This mode enables to solve the problem of determination of an elastic critical bending moment for a flexural member which is further used in the check of the stability of in-plane bending.
The calculation of the critical moment is performed using the analytical solution given in ENV 1993-1-1, depending on the character of the bending moment diagram, different boundary conditions of the bar element, restraints against warping, load application with respect to the shear center of the section, and also depending on the asymmetry of the section with respect to the axis of greater stiffness. Moreover, the calculation of the critical moment takes into account the pre-buckling curvature in accordance with the book L.Gardner, D.Nethercot, Designers Guide to Eurocode 3: Design of Steel Buildings, EN 1993-1-1, EN 1993-1-3, EN 1993-1-8. The calculations are performed only for the cross-sections symmetric with respect to the axis of the lower stiffness at their bending with respect to the axis of the greater stiffness. Moreover, the codes limit the use of this check method for the sections which are characterized by a significant rotation of the principal axes of inertia of the “effective” section with respect to the principal axes of inertia of the gross cross-section.
The calculations are performed only for the cross-sections symmetric with respect to the axis of the lower stiffness at their bending with respect to the axis of the greater stiffness.
The dialog box contains two tabs: Properties and Critical Moment.
The Properties tab is used to specify the cross-section of the member and its span length. The cross-section can be selected from the standard rolled profile database or from the custom welded profile database.
The Critical Moment tab is used to specify the type of the bending moment diagram by selecting it from six options given in the Annex of the French NAD of EN 1993-1-1. For the linear diagram, the ratio of end moments, ψ, has to be specified. Since the type of the moment diagram is specified, the restraints of the member in the bending plane are defined as well. Out-of-plane restraints are defined by the ratio of the effective length, l, to the length of the span, L, specified for the compressed chord.
In addition, to calculate the critical moment, two effective length factors should be specified. The factor k refers to end rotation on plan and the factor kw refers to end warping. Recommendations for assigning the coefficients k, kw for some special cases can be found in the books
Moreover, the distance from the load application point to the top chord level, za, should be specified. The sign of za is assigned according to a schematic given in this tab.
Clicking the Calculate button will display the value of the critical moment, which is the result of the analysis in this mode.
It should be noted that EN 1993-1-1 limits the use of this check method for the sections which are characterized by a significant rotation of the principal axes of inertia of the “effective” section with respect to the principal axes of inertia of the gross cross-section. The respective limitations are introduced in this mode as well.