<?xml version="1.0" encoding="UTF-8" ?>
<?xml-stylesheet type="text/xsl" href="https://communities.bentley.com/cfs-file/__key/system/syndication/rss.xsl" media="screen"?><rss version="2.0" xmlns:dc="http://purl.org/dc/elements/1.1/"><channel><title>RM Bridge: Stay Cable Vibration</title><link>https://communities.bentley.com/products/bridge_design___engineering/w/bridge_design_and_engineering__wiki/51625/rm-bridge-stay-cable-vibration</link><description /><dc:language>en-US</dc:language><generator>Telligent Community 12</generator><item><title>RM Bridge: Stay Cable Vibration</title><link>https://communities.bentley.com/products/bridge_design___engineering/w/bridge_design_and_engineering__wiki/51625/rm-bridge-stay-cable-vibration</link><pubDate>Mon, 29 May 2023 17:26:42 GMT</pubDate><guid isPermaLink="false">6dad98f5-dbc9-4c4d-a9ba-e9da8dc6aa8e:4d2b1fa2-ed16-4598-9ed7-3695af080102</guid><dc:creator>Ana Carla Peres</dc:creator><comments>https://communities.bentley.com/products/bridge_design___engineering/w/bridge_design_and_engineering__wiki/51625/rm-bridge-stay-cable-vibration#comments</comments><description>Current Revision posted to LARS | LEAP | OpenBridge | OpenTunnel | RM Wiki by Ana Carla Peres on 5/29/2023 5:26:42 PM&lt;br /&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&amp;nbsp;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:150%;"&gt;Objective&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;To perform and obtain the dynamic behavior of a stay cable and compare &lt;strong&gt;RM Bridge&lt;/strong&gt; results with the formulation presented in &lt;strong&gt;SETRA&lt;/strong&gt; &amp;ndash; Recommendations of French inter-ministerial commission on Prestressing.&lt;/p&gt;
&lt;p&gt;&lt;span style="font-family:inherit;font-size:75%;"&gt;&lt;span style="font-size:200%;"&gt;Structural Model&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;A stay cable fixed at two anchorages with a horizontal distance of 200 m and a vertical distance of 100 m apart was considered.&lt;/p&gt;
&lt;p&gt;A parallel-strand cable stay with a resisting section S consists of 15 mm strands of &lt;em&gt;f&lt;sub&gt;class&lt;/sub&gt;&lt;/em&gt; = 1770 MPa.&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " height="196" src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image003.png" width="440" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:150%;"&gt;Formulation&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;By &lt;strong&gt;SETRA&lt;/strong&gt; &amp;ndash; Recommendations of French inter-ministerial commission on Prestressing, in chapter 8 the following formulation was verified.&lt;/p&gt;
&lt;p&gt;A cable-stay can be considered to be a straight element tensioned to a tension &lt;em&gt;F&lt;/em&gt;, with a lineic mass &lt;em&gt;m&lt;/em&gt; and with negligible stiffness.&lt;/p&gt;
&lt;p&gt;Transverse vibration of cable stays is studied here with co-ordinate system (Axy). Where x is the direction of chord [AB] and y is a lateral direction.&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " height="132" src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image008.png" width="449" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;It is assumed that vibrations are of low amplitude and that tension &lt;em&gt;F&lt;/em&gt; is constant. If the cable-stay damping is overlooked, lateral displacement y(x,t) is given by the fundamental equation of dynamics applied to an infinitesimal element &lt;em&gt;dx&lt;/em&gt;:&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image009.png" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:inherit;"&gt;or,&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:inherit;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image011.png" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;defining c, the celerity of transverse waves as:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image013.png" /&gt;&lt;/p&gt;
&lt;p&gt;The equation is solved by obtaining y(x,t) in the form e(x) modal deformation and f(t), which makes it possible to separate variables x and t:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image015.png" /&gt;&lt;/p&gt;
&lt;p&gt;, where &lt;em&gt;w&lt;sup&gt;2&lt;/sup&gt;&lt;/em&gt; is an integration constant.&lt;/p&gt;
&lt;p&gt;Assuming&amp;nbsp;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image017.png" /&gt;&amp;nbsp; , the spatial equation can be written:&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image019.png" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;Boundary conditions y(0) = y(l) = 0 are used to deduce the form of the n&lt;sup&gt;th&lt;/sup&gt; order mode:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image021.png" /&gt;&lt;/p&gt;
&lt;p&gt;and the wave number:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image023.png" /&gt;&lt;/p&gt;
&lt;p&gt;The temporal equation is written&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image025.png" /&gt;&lt;/p&gt;
&lt;p&gt;Its general solution is&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image027.png" /&gt;&lt;/p&gt;
&lt;p&gt;This yields the taut-string formula for eigen period &lt;em&gt;T&lt;sub&gt;n&lt;/sub&gt;&lt;/em&gt; and &lt;em&gt;n&lt;sup&gt;th&lt;/sup&gt;&lt;/em&gt; &amp;ndash; order eigen frequency &lt;em&gt;N&lt;sub&gt;n&lt;/sub&gt;&lt;/em&gt;:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image029.png" /&gt;&lt;/p&gt;
&lt;p&gt;The free vibrations of the cable-stay are finally a superposition of sinusoidal modes of the form:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image031.png" /&gt;&lt;/p&gt;
&lt;p&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:150%;"&gt;Schedule Action&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;Only one schedule action is run to calculate the Cable eigen frequencies and eigenvectors (natural modes). The reference load case containing the definition of effective masses must be specified.&lt;/p&gt;
&lt;p&gt;After the calculation, a number of n load cases is presented and can be accessed from the load case pool, as &amp;lsquo;Outputfilename#n&amp;rsquo;, being n the eigenmode number. The load cases contain normalized eigenvectors as displacements that were used in graphic presentation.&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " height="284" src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image033.png" width="556" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:150%;"&gt;Results&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;In the verification example studied, the Cable model was discretized in 10 (ten) sub-cable elements and in the Recalculate path &amp;ldquo;Non-linear Stay Cables&amp;rdquo; was selected.&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " height="300" src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image035.png" width="541" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;The calculated and obtained results are the ones presented in the following table:&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " height="160" src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image038.png" width="545" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;The correspondent deformations for the first four eigenmodes are presented below:&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image039.jpg" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image041.jpg" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image043.jpg" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image045.jpg" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;a title="Stay Cable Vibration - Video" href="/products/bridge_design___engineering/m/bridge_design_and_engineering_gallery/274612"&gt;Stay Cable Vibration - Video&lt;/a&gt;&lt;/span&gt;&lt;/p&gt;&lt;div style="clear:both;"&gt;&lt;/div&gt;

&lt;div style="font-size: 90%;"&gt;Tags: RM, Cable Vibration, cable, RM Bridge, RM Bridge Enterprise, dynamics&lt;/div&gt;
