Steel Buildings in Europe

Part 4: Detailed Design of Portal Frames 4 - 28 6.4 Stable lengths adjacent to plastic hinges 6.4.1 Introduction EN 1993-1-1 introduces four types of stable length, L stable , L m , L k and L s . Each is discussed below. L k and L s are used to verify member stability between torsional restraints and recognise the stabilising effects of intermediate restraints to the tension flange. L stable (Clause 6.3.5.3(1)B) L stable is the basic stable length for a uniform beam segment under linear moment and without ‘significant’ axial compression. This simple base case is of limited use in the verification of practical portal frames. In this context, ‘significant’ may be related to the determination of α cr in EN 1993-1-1 § 5.2.1 4(B) Note 2B. The axial compression is not significant if cr Ed 0,09 N N  , as explained in Section 3.3.1 L m (Appendix BB.3.1.1) L m is the stable length between the torsional restraint at the plastic hinge and the adjacent lateral restraint. It takes account of both member compression and the distribution of moments along the member. Different expressions are available for:  Uniform members (Expression BB.5)  Three flange haunches (Expression BB.9)  Two flange haunches (Expression BB.10). L k (Appendix BB.3.1.2 (1)B) L k is the stable length between a plastic hinge location and the adjacent torsional restraint in the situation where a uniform member is subject to a constant moment, providing the spacing of the restraints to either the tension or compression flange is not greater than L m . Conservatively, this limit may also be applied to a non-uniform moment. L s (Appendix BB.3.1.2 (2)B) and (3)B L s is the stable length between a plastic hinge location and the adjacent torsional restraint, where a uniform member is subject to axial compression and linear moment gradient, providing the spacing of the restraints to either the tension or compression flange is not greater than L m . Different C factors and different expressions are used for linear moment gradients (Expression BB.7) and non-linear moment gradients (Expression BB.8). Where the segment varies in cross-section along its length, i.e. in a haunch, two different approaches are adopted:  For both linear and non-linear moments on three flange haunches – BB.11  For both linear and non-linear moments on two flange haunches – BB.12.