Available online at ScienceDirect. Procedia Engineering 153 (2016 )

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1 Avilble online t ScienceDirect Procedi Engineering 15 (2016 ) XXV Polish Russin Slovk Seminr Theoreticl Foundtion of Civil Engineering Bems with corrugted web: clcultion peculirities of bending torsion nlysis Alexey A. Lukin *, Igor S. Kholopov, Vdim Yu. Alptov, Alexey.V. Soloviev Smr Stte University of Architecture nd Civil Engineering, Molodogvrdeysky St., 194, Smr, 44001, Russi Abstrct The pper gives brief review of works describing bending torsion nlysis of bems with corrugted web. The uthors put forwrd solution specifying V. Vlsov's fmous thin-wlled brs theory which is generlly used to clculte stress-strin behviour of bems with corrugted web bending torsion. The specifiction lies in the following: the reserchers mesure flexure-torsion chrcteristics of the cross-section while incresing pure torsion moment of the cross section by mens of introducing equivlent flnge thickness into clcultions. To check the efficiency of the introduced method the uthors clculted five bems with sinusoidl corrugtion for two concentrted forces ction. The pper introduces the results of these five methods of bem clcultion including the one developed by the uthors. The obtined results showed tht the tension vlue in ech cse is lmost the sme (with mximum 7% difference in rtes). The reserch lso determines the scope limittions of the uthors' specified theory The Authors. Published by by Elsevier Elsevier Ltd. Ltd. This is n open ccess rticle under the CC BY-NC-ND license ( Peer-review under responsibility of the orgnizing committee of the XXV Polish Russin Slovk Seminr Theoreticl Peer-review Foundtion under of Civil responsibility Engineering. of the orgnizing committee of the XXV Polish Russin Slovk Seminr Theoreticl Foundtion of Civil Engineering. Keywords: Bem with corrugted web, Thin-wlled br theory, Bending torsion, Tension, Effective thickness, Finite elements method. Nomenclture I I k sectoril moment of inerti pure torsion moment * Corresponding uthor. Tel.: E-mil ddress:.o.lukin@yndex.ru The Authors. Published by Elsevier Ltd. This is n open ccess rticle under the CC BY-NC-ND license ( Peer-review under responsibility of the orgnizing committee of the XXV Polish Russin Slovk Seminr Theoreticl Foundtion of Civil Engineering. doi: /j.proeng

2 Alexey A. Lukin et l. / Procedi Engineering 15 ( 2016 ) h f h w t w b f t f L E G k s f e P x w flnge xis distnce web depth web thickness flnge width flnge thickness br length elstic module sher coefficient cross-section flexure-torsion chrcteristics rc length or semi-oscilltion pnel semi-oscilltion length semi-oscilltion depth eccentricity concentrted lod cross section norml stress combintion norml stress cross-bending norml stress bending torsion 1. Introduction Currently thin-wlled brs re widely used in civil engineering [1-9]. Work strin of open profile thin-wlled brs is chrcterized by cross-bending tension nd by dditionl bending torsion tension on condition tht sher lod does not directly ffect the bending center [10-1]. G. Azhermchev in one of his first experimentl tests [14] proved tht bems with corrugted web resists torsion more effectively thn bems with plne wll. When we consider bending torsion in bems with corrugted web it is importnt to point out tht there re two types of bending torsion: locl bending torsion ppering s result of the web shift from bem xis; generl bending torsion ppering s result of the force shift from the bem xis. Locl bending torsion nd its effect is nlyzed by A. Stepnenko [15], P. Egorov [16], H. Abbs, R. Suse, R. Driver [17]. Generl bending torsion is described by P. Semenov [18]. Other ppers [19, 20] ssess bending torsion effect on corrugted bem nd its work nd compre torsionl ngles of bems with vrious types of corrugtion. 2. Geometric chrcteristics specifiction for bems with corrugted web This pper specifies the thin-wlled brs theory to clculte stress-strin behviour of bems with corrugted web bending torsion which ppers s result of the force shift from the bem xis. The specifiction is s follows. V. Vlsov's thin-wlled brs serves s bsis for this reserch. Additionl torsionl resistnce ppers becuse of constnt shift from the bem xis. It cn be reimbursed if we increse crosssection flexure-torsion chrcteristics (1): k L GI k E I (1) This prmeter is closely connected with the following chrcteristics: sectoril moment of inerti I ; pure torsion moment I k. Sectoril moment of inerti l (in ny symmetricl cross section of bem with web shift from bem xis long the br length) cn be clculted by using the formul:

