6.2 Non-linear behaviour of plate shells
6.2.4 Connection stiffness
This section studies the influence of the connection stiffness parameters on the non-linear behaviour of plate shells.
The connection stiffness parameters generally used in the non-linear analysis in this chap- ter correspond to the glued-in plate connection design. In the following study, these parameters have been varied, to investigate the effect on the critical load.
The plate shell with fine faceting has been used, since any effects from the connection stiffness is likely to be enhanced in this model because of the larger number of connections. Imperfection A is added to the perfect geometry, and the load is uniform.
The FE models listed in Table 6.1 under the headline “Connection stiffness” have been
analyzed. In two models the rotational stiffness kmis reduced to 50% and 25% respectively,
Non-linear investigations 6.2 Non-linear behaviour of plate shells
Figure 6.6: Contour deformation plots (detail) of FacC Perf Uni at the critical load level (before and after failure). The contour scale is consistent in the two images. The difference in load level in the two images is 6%.
Figure 6.7: Contour deformation plots (detail) of FacF Perf Uni at the critical load level (before and after failure). The contour scale is consistent in the two images. The difference in load level in the two images is 10%.
6.2.4 Connection stiffness
This section studies the influence of the connection stiffness parameters on the non-linear behaviour of plate shells.
The connection stiffness parameters generally used in the non-linear analysis in this chap- ter correspond to the glued-in plate connection design. In the following study, these parameters have been varied, to investigate the effect on the critical load.
The plate shell with fine faceting has been used, since any effects from the connection stiffness is likely to be enhanced in this model because of the larger number of connections. Imperfection A is added to the perfect geometry, and the load is uniform.
The FE models listed in Table 6.1 under the headline “Connection stiffness” have been
6.2 Non-linear behaviour of plate shells Non-linear investigations
and in three models the axial stiffness kn is reduced to 50%, 25% and 5% respectively.
Table 6.4 lists the models, the relevant connection stiffness parameters and the joint parameters used in the models.
The calculated critical load of the models are given in Table 6.5. (The note “standard” indicates that the connection stiffness parameters in this model are the same as used in the other non-linear studies in this chapter.)
Model km kn tj Ej
(kN ) (kN/mm2) (mm) (kN/mm2)
FacF ImpA Uni (standard) 16 5 6.15 4.07 Reduction of km
FacF ImpA Uni km50 8 5 4.38 5.71 FacF ImpA Uni km25 4 5 3.10 8056
Reduction of kn
FacF ImpA Uni kn50 16 2.5 8.76 1.43 FacF ImpA Uni kn25 16 1.3 12.4 0.50 FacF ImpA Uni kn05 16 0.25 27.7 0.045 Table 6.4: Connection stiffness parameters and joint parameters used for modelling, for the models listed in Table 6.1 under “Connection stiffness”. tj and Ej have been determined as
described in Section 3.2.1 (page 27).
Model pcr/ kN/m2
FacF ImpA Uni (standard) 71 Reduction of km
FacF ImpA Uni km50 68 FacF ImpA Uni km25 69
Reduction of kn
FacF ImpA Uni kn50 67 FacF ImpA Uni kn25 52 FacF ImpA Uni kn05 25
Table 6.5: Critical loads, comparing varying connection stiffness parameters. For an overview of non-linear models, see Table 6.1.
The results in Table 6.5 clearly indicate a correlation between the critical load and the ax- ial stiffness kn. A reduction of the axial stiffness seems to result in a reduced critical load. This correlation has also been observed in [7] and [8], where a plate shell was subjected to non-linear FE analysis. Those results showed a strong influence of the axial stiffness on
the critical load, and almost no influence of the rotational stiffness km.13 Correspondingly,
13The structure that was investigated in [7] and [8] had a different geometry and the axial stiffness k
n
Department of Civil Engineering - Technical University of Denmark 77
6.2 Non-linear behaviour of plate shells Non-linear investigations
and in three models the axial stiffness kn is reduced to 50%, 25% and 5% respectively.
Table 6.4 lists the models, the relevant connection stiffness parameters and the joint parameters used in the models.
The calculated critical load of the models are given in Table 6.5. (The note “standard” indicates that the connection stiffness parameters in this model are the same as used in the other non-linear studies in this chapter.)
Model km kn tj Ej
(kN ) (kN/mm2) (mm) (kN/mm2)
FacF ImpA Uni (standard) 16 5 6.15 4.07 Reduction of km
FacF ImpA Uni km50 8 5 4.38 5.71 FacF ImpA Uni km25 4 5 3.10 8056
Reduction of kn
FacF ImpA Uni kn50 16 2.5 8.76 1.43 FacF ImpA Uni kn25 16 1.3 12.4 0.50 FacF ImpA Uni kn05 16 0.25 27.7 0.045 Table 6.4: Connection stiffness parameters and joint parameters used for modelling, for the models listed in Table 6.1 under “Connection stiffness”. tj and Ej have been determined as
described in Section 3.2.1 (page 27).
Model pcr/ kN/m2
FacF ImpA Uni (standard) 71 Reduction of km
FacF ImpA Uni km50 68 FacF ImpA Uni km25 69
Reduction of kn
FacF ImpA Uni kn50 67 FacF ImpA Uni kn25 52 FacF ImpA Uni kn05 25
Table 6.5: Critical loads, comparing varying connection stiffness parameters. For an overview of non-linear models, see Table 6.1.
The results in Table 6.5 clearly indicate a correlation between the critical load and the ax- ial stiffness kn. A reduction of the axial stiffness seems to result in a reduced critical load. This correlation has also been observed in [7] and [8], where a plate shell was subjected to non-linear FE analysis. Those results showed a strong influence of the axial stiffness on
the critical load, and almost no influence of the rotational stiffness km.13 Correspondingly,
13The structure that was investigated in [7] and [8] had a different geometry and the axial stiffness k
n
Non-linear investigations 6.2 Non-linear behaviour of plate shells
the results in Table 6.5 indicate only a slight reduction of the critical load for a reduced rotational stiffness.
In one model (FacC ImpA Uni Cor in Table 6.1 – the plate shell with coarse faceting, imposed by imperfection A, and subjected to the uniform load) the joint elements are modelled so that they connect the full length of the facet edges. In FacC ImpA Uni Cor the critical load is increased by 5% compared to FacC ImpA Uni, which is an identical model apart from the unconnected facet corners (the joint elements end 100mm from the facet corners). The unconnected facet corners thereby appear to be of minor importance to the critical load.