Theoretical Research on the Calculation of Bending Moment at Arc Vault in Steel Corrugated Plate

Transcription

1 Theoretical Reearch on the Calculation of Bending oment at Arc Vault in Steel Corrugated Plate Baijian Li, Liangheng Zhu, Xinha Fu, Xu Luo. School of Civil Engineering,Tranortation, South China Univerity of Technology, Guangzhou, Guangdong. School of echanic, Architectural Engineering, Jinan Univerity, Guangzhou, Guangdong Abtract: In order to tudy the calculation theory of bending moment at the arch vault of teel corrugated late, baed on the ummary of CHBDC (Canadian Highway Bridge Deign Code), the internal force calculation of arch tructure in teel corrugated late i exlored from a new angle. Firt, according to the theory of tructural analyi, two hinged arche are taken a the baic ytem to etablih a canonical equation of force method, the analytical value of vault bending moment i obtained, the formula and form are rovided. Second, conidering the interaction between tructure and oil, the relative tiffne of oil and tructure can be olved qualitatively by deriving the formula of deformation ratio, and two imortant arameter reflecting the relative tiffne of oil and tructure are obtained: axial tiffne coefficient α and the relative tiffne coefficient α. Third, combined with the reult of tructural finite element analyi, by changing the area A of ection, moment of inertia I, ecant modulu of oil E, filling height H and other arameter, we dicued the influence of thee arameter on vault bending moment and the correonding fitting formula i obtained: ζ =-.log (L E / EI), which i defined a the correction coefficient of bending moment. After the correction of the true bending moment value obtained by the coefficient tructural analyi, the obtained bending moment i the true bending moment at arch tructure of the teel corrugated late. Finally, a tyical examle i ued, by uing the method of thi aer, CHBDC method and finite element method to calculate the bending moment of vault, the comarative analyi reult how that thi method i cientific and rational. It rovide correonding theoretical guidance and ractice reference for the reearch and engineering alication of thi kind of tructure. Keyword: Traffic Engineering; Bending oment Calculation; Static Analyi; Arc Vault of Steel Corrugated Plate; Correction Coefficient Of Bending oment. Introduction So far, the develoment of teel corrugated late tructure ha been over a hundred year, due to the exitence of corrugation and the joint force of oil-involved tructure, the mechanical roertie of tructure and material are given full lay, with good deformation coordination erformance, and becaue of the wide alicability of the tructure, it ha a wide range of engineering alication and a broader alication roect in engineering. At reent, the theory of circumferential comreive tre ummarized on the bai of the theory of mechanical analyi of teel corrugated late i more mature and widely ued[-], which i uorted by the American Iron and Steel Intitute, comleted by Reynold K. Watkin at the Utah State Univerity Laboratory. Structural mechanical tet wa carried out by alying a vertical reure load from the to by embedding a corrugated teel ie in a region wraed by an oval-haed iron clad in a ecific ize a hown in Fig.. Figure.. Reearch device of Reynold K. Watkin The concluion of thi tudy i the rototye of the theory of ring comreion, that i, under the action of the uer load, tructural tre re-ditribution occur due to oil arching effect, the tre of the corrugated teel ie i ditributed to uniform annular reure. A the load continue to increae, the ultimate bearing caacity of the tructure i controlled by the yield of the material and the buckling of the tructure, deending on the tiffne of the ie wall. When the ie wall tiffne i large, the ring comreion tre will make the wall yield; and when the ie wall tiffne i mall, the tructure loe bearing caacity due to buckling intability. A a miletone in the hitory of tructural deign theory of teel corrugated late, the theory of ring comreion ha been adoted in a variety of deign method, but the theory i baed on ecific ideal tet condition: fixed area and ecific filling height range. The reure on the to of the exerimental device wa ued to imulate the oil reure of the tructure, and the interference of the oil outide the area wa hielded. In addition, due to the reence of the ellitical iron cladding, the interaction between oil i mainly tranmitted along the circumferential direction of the metal cladding, and the radial queezing action to the corrugated ie i made, thu forming the ringreing effect on the tructure. However, in actual engineering, the overall deformation trend of the fill i ettlement, and the tre i reditributed by the interaction with the tructure, o that the oil reure acting on the tructure i actually non-uniform, hence it i difficult to achieve the