REMAINING STRENGTH EVALUATION METHOD OF PLATE GIRDERS WITH CORRODED FLANGE UNDER SLEEPERS

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REMAINING STRENGTH EVALUATION METHOD OF PLATE GIRDERS WITH CORRODED FLANGE UNDER SLEEPERS Katashi FUJII 1, Naoki ASAO 1 Emerits Proessor, Universit o Hiroshima (1-4-1, Kagamiama,

1 REMAINING STRENGTH EVALUATION METHOD OF PLATE GIRDERS WITH CORRODED FLANGE UNDER SLEEPERS Katashi FUJII 1, Naoki ASAO 1 Emerits Proessor, Universit o Hiroshima (1-4-1, Kagamiama, Higashihiroshima-shi, Hiroshima , Japan) ken14@hiroshima-.ac.jp Dept. o International Projects, International Div., Paciic Consltants Co.,LTD. (3-, Kanda-Nishikicho, Chioda-k, Toko , Japan) naoki.asao@tk.paciic.co.jp For steel railwa bridges with open deck sstem, the local o compressive langes nder sleepers on plate girders cased b the local corrosion o langes leads to the collapse o bridges. The local corrosion is thoght to have a sbstantial impact on the ltimate strength o main girders. However, past research on ltimate strength contains ew inqiries into the relationship between the local corrosion o compressive langes and the ltimate strength o main girders, and a method o evalating the relationship has not et been established. This std proposed a remaining strength evalation method that takes into accont the local corrosion nder sleepers based on parameter analses that ocs on the strength interaction o plate girders sbjected to bending and local loads simltaneosl. In addition, the std veriied the applicabilit o this method rom existing experimental vales and analtical vales obtained throgh FEM to clari that ltimate strength can be evalated with a high degree o accrac. Ke Words : plate girder, sleeper, local corrosion, remaining strength, local 1. INTRODUCTION In Japan, man steel railwa bridges with open deck sstem have been in se or over 60 ears, and deterioration and damage de to corrosion is becoming obvios. Partial repairs and reinorcement as well as total replacement o girders have taken place in recent ears, bt it cannot be said with certaint that these measres have been selected ater proper, qantitative evalations o the remaining strength o the girders. In light o recent socioeconomic conditions, there is an even more pressing need to establish streamlined, economicall viable methods or maintaining these bridges. One phenomenon that reqires maintenance is local corrosion o the pper langes nder sleepers, a tpe o corrosion characteristic o steel railwa bridges that it shall be reerred to as corrosion nder sleepers throghot this report. Fig.1 shows that the coating on pper langes nder sleepers wears more easil and is more ssceptible to dampness than other parts de to the train load acting almost directl throgh the rails and sleepers onto the girders. Local corrosion progresses as a reslt. Man stdies on ltimate strength o plate girders (Basler & Thrlimann 1), Moriwaki et al. ),3), Fjino 4), Komats et al. 5), etc.) had been condcted b experiments and analses. However, none o them were taken accont o local corrosion despite the act o taking into accont corrosion nder the sleepers is vital toward accratel evalating the remaining strength o this tpe Fig.1 Steel railwa bridges with open deck sstem. 1

loads simltaneosl evalates the remaining strength o plate girders nder conditions o the load combination.

: vertical, lateral (lateral torsional ), and torsional.

This std evalates bending load bearing capacit ocsed on compressive langes, with lateral and torsional as the two tpes o lange.

BEARING CAPACITY Past stdies 6),7) show that local o compressive langes de to corrosion nder sleepers has a sbstantial impact on the residal bending load bearing capacit o girders.

