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<?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>02. How to apply Henry Bednar theory of Vortex Shedding</title><link>https://communities.bentley.com/products/pipe_stress_analysis/w/pipe_stress_analysis__wiki/51015/02-how-to-apply-henry-bednar-theory-of-vortex-shedding</link><description /><dc:language>en-US</dc:language><generator>Telligent Community 12</generator><item><title>02. How to apply Henry Bednar theory of Vortex Shedding</title><link>https://communities.bentley.com/products/pipe_stress_analysis/w/pipe_stress_analysis__wiki/51015/02-how-to-apply-henry-bednar-theory-of-vortex-shedding</link><pubDate>Tue, 18 Aug 2020 14:08:10 GMT</pubDate><guid isPermaLink="false">6dad98f5-dbc9-4c4d-a9ba-e9da8dc6aa8e:46688862-a417-4351-bcab-ed7dea97c509</guid><dc:creator>JamieP</dc:creator><comments>https://communities.bentley.com/products/pipe_stress_analysis/w/pipe_stress_analysis__wiki/51015/02-how-to-apply-henry-bednar-theory-of-vortex-shedding#comments</comments><description>Current Revision posted to AutoPIPE Wiki by JamieP on 8/18/2020 2:08:10 PM&lt;br /&gt;
&lt;ol&gt;
&lt;li&gt;Check vibration criteria. See points 1 and 2 in Kanti Mahajan.&lt;/li&gt;
&lt;/ol&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;ol start="2"&gt;
&lt;li&gt;Calculate maximum wind velocity at top of the structure. See points 5 and 6 in Kanti Mahajan.&lt;/li&gt;
&lt;/ol&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;ol start="3"&gt;
&lt;li&gt;Calculate first and second critical wind velocity, V&lt;sub&gt;&lt;span style="font-size:small;"&gt;1 &lt;/span&gt;&lt;/sub&gt;and V&lt;sub&gt;&lt;span style="font-size:small;"&gt;2&lt;/span&gt;&lt;/sub&gt;&lt;/li&gt;
&lt;/ol&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;&amp;nbsp;where &lt;em&gt;S&lt;/em&gt; = 0.2 (Strouhal number)&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;V&lt;sub&gt;&lt;span style="font-size:small;"&gt;2&lt;/span&gt;&lt;/sub&gt; = 6.25.&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;If the design wind velocity V&amp;gt;V&lt;sub&gt;&lt;span style="font-size:small;"&gt;1&lt;/span&gt;&lt;/sub&gt;, perform the detailed vibration analysis from step 3 below with V&lt;sub&gt;&lt;span style="font-size:small;"&gt;1 &lt;/span&gt;&lt;/sub&gt;&lt;/p&gt;
&lt;p&gt;If the design wind velocity V&amp;gt;V&lt;sub&gt;&lt;span style="font-size:small;"&gt;2&lt;/span&gt;&lt;/sub&gt;, perform the detailed vibration analysis from step 3 below with V&lt;sub&gt;&lt;span style="font-size:small;"&gt;2&lt;/span&gt;&lt;/sub&gt;&lt;/p&gt;
&lt;p&gt;If V&lt;sub&gt;&lt;span style="font-size:small;"&gt;1 &lt;/span&gt;&lt;/sub&gt;or V&lt;sub&gt;&lt;span style="font-size:small;"&gt;2&lt;/span&gt;&lt;/sub&gt; &amp;gt; 60 mph/27 m/s, ignore the calculation for that V value as there is cutoff for maximum critical wind speed for design consideration (page 120).&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;ol start="4"&gt;
&lt;li&gt;Consider default value of lift coefficient, C&lt;sub&gt;&lt;span style="font-size:small;"&gt;L&lt;/span&gt;&lt;/sub&gt;=0.5, normally lift coefficient is 0.4-0.6 (page 111) for practical engineering. Allow users to input C&lt;sub&gt;&lt;span style="font-size:small;"&gt;L&lt;/span&gt;&lt;/sub&gt; as optional to default.&lt;/li&gt;
&lt;/ol&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;ol start="5"&gt;
&lt;li&gt;Create table 4.3 (page 116) in 2 dropdown selections for evaluation of logarithmic decrement, &amp;delta; and Magnification Factor, M.F. Allow 2 dropdowns selections&lt;/li&gt;
&lt;/ol&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;Selection of soil types (Soft &amp;ndash; I, Stiff &amp;ndash; II, Rock, Very Stiff &amp;ndash; III)&lt;/li&gt;
&lt;li&gt;Equipment type (Tall process columns, unlined stacks, lined stacks)&lt;/li&gt;
&lt;/ul&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;p&gt;Determine &amp;delta; and M.F. from the above selected combinations&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;ol start="6"&gt;
