Semi-rigid composite frames with perfobond and T-rib connectors Part 2: Design models assessment

Journal of Constructional Steel Research 63 (2007) 280–292 www.elsevier.com/locate/jcsr

Semi-rigid composite frames with perfobond and T-rib connectors Part 2: Design models assessment S.A.L. de Andrade a,b , P.C.G. da S. Vellasco a,∗ , L.T.S. Ferreira c , L.R.O. de Lima a a Structural Engineering Department, State University of Rio de Janeiro, UERJ, Brazil b Civil Engineering Department, Pontifical Catholic University of Rio de Janeiro, PUC-Rio, Brazil c Structural Engineering Department, Federal University of Roraima, UFRR, Brazil

Received 9 August 2005; accepted 11 April 2006

Abstract This paper proposes a new design and construction system for composite semi-rigid portal frames. The system uses a perfobond shear connector and a T-rib connection element for composite action. Tests confirmed that the connector’s structural behaviour is compatible with the proposed structural solution [Ferreira LTS, de Andrade SAL, da S Vellasco PCG. A design model for bolted composite semi-rigid connections. In: Stability and ductility of steel structures. Elsevier; 1998. p. 293–306; Ferreira LTS, de Andrade SAL, da S Vellasco PCG. Composite semi-rigid connections for edge and corner columns. In: Eurosteel, 2nd European conference on steel structures. 1999]. Based on these results this paper presents two design models for bolted composite semi-rigid connections based on simple force paths. The models’ performances were validated through comparisons with experimental results in terms of moment–rotation curves, as well as initial stiffness and rotation capacity [da S Vellasco PCG, de Andrade SAL, Ferreira LTS, de Lima LRO. Semi-rigid composite frames with perfobond and T-rib connectors — Part 1: Full scale tests. Journal of Constructional Steel Research 2005 [submitted for publication] doi:10.1016/j.jcsr.2006.04.011; Ferreira LTS. Avaliac¸a˜ o de ligac¸o˜ es semi-r´ıgidas mistas aparafusadas. Ph.D. thesis. Civil Engineering Department, PUC-RIO, 2000 [in Portuguese]. [4]]. Finally, an evaluation of the actual stresses present in the tested composite frames and design models is presented based on experimental strains obtained in the connection and composite section key points. c 2006 Elsevier Ltd. All rights reserved.

Keywords: Composite steel connections; T-rib connector; Perfobond shear connector; Experimental analysis; Composite structural systems

1. Introduction The composite action was introduced in the connection design in the sixties as an alternative to the rigid steel connections. Unfortunately this strategy led to high reinforcing ratios and complex details. When the composite action was associated to semi-rigid connection design concepts it produced structural designs with reasonable reinforcing ratios and easy execution details. On the other hand, the composite action in hogging moment regions, of edge and corner columns, is still not considered by most structural designs. This was the main motivation for the present investigation to develop an efficient structural system for composite ∗ Corresponding address: State University of Rio de Janeiro, Structural Engineering Department, Rua S˜ao Francisco Xavier, 524, Maracan˜a, CEP 20550-900, Rio de Janeiro, RJ, Brazil. Tel.: +55 21 2587 7537; fax: +55 21 2587 7537. E-mail address: [email protected] (P.C.G. da S. Vellasco).

c 2006 Elsevier Ltd. All rights reserved. 0143-974X/$ - see front matter doi:10.1016/j.jcsr.2006.04.010

construction. The use of perfobond shear connectors for composite semi-rigid connections in internal columns (Fig. 1) is one of the proposed system key issues because it increases the erection speed and reduces the structural costs. Its adoption also enables the reinforcing bar anchorage in sagging moment regions to be made through the connector’s holes or simply by being perpendicularly superposed to reinforcing bars located inside the connector’s holes. The traditional solutions for external and edge composite connections use reinforcing bars lacing the columns. This strategy produces an elongation of the floor slab creating an overhang that complicates the use of vertically continuous window panels. The proposed solution for external column composite semi-rigid connections (Fig. 2) introduces the Trib connector [1,2], capable of transferring the reinforcing bar forces, located in the hogging moment region, directly to the column flange.

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List of symbols Ar , AsT dc E f y , σy fu g yk

Reinforcing bar area, T-rib area; Reinforcing bar diameter; Young’s modulus; Yielding stress; Ultimate strength; Distance between two adjacent plastic hinges in the deformed configuration of the T-rib flange; hc Column height; hi Bolt line lever arm; I S , IT , IW Seating angle, T-rib and web angle moment of inertia; ki Individual component initial stiffness [6]; Ki Connection initial stiffness [9]; K i S , K i W , K i As , K i T Seating angle, web angle, reinforcing bars and T-rib initial stiffness; K i T w , K i AsT T-rib initial stiffness calculated as a double web angle and reinforcing bar in tension; ls , lw , L As Seating angle, web angle and reinforcing bar anchoring lengths; LT T-rib anchoring lengths; M pl Connection flexural capacity; M pl , M plT , M plw , M pl As Seating angle, T-rib, web angle and reinforcing bars flexural capacity; i Bolt row identification; Sj Connection secant rotational stiffness; S j,ini Connection initial rotational stiffness; ts , twT , tw , t f Seating angle, T-rib web, web angle and beam/column flange thickness; V plc , V pls , V plw , V pT T-rib prying force, seating angle, web angle and T-rib bending shear capacity; V pu , V pm , V pl Top, middle and bottom part of the web angle shear capacity; z Lever arm.

