an-Performance of the PR connections under combined Axial-tension and moment loading

parametric the effects of the friction and the bolt pretension the overall response the bolted angle connections. studied the applicability of the FEM in predicting the cyclic response of the bolted angle connections. He method time-consuming accuracy the connection response. the effects of the shear force on the initial stiffness of the bolted TSDW an-Performance ABSTRACT: The inherent moment capacity of bolted top-seat angle connections with double web angles (TSDW), categorized as partially restrained (PR) connections according to AISC-LRFD specifications, can be considered in analyses of semi-rigid connections especially when an accurate analysis of such fames is de-sired. However, in some cases, developed internal forces in the frame elements may affect the connection behavior, considerably. Axial tension force is one of such internal forces that may be imposed on frame connections in some cases such as construction imperfections, seismic loading or under large deflections of the catenary action during the progressive collapse of the semi-rigid frames. This study aims at the effects of the axial tension force on the performance of the bolted TSDW angle connections using nonlinear finite element method (FEM). The obtained results show that the axial tension force reduces the connection moment capacity and stiffness, considerably. Based on the obtained moment-rotation curves, affected by this particular loading type, equations are proposed to estimate the reduction rate of the connection stiffness and moment capacity.


INTRODUCTION
Bolted top-seat angle connections with double web angles (TSDW) -categorized as partially restrained (PR) connections according to AISC-LRFD specifications (AISC, 1995) -are widely used to support the vertical reaction of the steel beams. However, their considerable moment capacity makes it possible to take into account their contribution in the beam moment redistribution, deduction of the column's effective length (Kishi et al, 1997) and also the lateral resistance of the frame (Nader M N& Astaneh-Asl A, 1996; Danesh Lots of studies have done on the performance of bolted or riveted angle connections. Azizinamini (Azizinamini A, 1982;Azizinamini A, 1985) studied the effect of several geometrical properties of bolted TSDW on the connections moment-rotation characteristics. ( Recently, FEM has become an efficient tool for studying the response of this type of connection. (Citipitioglu et al, 2002) performed a parametric study on the effects of the friction coefficient and the bolt pretension on the overall response of the bolted TSDW angle connections. (Pirmoz A, 2006) studied the applicability of the FEM in predicting the cyclic response of the bolted angle connections. He concluded the method is highly time-consuming despite its accuracy in predicting the connection response. ( ABSTRACT: The inherent moment capacity of bolted top-seat angle connections with double web angles (TSDW), categorized as partially restrained (PR) connections according to AISC-LRFD specifications, can be considered in analyses of semi-rigid connections especially when an accurate analysis of such fames is desired. However, in some cases, developed internal forces in the frame elements may affect the connection behavior, considerably. Axial tension force is one of such internal forces that may be imposed on frame connections in some cases such as construction imperfections, seismic loading or under large deflections of the catenary action during the progressive collapse of the semi-rigid frames. This study aims at the effects of the axial tension force on the performance of the bolted TSDW angle connections using nonlinear finite element method (FEM). The obtained results show that the axial tension force reduces the connection moment capacity and stiffness, considerably. Based on the obtained moment-rotation curves, affected by this particular loading type, equations are proposed to estimate the reduction rate of the connection stiffness and moment capacity.
gle connections and proposed an equation to estimate the reduction rate.  showed that the web angle has a major role on the shear carrying capacity of these connections. Considering the shear strength of the web angles, they proposed an equation to estimate the reduction of the initial rotational stiffness of these connections. Their method showed a very good accuracy with respect to the method proposed by . The effects of the axial tensional forces on the moment-rotation response of the bolted top-seat angle connections by Pirmoz et al ). They proposed a method for predicting the momentrotation response of this type of connection considering the reducing effects of the axial tensional forces. ) showed that the seat angle has a considerable role on the moment-rotation response of the bolted top-seat angle connections, especially in the nonlinear range of the connection response. Performance of the bolted TSDW angle connections during progressive collapse of semirigid frames is studied by (Pirmoz A, 2009). The results showed that due to the arching action of the beam a considerable compressive force is applied on the connection that changes the response of the connection and the yielding mechanism and consequently the global performance of the frame can be affected. Based on the obtained results a method is proposed to estimate the affected response of the connection in progressive collapse condition. By sing artificial neural networks (ANN), (Pirmoz A& Gholizadeh S, 2007) and (Salajegheh et al, 2008) estimated the moment-rotation response of bolted angle connections, accurately.
None of the researches on the performance of the bolted TSDW angle connections relates to the behavior of this type of connection under combined axial tension and moment loading. Despite the fact that bolted TSDW angle connections are mainly designed to sustain the shear forces of the gravitational loads or to provide moment capacity for semi-rigid frames, in some cases, this type of connection may be subjected to large axial forces. Results of shaking table tests of (Nader M N& Astaneh-Asl A, 1996) revealed that during an earthquake, some axial forces may be imposed on connections. Due to the column removal in semi-rigid frames, after linear and arching stage (Pirmoz A, 2009), frame connections enter in catenary action phase and subject to a combined moment (of gravitational loads) and an increasing axial-tension force of the catenary action. Current study aims at the behavior of bolted TSDW angle connections under initial constant axial tension force and moment.

