<?xml version="1.0" encoding="utf-8" standalone="yes"?>
<?application progid="SMath Studio Desktop" version="1.0.8206.25180"?>
<worksheet xmlns="http://smath.info/schemas/worksheet/1.0">
  <settings ppi="96">
    <identity>
      <id>4d80cf76-a5ff-4f22-bd72-be2cff298b68</id>
      <revision>2</revision>
    </identity>
    <calculation>
      <precision>2</precision>
      <exponentialThreshold>5</exponentialThreshold>
      <trailingZeros>true</trailingZeros>
      <significantDigitsMode>false</significantDigitsMode>
      <roundingMode>0</roundingMode>
      <approximateEqualAccuracy>1</approximateEqualAccuracy>
      <fractions>decimal</fractions>
    </calculation>
    <pageModel active="false" viewMode="2" printGrid="false" printAreas="true" simpleEqualsOnly="false" printBackgroundImages="true">
      <paper id="9" orientation="Portrait" width="827" height="1169" />
      <margins left="39" right="39" top="49" bottom="49" />
      <header alignment="Center" color="#a9a9a9">&amp;[DATE] &amp;[TIME] - &amp;[FILENAME]</header>
      <footer alignment="Center" color="#a9a9a9">&amp;[PAGENUM] / &amp;[COUNT]</footer>
      <backgrounds />
    </pageModel>
    <dependencies>
      <assembly name="SMath Studio Desktop" version="1.0.8206.25180" guid="a37cba83-b69c-4c71-9992-55ff666763bd" />
      <assembly name="MathRegion" version="1.11.8206.25180" guid="02f1ab51-215b-466e-a74d-5d8b1cf85e8d" />
      <assembly name="TextRegion" version="1.11.8206.25180" guid="485d28c5-349a-48b6-93be-12a35a1c1e39" />
    </dependencies>
  </settings>
  <regions type="content">
    <region left="99" top="18" width="246" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Courier New" fontSize="10">
        <content>
          <p>Table 1Properties of Sections</p>
        </content>
      </text>
    </region>
    <region left="99" top="54" width="294" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Courier New" fontSize="10">
        <content>
          <p>Case 27Regular Polygon with n Sides</p>
        </content>
      </text>
    </region>
    <region left="162" top="135" width="230" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Courier New" fontSize="10">
        <content>
          <p>Regular polygon withn sides</p>
        </content>
      </text>
    </region>
    <region left="9" top="414" width="118" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Courier New" fontSize="10">
        <content>
          <p>Notation file</p>
        </content>
      </text>
    </region>
    <region left="162" top="414" width="462" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Courier New" fontSize="10">
        <content>
          <p>Provides a description of Table 1 and the notation used.</p>
        </content>
      </text>
    </region>
    <region left="9" top="468" width="142" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Courier New" fontSize="10">
        <content>
          <p>Enter dimensions</p>
        </content>
      </text>
    </region>
    <region left="162" top="468" width="150" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Courier New" fontSize="10">
        <content>
          <p>Length of a side:</p>
        </content>
      </text>
    </region>
    <region left="315" top="468" width="66" height="24" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">a</e>
          <e type="operand">5</e>
          <e type="operand" style="unit">in</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="162" top="495" width="142" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Courier New" fontSize="10">
        <content>
          <p>Number of sides:</p>
        </content>
      </text>
    </region>
    <region left="315" top="495" width="46" height="24" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">n</e>
          <e type="operand">8</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="9" top="531" width="86" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Courier New" fontSize="10">
        <content>
          <p>Constants</p>
        </content>
      </text>
    </region>
    <region left="162" top="531" width="566" height="38" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Courier New" fontSize="10">
        <content>
          <p>The following constants are used to calculate the distances from the centroid to the extremities.</p>
        </content>
      </text>
    </region>
    <region left="162" top="603" width="94" height="41" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">α</e>
          <e type="operand">360</e>
          <e type="operand" style="unit">deg</e>
          <e type="operator" args="2">*</e>
          <e type="operand">2</e>
          <e type="operand">n</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="369" top="612" width="104" height="24" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">α</e>
        </input>
        <contract>
          <e type="operand" style="unit">deg</e>
        </contract>
        <result action="numeric">
          <e type="operand">22.50</e>
        </result>
      </math>
    </region>
    <region left="162" top="648" width="114" height="43" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">ρ.1</e>
          <e type="operand">a</e>
          <e type="operand">2</e>
          <e type="operand">α</e>
          <e type="function" args="1">sin</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="369" top="666" width="94" height="30" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">ρ.1</e>
        </input>
        <contract>
          <e type="operand" style="unit">in</e>
        </contract>
        <result action="numeric">
          <e type="operand">6.53</e>
        </result>
      </math>
    </region>
    <region left="162" top="702" width="116" height="43" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">ρ.2</e>
          <e type="operand">a</e>
          <e type="operand">2</e>
          <e type="operand">α</e>
          <e type="function" args="1">tan</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="369" top="711" width="94" height="30" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">ρ.2</e>
        </input>
        <contract>
          <e type="operand" style="unit">in</e>
        </contract>
        <result action="numeric">
          <e type="operand">6.04</e>
        </result>
      </math>
    </region>
    <region left="162" top="765" width="110" height="52" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">A</e>
          <e type="operand">a</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operand">n</e>
          <e type="operator" args="2">*</e>
          <e type="operand">4</e>
          <e type="operand">α</e>