ideal ring-reing tate, thi henomenon i articularly evident in culvert with high filling. China began to introduce large-cale teel corrugated late tructure at the beginning of the th century, which ha been aid much attention by reearcher in the indutry and gained rich theoretical and ractical reult, and accumulated a lot of exerimental data, among which, influential reearche are: Baed on the field exeriment of ie culvert tructure and finite element numerical method, Li Zhulong tudied the tre characteritic of corrugated teel ie culvert [4]. By taking the corrugated teel ie culvert on Zholiang Secondary Highway in Inner ongolia a the reearch object, Zhang iaoxin exounded the calculation method of oil reure in the vertical and horizontal direction of the tructure and comared it with the finite element analyi reult of the tructure [5]. Baed on the actual Journal of Reidual Science & Technology, Vol., No. 7, 6 6. doi:.78/in //7/6

2 engineering tructure and model tet, Wu Yanling dicued the tre and deformation characteritic of corrugated teel ie culvert with different ie diameter [6]. Other reearch intitute have alo carried out the correonding reearch, motly concentrated in the exerimental and tructural finite element analyi, omitted here. There are many meaured data how that the tre ditribution of the corrugated teel ie ection i actually non-uniform, that i, in the non-ring-reing tate, and the tructure i generally ubject to the bending moment, the maximum bending moment i generally located at the to of the tructure [4-6]. It can be een that all the corrugated late tructural deign theorie baed on the annular reure theory have certain limitation, but becaue thee deign theorie have tiulated the ecific working condition, the alication of thee deign theorie can atify the need of engineering even without taking into account the effect of bending moment on the tructural tre, thu obcuring the irrationality of thee deign method to ignore the bending moment effect [7]. For examle, the AISI deign method ecifie that it i only alicable to corrugated teel ie tructure with a bore diameter of le than 6 m. Internal force calculation conider only the axial force effect, but the alication condition of the teel corrugated late are much broader than thi. To um u, it i very imortant to tudy the characteritic of bending moment effect on teel corrugated late tructure, which directly affect whether the actual tre tate of the tructure i accurately graed. Thi i the remie of variou reearch and alication of teel corrugated late tructure. Thi aer will focu on the bending moment calculation of teel corrugated late arch tructure, and rovide ome theoretical guidance and ractical reference for further reearch and engineering alication in thi field.. Calculation of CHBDC Bending oment At reent, among the foreign deign method of teel corrugated late tructure [], the mot mature and the mot widely ued one are the AISI method and CHBDC method. Among them, AISI i a ermiive bearing caacity deign method, which i uitable for corrugated teel ie culvert with an le than 6m. When the tructure an i large and the tiffne i mall, the CHBDC method i adoted. Thi method take into account the interaction of axial force and bending moment, which i eecially uitable for long-an and low-filling tructure. CHBDC, the full name of the Canadian Highway Bridge Deign Code[8]. When the tructure i not uniform in radial oil reure, axial force and bending moment are generated in the tructure. Only CHBDC conider to check the tre tate of the tructure by combing bending moment and axial force. The calculation of bending moment conit of three art: The bending moment ( ) when the fill reache vault; The bending moment ( B) when the fill i H c; The bending moment ( C) roduced by the contruction live load. = + B + () C =krbγd () h B = -k R BγDh H () C C =krldhlc (4) Where: D h-tructure an; H c-filling height during contruction, m; k, k, k -coefficient; -combined bending moment, kn m/m; - the bending moment when the fill reache the vault; B-the bending moment when the fill i H c; c-the bending moment roduced by the contruction live load; R B-calculation arameter; γ-volume weight of fill. The bending moment when the fill exceed the vault The bending moment when the fill i high Figure..Schematic diagram for the calculation of CHBDC bending moment Temorarily not conidering bending moment c. and B are the bending moment aociated with the oil, a hown in Fig., reectively are the bending moment generated in the tructure jut when the fill i covered by vault and the bending moment when the fill i above a certain height H C [8]. The deign method of CHBDC i alicable to ie culvert and arch culvert. It can be ued in a wide range and the deign method i reaonable. Thi i alo the deign method and theoretical bai referred to by current dometic local deign tandard.. Analyi of Bending oment of Steel Corrugated Plate Arch. Baic tructure The foundation of teel corrugated late i to embed teel angle in the concrete, connect teel corrugated late and teel angle via bolt, the teel angle allow the corrugation late to have a certain rotational caacity, and the local comreion caacity of the teel corrugated late i weak in the foundation connection art. Conidering thee two factor, teel corrugated late tructure i imlified into two hinged arche, a hown in Fig.. Journal of Reidual Science & Technology, Vol., No. 7, 6 6. doi:.78/in //7/6