2 o steel railwa bridges. In this std, irstl load bearing capacit in terms o both pre bending and local loads is independentl evalated, then based on these reslts, a proposed strength interaction crve sbjected to the two loads simltaneosl evalates the remaining strength o plate girders nder conditions o the load combination. According to Basler s approach 1), the bending collapse mode or the plate girders is determined b one o the three tpes that compressive langes bckle as shown in Fig.: vertical, lateral (lateral torsional ), and torsional. O these, it is clear that vertical o langes occrs when the width-thickness ratio o the web is extremel small, bt it does not occr nder normal conditions. This std evalates bending load bearing capacit ocsed on compressive langes, with lateral and torsional as the two tpes o lange. the basic length o girders with corrosion nder sleepers shall be the spacing between lateral bracings (cross beams) or lateral and the sleeper width or torsional (Fig.3). BEARING CAPACITY Past stdies 6),7) show that local o compressive langes de to corrosion nder sleepers has a sbstantial impact on the residal bending load bearing capacit o girders. Also, as previosl explained, plate girders with corrosion nder sleepers collapse de to the lateral or torsional o compressive langes. In light o this inormation, this std proposes a method o evalating bending load bearing capacit based on FEM analsis with variable remaining thickness o compressive langes de to corrosion nder sleepers sing two tpes o analtical models that dier or lange length, width and or the nmber o corroded locations. This FEM analsis have been perormed with ABAQUS, a general-prpose FEM analsis program, and ocsed onl on compressive langes o plate girders modeled as perect elasto-plastic material sing iso-parametric shell element with 4 nodal points. Material properties are given a ield stress σ o 35 MPa, an elastic modls E o 00 GPa and a Poisson ratio ν o 0.3. Vertical Lateral Fig. Bckling modes o plate girders. Torsional (1) Lateral o compressive langes a) Overview o analsis Fig.4 shows an analtical model. The spacing between lateral bracings (cross beams) is given the basic length Lh in the evalation o bending load bearing capacit or lateral. It also shows a lange model with corrosion nder sleepers at three locations (the shaded areas) within basic length Lh. Both ends are sbjected to a niorml distribted axial compressive stress. Under these conditions, or the lange plate, the web bond parts at both ends have pinned spports, and the bond line between the web and the lange has a simple spport to restrain ot-o-plane deormation. Fig.4 Analtical model (Lateral ). Fig.3 Basic length o girders with corrosion nder sleepers.. EVALUATION OF BENDING LOAD

Table 1 shows the analtical parameters: lange width B is 30 mm, lange length (basic length) Lh is 000 mm in Case 1 and 600 mm in Case, and corrosion is present in three locations in Case 1 and or

3 Table 1 shows the analtical parameters: lange width B is 30 mm, lange length (basic length) Lh is 000 mm in Case 1 and 600 mm in Case, and corrosion is present in three locations in Case 1 and or locations in Case. The original thickness o each lange t0 is 30 mm, and the thickness at the corroded parts nder the sleepers is redced in increments o 3 mm to examine the bending load bearing capacit. These analtical models also take into accont residal stress de to initial imperections and welding. Table 1 Analtical parameters (Lateral ). Case 1 Case Flange length L h (mm) Flange width B (mm) Original thickness t 0 (mm) No. o corroded locations locations 3 4 b) Reslts o analsis (Lateral ) Table shows the maximm load P and maximm axial compressive stress σ obtained rom this analsis. The entries in the table marked with an asterisk (*) depict cases where torsional preceded lateral in the collapse. The table shows that maximm axial compressive stress σ or collapse nder lateral is nearl the same as ield stress σ. Fig.5 shows an example o this phenomenon, where the dominant deormation perpendiclar to the bridge axis is in a state o ltimate deormation de to the lateral. Fig.6 shows the load bearing capacit crve o lange lateral : the vertical axis is maximm axial compressive stress σ made dimensionless b ield stress σ, and the horizontal axis is slenderness ratio parameter λ. The dashed line represents Basler s proposed Eqation (1), and Eqation () expresses slenderness ratio parameter λ. The otlined plots in the igre are well accorded with Basler s load bearing capacit crve nder lange lateral (the dashed line). This shows that bending load bearing capacit nder lange lateral can be evalated b deriving bending load bearing stress σh rom Basler s proposed eqation. It is to be noted that the radis o gration r expressed in Eqation (3) is applied to the lange cross-section which takes into accont the corrosion wastage in Eqation (4). h 1 4 (1) 1 1 L h () r E σh = Bending load bearing stress nder lateral σ = Yield stress λ = Slenderness ratio parameter Lh = Basic length r = Radis o gration E = Elastic modls In addition, radis o gration r is obtained rom Eqations (3) and (4). I B r (3) A 1 3 B t I (4) 1 B = Total pper lange width t = Upper lange thickness or corrosion wastage A = Upper lange cross-sectional area or corrosion wastage Table Reslts o analsis (Lateral ). Case 1 Case t (mm) P (kn) σ (N/mm ) P (kn) σ (N/mm ) *668 * *331 *173 *360 *188 3 *11 *16 *157 *164 t = Upper lange thickness or corrosion wastage P = Maximm axial compressive orce σ = Maximm axial compressive stress Fig.5 Ultimate deormation state (Lateral ). 3