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The proposed composite semi-rigid structural system was validated by a three-phase test consisting of: perfobond pushout tests [1], pullout tests on the T-rib connector [2] and fullscale tests [3]. The full-scale tests were made on a two-storey framed structure with three columns spaced 4.5 and 6 m, respectively. The first storey structure was a composite beam with a solid cast in place slab 120 mm thick and 1.5 m wide while the second storey used rolled steel beams [3]. Simplified structural analyses of the tested composite semirigid portal frame were executed to generate upper and lower bounds for the experimental curves with the aid of an elastic structural analysis program, FTOOL [5]. Additionally, an estimation of the bending stresses acting on the composite connections and two composite beam sections was made based on strain gauge results positioned on the connection key points. Finally, moment–rotation curves were produced and classified according to the Eurocodes 3 and 4 [6,7] and Bjorhovde et al. [8] connection classification systems. One of the main objectives of this paper is to present two composite semi-rigid connection design models: the first model developed from Kishi and Chen [9], and a second model that incorporates the T-rib and the hogging moment reinforcing bar contributions in the Eurocode 3 component method [6], [7]. 2. Simplified numerical analysis In order to obtain boundary limits for the experimental load–rotation, load–moment and moment–rotation curves an approximated elastic analysis was performed for the larger span composite beam [3] using an elastic portal frame system, FTOOL [5]. Vertical deflections of the tested full-scale composite portal frame were recorded, at four points along the beam’s larger span, with the aid of LVDTs (Fig. 3). The fifth LVDT was located on the concrete slab and additional LVDTs were situated on the beam bottom flange. Table 1 contains these LVDT readings, as well as the corresponding second and third jack loads (located on the larger span beam). A preliminary non-sway linear elastic analysis was performed, considering only the inertia properties of the steel members to estimate the hogging and sagging moment region

Fig. 1. A composite semi-rigid connection detail for use in intermediate columns.

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Fig. 2. A composite semi-rigid connection detail for use in external columns.

Fig. 3. Larger span composite beam model.

Table 1 Experimental load and displacements used in the approximated numerical analysis Load 2nd Jack 3rd Jack Point 1 Lvdt7 (kN) (kN) (kN) (mm)

Point 2 Lvdt6 (mm)

Point 3 Lvdt 4-5 (mm)

Point 4 Lvdt3 (mm)

Rotation θ α (mrad)

Rotation θ b (mrad)

Moment Ma (kN m)

Moment Mb (kN m)

16 32 48 64 80 96 112 128 144 160

1.112 2.717 4.415 6.481 8.759 11.480 14.192 17.154 – –

1.681 3.876 6.115 8.749 11.666 15.166 18.731 23.386 31.045 46.982

0.140 0.320 0.505 0.735 1.017 1.387 1.674 2.075 2.581 3.666

2.374 3.961 5.404 6.886 8.350 9.795 11.196 12.656 14.020 15.186

2.359 3.932 5.365 6.833 8.286 9.725 11.122 12.576 13.932 15.135

36.88 61.59 84.03 107.10 129.89 152.28 173.96 196.61 217.77 235.19

36.19 60.24 82.21 104.67 126.91 149.03 170.53 192.88 213.69 232.86

17.04 35.39 51.94 69.07 85.95 102.23 117.93 134.43 149.93 166.56

14.99 31.42 46.54 61.87 77.10 92.56 107.65 123.23 137.65 153.12

0.154 0.241 0.500 1.079 1.379 2.006 2.402 2.909 3.893 5.010

limits. This was necessary to delimit the various inertia segments along the beam’s larger span (Fig. 3). Two linear elastic analyses were made considering pinned or fixed supports with the equivalent steel section inertia corresponding to the non- cracked composite section properties (Fig. 4). These two analyses were made to determine lower and upper limits for the load–rotation and moment–rotation curves. Rotations (pinned case) and moments (fixed case) at supports A (internal

column) and B (external column) were evaluated to enable the construction of load–rotation curves (Table 1). A subsequent model that can represent the beam’s largest span and the adjacent internal and external columns was conceived (Fig. 5). The model has two additional beam elements incorporated to reproduce the portal frame beam in column continuity. The beam span was divided into five segments representing two hogging and three sagging regions.

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Fig. 4. Lower and upper boundary structural solutions for the larger span composite beam.

Fig. 5. Approximate numerical analysis model.

