2. Cold-formed C-section members
2.4. Application rule-based design approach
2.4.4. Comparison of test and standard
magnitude as along the strong axis results an order of magnitude smaller contribution to the utilisation than the shift along the strong axis.
Due to this simplification in modelling the cross-section of the members, in the standard-based calculations no bending about the major axis is present: the members are in axial compression and bending about the weak axis. Hence, the design formulae of both versions of the standard can be directly used, the results are directly comparable.
Note, that lateral-torsional buckling was not considered in the calculations, as due to the simplified cross-sectional model there is no shift of the centroid along the weak axis, and there is no bending about the strong axis from loading in the members studied in the laboratory tests.
function of the member length, with minimum and maximum values. Note that the figures in the Annex show the results obtained using the formulae discussed in Chapter 2.4.5 as well.
Figure 61.: Comparison of test and design resistances (C16).
Figure 62.: Comparison of test and design resistances (C55).
In the following the comparisons of test and design resistances for both versions of the standard are presented in figures and tables for each test arrangement. In the figures the test and design resistances are shown as data points. The trend of the results is presented with a line obtained by linear regression, equation of the line and fitness are shown. The unity line drawn with black (Rt = Rd, with Rt standing for test resistance, Rd for design resistance) is shown as reference: the closer the data points and regression lines to this line are, the better the match of test and design resistance; regression lines over this line (Rd/Rt ratios greater than 1.00) indicate unsafe design. The tables containing the numerical values underlying the graphs are presented in the Annex, Tables A15 – A19.
The comparisons of test and design resistances of SimpleC specimens for both versions of the standard are presented in Figure 63. and the Annex, Table A15.
EC3-1-3:1996 y = 1.0044x R2 = 0.9964 EC3-1-3:2006
y = 1.0642x
R2 = 0.9829 Rt = Rd
0 20 40 60 80 100 120 140
0 20 40 60 80 100 120
Test resistances (Rt) [kN]
Design resistances (Rd) [kN]
1996 2006 Rt = Rd EC3-1-3:1996 trend EC3-1-3:2006 trend
Figure 63.: Test and design resistances of SimpleC specimens.
In general, although the regression lines indicate slightly unsafe design, both versions of the standard provide good match to the test results, the scatter of the data is small. The design
resistances calculated according to EC3-1-3:2006 are more on the unsafe side relative to those calculated according to EC3-1-3:1996 and the scatter is also bigger in this case.
The comparisons of test and design resistances of CompressionC specimens for both versions of the standard are presented in Figure 64. and the Annex, Table A16. Both versions of the standard provide good match; EC3-1-3:1996 yields slightly unsafe, EC3-1-3:2006 yields safe design.
EC3-1-3:1996 y = 1.0287x R2 = 0.9902
EC3-1-3:2006 y = 0.9448x R2 = 0.9964
Rt = Rd
0 20 40 60 80 100 120 140
0 20 40 60 80 100 120 140
Test resistances (Rt) [kN]
Design resistances (Rd) [kN]
1996 2006 Rt = Rd EC3-1-3:1996 trend EC3-1-3:2006 trend
Figure 64.: Test and design resistances of CompressionC specimens.
The comparisons of test and design resistances of C specimens for both versions of the standard are presented in Figure 65. and the Annex, Table A17.
EC3-1-3:1996 y = 0.9963x
R2 = 0.925 EC3-1-3:2006
y = 1.0033x R2 = 0.8887
Rt = Rd
0 20 40 60 80 100 120 140
0 20 40 60 80 100 120 140
Test resistances (Rt) [kN]
Design resistances (Rd) [kN]
1996 2006 Rt = Rd EC3-1-3:1996 trend EC3-1-3:2006 trend
Figure 65.: Test and design resistances of C specimens.
For specimens with a C arrangement both version of the standard provide results with a significant scatter (+/- 15%), but the regression shows that the tendencies of the results are good. Considering the results of tests C45, C55, and C56 – same section and length, eccentricities: 12.25 mm, 5.58 mm, 3.08 mm in case of EC3-1-3:1996 – shows, that with decreasing eccentricity the match of test and standard-based results gets worse; this implies that assuming uniform force distribution between the screws may be not true for all cases, the load is transferred primarily by the screws in the web. For C200/2.0 and C200/2.5 the formulae of both standards yield unsafe design in case of the shorter specimens (C72, C77) and a safe design for longer specimens (C48, C51), however, a common property to explain this tendency is not found.
