BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI Publicat de Universitatea Tehnică Gheorghe Asachi din Iaşi Tomul LIX (LXIII), Fasc. 1, 013 Secţia CONSTRUCŢII. ARHITECTURĂ A COMPARATIVE ANALYSIS OF WEB BUCKLING RESISTANCE: STEEL PLATE GIRDERS GIRDERS WITH CORRUGATED WEBS BY CĂTĂLIN MOGA, ALEXANDRA-DENISA DANCIU * and MIRCEA SUCIU Technical University o Cluj-Napoca Faculty o Civil Engineering Received: February 1, 013 Accepted or publication: February, 013 Abstract. In this paper e present a comparative analysis regarding the shear eb resistance beteen ive types o steel plate girders and a girder ith corrugated ebs. The eb buckling resistance o steel plate girders is established in accordance ith EN 1993-1-5: Plated Structural Elements- 5.3. In the case o girders ith corrugated ebs, the background or the shear resistance o the eb and the beam veriication is the Annex D to EN 1993-1-5: Plate Girders ith Corrugated Webs. Key ords: steel plate girders; girders ith corrugated ebs; comparative analysis; Euronorm EN 1993-1-5: Plated Structural Elements. 1. Introduction It is ell knon that in the case o steel plate girders the shear orce is preponderantly taken over by the girder eb, the contribution o the langes * Corresponding author: e-mail: alexandra.stan@cdp.utcluj.ro
176 Cătălin Moga, Alexandra-Denisa Danciu and Mircea Suciu being almost insigniicant and the shear is integrally taken over by the corrugated ebs in the case o girders ith corrugated ebs. As the eb is corrugated, it has no ability to sustain longitudinal stresses so, the conventional assumption is to ignore its contribution to the bending moment resistance (Åkesson, 007). In this paper e present a comparative analysis regarding the shear eb resistance beteen ive types o steel plate girders and a girder ith corrugated ebs (Johansson et al., 007; Moga et al., 01). The eb buckling resistance o steel plate girders is established in accordance ith EN 1993-1-5: Plated Structural Elements- 5.3. In the case o girders ith corrugated ebs, the background or the shear resistance o the eb and the beam veriication is the Annex D to EN 1993-1-5: Plate Girders ith Corrugated Webs (SR EN 1993-1-1, 006; SR EN 1993-1-5, 006; ESDEP, 1994). The obtained results can be useul in the optimal design o such type elements.. Resistance to Shear.1. Web Shear Resistance o Steel Plate Girders The contribution o a stiened or unstiened plate eb (Fig. 1) to the shear buckling resistance is given by V b. Rd ht. (1) 3 M 1 a b c Fig. 1 End supports: a no end post; b rigid end post; c non- rigid end post. For ebs ith transverse stieners at supports only and or ebs ith either intermediate transverse stieners or longitudinal stieners or both, the actor or the contribution o the eb to the shear buckling resistance should be obtained rom Table 1.
Bul. Inst. Polit. Iaşi, t. LIX (LXIII),. 1, 013 177 Table 1 Factor Rigid end post Non-rigid end post 0.83 / 0.83/ 1.08 0.83 / 1.08.37 / 0.7 The slenderness parameter, 0.83/ 1 0.83/, should be taken as here: is the yielding steel stress in the eb; / 3 h / t, () cr 37.4 k E t k 1 1 h the cr critical elastic shear stress; k the shear buckling resistance obtained as ollos: a) transverse stieners at supports only, k 5. 34 ; b) transverse stieners at supports and intermediate stieners 4 k 5.34, hen (a/h ) 1 ; a / h 5,34 k 4.00, hen (a/h ) < 1. a / h.. Shear Resistance o Corrugated Webs The shear resistance, V Rd, o a trapezoidal or sinusoidal corrugated eb (Fig. ) should be taken as c. V Rd c ht. (3) 3 M 1 The reduction actor, c, is the lesser o the values o reduction actors or local buckling,, and global buckling, c. g, obtained rom 1.15 c. 1, 0.9 c. c min 1.5 c. g 1, 0.5 c. g (4)
178 Cătălin Moga, Alexandra-Denisa Danciu and Mircea Suciu here the quantities in eq. (4) are given by relations cr. c. a3s E t h t 1(1 ) s cr. 3, (5) 5.34 or sinusoidal corrugated ebs, t 4.83 E ; amax max [ a1; a] or trapezoidal corrugated ebs, a max 4 3 ; D xdz 3 th (6) 3.4, (7) Fig. Geometric notations.
