such condition using exct nlysis nd stndrd softwre STAAD Pro. A coputer progr using Turo C++ hs een developed, nd ending oent coefficients nd deflection vlues re otined for different spect rtios t vrious loctions of verticl wll. The typicl results of ending oent coefficients otined y using two pproches re copred with ech other nd good greeent is exhiited. Bsed on the present investigtions, it y e inferred tht STAAD Pro y e used dvntgeously with resonle degree of ccurcy since the stndrd softwre is coputtionlly econoicl. Key-Words: - Uncrcked, STAAD, IS-3370, spect rtios, ntisyetricl, coefficients. 1 Introduction The nlysis nd design of underground tnks is sed on uncrcked section theory, to void lekge of stored liquid. In order to ensure ipereility through the wlls, rich concrete ix is used. The verticl wlls re designed either y the working stress or liit stte pproch considering wlls s () hinged t top nd otto () hinged t top nd fixed t otto nd (c) fixed t otto nd free t top, using IS (IV) [1]. The underground wter storge tnks re, however, norlly covered t top nd roof sl of such structures re norlly cst onolithic with the verticl wlls, giving condition where oth top nd otto ends of the verticl wll re fixed. The ville design code, however does not provide design tles for clculting ending oents coefficients for such conditions. Moreover, liited literture is ville for such underground tnks. Since the verticl wlls of underground wter tnks re sujected to hydro-sttic pressure fro inside, the prole cn e siulted to plte sujected to hydro-sttic pressure. The nlysis of rectngulr plte sujected to uniforly distriuted lod with oth ends fixed ws done y Wojtszk [] nd Evns [3] considering the solution given y Hencky s [] nd Boonov [5]. Curves were drwn for the coefficients to clculte ending oent, x. deflection nd sher for severl rtios of the sides of the plte. The prole of clped rectngulr plte with centrl concentrted lod ws however studied y Young [6]. Evns [3], however, proposed design tles for oents nd deflection for rectngulr plte fixed on ll edges nd sujected to uniforly distriuted lod. Oddley [7] further extended the work nd proposed design tles for clculting oent nd deflection for rectngulr plte for clped edges sujected to hydrosttic pressure in the for of two solutions; the first solution ws sed on usul procedure eployed in solving proles of thin pltes while the second ethod ws developed y Mrcus [8]. ISSN: Pge 106 ISBN:

2 nd IASME / WSEAS Interntionl Conference on GEOLOGY nd SEISMOLOGY (GES '08), Cridge, UK, Ferury 3-5, 008 Tioshenko [9], however, considered the prole of rectngulr plte with ll edges uiltin nd sujected to hydro-sttic pressure y considering the plte sujected to (i) uniforly distriuted lod nd (ii) ntisyetricl lod. The first prole ws solved y the ethod given y Evns [3] while the second one ws solved y using the ethod proposed y the Young [6]. Design tle for ending oent coefficients nd deflection ws developed for liited vlues of spect rtio [/] nd Poisson s rtio, n=0.3 t vrious loctions of the plte. Finite difference ethod using superposition ethod ws used in deriving the coefficients. Since, design coefficients for liited vlues of spect rtios [/] were proposed sed on coplex solution proposed y Evns [3] nd Young [6], IS: 3370 (IV) [1] proly didn t incorporte these tles in the stndrds. The present investigtions re therefore conducted to develop design coefficients y developing softwre for such cses. Anlyticl Investigtions The nlysis of plte uilt-in t ll edges nd suitted to hydrosttic pressure is n rduous tsk. Severl investigtors ttepted the prole considering plte for vrious other end conditions nd nlysis ws crried out for uniforly distriuted lod. It hs een oserved fro literture tht soe uthors hve investigted the prole considering doule cosine series expnsion nd exploittion of Morrison Woodury forul [16]. Nuericl solutions for rectngulr plte with vrious spect rtios were presented nd copred with the solution, proposed y Hencky []. Soe uthors hve nlysed the