3 416 Alexey A. Lukin et l. / Procedi Engineering 15 ( 2016 ) I b h t 6b t b h t 12h f t 24 6b t h t f f f f f f f w f w f f f w where h f, t w, b f, f re shown on Figure 1., (2) Fig. 1. Design model of the bem with corrugted web Fig. 2. Cross section of the bem with corrugted web Pure torsion moment l k for cross-section composed of severl thin brs is clculted by: I b t, () k i i where b i t i re depth nd length of the cross-section prts consequently; is 1, 2 for I-bems. In this pper cross-section flexure-torsion chrcteristics re incresed by incresing cross section pure torsion moment. It cn be done by including equivlent flnge thickness into the clcultions: t f. s tf, (4) where s nd re shown on Figure [22]; where Corrugted s = k 1 f k Tringulr s = 1 f Trpezoid s = f ; sin cos ; Fig.. Corrugted web profile Formul 4 shows tht if rc length s is equl to semi-oscilltion length we hve bem with effective flnge thickness geometricl thickness. It corresponds to fmous I-bem with plne wll with well-known solution. If we put (4) into Formul () together with the geometricl prmeters of the flnges nd webs we'll get the following eqution for clculting pure torsion moment of the bem with corrugted web: Iknp. 2 bf tf. hw tw (5)

4 Alexey A. Lukin et l. / Procedi Engineering 15 ( 2016 ) An exmple of clcultions bsed on the methodology described in the pper Let us consider hinged bem long its two sides: The bem is exposed to two concentrted forces. Let us introduce clcultions for five bems with sinusoidl corrugtion. The cross section here is symmetricl. Tble 1 gives these bems chrcteristics. The mteril used is steel. Tble 1. Bem with corrugted web chrcteristics L, h w, t w, b f, t f,, f, m mm mm mm mm mm mm f/ Notes BGS Zemn BGS Zemn BGS Deep BGS flt BGS The clcultions give cross-bending tension x, bending torsion w nd their totl = x + w (see Tble 2). Ppers [22, 2] describe the uthors' methodology of corrugted bems under cross-bending clcultions. The sme bems hve been clculted by the finite element method in "Lir" PC for relibility control. The simultion of the bems nd the finite element grid we used is described in pper [20]. Tble 2. Clcultion results BGS -1 BGS -2 BGS - BGS -4 BGS -5 Clcultion methodology 2 P, x() when x=l/2, MPs x(0), MPs, MPs FEM i 100% T.1.2 T.1.2 T P.I. Semenov Authors e=4m FEM P.I. Semenov Authors e=4m FEM P.I. Semenov e=4m Authors FEM P.I. Semenov e=4m Authors FEM P.I. Semenov Authors e=cm FEM x() T.1 FEM T.1 The dt in Tble 2 show tht tension difference in w ccording to the thin-wlled br theory (with ccount of the suggested specifiction for bems with corrugted web clcultions) nd ccording to FEM is less thn 5% when f/ 1/2. The difference increses to 7% if the corrugtion is deep f/ = If we use other methods of clcultions the difference rises to 24%. 4. Conclusion The reserch yielded the following conclusions: The pper presents new eqution for clculting pure torsion moment for the cross section of bems with corrugted web. Compred with other solutions this one gives the most exct results.