3 Figure.. Baic tructure of arc vault Through the tatic analyi theory, the baic force of the tructure can be olved. The baic tructure take the horizontal force a the baic unknown force, after olving the baic unknown force, the tructure i the ame a the curved beam tructure. The coordinate ytem take the acting oint of horizontal thrut (oint A in Fig. ) a the origin, the uward direction i the y-axi oitive direction and the right direction i the x-axi oitive direction.. Calculation of horizontal thrut According to the baic theory of tructural mechanic, the horizontal force calculation formula of the two hinged arche under the action of arc triangular load, vertical uniform load, horizontal triangular load and horizontal uniform load are ummarized in Table. Table horizontal force calculation of two hinged arch Load form Calculation formula Arc triangular load Uniform load Horizontal triangular load Horizontal uniform load Δ kgr +kgrr H =- =- 4 5 A δ kr +kr Δ kgr +kgrr H =- =- 6 7 A δ kr +kr 5 Δ kk 8 aγr H A =- = δ R k R + k r 4 Δ kk 9 aγr H A4 =- = δ R k R + k r k -k 9 in the table are the arameter related to the central angle in calculation, refer to literature[9]. Parameter: γ-volume weight of fill; K a-active oil reure coefficient; g -maximum load trength triangular ditribution of vault arc, g =γf (f i the arch height); g -uniform load value, g =γh (H i the filling height on the arch).. Bending moment of curved beam According to the above horizontal thrut, ectional bending moment can be obtained, the formula i: = H y = H R co ϕ coϕ (5) ( ) P A P A Load form Arc triangular load Vertical uniform load Horizontal triangular load Horizontal uniform load Table Calculation formula of Calculation formula Rg Rg = k m - coφ - coφ = gr (in φ -in φ) = K aγ(r co ϕ Rco ϕ) (R R co ϕ R co ϕ) = KaγH(R co ϕ R co ϕ) Where: i a hown in Table, φ i the central angle of the tructure, φ i the central angle of the oition of the deired ection. The calculated horizontal thrut and bending moment of curved beam are calculated by a central angle ranging from -9. To facilitate the deign uing the rie an ratio, the relationhi between radiu R and vector height f a well a an L i: L=Rinφ ; f=r- Rcoφ. R and φ in the above formula are converted into f and L. The horizontal thrut i obtained firt, then the bending moment of curved beam i olved (Table ), and finally the bending moment at arch vault i obtained via formula (5), a hown in Table. Load condition Table Calculation of bending moment at arch vault of two hinged arche Rie an ratio ultilier Journal of Reidual Science & Technology, Vol., No. 7, 6 6. doi:.78/in //7/6

4 Arc triangular load γl Vertical uniform load γhl Horizontal triangular load K aγl Horizontal uniform load K aγhl When the two hinged arche are under the action of the arc triangular load, vault bulge uward and uwar, o the value i negative in the table; while under the action of the vertical uniform load, the vault have a oitive bending moment and downwar. Becaue the arc triangular load, horizontal triangular load, vertical uniform load and horizontal uniform load imultaneouly exit, that i, lateral oil reure i bound to roduce under the vertical load, the difference between the lateral oil reure coefficient K a =tan (45 -φ/). Steel corrugated late tructure require that the tructure backfill area hould adot dene gravel oil, oil with large comreion coefficient hould not be ued, the correonding oil reure coefficient K a=.7-.. From another oint of view: under the joint action of the arc triangular load and horizontal triangular load, the tructure roduce an uward antiarch, the role of the two are the ame; while the load effect of the vertical uniform load and horizontal uniform load i ooite. In order to reduce the influence of the unneceary factor on the bending moment of the tructure, the bending moment value of the triangular load i added directly from the conervative oint of view (the lateral coefficient take ), uniform load neglect the horizontal load effect (the lateral coefficient take ), Table 4 i obtained. Table 4 Bending moment at arc arch vault in teel corrugated late Load condition Rie an ratio ultilier Triangular load γl Uniform load γhl Note: with known volume weight of fill γ, vault oil height H, tructure an L and rie an ratio f/l, the bending moment of teel corrugated late vault can be calculated directly from Table 4. Due to the interaction between the tructure and oil, the vertical oil reure caue the lateral deformation of the tructure to extrude the oil on both ide, which caue the oil on both ide to contrain the lateral deformation of the tructure, increaing the lateral oil reure. Therefore, if we want to calculate the bending moment of the tructure more accurately, we mut alo conider the effect of the oil-tructure interaction and relative tiffne on the vertical oil reure, and correct the obtained bending moment. 