here D x and D z are given by relations Bul. Inst. Polit. Iaşi, t. LIX (LXIII),. 1, 013 179 3 Et sinusoidal corrugated ebs, 1 1 s Dx 3 Et a1 a4 trapezoidal corrugated ebs; 1 1 a1 a EI z sinusoidal corrugated ebs ebs, Dz Eta3 3a1 a trapezoidal corrugated ebs; 1 a1 a4 I z second moment o area o one corrugation o length, (Fig. ). (8) (9) 3. Comparative Analysis In hat ollos, e conduct a comparative analysis regarding the shear eb resistance beteen ive types o steel plate girders and a girder ith corrugated ebs. Fig. 3 Constructive solution o case 1: girder ith trapezoidal corrugated eb (TC). The olloing cases are analysed: a) C a s e 1: Girder ith trapezoidal corrugated eb (TC) Design data:
180 Cătălin Moga, Alexandra-Denisa Danciu and Mircea Suciu Steel: S35; Constructive solution o girder (Fig. 3). b) C a s e : Steel plate girder (GP) Five types o plate girders are analysed (GP.1,...,GP.5), ith the olloing design data: Simple supported girder, made o steel S 35. Web dimensions: h t,000 t ; t = 6; 7 and 8 mm. Girders ith transverse stieners only, at a distance o a = 1,400; 1,500 and,000 mm. D x 3.. Case 1 Solution: Girder ith Trapezoidal Corrugated Web (TC) The solution is presented in the olloing eqs. 6 4 t cr. 4.83E 4.83.110 8,80 dan/cm a max 140, (10) c.,350 0.40, (11) 3 8, 80 3 cr. 3 6 3 1 4 a 1 a 1 (1 0.3 ) Et a a.110 0.4 140 50 10,77 dan.cm, (1) 1 1 140 78 6 3 3 1.110 0.4 6 3140 78 965.35 10 4 dan.cm, Et a a a Dz (13) 1 a1 a4 1 140 50 4 3 4 4 3 3.4 3.4 D 10,77(965.35 10 ) 3,569 dan/cm, xdz (14) t h 0.4 00,350 0.6. (15) 3 3,569 3 The reduction actor is 1.15 1.15 c. 0.88 1; 0.9 c. 0.9 0.40 c min 1.5 1.5 c. g 1.34 1, 0.5 c. g 0.5 0.6 consequently c 0.88. The eb shear buckling resistance is V,350 (16) Rd c ht 0.88 00 0.4 10 868 kn. (17) M 1 3 1.1 3
Bul. Inst. Polit. Iaşi, t. LIX (LXIII),. 1, 013 181 3.. Case Solution: Steel Plate Girder (GP) In Table the design parameters and the values o the eb shear buckling resistance, V Rd, are presented or each o ive girders. Table Design Parameters and Values o V b, [kn] Type h, [mm] t, [mm] a, [mm] k τ V b, [kn] GP.1,000 6,000 9.34.9 0.38 56 GP.,000 7,000 9.34.50 0.43 743 GP.3,000 8,000 9.34.18 0.48 947 GP.4,000 7 1,400 14.90 1.98 0.51 880 GP.5,000 7 1,500 13.49.08 0.49 846 4. Conclusions Steel girders ith corrugated ebs can be advantageous rom an economic point o vie in comparison ith steel plate girders having transverse or transverse and longitudinal stieners. Table 3 presents some data shoing the structural eiciency o steel girders ith corrugated ebs in comparison ith steel plate girders. Table 3 Eiciency Parameters Web eight, g Girder type ggp. i / g TC V b, [kn] TC GP. i V / kg/m b V b TC 36 1.00 868 1.00 GP.1 50 1.39 56 1.54 GP. 5 1.44 743 1.17 GP.3 65 1.80 947 0.9 GP.4 56 1.56 880 0.99 GP.5 57 1.58 846 1.03 Plate girder It can be observed that at the same shear resistance the eight o the eb o a plate girder is about 50%...55% greater than that o a corrugated eb. At the same time some disadvantages o the girder ith corrugated ebs can be mentioned: a higher manuacture to build up such elements; the automatic elding is diicult to be applied; the corrugated ebs have no ability to sustain longitudinal stresses, so, the conventional assumption is to ignore its contribution to the bending moment resistance; the joints ith other members are more complicated.
18 Cătălin Moga, Alexandra-Denisa Danciu and Mircea Suciu REFERENCES Åkesson B., Plate Buckling in Bridges and other Structures. Taylor & Francis, London, 007. Johansson B., Maquoi R., Sedlacek G., Müller C., Beg D., Commentary and Worked Examples to EN 1993-1-5 Plated Structural Elements (programme o CEN/TC 50). 007. Moga P., Guţiu Şt., Moga C., Proiectarea elementelor din oţel. Teorie şi aplicaţii. Edit. Univ. Tehn., Cluj-Napoca, 01. * * * Eurocod 3: Proiectarea structurilor de oţel. Partea 1-1: Reguli generale şi reguli pentru clădiri. SR EN 1993-1-1/006. * * * Eurocod 3: Proiectarea structurilor de oţel. Partea 1-5: Elemente din plăci plane solicitate în planul lor. SR EN 1993-1-5/006. * * * European Steel Design Education Programme. The ESDEP Soc., The Steel Constr. Inst. Bekshire, UK, ESDEP, 1994. ANALIZĂ COMPARATIVĂ PRIVIND REZISTENŢA LA VOALARE: GRINZI PLANE GRINZI CU INIMA DIN TABLĂ CUTATĂ (Rezumat) Se prezintă rezultatele unei analize comparative privind rezistenţa inimii la voalare din orecare a grinzilor metalice realizate în soluţia uzuală de grinzi cu inimă plină, respectiv grinzi cu inima din tablă proilată tablă cutată sau tablă ondulată. Rezistenţa inimii la voalare din orecare este stabilită în conormitate cu normativul SR EN 1993-1-5/006. Eurocod 3: Proiectarea structurilor de oţel. Partea 1-5: Elemente din plăci plane solicitate în planul lor. Baza de calcul teoretic este însoţită de o analiză comparativă numerică, în urma căreia au putut i ormulate unele concluzii şi observaţii utile în activitatea de proiectare a unor elemente metalice de tip grindă, solicitate la eorturi de orecare importante.