Steel Construction

The steel checks according to EN 1993-1-1 can be used for polygonal beam sections made of construction steel S235 - S450 as per EN 1993-1-1, Table 3.1. For this purpose the calculated load cases are assigned to the actions in accordance with EN 1991, Part 1. Taking into account the preset safety factors and combination coefficients, defined in EN 1990, the program automatically calculates the internal forces for the desired design situations.

See also: buckling eigenmodes, cable, cable meshes, EN 1993-1-1, lateral torsional buckling check, shear stresses, snap through problem

Classification

For every set of internal forces the cross-section class according to EN 1993-1-1, Chapter 5.5, is automatically determined. To this end, the stress distribution for simultaneous stress from biaxial bending and normal force in the center line of the section parts is used. A cross-section is generally classified by the most unfavorable class of its pressure-loaded section parts.

Cross-Section Resistance

The elastic cross-section resistance is verified for all cross-sections of the classes 1 to 4. Cross-sections of class 4 are treated like class 3 if the c/t ratio does not exceed the limits of class 3 increased by a factor according to Chapter 5.5.2(9). Otherwise the check is carried out with effective cross-section properties as per EN 1993-1-5, clause 4.3. The plastic cross-section resistance will be verified for all cross-sections of the classes 1 and 2 if the elastic cross-section resistance of the contemplated set of internal forces is exceeded.

Section Analysis

Within the scope of system checks, the following key values are determined for all used sections and then made available for use:

• centroid coordinates
• area of the section
• moments of inertia in relation to the coordinate axes
• deviation moment
• moments of inertia in relation to the main axes
• twisting angle of the main axes
• W_y and W_z moments of resistance
• torsion moment of inertia
• τ shear values for Q_y, Q_z and M_x and the W_t, W_qy and W_qz moments of resistance

To determine the stressing as a result of St. Venant torsion, the differential equation of the warping function is solved, and to establish the stressing as a result of lateral force, the differential equation of the shear warping is solved. The analysis is carried out for any thick or thin-walled polygon section and all library sections.

Stability Analyses

Two basic methods are available for analyzing stability problems:

• Calculating structures based on the second-order theory.
• Determining buckling eigenmodes with the relevant branching load factors.

For system calculation based on the second-order theory (equilibrium on the deformed system), a check is performed for beam buckling and toppling as well as for area element buckling. The calculation can take into account additional nonlinear effects such as the exclusion of tensile stresses for bedding and support, the failure of tensile or compression beams and nonlinear material behavior. The iteration method normally converges after a few steps. Stability failures are displayed by the singularity of the entire rigidity matrix. Determining the buckling eigenmodes allows you to define the branching load factors directly. The construction can then easily be evaluated using the associated failure figure.

Lateral Torsional Buckling

The lateral torsional buckling problem is solved for single- and double-symmetric I and U profiles. To create the required strain, specify the internal forces of the beam ends and a point load or uniformly distributed load in both principal directions. The ideal lateral torsional buckling moment M_Ki,y is calculated by varying the elastic potential. The resulting eigenvalue problem provides the smallest positive load factor and thus the sought-after lateral torsional buckling moment. This has the advantage that the user does not need to specify the moment coefficient ζ. Load eccentricity and elastic rotational bedding can be defined by the user. The calculation yields a detailed log of the results with system diagrams.