</description></item><item><title>RM Bridge: Stay Cable Vibration</title><link>https://communities.bentley.com/products/bridge_design___engineering/w/bridge_design_and_engineering__wiki/51625/rm-bridge-stay-cable-vibration/revision/10</link><pubDate>Wed, 01 Jun 2022 15:45:27 GMT</pubDate><guid isPermaLink="false">6dad98f5-dbc9-4c4d-a9ba-e9da8dc6aa8e:4d2b1fa2-ed16-4598-9ed7-3695af080102</guid><dc:creator>MarcosBeier</dc:creator><comments>https://communities.bentley.com/products/bridge_design___engineering/w/bridge_design_and_engineering__wiki/51625/rm-bridge-stay-cable-vibration#comments</comments><description>Revision 10 posted to LARS | LEAP | OpenBridge | OpenTunnel | RM Wiki by MarcosBeier on 6/1/2022 3:45:27 PM&lt;br /&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&amp;nbsp;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:150%;"&gt;Objective&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;To perform and obtain the dynamic behavior of a stay cable and compare &lt;strong&gt;RM Bridge&lt;/strong&gt; results with the formulation presented in &lt;strong&gt;SETRA&lt;/strong&gt; &amp;ndash; Recommendations of French inter-ministerial commission on Prestressing.&lt;/p&gt;
&lt;p&gt;&lt;span style="font-family:inherit;font-size:75%;"&gt;&lt;span style="font-size:200%;"&gt;Structural Model&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;A stay cable fixed at two anchorages with a horizontal distance of 200 m and a vertical distance of 100 m apart was considered.&lt;/p&gt;
&lt;p&gt;A parallel-strand cable stay with a resisting section S consists of 15 mm strands of &lt;em&gt;f&lt;sub&gt;class&lt;/sub&gt;&lt;/em&gt; = 1770 MPa.&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " height="196" src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image003.png" width="440" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:150%;"&gt;Formulation&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;By &lt;strong&gt;SETRA&lt;/strong&gt; &amp;ndash; Recommendations of French inter-ministerial commission on Prestressing, in chapter 8 the following formulation was verified.&lt;/p&gt;
&lt;p&gt;A cable-stay can be considered to be a straight element tensioned to a tension &lt;em&gt;F&lt;/em&gt;, with a lineic mass &lt;em&gt;m&lt;/em&gt; and with negligible stiffness.&lt;/p&gt;
&lt;p&gt;Transverse vibration of cable stays is studied here with co-ordinate system (Axy). Where x is the direction of chord [AB] and y is a lateral direction.&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " height="132" src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image008.png" width="449" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;It is assumed that vibrations are of low amplitude and that tension &lt;em&gt;F&lt;/em&gt; is constant. If the cable-stay damping is overlooked, lateral displacement y(x,t) is given by the fundamental equation of dynamics applied to an infinitesimal element &lt;em&gt;dx&lt;/em&gt;:&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image009.png" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:inherit;"&gt;or,&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:inherit;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image011.png" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;defining c, the celerity of transverse waves as:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image013.png" /&gt;&lt;/p&gt;
&lt;p&gt;The equation is solved by obtaining y(x,t) in the form e(x) modal deformation and f(t), which makes it possible to separate variables x and t:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image015.png" /&gt;&lt;/p&gt;
&lt;p&gt;, where &lt;em&gt;w&lt;sup&gt;2&lt;/sup&gt;&lt;/em&gt; is an integration constant.&lt;/p&gt;
&lt;p&gt;Assuming&amp;nbsp;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image017.png" /&gt;&amp;nbsp; , the spatial equation can be written:&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image019.png" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;Boundary conditions y(0) = y(l) = 0 are used to deduce the form of the n&lt;sup&gt;th&lt;/sup&gt; order mode:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image021.png" /&gt;&lt;/p&gt;
&lt;p&gt;and the wave number:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image023.png" /&gt;&lt;/p&gt;
&lt;p&gt;The temporal equation is written&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image025.png" /&gt;&lt;/p&gt;
&lt;p&gt;Its general solution is&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image027.png" /&gt;&lt;/p&gt;
&lt;p&gt;This yields the taut-string formula for eigen period &lt;em&gt;T&lt;sub&gt;n&lt;/sub&gt;&lt;/em&gt; and &lt;em&gt;n&lt;sup&gt;th&lt;/sup&gt;&lt;/em&gt; &amp;ndash; order eigen frequency &lt;em&gt;N&lt;sub&gt;n&lt;/sub&gt;&lt;/em&gt;:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image029.png" /&gt;&lt;/p&gt;
&lt;p&gt;The free vibrations of the cable-stay are finally a superposition of sinusoidal modes of the form:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image031.png" /&gt;&lt;/p&gt;
&lt;p&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:150%;"&gt;Schedule Action&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;Only one schedule action is run to calculate the Cable eigen frequencies and eigenvectors (natural modes). The reference load case containing the definition of effective masses must be specified.&lt;/p&gt;
&lt;p&gt;After the calculation, a number of n load cases is presented and can be accessed from the load case pool, as &amp;lsquo;Outputfilename#n&amp;rsquo;, being n the eigenmode number. The load cases contain normalized eigenvectors as displacements that were used in graphic presentation.&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " height="284" src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image033.png" width="556" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:150%;"&gt;Results&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;In the verification example studied, the Cable model was discretized in 10 (ten) sub-cable elements and in the Recalculate path &amp;ldquo;Non-linear Stay Cables&amp;rdquo; was selected.&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " height="300" src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image035.png" width="541" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;The calculated and obtained results are the ones presented in the following table:&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " height="160" src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image038.png" width="545" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;The correspondent deformations for the first four eigenmodes are presented below:&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image039.jpg" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image041.jpg" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image043.jpg" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image045.jpg" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;a title="Stay Cable Vibration - Video" href="/products/bridge_design___engineering/m/bridge_design_and_engineering_gallery/274612"&gt;Stay Cable Vibration - Video&lt;/a&gt;&lt;/span&gt;&lt;/p&gt;&lt;div style="clear:both;"&gt;&lt;/div&gt;

&lt;div style="font-size: 90%;"&gt;Tags: RM, Cable Vibration, cable, RM Bridge, RM Bridge Enterprise, dynamics&lt;/div&gt;
