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Why is 5% plastic strain limit used in material diagram for AISC?

Steel

AISC (USA)

Connection

Stress/strain

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Is it okay to consider 5% plastic strain as a limit value for the steel connection's check? Why is the yield strength not considered? Is this approach code (in this case, AISC) compliant? If you've ever asked any of these questions, read the following article, and find the answers.

Common methods

Every structural engineer is used to using the yield strength as the limit value of the check, as basically every standard and design code is based on this approach.

Nevertheless, this applies to the pure elastic behaviour of the material. This can lead to conservative design and sometimes unnecessary overdesigning of the structure, resulting in more material being consumed.

However, the real behaviour of steel is different, and it is okay to assume the plastic behaviour of the material after the yield strength has been exceeded.

IDEA StatiCa and the CBFEM method

Component Based Finite Element Method (CBFEM) is a synergy of the Component Method and Finite Element analysis.

The check of a joint in a standard component based method and in the CBFEM used in IDEA StatiCa Connection is based on the check of all parts of the joint – the components. Components can be bolts, anchors, welds, plates, and concrete at the footing.

CBFEM splits the whole joint into above mentioned separated components. Then the analysis model is created automatically by the software from each component.

All steel plates, like flanges or webs of cross-sections, stiffeners, ribs, haunches, etc., are modeled by finite elements. FEM is widely accepted in structural engineering and brings very good and trusted results.

The material behavior is based on the von Mises yield criterion. It is assumed to be elastic before reaching the design yield strength fyd.

The ultimate limit state criterion for regions not susceptible to buckling is reaching the limiting value of the principal membrane strain. A value of 5% is recommended (e.g. EN 1993-1-5, App. C, Par. C.8, Note 1).

ANSI/AISC 360-16 uses a different approach. In Chapter B – Design requirements, there is an article: “Connection Strength. The strength of a connection is the maximum moment that it is capable of carrying, Mn, as shown in Figure C-B3.2. The strength of a connection can be determined on the basis of an ultimate limit-state model of the connection, or from physical tests. If the moment-rotation response does not exhibit a peak load then the strength can be taken as the moment at a rotation of 0.02 rad (Hsieh and Deierlein, 1991; Leon et al., 1996).”

Figures are taken from ANSI/AISC 360-16, Comm. B3, p. 332, 333.

An example of a welded connection in IDEA StatiCa is presented:

The design bending resistance of this connection, according to this article in AISC 360, is determined as the bending moment at the rotation of 20 mrad (MRd = 408.5 kip-in). This resistance nearly equals to the bending resistance determined by limiting plastic strain to 5 % as suggested by EN 1993-1-5 (MRd = 402.5 kip-in).

Another example of a bolted connection shows similar results:

Again, the resistance determined by rotation 20 mrad (MRd = 372 kip-in) closely coincides with the resistance determined by limiting plastic strain to 5 % (MRd = 374.7 kip-in).

Conclusion

ANSI/AISC 360 leaves finite element modeling (see Appendix 1 – Design by advanced analysis and Chapter B – Design requirements – 4. Design of connections and supports – Structural analysis) to engineering judgment. The use of bilinear elastic-plastic material diagram for steel plates and the limitation of the plastic strain is a simple and reasonable approach allowing to solve all types of generally loaded connections. The results closely coincide with the approach suggested specifically by ANSI/AISC 360.

The limit of plastic strain can be edited in Code setup, although verification studies have been performed with a recommended value of 5 %. The value has generally low effect on the resistance of the connection. The difference in bending moment resistance between 2% limit strain and 10% limit strain is only 7 % in the second example of bolted connection.

References

ANSI/AISC 360-16 (2016), An American National Standard – Specification for Structural Steel Buildings, AISC, Chicago, 676 p.

EN1993-1-5 (2006), Eurocode 3: Design of steel structures - Part 1-5: General rules - Plated structural elements, CEN, Brussels, 53 p.

Hsieh, S.H. and Deierlein, G.G. (1991), “Nonlinear Analysis of Three-Dimensional Steel Frames with Semi-Rigid Connections,” Computers and Structures, Elsevier, Vol. 41, No. 5, pp. 995–1,009.

Leon, R.T. (1994), “Composite Semi-Rigid Construction,” Engineering Journal, AISC, Vol. 31. No. 2, pp. 57–67.