Table 2 Approximate numerical analysis assumed mechanical properties Section

E (kN/m2 )

Area (m2 )

I x x (m4 )

E I (kN/m2 )

SM100 SM 80 SM 30 SEC 1 SEC 3 S.AUX

2.05E+08 2.05E+08 2.05E+08 2.05E+08 2.05E+08 2.05E+08

2.4100E−02 2.4100E−02 2.4100E−02 5.4380E−03 5.4380E−03 4.8100E−03

2.2570E−04 1.8056E−04 6.7710E−05 7.8990E−05 7.4630E−05 5.1400E−05

46 268.50 37 014.80 13 880.55 16 192.95 15 299.15 10 537.00

The approximate analysis basically varied, for each loading step, the inertial properties of the five mentioned segments, and the column element lengths until similar vertical deflections measured in the experiments were achieved. Table 2 presents the obtained inertial properties. The SM100 section is related to the equivalent steel section corresponding to the noncracked composite section inertia properties. Sections SM80 to SM30 stiffness values varied from 80% to 30% of the SM100 section inertia. Sections SEC1, SEC3 and SAUX were related to the beam bare steel section and to the hogging reinforcing bar properties. Table 3 contains a full description of the adopted composite model inertia properties for some specific experimental load steps (adopted vertical deflections are presented in Table 1). Fig. 6 shows load–vertical displacement test curves, as well as equivalent curves obtained in the approximate analysis for points P1, P4 (composite beam extremities) and P2, P3 (beam quarter and centre span, respectively). A close inspection of

these graphs indicates that some results were satisfactory while others indicated the need of further mesh refinements on the beam hogging moment region. Fig. 7 shows similar numerical model moment–rotation curves adopting a semi-rigid beam to column connections. Fig. 8(a) depict two numerical curves for the external composite connection, one related to a non-linear semi-rigid analysis, while the other to a pinned linear analysis, constructed to serve as upper and lower reference limits for the test curves. Fig. 8(a) also shows the test load–rotation curves considering, or disregarding, the column rotation correction. In the 0–60 kN loading range the test load stiffness (with and without the column lateral displacements) was very similar to the numerical semi-rigid connection approach curve. From this point onwards there is a reduction in the test curve stiffness moving towards the numerical pinned connection approach, intercepting this curve in the 90–110 kN load range. Fig. 8(b) also contains similar curves for the internal composite connection. In the 0–18 kN loading range the experimental load stiffness is similar to the numerical semirigid curve. From this point onwards there is a reduction on the test curve inclination towards the numerical pinned stiffness, crossing it at around 80 kN. The internal composite connection presented a more flexible behaviour than predicted by the numerical analysis. A possible explanation for this difference in behaviour is due to the hogging moment reinforcing bars not having transmitted their forces directly to the internal column, since they are parallel to it. These bars did not lace the internal column, creating a less stiff connection component.

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Table 3 Numerical analysis properties Load step (kN)

16 32 48 64 80 96 112 128 144 160

First additional bar L1 EI (m) (section)

Segment 1 EI (section)

Segment 2A EI (section)

Segment 2B EI (section)

Segment 2C EI (section)

Segment 3 EI (section)

Second additional bar L2 EI (section) (m)

1.125 1.375 2.000 2.000 2.000 2.000 2.125 3.000 2.750 4.000

SM100 SM 80 SM 80 SM 70 SEC 1 SEC 1 SEC 1 SEC 1 SEC 1 SEC 1

SM100 SM 80 SM 80 SM 70 SM 70 SM 50 SM 50 SM 50 SM 40 SM 30

SM100 SM 80 SM 80 SM 70 SM 70 SM 60 SM 60 SM 50 SM 50 SM 30

SM100 SM 80 SM 80 SM 70 SM 70 SM 50 SM 50 SM 50 SM 40 SM 30

SM100 SM 80 SM 80 SM 70 SEC 3 SEC 3 SEC 3 SEC 3 SEC 3 SEC 3

3.625 5.375 6.000 6.000 6.000 6.000 6.750 4.500 6.000 8.250

S.AUX S.AUX S.AUX S.AUX S.AUX S.AUX S.AUX S.AUX S.AUX S.AUX

Composite beam

S.AUX S.AUX S.AUX S.AUX S.AUX S.AUX S.AUX S.AUX S.AUX S.AUX

(a) Internal connection.

Fig. 6. Numerical and experimental load–deflection curves, points, P1, P4, P2 and P3.

(b) External connection. Fig. 8. Numerical and experimental load–rotation curves, internal and external composite connections.

2.1. Connection bending moments

Fig. 7. Lower and upper boundary load–rotation curves — numerical analysis.

The bending moment evaluation, based on measured strains, was calculated for: external and internal column connections, as well as for two composite sections. Ideally the adopted rupture and yield strains for every connection component are determined by standard tension tests. Unfortunately the measured yield strain and respective stresses from these tests were very close to the rupture values. This was the reason for the adoption of a reduced yield stress value equal to the rupture stress divided by 1.25. All the steel sections and reinforcing bars used a Young’s modulus equal to 205 000 MPa. Table 4 shows the connection components’ stress and strains.

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Table 4 Connection components’ yield and rupture stress and strains Component

f y (MPa)

ε y (µε)

f u (MPa)

εu (µε)

T-rib Web angle Reinforcing bars (145.65)