4 Sleeper width Flange hal-width Original thickness Lt (mm) b (mm) t0 (mm) Case 1 Case Case 3 Case Fig.6 Load bearing capacit crve (Lateral ). () Torsional o compressive langes a) Overview o analsis Where there is no corrosion nder sleepers, the torsional length is thoght to be the spacing between the vertical stieners, bt when there is corrosion nder sleepers, basic length Lt is thoght to be the sleeper width o 00 mm. Thereore, the analsis o torsional is ocsed on corroded compressive langes nder sleepers, and the are modeled ocsing on protrding parts o the langes. Fig.7 shows the analtical model, where the pper lange plates nder sleepers are sbjected to orced displacement δ at both ends, and compressive plates with simple spport or three sides and ree or one side can be assmed. Table 3 shows the analtical parameters: basic length Lt is set as sleeper width, lange hal-width b varies in or dierent cases. In the same wa as the analsis described above.(1), the thickness at the corroded parts o pper langes nder the sleepers is gradall redced rom the original thickness o the pper lange t0 to examine the load bearing capacit. These analtical models also take into accont residal stress de to initial imperections and welding. Fig.7 Analtical model (Torsional ). Table 3 Analtical parameters (Torsional ). 4 b) Reslts o analsis (Torsional ) Table 4 shows the maximm load P and maximm axial compressive stress σ obtained rom this analsis. The entries in the table marked with an asterisk (*) depict cases where elastoplastic preceded total ield in the collapse. Fig.8 shows the state o ltimate deormation de to torsional. In addition, Fig.9 shows the load bearing capacit crve nder torsional obtained rom the analsis, and Basler s proposed eqation. As the igre shows, the analtical vales are smaller than those o Basler s proposed eqation. This is becase coeicient k is set to 0.43 when aspect ratio α is adopted as ininite in Basler s proposed eqation. In other words, Basler s proposed eqation cannot be applicable in these cases becase sleeper width is deined as basic length Lt. Ths, this std proposes Eqation (5), which takes accont o aspect ratio α based on the analtical reslts nder torsional. The width-thickness ratio parameter R or Eqation (5) is expressed in Eqation (6). Note that the act that basic width Lt is analzed in this std as sleeper width means that it is limited to sitations when corrosion nder sleepers between vertical stieners is in a single location. Fig.10 (a) throgh (c) demonstrates the wa o thinking abot length based on dierent corrosion conditions. When corrosion nder sleepers between vertical stieners is in two locations as in Fig.10 (c), the length shall be considered to be doble (or this case, 400 mm). t 1 R (5) R R 1 b 1 1 R (6) t k E σt = Bending load bearing stress nder torsional

R = Width-thickness ratio b = Flange hal-width t = Upper lange thickness or corrosion wastage ν = Poisson ratio k = Bckling coeicient: k = 0.

5 R = Width-thickness ratio b = Flange hal-width t = Upper lange thickness or corrosion wastage ν = Poisson ratio k = Bckling coeicient: k = (1 / α) α = Aspect ratio (or this analsis, Lt / b) σ = Yield stress E = Elastic modls Fig.8 Ultimate deormation state (Torsional ). Fig.9 Load bearing capacit crve (Torsional ). Table 4 Reslts o analsis (Torsional ). Case 1 Case Case 3 Case 4 t (mm) P (kn) σ (N/mm ) *35 *03 5 *85 * *687 *9 10 *376 *188 5 *93 * *991 *0 10 *499 *166 5 *1 * *1871 *34 15 *167 *11 10 *644 *161 5 *151 *76 t = Upper lange thickness or corrosion wastage P = Maximm axial compressive orce σ = Maximm axial compressive stress 3. EVALUATION OF LOCAL LOAD BEARING CAPACITY Mch research has been condcted on calclation eqations or the load bearing capacit o girders nder local loads. This std showed that Takimoto s proposed calclation eqation 8),9) allowed or accrate evalations o the load bearing capacit o girders with corrosion nder sleepers when the are nder local loads 10). This std sed Eqation (7) below, which is rther simpliied based on Takimoto s eqation. a t P 5tw w 4twt 1 (7) hw Fig.10 Wa o thinking abot length a. tw = Web plate thickness σw = Web ield stress t = Upper lange thickness σ = Upper lange ield stress 5

a = Width on which local load acts hw = Web height Table 5 Analtical parameters. 4.

bearing capacit nder bending and local loads respectivel.

actal bridges. This analsis is condcted b the se o the analtical parameters shown in Fig.

