th Interntionl onference on Arch Bridges October -7, 06, Wrocłw, Polnd INVESTIGATION OF ASSESSMENT METODS FOR RAIWAY MASONRY AR BRIDGES J. Wng, J. ynes,. Melbourne University of Slford, Directorte of ivil Engineering, Slford, UNITED KINGDOM. e-mils: j.wng@slford.c.uk, b.j.hynes@slford.c.uk, c.melbourne@slford.c.uk SUMMARY Although msonry rch bridge reserch over the lst few decdes hs spwned severl dvnced cpcity ssessment tools, the mintennce nd ssessment of these bridges is still constnt concern for the bridge owners. There hve been mny ppels for the MEXE method to be replced but no greed lterntive hs yet been found. Though the development of new, simple nd robust cpcity ssessment is importnt, there is n immedite need to identify criticl issues in the current ssessment methods which my led to unsfe cpcity ssessments. This pper provides criticl pprisl of the MEXE method proposed in the current Rilwy odes. Detils of the specific concerns re estblished, justified nd ssessed. onclusions re drwn which re potentilly of significnt prcticl interest. Keywords: Msonry, rch bridges, MEXE, rilwy, ssessment method.. INTRODUTION In the UK, the current method of determining the lod crrying cpcity of rilwy msonry rch bridge is embodied in the guidnce note for the structurl ssessment of underbridges NR/GN/IV/0 [] herefter referred to s the Rilwy code. The first level in the ssessment is to pply the so-clled MEXE method. The MEXE method evolved from the work undertken by Pipprd in the 90 s which included both field nd lbortory tests to clibrte theoreticl work []. The full review of Pipprd s equtions is presented by Wng nd Melbourne []. According to the Rilwy code, the MEXE method for rilwy structures hs been developed differently to tht for highwy structures s defined in BD []. The Provisionl Ale pcity for rilwy msonry rch bridge cn be determined using the envelope curves or clculted using the formule presented in the Rilwy code. This pper presents derivtion of the bsic equtions used for the envelope curves in the Rilwy code. Anomlies re identified nd discussed. 0
Msonry rch bridges. ONSIDERING ONGITUDINA IVE OAD DISTRIBUTION Pipprd s originl equtions re bsed on the nlysis of two-pinned prbolic rch with spn/rise rtio of four, subjected to point live lod pplied t the crown, i.e. no live lod distribution is considered. When live lod distribution through the fill in the longitudinl direction is considered, s shown in Fig., the following equtions re derived. 0 ls A q B V A VB Fig.. Unit live lod distribution through fill in longitudinl direction... orizontl thrust nd bending moment ls P= q Y A X V A B A B = - = V B V A = q ls V B = q ls b Fig.. Two-hinged prbolic rch I =I 0 sec. For concentrted unit lod, s shown in Fig., the totl horizontl thrust nd bending moment t the crown re: M 0 For uniform distributed lod q, s shown in Fig. b, thrust nd bending moment due to the increse of length d re given by: 0
d q d q d d q d q dm 0 0 Using symmetry, where l s Then, 0. q d q 6 0 0. q d q M 7 For uniformly distributed lod where s ql, the totl horizontl thrust nd bending moment t the crown re given by: l s l M s 9.. orizontl thrust stress nd bending stress If PU represents the horizontl thrust stress nd PUB represents the bending stress t the crown due to the effect of the unit live lod s shown in Fig., then: bd l bd PU s 0 6 6 bd l bd M PUB s.. The provisionl le cpcity If the vilble live lod stress P represents subtrcting the ded lod stress from the limiting compressive stress f c t the crown, then the provisionl le cpcity is given by: 0 th Interntionl onference on Arch Bridges October -7, 06, Wrocłw, Polnd
Msonry rch bridges P PA PU PUB The full derivtion of the provisionl le cpcity for uniformly distributed lod cross the crown is presented elsewhere [].. MEXE METOD IN TE RAIWAY ODE.. Avilble live lod stress The mthemticl epression of vilble live lod stress presented in the Rilwy code is s follows: d h d d d P 00 kn/m The derivtion of the bove eqution is presented elsewhere [],[]... ive lod effects... ongitudinl loded length od distribution is considered in the longitudinl direction nd the Rilwy code offers equtions nd to obtin the longitudinl loded length. m m l s h 0. loded length due to single lelod l b h. loded length due to bogie lod These equtions suggest tht lods re distributed from the bse of the sleeper through the fill onto the rch brrel t slope of horizontlly to verticlly in the longitudinl direction, s shown in Fig.. Fig.. ongitudinl live lod distribution through fill. 06