The comparisons of test and design resistances of Brace specimens for both versions of the standard are presented in Figure 66. and the Annex, Table A18.
EC3-1-3:1996 y = 0.9314x
R2 = 0.971
EC3-1-3:2006 y = 0.9191x R2 = 0.9458 Rt = Rd
0 20 40 60 80 100 120 140 160 180 200
0 20 40 60 80 100 120 140 160 180 200
Test resistances [kN]
Design resistances [kN]
1996 2006 Rt = Rd EC3-1-3:1996 trend EC3-1-3:2006 trend
Figure 66.: Test and design resistances of Brace specimens.
Both versions of the standard provide satisfactory match of test and design resistances, with EC3-1-3:1996 providing results only on the safe side.
As all studied arrangements can be considered the same from the design method point-of-view (i.e.: the difference is the magnitude of the eccentricity), displaying all results in one figure provides a general overview on the accuracy of the application rules of both versions of the standard. An overview on the results is given in Figure 67., Table A19 in the Annex contains statistical data on the results for all types of specimens.
EC3-1-3:1996 y = 0.975x
R2 = 0.98 EC3-1-3:2006
y = 0.9777x R2 = 0.9596
Rt = Rd
0 20 40 60 80 100 120 140 160 180 200
0 20 40 60 80 100 120 140 160 180 200
Test resistances (Rt) [kN]
Design resistances (Rd) [kN]
1996 2006 Rt = Rd EC3-1-3:1996 trend EC3-1-3:2006 trend
Figure 67.: Test and design resistances of all studied specimens.
The results of calculations carried out using the application rules was shown for each test arrangement made using a single C-section. Except for arrangement C a good agreement of test and design values and a relatively small scatter of the test/design resistance ratios were found. In case of the specimens with a C arrangement, significant scatter was observed, which is probably the result of a non-uniform load distribution between the self-drilling screws, a property that has not been taken into account in the calculations.
The failure mode of the members, according to the application rules is in most cases stability failure. In case of EC3-1-3:1996 this is due to the fact, that even in case of stub columns the
interaction coefficient in formula (19) is greater than 1.0, hence this yields the highest utilisation in all cases. In the case of EC3-1-3:2006 cross-section failure is the governing mode only for very short members.
Comparing the ratios of the design resistances obtained by the two versions of the standard (Figures presented in the Annex) shows that in case of SimpleC specimens for high web b/t ratios the design resistances from EC3-1-3:1996 are for all lengths higher than those from EC3-1-3:2006; with decreasing web b/t ratio the results of EC3-1-3:1996 are for short specimens lower, long specimens higher than those from EC3-1-3:2006; the transition length is higher for web smaller values of b/t ratio. In the case of Brace specimens the opposite of this tendency is observed, the results of EC3-1-3:1996 are in all cases lower than those from EC3-1-3:2006 for C200/1.5 members, and in all cases higher in case of C200/2.5 members. In case of C and CompressionC arrangements the tendency is the same as in the case of SimpleC specimens.
The minimum of the ratio of the design resistances calculated according to the two versions of the standard (EC3-1-3:1996/EC3-1-3:2006) is usually at cca. 1000-2000 mm member length, hence the biggest difference between the results of the two versions of the standard is approximately at the lengths important from the practical design point-of-view.
The comparison of the results clearly indicates that – due to the in some cases large differences between the values – in the checking formulae the contribution of the axial action and bending to the total utilisation is different, but as the results are in general in good agreement, both versions of the standard consist of a coherent method to calculate cross-sectional properties and design resistances over a wide range of parameters; however, the cross-sectional properties and formulae of the two versions of the standard may not be mixed.
Considering the slope and fitness of the regression lines and the standard deviations calculated, the application rules of EC3-1-3:1996 can be considered more accurate, although the differences between the results of the two versions of the standard are not significant. The comparison of test and design resistances also shows, that since the values of the partial safety factors is , according to the standard 1.0, the safety of the design method is equal to the safety of the material model.