Author Contributions
Conceptualization, E.T., A.F. and B.S.; data curation, E.T.; formal analysis, E.T.; funding acquisition, E.T., A.F. and B.S.; investigation, E.T.; methodology, E.T. and B.S.; project administration, E.T. and B.S.; resources, E.T.; software, E.T.; supervision, E.T., A.F., P.M., B.V.H. and B.S.; validation, E.T.; visualization, E.T.; writing—original draft, E.T.; writing—review & editing, E.T. All authors have read and agreed to the published version of the manuscript.
Figure 1.
Reinforcement by bolts and spacers: (A) Schematic view; (B) Along the upright.
Figure 1.
Reinforcement by bolts and spacers: (A) Schematic view; (B) Along the upright.
Figure 2.
Configuration of the details: (A) Upright configuration; (B) Frame configuration.
Figure 2.
Configuration of the details: (A) Upright configuration; (B) Frame configuration.
Figure 3.
Designation of specimens.
Figure 3.
Designation of specimens.
Figure 4.
Stress-strain diagram for 1.6 mm thickness specimen.
Figure 4.
Stress-strain diagram for 1.6 mm thickness specimen.
Figure 5.
Typical schematic four-point bending test.
Figure 5.
Typical schematic four-point bending test.
Figure 6.
Minor axis test set-up details: (A) Test specimen; (B) schematic front view; (C) schematic side view.
Figure 6.
Minor axis test set-up details: (A) Test specimen; (B) schematic front view; (C) schematic side view.
Figure 7.
Major axis test set-up details: (A) Test specimen; (B) schematic front view; (C) schematic side view.
Figure 7.
Major axis test set-up details: (A) Test specimen; (B) schematic front view; (C) schematic side view.
Figure 8.
Crippling of load points: (A) Typical crippling at flanges; (B) Specific crippling reinforcement.
Figure 8.
Crippling of load points: (A) Typical crippling at flanges; (B) Specific crippling reinforcement.
Figure 9.
Test set-up: (A) minor axis test, (B) major axis test.
Figure 9.
Test set-up: (A) minor axis test, (B) major axis test.
Figure 10.
Normalized bending moment–deflection about major axis curves: (A) SMJM; (B) 200RMJM; (C) 300RMJM.
Figure 10.
Normalized bending moment–deflection about major axis curves: (A) SMJM; (B) 200RMJM; (C) 300RMJM.
Figure 11.
The observed failure mode for unreinforced specimens during the major axis test: (A) SMJM-test1; (B) SMJM-test2; (C) SMJM-test3.
Figure 11.
The observed failure mode for unreinforced specimens during the major axis test: (A) SMJM-test1; (B) SMJM-test2; (C) SMJM-test3.
Figure 12.
The observed failure mode for reinforced specimens with 200 mm reinforcing pitch during the major axis test: (A) 200RMJM-test1; (B) 200RMJM-test2; (C) 200RMJM-test3.
Figure 12.
The observed failure mode for reinforced specimens with 200 mm reinforcing pitch during the major axis test: (A) 200RMJM-test1; (B) 200RMJM-test2; (C) 200RMJM-test3.
Figure 13.
The observed failure modes for reinforced specimens with 300 mm reinforcing space during the major axis test: (A) 300RMJM-test1; (B) 300RMJM-test2; (C) 300RMJM-test3.
Figure 13.
The observed failure modes for reinforced specimens with 300 mm reinforcing space during the major axis test: (A) 300RMJM-test1; (B) 300RMJM-test2; (C) 300RMJM-test3.
Figure 14.
The normalized major axis test average curves.
Figure 14.
The normalized major axis test average curves.
Figure 15.
The ultimate normalized moment for major axis test with respect to the reinforcement type.
Figure 15.
The ultimate normalized moment for major axis test with respect to the reinforcement type.
Figure 16.
Normalized bending moment–deflection about minor axis test curves: (A) SMIM; (B) 200RMIM; (C) 300RMIM.
Figure 16.
Normalized bending moment–deflection about minor axis test curves: (A) SMIM; (B) 200RMIM; (C) 300RMIM.
Figure 17.
The observed failure mode for unreinforced specimens during the minor axis test: (A) SMIM-test1; (B) SMIM-test2; (C) SMIM-test3.