plte y the ordinry theory of thin pltes s treted in Lgrnge s eqution for iddle surfce. The ethod of superposition ws used nd pplied for vrious different loding. Tioshenko [9] investigted the prole of rectngulr plte sujected to hydrosttic pressure for the liited vlues of spect rtios for clculting vrious force functions i.e. B.M., S.F. etc. t vrious loctions. In the present study, nlysis hs een further extended for other spect rtios for vrious loctions. The nlysis is crried out in susequent heds..1 Rectngulr Plte with ll Edges Built-in nd Sujected to Hydrosttic Pressure Net effect of hydrosttic pressure of intensity q on the rectngulr plte y e otined y coining the effect of uniforly distriuted lod of intensity q0/ nd the effect of ntisyetricl loding of intensity q0x/ using rectngulr plte of size sujected to hydrosttic pressure of xiu intensity q0 t otto. Expressing the intensity of pressure in the for q0 q0 x q0 = + (1).1.1 Rectngulr plte sujected to uniforly distriuted lod Considering rectngulr plte of size, sujected to unifor pressure of intensity q, the deflection of siply supported plte is represented in the following for s; ( ) ( 1 ) / q 1 πx α tnhα + w = 5 π D = 1,3, cos 1 coshα cosh 1 πy πy () + 1 sinh coshα Where, π α = The softwre ws developed to solve the vrious differentil equtions for different spect rtios nd vlues for different force functions re given in Tle 1 nd Tle, respectively. Tle 1 : Deflections nd Bending Moents Coefficients in Uniforly Loded Rectngulr Plte with Built-in-Edges / (w) x=0,y=0 (M x ) x=/,y=0 (M y ) x=0,y=/ (M x ) x=0,y=0 (M y ) x=0,y= q/D q q q q q/D q q 0.060q q q/D q q q 0.080q q/D q q q 0.00q q/D q q q 0.010q q/D q q q q q/D q q q q πy ISSN: Pge 107 ISBN:

3 nd IASME / WSEAS Interntionl Conference on GEOLOGY nd SEISMOLOGY (GES '08), Cridge, UK, Ferury 3-5, q/D q q q q q/D q q q q q/D q q q q q/D q q 0.010q q TABLE-: Deflections nd Bending Moents Coefficients in Uniforly Loded Rectngulr Plte for higher spect rtio (/) with Built-in- Edges x=0, y=0 x=/, y=0 x=-/, y=0 x=0, y=±/ q / W= D α β 1 β γ 1 γ δ 0 α M x =β 1 q 0 M y =β q 0 M x =γ 1 q 0 M x =γ q 0 M y =δq Rectngulr plte sujected to Antisyetricl Loding Now, to find solution of the differentil eqution of the iddle surfce of ent plte; w w w q + + = x x y y D Boundry Conditions for plte t; ( w ) x = ± =( w ) y = ± = 0 nd w w = = 0 x x=± y y =± This y e done y tking w s the su of three solution. w = w 1 +w +w 3 (3) w 1 - Deflection for siply supported plte crrying the given ntisyetricl lterl lod nd ( ) ( 1 ) / ( ) 1 +α cothα πy Ρ + w sinh [y.sinh 5 1 = 5 α π D 1,3,5.. y y y. π.cosh π ]cos π sinh α w - Deflection for siply supported plte with syetriclly distriuted edge oents pplied t y 1 = nd equl ut opposite oents pplied t 1 y =. For w, syetricl edge oents convenient to tke in the for of cosine series. 1 πx ( M y ) F ( ) y = 1 cos () =± = 1,3,5 nd then the function w is given y ( ) 1 F 1 w = [ α coth α. π D = 1,3,5... sinhα (5) πy πy πy πx sinh cosh ]cos w 3 - Deflection for siply supported plte with ntisyetriclly distriuted edge oents. For w 3, the solutions for siply syetricl plte with ntisyetriclly distriuted edge oents cn e otined s πy ( Mx) x Esin = =± (6) = 1 Applying long the edges x= ±/, the deflection function for this cse is given y; 1/ πy ( M x) x =± ( 1) Ecos = (7) = 1,3,5... E πx w 3 =. [ δ tnhδcosh 8π D = 1.. coshδ π x x x sinh π ]sin π (8) thus, fro the ove given solution the vlues for vrious design preters re clculted for vrious spect rtios nd given in the tle 3 nd, respectively. Tle-3 Deflections nd Bending Moents Coefficients in Antisyetriclly Loded Rectngulr Plte with Built-in-Edges / x=0, y=0 x=/, y=0 x=-/, y=0 x=0, y=±/ q 0 W= α M x =β 1 q 0 M y =β q 0 M x =γ 1 q 0 M x =γ q 0 M y =δq 0 D α β 1 β γ 1 γ δ ISSN: Pge 108 ISBN:

