Numerical Simulations of Bolted Steel Connections in Single and Double Shear Under Pretension Effect

Transcription

1 Numerical Simulations of Bolted Steel Connections in Single and Double Shear Under Pretension Effect O. Yılmaz 1, S. Bekiroğlu 2 1 Department of Civil Engineering, YTU, Istanbul, Turkey, yilmazo@yildiz.edu.tr 2 Department of Civil Engineering, YTU, Istanbul, Turkey, serkanb@yildiz.edu.tr Abstract This study presents implementation of numerical simulations on tension member connections with/without pretensioned bolts which are subjected to tension force aligned in direction of bolt line. Four groups and forty different models have been created. Half of these models have single shear and the others have double shear. First and second groups have single shear with one bolt line and two bolt lines, respectively, while third and fourth groups have double shear with one bolt line and two bolt lines, respectively. The number of bolts on the line in each group have been positioned with three, four, five, six, seven, respectively. High strength bolts are used and stress strain curves for all components in the models are taken as non-linear material. Contacts which provide interaction between components in the models are taken as linear or non-linear. Numerical simulations have been carried out by commercially available finite element software ANSYS. After analyzing the models, stress-deformation state of tension members, distribution of stresses between bolts for the models are successfully obtained and the obtained results are compared with each other. It is observed that, for the models without pretension effect, increasing number of bolts on a line causes increasing ratio of maximum stress value to minimum stress value and increasing number of bolts causes increasing displacement of tension member. Minimum stress values on bolts are usually observed on middle bolt of bolt line. Keywords: Tension member, pretensioned bolt, finite element model, non-linear analysis, contact. 1 Introduction This paper deals joints which tension member fasten to gusset plate by bolts. Loadings are transferred to gusset plate from tension member by the contact between the bolt and the plates. Many research have been performed to investigate behavior of bolt and tension plate in tension splice experimentally, theoretically and numerically (Schiffener and Droste gen. Helling, 1997, Kim and Yura, 1999, Puthli and Fleischer, 2001, Ju et al., 2004). Also different finite element modeling techniques of bolted joints were investigated (Kim et al., 2007). There are some studies which present effects of change of end and edge distances between bolt and tension plate and distance between two bolts with same number of bolt(s) (Moze and Beg, 2010, Moze and Beg, 2011, Moze and Beg, 2014). This paper presents finite element modeling of tension member splices. In this study, number of bolts, number of bolt line and shear status which is single or double shear are changed and observed effects of these changes. Each numerical model is also performed under bolt pretension effect. Trilinear stress strain curve is used to define material properties for steel components. However, bolts in model are taken as high strength bolts, so their stress strain curve is different from those of steel components. 2 Development of the Proposed Models In order to analyze bolted steel connections in single and double shear under static load with/without pretension effect, four groups and forty models are presented using the finite element software ANSYS (ANSYS Inc., 2011). First and second groups have single shear with one bolt line and two bolt lines, respectively, while third and fourth groups have double shear with one bolt line and two bolt lines, respectively. The number of bolts on the line in each group have been positioned with three, four, five, six, seven, respectively. Each model is investigated under static load with and without pretension. Properties of the models are shown in Table 1.

2 Table 1. Properties of the models. Gr Geo M NB NBL SS PE Gr Geo M NB NBL SS PE Single No Double No Single Yes Double Yes Single No Double No Single Yes Double Yes Single No Double No Single Yes Double Yes Single No Double No Single Yes Double Yes Single No Double No Single Yes Double Yes Single No Double No Single Yes Double Yes Single No Double No Single Yes Double Yes Single No Double No Single Yes Double Yes Single No Double No Single Yes Double Yes Single No Double No Single Yes Double Yes Gr: Group, Geo: Geometry, M: Model, NB: Number of Bolt, NBL: Number of Bolt Line, SS: Shear Status and PE: Pretension Effect. 2.1 Geometric Details of Connections Connections consist of gusset plate, tension member which are made by one or two tension plate, bolts and bolt nuts. Washers are not included in order to simplify the models. All the dimensions of connections and bolts are shown in Figure 1. Bolt numbers are entitled from inside bolt to outside bolt. Inside bolt and outside bolt mean bolt which the closest to support and force, respectively. Bolt nuts are modelled as cylindrical. The thickness of gusset plate and each plate in tension member are taken as 14 mm and 12 mm, respectively. Figure 1. The dimensions of connection and bolt 2.2 Finite Element Models The models are investigated by finite element software ANSYS (ANSYS Inc., 2011). Three-dimensional solid elements are used for finite element modeling. After completing geometrical model, due to geometrical symmetry about the central of gusset plate, for single shear one half of each model, for double shear one quarter of each model are taken into account for finite element analysis in order to reduce computation time. For example complete and reduced models for Group 1 and Group 4 are shown in Figure 2 and 3. Figure 2. Complete and reduced models for Group 1 in front view.