Figure 17.
The observed failure mode for unreinforced specimens during the minor axis test: (A) SMIM-test1; (B) SMIM-test2; (C) SMIM-test3.
Figure 18.
The observed failure mode for reinforced specimens with 200 mm reinforcing pitch during the minor axis test: (A) 200RMIM-test1; (B) 200RMIM-test2; (C) 200RMIM-test3.
Figure 18.
The observed failure mode for reinforced specimens with 200 mm reinforcing pitch during the minor axis test: (A) 200RMIM-test1; (B) 200RMIM-test2; (C) 200RMIM-test3.
Figure 19.
The observed failure mode for reinforced specimens with 300 mm reinforcing pitch during the minor axis test: (A) 300RMIM-test1; (B) 300RMIM-test2; (C) 300RMIM-test3.
Figure 19.
The observed failure mode for reinforced specimens with 300 mm reinforcing pitch during the minor axis test: (A) 300RMIM-test1; (B) 300RMIM-test2; (C) 300RMIM-test3.
Figure 20.
The normalized minor axis average curves.
Figure 20.
The normalized minor axis average curves.
Figure 21.
The ultimate normalized moment for the minor axis test by reinforcement type.
Figure 21.
The ultimate normalized moment for the minor axis test by reinforcement type.
Figure 22.
The finite element model arrangement: (A) major axis; (B) minor axis.
Figure 22.
The finite element model arrangement: (A) major axis; (B) minor axis.
Figure 23.
Typical finite element mesh of an upright section.
Figure 23.
Typical finite element mesh of an upright section.
Figure 24.
Interactions of the model components and bolt modelling.
Figure 24.
Interactions of the model components and bolt modelling.
Figure 25.
Finite element model and experimental curves for minor axis test set-up: (A) non-reinforced types; (B) 200 mm reinforced types; (C) 300 mm reinforced types.
Figure 25.
Finite element model and experimental curves for minor axis test set-up: (A) non-reinforced types; (B) 200 mm reinforced types; (C) 300 mm reinforced types.
Figure 26.
Comparison of finite element model against minor axis test results along with the linear regression: (A) and (B) non-reinforced model; (C) and (D) 200 mm reinforced model; (E) and (F) 300 mm reinforced model.
Figure 26.
Comparison of finite element model against minor axis test results along with the linear regression: (A) and (B) non-reinforced model; (C) and (D) 200 mm reinforced model; (E) and (F) 300 mm reinforced model.
Figure 27.
Comparison of failure modes: (A) non-reinforced upright type; (B) 300 mm reinforced upright type.
Figure 27.
Comparison of failure modes: (A) non-reinforced upright type; (B) 300 mm reinforced upright type.
Figure 28.
Finite element model and experimental curves for major axis test set-up: (A) non-reinforced frame types; (B) 200 mm reinforced frame types; (C) 300 mm reinforced frame types.
Figure 28.
Finite element model and experimental curves for major axis test set-up: (A) non-reinforced frame types; (B) 200 mm reinforced frame types; (C) 300 mm reinforced frame types.
Figure 29.
Comparison of finite element model against major axis test results along with the linear regression: (A) and (B) non-reinforced model; (C) and (D) 200 mm reinforced model; (E) and (F) 300 mm reinforced model.
Figure 29.
Comparison of finite element model against major axis test results along with the linear regression: (A) and (B) non-reinforced model; (C) and (D) 200 mm reinforced model; (E) and (F) 300 mm reinforced model.
Figure 30.
Comparison of failure mode: (A) non-reinforced upright type; (B) 300 mm reinforced upright type.
Figure 30.
Comparison of failure mode: (A) non-reinforced upright type; (B) 300 mm reinforced upright type.
Table 1.
Specimen configurations.
Table 1.
Specimen configurations.