th Interntionl onference on Arch Bridges October -7, 06, Wrocłw, Polnd... Influence line for bending moment The mthemticl epression of n influence line for bending moment t the crown is presented in the Rilwy code s: F 0.7 0. 0. 6 According to the Rilwy code, the eqution is obtined from close fit to the influence line curve for bending moment in the previous report nd ssessment code. Fig. shows comprison of this influence line nd tht constructed using eqution. Fig.. omprison of the bending moment influence lines. By integrting eqution 6 which clcultes the re under the influence line over the loded length, the following eqution is given in the Rilwy code A 0. 0.09 0. 7 The eqution is lter used to clculte the bending stress s presented in Section...... Influence line for horizontl thrust The mthemticl epression of n influence line for horizontl thrust t the crown is presented in the rilwy code s: T 0.7 07
Msonry rch bridges According to the Rilwy code, the eqution is n pproimtion to the influence line for horizontl thrust given in the previous report nd ssessment code. Fig. shows comprison of this influence line nd tht constructed using eqution for n rch with spn/rise rtio of. For n rch with spn/rise rtio of, the vlue of T is multiplied by to obtin the ctul thrust. Fig.. omprison of the horizontl thrust influence lines.... Section properties Section properties re given in the Rilwy code by the following epressions, d h. m h 0. m, B h. d m, M 9 6 d h. m 0. h 0.9 m, B h. d m, M 0 6 Where, B is defined s the cross sectionl re, M is defined s the section modulus, d is the thickness of rch ring t the crown, nd h is depth of fill between sleeper soffit nd rch ring t the crown. This suggests tht the effective width of the rch brrel dopted by the Rilwy code is h 0. m, b h. m 0. h 0.9 m, b h. m 0
th Interntionl onference on Arch Bridges October -7, 06, Wrocłw, Polnd... Unit live lod bending stress nd horizontl thrust stress The unit live lod bending stress is presented for single le lod in the Rilwy code by the following epression: PUB S A l M S For bogie lod, the subscript chnges to b, i.e. PUB b nd the loded length chnges to l b correspondingly. Replcing A with eqution 7, the unit live lod bending stress PUB S becomes PUB S 6 ls bd 0. 0.09 0. This suggests tht the bending moment t the crown in the Rilwy code is: M 0. 0.09 0. l S omprison of the results between this eqution nd those from Eq. 9, for unit spn rch, is s shown in Fig. 6. They produce lmost identicl moments s the loded length increses. Fig. 6. omprison of the bending moment t the crown. 09
Msonry rch bridges..6. Unit live lod horizontl thrust stress The unit live lod horizontl thrust stress is presented in the Rilwy code by the following epression: 0.9 T PU 6 B Where B is the cross sectionl re. This suggests tht the horizontl thrust t the crown in the Rilwy code is: 0.9 T 7 It is not cler how this horizontl thrust is obtined. owever, if the influence line in the Rilwy code, i.e. eqution, is used nd integrted over the loded length, different horizontl thrust eqution cn be obtined, which does produce the sme results s those from the bove eqution, i.e. eqution 7. Substituting T from eqution into eqution 7, the following epressions re obtined: 0.9 T 0.9 0.7 omprison of horizontl thrust obtined from this eqution nd tht from eqution spn/rise= is s shown in Fig. 7. Fig. 7. omprison of the horizontl thrust. 0
