GGU-LATPILE: 2nd order theory

The differential equation for a normal flexural member is:

The normal force N is taken into consideration for a buckling member:

For the sake of completeness, the differential equation for an additionally bedded system is shown here since the program also allows parallel processing of systems with 2^nd order theory and elastic bedding. The equation is:

Analysis is performed on the deformed system. In

• DIN EN 1993-5
  Design of Steel Structures,
  Part 5: Piling

analysis using 2^nd order theory is recommended for analysis of piles under buckling loads and

• DIN EN 1993-1-1
  Design of Steel Structures,
  Part 1-1: General Rules and Rules for Buildings

referred to. Analysis using 2^nd order theory produces more accurate results than the usual and simplified equivalent member method. Analysis of piles under buckling loads is performed in GGU-LATPILE compliant with DIN EN 1993-1-1.

Analysis using 2^nd order theory requires a predeformation or pre-curvature of the underlying system. Pre-curvature values are given in Table 5.1 of DIN EN 1993-1-1.

Pre-curvatures are given as a function of the buckling line. In simplification, piles can be analysed with a pre-curvature of e_0,d/L = 1/150.

Using embedded piles without additional displacement boundary conditions the deformed system is defined by an inclination of the pile.

Using embedded piles with a horizontal displacement boundary condition (wx = 0), the deformed system is defined by a linear pre-curvature from the support point to the top of the pile and a parabolic pre-curvature between the support points and the foot of the pile.

The length L is given per field. The procedure for piles with two displacement boundary conditions is shown in Figure 11.

The settings are defined in GGU-LATPILE in the analysis menu under "System/Analyse".

The size and direction of the pre-curvature can be specified. Whether a pre-curvature towards the passive side or the active side provides the more unfavourable design values is system-dependent: the following message will therefore be displayed once analysis begins:

You must therefore deactivate the "Pre-curvature to passive side" check box following successful analysis and check, in a new analysis, whether pre-curvature to the active side delivers less favourable values.

In an analysis using 2^nd order theory the necessary iteration process in terms of displacement is carried out using the design normal force N_d.

Subsequent design is based on a comparison of stresses

σ_d ≤ f_y,k / γ_M = f_y,k / 1,1 = f_y,d

The "Example" folder contains 4 GGU-LATPILE files, which deal with the classical Euler cases 1 to 4. If the vertical load V at the pile head is increased slightly using the "Editor 1/System input" menu item and the system analysed, the following error message appears:

The normal force given in the data files thus corresponds to the buckling force determined after Euler.