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  • Answer

    The critical load factor specifies the factor by which you can increase a load until the system fails. If it is smaller than one, a calculation according to the second-order analysis is usually unstable because the system is already stressed by the critical load. This factor is also taken into account in standardization. For example, Eurocode 3 specifies that a calculation according to the second-order analysis is no longer necessary from a critical load factor of 10.
    The critical load factor can be determined by the RSBUCK module or RF-STABILITY.
  • Answer

    The easiest way to do this is to use the add-on modules RSBUCK (RSTAB) or RF-STABILITY (RFEM).

    RSBUCK and RF-STABILITY perform an eigenvalue analysis for the entire model with a certain state of normal force. The axial forces are increased iteratively until the critical load case is reached. This stability load is characterized in the numerical calculation by the determinant of the stiffness matrix becoming zero.

    If the critical load factor is known, the buckling load and the buckling curve are determined from this. The effective lengths and effective length factors are then determined for this lowest buckling load.

    The result shows, depending on the required number of eigenvalues, the critical load factors with the corresponding buckling curves and for each member - according to its mode shape - effective length about the strong and the minor axis.

    Since usually, every load case has a different normal force state in the elements, a separate corresponding effective length result for the frame column arise for each load situation. The effective length whose buckling mode causes the column to buckle in the corresponding plane is the correct length for designing the respective load situation.

    Since this result may be different for each analysis due to the different load situations, the longest effective length of all calculated analyzes - equal for all load situations - is assumed for designing on the safe side.

    Example for manual calculation and RSBUCK/RF-STABILITY
    There is a 2D frame with a width of 12 m, a height of 7.5 m and pinned supports. The column cross-sections correspond to I240 and the frame beam to IPE 270. The columns are loaded with two different concentrated loads.

    l = 12 m
    h = 7.5 m
    E = 21000 kN/cm²
    Iy,R = 5790 cm4
    Iy,S = 4250 cm4

    NL = 75 kN
    NR = 50 kN

    $EI_R=E\ast Iy_R=12159\;kNm^2$
    $EI_S=E\ast Iy_S=8925\;kNm^2$

    $\nu=\frac2{{\displaystyle\frac{l\ast EI_S}{h\ast EI_R}}+2}=0.63$

    This results in the following critical load factor:

    $\eta_{Ki}=\frac{6\ast\nu}{(0.216\ast\nu^2+1)\ast(N_L+N_R)}\ast\frac{EI_S}{h^2}=4.4194$

    The effective lengths of the frame columns can be determined as follows:

    $sk_L=\pi\ast\sqrt{\frac{EI_S}{\eta_{Ki}\ast N_L}}=16.302\;m$

    $sk_R=\pi\ast\sqrt{\frac{EI_S}{\eta_{Ki}\ast N_R}}=19.966\;m$

    The results from the manual calculation correspond very well with those from RSBUCK or RF-STABILITY.

    RSBUCK
    $\eta_{Ki}=4.408$
    $sk_L=16.322\;m$
    $sk_R=19.991\;m$

    RF-STABILITY
    $\eta_{Ki}=4.408$
    $sk_L=16.324\;m$
    $sk_R=19.993\;m$
  • Answer

    The message means that your system is numerically unstable. Such instability is often due to incorrect support conditions or hinge definitions in RF-/FE-LTB. Therefore, check the degrees of freedom of the continuous member in windows 1.4 Nodal Supports and 1.7 Member Hinges.

    The reason: When selecting imperfections and also in the calculation, the critical load factor will be specified. Based on this, the critical load factor of the system is determined. This is characterized by the fact that either the determinant of the stiffness matrix becomes zero, or that very high deformations occur for very small load increases in the calculation.

  • Answer

    Check if the settings for considering the favorable effect by tension forces are the same in RSTAB and RSBUCK.

    RSTAB determines the critical load factor according to the nonlinear calculation method: The loading is increased gradually by the value of the load factor increment Δk until the system becomes unstable. On the other hand, RSBUCK performs a linear eigenvalue analysis. Therefore, the elements acting nonlinearly, such as failing members or supports, may have different effects in RSTAB and RSBUCK.

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Wind Simulation & Wind Load Generation

With the stand-alone program RWIND Simulation, wind flows around simple or complex structures can be simulated by means of a digital wind tunnel.

The generated wind loads acting on these objects can be imported to RFEM or RSTAB.

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