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      <paper id="1" orientation="Portrait" width="850" height="1100" />
      <margins left="39" right="39" top="39" bottom="39" />
      <header alignment="Center" color="#a9a9a9">&amp;[DATE] &amp;[TIME] - &amp;[FILENAME]</header>
      <footer alignment="Center" color="#a9a9a9">&amp;[PAGENUM] / &amp;[COUNT]</footer>
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  <region id="0" left="234" top="0" width="279" height="31" color="#000000" bgColor="#ffffff" fontSize="14">
    <text lang="eng">
      <p bold="true" underline="true">AISC 360-10 - Chapter H</p>
    </text>
  </region>
  <region id="1" left="621" top="0" width="78" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>Eng: BMS</p>
    </text>
  </region>
  <region id="2" left="621" top="27" width="119" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>Date: 4/10/13</p>
    </text>
  </region>
  <region id="3" left="207" top="36" width="359" height="31" color="#000000" bgColor="#ffffff" fontSize="14">
    <text lang="eng">
      <p bold="true">H3. MEMBERS SUBJECT TO TORSION</p>
    </text>
  </region>
  <region id="4" left="621" top="54" width="78" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>Project:</p>
    </text>
  </region>
  <region id="5" left="216" top="63" width="348" height="31" color="#000000" bgColor="#ffffff" fontSize="14">
    <text lang="eng">
      <p bold="true">AND COMBINED TORSION,FLEXURE,</p>
    </text>
  </region>
  <region id="6" left="243" top="90" width="290" height="31" color="#000000" bgColor="#ffffff" fontSize="14">
    <text lang="eng">
      <p bold="true">SHEAR AND/OR AXIAL FORCE</p>
    </text>
  </region>
  <region id="7" left="171" top="144" width="120" height="34" color="#000000" bgColor="#ffffff" fontSize="16">
    <text lang="eng">
      <p bold="true">SECTION:</p>
    </text>
  </region>
  <region id="8" left="306" top="144" width="173" height="34" border="true" color="#000000" bgColor="#ffffff" fontSize="16">
    <text lang="eng">
      <p bold="true">HSS 12X6X1/4</p>
    </text>
  </region>
  <region id="9" left="0" top="180" width="86" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p underline="true">Variables</p>
    </text>
  </region>
  <region id="10" left="549" top="198" width="77" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">Φ.t</e>
        <e type="operand">0.90</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="11" left="639" top="198" width="107" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">E</e>
        <e type="operand">29000</e>
        <e type="operand" style="unit">ksi</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="12" left="0" top="207" width="115" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">h</e>
        <e type="operand">11.3005</e>
        <e type="operand" style="unit">in</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="13" left="198" top="207" width="73" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">B</e>
        <e type="operand">12</e>
        <e type="operand" style="unit">in</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="14" left="270" top="207" width="127" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>&gt;overall width</p>
    </text>
  </region>
  <region id="15" left="639" top="225" width="91" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">F.y</e>
        <e type="operand">46</e>
        <e type="operand" style="unit">ksi</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="16" left="0" top="234" width="98" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">t</e>
        <e type="operand">0.233</e>
        <e type="operand" style="unit">in</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="17" left="198" top="234" width="65" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">H</e>
        <e type="operand">6</e>
        <e type="operand" style="unit">in</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="18" left="270" top="234" width="135" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>&gt;overall height</p>
    </text>
  </region>
  <region id="19" left="0" top="261" width="82" height="41" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">h</e>
        <e type="operand">t</e>
        <e type="operator" args="2">/</e>
      </input>
      <result action="numeric">
        <e type="operand">48.5</e>
      </result>
    </math>
  </region>
  <region id="20" left="0" top="306" width="464" height="31" color="#000000" bgColor="#ffffff" fontSize="14">
    <text lang="eng">
      <p bold="true" underline="true">H3.1 Rectangular HSS Subject to Torsion</p>
    </text>
  </region>
  <region id="21" left="9" top="342" width="241" height="376" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">h</e>
        <e type="operand">t</e>
        <e type="operator" args="2">/</e>
        <e type="operand">2.45</e>
        <e type="operand">E</e>
        <e type="operand">F.y</e>
        <e type="operator" args="2">/</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">≤</e>
        <e type="operand">F.cr</e>
        <e type="operand">0.6</e>
        <e type="operand">F.y</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
        <e type="operand">2.45</e>
        <e type="operand">E</e>
        <e type="operand">F.y</e>
        <e type="operator" args="2">/</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operator" args="2">*</e>