th Interntionl onference on Arch Bridges October -7, 06, Wrocłw, Polnd.. Provisionl le cpcity The provisionl le cpcity in the Rilwy code is obtined by dividing the vilble live lod stress by the sum of the unit live lod horizontl thrust nd bending stresses nd epressed by equtions 9 nd 0. For single le lod, P S 9 PU S PUBS For bogie lod, b PU 0.P 0 b PUB b The provisionl le cpcity is tken s the minimum of s or b nd both re represented grphiclly in Fig.. Fig.. Provisionl le cpcity for n rch with d=00mm nd h= 00mm.. ANOMAIES IN TE RAIWAY ODE.. od distribution in the longitudinl direction luse 6.. in the Rilwy code sttes tht lods should be distributed from the bse of the sleeper through the fill onto the rch brrel t slope of horizontlly to verticlly in the longitudinl direction. owever, the loded length i.e. equtions nd, dopted in the clcultions for producing the envelope curves re bsed on the slope of horizontlly to verticlly. For this inconsistency, typicl m spn rch with 00 mm
Msonry rch bridges crown ring thickness nd 00mm fill cover, hs provisionl le cpcity of 6. tonnes for : lod distribution, which is % higher thn tht for : lod distribution... Effective width The influence of effective width hs been presented elsewhere [7]. The rch cpcity envelope curves set out in the Rilwy code re bsed upon effective width ssumptions which re shown in Fig. 9, however, there ppers to be no logicl connection between these effective width equtions nd the descriptions given in Figure 6. of the Rilwy code. Fig. 9. Effective width of ril rch bridges... Provisionl le cpcity luse 6... in the Rilwy code sttes tht the provisionl le cpcities obtined from the envelope curves re likely to be conservtive becuse ssumptions bout lod dispersl lterlly nd longitudinlly re pessimistic. It goes on to suggest tht where higher cpcity is sought, there is scope to justify greter lod spred thn originlly ssumed. owever, when cpcity predictions using severl sources re compred, s shown in Fig., it is evident tht those using Pipprd s originl equtions suggest much lower cpcities thn the Rilwy code Single le nd Bogie. The cpcities from the Rilwy code drop to zero becuse the Rilwy MEXE method pplies Pipprd s compressive stress criteri i.e. 00 kn/m under the self-weight only.
th Interntionl onference on Arch Bridges October -7, 06, Wrocłw, Polnd Fig. 0. omprison of provisionl le cpcity d=00 mm nd h= 00 mm.. ONUSIONS.. onclusions The elstic cpcity ssessment produced by Pipprd is bsed upon well estblished nd ccepted ssumptions. To derive the envelope curves, the Rilwy code inconsistently pplies its own ssumptions bout: od distribution ngle through fill Effective width of the rch brrel Additionlly there is no check on the tensile stress level included in the Rilwy code. pcity predictions using the Rilwy code re significntly higher thn those obtined using Pipprd s equtions. This is most significnt t shorter spns... Recommendtions The equtions used in the Rilwy code re bsed upon best fit pproimtions, however these hve lost their physicl representtion nd it would be more intuitive to use the fundmentl reltionships upon which they re bsed. In order to estblish the rel dispersl of loding through fill, further physicl testing is required. This should ddress both longitudinl nd lterl lod spred through shllow nd deep bllst. In prticulr this must estblish useble dispersl pttern for deep fill where lod dispersl ptterns interfere, nd must be comptible with equilibrium. REFERENES [] NR/GN/IV/0. 06. The structurl ssessment of underbridges. Network Ril Guidnce Note. Network Ril.
Msonry rch bridges [] MKIBBINS,., MEBOURNE,., SAWAR, N. nd GAIARD,.S., Msonry rch bridges: condition pprisl nd remedil tretment. IRIA 66. 006 [] WANG, J. nd MEBOURNE,., Mechnics behind the MEXE method for msonry rch ssessment. Proceedings of the Institution of ivil Engineers, Engineering nd omputtionl Mechnics. Volume 6, EM, 00, pp.7 0. [] BD /0. The Assessment of highwy bridges nd structures. Design mnul for rods nd bridges, Volume, Section, Prt, ighwys Agency, 00 [] MEBOURNE,. nd WANG, J., Independent check on the proposed modifictions nd of limittions for the MEXE method, Improving Assessment, Optimistion of Mintennce nd Development of Dtbse for Msonry Arch Bridges UI Project I/0/U/, 00. [6] BA 6/97, The Assessment of highwy bridges nd structures. Design mnul for rods nd bridges, Volume, Section, Prt, ighwys Agency, 997 [7] WANG, J., AYNES, J. nd MEBOURNE,., A comprison between the MEXE nd Pipprd's methods of ssessing the lod crrying cpcity of msonry rch bridges, AR 7th Interntionl onference on Arch Bridges, roti, 0, pp.9 96