EUROSTEEL 2008, 3-5 September 2008, Graz, Austria 561

CHS GUSSET PLATE CONNECTIONS ANALYSES Theoretical and Experimental Approaches

Arlene M. S. Freitas a, Daniela G. V. Minchillo b, João A. V. Requena c, Afonso H. M. Araújo d

a Escola de Minas, UFOP - Universidade Federal de Ouro Preto, Ouro Preto, Brasil b, c Faculdade de Engenharia Civil, Arquitetura e Urbanismo, Unicamp - Universidade Estadual de Campinas,

Campinas, Brasil d V&M do Brasil - Vallourec & Mannesmann Tubes

INTRODUCTION

Gusset plate connections are used to reinforce or connect structural elements. They are very useful, especially in tubular structures. The connection in this study consists of a gusset plate welded on top of a tubular section chord. The bracings are joined to the plate by bolts. But in this case only one bolt is used, turning this, a pinned connection. The great advantage of this connection is fabrication and erection facility and standardization possibility. In CIDECT[1] we have a design procedure for gusset plate connections. This procedure consists of parameters verifications and calculation of the connection resistance. The bolts and the plates have to be checked in the normally way for shear, contact pressure and failure of the cross sectional area, as recommend by the codes such Eurocode 3[2] or AISC [4,5]. Fig. 1 displays an example of a multi-planar truss gusset plate connection. In this case, plates are used in the end of the pinned bracings which are fixed to the gusset plate by bolts.

Fig. 1. Multi-planar truss gusset plate connection.

1 DESIGN PROCEDURE

In this work will treat of a uni-planar connection, considering the symmetry between the planes of a multi-planar truss. Fig. 2 shows the actuating loads at the gusset plate connection. This connection has an eccentricity e2 due to the change of the connection working point. This eccentricity is half of the chord tubular section diameter do/2, plus e1, as shown in Fig. 2. The eccentricity e1 is the one that acts on the weld between the plate and the chord. It is the distance between the top of the cord section and the plate bolt hole center. F* is the horizontal resultant of the bracings forces F1 and F2. The chord bending moment is M0.Sd plus the moment M2* due the eccentricity e2, and the axial force turns into N0.Sd plus F*. The bending moments M1* and M2* are given by Eq. (1) and Eq. (2).

11 ** eFM ×= (1)

22 ** eFM ×= (2)

562

10

2 2e

de += (3)

where M1* , M2* = chord bending moment due to eccentricity e1 and e2, respectively; e1 = distance between the top of the cord section and the plate hole center.

Fig. 2. Forces in the connection adapted from CIDECT[1]

Fig. 3. Detail of the change in the angle between the bracings and the chord

In this connection, it is necessary to rectify the angle between the bracings and the chord. This inclination change occurs due the eccentricity e2, due the placement of the gusset plate. Fig. 3 shows schematically the inclination change of the bracings. where BS , BI = superior and inferior truss chords, respectively; D1, D2 and D3 = truss bracings; θ1 , θ2 = originals angles between the truss bracings and chords;

θ1F , θ2F = angles changed by eccentricity e2; e2BS , e2BI = superior and inferior truss chords eccentricities, respectively; ht = truss height; L = truss bracings projections, as shown in Fig. 3.

The definition of the angles θ1F and θ2F depends on the superior and inferior chord plate dimensions.

−−==

L

eehtarcTan BIBS

FF11

21 θθ (4)

where e1BS , e1BI = distances between the top of the superior and inferior chord section and the center of the plate hole. This real angles are used to calculate the horizontal resultant of the bracings forces F*.

)cos()cos(* 2211 FF FFF θθ ×+×= (5)

1.1 Validity ranges

According to CIDECT [1] and Rautaruukki [3] this verifications are necessary to avoid local effects as local buckling or punching shear at the chord wall.