</description></item><item><title>RM Bridge: Stay Cable Vibration</title><link>https://communities.bentley.com/products/bridge_design___engineering/w/bridge_design_and_engineering__wiki/51625/rm-bridge-stay-cable-vibration/revision/9</link><pubDate>Mon, 15 Nov 2021 19:29:50 GMT</pubDate><guid isPermaLink="false">6dad98f5-dbc9-4c4d-a9ba-e9da8dc6aa8e:4d2b1fa2-ed16-4598-9ed7-3695af080102</guid><dc:creator>Ana Carla Peres</dc:creator><comments>https://communities.bentley.com/products/bridge_design___engineering/w/bridge_design_and_engineering__wiki/51625/rm-bridge-stay-cable-vibration#comments</comments><description>Revision 9 posted to LARS | LEAP | OpenBridge | OpenTunnel | RM Wiki by Ana Carla Peres on 11/15/2021 7:29:50 PM&lt;br /&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&amp;nbsp;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:150%;"&gt;Objective&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;To perform and obtain the dynamic behavior of a stay cable and compare &lt;strong&gt;RM Bridge&lt;/strong&gt; results with the formulation presented in &lt;strong&gt;SETRA&lt;/strong&gt; &amp;ndash; Recommendations of French inter-ministerial commission on Prestressing.&lt;/p&gt;
&lt;p&gt;&lt;span style="font-family:inherit;font-size:75%;"&gt;&lt;span style="font-size:200%;"&gt;Structural Model&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;A stay cable fixed at two anchorages with a horizontal distance of 200 m and a vertical distance of 100 m apart was considered.&lt;/p&gt;
&lt;p&gt;A parallel-strand cable stay with a resisting section S consists of 15 mm strands of &lt;em&gt;f&lt;sub&gt;class&lt;/sub&gt;&lt;/em&gt; = 1770 MPa.&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " height="196" src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image003.png" width="440" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:150%;"&gt;Formulation&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;By &lt;strong&gt;SETRA&lt;/strong&gt; &amp;ndash; Recommendations of French inter-ministerial commission on Prestressing, in chapter 8 the following formulation was verified.&lt;/p&gt;
&lt;p&gt;A cable-stay can be considered to be a straight element tensioned to a tension &lt;em&gt;F&lt;/em&gt;, with a lineic mass &lt;em&gt;m&lt;/em&gt; and with negligible stiffness.&lt;/p&gt;
&lt;p&gt;Transverse vibration of cable stays is studied here with co-ordinate system (Axy). Where x is the direction of chord [AB] and y is a lateral direction.&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " height="132" src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image008.png" width="449" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;It is assumed that vibrations are of low amplitude and that tension &lt;em&gt;F&lt;/em&gt; is constant. If the cable-stay damping is overlooked, lateral displacement y(x,t) is given by the fundamental equation of dynamics applied to an infinitesimal element &lt;em&gt;dx&lt;/em&gt;:&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image009.png" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:inherit;"&gt;or,&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:inherit;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image011.png" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;defining c, the celerity of transverse waves as:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image013.png" /&gt;&lt;/p&gt;
&lt;p&gt;The equation is solved by obtaining y(x,t) in the form e(x) modal deformation and f(t), which makes it possible to separate variables x and t:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image015.png" /&gt;&lt;/p&gt;
&lt;p&gt;, where &lt;em&gt;w&lt;sup&gt;2&lt;/sup&gt;&lt;/em&gt; is an integration constant.&lt;/p&gt;
&lt;p&gt;Assuming&amp;nbsp;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image017.png" /&gt;&amp;nbsp; , the spatial equation can be written:&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image019.png" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;Boundary conditions y(0) = y(l) = 0 are used to deduce the form of the n&lt;sup&gt;th&lt;/sup&gt; order mode:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image021.png" /&gt;&lt;/p&gt;
&lt;p&gt;and the wave number:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image023.png" /&gt;&lt;/p&gt;
&lt;p&gt;The temporal equation is written&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image025.png" /&gt;&lt;/p&gt;
&lt;p&gt;Its general solution is&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image027.png" /&gt;&lt;/p&gt;
&lt;p&gt;This yields the taut-string formula for eigen period &lt;em&gt;T&lt;sub&gt;n&lt;/sub&gt;&lt;/em&gt; and &lt;em&gt;n&lt;sup&gt;th&lt;/sup&gt;&lt;/em&gt; &amp;ndash; order eigen frequency &lt;em&gt;N&lt;sub&gt;n&lt;/sub&gt;&lt;/em&gt;:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image029.png" /&gt;&lt;/p&gt;
&lt;p&gt;The free vibrations of the cable-stay are finally a superposition of sinusoidal modes of the form:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image031.png" /&gt;&lt;/p&gt;
&lt;p&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:150%;"&gt;Schedule Action&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;Only one schedule action is run to calculate the Cable eigen frequencies and eigenvectors (natural modes). The reference load case containing the definition of effective masses must be specified.&lt;/p&gt;
&lt;p&gt;After the calculation, a number of n load cases is presented and can be accessed from the load case pool, as &amp;lsquo;Outputfilename#n&amp;rsquo;, being n the eigenmode number. The load cases contain normalized eigenvectors as displacements that were used in graphic presentation.&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " height="284" src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image033.png" width="556" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:150%;"&gt;Results&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;In the verification example studied, the Cable model was discretized in 10 (ten) sub-cable elements and in the Recalculate path &amp;ldquo;Non-linear Stay Cables&amp;rdquo; was selected.&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " height="300" src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image035.png" width="541" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;The calculated and obtained results are the ones presented in the following table:&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " height="160" src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image038.png" width="545" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;The correspondent deformations for the first four eigenmodes are presented below:&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image039.jpg" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image041.jpg" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image043.jpg" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image045.jpg" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;a title="Stay Cable Vibration - Video" href="/products/bridge_design___engineering/m/bridge_design_and_engineering_gallery/274612"&gt;Stay Cable Vibration - Video&lt;/a&gt;&lt;/span&gt;&lt;/p&gt;&lt;div style="clear:both;"&gt;&lt;/div&gt;

&lt;div style="font-size: 90%;"&gt;Tags: RM, Cable Vibration, cable, RM Bridge, RM Bridge Enterprise, dynamics&lt;/div&gt;
</description></item><item><title>RM Bridge: Stay Cable Vibration</title><link>https://communities.bentley.com/products/bridge_design___engineering/w/bridge_design_and_engineering__wiki/51625/rm-bridge-stay-cable-vibration/revision/8</link><pubDate>Thu, 22 Jul 2021 15:26:41 GMT</pubDate><guid isPermaLink="false">6dad98f5-dbc9-4c4d-a9ba-e9da8dc6aa8e:4d2b1fa2-ed16-4598-9ed7-3695af080102</guid><dc:creator>MarcosBeier</dc:creator><comments>https://communities.bentley.com/products/bridge_design___engineering/w/bridge_design_and_engineering__wiki/51625/rm-bridge-stay-cable-vibration#comments</comments><description>Revision 8 posted to LARS | LEAP | OpenBridge | OpenTunnel | RM Wiki by MarcosBeier on 7/22/2021 3:26:41 PM&lt;br /&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&amp;nbsp;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:150%;"&gt;Objective&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;To perform and obtain the dynamic behavior of a stay cable and compare &lt;strong&gt;RM Bridge&lt;/strong&gt; results with the formulation presented in &lt;strong&gt;SETRA&lt;/strong&gt; &amp;ndash; Recommendations of French inter-ministerial commission on Prestressing.&lt;/p&gt;