          <e type="function" args="1">tan</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="9" top="783" width="46" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Courier New" fontSize="10">
        <content>
          <p>Area</p>
        </content>
      </text>
    </region>
    <region left="369" top="783" width="114" height="33" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">A</e>
        </input>
        <contract>
          <e type="operand" style="unit">in</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
        </contract>
        <result action="numeric">
          <e type="operand">120.71</e>
        </result>
      </math>
    </region>
    <region left="9" top="846" width="198" height="38" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Courier New" fontSize="10">
        <content>
          <p>Distances from<br />centroid to extremities</p>
        </content>
      </text>
    </region>
    <region left="117" top="882" width="560" height="62" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">y.1</e>
          <e type="operand">ρ.1</e>
          <e type="operand">α</e>
          <e type="operand">n</e>
          <e type="operand">1</e>
          <e type="operator" args="2">+</e>
          <e type="operand">2</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">*</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="function" args="1">cos</e>
          <e type="operator" args="2">*</e>
          <e type="operand">1</e>
          <e type="operator" args="1">-</e>
          <e type="bracket">(</e>
          <e type="operand">n</e>
          <e type="operator" args="2">^</e>
          <e type="operand">1</e>
          <e type="operator" args="1">-</e>
          <e type="operator" args="2">≡</e>
          <e type="bracket">(</e>
          <e type="operator" args="2">*</e>
          <e type="operand">ρ.1</e>
          <e type="operand">1</e>
          <e type="operator" args="1">-</e>
          <e type="bracket">(</e>
          <e type="operand">n</e>
          <e type="operand">2</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">^</e>
          <e type="operand">1</e>
          <e type="operator" args="1">-</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">ρ.2</e>
          <e type="operand">1</e>
          <e type="operator" args="1">-</e>
          <e type="bracket">(</e>
          <e type="operand">n</e>
          <e type="operand">2</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">^</e>
          <e type="operand">1</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="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="369" top="954" width="94" height="30" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">y.1</e>
        </input>
        <contract>
          <e type="operand" style="unit">in</e>
        </contract>
        <result action="numeric">
          <e type="operand">6.04</e>
        </result>
      </math>
    </region>
    <region left="117" top="981" width="560" height="62" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">y.2</e>
          <e type="operand">ρ.1</e>
          <e type="operand">α</e>
          <e type="operand">n</e>
          <e type="operand">1</e>
          <e type="operator" args="2">+</e>
          <e type="operand">2</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">*</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="function" args="1">cos</e>
          <e type="operator" args="2">*</e>
          <e type="operand">1</e>
          <e type="operator" args="1">-</e>
          <e type="bracket">(</e>
          <e type="operand">n</e>
          <e type="operator" args="2">^</e>
          <e type="operand">1</e>
          <e type="operator" args="1">-</e>
          <e type="operator" args="2">≡</e>
          <e type="bracket">(</e>
          <e type="operator" args="2">*</e>
          <e type="operand">ρ.2</e>
          <e type="operand">1</e>
          <e type="operator" args="1">-</e>
          <e type="bracket">(</e>
          <e type="operand">n</e>
          <e type="operand">2</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">^</e>
          <e type="operand">1</e>
          <e type="operator" args="1">-</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">ρ.1</e>
          <e type="operand">1</e>
          <e type="operator" args="1">-</e>
          <e type="bracket">(</e>
          <e type="operand">n</e>
          <e type="operand">2</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">^</e>
          <e type="operand">1</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="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="369" top="1053" width="94" height="30" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">y.2</e>
        </input>
        <contract>
          <e type="operand" style="unit">in</e>
        </contract>
        <result action="numeric">
          <e type="operand">6.53</e>
        </result>
      </math>
    </region>
    <region left="9" top="1107" width="158" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Courier New" fontSize="10">
        <content>
          <p>Moments of inertia</p>
        </content>
      </text>
    </region>
    <region left="162" top="1107" width="181" height="43" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">I.1</e>
          <e type="operand">1</e>
          <e type="operand">24</e>
          <e type="operator" args="2">/</e>
          <e type="operand">A</e>
          <e type="operator" args="2">*</e>
          <e type="operand">6</e>
          <e type="operand">ρ.1</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">*</e>
          <e type="operand">a</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">-</e>
          <e type="bracket">(</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="369" top="1107" width="128" height="39" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">I.1</e>
        </input>
        <contract>
          <e type="operand" style="unit">in</e>
          <e type="operand">4</e>
          <e type="operator" args="2">^</e>
        </contract>
        <result action="numeric">
          <e type="operand">1162.17</e>
        </result>
      </math>
    </region>
    <region left="369" top="1143" width="80" height="39" color="#000000" fontSize="10">
      <math error="2" errorLocation="0">
        <input>
          <e type="operand">I.2</e>
        </input>
        <contract>
          <e type="operand" style="unit">in</e>
          <e type="operand">4</e>
          <e type="operator" args="2">^</e>
        </contract>
        <result action="numeric">
          <e type="operand">#</e>
        </result>
      </math>
    </region>
    <region left="162" top="1152" width="56" height="30" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">I.2</e>