Characteristics of the connections
The speciemens tested by Azizinamini (1982) consisted of two beams which were symmetrically connected to a stub column through bolted top and seat with double web angles (figure 1). The speciemens were in two groups which were different in the beam section, the stub column section and the number of the bolt rows of the web angles. The first group, named as 14SX scpesimens and the second group, 8SX, included relatively lighter specimens with two rows of the web angle bolts, shorter web angles and a W821 beam section. The clear distance between the beam and column flange was reported to be 12mm and the gap between the bolt shank and the hole was considered to be 1.6mm. Table (1) presents the geometry of the specimens. The bolts were high strength A325 bolts and the material of the angles, beams and stub columns was A36 steel.

FE modeling of the connections
The modeling is done by ANSYS multy-purpose finite element modeling code. Implementing ANSYS Parametric Design Language (APDL), parametric FE models are created while the geometrical and mechanical properties of the connections were as the parameters.
Numerical modeling of the connection is done including following considerations: all components of connection such as beam, column, angles and bolts are modeled using eight node first order SOLID45 elements and bolt shanks are modeled using SOL-ID64 element which can consider thermal gradient used to apply pretensioning force on bolts. Only half of the connection is modeled because of the symmetry exists about the web plane. Since the stub column and the beams were strong enough with respect to the connections, these segments remained elastic and thus negligible deformations were expected to occure in the beam, column flanges and web. The interaction between adjacent surfaces, including anglebeam flange, bolt head-nut, bolt hole-bolt shank and also the effect of friction were modeled using CON-TA174 and TARGE170 contact elements. This proper modeling of the component interactions acquires the interaction between the nut and the head with the corresponding surfaces when a negative thermal gradient is applied on the bolt shank and this restraining, pretensions the bolts. 178 kN pretensioning force is applied to 22.3 mm bolt diameter and 133 kN for 19.1 mm bolt diameter. Figure (2-a) presents the FE model of the 14S2 specimen and figure (2-b) shows its deformed shape.
More information about the modeling, material properties and validating the FE models are presented in ( Moment-rotation responses of two models are presented in fig. (3). A relatively fair accuracy is obtained for FE models. A peer discussion on the accuracy of the models and the sources of the error are documented in the previous works by the frist author