297.28 341.20 664.20

1450.1 1664.4 3240.0

371.60 426.52 788.60

1812.7 2080.6 3846.8

2.2. Load–rotation curves and connection initial stiffness evaluation Fig. 9 presents three external column composite connection moment–rotation curves. The first curve was obtained through the numerical analysis while the second curve was constructed from experimental strains (bending moment) and experimental deflections (rotations). Finally, the third curve was built from the numerical analysis results (bending moments) and experimental deflections (rotations). The second curve was stiffer then the numerical analysis (first curve). This is explained by the fact that the T-rib directly transmits its force to the external column, creating a stiffer connection component group. This curve can be used to estimate the connection initial stiffness in the 0–20 kN range. The third curve results (experimental rotation) were close to their equivalent numerical values. Fig. 9 also contains five moment–rotation curves for the internal composite semi-rigid connection. Once again the first curve was obtained through the numerical analysis. The additional curves were made in two pairs where the first curve of each pair was constructed from the experimental strains (bending moment) and experimental deflections (rotations). The second curve of each pair was built using the numerical analysis results (bending moments) and experimental deflections (rotations). External composite connection moment–rotation curves were evaluated through the Eurocode 3 [6] and Bjorhovde et al. [8] joint classification criteria (Fig. 10). According to Bjorhovde, where the global structural response is disregarded, the curves presented a stiffer classification when compared to Eurocode 3 criteria [6], that classified them then as semi-rigid. Similarly internal composite connection moment–rotation curves were evaluated through the Eurocode 3 [6] and Bjorhovde et al. [8] connection classification criteria (Fig. 11). According to the Eurocode 3 criterion the curve’s response is close to the behaviour of flexible connections.

Fig. 9. Moment–rotation (numerical); and moment (experimental strains)– rotation (experimental) and moment (numerical)–rotation (experimental) curves, internal and external connections.

(a) Eurocode 3 classification [6].

3. Design models for composite semi-rigid connections This section describes the proposed design models for the two composite semi-rigid connections used in internal and external columns presented in Figs. 1 and 2, respectively.

(b) Bjorhovde et al. classification [8].

3.1. First design model

Fig. 10. Moment (experimental strains)–rotation (experimental) and moment (numerical)–rotation (experimental) curves, external connection classification.

The proposed model, based on an exponential model developed by Kishi and Chen [9], can predict the initial stiffness and the bending moment capacity of semi-rigid connections by

a simple mechanism developed in the connecting angles. In this mechanism, the centre of rotation is assumed to be located at a point on the outstanding leg of the seating angle (Fig. 12).

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where E is the Young’s modulus, Iw is the double web angle inertia moment, d3 is the distance from the connection rotation centre to the web angle resultant force application point, g3 is the web angle width, tw is the web angle thickness and Is is the seating angle inertia moment. The initial stiffness of the T-rib connector web (K i AsT ) can be obtained as due to the stiffness of a reinforcing bar with a cross section area (As ) equal to the T-rib connector web net area (AsT ): K i AsT =

(a) Eurocode 3 classification [6].

E AsT d12 LT

(3)

where E is the Young’s modulus and L t is the length T-rib connector. The initial stiffness of the T-rib connector flange (K i T w ) presented in Fig. 13 can also be obtained in a similar manner used for the web angle’s stiffness, Eq. (4) Ki T w =

(b) Bjorhovde et al. classification [8]. Fig. 11. Moment (experimental strains)–rotation (experimental) and moment (numerical)–rotation (experimental) curves, internal connection classification.

3.1.1. Connection initial stiffness The connection initial stiffness (K i ) presented in Eq. (1) is the sum of the individual initial stiffness capacity of the web angle (K iw ), seating angle (K is ) and the reinforcing bars (K i As ) or the T-rib connector calculated as reinforcing bars (K i AsT ) or as double web (K i AsT ), respectively. The smallest value among the three estimates is the connection initial stiffness K i = K iw + K is + K i As or

or

K i = K iw + K is + K i AsT

K i = K iw + K is + K i T w .

(1)

The full development of the first and second terms is given by Kishi and Chen model [9] leading to: K iw =

6E Iw (d3 )2 g3 (g32 + 0.78tw2 )

and

K is =

4E Is ls

(2)

6E IT (d1 )2 g1 (g12 + 0.78tT2 )

(4)

where IT is the T-rib connector inertia moment, d1 is the distance from the connection rotation centre to the T-rib resultant force application point, g1 is the horizontal distance between the flange hole and the centre line of the T-rib and tT is the T-rib flange thickness. The reinforcing bar’s initial stiffness (K i T ) can be evaluated by: K i T = K i As =

E Ar (d5 )2 L As

(5)

where Ar is the reinforcing bar area, d5 is the distance between the reinforcing bars and the connection rotation centre and L As is the hogging moment bar length. Ahmed [11], suggested that the hogging moment bar length, L As should be:   hc + 225 (in mm) (6) L As = 2 where h c is the column cross section height. This expression was confirmed by Anderson and Najafi tests [10]. Ahmed and Nethercot [11] also stated that when the composite beam’s first stud is very close to the column

Fig. 12. A design model for semi-rigid connections, after Kishi and Chen [9].

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The developments of the second and third terms are given by Kishi and Chen [9] σ y ls (ts )2 (8) 4 where V plw is the web angle shear capacity, d4 is the distance between the connection rotation centre and the application point of V plw , σ y is the seating angle yielding stress, ls is the seating angle width and ts is the seating angle thickness. The reinforcing bar’s contribution is: M plw = 2V plw d4

(a) T-rib considered as double web angle.

and

M pls =

M pl As = As σ y d5

(9)

where As is the hogging moment reinforcing bar area, σ y is the hogging moment reinforcing bar yield stress and d5 is the distance from the connection rotation centre to the hogging bar’s gravity centre. The T-rib contribution is evaluated by the lower value of the two ultimate limit states: M plT = V plc d1

if V plc ≤ 2V pT

M plT = V pT d1

if 2V pT < V plc

(10)

where V plc is the T-rib connector prying force capacity, 2V pT is the T-rib plastic shear force capacity and d1 is the distance from the connection rotation centre to the T-rib resultant force application point. The T-rib connector prying force capacity can be determined, for instance, according to the Canadian Institute of Steel Construction [12] and the T-rib plastic shear force capacity can be determined in a similar procedure as in the double web angles

(b) T-rib geometrical properties.

