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<!DOCTYPE document PUBLIC "-//CNX//DTD CNXML 0.5 plus MathML//EN" "http://cnx.rice.edu/cnxml/0.5/DTD/cnxml_mathml.dtd">
<document xmlns="http://cnx.rice.edu/cnxml" xmlns:md="http://cnx.rice.edu/mdml/0.4" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" id="m10792">
  <name>Staggered Holes</name>
  <metadata>
  <md:version>2.2</md:version>
  <md:created>2002/08/07</md:created>
  <md:revised>2003/07/25 10:10:03 GMT-5</md:revised>
  <md:authorlist>
      <md:author id="terk">
      <md:firstname>Michael</md:firstname>
      
      <md:surname>Terk</md:surname>
      <md:email>terk@rice.edu</md:email>
    </md:author>
  </md:authorlist>

  <md:maintainerlist>
    <md:maintainer id="Joanna">
      <md:firstname>Joanna</md:firstname>
      
      <md:surname>Gonzalez</md:surname>
      <md:email>joannag@owlnet.rice.edu</md:email>
    </md:maintainer>
    <md:maintainer id="terk">
      <md:firstname>Michael</md:firstname>
      
      <md:surname>Terk</md:surname>
      <md:email>terk@rice.edu</md:email>
    </md:maintainer>
    <md:maintainer id="jsilv">
      <md:firstname>Jeffrey</md:firstname>
      
      <md:surname>Silverman</md:surname>
      <md:email>jsilv@rice.edu</md:email>
    </md:maintainer>
  </md:maintainerlist>
  
  <md:keywordlist>
    <md:keyword>bolt</md:keyword>
    <md:keyword>fracture</md:keyword>
    <md:keyword>hole</md:keyword>
    <md:keyword>stagger</md:keyword>
    <md:keyword>tension</md:keyword>
  </md:keywordlist>

  <md:abstract>(Blank Abstract)</md:abstract>
</metadata>

  <content>

   <section id="intro">
    <name>Failure due to Staggered Holes</name>
    <para id="intro1">
     When a member has staggered bolt holes, a different approach to finding
     <m:math>
      <m:ci>
       <m:msub>
        <m:mi>A</m:mi>
        <m:mi>e</m:mi>
       </m:msub>
      </m:ci>
     </m:math>
     for the fracture limit state is taken.  This is because the
     effective net area (<m:math><m:ci>t</m:ci></m:math> x
     <m:math>
      <m:ci>
       <m:msub>
        <m:mi>w</m:mi>
        <m:mi>n</m:mi>
       </m:msub>
      </m:ci>
     </m:math>
     ) is different as the line of fracture changes due to the stagger
     in the holes.  The test for the yielding limit state remains
     unchanged (the gross area is still the same).
    </para>
   </section>

   <section id="fline">
    <name>Failure Lines</name>
    <para id="fline1">
     The net width now must account for the change in direction of the
     line of fracture.  First, look at different ways a tension member
     with staggered holes can fracture.  These pictures depict the
     different lines of failure.  When analyzing a member like this,
     it is important to find all the lines of failure and then
     determine which line of failure is the weakest cross section.
     That cross section will be taken as the net width,
     <m:math>
      <m:ci>
       <m:msub>
        <m:mi>w</m:mi>
        <m:mi>n</m:mi>
       </m:msub>
      </m:ci>
     </m:math>.
    </para>

    <figure id="fline2">
     <media type="image/bmp" src="redline.bmp"/>
    </figure>
   </section>

   <section id="width">
    <name>Net Width</name>
    <para id="width1">
     In order to find the net width, first the variables
     <m:math><m:ci>s</m:ci></m:math> and <m:math><m:ci>g</m:ci></m:math>
     must be known.  They are shown in <cnxn target="width2"/>.
    </para>

    <figure id="width2">
     <media type="image/bmp" src="sg.bmp"/>
    </figure>

    <equation id="width3">
     <m:math>
      <m:apply>
       <m:eq/>
        <m:ci>
         <m:msub>
          <m:mi>w</m:mi>
          <m:mi>n</m:mi>
         </m:msub>
        </m:ci>
        <m:apply>
         <m:minus/>
          <m:ci>
           <m:msub>
            <m:mi>w</m:mi>
            <m:mi>g</m:mi>
           </m:msub>
          </m:ci>
          <m:apply>
           <m:plus/>
            <m:apply>
             <m:times/>
              <m:ci>N</m:ci>
              <m:ci>
               <m:msub>
                <m:mi>φ</m:mi>
                <m:mi>d</m:mi>
               </m:msub>
              </m:ci>
            </m:apply>
            <m:apply>
             <m:divide/>
		    <m:apply>
		      <m:power/>
		      <m:ci>s</m:ci>
		      <m:cn>2</m:cn>
		    </m:apply>
		    <m:apply>
		      <m:times/>
		      <m:cn>4</m:cn>
		      <m:ci>g</m:ci>
		    </m:apply>
            </m:apply>
          </m:apply>
        </m:apply>
      </m:apply>
     </m:math>
    </equation>
          
    <list id="width4">
     <name>where:</name>
     <item>
      <m:math>
       <m:ci>
        <m:msub>
         <m:mi>w</m:mi>
         <m:mi>n</m:mi>
        </m:msub>
       </m:ci>
      </m:math>
      = net width
     </item>

     <item>
      <m:math>
       <m:ci>
        <m:msub>
         <m:mi>w</m:mi>
         <m:mi>g</m:mi>
        </m:msub>
       </m:ci>
      </m:math>
      = gross width
     </item>

     <item>
      <m:math>
       <m:apply>
        <m:eq/>
         <m:ci>
          <m:msub>
           <m:mi>φ</m:mi>
           <m:mi>d</m:mi>
          </m:msub>
         </m:ci>
         <m:apply>
          <m:plus/>
           <m:ci>
            <m:msub>
             <m:mi>φ</m:mi>
             <m:mi>b</m:mi>
            </m:msub>
           </m:ci>
           <m:apply>
            <m:divide/>
             <m:cn>1</m:cn>
             <m:cn>16</m:cn>
           </m:apply>
           <m:apply>
            <m:divide/>
             <m:cn>1</m:cn>
             <m:cn>16</m:cn>
           </m:apply>
         </m:apply>
       </m:apply>
      </m:math>
      where:
      <m:math>
       <m:ci>
        <m:msub>
         <m:mi>φ</m:mi>
         <m:mi>b</m:mi>
        </m:msub>
       </m:ci>
      </m:math>
       = diameter of the bolt
     </item>

     <item>
     <m:math><m:ci>N</m:ci></m:math> = number of bolts in cross section
     </item>

     <item>
      <m:math><m:ci>s</m:ci></m:math> = longitudinal center-to-center
      spacing of any two consecutive holes, in.
     </item>

     <item>
      <m:math><m:ci>g</m:ci></m:math> = transverse center-to-center
     spacing between fastener gage lines, in.  </item>
    
     <item>
      The term 
	    <m:math>
	      <m:apply>
		<m:divide/>
		<m:apply>
		  <m:power/>
		  <m:ci>s</m:ci>
		  <m:cn>2</m:cn>
		</m:apply>
		<m:apply>
		  <m:times/>
		  <m:cn>4</m:cn>
		  <m:ci>g</m:ci>
		</m:apply>
	      </m:apply>
	    </m:math>
      is added for every non-straight segment    
     </item>
    </list>

   </section>  

  </content>
  
</document>