&lt;p&gt;&lt;span style="font-family:inherit;font-size:75%;"&gt;&lt;span style="font-size:200%;"&gt;Structural Model&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;A stay cable fixed at two anchorages with a horizontal distance of 200 m and a vertical distance of 100 m apart was considered.&lt;/p&gt;
&lt;p&gt;A parallel-strand cable stay with a resisting section S consists of 15 mm strands of &lt;em&gt;f&lt;sub&gt;class&lt;/sub&gt;&lt;/em&gt; = 1770 MPa.&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " height="196" src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image003.png" width="440" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:150%;"&gt;Formulation&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;By &lt;strong&gt;SETRA&lt;/strong&gt; &amp;ndash; Recommendations of French inter-ministerial commission on Prestressing, in chapter 8 the following formulation was verified.&lt;/p&gt;
&lt;p&gt;A cable-stay can be considered to be a straight element tensioned to a tension &lt;em&gt;F&lt;/em&gt;, with a lineic mass &lt;em&gt;m&lt;/em&gt; and with negligible stiffness.&lt;/p&gt;
&lt;p&gt;Transverse vibration of cable stays is studied here with co-ordinate system (Axy). Where x is the direction of chord [AB] and y is a lateral direction.&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " height="132" src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image008.png" width="449" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;It is assumed that vibrations are of low amplitude and that tension &lt;em&gt;F&lt;/em&gt; is constant. If the cable-stay damping is overlooked, lateral displacement y(x,t) is given by the fundamental equation of dynamics applied to an infinitesimal element &lt;em&gt;dx&lt;/em&gt;:&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image009.png" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:inherit;"&gt;or,&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:inherit;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image011.png" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;defining c, the celerity of transverse waves as:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image013.png" /&gt;&lt;/p&gt;
&lt;p&gt;The equation is solved by obtaining y(x,t) in the form e(x) modal deformation and f(t), which makes it possible to separate variables x and t:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image015.png" /&gt;&lt;/p&gt;
&lt;p&gt;, where &lt;em&gt;w&lt;sup&gt;2&lt;/sup&gt;&lt;/em&gt; is an integration constant.&lt;/p&gt;
&lt;p&gt;Assuming&amp;nbsp;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image017.png" /&gt;&amp;nbsp; , the spatial equation can be written:&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image019.png" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;Boundary conditions y(0) = y(l) = 0 are used to deduce the form of the n&lt;sup&gt;th&lt;/sup&gt; order mode:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image021.png" /&gt;&lt;/p&gt;
&lt;p&gt;and the wave number:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image023.png" /&gt;&lt;/p&gt;
&lt;p&gt;The temporal equation is written&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image025.png" /&gt;&lt;/p&gt;
&lt;p&gt;Its general solution is&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image027.png" /&gt;&lt;/p&gt;
&lt;p&gt;This yields the taut-string formula for eigen period &lt;em&gt;T&lt;sub&gt;n&lt;/sub&gt;&lt;/em&gt; and &lt;em&gt;n&lt;sup&gt;th&lt;/sup&gt;&lt;/em&gt; &amp;ndash; order eigen frequency &lt;em&gt;N&lt;sub&gt;n&lt;/sub&gt;&lt;/em&gt;:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image029.png" /&gt;&lt;/p&gt;
&lt;p&gt;The free vibrations of the cable-stay are finally a superposition of sinusoidal modes of the form:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image031.png" /&gt;&lt;/p&gt;
&lt;p&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:150%;"&gt;Schedule Action&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;Only one schedule action is run to calculate the Cable eigen frequencies and eigenvectors (natural modes). The reference load case containing the definition of effective masses must be specified.&lt;/p&gt;
&lt;p&gt;After the calculation, a number of n load cases is presented and can be accessed from the load case pool, as &amp;lsquo;Outputfilename#n&amp;rsquo;, being n the eigenmode number. The load cases contain normalized eigenvectors as displacements that were used in graphic presentation.&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " height="284" src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image033.png" width="556" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:150%;"&gt;Results&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;In the verification example studied, the Cable model was discretized in 10 (ten) sub-cable elements and in the Recalculate path &amp;ldquo;Non-linear Stay Cables&amp;rdquo; was selected.&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " height="300" src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image035.png" width="541" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;The calculated and obtained results are the ones presented in the following table:&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " height="160" src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image038.png" width="545" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;The correspondent deformations for the first four eigenmodes are presented below:&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image039.jpg" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image041.jpg" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image043.jpg" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image045.jpg" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;a title="Stay Cable Vibration - Video" href="/products/bridge_design___engineering/m/bridge_design_and_engineering_gallery/274612"&gt;Stay Cable Vibration - Video&lt;/a&gt;&lt;/span&gt;&lt;/p&gt;&lt;div style="clear:both;"&gt;&lt;/div&gt;

&lt;div style="font-size: 90%;"&gt;Tags: RM, Cable Vibration, cable, RM Bridge, RM Bridge Enterprise, dynamics&lt;/div&gt;
</description></item><item><title>RM Bridge: Stay Cable Vibration</title><link>https://communities.bentley.com/products/bridge_design___engineering/w/bridge_design_and_engineering__wiki/51625/rm-bridge-stay-cable-vibration/revision/7</link><pubDate>Tue, 02 Feb 2021 18:39:32 GMT</pubDate><guid isPermaLink="false">6dad98f5-dbc9-4c4d-a9ba-e9da8dc6aa8e:4d2b1fa2-ed16-4598-9ed7-3695af080102</guid><dc:creator>Ana Carla Peres</dc:creator><comments>https://communities.bentley.com/products/bridge_design___engineering/w/bridge_design_and_engineering__wiki/51625/rm-bridge-stay-cable-vibration#comments</comments><description>Revision 7 posted to LARS | LEAP | OpenBridge | OpenTunnel | RM Wiki by Ana Carla Peres on 2/2/2021 6:39:32 PM&lt;br /&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&amp;nbsp;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:150%;"&gt;Objective&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;To perform and obtain the dynamic behavior of a stay cable and compare &lt;strong&gt;RM Bridge&lt;/strong&gt; results with the formulation presented in &lt;strong&gt;SETRA&lt;/strong&gt; &amp;ndash; Recommendations of French inter-ministerial commission on Prestressing.&lt;/p&gt;
&lt;p&gt;&lt;span style="font-family:inherit;font-size:75%;"&gt;&lt;span style="font-size:200%;"&gt;Structural Model&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;A stay cable fixed at two anchorages with a horizontal distance of 200 m and a vertical distance of 100 m apart was considered.&lt;/p&gt;
