Finite Element Simulations on the Tensile Resistance of Bolted End-Plate Connections with Tubular Members

2.1. Component Method

The EC3-compliant component method schematizes the joint as a mechanical systems made of elementary components that are characterized by an elastic-plastic force-deformation response curve. The calculation procedure can be summarized in three main steps:

• Component identification: Determination of contributing components in compression, tension and shear in view of connecting elements and load introduction into the column web panel.
• Component characterization: Determination of the force-deformation response of each component as a mechanical spring.
• Component assembly: Assembling all the translational springs that can be distributed in series and/or in parallel to obtain the overall response of the joint.

In bolted connections an equivalent T-stub in tension may be used to model the design resistance of the following basic components:

• Column flange in bending.
• End-plate in bending.
• Flange cleat in bending.
• Base plate in bending under tension.

T-stub model for unstiffened plated components was developed by Zoetemeijer [9] and then extended it to some stiffened configuration. Later, Jaspart [10] applied the concept to various plate configurations.

In the case of bolted connection, the resistance of each bolt row depends on the effective length (l_eff) that guarantees the equivalence with a simple T-Stub connection. The determination of the effective length of the equivalent T-stub is crucial to obtain the correct resistance. Unfortunately, the current version of EN1993:1-8 [7] does not cover the entireall bolt row configuration in the case of bolted end plate joints with hollow members.

Parker et al. [11] developed one dimensional yield line model for connection with bolts on two sides of hollow section, showing six possible failure modes (Fig. 2) given as follows:

• Failure mode 1: Rupture of the bolts without prying force.
• Failure mode 2: The yielding of the hollow section.
• Failure mode 3: The failure due to the combination of bolt fracture and plastic hinge formation in the flanges at the weld.
• Failure mode 4: A more general version of mechanism 3, whereby the flange plate plastic hinge is permitted to form within the tube.
• Failure mode 5: The mechanism due to the combination of the flange-plate failure and flange-plate bent in double curvature without bolt failure.
• Failure mode 6: The mechanism due to the flange-plate failure, flange-plate bent in double curvature, inner plastic hinge within the hollow section.

In order to assess the accuracy of the available analytical methods described in the previous Section, the theoretical prediction hashave been verified against some test data on different connection configurations as given by Packer et al. [1], Willibald [4] and Kato and Mukai [12]. In order to univocally identify the type of connection geometry, the following labelling code was used:

• C1 for specimens with two side bolts (4\6 bolts), shown in Fig. (3a).
• C2 for specimens with four side bolts (8 bolts), shown in Fig. (3b).
• C3 for specimens with four side bolts (10 bolts), shown in Fig. (3c).

C1 configuration C2 configuration C3 configuration

2.2. C1 Configuration

Bolted connections of tubular members with bolts located only on two sides generally behave as partial strength. After a series of tests, Packer et al. [1] proposed an idealized bending stress distribution through the thickness of the end-plate, the significant contribution of strain-hardening is incorporated and the resulting flexural capacity is in closer agreement with the actual ultimate plate bending strength. The maximum bending moment capacity for flange plate is:

(1)

Where:

(2)

f_yp: Yield strength of the end-plate.

f_up: Ultimate tensile strength of the end-plate.

Four different approaches were adopted to compute the ultimate resistance and the corresponding failure mode of the specimens tested by Packer et al. [1]:

• Approach 1: The failure modes 4 and 6 postulated in [11] were added to the typical failure modes of EC3 [7].

In order to compute the bending strengths of mode 1 and 2 of EC3 (i.e. M_pl,1 and M_pl,2), the hardened stress f_p

was used.

• Approach 2: To compute M_pl,1 was applied method 2 from EC3-8 table 6.2 and hardened stress f_p for M_pl,2.
• Approach 3: To take into account the possibility of a plastic hinge inside the wall tube, the value “m” is computed as the distance between the half hollow section thickness and the bolt center (i.e. m = e_x + t/2).
• Approach 4: The ultimate tensile stress fup was applied to compute M_pl,1 and the hardened stress f_p for M_pl,2.

The comparison between the theoretical approaches and the experimental results are reported in Table 1. As it can be observed, the approach 3 is the most accurate one, giving calculated resistances closest to the experimental values. The cases with larger differences are those characterized by axial yielding of the walls of tubular member constituting the web of the L-stub. The resistance of this failure mode is not accounted for in these four methods.