In addition, Fig.1 shows the analtical model and bondar conditions at nodal points and sides, and Fig.

sleepers as well as vertical shear orces to the web cross-sections above the spporting points to balance ot the line load. And as shown in Fig.

6 a = Width on which local load acts hw = Web height Table 5 Analtical parameters. 4. EVALUATING LOAD BEARING CAPACITY OF GIRDERS UNDER COMBINED LOADS (1) Overview o analsis Ths ar separate evalation eqations were proposed or load bearing capacit nder bending and local loads respectivel. it is examined analticall that the ltimate states and load bearing capacit o girders nder bending and local loads simltaneosl, as is the case with actal bridges. This analsis is condcted b the se o the analtical parameters shown in Fig.11 and Table 5, and b considering combined bending and local loads acting on girders with corrosion in a single central location nder sleepers. In addition, Fig.1 shows the analtical model and bondar conditions at nodal points and sides, and Fig.13 shows the load conditions that it is applied as a line load to the joint part between the web and the pper lange where there is corrosion nder sleepers as well as vertical shear orces to the web cross-sections above the spporting points to balance ot the line load. And as shown in Fig.13, rigid elements are applied to the end plates o the girder and acted on b cople o orces to work as the bending moment. These analtical models also take into accont residal stress de to initial imperections in the ot-o-plane direction on the web between the vertical stieners, and welding between the web and the pper lange. Fig.1 Bondar conditions. Fig.11 Conigrations targeted or analsis. Fig.13 Load conditions. 6

7 () Reslts o analsis Fig.14 and Fig.15 show the states o ltimate deormation and the von Mises stress at peak load in Case 3 or each o combined and pre bending loads. Most analses reslted in collapse de to local o the compressive lange as shown in Fig.14, bt when bending is the sperior orce or when there is a major redction in thickness de to corrosion nder sleepers, the collapse occrs de to torsional o the lange as shown in Fig.15. The stressed condition in Fig.14 demonstrates that compressive stress on the pper lange occrs and a local load increases marked local stress on the web. In addition, Fig.15 shows that pre bending concentrates compressive stress on the corroded parts nder sleepers. Fig.16 shows the reslts o the analsis plotted on an interactive crve. All the analtical vales or local load and bending moment on this igre are nearl on the crve that represents Eqation (8). Thereore, Eqation (8) can be sed to evalate the load bearing capacit o girders nder combined loads. P M 1 P M (8) P = Local load (or combined load) M = Bending moment (or combined load) P = Local load (or individal load) M = Bending moment (or individal load) Fig.14 Case 3 50% redction in THK (For combined load). Fig.15 Case 3 50% redction in THK (For pre bending). P/P Fig.16 Interactive crve. 5. EVALUATION METHOD OF REMAINING STRENGTH Ths ar this std has examined and evalated the load bearing capacit o plate girders with corrosion nder sleepers nder bending (lateral/torsional ) and local loads, and the interactive relation o load bearing capacit nder combined loads o both orces. this std proposes a speciic method or evalating the remaining strength o plate girders with corrosion nder sleepers based on the reslts o these evalations. Below is the procedre or this proposal. First, Eqations (1) and (5) are sed to calclate the bending load bearing stress or each o lateral and torsional o girders nder pre bending orce. h 1 4 (1) 1 t 1 R (5) R 0.89 M /M R The smaller vale o calclated bending load bearing stresses σh or σt contribtes to the actal state o and determines the applicable bending load bearing stress σ or girders. This stress σ shall be sed in beam theor Eqation (9) to calclate the load bearing bending moment M nder pre bending orce. 7