2,00

1 ≤d

t (6)

40

1 ≤=d

hη (7)

d0

t0 M0.Sd+M2* M0.Sd

N0.Sd + F* N0.Sd

h1 t1

F1 F2

e1 θ2F θ1F

F* M1*

F*

F* M2*

e2 h2

θ1F θ1 θ2

ht

BS

BI

D1 D2 D3

e1BS

e1BI

L L

θ2F

563

50100

0 ≤≤t

d (8)

where h1 , t1 = plate depth and thickness, respectively; d0 , t0 = chord external diameter and thickness, respectively.

1.2 np coefficient

⋅++

⋅+⋅

=00

2.0

00

.00 **1,1 y

Sd

y

SdMjMp fW

MM

fA

FNn

γγ (9)

where N0.Sd, M0.Sd = design chord axial force and bending moment, respectively; A0, W0= cross sectional chord area and elastic modulus, respectively; fy0 = chord section design yield strain; γM0, γMj = coefficients equal to 1,1; M2* = chord bending moment due to eccentricity e2; F* is the horizontal resultant of the bracings forces F1 and F2.

1.3 kp coefficient

The coefficient kp, that must assume one of the following values, depending on chord force being in tension or in compression:

• Tension chord: 1=pk (10)

• Compression chord: 1)(3,01 2 ≤+−= ppp nnk (11)

1.4 Axial force resistance

0

200.1

1,1)25,01(5

MMjypRd tfkN

γγη

⋅×+×××= (12)

1.5 Bending moment resistance

21.1 *. eFhN Rd ×≥ (13)

2 EXPERIMENTAL AND NUMERICAL ANALYSIS OF THE CONNECTION

2.1 Experimental tests

A set of experimental tests of the gusset plate connection where performed. In order to simulate the effects of the forces transmitted by the pinned bracings to the chord, an axial eccentric load was applied at the plate of to the tubular section. The axial force was applied at the bolt region and the specimens were fixed by two plates welded at end of the tubular section. Thus the experimental specimens took the geometry shown in Fig. 4. The main purposes of this tests, are detach an evaluation of the connection efficiency through the identification of the collapses modes and the ultimate load, the check the chord plastification and the plate dimensions. The instrumentation consists on a strain gage positioned on the gusset plate just below the bolt hole and a second strain gage at the tubular section above the welding line, as shown in Fig. 5. A 10 ton load-cell was used.

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Fig. 4. Experimental models of pinned gusset plate connection

The tests where performed with models of tubular section of different diameters and different plate depths. The diameters of tubular sections tested were: 60,3 mm, 73,0 mm, 76,5 mm and 96,5 mm. The plate depths were 100 mm and 150 mm. The plate heights were fixed in 90 mm and the plate thickness was fixed in 3 mm. The bolt hole diameter was 14mm.

Fig. 5. Strain gages positions in experimental analysis

Fig. 6. Finite element model.

2.2 Numerical Analysis

Numerical analysis trough finite element method is a resource of great utility in the structural study and development. It turns possible the simulation of the structural behavior, reducing the development time and the costs, increasing the product performance. This finite element model consists of a tubular section with 96,5 mm diameter and 4,0 mm thickness and a 90x100 mm plate. A three-dimensional nonlinear analysis using SHELL181 Ansys element and bilinear material type was performed. Fig. 6 shows the finite element model mesh. The force was applied in the bolt position, corresponding to the horizontal component of diagonals forces. This force was obtained with experimental analyses. Once the structural geometry or connection analyzed is reproduced in the finite element software, and depending on the analysis and the element type, it is easy to evaluate the structural behavior, varying the load and the thickness of the studied parts.

100

565

3 RESULTS

3.1 Theoretical and experimental analysis evaluation

The ultimate load value obtained in the tests reached an average of 45000 N. The experimental analysis load values in Table 1 were obtained at the maximum stress in the tubular section strain-gage in experimental tests. The load values obtained from the theoretical equations, and its corresponding experimental load values are presented on Table l for each tested specimen. The difference between these two analyses is calculated. It is possible to observe that the average between the differences is approximately 37%. The graphic in Fig. 7 shows these results. It is also possible to verify that the specimen number 3, with a 150 mm height plate resisted the higher load.