LT (V pu + 2V pm + V pl ) (11) 4 where L T is the T-rib length, V pu is the shear force in the T-rib top extremity, V pm is the shear force in the middle height of the T-rib and V pl is the shear force in the T-rib bottom extremity. The terms V pu , V pm and V pl are obtained with: ! g yk V03 σ y twT 4 V pk − V04 = 0 with V0 = (12) V pk + twT 2 V pT =

(c) Deformed shape. Fig. 13. The T-rib shear connector.

flange, the length (L As ) should be equal to the distance from the column flange to the next stud connector. In this work, L As was taken as the distance from the column flange to the first perfobond connector.

3.1.2. Connection flexural capacity Similarly, the connection bending moment capacity (M pl ) is evaluated by the sum of the individual web angles bending moment capacity (M plw ), the seating angle (M pls ) and the T-rib (M plT ) or reinforcing bars (M pl As ), respectively. The smallest value between the two estimates presented in Eq. (7) is the connection bending moment capacity M pl = M plw + M pls + M plT M pl = M plw + M pls + M pl As .

or

(7)

where g yk is the distance between two adjacent plastic hinges in the deformed configuration of the T-rib flange, twT is the T-rib web thickness and σ y is the T-rib web yield stress. The use of the proposed model in intermediate column connections is possible with a few modifications. To calculate the initial stiffness and bending moment capacity of the composite semirigid connection, Eqs. (1) and (7) can be used. The only needed modification requires discarding the terms related to the T-rib contribution and considering only the reinforcing bar’s term. This assumption is valid if the reinforcing bars are adequately anchored in the perfobond shear connectors along the beam span. 3.2. Second design model In Eurocode 3 [6], semi-rigid connection bending capacity is based on a load path model called the component method.

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Fig. 14. External and internal beam to column connection models according to Eurocode 3 [6].

In this model a force couple, FRd , with a lever arm “z”, acts on the tension bolts and on the connection compression centre. The force FRd is determined from the lowest connection component capacity. In the present connection modelling a simplified procedure according to Eurocode 3 was adopted. This procedure disregards the contribution of bolt lines close to the beam bottom flange (within 40% of the distance from the farthest bolt line to the connection rotation centre). This assumption is valid if at least 50% of the bolt lines were considered and leads to underestimation of the connection bending moment capacity of 15% or less than this maximum margin. Fig. 14 illustrates the Eurocode 3 internal and external connection models incorporating the additional composite action terms. The composite terms, ki∗ , not specified in Eurocode 4 [7] were incorporated. A similar contribution of the column flange to the bending term was used in the T-rib connector flange. The bolt component in tension/shear terms was adapted for use in the reinforcing bar’s components. Finally, the T-rib web component used a similar contribution evaluated in terms of the bolt in tension. The beam flange/web in compression stiffness (7) and the beam web in tension stiffness (8) were assumed to be infinite (rigid links). The numbers inside each bracket correspond to their component reference number defined in Eurocode 3 [6].

The stiffness coefficients ki represent: k1 is the column web panel in shear; k2 is the column web in transverse compression; k3 is the column web in transverse tension; k4 is the column flange in bending; k4∗ is the T-rib connector flange in bending; k6 is the double web angle in bending; k10 is the bolt in tension; ∗∗ is the T-rib connector ks,r is the reinforcing bars in tension; k10 ∗ is the web net area in tension; k11 is the bolt in shear; k11 reinforcing bars in shear and k12 are the bolts, seating angle and beam bottom flange in bearing. 3.2.1. Connection initial stiffness The mechanical model stiffness is obtained by the substitution of the springs in series and/or in parallel by equivalent springs to further simplify the model: Sj =

µ

E z2 P 1 i

(13)

ki

where S j,ini is the initial rotational stiffness of the connection, E is the Young’s modulus, z is the connection lever arm defined by the distance from the farthest tension bolt line to the connection compression centre, ki is the stiffness coefficient for basic connection component and µ is the stiffness ratio (S j,ini /S j ). When µ = 1, S j,ini represents the connection initial rotational stiffness.

