Validation of the numerical models in compression and combined loading

The numerical models representing stainless steel RHS and SHS cross-sections and members subjected to pure compression and combined loading conditions have been conducted following similar procedures and are therefore presented together. The accuracy of these models is investigated by comparing the experimental ultimate loads and load-deflection histories to those predicted by the FE models, as well as the failure mode shapes.

The edge elements at the ends of the specimens were kinematically coupled and connected to two reference points, where the relevant degrees of freedom were defined. For stub columns subjected to compression all degrees of freedom were fixed at the lower reference point while only longitudinal displacement was set free at the upper one.

Tests on stub columns subjected to combined loading and members subjected to both pure compression and combined loading conditions were conducted under pin-ended boundary conditions. In these models the ends of the specimens were also coupled to two reference points, set 50mm away from each specimen end as described in the test setups, and assuming the effective length of the columns equal to the distance between knife-edges. All degrees of freedom except the rotation around the relevant axis were restrained at the lower reference point, while longitudinal displacement and relevant rotations were set free in the upper one. Loads were introduced as imposed displacements at the upper reference points in all the models and no restrictions were defined in the rest of the nodes.

The behaviour of ferritic stainless steel stub columns subjected to compression and combined loading conditions was reproduced from numerical models by performing a nonlinear analysis with a modified Riks analysis, where local geometric imperfections, considering imperfection amplitudes equal to those measured from each specimen, were introduced. The comparison of the results derived from the FE models with the experimental results is presented in Tables 5.1 and 5.2 for stub columns subjected to compression and combined loading conditions respectively. These Tables report the numerical-to-experimental normalized loads Nu,FE/Nu,exp for

each specimen, together with the mean and coefficients of variation (COVs). The comparison between the predicted and experimental end shortenings and end rotations at Nu are also

provided. Results corresponding to the two material definitions contemplated in the FE model validation have been included in Tables 5.1 and 5.2, those corresponding to the measured constitutive laws in flat and corner regions and to the weighted average material behaviour in the entire cross-section. Results demonstrate that although the most accurate results are obtained when the measured stress-strain curves are considered, the adoption of the simplified weighted average material properties still provides excellent results for both compression and combined loading conditions.

Table 5.1. Comparison of the stub column test results with FE results.

Specimen

Flat and corner material Weighted average material

Nu,FE/Nu,exp u,FE/u,exp Nu,FE/Nu,exp u,FE/u,exp

S1 – C 0.99 0.83 0.94 0.92 S2 – C 0.99 0.84 0.94 0.80 S3 – C 0.98 0.97 0.91 0.92 S4 – C 0.97 0.84 0.95 0.74 S5 – C 1.00 0.94 1.01 1.02 Mean 0.99 0.88 0.95 0.88 COV 0.012 0.072 0.040 0.125

Table 5.2. Comparison of the stub column combined loading test results with FE results.

Specimen

Flat and corner material Weighted average material

Nu,FE/Nu,exp u,FE/u,exp Nu,FE/Nu,exp u,FE/u,exp

S1 – CL 1.02 1.03 0.98 1.03 S2 – CL 0.97 0.90 0.96 0.81 S3-Mj – CL 0.99 0.96 0.96 0.86 S3-Mi – CL 1.00 0.95 0.96 0.89 S4-Mj – CL 1.03 0.99 0.98 1.01 S4-Mi – CL 1.02 0.96 1.01 0.98 S5-Mj – CL 1.01 1.05 0.99 0.85 S5-Mi – CL 0.99 1.03 1.01 0.91 Mean 1.00 0.98 0.98 0.92 COV 0.019 0.053 0.022 0.089

Figures 5.1a and 5.2a present the comparison of the experimental and FE load-end shortening histories (end rotation for the combined loading test) for the measured (FE) and weighted average (FE,average material) material definitions, while the comparison of the local failure modes for typical specimens are presented in Figure 5.1b and Figure 5.2b for compression and combined loading conditions respectively. Tables 5.1 and 5.2, together with Figures 5.1 and 5.2, demonstrate that in addition to provide excellent ultimate load predictions, the conducted FE models accurately capture the stiffness and the general shape of the response of the specimens. The obtained local buckling failure modes are also found to be in good agreement with those observed after the tests.

a) Experimental and numerical load-end shortening curves b) Experimental and FE failure modes

Fig. 5.1. Comparison of experimental and FE results for typical specimens in compression.

a) Experimental and numerical load-end rotation curves b) Experimental and FE failure modes

Fig. 5.2. Comparison of experimental and FE results for typical specimens under combined loading.

Regarding the tests conducted on ferritic stainless steel members subjected to compression and combined loading, experimental curves have also been compared to the corresponding FE results considering the two different material definitions. Load-lateral deflections corresponding to the measured constitutive laws in flat and corner regions (FE) and the weighted average material properties in the entire cross-section (FE, average material) are compared with the experimental curves in Figure 5.3 for typical column and beam-column specimens.

Fig. 5.3. Experimental and FE load-lateral deflection curves for typical column and beam-column specimens.

Table 5.3 reports the mean values and COVs of the numerical-to-experimental ratios of the ultimate loads and the corresponding lateral deflections, showing excellent results for both material definitions considered. It is also remarkable that the failure modes of the obtained FE models are in good agreement with experimental results, as demonstrated in Figure 5.4. Therefore, these comparisons demonstrate that the derived numerical analyses are capable of accurately predicting the ultimate loads, the full experimental histories and the failure modes of ferritic columns and beam-columns when measured material properties are adopted, but also when the weighted average material is considered.

Table 5.3. Comparison of the column and beam-column test results with FE results.

Specimen Flat and corner material Weighted average material

Nu,FE/Nu,exp du,FE/du,exp Nu,FE/Nu,exp du,FE/du,exp

S1 – CC 1.00 0.93 1.04 1.07 S1 – EC1 1.02 1.08 0.99 0.94 S1 – EC2 1.02 1.04 0.99 1.05 S2 – CC 1.02 0.99 1.03 0.88 S2 – EC1 1.01 1.02 1.02 1.02 S3 – CC 1.01 1.03 1.02 0.85 S3 – EC1 1.03 1.03 1.04 0.96 S4 – CC 0.97 0.80 1.00 0.83 S4 – EC1 0.99 0.87 0.99 1.02 S5 – CC 1.02 1.00 1.02 1.00 Column S1 – CC Beam-column S2 – EC1

Fig. 5.4. Comparison of the experimental and numerical deformed shapes for S3 and S4 specimens.