4. Relative Stiffne of the Soil-tructure Steel corrugated late tructure ha a trong deformation caacity, and can adjut it own force through deformation, which make the tructure and the concrete tructure are eentially different. According to literature[], the ecific value of deformation can be ued to determine the tructure and oil interaction, or adjut the force. According to tructural analyi theory[], the deflection of vault under uniform load i: N N (6) = d + d EI EA ϕ The vault deformation conit of two art: the bending moment and the axial force. Where, the vault deformation caued by bending moment i: φinφ in φ + φin φ (7) 4 gr inφin φ = + in φcoφ + coφ EI 4 co φ in φ φ in φ co φ k coφ + co φ The vault deformation caued by axial force and the vertical deformation of the oil in the arch height range are: glr = ( coϕ ) (8) N EA gr ( co φ) = (9) E The deformation of the tructure i decomoed while taking into account the force aociated with EA and EI, reectively. The axial tiffne coefficient α and the relative tiffne coefficient α are defined. N LE LE = κ α = () EA EA L E L E = ξ α = () EI EI Where: E-elaticity modulu of teel corrugated late, Pa; E -ecant modulu of oil, Pa; I-anti-bending inertia moment of teel corrugated late, mm 4 ; L-tructure an, mm; R-tructure radiu, mm; k, κ, ξ-arameter relating to the central angle φ. Calculating the deformation ratio i to find the arameter that affect the force of the tructure. Therefore, we can neglect the arameter k, κ and ξ relating to the central angle, and the above roblem are concluded a the effect of axial tiffne coefficient α and the relative tiffne coefficient α on treing roertie of the tructure. ϕ Journal of Reidual Science & Technology, Vol., No. 7, doi:.78/in //7/6

5 The above i a qualitative analyi, and ignore the arameter k, κ and ξ, o the defined α and α can not be directly ued for internal force analyi. To determine the ecific exreion, the finite element analyi method will be ued to calculate the change law of the tructural internal force, o a to obtain the correonding fitting formula. 5. Finite Element Analyi and Data Fitting ANSYS wa ued to etablih the lane train model for teel corrugated late [], and the boundary condition choe hinge uort. BEA beam element wa ued to imulate teel corrugated late tructure. PLANE8 lane train element i ued to imulate the oil body. The contitutive relation of teel i baed on the claical bilinear iotroic model (BISO) and obey the iotroic hardening failure criterion. The oil contitutive relation adot D-P model [4]. Select the baic model: m (an) 6.5m (high vector) emi-arched tructure; oil height4m; oil volume weight 9.6KN/m ; teel elaticity modulu. 5 a. Sectional area A=-mm /mm; anti-bending moment of inertia I=7- mm 4 /mm; ecant modulu of oil E =6-a. The variation range of the above arameter cover the corrugation arameter of mot teel corrugated late and the ecant modulu of oil, which i uitable for tudying the internal force variation law of teel corrugated late tructure. Table 5 Parameter table of finite element analyi Steel corrugated late arameter Structure arameter odel arameter Steel Structure 4 5mm m corrugated an late Corrugationl d Sectional area A oment of inertia I Elaticity modulu E BEA- -mm /mm Soil height 4m Soil body PLANE-8 7-mm 4 /mm. 5 a Soil volume weight Secant modulu 9.6KN/m 6-a Steel contitutive Soil contitutive Claical bilinear iotroic model D-P model () When the ectional area A=-mm /mm change, the oil reure, axial force and bending moment of the tructure are increaed, but the magnitude of the increae i not ignificant. Fig. 4 i obtained by normalizing oil reure, axial force and bending moment, we found that the trend line are conitent. In fact, the axial force and bending moment of the tructure are calculated from the oil reure. When the increae trend of axial force and bending moment are in agreement with that of the oil reure, the change of the cro-ection only affect the oil reure value intead on axial force and bending moment. Therefore, the effect of axial tiffne coefficient α on bending moment i eliminated. Figure. 4 Change law of internal force along with ectional area Figure. 