5 418 Alexey A. Lukin et l. / Procedi Engineering 15 ( 2016 ) The pper limits the scope of use for Formul 5. The eqution cn be effectively used in cse the corrugtion geometry if f/ 1/2. References [1] I.S. Kholopov, V.S. Shirokov, A.V. Solovjev, Yu.D. Mkrov, The Strin-Stress Stte Anlysis of Prefb Building, Indistril nd civil engineering, 2015, 6, pp (in [2] I.S. Holopov, V. S. Shirokov, A.V. Solovjov, Strengthening the bering constructions nd nodl connections of the prefbricted modulr building for the purpose of ensuring its sfe opertion, Vestnik of LSTU, 2015, 4, pp (in [] I.S. Kholopov, V.I. Tur, A.V. Tur, Investigtion of stress-strin stte connections mesh nodes dome, High institutions proceedings, Building, no 4, 2012, pp (in [4] I.S. Kholopov, V.I. Tur, A.V. Tur, Mesh Dome with New Nodl Connections, Indistril nd civil engineering, 2012, 10, pp (in [5] N.I. Vtin, A.S. Sinelnikov, Footwy bridges: cold formed steel cross section, Construction of Unique Buildings nd Structures, 2012,, pp (in [6] A.O. Lukin, A.A. Suvorov, Bridge spns with corrugted steel webs, Construction of Unique Buildings nd Structures, 2016, 2, pp (in [7] I.S. Kholopov, A.O. Lukin, V.Yu. Alptov, A.V. Solovjev, K.N. Gudkov, Lightweight metl structure experience, development, implementtion, Building mterils, equipment, technologies of the 21 century, 2011, No.12 (155), pp (in [8] I.S. Holopov, A.V. Solovjov, Stress-strin stte frmework of low-rise buildings thin-wlled profiles, Trdition nd innovtion in construction nd rchitecture. Proceedings of the 72 th nniversry of All-Russin scientific nd technicl conference on the results of R & D in 2014, Smr Stte University of Architecture nd Civil Engineering, 2015, pp (in [9] V.I.Mksk, T.V.Mksk, Clcultion of thin-wlled bem s n open profile brcket, Vestnik of TSUAB, 2012, no 2, pp (in [10] A.V. Solovjev, Constrined torsion of steel bems in the development of limited plstic deformtions: PhD Thesis: , SSAACE, Smr, 1998, 169 p. (in [11] A.R. Tusnin, The numericl clcultion of constructions mde of thin-wlled open profile brs, Moscow,, 2009, 14 p. (in [12] R. Pvzz, Torsion of thin-wlled bems of open section with influence of sher, Interntionl Journl of Mechnicl Sciences, 2005, No 47, pp [1] I. Senjnovi, S. Rudn, N. Vldimir, Influence of sher on torsion of thin-wlled girders, Trnsction of FAMENA, 2009, No, 2, pp [14] G.A. Azhermchev, Bems with wvy web, Industril nd civil engineering, 196, no. 4, pp (in [15], Steel I-rods with wvy web, Khbrovsk, Khstu, 1999, 115 p. (in [16] P.I. Egorov,, Providing steel I-shped cores with thin corrugted web resistibility nd rigidness. Building nd reconstruction, 2010, no 2, pp (in [17] H.H. Abbs, R. Suse, R.G. Driver, Behvior of corrugted web I-Girders under in-plne lods, Journl of Engineering Mechnics, Vol. 12, Issue 8, August 2006, pp [18] P.I. Semenov, Clcultion of strength nd deformbility of the nisotropic thin-wlled open section, Kiev, Vishh shkol, 1974, 184 p. (in [19] A.V. Solovjev, A.O. Lukin, Estimting constrined torsion influence on bem with corrugted web work, High institutions proceedings, Building, no 6, 2012, pp (in [20] A.V. Solovjev, A.O. Lukin, V.Yu. Alptov, V.N. Sevstynov, On peculrities of bems with corrugted web work while clculting constrined torsion influence, Vestnik of MGSU, 201, no 11, pp (in [21] V.Z. Vlsov, Thin-Wlled Elstic Rods, Moscow, Fizmtgiz, 1959, 574 p. [22]. A.O. Lukin, Defining bems with corrugted web deflexion with ccount of sher deformtion, Inzhenerny Vestnik Don, 1, 201, ISSN , URL: (in [2] A.O. Lukin, Improved clcultion of the stress-strin condition of bems with corrugted web, Building mechnics nd structures design, 5, 201, pp (in [24] I.M. Blznnikov, I.S. Kholopov, V.Yu. Alptov, A.O. Lukin, Stress nd strin stte in bems with corrugted web nd their use in hydrulic engineering structures. Procedi Engineering. Vol. 111, pp