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TR.27.4 Multilinear Spring Support Specification

When soil is modeled as spring supports, the varying resistance it offers to external loads can be modeled using this facility, such as when its behavior in tension differs from its behavior in compression.

General Format

joint-list SPRINGS d1 s1 d2 s2 … dn sn


  • di si pairs represent displacement and spring constant pairs (si is zero or positive), starting from the maximum negative displacement to the maximum positive displacement.

The first pair defines the spring constant from negative infinity displacement up to the displacement defined in the second pair. The second pair define the spring constant when the support displaces in the range from the displacement defined in the second pair, up to the displacement defined in the third pair. This continues for each displacement and spring constant pair until the last pair which defines the spring constant for displacements greater than the displacement in the last pair to positive infinity.

Each load case in a multilinear analysis must be separated by a CHANGE command and have its own PERFORM ANALYSIS command. There may not be any PDELTA, NONLIN, dynamics, CABLE, or TENSION/COMPRESSION analysis included. The multilinear spring command will initiate an iterative analysis and convergence check cycle. The cycles will continue until the root mean square (RMS) of the effective spring rates used remain virtually the same for two consecutive cycles.


2 4 SPRINGS -1 40.0 -0.50 50.0 0.5 65.0

Load-Displacement characteristics of soil can be represented by a multilinear curve. Amplitude of this curve will represent the spring characteristic of the soil at different displacement values. A typical spring characteristic of soil may be represented as the step curve as shown in the figure below. In the above example, the multilinear spring command specifies soil spring at joints 2 and 4. (Note that the amplitude of the step curve does not change after the first point.)


  1. SUPPORT springs must have previously been entered for each spring entered here. For the first cycle, the spring value used will be the support spring value (not the zero displacement value here). Use a realistic and stable value.
  2. All directions that have been defined with an initial spring stiffness in the SUPPORT command will become multilinear with this one curve.
  3. This command can be continued to up to 11 lines by ending all but last with a hyphen. The semi-colons and the XRANGE, YRANGE, ZRANGE list items may not be used.
  4. This command needs a minimum of two displacement and spring constant pairs.

    Spring constant is always positive or zero. F = Force Units, L = Length Units

  5. Multilinear springs should not be used in the following conditions:
    • Modal dynamics
    • Buckling analysis
    • Imperfection analysis
    • PDELTA analysis
    • NONLINEAR analysis
    • Advanced cable analysis
    • Direct analysis
    • Models with tension/compression members and/or supports
    • Models with inclined supports