3 Figure 3. Complete and reduced models for Group 4 in front view. All components in the models are meshed by hexahedral elements. In meshing process, parts which the stress distribution is important such as bolts and perimeter of holes of plates are meshed finer to obtain results more sensitive. Increasing mesh density causes less numerical error but more computation time. Several analysis were performed on several models to obtain optimum mesh density and obtained mesh density are used for all models. Typical finite element model of connection and plates and bolt of connection are shown in Figure 4 and 5. Figure 4. Finite element model of a sample model. Figure 4. Finite element models of components. 2.3 Contact Properties Bolted joints consist of many components such as bolt, plate. There is interaction between components which contact each other. The components which contact each other and types of contact such as linear or non-linear are shown Table 2. Table 2. Contact regions and contact types in the models. Contact Region Gusset plate Tension plate Gusset plate Bolt Gusset plate Nut Tension plate Bolt Tension plate Nut Bolt Nut Contact Type Non-linear Non-linear Linear Non-linear Linear Linear 2.4 Material Properties Trilinear stress strain curve is used to define material properties for steel components. However, bolts in model are taken as high strength bolts, so their stress strain curve is different from those of steel components. The poisson s ratio is taken as 0.3 for all components in the models. Stress strain curves are shown in Figure 5.

4 Figure 5. Trilinear stress strain curves (Mashaly et al., 2011). 2.5 Loading The analysis of the models having pretension force consists of two load steps. Firstly, only pretension forces are applied to the bolts. Secondly, after solving first load step, tension force are applied to the tension member. The pretension force and tension force are taken as 155 kn and 100 kn, respectively. Used tension force value effects 0.5σ y and 0.224σ y on tension member for the models which have one bolt line and two bolt lines, respectively. The analysis of the models having not pretension force consists of one load step under tension force. Each load step for all models is divided into at least 10 substeps. So, forces subject step by step instead of at a time because of steady-state non-linear analysis. 3. Results and Discussion The maximum equivalent (Von-Mises) stress values on bolts of each model with/without pretension effect are shown in Figure 6 and 7. The models which have not pretension effect are subjected to only static load. As shown Figure 6, for single shear, the maximum equivalent stress values are obtained on inside bolts. The stress values on other bolts lower, but on middle bolts are obtained as minimum except that the models have three bolts. The minimum stress values in models which have single shear and three bolts are obtained on outside bolts. For double shear, the maximum stress values on bolts are obtained on outside bolts for one bolt line and inside bolts for two bolt lines. The minimum stress values are obtained on middle bolts for both group. Figure 6. The maximum equivalent stress values on bolts without pretension effect.

5 The models having pretension effect are also subjected to static load. As shown in Figure 7, for all groups, the maximum and minimum stress values are obtained on inside and outside bolts, respectively, so shear status does not matter. For all models, stress values of bolts do not reach yield stress. Figure 8 and 9 show equivalent stress distribution on bolts for double shear, two bolt line, without and with under pretension stress, respectively. These distributions show that maximum stresses on bolts occurs at between gusset plate and tension plate. Under pretension effect, for double shear, tension plate are curved, as shown in Figure 9, because of contraction of bolts. So, tension force are also transferred from tension plate to gusset plate because of increasing friction force between tension plate and gusset plate. Figure 7. The maximum equivalent stress values on bolts with pretension effect. Figure 8. The stress distribution on bolts for double shear, two bolt line, without pretension. (Deformation scale factor = 200) Figure 9. The stress distribution on bolts for double shear, two bolt line, with pretension. (Deformation scale factor = 200)

