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h1. Overview

When line or area springs are assigned to an object, [SAP2000|sap2000:home] generates equivalent [joint|kb:Joint] springs at each node created during [auto-meshing|kb:Discretization]. Joint-spring stiffness is determined from tributary area and the line\- or area-spring stiffness which is assigned to the object. As a result, joint springs which support interior joints are stiffer than those at corner joints. Since contact pressure is proportional to joint-spring deformation and the displacement of those joints to which springs are attached, users may obtain contact pressure through the product of spring-stiffness constant and displacement, available for output in both graphic and tabular format.

h1. Example model

The example model, attached for reference, contains two [area|kb:Shell] objects (2m x 2m and 1m x 1m), each auto-meshed into four area objects, two [frame|kb:Frame] objects (2m and 1m), each auto-meshed into two frame objects, and one [point|kb:Joint] object. A link (LIN1) is assigned to the area objects as an area spring, to the frame objects as a line spring, and to the point object as a joint link.

[Link|kb:Link] stiffness is defined as follows:

* 1kN/m when used as a joint link

* 1kN/m/m when used as a line spring

* 1kN/m/m ^2^ when used as an area spring

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The Factors For Line, Area, and Solid Springs, available on the Link/Support Property Data menu, are explained in Figure 1:

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!Link_and_support_property_data.png|align=center,border=0!

{center-text}Figure 1 - Link and support property data{center-text}

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The SPRING-LOAD [load case|kb:Load case] applies a unit load to objects, including 1kN/m ^2^ for the area objects, 1kN/m for the frame objects, and 1kN for the point object. UZ displacement of 1m at all joints indicates consistency between applied loading and assigned stiffness.

The stiffness of automatically-created internal springs could be indirectly determined by dividing joint reaction by its displacement. These values are available in the output tables, where internally created joints are preceded by a tilda symbol (~).


h1. Model screenshots and results

h2. Area-spring and auto-mesh assignment

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!Area_spring_and_automesh_assignement.png|align=center,border=0!

{center-text}Figure 2 - Area-spring and auto-mesh assignment{center-text}


h2. Equivalent joint springs

The software automatically creates equivalent joint springs which represent those line and area springs which are assigned to an object. These joint springs are displayed through View > Set Display Options > Show Analysis Model, as shown in Figures 3 and 4:

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!Show_Analysis_Model_Form.png|align=center,border=0!

{center-text}Figure 3 - Show analysis model{center-text}

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!Equivalent_joint_springs_generated_for_area_spring.png|align=center,border=0!

{center-text}Figure 4 - Equivalent joint springs{center-text}


h1. Attachments

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