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3.2.2. Connection flexural capacity The evaluation of the connection capacity begins with evaluation of the tension bolt lines effective capacity as presented in Fig. 14. The first tension bolt line (T-rib bolt line) acts as an independent line from the double web angle group lines and should satisfy the components related to: column web in transverse tension (3), column flange in bending (4), bolts in tension (10), T-rib flange in bending (4*), T-rib web in tension (10**), reinforcing bar in shear (in the T-rib hole) (11*) and reinforcing bar in tension (s, r ). This first bolt line (T-rib bolt line) should also satisfy the components in the compression zone, i.e., column web panel in shear (1), column web in transverse compression (2), beam flange and column web in compression (7), bolts in shear (11) and plate in bearing of the seating angle and beam flange (12) in order to keep the system in equilibrium. The numbers inside each bracket correspond to their component reference number defined in Eurocode 3 [6]. From the second to the fourth tension bolt line capacity, each bolt line is first evaluated as an independent line satisfying: column web in transverse tension (3), column flange in bending (4), web angles in bending (6), beam web in tension (8), bolts in tension (10), bolts in shear (11) and plates in bearing of web angles and beam flange (12). These bolt lines should also satisfy the components related to: column web panel in shear (1), column web in transverse compression (2), beam flange and column web in compression (7), bolts in shear and plates in bearing of the seating angle and beam flange (12). These bolt lines should also be evaluated as part of a group satisfying: column web in transverse tension (3), column flange in bending (4), web angles in bending (6) and beam web in tension (8). These bolt lines should also be considered as part of a group formed for two or more lines, successively. With each bolt line resistance in hand (Fi,Rd ), the connection bending capacity can be evaluated by: M j,Rd =

nb X

(14)

h i · Fi,Rd

i=1

where M j,Rd , is the connection moment capacity, Fi,Rd is the effective capacity of the “i” bolt line and h i is the distance from the “i” bolt line to the connection compression centre. 3.3. Internal composite semi-rigid connections The internal composite connection investigated in this work uses a perfobond shear connector to enable the anchorage of the hogging moment reinforcing bars in the sagging moment regions (Fig. 1). The determination of the first tension line capacity disregards the contribution of the second to fourth

tension lines. The first line (reinforcing bars) acts as an independent line, not transferring any stress to the internal column. This is the main reason for only verifying its tension resistance as a reinforcing bar in tension (s, r ). Additional compression and shear checks need to be made: column web panel in shear (1), column web in transverse compression (2), beam flange and column web in compression (7), bolts in shear (11) and plates in bearing of seating angle and beam flange (12). The capacity of all the other lines can be made as in the external column connection case already mentioned. When these preliminary steps are finished, the internal composite connection initial stiffness and bending moment capacity can be evaluated through similar procedures used for external column connections. 4. Proposed model’s evaluation of the connections initial stiffness and flexural capacity Initial stiffness and bending capacity values were calculated according to the model based on Kishi and Chen [9] for the external and internal composite connections (Table 5). In the external connections different initial stiffnesses for the T-rib and reinforcing bars parcels are depicted. The T-rib initial stiffness calculated as a double web angle is substantially higher than the value obtained considering it as a bar in tension. Previous tests have shown that the ductile failure of this component, associated to a tensile rupture in the T-rib cross section net area, near the web hole close to the T-rib flange, was similar to a tension bar failure [2]. The validation of the implementation of the Eurocode 3 model [6] in beam-to-column global response can be found in the following references. Silva et al. compared the Eurocode 3 model to the test results of endplate beam-to-column composite connections subjected to monotonical loading [13]. Sim˜oes et al. also used this model to evaluate the cyclic behaviour of composite connections [14]. Lima et al. proposed some modifications in the Eurocode 3 model to predict the global response of minor axis beam-to-column connections [15]. Lima et al. performed a series of beam-to-column connection tests subjected to bending and axial forces. The reference tests considering only the application of bending moment to the connection were also used to validate the Eurocode 3 model [16,17]. Connection bending capacity values calculated according to the Eurocode 3 model [6], for the external and internal composite connections, are presented in Table 6. In this model the connection capacity is calculated from the maximum bolt line force resultants individually, or as a group of lines.

Table 5 Connection initial stiffness and bending capacity evaluation by the first model Component Reinforcing bars/T-rib Web angle in bending Seating angle in bending Total (kN m/rad) or (kN m)

External connection Initial stiffness

Bending capacity

Internal connection Initial stiffness

Bending capacity

34 305.5/261 839.3 11 077.6 104.0 273 021.0/45 487.1

31.56 47.27 1.43 80.26

16 690.0 11 116.8 103.8 27 910.6

145.65 47.27 1.43 194.35

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Table 6 Connection bending moment capacity evaluation by the second model Tension bolt lines T-rib Reinforcing bars Web angle in bending — L1 Web angle in bending — L2 Bending moment capacity

External (kN m) Individual lines

Groups

31.84 – 20.11 20.69 72.64

31.84 – 20.11 0.00 51.95

Internal (kN m) Individual lines

Groups

–

–

89.43 20.11 18.81 128.35

89.43 20.11 9.50 119.05

Table 7 Connection initial stiffness evaluation by the second model Spring lines Components in tension

Components in compression

External

T-rib (mm) Reinforcing bars Web angle in bending — L1 (mm) Web angle in bending — L2 (mm) Equivalent spring (mm) Lever arm (mm)

0.55 –

Column web panel in shear (mm) Column web in transverse compression (mm) Bolts in bearing (mm) Bolts in shear (mm) Lever arm (mm) Initial stiffness (kN m/rad)

