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{{Test Problem
name = Line and area springs |
description = Demonstration of line and area springs. |
keyword = spring; line spring; area spring |
program = SAP2000 |
version = na |
status = done |
id = ok/springs - line and area}} |
Overview
When line spring On this page:
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Overview
When line or area springs are assigned to an object, SAP2000 automatically generates equivalent joint springs at each joint created by 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 node created during auto-meshing. 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 the joint springs supporting those at corner joints). Since the contact pressure would be is proportional to the deformation of these joint springs or to joint-spring deformation and the displacement of those joints to which these joint springs are attached, you can users may 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 simple model that illustrates this. 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 UZ displacements for "SPRING-LOAD" load case. You will find that the displacements are consistent with the applied loads and stiffness assigned to the area and line springs.
Screenshots
Link/Support Property Data - Explanation of "Factors For Line, Area and Solid Springs"
Area spring and automesh assignment to an area object
Display of equivalent joint springs created by the program to represent line and area springs assigned to an object
Using "through the product of spring-stiffness constant and displacement, available for output in both graphic and tabular format.
Example model
The example model, attached for reference, contains two area objects (2m x 2m and 1m x 1m), each auto-meshed into four area objects, two frame objects (2m and 1m), each auto-meshed into two frame objects, and one point 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 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
The values specified for Factors For Line, Area, and Solid Springs, available on the Link/Support Property Data menu, are explained in Figure 1:
Figure 1 - Link and support property data
The SPRING-LOAD 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. Here, internally created joints are preceded with a tilda (~).
Model screenshots and results
Area-spring and auto-mesh assignment
Figure 2 - Area-spring and auto-mesh assignment
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" menu command, you can display the equivalent joint springs created by the program for an area spring → 
Attachments
...
, as shown in Figures 3 and 4:
Figure 3 - Show analysis model
Figure 4 - Equivalent joint springs
Attachments
- .zip | title = Springs line and area V12.0.0.zip (Zipped SDB file, 12 kB)
...
model (zipped .SDB file)
Metadata
Name: Line and area springs
Description: This test problem demonstrates and validates the application of line and area springs.
Program: SAP2000
Program Version: 12.0.0
Model ID: na