Table 1. Theoretical and experimental analysis load value comparison for all specimens.

Diameter Plate Experimental Analysis Theoretical Analysis Difference Specimen

mm mm N N % 1 60,3 100 38001,59 21911,12 42,34 2 73,0 100 39992,83 24585,52 38,53 3 73,0 150 59984,20 41582,15 30,68 4 76,5 100 43125,09 23865,78 44,66 5 96,5 100 28029,05 19369,09 30,90

3.2 Numerical and experimental analysis evaluation

In order to perform comparisons between the numerical and experimental analysis the specimen number 5 described on Table 1 was used. The load applied in the bolt position was divided in 50 load steps in the numerical model, and the stress obtained was compared with the experimental results. In the graphic of Fig. 8 the comparisons between the numerical analysis and experimental analysis is presented.

0

10000

20000

3000040000

50000

60000

70000

1 2 3 4 5Specimens

Loa

d ( N

)

Theoretical

Experimental

0

10000

20000

30000

40000

50000

-150 -125 -100 -75 -50 -25 0Stress (MPa)

Loa

d (N

)

Experimental

Numerical

Fig. 7. Experimental and theoretical analysis comparison.

Fig. 8. Experimental and numerical analysis comparison.

The results in Fig. 8 demonstrate that numerical stress results are very close to the experimental stress results obtained. In Fig. 9 it is possible to observe the first principal stress distribution (σ1) at a detail of the connection in external and internal view. The maximum stress value is 364,64 MPa at the region of contact between the plate and the tubular section.

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Fig. 9. Principal stress σ1 at the connection - external view and internal view, respectively.

4 CONSIDERATIONS

Through the obtained results, it was possible to detach that the gusset plate depth and the tubular section thickness has a lot of influence on the connection collapse mode, and the plate thickness is critical in the determination of the connection resistance. Both, experimental and numerical analyses show that to obtain good stress distribution in a connection, the rigidity of each part should be similar. In other words, if the gusset plate rigidity goes much higher than the tubular section rigidity, there is an increase of tensions in the tubular section and vice-versa. In that case, the plate presents rigid body motion behavior, inducing flexure on the tube wall. In summary, it can be observed that is necessary to look for harmony between the connection parts - thickness and dimensions about same magnitude. These results are the first part of others set of test that will be performed soon, with specimens of different gusset plate thickness. This work is part of the doctor’s degree research program of Minchillo, and it is being developed in a partnership at Universidade Estadual de Campinas and at Universidade Federal de Ouro Preto.

5 ACKNOWLEDGMENT

The authors are grateful to be supported by the Brazilian federal and state council of research: CNPq, CAPES, FAPEMIG and the V&M do Brasil - Vallourec & Mannesmann Tubes company.

REFERENCES

[1] CIDECT – Comité International pour le Développement et l'Etude de la Construction Tubulaire - Design Guides, 1991.

[2] Eurocode 3 - EUROPEAN COMMITEE FOR STANDARDISATION, Design of steel structures: ENV 1993 – 1 - 1: General rules and rules for buildings, 1992.

[3] Rautaruukki Oyj; Hannu Vainio, 1998 - Design Handbook for Rautaruukki Structural Hollow Sections. Hämeenlinna, Finlândia.

[4] AISC-AMERICAN INSTITUTE OF STEEL CONSTRUCTION. Hollow Structural Sections, Connections Manual, 1997.

[5] AISC-AMERICAN INSTITUTE OF STEEL CONSTRUCTION. Manual of steel construction, Load and Resistance Factor Design-LRFD, VOL.1&2, 2nd edition, Illinois, 1996.