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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 2nd 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 2nd 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 2nd 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 2nd 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 e0,d/L = 1/150.

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

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Figure 9 Embedded 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.

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Figure 10 Pile with a displacement boundary condition (wx = 0)

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

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Figure 11 Pile with two displacement boundary conditions

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 2nd order theory the necessary iteration process in terms of displacement is carried out using the design normal force Nd.

Subsequent design is based on a comparison of stresses

σd ≤ fy,k / γM = fy,k / 1,1 = fy,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.

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