5Change law of internal force along with anti-bending inertia moment () When the inertia moment I=4-mm 4 /mm changed, oil reure lightly decreaed, axial force lightly increaed, but the change i not ignificant. The change i the mot obviou in bending moment value, which increaed with the increae of anti-bending inertia moment. For the viual exreion, Fig. 5 i made after numerical normalization. It can be een from the figure that the change of anti-bending inertia moment ha the greatet influence on bending moment, and the trend curve of bending moment i fitted by the function ζ =-.log (L E / EI), and ζ i defined a the correction coefficient of bending moment. The coefficient ζ i fitted by changing I, which i not only related to I, but alo to E, o we changed E to verify whether the coefficient are correct. () When E=6-a change, the oil reure increae with the increae of ecant modulu, but the increae i not ignificant. The bending moment decreae with the increae of ecant modulu of oil, with ignificant decreae. And the value of correction coefficient of bending moment and bending moment are lightly deviated in fitting, which reult from loe. When ζ =-.log (L E /EI), the fitting i better (Fig.5). That i to ay, the fitting curve of ζ obtained according to the change of I and E i only the difference between log coefficient. and.. Becaue the value change of ecant modulu of oil in ractical engineering i le, the individual arameter Journal of Reidual Science & Technology, Vol., No. 7, doi:.78/in //7/6

6 uch a 6a and a are generally adoted, o the loe take. (mainly to change the curve of I-baed fitting). The difference caued by the E change can be corrected by adjuting the intercet to enure that the fitting curve lie above the bending moment curve, making it biaed to afety. Figure. 5 Change law of internal force along with ecant modulu By changing the two arameter, the fitting function of I and E can better reflect the change law of the bending moment of the tructure along with the arameter, but alo the influence of the tructure an L on the internal force of the tructure. In fact, by changing the tructure an to analyze the internal force of the tructure doe not rove the correctne of the above arameter, becaue the calculation reult of the tructural bending moment are very enitive to it an. In addition, due to the internal force variation caued by the an change, and the above correction coefficient are not in the ame order of magnitude, making the analyi difficult. Figure. 6 Change law of internal force along with tructure an (4) When the tructure an L=4-mm i changed, the change law of oil reure, axial force, bending moment and L i obtained. Fig.6 i obtained by changing the tructure an under the ame filling height, the following change law are obtained: With the increae of tructure an, the oil reure gradually decreae, reaching the minimum value (correonding to the an of about 8m) and then gradually increae; With the increae of an, the axial force increae aroximately linearly; With the increae of an, the bending moment increae gradually and gradually decreae uon reaching a certain maximum value (correonding to the an of about 6.5m). The change law doe not accord with the fitting curve of the correction coefficient of bending moment. Due to the econd (vertical uniform load) or third (arc back triangular load) ower function relationhi between the bending moment and the tructure an, negative bending moment will be roduced under the action of the arc back triangular load, and oitive bending moment will be roduced under the action of vertical uniform load. The reult of ANSYS analyi give the final bending moment of the tructure, which i the reult of the ueroition of the oitive and negative bending moment, o the changing curve of bending moment i hown in Fig. 6. When the ecific value of filling height and tructure an i large, the growth rate of oitive bending moment i greater than that of negative bending moment, o the final ueroition reult trend i gradually increaing; when the ecific value of filling height and tructure an i mall, arc back triangular load begin to dominate, namely the growth rate of oitive bending moment i maller than that of negative bending moment, o the final ueroition reult trend i gradually decreaing; when the tructure an continue to increae, the negative bending moment will continue to increae, eventually exceeding the oitive bending moment, reulting in the final uwar deformation of the arch tructure. 6. Verification of Algorithm Taking a teel corrugated late arch tructure a an examle, the reult of the internal force calculation method, CHBDC deign method and finite element numerical method in thi aer are ued for a comarative analyi. Auming the tructure i a emicircular arch with a an of m and a vector height of 6.5m; the filling i grit, filling height i 4m, ecant modulu i Pa, and oil volume i 9.6kN/m ; the corrugated teel ha a yield trength of F y=75pa, a tenile trength of F u=8pa and a corrugated teel elaticity modulu E=. 5 Pa. The teel corrugated late ecification: wave ditance l=4mm, wave height d=5mm, wall thickne t=7mm. Table 6 Calculation reult of different method Item CHBDC Finite element numerical method ethod in thi aer Anti-bending moment -6.7 KN m/m -5.8 KN m/m Poitive bending moment 4.5 KN m/m 5.7 KN m/m 47. KN m/m Total bending moment.8 KN m/m.5 KN m/m According to the reult in Table 6, the final bending moment calculated by the method in thi aer i the larget, followed by ANSYS finite element method and CHBDC deign method. Comared with the CHBDC deign method, the anti-bending moment calculated by the method in thi aer i relatively mall and the oitive bending moment i relatively large, but the value are cloe. Journal of Reidual Science & Technology, Vol., No. 7, doi:.78/in //7/6