Specimen Type | Geometry (mm) | Reinforcement | Loading Direction |
---|
* Length | ** Thickness | *** Width | **** Sp | Major Axis | Minor Axis |
---|
SMIM | 2400 | 1.6 | 600 | - | No | | • |
SMIM | - | No | | • |
SMIM | - | No | | • |
SMJM | - | No | • | |
SMJM | - | No | • | |
SMJM | - | No | • | |
200RMIM | 200 | Yes | | • |
200RMIM | 200 | Yes | | • |
200RMIM | 200 | Yes | | • |
200RMJM | 200 | Yes | • | |
200RMJM | 200 | Yes | • | |
200RMJM | 200 | Yes | • | |
300RMIM | 300 | Yes | | • |
300RMIM | 300 | Yes | | • |
300RMIM | 300 | Yes | | • |
300RMJM | 300 | Yes | • | |
300RMJM | 300 | Yes | • | |
300RMJM | 300 | Yes | • | |
Table 2.
Material properties of the upright section.
Table 2.
Material properties of the upright section.
Section Type | Yield Stress, σy (MPa) | Ultimate Stress, σu (MPa) | Elongation (%) |
---|
Upright with 1.6 mm thickness (Test 1) | 561 | 578 | 10.3 |
Upright with 1.6 mm thickness (Test 2) | 557 | 585 | 9.6 |
Upright with 1.6 mm thickness (Test 3) | 571 | 610 | 10.1 |
Average | 563 | 591 | 10 |
Table 3.
The ultimate normalized bending capacity of specimens in the major axis test.
Table 3.
The ultimate normalized bending capacity of specimens in the major axis test.
Test Specimen | |
---|
SMJM-Test1 | 0.330997561 |
SMJM-Test2 | 0.342394439 |
SMJM-Test3 | 0.325000724 |
Average | 0.332797575 |
Standard deviation | 0.008835461 |
200RMJM-Test1 | 0.379727867 |
200RMJM-Test2 | 0.391261742 |
200RMJM-Test3 | 0.388300744 |
Average | 0.386430118 |
Standard deviation | 0.005990158 |
300RMJM-Test1 | 0.354944611 |
300RMJM-Test2 | 0.361971684 |
300RMJM-Test3 | 0.356490403 |
Average | 0.357802233 |
Standard deviation | 0.003692643 |
Table 4.
The ultimate normalized bending capacity of specimens in the minor axis tests.
Table 4.
The ultimate normalized bending capacity of specimens in the minor axis tests.
Test Specimen | Normalized Ultimate Bending Moment |
---|
SMIM-Test1 | 0.193595703 |
SMIM-Test2 | 0.203694478 |
SMIM-Test3 | 0.195419898 |
Average | 0.197570026 |
Standard deviation | 0.005381785 |
200RMIM-Test1 | 0.232982073 |
200RMIM-Test2 | 0.239285101 |
200RMIM-Test3 | 0.242392113 |
Average | 0.238219762 |
Standard deviation | 0.004794624 |
300RMIM-Test1 | 0.211013767 |
300RMIM-Test2 | 0.21581945 |
300RMIM-Test3 | 0.202362802 |
Average | 0.209732006 |
Standard deviation | 0.006819276 |
Table 5.
Finite element model vs experimental results accuracy details in terms of evaluation criteria.
Table 5.
Finite element model vs experimental results accuracy details in terms of evaluation criteria.
Non-reinforced model | Evaluation criteria |
Standard deviation | 0.0618701 |
Pearson (r) | 0.998139545 |
R2 | 0.9963 |
200 mm reinforced model | Evaluation criteria |
Standard deviation | 0.08034494 |
Pearson (r) | 0.993668695 |
R2 | 0.998 |
300 mm reinforced model | Evaluation criteria |
Standard deviation | 0.069798432 |
Pearson (r) | 0.998023512 |
R2 | 0.9961 |
Table 6.
Finite element model vs experimental results accuracy details in terms of evaluation criteria.
Table 6.
Finite element model vs experimental results accuracy details in terms of evaluation criteria.
Non-reinforced model | Evaluation criteria |
Standard deviation | 0.124180809 |
Pearson (r) | 0.998891538 |
R2 | 0.9978 |
200 mm reinforced model | Evaluation criteria |
Standard deviation | 0.135695798 |
Pearson (r) | 0.995707933 |
R2 | 0.9914 |
300 mm reinforced model | Evaluation criteria |
Standard deviation | 0.122399695 |
Pearson (r) | 0.999038872 |
R2 | 0.9981 |