EUROSTEEL 2, August 3 September 2, 2, Buapest, Hungary A NUMERICAL EVALUATION OF CHS T JOINTS UNDER AXIAL LOADS Raphael S. a Silva a, Luciano R. O. e Lima b, Pero C. G. a S. Vellasco b, José G. S. a Silva b an Luis F. a C. Neves c a PGECIV, Civil Engineering Post-Grauate Program, UERJ State University of Rio e Janeiro, Brazil b Structural Engineering Department, UERJ State University of Rio e Janeiro, Brazil. c Civil Engineering Department, ISISE - FCTUC University of Coimbra, Portugal. INTRODUCTION The intensive worlwie use of tubular structural elements, such as the examples epicte in Figure, mainly ue to its associate aesthetical an structural avantages, le esigners to be focuse on their technologic an esign issues. Nowaays in Brazil, there is still a lack of coe that eals specificc with tubular joint esign. This fact inuces esigners to use other international tubular joint esign coes. Consequently, their esign methos accuracy plays a funamental role when economical an safety points of view are consiere. Aitionally, recent tubular joint stuies inicate that further research is neee, especially for some particular geometries. This is even more significant for some failure moes where the collapse loa preictions lea to unsafe or uneconomical solutions. a) Footbrige Rio e Janeiro CHS K an N joints b) V&M Office Builing Belo Horizonte RHS/CHS joints c) Footbrige Rio e Janeiro CHS K joints ) Maria Lenk Aquatic Center Rio e Janeiro CHS T joints Fig.. Examples of structures using hollow sections in Brazil. The first comprehensive investigation publishe in this area was mae by Korol an Mirza [] concerning a numerical moel with shell elements an inicate a simultaneous increase of the joint resistance with the variable β an/or with the ecrease of the variable γ. The authors also referre to the nee for creating a eformation limit criteria for those connections. Recently Lu et al. (cite in Kosteski et al. [2]), with results also valiate an accepte by Zhao [3], establishe an approximate 3% % eformation limit. This 3% limit is nowaays wiely accepte an is also the value aopte by the International Institute of Weling (IIW) for the maximum acceptable isplacement associate to the ultimate limit state while a % limit is aopte for the
service limit states. If the ratio of N u u/n s is greater than.5, the joint strength shoul be base on the ultimate limit state, an if N u /N s <.5, the serviceability limit state controls the esign. In the case of CHS joints, N u /N s >.5 an the appropriate eformation limit to be use to etermine the ultimate joint strength shoul be equal to.3. In this paper a numerical (i.e. non-linear FEM simulations) base on a parametric stuy is presente, for the analysis of T tubular joints where both chors an braces use circularr hollow sections. The propose moel was valiate by comparison to analytical results suggeste by the Eurocoe 3 [4], by the new CIDECT [5] an to literature classic eformation limits. The main variables of the present stuy were the brace iameter to chor iameter ratio an the thickness to chor face iameter ratio. These parameters were chosen base on recent stuies results that inicate some Eurocoe 3 rules iscrepancies. EUROCODE 3 AND CIDECT DESIGN CODES PROVISIONS Accoring to Eurocoe 3 [4] an CIDECT [5], some geometrical limits nee to be verifie prior to the evaluation of the joint resistance. These limits are presente in Figure 2 where an t represent, respectively, the tube iameter an thickness...2. () 2 t i, i, 5 (2) t t (3) Fig. 2. Geometrical properties of the CHS T joint in tension [2]. When CHS T joints are consiere, some ultimate limit states shoul be verifie. Despite this fact, the chor plastification controls the CHS T joint esign in the majority of the cases. Eurocoe 3 [4], expresses this ultimate limit state in eq. (4)..2 N k f 2 p y t, R 2.8 4 2 sin where N,R