CHS GUSSET PLATE CONNECTIONS ANALYSES Theoretical and Experimental Approaches

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1 EUROSTEEL 8, 3-5 Setember 8, Graz, Austria 561 CHS GUSSET PLATE CONNECTIONS ANALYSES Theoretical an Exerimental Aroaches Arlene M. S. Freitas a, Daniela G. V. Minchillo b, João A. V. Requena c, Afonso H. M. Araújo a Escola e Minas, UFOP - Universiae Feeral e Ouro Preto, Ouro Preto, Brasil b, c Faculae e Engenharia Civil, Arquitetura e Urbanismo, Unicam - Universiae Estaual e Caminas, Caminas, Brasil V&M o Brasil - Vallourec & Mannesmann Tubes INTRODUCTION Gusset late connections are use to reinforce or connect structural elements. They are very useful, esecially in tubular structures. The connection in this stuy consists of a gusset late wele on to of a tubular section chor. The bracings are joine to the late by bolts. But in this case only one bolt is use, turning this, a inne connection. The great avantage of this connection is fabrication an erection facility an stanarization ossibility. In CIDECT [1] we have a esign roceure for gusset late connections. This roceure consists of arameters verifications an calculation of the connection resistance. The bolts an the lates have to be checke in the normally way for shear, contact ressure an failure of the cross sectional area, as recommen by the coes such Eurocoe 3 [] or AISC [4,5]. Fig. 1 islays an examle of a multi-lanar truss gusset late connection. In this case, lates are use in the en of the inne bracings which are fixe to the gusset late by bolts. Fig. 1. Multi-lanar truss gusset late connection. 1 DESIGN PROCEDURE In this work will treat of a uni-lanar connection, consiering the symmetry between the lanes of a multi-lanar truss. Fig. shows the actuating loas at the gusset late connection. This connection has an eccentricity e ue to the change of the connection working oint. This eccentricity is half of the chor tubular section iameter o /, lus e 1, as shown in Fig.. The eccentricity e 1 is the one that acts on the wel between the late an the chor. It is the istance between the to of the cor section an the late bolt hole center. F* is the horizontal resultant of the bracings forces F 1 an F. The chor bening moment is M.S lus the moment M * ue the eccentricity e, an the axial force turns into N.S lus F*. The bening moments M 1 * an M * are given by Eq. (1) an Eq. (). M * = e1 (1) M * = e () 1 F * F *

2 56 = e1 (3) e + where M 1 *, M * = chor bening moment ue to eccentricity e 1 an e, resectively; e 1 = istance between the to of the cor section an the late hole center. F 1 F BS M.S N.S h h 1 θ 1F M 1 * M * θ F F* F* F* e 1 e M.S +M * N.S + F* t 1 t θ 1F e 1BS D 1 D D 3 θ 1 θ L L θ F e 1BI BI ht Fig.. Forces in the connection aate from CIDECT [1] Fig. 3. Detail of the change in the angle between the bracings an the chor In this connection, it is necessary to rectify the angle between the bracings an the chor. This inclination change occurs ue the eccentricity e, ue the lacement of the gusset late. Fig. 3 shows schematically the inclination change of the bracings. where BS, BI = suerior an inferior truss chors, resectively; D 1, D an D 3 = truss bracings; θ 1, θ = originals angles between the truss bracings an chors; θ 1F, θ F = angles change by eccentricity e ; e BS, e BI = suerior an inferior truss chors eccentricities, resectively; ht = truss height; L = truss bracings rojections, as shown in Fig. 3. The efinition of the angles θ 1F an θ F eens on the suerior an inferior chor late imensions. ht e1bs e1bi θ 1F = θ F = arctan (4) L where e 1BS, e 1BI = istances between the to of the suerior an inferior chor section an the center of the late hole. This real angles are use to calculate the horizontal resultant of the bracings forces F*. 1.1 Valiity ranges F = F cos( θ ) + F cos( θ ) (5) * 1 1F F Accoring to CIDECT [1] an Rautaruukki [3] this verifications are necessary to avoi local effects as local buckling or unching shear at the chor wall. t 1, (6) h η = 1 4 (7)

3 t where h 1, t 1 = late eth an thickness, resectively;, t = chor external iameter an thickness, resectively. (8) 1. n coefficient n γ = γ N. A M Mj S + F * M. S + M * + 1,1 f y W f y where N.S, M.S = esign chor axial force an bening moment, resectively; A, W = cross sectional chor area an elastic moulus, resectively; f y = chor section esign yiel strain; γ M, γ Mj = coefficients equal to 1,1; M * = chor bening moment ue to eccentricity e ; F* is the horizontal resultant of the bracings forces F 1 an F. (9) 1.3 k coefficient The coefficient k, that must assume one of the following values, eening on chor force being in tension or in comression: Tension chor: k = 1 (1) = Comression chor: k 1,3( n + n ) 1 (11) 1.4 Axial force resistance N 1. R 1,1 = 5k f y t (1 +,5η ) (1) γ γ Mj M 1.5 Bening moment resistance N R. e (13) 1. h1 F * EXPERIMENTAL AND NUMERICAL ANALYSIS OF THE CONNECTION.1 Exerimental tests A set of exerimental tests of the gusset late connection where erforme. In orer to simulate the effects of the forces transmitte by the inne bracings to the chor, an axial eccentric loa was alie at the late of to the tubular section. The axial force was alie at the bolt region an the secimens were fixe by two lates wele at en of the tubular section. Thus the exerimental secimens took the geometry shown in Fig. 4. The main uroses of this tests, are etach an evaluation of the connection efficiency through the ientification of the collases moes an the ultimate loa, the check the chor lastification an the late imensions. The instrumentation consists on a strain gage ositione on the gusset late just below the bolt hole an a secon strain gage at the tubular section above the weling line, as shown in Fig. 5. A 1 ton loa-cell was use.