&lt;p&gt;A parallel-strand cable stay with a resisting section S consists of 15 mm strands of &lt;em&gt;f&lt;sub&gt;class&lt;/sub&gt;&lt;/em&gt; = 1770 MPa.&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " height="196" src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image003.png" width="440" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:150%;"&gt;Formulation&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;By &lt;strong&gt;SETRA&lt;/strong&gt; &amp;ndash; Recommendations of French inter-ministerial commission on Prestressing, in chapter 8 the following formulation was verified.&lt;/p&gt;
&lt;p&gt;A cable-stay can be considered to be a straight element tensioned to a tension &lt;em&gt;F&lt;/em&gt;, with a lineic mass &lt;em&gt;m&lt;/em&gt; and with negligible stiffness.&lt;/p&gt;
&lt;p&gt;Transverse vibration of cable stays is studied here with co-ordinate system (Axy). Where x is the direction of chord [AB] and y is a lateral direction.&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " height="132" src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image008.png" width="449" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;It is assumed that vibrations are of low amplitude and that tension &lt;em&gt;F&lt;/em&gt; is constant. If the cable-stay damping is overlooked, lateral displacement y(x,t) is given by the fundamental equation of dynamics applied to an infinitesimal element &lt;em&gt;dx&lt;/em&gt;:&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image009.png" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:inherit;"&gt;or,&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:inherit;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image011.png" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;defining c, the celerity of transverse waves as:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image013.png" /&gt;&lt;/p&gt;
&lt;p&gt;The equation is solved by obtaining y(x,t) in the form e(x) modal deformation and f(t), which makes it possible to separate variables x and t:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image015.png" /&gt;&lt;/p&gt;
&lt;p&gt;, where &lt;em&gt;w&lt;sup&gt;2&lt;/sup&gt;&lt;/em&gt; is an integration constant.&lt;/p&gt;
&lt;p&gt;Assuming&amp;nbsp;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image017.png" /&gt;&amp;nbsp; , the spatial equation can be written:&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image019.png" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;Boundary conditions y(0) = y(l) = 0 are used to deduce the form of the n&lt;sup&gt;th&lt;/sup&gt; order mode:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image021.png" /&gt;&lt;/p&gt;
&lt;p&gt;and the wave number:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image023.png" /&gt;&lt;/p&gt;
&lt;p&gt;The temporal equation is written&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image025.png" /&gt;&lt;/p&gt;
&lt;p&gt;Its general solution is&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image027.png" /&gt;&lt;/p&gt;
&lt;p&gt;This yields the taut-string formula for eigen period &lt;em&gt;T&lt;sub&gt;n&lt;/sub&gt;&lt;/em&gt; and &lt;em&gt;n&lt;sup&gt;th&lt;/sup&gt;&lt;/em&gt; &amp;ndash; order eigen frequency &lt;em&gt;N&lt;sub&gt;n&lt;/sub&gt;&lt;/em&gt;:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image029.png" /&gt;&lt;/p&gt;
&lt;p&gt;The free vibrations of the cable-stay are finally a superposition of sinusoidal modes of the form:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image031.png" /&gt;&lt;/p&gt;
&lt;p&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:150%;"&gt;Schedule Action&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;Only one schedule action is run to calculate the Cable eigen frequencies and eigenvectors (natural modes). The reference load case containing the definition of effective masses must be specified.&lt;/p&gt;
&lt;p&gt;After the calculation, a number of n load cases is presented and can be accessed from the load case pool, as &amp;lsquo;Outputfilename#n&amp;rsquo;, being n the eigenmode number. The load cases contain normalized eigenvectors as displacements that were used in graphic presentation.&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " height="284" src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image033.png" width="556" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:150%;"&gt;Results&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;In the verification example studied, the Cable model was discretized in 10 (ten) sub-cable elements and in the Recalculate path &amp;ldquo;Non-linear Stay Cables&amp;rdquo; was selected.&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " height="300" src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image035.png" width="541" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;The calculated and obtained results are the ones presented in the following table:&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " height="160" src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image038.png" width="545" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;The correspondent deformations for the first four eigenmodes are presented below:&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image039.jpg" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image041.jpg" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image043.jpg" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image045.jpg" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;a title="Stay Cable Vibration - Video" href="/products/bridge_design___engineering/m/bridge_design_and_engineering_gallery/274612"&gt;Stay Cable Vibration - Video&lt;/a&gt;&lt;/span&gt;&lt;/p&gt;&lt;div style="clear:both;"&gt;&lt;/div&gt;

&lt;div style="font-size: 90%;"&gt;Tags: RM, Cable Vibration, cable, RM Bridge, RM Bridge Enterprise, dynamics&lt;/div&gt;
</description></item><item><title>RM Bridge: Stay Cable Vibration</title><link>https://communities.bentley.com/products/bridge_design___engineering/w/bridge_design_and_engineering__wiki/51625/rm-bridge-stay-cable-vibration/revision/6</link><pubDate>Mon, 28 Sep 2020 23:48:57 GMT</pubDate><guid isPermaLink="false">6dad98f5-dbc9-4c4d-a9ba-e9da8dc6aa8e:4d2b1fa2-ed16-4598-9ed7-3695af080102</guid><dc:creator>MarcosBeier</dc:creator><comments>https://communities.bentley.com/products/bridge_design___engineering/w/bridge_design_and_engineering__wiki/51625/rm-bridge-stay-cable-vibration#comments</comments><description>Revision 6 posted to LARS | LEAP | OpenBridge | OpenTunnel | RM Wiki by MarcosBeier on 9/28/2020 11:48:57 PM&lt;br /&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&amp;nbsp;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:150%;"&gt;Objective&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;To perform and obtain the dynamic behavior of a stay cable and compare &lt;strong&gt;RM Bridge&lt;/strong&gt; results with the formulation presented in &lt;strong&gt;SETRA&lt;/strong&gt; &amp;ndash; Recommendations of French inter-ministerial commission on Prestressing.&lt;/p&gt;
&lt;p&gt;&lt;span style="font-family:inherit;font-size:75%;"&gt;&lt;span style="font-size:200%;"&gt;Structural Model&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;A stay cable fixed at two anchorages with a horizontal distance of 200 m and a vertical distance of 100 m apart was considered.&lt;/p&gt;
&lt;p&gt;A parallel-strand cable stay with a resisting section S consists of 15 mm strands of &lt;em&gt;f&lt;sub&gt;class&lt;/sub&gt;&lt;/em&gt; = 1770 MPa.&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " height="196" src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image003.png" width="440" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:150%;"&gt;Formulation&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;By &lt;strong&gt;SETRA&lt;/strong&gt; &amp;ndash; Recommendations of French inter-ministerial commission on Prestressing, in chapter 8 the following formulation was verified.&lt;/p&gt;
&lt;p&gt;A cable-stay can be considered to be a straight element tensioned to a tension &lt;em&gt;F&lt;/em&gt;, with a lineic mass &lt;em&gt;m&lt;/em&gt; and with negligible stiffness.&lt;/p&gt;