For external and internal composite connections, initial stiffness values calculated according to the Eurocode 3 model [6] are presented in Table 7. The internal connection hogging reinforcing bars were associated with an independent tension line. This new line did not significantly affect the overall equivalent tension or compression resultants (Table 7). 5. Design models and load–rotation curve comparisons Unfortunately only one of the web angles had strain measurements considered in this analysis, taking twice its value for the full external connection contribution. Table 8 shows the T-rib and double web angles contribution to the connection capacity evaluated through their measured strains. The seating angle contribution was disregarded due to its reduced value (1.43 kN m) when compared to other components. As a reference, inside the parentheses is presented each component’s contribution calculated according to the first proposed model (this value includes the seating angle contribution). The connection moment capacity, evaluated using the measured experimental strains, was considered to be satisfactory when compared to this paper’s first proposed model. Table 9 contains the hogging reinforcing strains for the four instrumented bars presented in Fig. 15. In the internal composite connection moment capacity the active components were the reinforcing bars and the double web angles. Inside the parentheses, the component’s contribution evaluated according to the first proposed model is presented (these values include the seating angle contribution, i.e., 1.43 kN m). The strain measurements at the first and second instrumented composite sections demonstrated that a partial shear connection

Internal –

0.13 0.12 0.75 291.26

2.57 0.14 0.12 2.76 355.33

2.62 2.55 3.12 2.92 318.75

2.30 2.55 3.12 2.92 363.65

7511.7

14 625.3

Table 8 External connection bending capacity — web angles and T-rib contribution Load (kN) 15.2 49.9 80.1 96.2

Moment (kN m) T-rib (31.56)

Web angle (47.27)

Total (80.26)

4.39 13.85 28.56 31.55

0.00 2.98 11.43 45.24

4.39 16.84 39.99 76.79

Fig. 15. Reinforcing bar strain gage location.

was developed between the steel beam and concrete slab. This fact did not allow an effective estimation of the concrete slab compression resultant and made ineffective the estimation of the developed composite section bending moment. A possible

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Reinforcing bar strain εs (µε) 2 3 6

7

Moment (kN m) Reinforcing bars (145.65)

Web angles (47.27)

Total (194.35)

69.3 255.4 553.4 846.6 1289.8

106.0 364.0 638.5 1105.7 1430.4

3.47 12.13 24.66 41.76 59.16

0.00 1.16 15.47 24.15 41.19

3.47 13.29 40.13 65.91 100.34

25.6 100.0 351.8 668.8 1124.4

107.5 360.0 650.8 1094.4 1419.4

Table 10 Composite semi-rigid connection initial stiffness Initial stiffness (kN m/rad)

Numerical analysis

Moment (strain)–rotation (experiments)

Moments (num. anal.)–rotation (experiments)

1◦ model

2◦ model

External Internal 7, 8 (6, 7, 8)

5 856.5 15 209.1

4838.7 5361.9 (8264.5)

3787.9 8968.6 (7220.2)

45 487.1 27 910.6

7 511.7 14 625.3

way to overcome this difficulty in experiments is to use additional strain gauges at the concrete slab bottom face. Table 10 depicts an estimation of the composite connection’s initial stiffness from the Fig. 9 curves. These stiffness values are also compared to both proposed design models. Table 10 also illustrates the external composite connection initial stiffness evaluation with the aid of the experimental moment–rotation curves and the two proposed design models. The first design model stiffness prediction overestimated the experimental and numerical analysis values. The results based on the Eurocode 3 design model, despite considering the T-rib web stiffness in tension component, overestimated the experimental data because the column, bolt and beam deformations have not been considered in the Kishi and Chen model [9]. Similar predictions for the internal composite connection initial stiffness are also depicted in Table 10. The second design model stiffness (Eurocode 3) was close to the numerical results but overestimated the test value. The first model stiffness overestimated both numerical and test values. The initial stiffness obtained through the second model (Eurocode 3) led to values compatible to their numerical analysis counterparts (22% less and 4% higher for external and internal connections). When the experimental values are considered, the results varied from 36% to 50% for the internal, and from 43% to 63% for the external connections, demonstrating that the second model results were stiffer than the tests. The composite connection bending moment capacity, evaluated through the experimental moment–rotation curves and the two proposed design models are depicted in Table 11. The first model connection capacity was 5% for the external connection and 52% for the internal connection, higher than the tests while the second model connection capacity was 32% for the external connection and 7% for the internal connection lower than the tests. The Eurocode 3 model is based on the lowest prediction from the tension bolt lines analysed individually, or as a group. If the line group predictions could be disregarded then the connection capacities will increase from 52 to 72.6 kN m for the external connections (from 32% to 5%

less than the tests) and from 119 to 128.4 kN m for the internal connections (from 7% less to equal to the tests). 6. Final remarks The main objective of the present investigation was to develop an efficient and cost-effective building system for steel construction leading to a semi-rigid composite system. One of the major contributions of the proposed composite system was the development and use of perfobond and TRib shear connectors to insure the transmission of the force developed in the reinforcing bars to the column flange. This approach helps to solve the continuity problem for connections at external and intermediate building columns. The simple Trib connector presents low fabrication costs and improves the structure assembly process. In order to evaluate the proposed system’s structural response a full-scale semi-rigid composite portal frame was constructed and tested up to collapse [3]. These tests enabled the determination of moment–rotation curves and an estimate of the bending stresses acting on the composite connections from strain gauges located on key points. Two composite connection design models were developed from Kishi and Chen [9] and the Eurocode 3 component method [6]. Composite terms related to the T-rib connector and reinforcing bars, for external and internal connections, respectively, were incorporated in both models later to be calibrated against experimental tests [3]. An approximate numerical analysis was also performed to define upper and lower limits for the connection moment–rotation curves. Load–rotation curves obtained from the experimental loaddeflection curves were demonstrated to be consistent with similar curves produced by the numerical analysis. The experimental moment–rotation curves for the internal and external composite connections characterized them as flexible and semi-rigid according to the Eurocode 3 classification system [6]. The determination of moment–rotation curves from the load–deflection test curves enabled a comparison of the