8 M I (9) h I = Second moment o area o corroded part h = Distance rom netral axis to the top o pper lange o corroded part Next, the load bearing capacit P o girders onl nder local load can be calclated b sing Eqation (7). a t P 5tw w 4twt 1 (7) hw Finall, b sing the vales o M and P that are calclated above, and the vales o bending moment M or local load P which acts on actal girders, Evalation Eqation (8) can estimate remaining load bearing capacit o girders nder combined loads. P M 1 P M (8) 6. APPLICABILITY OF PROPOSED EVALUATION METHOD Fig.17 and Fig.18 show comparisons between analtical vales and the respective evalation vales or bending moment M and local load P calclated sing Evalation Eqation (8). The illed-in plots on these graphs represent reslts nder pre bending alone or local load alone, respectivel. The evalation reslts are well accorded with the analtical ones and rthermore, the act that the evalation reslts tend to be lower than the analtical ones Fig.17 Comparison o analtical and evalation vales (Bending moment M ). Fig.18 Comparison o analtical and evalation vales (Local load P ). shows that the vales obtained rom the evalation eqation can be estimated on the sae side. To compare the vales obtained rom the evalation eqation proposed b this std, circles representing the reslts o experiments rom reerence materials 7),10) are plotted on the graphs. These reslts also demonstrate that the proposed evalation method and eqation are well accorded with vales obtained rom experiments. 7. CONCLUSION As this std aimed to propose a remaining strength evalation method or plate girders with corrosion nder sleepers, the load bearing capacit or bending has been investigated irst. This investigation o bending load bearing capacit demonstrated analticall abot the tpes o collapse triggered b lateral or torsional o compressive langes. The reslts o the analsis showed that the bending load bearing capacit o plate girders cold be evalated b taking onl compressive langes rom plate girders, that lateral can be obtained rom Basler s proposed eqation, and that torsional can be obtained rom the evalation eqation proposed in this std. The analsis also showed that the bending load bearing capacit obtained rom the evalation eqation can depict bending load bearing capacit obtained rom past experiments with accrac and can be estimated on the sae side. In addition, since bending and local loads act simltaneosl on actal railwa bridges, elastoplastic non-linear FEM analsis has been sed to investigate the remaining load bearing capacit o plate girders that bear varios combined loads. Given these reslts, this std clariied an interactive crve or plate girders with corrosion nder sleepers nder 8

9 combined loads, and proposed a remaining strength evalation method. Finall, examining and comparing the vales obtained rom this evalation method with the FEM analsis reslts cold veri that this method is an applicable wa to calclate the remaining strength o plate girders with corrosion o pper langes nder sleepers. REFERENCES 1) Basler, K. & Thrlimann, B. : Strength o plate girders in bending, Proc. o ASCE, Vol. 87, No. ST6, pp , ) Yoshikaz, M. and Masaki, F. : Experimental std on shear strength o plate girders with initial imperections, Jornal o JSCE, No. 48, pp , ) Yoshikaz, M. and Masaki, F. : Experimental std on pre bending strength o plate girders with initial imperections, Jornal o JSCE, No. 64, pp. 1-15, ) Masaki, F. : Experimental std on combined strength o plate girders with initial imperections, Jornal o JSCE, No. 69, pp. 1-15, ) Sadao, K., Yoshikaz, M., Masaki, F., Tetsshiro T. : Ultimate strength o plate girders nder combined bending and shear, Jornal o JSCE, No. 31, pp. 1-14, ) Tatsmasa, K., Katashi, F., Masasjo, M., Minor, U., Hidehar, N. : An experimental std on remaining bending strength o corroded plate girder, Jornal o Strctral Engineering, JSCE, Vol. 51A, pp , ) Taishi, N., Taka, K., Toshiki, I., Kenta, S., Shigeki, M. : Std on decrease o load carring o girder de to corrosion o pper lange nder sleeper, Proc. o JSCE, The 6 nd Annal Academic Lectre Meeting, I-370, ) Yoshikaz, M., Tetsshiro, T., Yichi, M. : Ultimate strength o girders nder patch loading, Jornal o JSCE, No. 339, pp , ) Yoshikaz, M., Tetsshiro, T., Yoshinori, Y. : An extended calclation method o the ltimate strength o girders nder patch loading, Jornal o JSCE, No. 39, pp , ) Taishi, N., Shota, O., Taka, K., Katashi, F., Shigeki, M. : Remaining strength o plate girder with local corrosion nder railwa sleeper in the pper lange, Jornal o Strctral Engineering, JSCE, Vol. 56A, pp , 010. (Received Jne 7, 017) 9

INVESTIGATION ON THE LOAD TRANSFER MECHANISM FOR THE JOINT OF REINFORCED CONCRETE COLUMN AND STEEL BEAM

INVESTIGATION ON THE LOAD TRANSFER MECHANISM FOR THE JOINT OF REINFORCED CONCRETE COLUMN AND STEEL BEAM Seng Hn KIM 1, Sang Whan HAN 2 And Li Hng LEE SUMMARY The composite framed strctres, which consist