&lt;p&gt;Transverse vibration of cable stays is studied here with co-ordinate system (Axy). Where x is the direction of chord [AB] and y is a lateral direction.&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " height="132" src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image008.png" width="449" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;It is assumed that vibrations are of low amplitude and that tension &lt;em&gt;F&lt;/em&gt; is constant. If the cable-stay damping is overlooked, lateral displacement y(x,t) is given by the fundamental equation of dynamics applied to an infinitesimal element &lt;em&gt;dx&lt;/em&gt;:&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image009.png" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:inherit;"&gt;or,&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:inherit;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image011.png" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;defining c, the celerity of transverse waves as:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image013.png" /&gt;&lt;/p&gt;
&lt;p&gt;The equation is solved by obtaining y(x,t) in the form e(x) modal deformation and f(t), which makes it possible to separate variables x and t:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image015.png" /&gt;&lt;/p&gt;
&lt;p&gt;, where &lt;em&gt;w&lt;sup&gt;2&lt;/sup&gt;&lt;/em&gt; is an integration constant.&lt;/p&gt;
&lt;p&gt;Assuming&amp;nbsp;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image017.png" /&gt;&amp;nbsp; , the spatial equation can be written:&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image019.png" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;Boundary conditions y(0) = y(l) = 0 are used to deduce the form of the n&lt;sup&gt;th&lt;/sup&gt; order mode:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image021.png" /&gt;&lt;/p&gt;
&lt;p&gt;and the wave number:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image023.png" /&gt;&lt;/p&gt;
&lt;p&gt;The temporal equation is written&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image025.png" /&gt;&lt;/p&gt;
&lt;p&gt;Its general solution is&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image027.png" /&gt;&lt;/p&gt;
&lt;p&gt;This yields the taut-string formula for eigen period &lt;em&gt;T&lt;sub&gt;n&lt;/sub&gt;&lt;/em&gt; and &lt;em&gt;n&lt;sup&gt;th&lt;/sup&gt;&lt;/em&gt; &amp;ndash; order eigen frequency &lt;em&gt;N&lt;sub&gt;n&lt;/sub&gt;&lt;/em&gt;:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image029.png" /&gt;&lt;/p&gt;
&lt;p&gt;The free vibrations of the cable-stay are finally a superposition of sinusoidal modes of the form:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image031.png" /&gt;&lt;/p&gt;
&lt;p&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:150%;"&gt;Schedule Action&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;Only one schedule action is run to calculate the Cable eigen frequencies and eigenvectors (natural modes). The reference load case containing the definition of effective masses must be specified.&lt;/p&gt;
&lt;p&gt;After the calculation, a number of n load cases is presented and can be accessed from the load case pool, as &amp;lsquo;Outputfilename#n&amp;rsquo;, being n the eigenmode number. The load cases contain normalized eigenvectors as displacements that were used in graphic presentation.&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " height="284" src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image033.png" width="556" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:150%;"&gt;Results&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;In the verification example studied, the Cable model was discretized in 10 (ten) sub-cable elements and in the Recalculate path &amp;ldquo;Non-linear Stay Cables&amp;rdquo; was selected.&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " height="300" src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image035.png" width="541" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;The calculated and obtained results are the ones presented in the following table:&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " height="160" src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image038.png" width="545" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;The correspondent deformations for the first four eigenmodes are presented below:&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image039.jpg" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image041.jpg" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image043.jpg" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image045.jpg" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;a title="Stay Cable Vibration - Video" href="/products/bridge_design___engineering/m/bridge_design_and_engineering_gallery/274612"&gt;Stay Cable Vibration - Video&lt;/a&gt;&lt;/span&gt;&lt;/p&gt;&lt;div style="clear:both;"&gt;&lt;/div&gt;

&lt;div style="font-size: 90%;"&gt;Tags: RM, Cable Vibration, cable, RM Bridge, RM Bridge Enterprise, dynamics&lt;/div&gt;
</description></item><item><title>RM Bridge: Stay Cable Vibration</title><link>https://communities.bentley.com/products/bridge_design___engineering/w/bridge_design_and_engineering__wiki/51625/rm-bridge-stay-cable-vibration/revision/5</link><pubDate>Mon, 28 Sep 2020 22:37:12 GMT</pubDate><guid isPermaLink="false">6dad98f5-dbc9-4c4d-a9ba-e9da8dc6aa8e:4d2b1fa2-ed16-4598-9ed7-3695af080102</guid><dc:creator>Ana Carla Peres</dc:creator><comments>https://communities.bentley.com/products/bridge_design___engineering/w/bridge_design_and_engineering__wiki/51625/rm-bridge-stay-cable-vibration#comments</comments><description>Revision 5 posted to LARS | LEAP | OpenBridge | OpenTunnel | RM Wiki by Ana Carla Peres on 9/28/2020 10:37:12 PM&lt;br /&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&amp;nbsp;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:150%;"&gt;Objective&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;To perform and obtain the dynamic behavior of a stay cable and compare &lt;strong&gt;RM Bridge&lt;/strong&gt; results with the formulation presented in &lt;strong&gt;SETRA&lt;/strong&gt; &amp;ndash; Recommendations of French inter-ministerial commission on Prestressing.&lt;/p&gt;
&lt;p&gt;&lt;span style="font-family:inherit;font-size:75%;"&gt;&lt;span style="font-size:200%;"&gt;Structural Model&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;A stay cable fixed at two anchorages with a horizontal distance of 200 m and a vertical distance of 100 m apart was considered.&lt;/p&gt;
&lt;p&gt;A parallel-strand cable stay with a resisting section S consists of 15 mm strands of &lt;em&gt;f&lt;sub&gt;class&lt;/sub&gt;&lt;/em&gt; = 1770 MPa.&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " height="196" src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image003.png" width="440" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:150%;"&gt;Formulation&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;By &lt;strong&gt;SETRA&lt;/strong&gt; &amp;ndash; Recommendations of French inter-ministerial commission on Prestressing, in chapter 8 the following formulation was verified.&lt;/p&gt;
&lt;p&gt;A cable-stay can be considered to be a straight element tensioned to a tension &lt;em&gt;F&lt;/em&gt;, with a lineic mass &lt;em&gt;m&lt;/em&gt; and with negligible stiffness.&lt;/p&gt;
