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STRENGTH AND STIFFNESS OF RHS BEAM TO RHS CONCRETE FILLED COLUMN JOINTS

J. K. Szlendak, Bialystok Technical University, Poland

ABSTRACT Composite connection made with RHS chord or column filled by concrete and branches with RHS steel profile are studied herein. The aim of this paper is deriving a simple theoretical formula for calculating the strength and stiffness of such joints. Test results of twelve connections in natural scale are described. Geometry and material properties of the tested joints are given. Theoretical solution of the joint strength and stiffness are proposed and the comparisons between theoretical and experimental results are presented.

INTRODUCTION European Code EC 4 (1) makes possibility to design much more effective structures which combined advantages of steel structural sections and concrete structures. However many of structural problems are not included in this regulation. If the steel Vierendeel girder should be loaded by the significant load the interesting solution is such design where RHS or box chords section are concrete filling. From the structural point of view the box chords section ought to have the possibly large dimensions and their wall thickness ought to as small as possible. However in such situation two problems arise. Local instability of section walls leads to degradation of chord resistance and very thin walls decrease the strength and stiffness of joints. It leads to decreasing the overall carrying capacity of such structure. The strengthening of joints is possible by the steel plate welded to the face of chord. This however, does not strength the slender webs of box section. The other possibility is concrete filling of hollow section. Such filling leads also to increasing the thermal capacity of structure and its fire resistance. The comparison of these two ways of strengthening is given in (2). Strength and stiffness of T concrete filled joints made with RHS are the aim of this paper. TEST RIG, TEST SPECIMENS AND MEASUREMENTS Test rig is shown in figure 1. Twelve joints in natural scale were tested here up to failure.Ten of specimens, made with RHS, have the concrete filling chords. Two additional specimens are not concrete filling and are used for comparison how the concrete filling is effective compare with the pure steel RHS joints. The compression load equal to 420 kN, simulating the load in real structure, was applied to chord before the branch was loaded. Therefore in several steps the branch was loaded up to the reach the failure load. After each loading step, the joint was unloaded to measure the permanent deformations of the tested specimen. Typical type of joint failure was the inelastic deformation of the flange in the tension zone and finally cracking of welds, see figure 2. In Table 1 the geometry of the specimens, mechanical properties, and failure moment are given. The mechanical properties are the medium value from three tension coupons tests. The concrete mechanical properties were obtained from tests of five concrete standard cubes 100x100x100mm. Results obtained shown that the filling concrete has characteristic stress 42 MPa. Thickness of welds was equal to a = 1,2 tn.

Connections in Steel Structures V - Amsterdam - June 3-4, 2004 403

Four LVDT gauges were used to measure the displacements and rotations, see figure 2. Registrations of the results were made permanently during full loading and unloading process, up to failure. After each loading step the joint was unloaded to measure the permanent deformations. For the control of obtained data from LVDT, the additional dial gauges were used, see figure 1. Table 1. Geometrical dimensions and mechanical properties.

Geometrical dimensions Yield stress Parameters

No of joint

RHS chord bo x ho

mm

RHS branch bn x hn

mm

chord wall thick

to mm

branch wall thick

tn mm

branch

fyn

MPa

chord

fyo

MPa

o

length of

branch

m

ultimatefailure

moment

kNm BS1 140x140 80x80 5,2 4,3 400 479 0,57 0,57 26,9 0,415 8,51 S2

steel 140x140 100x100 7,1 5,1 380 457 0,71 0,71 19,7 0,415 20,23

BS3 140x140 120x120 7,05 5,15 369 404 0,86 0,86 19,9 0,41 32,80 BS4 140x140 100x100 5,1 5,1 373 457 0,71 0,71 27,5 0,415 14,94 BS5 140x140 100x100 7,05 5,15 380 457 0,71 0,71 19,9 0,405 23,49 BS6 140x140 80x80 7,1 4,4 392 479 0,57 0,57 19,7 0,408 13,06 BS7 140x140 100x100 5,35 4,3 373 457 0,71 0,71 26,2 0,407 14,25 BS8 140x140 100x100 7 4,3 369 457 0,71 0,71 20 0,4 20,00 BS9 140x140 120x120 7 5,2 375 404 0,86 0,86 20 0,41 31,78

BS10 140x140 120x120 5,2 5,2 373 404 0,86 0,86 26,9 0,41 26,24 BS11 140x140 80x80 7 4,15 400 479 0,57 0,57 20 0,411 14,39 S12 steel 140x140 100x100 7,15 4,15 380 460 0,71 0,71 19,6 0,408 16,73

Figure 1. Specimen during test. Figure 2. Joint failure (crack of welds).