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Table 11 Composite semi-rigid connection flexural capacity Connection (kN m)

Moment (measured strains) (A)

Moment 1◦ model (B)

(B)/(A)

Moment 2◦ model (C)

(C)/(A)

External Internal

76.79 128.30

80.26 194.35

1.05 1.52

51.95 (72.84) 119.05 (128.35)

0.68 0.93

connection’s initial stiffness evaluated through both proposed models to be made. The model based on Kishi and Chen overestimated the connection initial stiffness because it does not consider all the connection components, discarding terms related to the column, beam and bolt deformations. The second design model initial stiffness was close to the numerical results. When the model’s initial stiffnesses were compared to the stiffnesses obtained through moment–rotation test curves the results ranged from 50% to 64% for the internal connections and from 37% to 57% for the external connections, demonstrating that both connections were more flexible than what was initially expected. The bending moment capacity for the external (internal) composite connections, evaluated with the aid of the first model, were 5% (52%) apart from the experimental values obtained with strain gauge readings. The second design model bending capacity for external and internal connection were 32% (7%) lower than the experiments when the line group capacity is taken into account and 5% lower (and coincides) with the experimental results when only the individual line capacity was considered. The authors believe that future investigations should consider additional tests of the proposed composite system under cyclic loading, a dynamical assessment of the structural system and further refinements of the composite model terms used in the second proposed design model. Acknowledgements The authors would like to thank UERJ, PUC-Rio, CAPES and FINEP for the financial support for this research project. Thanks are also due to the Structures and Materials Laboratory, PUC-Rio, administration and personnel where the tests were conducted. References [1] Ferreira LTS, de Andrade SAL, da S. Vellasco PCG. A design model for bolted composite semi-rigid connections. In: Stability and ductility of steel structures. Elsevier; 1998. p. 293–306.

[2] Ferreira LTS, de Andrade SAL, da S. Vellasco PCG. Composite semi-rigid connections for edge and corner columns. In: Eurosteel, 2nd European conference on steel structures. 1999. [3] da S Vellasco PCG, de Andrade SAL, Ferreira LTS, de Lima LRO. Semirigid composite frames with perfobond and T-rib connectors — Part 1: Full scale tests. Journal of Constructional Steel Research 2005 [submitted for publication] doi:10.1016/j.jcsr.2006.04.011. [4] Ferreira LTS. Avaliac¸a˜ o de ligac¸o˜ es semi-r´ıgidas mistas aparafusadas. Ph.D. thesis, Civil Engineering Department, PUC-RIO, 2000 [in portuguese]. [5] Martha LF. FTOOL — Two dimensional frame analysis tool — user manual. TECGRAF — PUC-Rio, Brazil, 2003. [6] EUROCODE 3. Design of steel structures, Part 1.8: Design of Connections. European Standard: prEN 1993-1-8. Brussels; 2003. [7] EUROCODE 4. Design of composite steel and concrete structures, Part 1.1: General rules and rules for buildings. European Standard prEN 19941-1, CEN/TC250/SC4/N259, Brussels; 2002. [8] Bjorhovde R, Colson A, Brozzetti J. Classification system for beam-tocolumn connections. Journal of Structural Divisions, ASCE 1990;116: 3059–76. [9] Chen WF, Lorens RF, Kato B. Semi-rigid connections in steel frames. Council on tall buildings and urban habitat, McGraw-Hill; 1993. [10] Anderson D, Najafi AA. Performance of composite connections: Major axis end plate connections. Journal of Constructional Steel Research 1994;31:31–57. [11] Ahmed B. Design of composite findplate and angle angled connections. Journal of Constructional Steel Research 1997;41:1–29. [12] Handbook of Steel Construction. Canada: Canadian Institute of Steel Construction; 1995. [13] Sim˜oes da Silva L, Sim˜oes R, Cruz PJ. Experimental behaviour of endplate beam-to-column composite connections under monotonical loading. Engineering Structures 2001;23(11):1383–409. [14] Sim˜oes R, Sim˜oes da Silva L, Cruz P. Cyclic behaviour of end-plate beam-to-column composite connections. International Journal of Steel and Composite Structures 2001;1(3):355–76. [15] de Lima LRO, da S. Vellasco PCG, de Andrade SAL, da Silva LS. Experimental and mechanical model for predicting the behaviour of minor axis beam-to-column semi-rigid connections. International Journal of Mechanical Sciences, Australia 2002;44(6):1047–65. [16] de Lima LRO, da S. Vellasco PCG, da Silva LS, de Andrade SAL. Experimental evaluation of extended endplate beam-to-column connections subjected to bending and axial force. Engineering Structures, USA 2004; 46(7):1–15. [17] da Silva LS, de Lima LRO, da S. Vellasco PCG, de Andrade SAL. Behaviour of flush end-plate beam-to-column connections under bending and axial force. International Journal of Steel and Composite Structures, Korea 2004;4(2):77–94.