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h1. Overview

When [line spring|kb:line spring] or [area springs|kb:area spring] are assigned to an object, SAP2000 automatically generates equivalent joint springs at each joint created by [automeshing|kb:automeshing] of such object. Stiffness of these joint springs is determined from the stiffness of the line or area spring assigned to the object and the tributary area for each joint spring (joint springs supporting interior joints are stiffer than the joint springs supporting corner joints). Since the contact pressure would be proportional to the deformation of these joint springs or to the displacement of joints to which these joint springs are attached, you can obtain the contact pressure by multiplying the displacements (that can be readily output both graphically and in a tabular format) by a constant related to the spring stiffness.

I have attached a simpleh1. Example model

An example model that illustrates the above has been attached to this page.

The example model contains 2 area objects (2m by 2m and 1m by 1m, each auto meshed into 4 area objects), 2 frame objects (2m long and 1m long, each auto meshed into 2 frame objects), and 1 point object. Link with property LIN1 is assigned as area spring to the area objects, as line spring to the frame objects and also to the point object. Below are few more comments and screenshots from the attached model that you may find useful.

In the attached model, I would recommend you to review The stiffness of the LIN1 was defined as follows:

* 1kN/m when used as joint link
* 1kN/m/m when used as line spring
* 1kN/m/m^2 when used as area spring

The "Factors For Line, Area and Solid Springs" on the "Link/Support Property Data" form are explained in the figure below:

!Link_and_support_property_data.png!

A unit load (1kN/m^2 for the area objects, 1kN/m for the frame objects and 1kN for the point object) was applied to the objects in the SPRING-LOAD load case. Reviewing the UZ displacements for the "SPRING-LOAD" load case. You will find that indicates that the displacements of 1m at all the displacementsjoints are consistent with the applied loads and stiffness assigned to the area and line springs.

Stiffness of the internal springs created by the program could be indirectly determined by dividing a reaction for a particular joint by h1. Screenshots

h2. Link/Support Property Data - Explanation of "Factors For Line, Area and Solid Springs"

!Link_and_support_property_data.png!


h2its displacement. The joint reactions and displacements are available in the output tables. The internally created joints are preceded by a "~" (tilda) symbol.

h2. Screenshots of the model and results

h3. Area spring and automeshauto mesh assignment to an area object

!Area_spring_and_automesh_assignement.png!


h2h3. Display of equivalent joint springs created by the program to represent line and area springs assigned to an object

Using "View > Set Display Options > Show Analysis Model" menu command, you can display the equivalent joint springs created by the program for an area spring → !Show_Analysis_Model_Form.png!

!Equivalent_joint_springs_generated_for_area_spring.png!

h1. Attachments

* [SAP2000 V12.0.0 model file|^springs line and area V12.0.0.zip] (Zipped SDB file)