7 Becaue the method of calculating bending moment of the teel corrugated late rooed in thi aer i an analytic olution baed on the claical mechanic theory, and correonding correction were made conidering the interaction of the oil tructure, the numerical olution of the finite element analyi ha high cientificity and a more olid theoretical bai. In addition, the reult of the ingle bending moment calculation of the rooed method are in good agreement with the CHBDC deign method, which i acceted by both home and abroad, and can be ued to rereent the current technological level. The final total bending moment calculation reult are alo afe, more conducive to enure the normal ue of the tructure under the load effect. 7. Concluion Through the above analyi, the following concluion are reached: () On the bai of tructural mechanic, the analytical olution of the vault bending moment at arc arch tructure (two hinged arche) in teel corrugated late i deduced and the correonding theoretical formula are derived. And the maximum bending moment value (at vault) under the different rie an ratio and different ditributed load are calculated, ummarized in Table 4 in cae of ue in engineering deign. () Conidering the interaction between tructure and oil, the relative tiffne of oil and tructure can be olved qualitatively by deriving the formula of deformation ratio, and two imortant arameter reflecting the relative tiffne of oil and tructure are obtained: axial tiffne coefficient α and the relative tiffne coefficient α, and the correonding fitting formula i obtained: ζ =-.log (L E / EI). Thi i the correction factor for calculating bending moment in Table 4, which effectively reflect the effect of oil tiffne on the bending moment of the tructure, making the modified bending moment more in line with the actual tre ituation of the tructure. () A tyical examle of teel corrugated late tructure i ued, by uing the method of thi aer, CHBDC method and finite element method to calculate the bending moment of vault, the comarative analyi reult fully how that thi method i cientific and rational. It rovide correonding theoretical guidance and ractice reference for the reearch and engineering alication of thi kind of tructure. Reference [] Shane Finlay, P., Patrick Biro, B., Heba Ahmed, B.. Soil-Steel Structure and the Canadian Highway Bridge Deign Code. Bridge Engineering Imacting Society Seion of the Annual Conference of the Tranortation Aociation of Canada St. John, Newfoundland and Labrador.. [] AASHTO. LRFD Bridge Deign Secification, American Aociation of State Highway and Tranortation Official. 444N.Caital St.,N.W.,Ste.49, Wahington, D.C.. [] Watkin,R.K., and oer,r.p.. The Structural Performance of Buried Corrugated Steel Pie. Logan, Utah: Utah State Univerity, 969. [4] LI Zhu-long. Study on Deign and Contruction of Corrugated Steel Pie Culvert. Xi an: Chang an Univerity [5] Zhang iao-xin.structural echanic Performance of Buried Corrugated Steel Pie Culvert Conidering Rigidity and Flexibility.Beijing: Beijing Jiaotong Univerity.. [6] Wu Yan-ling.Force Deformation Characteritic and It Alication of Corrugated Steel Pie Culvert of Highway.Xi an: Chang an Univerity.. [7] American Iron and Steel Intitute. Hand Book of Steel Drainage & Highway Contruction Product(Canada Edition). Canada: Corrugated Steel Pie Intitute,. [8] CAN/CSA-S6-. Canadian Highway Bridge Deign Code. A National Standard of Canada,Section 7 Buried Structure. Section 7.6 Soil-etal Structure. CSA.. [9] Comile Grou of Deign anual for Highway and Bridge and Culvert. Arch Bridge.Beijing: The Peole' Communication Publihing Comany [] Xiong Qi-jun. Culvert[]. Beijing: China WaterPower Pre.6.. [] GB 5-.Structrual deign code for ieline of water uly and wate water engineering... [] WANG Huan-ding, QI Kai. Structure mechanic. Beijing. Tinghua univerity re.6.8. [] Li Bai-jian, Fu Xin-ha. Finite Element Analyi of Corrugated Steel Plate Low Arch Bridge. Journal of Highway and Tranortation Reearch and Develoment..7. [4] WANG Xin-min. ANSYS Numerical Analyi of Engineering tructure. Beijing: China Communication Pre,7.. Journal of Reidual Science & Technology, Vol., No. 7, doi:.78/in //7/6