4 nd IASME / WSEAS Interntionl Conference on GEOLOGY nd SEISMOLOGY (GES '08), Cridge, UK, Ferury 3-5, 008 Tle- Deflections nd Bending Moents Coefficients in n Un-syetriclly Loded Rectngulr Plte with Built-in-Edges x=0, y=0 x=/, y=0 x=-/, y=0 x=0, y=±/ / q 0 W= α M x =β 1 q 0 M y =β q 0 M x =γ 1 q 0 M x =γ q 0 M y =δq 0 D α β 1 β γ 1 γ δ Anlysis of Plte Using STAAD-PRO In order to vlidte the prole of rectngulr plte with ll uilt in edges under hydrosttic pressure nlysed erlier, the rectngulr pltes with vrious spect rtios were creted in Grphicl Used Interfce (GUI) y using plte eleent. The vlidity of the prole hs een checked y considering test prole for rectngulr plte with the otto ends fixed, top end free, nd good greeent etween the vlues given y IS 3370 [1] nd STAAD Pro is exhiited. The odeling of rectngulr plte in question creted in GUI ws nlysed under hydrosttic pressure to otin ending oent t vrious loctions long the length nd depth of the plte. The vlues of ending oent otined t vrious loctions using the STAAD-Pro were then converted to ending oent coefficients y dividing the ending oent y unit weight of wter ties the squre of height of wll. The vlues of ending oent coefficients rectngulr plte with ll uilt in edges nd for top edge free nd ll other clped re clculted y using STAAD Pro nd copred with the given vlues y IS:3370, s given in Tle 8 for the purpose of coprison. Tle-5 Bending Moent coefficients in Unsyetriclly Loded Rectngulr Plte with Built-in-Edges (using STAAD Pro) / X/ y=0 y=/ y=/ Mx My Mx My Mx My Anlysis of Results nd discussion.1 Bending Moent Coefficients long X-Axis The typicl vlues of ending oent coefficients for verticl wll of the underground tnk for vrious spect rtios, / =1.5, 1.0 nd 0.5 using exct nlysis t vrious loctions, re tulted in Tle 6. Se set of vlues were lso clculted y Tioshenko et l [9] using finite difference ethod. The Bending oent coefficients nd deflections re lso clculted y stndrd softwre STAAD-Pro given in Tle 7. The vlidity of STAAD Pro results hs een verified y checking test prole, nd results re shown in Tle 8. A close greeent etween the vlues otined fro STAAD Pro nd IS:3370 results is exhiited. The coefficients re found to e in close greeent with those given y the exct nlysis. The design tle s illustrted in Tle 8 for vrious spect rtios is finlly otined for verticl wll for the test prole. Tle-6 Moents Coefficients for Rectngulr Plte with Built-in-Edges nd Sujected to Hydrosttic Loding (Author) / x/ y=0 y=/ Mx My My ISSN: Pge 109 ISBN:

5 nd IASME / WSEAS Interntionl Conference on GEOLOGY nd SEISMOLOGY (GES '08), Cridge, UK, Ferury 3-5, Tle-7 Moents Coefficients for Rectngulr Plte with Built-in-Edges nd Sujected to Hydrosttic Loding (As per STAAD Pro) / x/ y=0 y=/ Mx My My Tle-8 Bending Moents Coefficients for Rectngulr Plte with Top Free, Botto nd Verticl Edges Fixed (As per STAAD Pro) y=0 Y=/ / x/ Mx My Mx My STAAD IS:3370 STAAD IS:3370 STAAD IS:3370 STAADIS: the vrition in Mx for / = 1.0 is found to e 13%. The vlues otined y exct nlysis however, re generlly found to e on higher side thn those otined y STAAD Pro, s shown in Fig. 1(). Siilr trend is lso otined for / =0.5 when the ending oent coefficients re copred. The xiu vrition is however found to e 9%. The close greeent etween exct nlysis nd nlysis using STAAD Pro illustrtes the vlidity of these two ethods nd s such cn e very well used to nlyse rectngulr plte for given oundry conditions. The close coprison of ending oent coefficient My using two pproches further illustrtes tht vlues re on higher sides using exct nlysis for /=1.5, s shown in Fig.. The vrition however rnges fro to 9%. Siilr oservtion re de when the vlues re copred for /=1.0 nd 0.5 respectively. The vrition once gin is found to e in the rnge of to 13%. The close greeent etween two vlues illustrtes tht the exct nlysis s well s STAAD Pro y e ppropritely used for the nlysis of verticl wll with clped edges under hydrosttic pressure. It is noteworthy to ention tht the ending oent coefficient Mx nd My using STAAD Pro for /=1.5, 1.0 nd 0.5 for the test prole, when copred with those given y IS 3370 [1] re lso found to e in good greeent s illustrted fig. 3 nd respectively. The Mxiu vrition once gin is however found to e % nd 15% for the two cses of ending oent coefficients. The nlysis of tnk wll using STAAD Pro softwre, further possess n edge over the exct nlysis in the sense tht clcultion of ending oents nd deflections re quite cuersoe in exct nlysis ethod nd is lso coputtionlly uneconoicl. It y, therefore, e concluded tht STAAD Pro y conveniently e used within the resonle degree of ccurcy for the nlysis of such pltes, econoiclly nd sfely. Underground wter tnks of ny size with ll edges clped y therefore e designed y using the design odule of stndrd softwre or ny other design ethod. 