4 564 1 Fig. 4. Exerimental moels of inne gusset late connection The tests where erforme with moels of tubular section of ifferent iameters an ifferent late eths. The iameters of tubular sections teste were: 6,3 mm, 73, mm, 76,5 mm an 96,5 mm. The late eths were 1 mm an 15 mm. The late heights were fixe in 9 mm an the late thickness was fixe in 3 mm. The bolt hole iameter was 14mm. Fig. 5. Strain gages ositions in exerimental analysis Fig. 6. Finite element moel.. Numerical Analysis Numerical analysis trough finite element metho is a resource of great utility in the structural stuy an eveloment. It turns ossible the simulation of the structural behavior, reucing the eveloment time an the costs, increasing the rouct erformance. This finite element moel consists of a tubular section with 96,5 mm iameter an 4, mm thickness an a 9x1 mm late. A three-imensional nonlinear analysis using SHELL181 Ansys element an bilinear material tye was erforme. Fig. 6 shows the finite element moel mesh. The force was alie in the bolt osition, corresoning to the horizontal comonent of iagonals forces. This force was obtaine with exerimental analyses. Once the structural geometry or connection analyze is rerouce in the finite element software, an eening on the analysis an the element tye, it is easy to evaluate the structural behavior, varying the loa an the thickness of the stuie arts.

5 565 3 RESULTS 3.1 Theoretical an exerimental analysis evaluation The ultimate loa value obtaine in the tests reache an average of 45 N. The exerimental analysis loa values in Table 1 were obtaine at the maximum stress in the tubular section straingage in exerimental tests. The loa values obtaine from the theoretical equations, an its corresoning exerimental loa values are resente on Table l for each teste secimen. The ifference between these two analyses is calculate. It is ossible to observe that the average between the ifferences is aroximately 37%. The grahic in Fig. 7 shows these results. It is also ossible to verify that the secimen number 3, with a 15 mm height late resiste the higher loa. Table 1. Theoretical an exerimental analysis loa value comarison for all secimens. Secimen Diameter Plate Exerimental Analysis Theoretical Analysis Difference mm mm N N % 1 6, , ,1 4,34 73, , ,5 38, , , 4158,15 3, , ,9 3865,78 44, ,5 1 89, ,9 3,9 3. Numerical an exerimental analysis evaluation In orer to erform comarisons between the numerical an exerimental analysis the secimen number 5 escribe on Table 1 was use. The loa alie in the bolt osition was ivie in 5 loa stes in the numerical moel, an the stress obtaine was comare with the exerimental results. In the grahic of Fig. 8 the comarisons between the numerical analysis an exerimental analysis is resente. Loa ( N ) Theoretical Exerimental Secimens Exerimental Numerical Stress (MPa) Loa (N) Fig. 7. Exerimental an theoretical analysis comarison. Fig. 8. Exerimental an numerical analysis comarison. The results in Fig. 8 emonstrate that numerical stress results are very close to the exerimental stress results obtaine. In Fig. 9 it is ossible to observe the first rincial stress istribution (σ 1 ) at a etail of the connection in external an internal view. The maximum stress value is 364,64 MPa at the region of contact between the late an the tubular section.

6 566 Fig. 9. Princial stress σ 1 at the connection - external view an internal view, resectively. 4 CONSIDERATIONS Through the obtaine results, it was ossible to etach that the gusset late eth an the tubular section thickness has a lot of influence on the connection collase moe, an the late thickness is critical in the etermination of the connection resistance. Both, exerimental an numerical analyses show that to obtain goo stress istribution in a connection, the rigiity of each art shoul be similar. In other wors, if the gusset late rigiity goes much higher than the tubular section rigiity, there is an increase of tensions in the tubular section an vice-versa. In that case, the late resents rigi boy motion behavior, inucing flexure on the tube wall. In summary, it can be observe that is necessary to look for harmony between the connection arts - thickness an imensions about same magnitue. These results are the first art of others set of test that will be erforme soon, with secimens of ifferent gusset late thickness. This work is art of the octor s egree research rogram of Minchillo, an it is being eveloe in a artnershi at Universiae Estaual e Caminas an at Universiae Feeral e Ouro Preto. 5 ACKNOWLEDGMENT The authors are grateful to be suorte by the Brazilian feeral an state council of research: CNPq, CAPES, FAPEMIG an the V&M o Brasil - Vallourec & Mannesmann Tubes comany. REFERENCES [1] CIDECT Comité International our le Déveloement et l'etue e la Construction Tubulaire - Design Guies, [] Eurocoe 3 - EUROPEAN COMMITEE FOR STANDARDISATION, Design of steel structures: ENV : General rules an rules for builings, 199. [3] Rautaruukki Oyj; Hannu Vainio, Design Hanbook for Rautaruukki Structural Hollow Sections. Hämeenlinna, Finlânia. [4] AISC-AMERICAN INSTITUTE OF STEEL CONSTRUCTION. Hollow Structural Sections, Connections Manual, [5] AISC-AMERICAN INSTITUTE OF STEEL CONSTRUCTION. Manual of steel construction, Loa an Resistance Factor Design-LRFD, VOL.1&, n eition, Illinois, 1996.