404 Connections in Steel Structures V - Amsterdam - June 3-4, 2004

THEORETICAL ESTIMATIONS Strength prediction For prediction the theoretical strength of filled joints, from the observations which were done during experimental tests, the following assumptions are adopted:

Figure 3. Failure model of joint yield line mechanism. 1. Yield line mechanism, which is created in the tension zone of joint, is deceived. Erasing

inelastic deformations leads finally to situation that steel loaded flange looses the contact with filled concrete.

2. In compression zone the connection is almost absolutely stiff. So, for the simplicity could be assumed that this part of joint is compact.

3. In tension zone range of yield line mechanism is larger then in compression one. From the tests the assumption is adopted that in tension zone range of yield line mechanism is equal to 0,65hn

For the prediction of theoretical strength the yield line mechanism is proposed, similar to that as for unstrengthen steel joints (3). Proposed theoretical model is shown in figure 3. From the equation that the virtual work dissipated in the hinges by inner forces on the virtual rotations and deformations is equal to outer forces work on the virtual displacements the formula to predict strength of joints is given From the condition dMip,1,Rd/dx = 0 occurs

Mip,1,Ed

hn

bo

ho

bn to

0,65hn

concrete

df 3 f 1

f 2

f 2

Legend:1, 2 , 3- virtual rotations in plastic hinges- virtual displacement0,65hn - range of the tension zone

xbo

)1(08,3)65,0(1

82,1, ++

+= xxmb

M

plo

Rdip

)2(2

1 =x

Connections in Steel Structures V - Amsterdam - June 3-4, 2004 405

After substitution (2) to (1) the design formula is obtained

Initial stiffness Initial stiffness Sj,ini is a coefficient in the linear function between the bending moment applied to the joint and its local rotation (M = Sj,ini ). For pure steel joints the power function is assumed to predict the initial stiffness of the joints when > 0,4, see (4). Analysis of the influence of particular parameters leads to the following formula:

Sj,ini = ks E to3 y4 y5oy6 (4) After the numerical simulation the followings exponents were obtained: y4 = 2, y5 = 3, y6 = 1. For eliminating the false results the Chauvenet rule was used (4). For assumption that the level of confidence will be 0,95 and when coefficient M5 = 1,1 the coefficient ks = 6 was obtained. Then, the design value of the joints initial stiffness could be calculated as below:

Sj,ini = 6 E to3 2 3 o (5) However, for the concrete filled joints, after the numerical simulation, the increasing coefficient 1,3 is suggested and the design value of the joints initial stiffness could be calculated as below:

Sj,ini = 7.8 E to3 2 3 o (6)

Secant stiffness According the recommendations which are given in EC-3, see part 5.1.2 (5), as a simplification, the rotational, secant stiffness may be taken as Sj,ini / in the analysis for all values of the design moment. Therefore, the secant stiffness of concrete filled joints is suggested to be calculated using coefficient = 2, see Table 5.2 (5), as below:

Sj,sec = 3.9 E to3 2 3 o (7) COMPARISON OF EXPERIMENTAL RESULTS AND THEORETICAL ESTIMATIONS In figure 4 to 15 the moment-rotation curves (M - ) for each tested joints are presented. They are shown not only loading but also unloading curves registered by LVDT and dial gauges. Unloading curves gives possibility to obtain the end of its elastic behaviour and show the arising of the joint permanent deformations. In Table 2 the comparison between the theoretical prediction and the test results is presented.

)3(08,3)1

65,01(1

8,1, +

+

= plo

Rdip

mbM

406 Connections in Steel Structures V - Amsterdam - June 3-4, 2004

BS1

0

2

4

6

8

10

0 1,5 3 4,5 6Rotation x 10-2 rad

Mom

ent k

Nm

LVDT Loading

LVDT Unloading

Dial gauge Loading

Dial gauge Unloading

Initial stif fness (6)

Secant stiffness (7)

Design load (3)

BS3

0

5

10

15

20

25

30

35

0 1,5 3 4,5 6Rotation x 10-2 rad

Mom

ent k

Nm

LVDT Loading

LVDT Unloading

Dial gauge Loading

Dial gauge Unloading

Welds failure

Initial stif fness (6)

Secant stif fness (7)

Figure 4. Joint BS1 = 0.57,