        <e type="operand">h</e>
        <e type="operand">t</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">&lt;</e>
        <e type="operand">3.07</e>
        <e type="operand">E</e>
        <e type="operand">F.y</e>
        <e type="operator" args="2">/</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">≤</e>
        <e type="operand">F.cr</e>
        <e type="operand">0.6</e>
        <e type="operand">F.y</e>
        <e type="operator" args="2">*</e>
        <e type="operand">2.45</e>
        <e type="operand">E</e>
        <e type="operand">F.y</e>
        <e type="operator" args="2">/</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operator" args="2">*</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">*</e>
        <e type="operand">h</e>
        <e type="operand">t</e>
        <e type="operator" args="2">/</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">:</e>
        <e type="operand">3.07</e>
        <e type="operand">E</e>
        <e type="operand">F.y</e>
        <e type="operator" args="2">/</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operator" args="2">*</e>
        <e type="operand">h</e>
        <e type="operand">t</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">&lt;</e>
        <e type="operand">260</e>
        <e type="operator" args="2">≤</e>
        <e type="operand">F.cr</e>
        <e type="operand">0.458</e>
        <e type="operand">π</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operand">E</e>
        <e type="operator" args="2">*</e>
        <e type="operand">h</e>
        <e type="operand">t</e>
        <e type="operator" args="2">/</e>
        <e type="bracket">(</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">:</e>
        <e type="operand" style="string">NA</e>
        <e type="function" preserve="true" args="3">if</e>
        <e type="function" preserve="true" args="3">if</e>
        <e type="function" preserve="true" args="3">if</e>
      </input>
    </math>
  </region>
  <region id="22" left="261" top="351" width="61" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>(H3-3)</p>
    </text>
  </region>
  <region id="23" left="261" top="432" width="61" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>(H3-4)</p>
    </text>
  </region>
  <region id="24" left="270" top="567" width="61" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>(H3-5)</p>
    </text>
  </region>
  <region id="25" left="36" top="729" width="114" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">F.cr</e>
      </input>
      <contract>
        <e type="operand" style="unit">ksi</e>
      </contract>
      <result action="numeric">
        <e type="operand">27.6</e>
      </result>
    </math>
  </region>
  <region id="26" left="0" top="783" width="98" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p bold="true">User Note: </p>
    </text>
  </region>
  <region id="27" left="108" top="783" width="480" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>The torsional constant,C, may be conservatively taken as:</p>
    </text>
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  <region id="28" left="0" top="819" width="255" height="34" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">C</e>
        <e type="operand">2</e>
        <e type="operand">B</e>
        <e type="operand">t</e>
        <e type="operator" args="2">-</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">*</e>
        <e type="operand">H</e>
        <e type="operand">t</e>
        <e type="operator" args="2">-</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">*</e>
        <e type="operand">t</e>
        <e type="operator" args="2">*</e>
        <e type="operand">4.5</e>
        <e type="operand">4</e>
        <e type="operand">π</e>
        <e type="operator" args="2">-</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">*</e>
        <e type="operand">t</e>
        <e type="operand">3</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">-</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="29" left="261" top="819" width="108" height="33" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">C</e>
      </input>
      <contract>
        <e type="operand" style="unit">in</e>
        <e type="operand">3</e>
        <e type="operator" args="2">^</e>
      </contract>
      <result action="numeric">
        <e type="operand">31.57</e>
      </result>
    </math>
  </region>
  <region id="30" left="0" top="864" width="102" height="33" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">C</e>
        <e type="operand">31.6</e>
        <e type="operand" style="unit">in</e>
        <e type="operand">3</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="31" left="0" top="927" width="84" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">T.n</e>
        <e type="operand">F.cr</e>
        <e type="operand">C</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="32" left="117" top="936" width="61" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>(H3-1)</p>
    </text>
  </region>
  <region id="33" left="0" top="981" width="160" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">Φ.t</e>
        <e type="operand">T.n</e>
        <e type="operator" args="2">*</e>
      </input>
      <contract>
        <e type="operand" style="unit">kip</e>
        <e type="operand" style="unit">ft</e>
        <e type="operator" args="2">*</e>
      </contract>
      <result action="numeric">