2.3. C2 and C3 Configurations

The configurations with four-side bolted splices were tested by [4, 12]. Based on Willibald model [14], Steige and Weynand [5] proposed an equation for the effective length, which is used here to calculate an effective length for the corner bolts. Setting this design resistance equal to the resistance of a half T-stub produces the estimated effective length in Eq. (3), as follows:

(3)

This equation is not practical for hand calculation. The effective length can be simplified with the following equation proposed by Couchaux [13]:

(4)

With

(5)

Three different approaches to calculate the connection resistance were adopted, namely:

• Approach 1: Two-dimensional yielding line procedure proposed by Willibald [4].
• Approach 2: Eurocode procedure adding the formulation of l_{eff, i} proposed by Steige and Weynand [5].
• Approach 3: Eurocode procedure adding the formulation of l_{eff, nc} proposed by Couchaux [13]. The effective lengths adopted for the approaches 2 and 3 are reported in the Table 2.

The comparison between these analytical predictions and the experimental data is reported in Table 3. As it can be observed, all methods overestimate the experimental resistance and approaches 2 and 3 lead to very similar results, but the method 3 is simpler to be use.

3.1. Investigated Joints

The geometrical features of the connections are reported in Table 4 and shown in Fig. (4). All connections have the same hollow sections 152×152×9.4 mm. It should be noted that connections from C2-1 to C2-7 were extracted from uniaxial tensile tests carried out by Willibald [4]. In the other joints, the thickness of the end-plate, the type of welds and two positions of corner bolts (i.e. designated as c1 and c2) were varied.

3.2. Modelling Assumptions

The finite element models were carried out in Abaqus 6.14 [15]. Due to the geometry and loading symmetry of the specimen, the geometry of ¼ of the connection was modelled in order to reduce the computational time toat the minimum.

The material properties are consistent with those given by [4]. The plastic hardening was simulated using both nonlinear kinematic and isotropic hardening law.

The tubular member, the end-plate, the bolts and welds were modelled using C3D8R (i.e. an 8-node linear brick, reduced integration, hourglass control) solid finite elements.

The model is completed by a rigid 3D planar shell part interacting with the end-plate. The interaction between the steel surfaces in contact was modelled introducing the contact interaction that allows accounting for the interaction between surfaces characterized by friction sliding with Coulomb friction coefficient equal to 0.3, while “Hard contact” was selected to characterize the normal behaviour.

The bolts used in this numerical model are grade 8.8 M16. The hexagonal head of the bolts was modelled and the pre-tensioning was disregarded. The tensile plastic behaviour of the bolts was modelled similarly as reported in [16, 17] for HR bolts.

3.3. Validation of Numerical Models Against Experimental Results

To validate the numerical modeling, four specimens of the experimental program carried out by Willibald [4] have been modeled. The predicted resistances of the FEM-models are compared to the results of the tensile tests in Fig. (5), where it can be recognized the good agreement between the experimental response curves and the corresponding finite element simulations can be recognized. Indeed the mean ratio between the test strength N_ux over the numerical resistance N_u,FEM is equal to 1.02 and coefficient of variation is equal to 3.4%.

3.3. Numerical Results

Fig. (6) shows the comparison between the tension response curves of C2-3, C2-3c1 and C2-3c2. As expected the later connection is characterized by the larger resistance since the corner bolts are closer to the tubular profile. Fig. (6) shows the comparison of connection response varying the thickness of the end-plate. The connections with thinner end-plate (i.e. t_p = 10 - 12 mm) are characterized by mode 5 (Fig. 2) with very ductile failure response curves. The cases with thicker end-plate (i.e. t_p = 16-20-25 mm) exhibit less ductility due to the activation of bolt failure in mode 3 and 4 (Fig. 2).

The tension resistances for all the models are reported in Fig. (7), where it can be easily recognized the crucial role of corner bolts can be easily recognized. Indeed, the connections with corner bolts exhibit larger resistance that increases when the bolts are closer to the corner of the tubular member (i.e. the configuration C2). However, reducing the distance e_x (Fig. 1) between the bolt and the wall of the tubular section can affect the splice ductility. In so doing, three different types of failure mode can occur, namely i) the failure of the bolts, ii) the failure of fillet welds, and iii) the yielding of the walls of the tubular member. The first two are brittle mechanisms that should be avoided.