is the chor face failure resistance, is a geometrical parameter accoring to eq. (2), k p is taken equal to. for tension brace loas, f y is the chor yiel stress taken equal to 355MPa, is a geometrical parameter accoring to eq. (), M5 is the partial safety factor, in this case equal to.. 2 / M 5 (4) The new joint strength equation (5) for chor plastification accoring to CIDECT [5] are expresse in terms of Q u (influencee of the parameters an ) an Q f (influence of the parameter n). In these equations, the parameterr C is taken equal to.45-.25 for chor compression stresses (n<) an equal to.2 for chor tension stresses (n ). For the istinction with the formulae present in the previous eition, which are incorporate in various national an international coes, a slightly ifferent presentation is use an presente below. * N i Q Q u f f t 2 y sin with Q u 2.2 2.6 6.8, Q f C n an n N N pl, M M pl, (5)
2 NUMERICAL MODEL The propose numerical moel aopte shell elements presente in the Ansys Element Library [6]. The moel was evelope using four-noe thick shell elements (SHELL8), therefore consiering bening, shear an membranee eformations. The finite element mesh was more refine near the wel, where the stress concentration is likely to happen, an the more regular as possible, with well- accoring to Lee [ ] Figure 3(c). Figure 3(a) presents the general aspect of the evelope finite element moel. A full nonlinear analysis was performe consiering material an geometrical nonlinearities. The aopte material presente a bilinear behaviour with no strain-harening before failure with yiel stresses of 355 MPa an 6 MPa for connecte members an wel elements, respectively. proportione elements to avoi numerical problems. The wels were consiere as shell elements Brace loa (isplacement) a) full moel b) wel etail c) wel moel after Lee [7] Fig. 3. CHS T joint moel. A parametric stuy varying some geometrical parameters was performe to evaluate their influence in the connection resistance. Table presents the variables use in the parametric stuy that totalize 5 simulations. It is important to emphasise thatt these combinations were chosen consiering the limits impose by the chor bening moment an brace normal plastic resistances. Three ifferent profiles for the chor were use, 88.9x8, 298.5x25 an 66.x6. For each chor, five braces were also chosen. The wel thickness was aopte as the minimum thickness of the plates to be connecte. In this table are also presente the joints resistance consiering the chor plastification failure accoring to Eurocoe 3 [4] an CIDECT [5]. It is important to mention that, for all stuie cases, the CIDECT resistance values were greaterr than the Eurocoe 3 provisions. 3 NUMERICAL RESULTS As previously explaine for this joint type, the ultimate limit state that governs the joint esign is the chor plastification resistance. Accoring to the eformation limit criteria of 3% [2], [3], for the stuie joints, the chor out of plane isplacement limits are equal to 2.7, 8.9 an 9.8 mm, respectively. In orer to ientify an confirm the initial assumptions regaring the ultimate limit state for CHS tubular joints, the joint between a 298.5x25 chor an a 4..3x6 brace was analyze in terms of Von Mises stress istribution with its corresponing results presente in Figure 4. In this figure, it can be observe that the joint failure is controlle by the chor plastification an the Eurocoe 3 an CIDECT resistances are less than the joint ultimate loa. If the partial coefficient factor M5 was use, the joint esign will lea to even more conservative limits. Figure 5 to 7 present the loa versus isplacement curves for alll the investigate numerical moels where the eformation limit criteria is marke in ashe lines. The application of this criteria (N u an N s ) is summarize in Table. The conclusions will be presente in the next section of this paper.