&lt;li&gt;Determine equivalent force F=0.00086 (C&lt;sub&gt;&lt;span style="font-size:small;"&gt;L &lt;/span&gt;&lt;/sub&gt;x M.F.)(d x H x V&lt;span style="font-size:small;"&gt;&lt;sub&gt;1&lt;/sub&gt;&lt;sup&gt;2&lt;/sup&gt;&lt;/span&gt;) (&lt;em&gt;replace V&lt;sub&gt;&lt;span style="font-size:small;"&gt;1&lt;/span&gt;&lt;/sub&gt; by V&lt;sub&gt;&lt;span style="font-size:small;"&gt;2&lt;/span&gt;&lt;/sub&gt; as needed&lt;/em&gt;)&lt;/li&gt;
&lt;/ol&gt;
&lt;p&gt;Where, d = outside projected dia., ft., H= total column height, ft.&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;ol start="7"&gt;
&lt;li&gt;This force F acts on the top of the column so calculate the moments at each level in same way as static wind load analysis.&lt;/li&gt;
&lt;/ol&gt;
&lt;p&gt;Note in the example only the moment at the junction of column and skirt is considered but APV has different approach of calculating at each individual level&lt;/p&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;ol start="8"&gt;
&lt;li&gt;Perform fatigue analysis at the bottom tangent line weld joint&lt;/li&gt;
&lt;/ol&gt;
&lt;p&gt;&amp;nbsp;&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;Evaluate the cyclical stress range S&lt;sub&gt;&lt;span style="font-size:small;"&gt;R&lt;/span&gt;&lt;/sub&gt;=2S, where S is the bending stress due to F acting at the top. We&amp;rsquo;ll be taking the maximum of |&amp;sigma;&lt;sub&gt;&lt;span style="font-size:small;"&gt;M&lt;/span&gt;&lt;/sub&gt;| , |&amp;sigma;&lt;sub&gt;&lt;span style="font-size:small;"&gt;z&lt;/span&gt;&lt;/sub&gt;| , |&amp;sigma;&lt;sub&gt;&lt;span style="font-size:small;"&gt;eq&lt;/span&gt;&lt;/sub&gt;| &amp;nbsp;.The calculation of S&lt;sub&gt;&lt;span style="font-size:small;"&gt;R &lt;/span&gt;&lt;/sub&gt;in the example is confusing and we need to follow the standard practice of calculating the bending stress as implemented in the program S= &amp;sigma; = M/section modulus, section modulus = &amp;pi; (r&lt;span style="font-size:small;"&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;sup&gt;4&lt;/sup&gt;&lt;/span&gt;-r&lt;span style="font-size:small;"&gt;&lt;sub&gt;1&lt;/sub&gt;&lt;sup&gt;4&lt;/sup&gt;&lt;/span&gt;)/4r&lt;sub&gt;&lt;span style="font-size:small;"&gt;2&lt;/span&gt;&lt;/sub&gt;&lt;/li&gt;
&lt;li&gt;calculate number of cycles to failure, N = (K/&amp;beta;S&lt;sub&gt;&lt;span style="font-size:small;"&gt;R&lt;/span&gt;&lt;/sub&gt;)&lt;sup&gt;&lt;span style="font-size:small;"&gt;n &lt;/span&gt;&lt;/sup&gt;(page 118)&lt;/li&gt;
&lt;li&gt;where, n=5, K=780,000 (these values are for carbon steel, no other value specified for any other grade or type of steel)&amp;nbsp;&lt;/li&gt;
&lt;/ul&gt;
&lt;p style="padding-left:30px;"&gt;stress intensification factor, &amp;beta; as follows&lt;/p&gt;
&lt;p style="padding-left:30px;"&gt;&amp;beta; = 1.2, shell plate with smooth finish,&lt;/p&gt;
&lt;p style="padding-left:30px;"&gt;&amp;beta; = 1.8, butt weld&lt;/p&gt;
&lt;p style="padding-left:30px;"&gt;&amp;beta; = 3.0 fillet weld&lt;/p&gt;
&lt;ul&gt;
&lt;li style="padding-left:30px;"&gt;Allow users to select value for &amp;beta; from dropdown, default &amp;beta; = 2.0&lt;/li&gt;
&lt;li style="padding-left:30px;"&gt;Allow user to specify safety factor, S.F. Default S.F.=20.&lt;/li&gt;
&lt;li style="padding-left:30px;"&gt;Safe vibration time or service life considering weld fatigue due to wind vortex induced vibration = (N/S.F.)x T/3600 x(1/24)x(1/365) years&lt;/li&gt;
&lt;li style="padding-left:30px;"&gt;T=time period (seconds per cycle) = 1/f&lt;/li&gt;
&lt;/ul&gt;
&lt;p&gt;Reference: Henry H. Bednar, PE. (1991). &lt;em&gt;Pressure Vessel Design Handbook Second Edition&lt;/em&gt;. Malabar, FL: Krieger Publishing Company.&lt;/p&gt;&lt;div style="clear:both;"&gt;&lt;/div&gt;

&lt;div style="font-size: 90%;"&gt;Tags: vortex shedding, Bednar&lt;/div&gt;
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