Thin-Walled Structures Group

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1 Thin-Walled Structures Group JOHNS HOPKINS UNIVERSITY RESEARCH REPORT Identifying targeted cold- formed steel beam- columns for testing TWG- RR03-12 Y. Shifferaw July 2012

2 This report was prepared as part of the American Iron and Steel Institute sponsored project: Direct Strength Prediction of Cold-Formed Steel Beam Columns. The project also received supplementary support and funding from the Metal Building Manufacturers Association. Project updates are available at Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the author and do not necessarily reflect the views of the American Iron and Steel Institute, nor the Metal Building Manufacturers Association. Acknowledgements: The authors would like to acknowledge AISI and MBMA for their support throughout the duration of this project.

3 Identifying targeted cold-formed steel beam-columns for testing 1. Introduction Cold-formed steel beam-column testing under local and distortional collapse buckling of members subjected to combined axial-loading and bending actions is to be undertaken. Separation of these limit states is a critical component of the development of new design approach for cold-formed steel beam-columns that considers direct analysis of the combined stresses instead of a simplified linear interaction approach based on separate compression and bending actions currently in use. To this end, identifying targeted coldformed steel beam-columns for testing is a significant step for developing a test-matrix that will be the foundation for the development of appropriate finite element collapse models for further comprehensive parametric studies and Direct Strength Method style design formulations of cold-formed steel members subjected to combined actions. 2. Limit state examination With the development of test sections in mind, SSMA sections are examined for the limit states in the compression-bending (P-M) design space. Among the SSMA sections, 600S162 and 800S200 test series are adopted as the preliminary sections for first phase experimental examination. Current anchor points in the P-M space for pure compression and pure bending (major axis) are determined as shown in Table 1. Limit states are identified for each section to aid in the decision of targeted sections for testing. The sections represent the full space of limit states among the SSMA sections. DSM anchor points with P-M limit state combinations of pure local (L-L), pure distortional (D-D), switching mode of (D-L) and inelastic reserve capacities (Mn>My) are represented in these section series (D y =Distortion dominated inelastic reserve). Moreover, these two sections are applied in the CFS-NEES building and are among those test sections that have available test data from the pure bending tests for local and distortional limit states (Yu, 2003, 2006).

4 Table 1 Current DSM strength (separate compression and bending nominal strengths) for SSMA sections under considerations for beam-column tests Section( Fy( Py My_xx Mp_xx Pnl Pnd Mnl_xx Mnd_xx Pn Mnx 600S162& L L 600S162& L D 600S162& L D 600S162& D D 600S162& D Dy 600S162& D D 600S162& D Dy 600S162& D Dy 600S162& D Dy 600S162& D Dy 800S200& L L 800S200& L L 800S200& L D 800S200& D D 800S200& D D 800S200& D D 800S200& D Dy 800S200& D D 800S200& D Dy 800S200& D Dy 3. Efficiency examination Efficiency of the selected SSMA sections is examined. In order to study the efficiency of these sections a plot of nominal compression and bending capacities normalized with area for structural SSMA sections is given in Figure 1. For a fixed angle (direction) as measured from, say the Mn/A axis, the larger the radial distance from the origin the more efficient that section is (either as a column, beam or beam-column) in comparison with shorter radial distance along that line. Hence those sections that form the outer boundary represent the efficient group of sections under the different applications. Overall, the selected sections represent sections that can be commonly adopted in beam-column applications as can be observed on the efficiency plot of Figure 1.

5 Figure 1 Efficiency of selected SSMA sections 4. Preliminary DSM prediction examination The local buckling strength of a globally-braced section (i.e. no global buckling occurs) in the existing DSM follows the same format for compression and bending. If one assumes this expression holds in general, then the nominal local strength, β nl, is: for λ β n = β ne (1) for λ > β β cr cr β n = β (2) β β y y y where λ = β y / β cr (3) β cr = Critical elastic local buckling magnitude under combined P-M resultant

6 β y = First yield under combined P-M resultant. The distortional buckling strength in the existing DSM uses slightly different prediction equations for axial load and bending. Thus, combining them into one consistent formula for all combinations of P and M is slightly more complicated than for local bucking. A preliminary formulation that provides this combination and still yields the current P nd and M nd for the nominal distortional strength, β nd, is: for λ d for λ d where 0.673c β nd = βy (4) > c 0.5b 0.5b β β β a crd crd nd = β (5) β β y y y γ / π 2γ / π 2γ / π, and 2 a = ( 1.136) b = (1.2) c = (0.834) λ d = βy / β (6) crd β crd = Critical elastic distortional buckling P-M resultant γ = Angular direction (in radians) in the P-M space measured from the positive x- axis for the first quadrant and from the negative x-axis for the second quadrant. The selected SSMA sections are examined using the preliminary DSM beam-column formulations of equations (1-6). Local domination in the P-M space is observed for section 600S (Figure 2) and distortion dominates for section 800S (Figure 3). Applications of the initial DSM formulations are given in Appendix for the selected SSMA sections. Overall, the DSM formulations reflect the elastic critical buckling and yield surface behaviors well.

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8 Figure 2 Preliminary DSM formulation for section 600S162-33

9 Figure 3 Preliminary DSM formulation for section 800S200-68

10 50 45 Pnl,Pnd,Pne (L) 800S Pnl Pnd Pne Pnl(L),Pnd(L),Pne(L) L/12 (ft) Figure 4 DSM strength as a function of specimen length for section 800S Conclusion In order to facilitate selection of sections for beam-column testing, SSMA sections are examined for limit states and efficiency in beam-column applications using current DSM equations for pure compression and pure bending. Moreover, initial DSM formulations for beam-columns are applied to examine strength in the P-M space under combined loading. These examinations indicate that SSMA sections of the 600S162 and 800S200 series provide sufficient diversity in limit state behavior for undertaking the first phase testing of beam-columns for local and distortional buckling under combined actions. In addition, the applications of these sections in currently ongoing CFS-NEES project, and the availability of bending test data for separate local and distortional buckling undertaken at JHU s Thin-walled structures lab further complements the selection of these sections for local and distortional tests under combined actions. References

11 Yu, C. (2003). Local buckling tests on cold- formed steel beams. Journal of structural engineering, 129(12), Yu, C. (2006). Distortional buckling tests on cold- formed steel beams. Journal of structural engineering, 132(4),

12 Appendix 600S162-33

13 600S162-43

14 600S162-54

15 800S200-33

16 800S200-43

17 800S200-54

18 800S200-68