&lt;p&gt;Transverse vibration of cable stays is studied here with co-ordinate system (Axy). Where x is the direction of chord [AB] and y is a lateral direction.&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " height="132" src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image008.png" width="449" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;It is assumed that vibrations are of low amplitude and that tension &lt;em&gt;F&lt;/em&gt; is constant. If the cable-stay damping is overlooked, lateral displacement y(x,t) is given by the fundamental equation of dynamics applied to an infinitesimal element &lt;em&gt;dx&lt;/em&gt;:&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image009.png" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:inherit;"&gt;or,&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:inherit;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image011.png" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;defining c, the celerity of transverse waves as:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image013.png" /&gt;&lt;/p&gt;
&lt;p&gt;The equation is solved by obtaining y(x,t) in the form e(x) modal deformation and f(t), which makes it possible to separate variables x and t:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image015.png" /&gt;&lt;/p&gt;
&lt;p&gt;, where &lt;em&gt;w&lt;sup&gt;2&lt;/sup&gt;&lt;/em&gt; is an integration constant.&lt;/p&gt;
&lt;p&gt;Assuming&amp;nbsp;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image017.png" /&gt;&amp;nbsp; , the spatial equation can be written:&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image019.png" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;Boundary conditions y(0) = y(l) = 0 are used to deduce the form of the n&lt;sup&gt;th&lt;/sup&gt; order mode:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image021.png" /&gt;&lt;/p&gt;
&lt;p&gt;and the wave number:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image023.png" /&gt;&lt;/p&gt;
&lt;p&gt;The temporal equation is written&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image025.png" /&gt;&lt;/p&gt;
&lt;p&gt;Its general solution is&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image027.png" /&gt;&lt;/p&gt;
&lt;p&gt;This yields the taut-string formula for eigen period &lt;em&gt;T&lt;sub&gt;n&lt;/sub&gt;&lt;/em&gt; and &lt;em&gt;n&lt;sup&gt;th&lt;/sup&gt;&lt;/em&gt; &amp;ndash; order eigen frequency &lt;em&gt;N&lt;sub&gt;n&lt;/sub&gt;&lt;/em&gt;:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image029.png" /&gt;&lt;/p&gt;
&lt;p&gt;The free vibrations of the cable-stay are finally a superposition of sinusoidal modes of the form:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image031.png" /&gt;&lt;/p&gt;
&lt;p&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:150%;"&gt;Schedule Action&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;Only one schedule action is run to calculate the Cable eigen frequencies and eigenvectors (natural modes). The reference load case containing the definition of effective masses must be specified.&lt;/p&gt;
&lt;p&gt;After the calculation, a number of n load cases is presented and can be accessed from the load case pool, as &amp;lsquo;Outputfilename#n&amp;rsquo;, being n the eigenmode number. The load cases contain normalized eigenvectors as displacements that were used in graphic presentation.&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " height="284" src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image033.png" width="556" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:150%;"&gt;Results&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;In the verification example studied, the Cable model was discretized in 10 (ten) sub-cable elements and in the Recalculate path &amp;ldquo;Non-linear Stay Cables&amp;rdquo; was selected.&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " height="300" src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image035.png" width="541" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;The calculated and obtained results are the ones presented in the following table:&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " height="160" src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image038.png" width="545" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;The correspondent deformations for the first four eigenmodes are presented below:&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image039.jpg" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image041.jpg" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image043.jpg" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image045.jpg" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;a title="Stay Cable Vibration - Video" href="/products/bridge_design___engineering/m/bridge_design_and_engineering_gallery/274612"&gt;Stay Cable Vibration - Video&lt;/a&gt;&lt;/span&gt;&lt;/p&gt;&lt;div style="clear:both;"&gt;&lt;/div&gt;

&lt;div style="font-size: 90%;"&gt;Tags: RM, Cable Vibration, cable, RM Bridge, RM Bridge Enterprise, dynamics&lt;/div&gt;
</description></item><item><title>RM Bridge: Stay Cable Vibration</title><link>https://communities.bentley.com/products/bridge_design___engineering/w/bridge_design_and_engineering__wiki/51625/rm-bridge-stay-cable-vibration/revision/4</link><pubDate>Mon, 28 Sep 2020 22:20:59 GMT</pubDate><guid isPermaLink="false">6dad98f5-dbc9-4c4d-a9ba-e9da8dc6aa8e:4d2b1fa2-ed16-4598-9ed7-3695af080102</guid><dc:creator>Ana Carla Peres</dc:creator><comments>https://communities.bentley.com/products/bridge_design___engineering/w/bridge_design_and_engineering__wiki/51625/rm-bridge-stay-cable-vibration#comments</comments><description>Revision 4 posted to LARS | LEAP | OpenBridge | OpenTunnel | RM Wiki by Ana Carla Peres on 9/28/2020 10:20:59 PM&lt;br /&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;RM Bridge: Stay Cable Vibration&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:150%;"&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:150%;"&gt;Objective&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;To perform and obtain the dynamic behavior of a stay cable and compare &lt;strong&gt;RM Bridge&lt;/strong&gt; results with the formulation presented in &lt;strong&gt;SETRA&lt;/strong&gt; &amp;ndash; Recommendations of French inter-ministerial commission on Prestressing.&lt;/p&gt;
&lt;p&gt;&lt;span style="font-family:inherit;font-size:75%;"&gt;&lt;span style="font-size:200%;"&gt;Structural Model&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;A stay cable fixed at two anchorages with a horizontal distance of 200 m and a vertical distance of 100 m apart was considered.&lt;/p&gt;
&lt;p&gt;A parallel-strand cable stay with a resisting section S consists of 15 mm strands of &lt;em&gt;f&lt;sub&gt;class&lt;/sub&gt;&lt;/em&gt; = 1770 MPa.&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " height="196" src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image003.png" width="440" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:150%;"&gt;Formulation&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;By &lt;strong&gt;SETRA&lt;/strong&gt; &amp;ndash; Recommendations of French inter-ministerial commission on Prestressing, in chapter 8 the following formulation was verified.&lt;/p&gt;
&lt;p&gt;A cable-stay can be considered to be a straight element tensioned to a tension &lt;em&gt;F&lt;/em&gt;, with a lineic mass &lt;em&gt;m&lt;/em&gt; and with negligible stiffness.&lt;/p&gt;
&lt;p&gt;Transverse vibration of cable stays is studied here with co-ordinate system (Axy). Where x is the direction of chord [AB] and y is a lateral direction.&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " height="132" src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image008.png" width="449" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;It is assumed that vibrations are of low amplitude and that tension &lt;em&gt;F&lt;/em&gt; is constant. If the cable-stay damping is overlooked, lateral displacement y(x,t) is given by the fundamental equation of dynamics applied to an infinitesimal element &lt;em&gt;dx&lt;/em&gt;:&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image009.png" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:inherit;"&gt;or,&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:inherit;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image011.png" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;defining c, the celerity of transverse waves as:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image013.png" /&gt;&lt;/p&gt;
