# Multi-linear elastic link in construction staging analysis

**Question:**

In the file attached I am experimenting with the multi-linear elastic link in a construction staging analysis. Please verify results - unloading gives grossly incorrect results. For example, in Stage H2 the theoretical displacement of the system on the left side is 0.52", the MIDAS calculated displacement is 10.51". Also, MIDAS shows that the system on the right side experiences displacements in Stages H2 and H3, even though no loads are applied on that system during these stages.

Is the multi-linear spring supposed to work with construction staging analysis? If so, should the setting be linear or non-linear analysis?

**Answer:**

Hi,

Multi-linear elastic links for the rail-structure interaction has been implemented with the following assumptions:

- The multi-linear elastic links should be generated by the 'Rail Track Analysis' wizard.

- Thus, the model should have two stages only, i.e. unloaded stage (temperature loads), loaded stage (train loads).

- The multi-linear elastic links representing ballast should have the elasto-perfectly plastic relationship between force and displacement relationship.

Otherwise, the multi-linear elastic link will not work.

For your information, I have created a model with the 'Rail Track Analysis' wizard and modified it to a simple model to verify the behavior of the multi-linear elastic link as shown below. The link is elasto-perfectly plastic and thus, comp.-only elements with gap=0.02 in. are attached to at the top of the link.

The property of the link is as shown below.

Comp.-only element: E = 10 kips/in2, A = 1 in2, L = 4 in. Thus, the axial stiffness is EA/L = 2.5 kips/in.

At the first stage, -11 kips is applied at the top of the link.

- Elastic displacement = -0.02 in., plastic displacement = -1/2.5 = -0.4 in. Sum = -0.42 in.

At the second stage, +21 kips is applied at the top of the link.

- Elastic displacement = +0.04 in., plastic displacement = +1/2.5 = +0.4 in. Sum (incremental) = +0.44 in., Sum (accumulate) = -0.42 in. + 0.44 in. = +0.02 in.

The program results match the manual calculation.

Please refer to the attached file. Complete.mcb

Regards,

DK

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