        <e type="operand">65.41</e>
      </result>
    </math>
  </region>
  <region id="34" left="216" top="981" width="85" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">T.c</e>
        <e type="operand">Φ.t</e>
        <e type="operand">T.n</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="35" left="0" top="1053" width="522" height="31" color="#000000" bgColor="#ffffff" fontSize="14">
    <text lang="eng">
      <p bold="true" underline="true">H3.2 HSS Subject to Combined Torsion, Shear,</p>
    </text>
  </region>
  <region id="36" left="0" top="1080" width="290" height="31" color="#000000" bgColor="#ffffff" fontSize="14">
    <text lang="eng">
      <p bold="true" underline="true">Flexure, and Axial Force</p>
    </text>
  </region>
  <region id="37" left="0" top="1143" width="83" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">P.r</e>
        <e type="operand">0</e>
        <e type="operand" style="unit">kip</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="38" left="162" top="1143" width="299" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>&gt;required axial strength LRFD, kips</p>
    </text>
  </region>
  <region id="39" left="0" top="1179" width="108" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">P.c</e>
        <e type="operand">90.3</e>
        <e type="operand" style="unit">kip</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="40" left="162" top="1179" width="536" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>&gt;ΦPn design tensile or compressive strength Chapter D or E, kips</p>
    </text>
  </region>
  <region id="41" left="0" top="1215" width="105" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">M.r</e>
        <e type="operand">5</e>
        <e type="operand" style="unit">kip</e>
        <e type="operator" args="2">*</e>
        <e type="operand" style="unit">ft</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="42" left="162" top="1215" width="340" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>&gt;required flexural strength LRFD, kip-in</p>
    </text>
  </region>
  <region id="43" left="0" top="1251" width="122" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">M.c</e>
        <e type="operand">107</e>
        <e type="operand" style="unit">kip</e>
        <e type="operator" args="2">*</e>
        <e type="operand" style="unit">ft</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="44" left="162" top="1251" width="405" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>&gt;ΦbMn design flexural strength Chapter F, kip-in</p>
    </text>
  </region>
  <region id="45" left="0" top="1287" width="83" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">V.r</e>
        <e type="operand">5</e>
        <e type="operand" style="unit">kip</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="46" left="162" top="1287" width="299" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>&gt;required shear strength LRFD, kips</p>
    </text>
  </region>
  <region id="47" left="0" top="1323" width="91" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">V.c</e>
        <e type="operand">10</e>
        <e type="operand" style="unit">kip</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="48" left="162" top="1323" width="364" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>&gt;ΦvVn design shear strength Chapter G, kips</p>
    </text>
  </region>
  <region id="49" left="0" top="1359" width="105" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">T.r</e>
        <e type="operand">5</e>
        <e type="operand" style="unit">kip</e>
        <e type="operator" args="2">*</e>
        <e type="operand" style="unit">ft</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="50" left="162" top="1359" width="348" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>&gt;required torsional strength LRFD, kip-in</p>
    </text>
  </region>
  <region id="51" left="0" top="1395" width="136" height="32" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">T.c</e>
      </input>
      <contract>
        <e type="operand" style="unit">kip</e>
        <e type="operand" style="unit">ft</e>
        <e type="operator" args="2">*</e>
      </contract>
      <result action="numeric">
        <e type="operand">65.41</e>
      </result>
    </math>
  </region>
  <region id="52" left="162" top="1395" width="438" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>&gt;ΦtTn design torsional strength Section H3.1, kip-in</p>
    </text>
  </region>
  <region id="53" left="0" top="1485" width="221" height="68" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">P.r</e>
        <e type="operand">P.c</e>
        <e type="operator" args="2">/</e>
        <e type="operand">M.r</e>
        <e type="operand">M.c</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">+</e>
        <e type="bracket">(</e>
        <e type="operand">V.r</e>
        <e type="operand">V.c</e>
        <e type="operator" args="2">/</e>
        <e type="operand">T.r</e>
        <e type="operand">T.c</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">+</e>
        <e type="bracket">(</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">+</e>
      </input>
      <result action="numeric">
        <e type="operand">0.38</e>
      </result>
    </math>
  </region>
  <region id="54" left="207" top="1512" width="53" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>≤ 1.0</p>
    </text>
  </region>
</regions>