6 The stress values on bolts are normalized and given in Table 3. The minimum stress values are indicated as 1 and other stress values are divided to the minimum stress values. It is observed that, for the models without pretension effect, increasing number of bolts on a line causes increasing ratio of maximum stress value to minimum stress value. These ratio values increases in the models which have two bolt lines and these values in the models which have single shear are higher than with double shear. For example, the ratio for Model 19 is maximum 11.04, but for Model 39 is maximum Table 3. Normalized stress values on bolts (from inside to outside bolts). Group Number Of Bolt Without Pretension Effect With Pretension Effect ; 1.05; ; 1.03; ; 1.58; 1; ; 1.02; 1; ; 2.11; 1; 1.09; ; 1.06; 1.04; 1.02; ; 2.3; 1.17; 1; 1.31; ; 1.02; 1.01; 1.01; 1.01; ; 3.14; 1.3; 1; 1.06; 1.48; ; 1.04; 1.02; 1.02; 1.02; 1.01; ; 1.28; ; 1.01; 1 4 6; 1.85; 1; ; 1.02; 1.01; ; 2.4; 1.09; 1; ; 1.01; 1.01; 1; ; 3.24; 1.41; 1; 1.21; ; 1.02; 1.01; 1; 1; ; 3.32; 1.4; 1; 1; 1.2; ; 1.02; 1.01; 1.01; 1; 1; ; 1; ; 1.02; ; 1; 1.16; ; 1.04; 1.02; ; 1.04; 1; 1.44; ; 1.04; 1.03; 1.02; ; 1.25; 1; 1.25; 1.99; ; 1.04; 1.03; 1.04; 1.03; ; 1.41; 1; 1.04; 1.46; 2.43; ; 1.04; 1.04; 1.04; 1.04; 1.02; ; 1; ; 1.01; ; 1.04; 1; ; 1.01; 1.01; ; 1.19; 1; 1.23; ; 1.02; 1.02; 1.01; ; 1.41; 1; 1.1; 1.54; ; 1.02; 1.02; 1.02; 1.01; ; 1.69; 1.07; 1; 1.25; 1.88; ; 1.02; 1.02; 1.02; 1.02; 1.01; 1 Figure 10 and 11 show maximum equivalent stress maximum displacement which direction of force on tension plate diagrams for each group without and with pretension effect, respectively. It is observed that increasing number of bolt causes increasing displacement for all models, because of increasing number of holes in plates. The diagrams of models which have two bolt lines without pretension effect are linear, because stresses on tension member are within the elastic limit. In these diagrams, maximum stresses are obtained at perimeter of hole of tension plate. Maximum displacements are obtained on application point of tension force for the models without pretension effect and second load step for the models with pretension effect. For first load step, maximum displacement are obtained on perimeter of hole of tension plate. In Figure 11, first and second indicators show finishing point of first and second load step, respectively. The indicators in Figure 10 are not the same. Figure 10. Max. equivalent stress max. displacement on tension member diagrams without pretension effect.

7 Figure 11. Max. equivalent stress max. displacement on tension member diagrams with pretension effect. 4. Conclusion This study presents numerical simulation of bolted steel connections under pretension effect. Numerical simulations were performed by Finite Element Software ANSYS (ANSYS Inc., 2011). It is observed that, for the models without pretension effect, increasing number of bolts on a line causes increasing ratio between maximum and minimum stress values. For the models without pretension effect, there is a rule that each bolt line can have maximum five bolts it makes no matter shear status (Deren H. et. al, 2012), because of increasing ratio of maximum to minimum stresses on bolts. It is observed that this rule is acceptable. The ratio is very high in the models which have single shear, this shear status also allows bending, so it is recommended to avoid this shear status as much as possible. With pretension effect the ratio is almost same for all models. Also it is observed that increasing number of bolt causes increasing displacement for all models, because of increasing number of holes in plates. References ANSYS version 14. (2011). ANSYS Inc. Deren, H., Uzgider, E., Piroğlu, F., Çağlayan, Ö. (2012). Çelik Yapılar 4 th Edition. Çağlayan Yayınevi. Ju, S. H., Fan, C. Y., Wu, G. H. (2004). Three dimensional finite elements of steel bolted connections. Engineering Structures. Vol. 26, pp Kim, J., Yoon, J. C., Kang, B. S. (2007). Finite element analysis and modeling of structure with bolted joints. Applied Mathematical Modelling. Vol. 31, pp Kim, H. J., Yura, J. A. (1999). The effect of ultimate-to-yield ratio on the bearing strength of bolted connections. Journal of Constructional Steel Research. Vol. 57, pp Mashaly, E., El-Heweity, M., Elfath, H. A., Osman, M. (2011). Finite element analysis of beam-to-column joints in steel frames under cyclic loading. Alexandria Engineering Journal. Vol. 50, pp Moze, P., Beg, D. (2010). High strength steel tension splices with one or two bolts. Journal of Constructional Steel Research. Vol. 66, pp Moze, P., Beg, D. (2011).Investigation of high strength steel connections with several bolts in double shear. Journal of Constructional Steel Research. Vol. 67, pp Moze, P., Beg, D. (2014). A complete study of bearing stress in single bolt connections. Journal of Constructional Steel Research. Vol. 95, pp Puthli, R., Fleischer, O. (2001). Investigation on bolted connections for high strength steel members. Journal of Constructional Steel Research. Vol. 57, pp Schiffer, K., Droste gen Helling, C. (1997). Simulation of prestressed screw joints in complex structures. Computer & Structures. Vol. 64, pp