          <e type="operand">I.1</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="9" top="1215" width="302" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Courier New" fontSize="10">
        <content>
          <p>Radii of gyration about central axes</p>
        </content>
      </text>
    </region>
    <region left="162" top="1260" width="171" height="45" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">r.1</e>
          <e type="operand">1</e>
          <e type="operand">24</e>
          <e type="operator" args="2">/</e>
          <e type="operand">6</e>
          <e type="operand">ρ.1</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">*</e>
          <e type="operand">a</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">-</e>
          <e type="bracket">(</e>
          <e type="operator" args="2">*</e>
          <e type="function" args="1">sqrt</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="369" top="1269" width="68" height="30" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">r.1</e>
        </input>
        <contract>
          <e type="operand" style="unit">in</e>
        </contract>
        <result action="numeric">
          <e type="operand">#</e>
        </result>
      </math>
    </region>
    <region left="162" top="1314" width="56" height="30" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">r.2</e>
          <e type="operand">r.1</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="369" top="1314" width="68" height="30" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">r.2</e>
        </input>
        <contract>
          <e type="operand" style="unit">in</e>
        </contract>
        <result action="numeric">
          <e type="operand">#</e>
        </result>
      </math>
    </region>
    <region left="9" top="1359" width="190" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Courier New" fontSize="10">
        <content>
          <p>Plastic section moduli</p>
        </content>
      </text>
    </region>
    <region left="27" top="1395" width="62" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Courier New" fontSize="10">
        <content>
          <p>Case 8</p>
        </content>
      </text>
    </region>
    <region left="153" top="1395" width="390" height="38" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Courier New" fontSize="10">
        <content>
          <p>For n=3, see Case 8.<br />For n=4, see Cases 1 (square) and 12 (diamond).</p>
        </content>
      </text>
    </region>
    <region left="27" top="1431" width="62" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Courier New" fontSize="10">
        <content>
          <p>Case 1</p>
        </content>
      </text>
    </region>
    <region left="27" top="1458" width="70" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Courier New" fontSize="10">
        <content>
          <p>Case 12</p>
        </content>
      </text>
    </region>
    <region left="162" top="1503" width="86" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Courier New" fontSize="10">
        <content>
          <p>If n = 5:</p>
        </content>
      </text>
    </region>
    <region left="162" top="1530" width="176" height="39" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">Z.1</e>
          <e type="operand">0.8825</e>
          <e type="operand">ρ.1</e>
          <e type="operand">3</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">*</e>
          <e type="operand">n</e>
          <e type="operand">5</e>
          <e type="operator" args="2">≡</e>
          <e type="bracket">(</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="342" top="1530" width="78" height="39" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">Z.1</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">#</e>
        </result>
      </math>
    </region>
    <region left="162" top="1566" width="176" height="39" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">Z.2</e>
          <e type="operand">0.8825</e>
          <e type="operand">ρ.1</e>
          <e type="operand">3</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">*</e>
          <e type="operand">n</e>
          <e type="operand">5</e>
          <e type="operator" args="2">≡</e>
          <e type="bracket">(</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="342" top="1566" width="78" height="39" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">Z.2</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">#</e>
        </result>
      </math>
    </region>
    <region left="162" top="1620" width="310" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Courier New" fontSize="10">
        <content>
          <p>For an axis perpendicular to axis 1, </p>
        </content>
      </text>
    </region>
    <region left="414" top="1620" width="115" height="39" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">Z</e>
          <e type="operand">0.8838</e>
          <e type="operand">ρ.1</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 left="162" top="1656" width="502" height="38" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Courier New" fontSize="10">
        <content>
          <p>The location of this axis is 0.7007a from that side which is perpendicular to axis 1.</p>
        </content>
      </text>
    </region>
    <region left="162" top="1701" width="398" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Courier New" fontSize="10">
        <content>
          <p>For n ³ 6 a neutral axis of any inclination has:</p>
        </content>
      </text>
    </region>
    <region left="162" top="1737" width="386" height="54" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">Z</e>
          <e type="operand">ρ.1</e>
          <e type="operand">3</e>
          <e type="operator" args="2">^</e>
          <e type="operand">1.333</e>
          <e type="operand">13.908</e>
          <e type="operand">1</e>
          <e type="operand">n</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">12.528</e>
          <e type="operand">1</e>
          <e type="operand">n</e>
          <e type="operator" args="2">/</e>
          <e type="bracket">(</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="bracket">(</e>
          <e type="operator" args="2">*</e>
          <e type="operand">n</e>
          <e type="operand">6</e>
          <e type="operator" args="2">≥</e>
          <e type="bracket">(</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="162" top="1800" width="72" height="33" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">Z</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">#</e>
        </result>
      </math>
    </region>
  </regions>
</worksheet>