&lt;p&gt;The equation is solved by obtaining y(x,t) in the form e(x) modal deformation and f(t), which makes it possible to separate variables x and t:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image015.png" /&gt;&lt;/p&gt;
&lt;p&gt;, where &lt;em&gt;w&lt;sup&gt;2&lt;/sup&gt;&lt;/em&gt; is an integration constant.&lt;/p&gt;
&lt;p&gt;Assuming&amp;nbsp;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image017.png" /&gt;&amp;nbsp; , the spatial equation can be written:&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image019.png" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;Boundary conditions y(0) = y(l) = 0 are used to deduce the form of the n&lt;sup&gt;th&lt;/sup&gt; order mode:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image021.png" /&gt;&lt;/p&gt;
&lt;p&gt;and the wave number:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image023.png" /&gt;&lt;/p&gt;
&lt;p&gt;The temporal equation is written&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image025.png" /&gt;&lt;/p&gt;
&lt;p&gt;Its general solution is&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image027.png" /&gt;&lt;/p&gt;
&lt;p&gt;This yields the taut-string formula for eigen period &lt;em&gt;T&lt;sub&gt;n&lt;/sub&gt;&lt;/em&gt; and &lt;em&gt;n&lt;sup&gt;th&lt;/sup&gt;&lt;/em&gt; &amp;ndash; order eigen frequency &lt;em&gt;N&lt;sub&gt;n&lt;/sub&gt;&lt;/em&gt;:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image029.png" /&gt;&lt;/p&gt;
&lt;p&gt;The free vibrations of the cable-stay are finally a superposition of sinusoidal modes of the form:&lt;/p&gt;
&lt;p&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image031.png" /&gt;&lt;/p&gt;
&lt;p&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:150%;"&gt;Schedule Action&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;Only one schedule action is run to calculate the Cable eigen frequencies and eigenvectors (natural modes). The reference load case containing the definition of effective masses must be specified.&lt;/p&gt;
&lt;p&gt;After the calculation, a number of n load cases is presented and can be accessed from the load case pool, as &amp;lsquo;Outputfilename#n&amp;rsquo;, being n the eigenmode number. The load cases contain normalized eigenvectors as displacements that were used in graphic presentation.&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " height="284" src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image033.png" width="556" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:150%;"&gt;Results&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;In the verification example studied, the Cable model was discretized in 10 (ten) sub-cable elements and in the Recalculate path &amp;ldquo;Non-linear Stay Cables&amp;rdquo; was selected.&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " height="300" src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image035.png" width="541" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;The calculated and obtained results are the ones presented in the following table:&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " height="160" src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image038.png" width="545" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;The correspondent deformations for the first four eigenmodes are presented below:&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image039.jpg" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image041.jpg" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image043.jpg" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;img alt=" " src="/resized-image/__size/320x240/__key/communityserver-wikis-components-files/00-00-00-00-15/image045.jpg" /&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;a title="Stay Cable Vibration - Video" href="/products/bridge_design___engineering/m/bridge_design_and_engineering_gallery/274612"&gt;Stay Cable Vibration - Video&lt;/a&gt;&lt;/span&gt;&lt;/p&gt;&lt;div style="clear:both;"&gt;&lt;/div&gt;

&lt;div style="font-size: 90%;"&gt;Tags: RM, Cable Vibration, cable, RM Bridge, RM Bridge Enterprise, dynamics&lt;/div&gt;
</description></item><item><title>RM Bridge: Stay Cable Vibration</title><link>https://communities.bentley.com/products/bridge_design___engineering/w/bridge_design_and_engineering__wiki/51625/rm-bridge-stay-cable-vibration/revision/3</link><pubDate>Mon, 28 Sep 2020 21:46:56 GMT</pubDate><guid isPermaLink="false">6dad98f5-dbc9-4c4d-a9ba-e9da8dc6aa8e:4d2b1fa2-ed16-4598-9ed7-3695af080102</guid><dc:creator>Ana Carla Peres</dc:creator><comments>https://communities.bentley.com/products/bridge_design___engineering/w/bridge_design_and_engineering__wiki/51625/rm-bridge-stay-cable-vibration#comments</comments><description>Revision 3 posted to LARS | LEAP | OpenBridge | OpenTunnel | RM Wiki by Ana Carla Peres on 9/28/2020 9:46:56 PM&lt;br /&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;a title="Stay Cable Vibration" href="/products/bridge_design___engineering/m/bridge_design_and_engineering_gallery/274612"&gt;Stay Cable Vibration&lt;/a&gt;&lt;/span&gt;&lt;/p&gt;&lt;div style="clear:both;"&gt;&lt;/div&gt;

&lt;div style="font-size: 90%;"&gt;Tags: RM, Cable Vibration, cable, RM Bridge, RM Bridge Enterprise, dynamics&lt;/div&gt;
</description></item><item><title>RM Bridge: Stay Cable Vibration</title><link>https://communities.bentley.com/products/bridge_design___engineering/w/bridge_design_and_engineering__wiki/51625/rm-bridge-stay-cable-vibration/revision/2</link><pubDate>Mon, 28 Sep 2020 21:42:11 GMT</pubDate><guid isPermaLink="false">6dad98f5-dbc9-4c4d-a9ba-e9da8dc6aa8e:4d2b1fa2-ed16-4598-9ed7-3695af080102</guid><dc:creator>Ana Carla Peres</dc:creator><comments>https://communities.bentley.com/products/bridge_design___engineering/w/bridge_design_and_engineering__wiki/51625/rm-bridge-stay-cable-vibration#comments</comments><description>Revision 2 posted to LARS | LEAP | OpenBridge | OpenTunnel | RM Wiki by Ana Carla Peres on 9/28/2020 9:42:11 PM&lt;br /&gt;
&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;a title="Stay Cable Vibration" href="https://bentley-my.sharepoint.com/personal/anacarla_peres_bentley_com/_layouts/15/onedrive.aspx?id=%2Fpersonal%2Fanacarla%5Fperes%5Fbentley%5Fcom%2FDocuments%2FAC%5FVideos%2FStayCable%20Vibration%2Emp4&amp;amp;parent=%2Fpersonal%2Fanacarla%5Fperes%5Fbentley%5Fcom%2FDocuments%2FAC%5FVideos" rel="noopener noreferrer" target="_blank"&gt;Stay Cable Vibration&lt;/a&gt;&lt;/span&gt;&lt;/p&gt;&lt;div style="clear:both;"&gt;&lt;/div&gt;

&lt;div style="font-size: 90%;"&gt;Tags: RM, Cable Vibration, cable, RM Bridge, RM Bridge Enterprise, dynamics&lt;/div&gt;
</description></item><item><title>RM Bridge: Stay Cable Vibration</title><link>https://communities.bentley.com/products/bridge_design___engineering/w/bridge_design_and_engineering__wiki/51625/rm-bridge-stay-cable-vibration/revision/1</link><pubDate>Mon, 28 Sep 2020 21:18:01 GMT</pubDate><guid isPermaLink="false">6dad98f5-dbc9-4c4d-a9ba-e9da8dc6aa8e:4d2b1fa2-ed16-4598-9ed7-3695af080102</guid><dc:creator>Ana Carla Peres</dc:creator><comments>https://communities.bentley.com/products/bridge_design___engineering/w/bridge_design_and_engineering__wiki/51625/rm-bridge-stay-cable-vibration#comments</comments><description>Revision 1 posted to LARS | LEAP | OpenBridge | OpenTunnel | RM Wiki by Ana Carla Peres on 9/28/2020 9:18:01 PM&lt;br /&gt;

&lt;p&gt;&lt;span style="font-size:200%;"&gt;&lt;a title="Stay Cable Vibration" href="https://sway.office.com/4LztpxDU60SttuNr?ref=Link"&gt;Stay Cable Vibration&lt;/a&gt;&lt;/span&gt;&lt;/p&gt;&lt;div style="clear:both;"&gt;&lt;/div&gt;

&lt;div style="font-size: 90%;"&gt;Tags: RM, Cable Vibration, cable, RM Bridge, RM Bridge Enterprise, dynamics&lt;/div&gt;
</description></item></channel></rss>