Table. Summary of the numerical moels t =2 /t t =2 /t 33.7 6.3 2.67 42.4 6.3 3.37 8. 5.56 48.3 6.3 3.83 5. 6.3 4.5 6.3 6.3 4.79 4.3 6. 3.57 39.7 6. 4.37 25. 5.97 59. 6. 4.97 68.3 6. 5.26 93.7 6. 6.5 244.5 4. 3.6 323.9 4. 4.5 6. 5.5 355.6 4. 4.45 368. 4. 4.6 457. 4. 5.7 [] If N u /N s >.5 then N = N u elsee N=N s imensions [mm] an loas [kn] 66. 298.5 88.9 Chor Brace.38.48.54.57.68.38.47.53.56.65.37.49.54.56.69 N,R (EC3) 54.9 93. 223.8 239.2 298.8 548.4 874.6 266. 239.8 2784.6 8534.6 78.7 244.6 2966.3 7268. * N i (CIDECT) 64.5 22. 25.3 269.5 343.6 646.8 252.9 245.7 267.3 385.9 933.4 2325.5 3896.8 455.3 997.3 N u N s N *, R N i (ANSYS) [] N N 85.8 87.7.86.94 249.4 225..9. 293. 249.8.9.3 38.9 26.5.99.4 344.6 3.8.95.2 697.5 622.2.. 263. 87.2.5.7 252.4 256.9.8.2 2695.9 247.7.6.33 324. 2397.5.86.94 927.4 8762.3.97.3 234.6 235.8.9. 3492. 3739.6.9. 3937.2 4297.8.9.2 6962.8 8325..94.9 a) applie loa = 29 kn (point ) b) applie loa = 475 kn (point 2) c) applie loa = 697 kn (point 3) Fig. 4. CHS 298.5x25 with 4.3x6 Von Mises stress istribution
Fig. 5. CHS 88.9 chor loas versus isplacement curves Fig. 6. CHS 298.5 chor loas versus isplacement curves Fig. 7. CHS 66. chor loas versus isplacement curves
4 FINAL REMARKS This paper presente an Ansys numerical stuy of CHS T tubular joints subjecte to tensione braces. Three ata set were consiere keeping the same variation for the parameter. These sets consiere chors with small, meium an large iameter accoring to V&M profile table[8]. The numerical results were compare to analytical results propose by Eurocoe 3 [4] an CIDECT [5] recommenations. It is important to emphasise that for this joint type, the Eurocoe 3 results were more conservative when compare with the CIDECT results. Figures 5 to 7 inicate that when the parameter increase, the joints resistances also increase accoring to eq. (4) an (5). It coul also be observe that the parameter also contribute to the joint resistance increase. The ultimate limit state for this joint type was the chor plastification accoring to the Eurocoe 3 [4], CIDECT [5] an to the numerical results. For the first an thir set of joints, accoring to the observation of Table, the numerical resistances obtaine from the eformation limit criteria were higher than the Eurocoe 3 provisions eviencing the coe safety. For these same set of joints, some cases presente a ratio higher than. when CIDECT recommenations were use. For the secon set of joints, both Eurocoe 3 an CIDECT recommenations provie higher resistances than the numerical analysis inicating an unsafe esign. 5 ACKNOLEDGMENTS The authors woul like to thank CAPES, CNPq an FAPERJ for the financial support to this research program. REFERENCES [] R. Korol, F. Mirza, "Finite element analysis of RHS T-joints", Journal of the Structural Division, ASCE, vol. 8, No.ST9, pp. 28-298, 982. [2] N. Kosteski, J.A. Packer, R.S. Puthli, "A finite element metho base yiel loa etermination proceure for hollow structural section connections", Journal of Constructional Steel Research, vol. 59, pp 453-47, 23. [3] X. Zhao, Deformation limit an ultimate strength of wele T-joints in col-forme RHS sections, Journal of Constructional Steel Research, vol. 53, pp 49-65, 2. [4] Eurocoe 3, ENV 993--, 23: Design of steel structures - Structures Part -: General rules an rules for builings. CEN, European Committee for Stanarisation, Brussels, 23. [5] J. Warenier, Y. Kurobane, J.A. Packer, G.J. van er Vegte an X.-L. Zhao, Design Guie - For Circular Hollow Section (CHS) Joints Uner Preominantly Static Loaing 2 n Eition, CIDECT, 28. [6] Ansys 2., ANSYS - Inc. Theory Reference, 2. [7] M.M.K. Lee, Strength, stress an fracture analyses of offshore tubular joints using finite elements, Journal of Constructional Steel Research, vol. 5, pp 265-286, 999. [8] Technical Information No. : Structural hollow sections (MSH) circular, square, rectangular. Valourec & Mannesmann (http://www.vmtubes.e/content/vmtubes/vmtubes522/ S_MSH_p.pf), 22.