EFFECT OF AXIAL TENSION FORCE ON CONNECTION BEHAVIOR
As cited previously, variable or constant axial forces could be developed in the frames connections during an earthquake (Nader M N& Astaneh-Asl A, 1996), progressive collapse (Pirmoz A, 2009) or during the construction processes. Fig. (4) presents the axial tension-axial deflection curve of the 14S8 specimen at the beam end, where the axial load is imposed. As seen from this figure, after 1.0mm axial deflection, which corresponds to an almost 420 kN axial force, the beam slippage starts (the horizontal part of the curve). This horizontal portion of the curve almost equals to the gap distance between the bolt shank and the beam or the angle hole. After approximately 1.5 mm slippage, connection axial stiffness recovers due to the contact of the bolt shank and the surface of the hole. The curve includes the axial deformations of the beam which is ignoring because of the relatively higher axial stifnness of the beam. The effects of the axial tensional force on the moment-rotation response of the connections are studied in this section. For this purpose, after applying the bolts pretension, an axial tensional force is applied on the nodes of the beam end as the second load case and then the monotonic moment loading is applied on the connection by downward pushing of the beam end. The imposed load on the connection during the stated loading conditions can also be increasing (monotonic). However, the studies by (Pirmoz et al, 2009) showed that the constant axial tensional force has a sever effect on the connection. Ac-Accordingly, the current study considers only the constant axial loading which is combined with monotonic moment loading. Five specimens of Azizinamini's tests are selected randomly and each specimen is analyzed under five different magnitudes of the axial tensional force and monotonic moment loading. The name of the specimens and the magnitude of the applied axial-tensional forces on the con- nections are listed in table (2). A total of 25 models under axial tension and moment loading are analyzed. Moment-rotation response of the connections under different loading magnitudes is shown in figure (6). As seen from this figure, axial tensional load decreases the connection initial stiffness and its moment capacity. The numbers assigned for each curve denotes the magnitude of the applied axial force on the connection. Since the 14S8 has relatively higher moment capacity with respect to other four connections, greater axial load, 350 kN, is applied on it to observe a sensible reduction on its response. To estimate the moment-rotation curve of the connection under combined axial tension and moment loading, the rate of the changes in the momentrotation response of the connection due to the applied axial load is studied first. To achieve this, the ratio of Mt/Mo is plotted against the connection rotation for each specimen. In which, Mt is the reduced moment capacity of the connection due to the applied axial tension force and Mo denotes its moment capacity without any axial force at a given rotation. The plots of the Mt/Mo are shown in figure (6) for 14S1 specimen under 100 kN and 250 kN of axial force. It can be seen that the rate of the moment changes is almost linear for rotations larger than 0.005 radians. Within smaller rotations, moment capacity of the connection is more affected. Increasing of the connection rotation decreases the sensitivity of the connection response to the applied axial force. For each series of the data, a curve is fitted using interpolation technique. Table (2) presents the equations of the fitted curves for each model. As seen from table (2), it is clear that an equation in its general form of eq. (1) can estimate the connection response under a specific axial tensional force, accurately.  (1) However, for engineering applications, a general equation is needed to estimate a given connection response, affected by a given axial load. Practical connections vary considerably in their geometrical and mechanical properties. On the other hand, the effects of such properties reflect on the connection moment-rotation response characteristics, such as its initial stiffness or moment capacity.
The yield moment is one of the major characteristics of the connection. Figure (7) illustrates the way for determining the yield moment, M y . This parameter is used later as a representative of the connection moment-rotation response. Another parameter is defined for the connections as the equivalent moment, M e . The effect of the axial tensional force on the connection angles is set to be equal with the effect of a corresponding moment loading. In other words, the horizontal displacement of the top angle due to a given tensional load needs a moment, M e , which can be calculated using eq. (2). Visual illustration of the method is presented in figure (8). Figure 8. Visual illustration of the equivalent moment of tension force determination Table (3) list the "a" and "b" of equation (1) for the equations presented in table (1). The "a" and "b" of each equation of table (2) are plotted against the ratio of M e /M y . Table (2) also contains the M e and M y properties of each model. Plots of "a" and "b" against the ratio of M e /M y , shown in figure (9), clarify that a second-order polynomial equation would be considered between these parameters and the ratio of M e /M y .
According to figure (9) and a little simplification "a" and "b" parameters could be calculated by eq. (3, 4): (4) Figure 9. Plots of "a" and "b" parameters against M e /M y .
Replacing eq. (3) and (4) in eq. (1) and yields the affected moment values for a given rotation, R, and the applied axial-tension force, F in form of equation (5). To examine the accuracy of the proposed equation for models beyond the studied models, two different connections, 14S3 and 8S1 specimens, are chosen and analyzed under 150 and 100 (kN) axial tension force, respectively. The response of the connections, obtained by FEM, agrees well with results of eq. (5). Figure (10) shows the comparisons between the results of FEM and eq. (5).

CONCLUSION
Axial tensional forces, developed in the connections of a semi-rigid frame during seismic excitations, construction tolerances or other probable causes, affect the connection moment-rotation response considerably. Using nonlinear FEM, a method is presented to estimate the moment-rotation response of bolted TSDW angle connections under combined axial tensional forces and monotonic moment loading. All the connection components are modeled using solid elements and the contact elements are used to take into account the effect of the interaction of the adjacent components of the connection. Applying a negative thermal gradient on the bolts shanks, the bolts pretension force is applied as the first load case. Several FE models of previously tested specimens are created and analyzed under combination of different magnitudes of the axial-tension and monotonic moment loading. Results of analyzing these models cleared that the axial-tension force decreases the connection initial rotational stiffness, moment capacity and energy absorbance capacity. Altering the applied axial tensional force into an equivalent moment and dividing this value by the yield moment of the connection, a series of dimensionless data are obtained. Then, by using interpolation technique a formula is suggested to estimate the momentrotation curve of the connection under combined tension-moment loading. Comparing the accuracy of the proposed equation with those obtained by FEM showed that the method has a good accuracy and can be used easily for engineering applications.