5. Coprtive Study The ending oent coefficients for verticl wll sujected to hydrosttic pressure using exct nlysis for vrious spects rtios, re copred with those otined y STAAD Pro. The vlues of Mx found y STAAD Pro, re on higher side thn those otined y exct nlysis. At, /=1.5 the xiu vrition in Mx is found to e -13% s Fig. 1(). But ISSN: Pge 110 ISBN:

6 nd IASME / WSEAS Interntionl Conference on GEOLOGY nd SEISMOLOGY (GES '08), Cridge, UK, Ferury 3-5, 008 Figure 1 Moent Coefficients Vrition of Mx (Built-in-Edges) Cse -I /=1.5 Cse -II /=1.0 Cse -II /=1.0 Cse -III /=0.5 Cse -III /=0.5 Figure 3 Moent Coefficients Vrition of Mx (Top Free, 3 Sides Fixed) Cse -I /=1.5 Figure Moent Coefficients Vrition of My (Built-in-Edges) Cse -II /=0.5 Cse -I /=1.5 ISSN: Pge 111 ISBN:

7 nd IASME / WSEAS Interntionl Conference on GEOLOGY nd SEISMOLOGY (GES '08), Cridge, UK, Ferury 3-5, 008 Figure Moent Coefficients Vrition of My (Top Free, 3 Sides Fixed) Cse -I /=1.5 Cse -II /=1.0 Cse -III /= Conclusions On the sis of present investigtions, following conclusions cn e drwn. The exct nlysis nd STAAD Pro y conveniently e used to nlyse verticl wll of rectngulr tnk with ll edges clped under hydrosttic pressure.the xiu vrition in ending oent coefficient Mx is found to e 9 percent. The xiu vrition in ending oent coefficient My is found to e 13 percent. A close greeent etween ending oent coefficients for two pproches is exhiited. References [1] I.S.: 3370 (Prt-I)-1967, Indin Stndrd Code of Prctice for Concrete Structures for the Storge of Liquids, B.I.S, New Delhi, [] Wojtszk, I.A., The clcultion of xiu deflection, oent, nd sher for uniforly loded rectngulr plte with clped edges, Journl of Applied Mechnics, V-59,PP A173- A176, [3] Evns,T.H. nd Chrlottesville,V.A., Tles of oents nd deflections for rectngulr plte fixed on ll edges nd crrying uniforly distriuted lod, Journl of Applied Mechnics, V-61,PP A7-A10, [] Hencky. Der Spnnungszustnd in Rechteckigen Pltten, Munich, [5] Boonov, Theory of Structures of Ships, Vol., St. Petersurg, 191. [6] Young, D nd Storrs,C., Anlysis of Clped Rectngulr Pltes. Journl of Applied Mechnics, 6:A139-A1, 190. [7] Oddley, E.G., Deflections nd Moents of Rectngulr Plte Clped on All Edges nd Under Hydrosttic Pressure, Journl of Applied Mechnics, Vol. 1, 197. [8] Mrcus, Deflections nd Moents of Rectngulr Plte Clped on All Edges nd Under Hydrosttic Pressure, Journl of Applied Mechnics, Vol. 1, 197. [9] Tioshenko, S.P. nd Krieger, S.W., Theory of Pltes nd Shells, McGrw-Hill, New York, nd Edition, [10] Mnhttn, K. nd Pickett, G., Solution of Rectngulr Clped Plte with Lterl Lod y Generlized Energy Method, Journl of Applied Mechnics, Vol. 1, 197. [11] Sydney, N.S.W. nd Shuleshko,P., Buckling of Rectngulr Pltes with Two Unsupported Edges, Journl of Applied Mechnics, Vol. 78, [1] Stiles, W.B. nd Aes,I., Bending of Clped Pltes, Journl of Applied Mechnics, [13] Deverll, L.I. nd Dugwy, U., Solution of Soe Proles in Bending of Thin Clped Pltes y Mens of the Method of Muskhelishvili, Journl of Applied Mechnics, [1] Rju, N.K., Moent Coefficients for the Design of Rectngulr Sls with Short Discontinuous Edges, Indin Concrete Journl, Vol.11, 197. [15] Kurin, N.P. nd Vrghese, P.C., A Siplified Approch to the Bending of Urell Shell, nd Single Hypr nd Plte on Elstic Foundtion, Indin Concrete Journl Vol [16] Tylor et l., Solution of clped rectngulr plte proles, University of Cliforni, Berkeley, CA, USA, UCB/SEMM-00. ISSN: Pge 11 ISBN: