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        <content>
          <p style="font-size: 20px;">Chapter 12 Example Problems</p>
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    <region left="99" top="45" width="578" height="54" color="#000000" fontSize="15">
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        <content>
          <p style="font-size: 15px;">12.4.1 Thin Multielement Shells of Revolution: Maximum Stress Due to Internal Pressure </p>
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    <region left="162" top="108" width="598" height="143" color="#000000" fontSize="10">
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          <p>The vessel shown in quarter longitudinal section in Fig. 12.8a consists of a cylindrical shell (R = 24 in and t = 0.633 in) with conical ends (a = 45o and t = 0.755 in). The parts are welded together, and the material is steel, for which <br />E = 30(106) lbf/in2 and n = 0.25. It is required to determine the maximum stresses at the junction of the cylinder and cone due to an internal pressure of 300 lbf/in2.(This vessel corresponds to one for which the results of a supposedly precise analysis and experimentally determined stress values are available. See Ref. 17.)</p>
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    <region left="0" top="261" width="334" height="23" color="#000000" fontSize="10">
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          <p style="font-weight: bold;">Enter dimensions, properties and loading</p>
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        <raw format="png" encoding="base64"> </raw>
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    <region left="630" top="261" width="86" height="23" color="#000000" fontSize="10">
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        <content>
          <p>Fig. 12.8</p>
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          <e type="operand">E</e>
          <e type="operand">30</e>
          <e type="operand">10</e>
          <e type="operand">6</e>
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        <content>
          <p>Modulus of elasticity, E:</p>
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        <content>
          <p>Poisson's ratio, n:</p>
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      <math>
        <input>
          <e type="operand">ν</e>
          <e type="operand">0.25</e>
          <e type="operator" args="2">:</e>
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          <p>Radius of curvature, R:</p>
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    <region left="621" top="351" width="95" height="107" color="#000000">
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        <raw format="png" encoding="base64"> </raw>
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          <e type="operand">R</e>
          <e type="operand">24</e>
          <e type="operand" style="unit">in</e>
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          <p>Thickness of conical ends, t0:</p>
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          <e type="operand">t.0</e>
          <e type="operand">0.755</e>
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          <e type="operand">q</e>
          <e type="operand">300</e>
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          <p>Internal pressure, q:</p>
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          <p>Cone angle a:</p>
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          <e type="operand">α</e>
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          <p>Thickness of cylindrical shell, t1:</p>
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          <e type="operand">t.1</e>
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          <p style="font-weight: bold;">Calculation procedure</p>
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          <p>For the cone, Case 2a in Table 28 and Cases 4a and 4b in Table 30 can be used. The following conditions exist at the end of the cone: from Table 28, Case 2a, for the load T and pressure q: </p>
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          <p>Table 28, Case 2a</p>
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        <input>
          <e type="operand">σ.10</e>
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          <e type="operand">σ.10</e>
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          <e type="operand">1</e>
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          <e type="operand">13486.54</e>
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          <e type="operand">0.00</e>
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          <e type="operand">T</e>
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          <e type="operand">T</e>
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        <contract>
          <e type="operand" style="unit">lbf</e>
          <e type="operand" style="unit">in</e>
          <e type="operator" args="2">/</e>
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          <e type="operand">5091.17</e>
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        <input>
          <e type="operand">ΔR.0</e>
          <e type="operand">q</e>
          <e type="operand">R</e>
          <e type="operand">2</e>
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          <e type="operand">E</e>
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          <e type="operand">ΔR.0</e>
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          <e type="operand" style="unit">in</e>
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          <e type="operand">0.01</e>
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          <e type="operand">ψ.0</e>
          <e type="operand">3</e>
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          <e type="operand">ψ.0</e>
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          <p>Table 30, Case 4a</p>
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          <p>From Table 30, Case 4a, for the radial edge load Qo:</p>
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          <e type="operand">Q.o</e>
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          <e type="operand">R.A</e>
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          <e type="operand">0.25</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">:</e>
        </input>
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          <e type="operand">k.A</e>
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        <result action="numeric">
          <e type="operand">24.56</e>
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        <input>
          <e type="operand">β</e>
          <e type="operand">12</e>
          <e type="operand">1</e>
          <e type="operand">ν</e>
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          <e type="operator" args="2">^</e>
          <e type="operator" args="2">-</e>
          <e type="bracket">(</e>
          <e type="operator" args="2">*</e>
          <e type="bracket">(</e>
          <e type="operand">0.5</e>
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          <e type="operand">β</e>
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          <e type="operand">3.35</e>
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          <p>Only values at R = RA are needed for this solution. Therefore, the series solutions for the constants can be used to give </p>
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      </text>
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          <e type="operand">F.1A</e>
          <e type="operand">0</e>
          <e type="operator" args="2">:</e>
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          <e type="operand">F.2A</e>
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          <e type="operand">2.652</e>
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          <e type="operand">3.516</e>
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          <e type="operand">2.610</e>
          <e type="operand">k.A</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="operand">0.038</e>
          <e type="operand">k.A</e>
          <e type="operand">4</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 left="207" top="1287" width="58" height="30" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">F.3A</e>
          <e type="operand">0</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="207" top="1314" width="305" height="56" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">F.4A</e>
          <e type="operand">1</e>
          <e type="operand">3.359</e>
          <e type="operand">k.A</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">-</e>
          <e type="operand">5.641</e>
          <e type="operand">k.A</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">9.737</e>
          <e type="operand">k.A</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="operand">14.716</e>
          <e type="operand">k.A</e>
          <e type="operand">4</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>
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    <region left="207" top="1368" width="305" height="56" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">F.5A</e>
          <e type="operand">1</e>
          <e type="operand">3.359</e>
          <e type="operand">k.A</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">-</e>
          <e type="operand">7.266</e>
          <e type="operand">k.A</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">10.068</e>
          <e type="operand">k.A</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="operand">5.787</e>
          <e type="operand">k.A</e>
          <e type="operand">4</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 left="207" top="1422" width="297" height="56" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">F.6A</e>
          <e type="operand">1</e>
          <e type="operand">2.652</e>
          <e type="operand">k.A</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">-</e>
          <e type="operand">1.641</e>
          <e type="operand">k.A</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">0.290</e>
          <e type="operand">k.A</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="operand">2.211</e>
          <e type="operand">k.A</e>
          <e type="operand">4</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 left="207" top="1476" width="73" height="30" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">F.7A</e>
          <e type="operand">F.6A</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="207" top="1512" width="73" height="30" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">F.8A</e>
          <e type="operand">F.5A</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="207" top="1539" width="182" height="49" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">F.9A</e>
          <e type="operand">F.5A</e>
          <e type="operand">2</e>
          <e type="operand">2</e>
          <e type="function" args="1">sqrt</e>
          <e type="operator" args="2">*</e>
          <e type="operand">ν</e>
          <e type="operator" args="2">*</e>
          <e type="operand">k.A</e>
          <e type="operator" args="2">/</e>
          <e type="operand">F.2A</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">+</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="207" top="1584" width="80" height="30" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">F.10A</e>
          <e type="operand">F.6A</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="207" top="1620" width="378" height="33" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">F.1A</e>
          <e type="operand">F.2A</e>
          <e type="operand">F.3A</e>
          <e type="operand">F.4A</e>
          <e type="operand">F.5A</e>
          <e type="operand">1</e>
          <e type="operand">5</e>
          <e type="function" args="7">mat</e>
        </input>
        <result action="numeric">
          <e type="operand">0.00</e>
          <e type="operand">0.90</e>
          <e type="operand">0.00</e>
          <e type="operand">0.87</e>
          <e type="operand">0.87</e>
          <e type="operand">1</e>
          <e type="operand">5</e>
          <e type="function" args="7">mat</e>
        </result>
      </math>
    </region>
    <region left="207" top="1665" width="384" height="33" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">F.6A</e>
          <e type="operand">F.7A</e>
          <e type="operand">F.8A</e>
          <e type="operand">F.9A</e>
          <e type="operand">F.10A</e>
          <e type="operand">1</e>
          <e type="operand">5</e>
          <e type="function" args="7">mat</e>
        </input>
        <result action="numeric">
          <e type="operand">0.89</e>
          <e type="operand">0.89</e>
          <e type="operand">0.87</e>
          <e type="operand">0.90</e>
          <e type="operand">0.89</e>
          <e type="operand">1</e>
          <e type="operand">5</e>
          <e type="function" args="7">mat</e>
        </result>
      </math>
    </region>
    <region left="207" top="1701" width="67" height="30" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">C.1</e>
          <e type="operand">F.9A</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="459" top="1701" width="74" height="30" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">C.1</e>
        </input>
        <result action="numeric">
          <e type="operand">0.90</e>
        </result>
      </math>
    </region>
    <region left="207" top="1737" width="384" height="67" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">Q.o</e>
          <e type="function" args="1">ΔR.A1</e>
          <e type="operand">Q.o</e>
          <e type="operand">R.A</e>
          <e type="operator" args="2">*</e>
          <e type="operand">E</e>
          <e type="operand">t.0</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">/</e>
          <e type="operand">α</e>
          <e type="function" args="1">sin</e>
          <e type="operator" args="2">*</e>
          <e type="operand">k.A</e>
          <e type="operand">2</e>
          <e type="function" args="1">sqrt</e>
          <e type="operand">C.1</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">*</e>
          <e type="operand">F.4A</e>
          <e type="operand">4</e>
          <e type="operand">ν</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">*</e>
          <e type="operand">k.A</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">/</e>
          <e type="operand">F.2A</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="207" top="1791" width="235" height="50" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">Q.o</e>
          <e type="function" args="1">ΔR.A1</e>
        </input>
        <contract>
          <e type="operand">Q.o</e>
          <e type="bracket">(</e>
          <e type="operand" style="unit">in</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operand" style="unit">lbf</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">*</e>
        </contract>
        <result action="numeric">
          <e type="operand">1.26</e>
          <e type="operand">10</e>
          <e type="operand">5</e>
          <e type="operator" args="1">-</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">*</e>
        </result>
      </math>
    </region>
    <region left="207" top="1845" width="194" height="62" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">Q.o</e>
          <e type="function" args="1">ψ.A1</e>
          <e type="operand">Q.o</e>
          <e type="operand">R.A</e>
          <e type="operator" args="2">*</e>
          <e type="operand">β</e>
          <e type="operator" args="2">*</e>
          <e type="operand">E</e>
          <e type="operand">t.0</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">*</e>
          <e type="operand">C.1</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">/</e>
          <e type="operand">F.10A</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="207" top="1899" width="225" height="42" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">Q.o</e>
          <e type="function" args="1">ψ.A1</e>
        </input>
        <contract>
          <e type="operand">Q.o</e>
          <e type="bracket">(</e>
          <e type="operand" style="unit">in</e>
          <e type="operand" style="unit">lbf</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">*</e>
        </contract>
        <result action="numeric">
          <e type="operand">4.68</e>
          <e type="operand">10</e>
          <e type="operand">6</e>
          <e type="operator" args="1">-</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">*</e>
        </result>
      </math>
    </region>
    <region left="207" top="1953" width="125" height="31" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">N.1A</e>
          <e type="operand">Q.o</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>
        </input>
      </math>
    </region>
    <region left="567" top="1953" width="113" height="41" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">N.1A</e>
        </input>
        <contract>
          <e type="operand" style="unit">lbf</e>
          <e type="operand" style="unit">in</e>
          <e type="operator" args="2">/</e>
        </contract>
        <result action="numeric">
          <e type="operand">0.71</e>
        </result>
      </math>
    </region>
    <region left="207" top="1989" width="111" height="41" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">M.1A</e>
          <e type="operand">0</e>
          <e type="operand" style="unit">lbf</e>
          <e type="operator" args="2">*</e>
          <e type="operand" style="unit">in</e>
          <e type="operand" style="unit">in</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="207" top="2052" width="290" height="56" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">N.2A</e>
          <e type="operand">Q.o</e>
          <e type="operand">α</e>
          <e type="function" args="1">sin</e>
          <e type="operator" args="2">*</e>
          <e type="operand">k.A</e>
          <e type="operator" args="2">*</e>
          <e type="operand">2</e>
          <e type="function" args="1">sqrt</e>
          <e type="operand">C.1</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">/</e>
          <e type="operand">F.4A</e>
          <e type="operand">2</e>
          <e type="function" args="1">sqrt</e>
          <e type="operand">ν</e>
          <e type="operator" args="2">*</e>
          <e type="operand">k.A</e>
          <e type="operator" args="2">/</e>
          <e type="operand">F.8A</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="567" top="2070" width="109" height="30" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">N.2A</e>
        </input>
        <contract>
          <e type="operand">Q.o</e>
        </contract>
        <result action="numeric">
          <e type="operand">12.06</e>
        </result>
      </math>
    </region>
    <region left="207" top="2106" width="255" height="63" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">M.2A</e>
          <e type="operand">Q.o</e>
          <e type="operand">α</e>
          <e type="function" args="1">sin</e>
          <e type="operator" args="2">*</e>
          <e type="operand">1</e>
          <e type="operand">ν</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="operand">t.0</e>
          <e type="operator" args="2">*</e>
          <e type="operand">β</e>
          <e type="operand">C.1</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">/</e>
          <e type="operand">F.10A</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="567" top="2124" width="122" height="30" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">M.2A</e>
        </input>
        <contract>
          <e type="operand">Q.o</e>
          <e type="operand" style="unit">in</e>
          <e type="operator" args="2">*</e>
        </contract>
        <result action="numeric">
          <e type="operand">0.15</e>
        </result>
      </math>
    </region>
    <region left="9" top="2178" width="150" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Courier New" fontSize="10">
        <content>
          <p>Table 30, Case 4b</p>
        </content>
      </text>
    </region>
    <region left="162" top="2178" width="598" height="38" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Courier New" fontSize="10">
        <content>
          <p>From Table 30, Case 4b, for the edge moment MA and a unit applied couple Mo (solutions will be in terms of Mo):</p>
        </content>
      </text>
    </region>
    <region left="207" top="2241" width="93" height="41" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">M.o</e>
          <e type="operand" style="unit">lbf</e>
          <e type="operand" style="unit">in</e>
          <e type="operand" style="unit">in</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="207" top="2304" width="196" height="62" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">M.o</e>
          <e type="function" args="1">ΔR.A2</e>
          <e type="operand">M.o</e>
          <e type="operand">β</e>
          <e type="operator" args="2">*</e>
          <e type="operand">R.A</e>
          <e type="operator" args="2">*</e>
          <e type="operand">E</e>
          <e type="operand">t.0</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">*</e>
          <e type="operand">C.1</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">/</e>
          <e type="operand">F.7A</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="207" top="2376" width="213" height="47" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">M.o</e>
          <e type="function" args="1">ΔR.A2</e>
        </input>
        <contract>
          <e type="operand">M.o</e>
          <e type="operand" style="unit">in</e>
          <e type="operator" args="2">*</e>
          <e type="operand" style="unit">lbf</e>
          <e type="operator" args="2">/</e>
        </contract>
        <result action="numeric">
          <e type="operand">4.68</e>
          <e type="operand">10</e>
          <e type="operand">6</e>
          <e type="operator" args="1">-</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">*</e>
        </result>
      </math>
    </region>
    <region left="207" top="2448" width="251" height="72" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">M.o</e>
          <e type="function" args="1">ψ.A2</e>
          <e type="operand">M.o</e>
          <e type="operand">2</e>
          <e type="operator" args="2">*</e>
          <e type="operand">2</e>
          <e type="function" args="1">sqrt</e>
          <e type="operator" args="2">*</e>
          <e type="operand">β</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="bracket">(</e>
          <e type="operator" args="2">*</e>
          <e type="operand">R.A</e>
          <e type="operator" args="2">*</e>
          <e type="operand">E</e>
          <e type="operand">t.0</e>
          <e type="operand">3</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">*</e>
          <e type="operand">k.A</e>
          <e type="operator" args="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="operand">F.2A</e>
          <e type="operand">C.1</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="207" top="2529" width="233" height="42" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">M.o</e>
          <e type="function" args="1">ψ.A2</e>
        </input>
        <contract>
          <e type="operand">M.o</e>
          <e type="operand" style="unit">in</e>
          <e type="operand" style="unit">lbf</e>
          <e type="operand" style="unit">in</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">*</e>
        </contract>
        <result action="numeric">
          <e type="operand">3.40</e>
          <e type="operand">10</e>
          <e type="operand">6</e>
          <e type="operator" args="1">-</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">*</e>
        </result>
      </math>
    </region>
    <region left="207" top="2601" width="91" height="41" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">N.1A</e>
          <e type="operand">0</e>
          <e type="operand" style="unit">lbf</e>
          <e type="operand" style="unit">in</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="207" top="2664" width="153" height="47" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">N.2A</e>
          <e type="operand">M.o</e>
          <e type="operand">β</e>
          <e type="operand">t.0</e>
          <e type="operand">C.1</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">*</e>
          <e type="operand">F.7A</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="567" top="2664" width="105" height="47" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">N.2A</e>
        </input>
        <contract>
          <e type="operand">M.o</e>
          <e type="operand" style="unit">in</e>
          <e type="operator" args="2">/</e>
        </contract>
        <result action="numeric">
          <e type="operand">4.41</e>
        </result>
      </math>
    </region>
    <region left="207" top="2745" width="67" height="30" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">M.1A</e>
          <e type="operand">M.o</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="207" top="2790" width="251" height="60" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">M.2A</e>
          <e type="operand">M.o</e>
          <e type="operand">ν</e>
          <e type="operand">2</e>
          <e type="operand">2</e>
          <e type="function" args="1">sqrt</e>
          <e type="operator" args="2">*</e>
          <e type="operand">1</e>
          <e type="operand">ν</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="operand">k.A</e>
          <e type="operand">C.1</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">/</e>
          <e type="operand">F.2A</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="567" top="2808" width="101" height="30" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">M.2A</e>
        </input>
        <contract>
          <e type="operand">M.o</e>
        </contract>
        <result action="numeric">
          <e type="operand">0.36</e>
        </result>
      </math>
    </region>
    <region left="9" top="2826" width="18" height="24" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">.</e>
        </input>
      </math>
    </region>
    <region left="162" top="2862" width="598" height="68" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Courier New" fontSize="10">
        <content>
          <p>For the cylinder, Case 1c in Table 28 and Cases 8 and 10 in Table 29 can be used (It is assumed that the other end of the cylinder is far enough away so as to not affect the deformations and stresses at the cone-cylinder junction).</p>
        </content>
      </text>
    </region>
    <region left="207" top="2934" width="166" height="76" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">λ</e>
          <e type="operand">3</e>
          <e type="operand">1</e>
          <e type="operand">ν</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">-</e>
          <e type="operand">R.A</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operand">t.1</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="operator" args="2">*</e>
          <e type="bracket">(</e>
          <e type="operand">0.25</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="567" top="2952" width="111" height="33" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">λ</e>
        </input>
        <contract>
          <e type="operand" style="unit">in</e>
          <e type="operand">1</e>
          <e type="operator" args="1">-</e>
          <e type="operator" args="2">^</e>
        </contract>
        <result action="numeric">
          <e type="operand">0.33</e>
        </result>
      </math>
    </region>
    <region left="207" top="2997" width="140" height="67" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">D</e>
          <e type="operand">E</e>
          <e type="operand">t.1</e>
          <e type="operand">3</e>
          <e type="operator" args="2">^</e>
          <e type="operand">12</e>
          <e type="operand">1</e>
          <e type="operand">ν</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>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="567" top="3015" width="151" height="33" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">D</e>
        </input>
        <contract>
          <e type="operand" style="unit">lbf</e>
          <e type="operand" style="unit">in</e>
          <e type="operator" args="2">*</e>
        </contract>
        <result action="numeric">
          <e type="operand">6.76</e>
          <e type="operand">10</e>
          <e type="operand">5</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">*</e>
        </result>
      </math>
    </region>
    <region left="9" top="3123" width="150" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Courier New" fontSize="10">
        <content>
          <p>Table 28, Case 1c</p>
        </content>
      </text>
    </region>
    <region left="162" top="3123" width="574" height="38" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Courier New" fontSize="10">
        <content>
          <p>The following conditions exist at the end of the cylinder: from Table 28, Case 1c, for the axial load H and the pressure q:</p>
        </content>
      </text>
    </region>
    <region left="207" top="3177" width="364" height="56" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">σ.11</e>
          <e type="operand">σ.21</e>
          <e type="operand">σ'.11</e>
          <e type="operand">σ'.21</e>
          <e type="operand">1</e>
          <e type="operand">4</e>
          <e type="function" args="6">mat</e>
          <e type="operand">q</e>
          <e type="operand">R.A</e>
          <e type="operator" args="2">*</e>
          <e type="operand">2</e>
          <e type="operand">t.1</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">/</e>
          <e type="operand">q</e>
          <e type="operand">R.A</e>
          <e type="operator" args="2">*</e>
          <e type="operand">t.1</e>
          <e type="operator" args="2">/</e>
          <e type="operand">0</e>
          <e type="operand" style="unit">lbf</e>
          <e type="operand" style="unit">in</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">0</e>
          <e type="operand" style="unit">lbf</e>
          <e type="operand" style="unit">in</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">1</e>
          <e type="operand">4</e>
          <e type="function" args="6">mat</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="207" top="3258" width="417" height="50" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">σ.11</e>
          <e type="operand">σ.21</e>
          <e type="operand">σ'.11</e>
          <e type="operand">σ'.21</e>
          <e type="operand">1</e>
          <e type="operand">4</e>
          <e type="function" args="6">mat</e>
        </input>
        <contract>
          <e type="operand" style="unit">lbf</e>
          <e type="operand" style="unit">in</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">/</e>
        </contract>
        <result action="numeric">
          <e type="operand">5687.20</e>
          <e type="operand">11374.41</e>
          <e type="operand">0.00</e>
          <e type="operand">0.00</e>
          <e type="operand">1</e>
          <e type="operand">4</e>
          <e type="function" args="6">mat</e>
        </result>
      </math>
    </region>
    <region left="207" top="3303" width="86" height="30" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">H</e>
          <e type="operand">σ.11</e>
          <e type="operand">t.1</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="549" top="3303" width="124" height="41" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">H</e>
        </input>
        <contract>
          <e type="operand" style="unit">lbf</e>
          <e type="operand" style="unit">in</e>
          <e type="operator" args="2">/</e>
        </contract>
        <result action="numeric">
          <e type="operand">3600.00</e>
        </result>
      </math>
    </region>
    <region left="207" top="3330" width="159" height="62" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">ΔR.3</e>
          <e type="operand">q</e>
          <e type="operand">R.A</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="operand">t.1</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">/</e>
          <e type="operand">1</e>
          <e type="operand">ν</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="549" top="3348" width="102" height="30" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">ΔR.3</e>
        </input>
        <contract>
          <e type="operand" style="unit">in</e>
        </contract>
        <result action="numeric">
          <e type="operand">0.01</e>
        </result>
      </math>
    </region>
    <region left="207" top="3393" width="52" height="30" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">ψ.3</e>
          <e type="operand">0</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="9" top="3429" width="142" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Courier New" fontSize="10">
        <content>
          <p>Table 29, Case 8</p>
        </content>
      </text>
    </region>
    <region left="162" top="3429" width="414" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Courier New" fontSize="10">
        <content>
          <p>From Table 29, Case 8, for the radial end load Vo:</p>
        </content>
      </text>
    </region>
    <region left="207" top="3456" width="72" height="41" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">V.o</e>
          <e type="operand" style="unit">lbf</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="207" top="3501" width="142" height="56" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">V.o</e>
          <e type="function" args="1">ψ.A4</e>
          <e type="operand">V.o</e>
          <e type="operand">2</e>
          <e type="operand">D</e>
          <e type="operator" args="2">*</e>
          <e type="operand">λ</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="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="207" top="3546" width="205" height="47" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">V.o</e>
          <e type="function" args="1">ψ.A4</e>
        </input>
        <contract>
          <e type="operand">V.o</e>
          <e type="operand" style="unit">in</e>
          <e type="operator" args="2">*</e>
          <e type="operand" style="unit">lbf</e>
          <e type="operator" args="2">/</e>
        </contract>
        <result action="numeric">
          <e type="operand">6.70</e>
          <e type="operand">10</e>
          <e type="operand">6</e>
          <e type="operator" args="1">-</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">*</e>
        </result>
      </math>
    </region>
    <region left="207" top="3582" width="150" height="56" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">V.o</e>
          <e type="function" args="1">ΔR.A4</e>
          <e type="operand">V.o</e>
          <e type="operator" args="1">-</e>
          <e type="operand">2</e>
          <e type="operand">D</e>
          <e type="operator" args="2">*</e>
          <e type="operand">λ</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 left="207" top="3627" width="236" height="56" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">V.o</e>
          <e type="function" args="1">ΔR.A4</e>
        </input>
        <contract>
          <e type="operand">V.o</e>
          <e type="operand" style="unit">in</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">*</e>
          <e type="operand" style="unit">lbf</e>
          <e type="operator" args="2">/</e>
        </contract>
        <result action="numeric">
          <e type="operand">2.02</e>
          <e type="operand">10</e>
          <e type="operand">5</e>
          <e type="operator" args="1">-</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="1">-</e>
        </result>
      </math>
    </region>
    <region left="207" top="3690" width="93" height="50" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">σ.12</e>
          <e type="operand">0</e>
          <e type="operand" style="unit">lbf</e>
          <e type="operand" style="unit">in</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="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="549" top="3690" width="101" height="50" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">σ'.12</e>
          <e type="operand">0</e>
          <e type="operand" style="unit">lbf</e>
          <e type="operand" style="unit">in</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="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="207" top="3744" width="168" height="41" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">V.o</e>
          <e type="function" args="1">σ.22</e>
          <e type="operand">V.o</e>
          <e type="function" args="1">ΔR.A4</e>
          <e type="operand">E</e>
          <e type="operand">R</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="549" top="3744" width="101" height="50" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">σ'.22</e>
          <e type="operand">0</e>
          <e type="operand" style="unit">lbf</e>
          <e type="operand" style="unit">in</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="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="207" top="3789" width="404" height="47" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">σ.12</e>
          <e type="operand">σ'.12</e>
          <e type="operand">V.o</e>
          <e type="function" args="1">σ.22</e>
          <e type="operand">σ'.22</e>
          <e type="operand">1</e>
          <e type="operand">4</e>
          <e type="function" args="6">mat</e>
        </input>
        <contract>
          <e type="operand">V.o</e>
          <e type="operand" style="unit">in</e>
          <e type="operator" args="2">/</e>
        </contract>
        <result action="numeric">
          <e type="operand">0.00</e>
          <e type="operand">0.00</e>
          <e type="operand">25.19</e>
          <e type="operator" args="1">-</e>
          <e type="operand">0.00</e>
          <e type="operand">1</e>
          <e type="operand">4</e>
          <e type="function" args="6">mat</e>
        </result>
      </math>
    </region>
    <region left="9" top="3852" width="150" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Courier New" fontSize="10">
        <content>
          <p>Table 29, Case 10</p>
        </content>
      </text>
    </region>
    <region left="162" top="3852" width="382" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Courier New" fontSize="10">
        <content>
          <p>From Table 29, Case 10, for the end moment Mo:</p>
        </content>
      </text>
    </region>
    <region left="207" top="3870" width="115" height="47" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">M.o</e>
          <e type="function" args="1">ψ.A5</e>
          <e type="operand">M.o</e>
          <e type="operator" args="1">-</e>
          <e type="operand">D</e>
          <e type="operand">λ</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="207" top="3906" width="205" height="47" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">M.o</e>
          <e type="function" args="1">ψ.A5</e>
        </input>
        <contract>
          <e type="operand">M.o</e>
          <e type="operand" style="unit">lbf</e>
          <e type="operator" args="2">/</e>
        </contract>
        <result action="numeric">
          <e type="operand">4.45</e>
          <e type="operand">10</e>
          <e type="operand">6</e>
          <e type="operator" args="1">-</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="1">-</e>
        </result>
      </math>
    </region>
    <region left="207" top="3942" width="150" height="56" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">M.o</e>
          <e type="function" args="1">ΔR.A5</e>
          <e type="operand">M.o</e>
          <e type="operand">2</e>
          <e type="operand">D</e>
          <e type="operator" args="2">*</e>
          <e type="operand">λ</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="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="207" top="3987" width="213" height="47" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">M.o</e>
          <e type="function" args="1">ΔR.A5</e>
        </input>
        <contract>
          <e type="operand">M.o</e>
          <e type="operand" style="unit">in</e>
          <e type="operator" args="2">*</e>
          <e type="operand" style="unit">lbf</e>
          <e type="operator" args="2">/</e>
        </contract>
        <result action="numeric">
          <e type="operand">6.70</e>
          <e type="operand">10</e>
          <e type="operand">6</e>
          <e type="operator" args="1">-</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">*</e>
        </result>
      </math>
    </region>
    <region left="207" top="4032" width="93" height="50" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">σ.13</e>
          <e type="operand">0</e>
          <e type="operand" style="unit">lbf</e>
          <e type="operand" style="unit">in</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="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="207" top="4068" width="167" height="62" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">M.o</e>
          <e type="function" args="1">σ.23</e>
          <e type="operand">2</e>
          <e type="operand">M.o</e>
          <e type="operator" args="2">*</e>
          <e type="operand">λ</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">*</e>
          <e type="operand">R</e>
          <e type="operator" args="2">*</e>
          <e type="operand">t.1</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="549" top="4068" width="147" height="56" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">M.o</e>
          <e type="function" args="1">σ.23</e>
        </input>
        <contract>
          <e type="operand">M.o</e>
          <e type="operand" style="unit">in</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">/</e>
        </contract>
        <result action="numeric">
          <e type="operand">8.37</e>
        </result>
      </math>
    </region>
    <region left="207" top="4122" width="140" height="62" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">M.o</e>
          <e type="function" args="1">σ'.13</e>
          <e type="operand">6</e>
          <e type="operator" args="1">-</e>
          <e type="operand">M.o</e>
          <e type="operator" args="2">*</e>
          <e type="operand">t.1</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="549" top="4131" width="175" height="56" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">M.o</e>
          <e type="function" args="1">σ'.13</e>
        </input>
        <contract>
          <e type="operand">M.o</e>
          <e type="operand" style="unit">in</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">/</e>
        </contract>
        <result action="numeric">
          <e type="operand">14.97</e>
          <e type="operator" args="1">-</e>
        </result>
      </math>
    </region>
    <region left="207" top="4203" width="172" height="32" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">M.o</e>
          <e type="function" args="1">σ'.23</e>
          <e type="operand">ν</e>
          <e type="operand">M.o</e>
          <e type="function" args="1">σ'.13</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="549" top="4203" width="167" height="56" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">M.o</e>
          <e type="function" args="1">σ'.23</e>
        </input>
        <contract>
          <e type="operand">M.o</e>
          <e type="operand" style="unit">in</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">/</e>
        </contract>
        <result action="numeric">
          <e type="operand">3.74</e>
          <e type="operator" args="1">-</e>
        </result>
      </math>
    </region>
    <region left="162" top="4257" width="582" height="83" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Courier New" fontSize="10">
        <content>
          <p>Now solve for Qo, Vo and Mo. Equate the sum of the radial deflections for the end of the cone to the sum for the cylinder; equate the sum of the meridian cone rotations to the sum of the meridian cylinder rotations; and equate the radial forces. Solve the system of equations with the aid of the following constants:</p>
        </content>
      </text>
    </region>
    <region left="207" top="4347" width="117" height="55" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">k.01</e>
          <e type="operand">Q.o</e>
          <e type="function" args="1">ΔR.A1</e>
          <e type="operand">Q.o</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="441" top="4347" width="117" height="55" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">k.02</e>
          <e type="operand">M.o</e>
          <e type="function" args="1">ΔR.A2</e>
          <e type="operand">M.o</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="207" top="4401" width="117" height="55" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">k.04</e>
          <e type="operand">V.o</e>
          <e type="function" args="1">ΔR.A4</e>
          <e type="operand">V.o</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="441" top="4401" width="117" height="55" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">k.05</e>
          <e type="operand">M.o</e>
          <e type="function" args="1">ΔR.A5</e>
          <e type="operand">M.o</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="207" top="4455" width="109" height="55" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">k.11</e>
          <e type="operand">Q.o</e>
          <e type="function" args="1">ψ.A1</e>
          <e type="operand">Q.o</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="441" top="4455" width="109" height="55" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">k.12</e>
          <e type="operand">M.o</e>
          <e type="function" args="1">ψ.A2</e>
          <e type="operand">M.o</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="207" top="4500" width="109" height="57" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">k.14</e>
          <e type="operand">V.o</e>
          <e type="function" args="1">ψ.A4</e>
          <e type="operand">V.o</e>
          <e type="bracket">(</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="441" top="4500" width="109" height="55" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">k.15</e>
          <e type="operand">M.o</e>
          <e type="function" args="1">ψ.A5</e>
          <e type="operand">M.o</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="216" top="4581" width="85" height="41" color="#000000" fontSize="10">
      <math evaluate="false">
        <input>
          <e type="operand">Q.o</e>
          <e type="operand">1</e>
          <e type="operand" style="unit">lbf</e>
          <e type="operand" style="unit">in</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="324" top="4581" width="85" height="41" color="#000000" fontSize="10">
      <math evaluate="false">
        <input>
          <e type="operand">V.o</e>
          <e type="operand">1</e>
          <e type="operand" style="unit">lbf</e>
          <e type="operand" style="unit">in</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="450" top="4581" width="93" height="41" color="#000000" fontSize="10">
      <math evaluate="false">
        <input>
          <e type="operand">M.o</e>
          <e type="operand" style="unit">lbf</e>
          <e type="operand" style="unit">in</e>
          <e type="operand" style="unit">in</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="216" top="4626" width="187" height="32" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">Q.o</e>
          <e type="operand">V.o</e>
          <e type="operand">M.o</e>
          <e type="function" args="3">Clear</e>
        </input>
        <result action="numeric">
          <e type="operand">1.00</e>
        </result>
      </math>
    </region>
    <region left="198" top="4653" width="374" height="128" color="#000000" fontSize="10">
      <mathcadblock width="364" height="120">
        <input>
          <e type="operand">system</e>
        </input>
      </mathcadblock>
    </region>
    <region left="207" top="4671" width="331" height="30" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">ΔR.0</e>
          <e type="operand">k.01</e>
          <e type="operand">Q.o</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">+</e>
          <e type="operand">k.02</e>
          <e type="operand">M.o</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">+</e>
          <e type="operand">ΔR.3</e>
          <e type="operand">k.04</e>
          <e type="operand">V.o</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">+</e>
          <e type="operand">k.05</e>
          <e type="operand">M.o</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">+</e>
          <e type="operator" args="2">≡</e>
        </input>
      </math>
    </region>
    <region left="207" top="4698" width="315" height="30" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">ψ.0</e>
          <e type="operand">k.11</e>
          <e type="operand">Q.o</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">+</e>
          <e type="operand">k.12</e>
          <e type="operand">M.o</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">+</e>
          <e type="operand">ψ.3</e>
          <e type="operand">k.14</e>
          <e type="operand">V.o</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">+</e>
          <e type="operand">k.15</e>
          <e type="operand">M.o</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">+</e>
          <e type="operator" args="2">≡</e>
        </input>
      </math>
    </region>
    <region left="207" top="4734" width="143" height="31" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">Q.o</e>
          <e type="operand">T</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="operand">V.o</e>
          <e type="operator" args="2">≡</e>
        </input>
      </math>
    </region>
    <region left="198" top="4797" width="316" height="40" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">system</e>
          <e type="function" args="1">sys2mat</e>
          <e type="function" args="1">Unknowns</e>
          <e type="function" args="1">transpose</e>
        </input>
        <result action="symbolic">
          <e type="operand">M.o</e>
          <e type="operand">Q.o</e>
          <e type="operand">V.o</e>
          <e type="operand">1</e>
          <e type="operand">3</e>
          <e type="function" args="5">mat</e>
        </result>
      </math>
    </region>
    <region left="198" top="4824" width="444" height="126" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">M.o</e>
          <e type="operand">Q.o</e>
          <e type="operand">V.o</e>
          <e type="operand">1</e>
          <e type="operand">3</e>
          <e type="function" args="5">mat</e>
          <e type="operand">system</e>
          <e type="function" args="1">sys2mat</e>
          <e type="operand" style="unit">lbf</e>
          <e type="operand" style="unit">in</e>
          <e type="operand" style="unit">in</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">*</e>
          <e type="operand" style="unit">lbf</e>
          <e type="operand" style="unit">in</e>
          <e type="operator" args="2">/</e>
          <e type="operand" style="unit">lbf</e>
          <e type="operand" style="unit">in</e>
          <e type="operator" args="2">/</e>
          <e type="operand">3</e>
          <e type="operand">1</e>
          <e type="function" args="5">mat</e>
          <e type="operand">10</e>
          <e type="operand">6</e>
          <e type="operator" args="1">-</e>
          <e type="operator" args="2">^</e>
          <e type="function" args="3">FindRoot</e>
          <e type="function" args="1">transpose</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="207" top="4959" width="143" height="41" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">Q.o</e>
        </input>
        <contract>
          <e type="operand" style="unit">lbf</e>
          <e type="operand" style="unit">in</e>
          <e type="operator" args="2">/</e>
        </contract>
        <result action="numeric">
          <e type="operand">2110.01</e>
          <e type="operator" args="1">-</e>
        </result>
      </math>
    </region>
    <region left="549" top="4959" width="130" height="41" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">V.o</e>
        </input>
        <contract>
          <e type="operand" style="unit">lbf</e>
          <e type="operand" style="unit">in</e>
          <e type="operator" args="2">/</e>
        </contract>
        <result action="numeric">
          <e type="operand">1489.99</e>
        </result>
      </math>
    </region>
    <region left="207" top="4995" width="151" height="41" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">M.o</e>
        </input>
        <contract>
          <e type="operand" style="unit">lbf</e>
          <e type="operand" style="unit">in</e>
          <e type="operand" style="unit">in</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">*</e>
        </contract>
        <result action="numeric">
          <e type="operand">2443.81</e>
        </result>
      </math>
    </region>
    <region left="162" top="5031" width="142" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Courier New" fontSize="10">
        <content>
          <p>In the cylinder:</p>
        </content>
      </text>
    </region>
    <region left="207" top="5058" width="145" height="30" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">σ.1</e>
          <e type="operand">σ.11</e>
          <e type="operand">σ.12</e>
          <e type="operator" args="2">+</e>
          <e type="operand">σ.13</e>
          <e type="operator" args="2">+</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="549" top="5058" width="132" height="50" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">σ.1</e>
        </input>
        <contract>
          <e type="operand" style="unit">lbf</e>
          <e type="operand" style="unit">in</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">/</e>
        </contract>
        <result action="numeric">
          <e type="operand">5687.20</e>
        </result>
      </math>
    </region>
    <region left="207" top="5094" width="209" height="32" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">σ.2</e>
          <e type="operand">σ.21</e>
          <e type="operand">V.o</e>
          <e type="function" args="1">σ.22</e>
          <e type="operator" args="2">+</e>
          <e type="operand">M.o</e>
          <e type="function" args="1">σ.23</e>
          <e type="operator" args="2">+</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="549" top="5094" width="145" height="50" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">σ.2</e>
        </input>
        <contract>
          <e type="operand" style="unit">lbf</e>
          <e type="operand" style="unit">in</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">/</e>
        </contract>
        <result action="numeric">
          <e type="operand">5708.17</e>
          <e type="operator" args="1">-</e>
        </result>
      </math>
    </region>
    <region left="207" top="5139" width="209" height="32" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">σ'.1</e>
          <e type="operand">σ'.11</e>
          <e type="operand">σ'.12</e>
          <e type="operator" args="2">+</e>
          <e type="operand">M.o</e>
          <e type="function" args="1">σ'.13</e>
          <e type="operator" args="2">+</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="549" top="5139" width="161" height="50" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">σ'.1</e>
        </input>
        <contract>
          <e type="operand" style="unit">lbf</e>
          <e type="operand" style="unit">in</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">/</e>
        </contract>
        <result action="numeric">
          <e type="operand">36594.15</e>
          <e type="operator" args="1">-</e>
        </result>
      </math>
    </region>
    <region left="207" top="5184" width="209" height="32" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">σ'.2</e>
          <e type="operand">σ'.21</e>
          <e type="operand">σ'.22</e>
          <e type="operator" args="2">+</e>
          <e type="operand">M.o</e>
          <e type="function" args="1">σ'.23</e>
          <e type="operator" args="2">+</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="549" top="5184" width="153" height="50" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">σ'.2</e>
        </input>
        <contract>
          <e type="operand" style="unit">lbf</e>
          <e type="operand" style="unit">in</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">/</e>
        </contract>
        <result action="numeric">
          <e type="operand">9148.54</e>
          <e type="operator" args="1">-</e>
        </result>
      </math>
    </region>
    <region left="162" top="5247" width="502" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Courier New" fontSize="10">
        <content>
          <p>The combined hoop stresses on the outside/inside are sho/shi:</p>
        </content>
      </text>
    </region>
    <region left="207" top="5283" width="108" height="30" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">σ.ho</e>
          <e type="operand">σ.2</e>
          <e type="operand">σ'.2</e>
          <e type="operator" args="2">+</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="549" top="5283" width="159" height="50" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">σ.ho</e>
        </input>
        <contract>
          <e type="operand" style="unit">lbf</e>
          <e type="operand" style="unit">in</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">/</e>
        </contract>
        <result action="numeric">
          <e type="operand">14856.71</e>
          <e type="operator" args="1">-</e>
        </result>
      </math>
    </region>
    <region left="207" top="5328" width="106" height="30" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">σ.hi</e>
          <e type="operand">σ.2</e>
          <e type="operand">σ'.2</e>
          <e type="operator" args="2">-</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="549" top="5328" width="139" height="50" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">σ.hi</e>
        </input>
        <contract>
          <e type="operand" style="unit">lbf</e>
          <e type="operand" style="unit">in</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">/</e>
        </contract>
        <result action="numeric">
          <e type="operand">3440.36</e>
        </result>
      </math>
    </region>
    <region left="162" top="5373" width="550" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Courier New" fontSize="10">
        <content>
          <p>The combined meridional stresses on the outside/inside are smo/smi:</p>
        </content>
      </text>
    </region>
    <region left="207" top="5409" width="108" height="30" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">σ.mo</e>
          <e type="operand">σ.1</e>
          <e type="operand">σ'.1</e>
          <e type="operator" args="2">+</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="549" top="5409" width="159" height="50" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">σ.mo</e>
        </input>
        <contract>
          <e type="operand" style="unit">lbf</e>
          <e type="operand" style="unit">in</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">/</e>
        </contract>
        <result action="numeric">
          <e type="operand">30906.95</e>
          <e type="operator" args="1">-</e>
        </result>
      </math>
    </region>
    <region left="207" top="5463" width="106" height="30" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">σ.mi</e>
          <e type="operand">σ.1</e>
          <e type="operand">σ'.1</e>
          <e type="operator" args="2">-</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="549" top="5463" width="147" height="50" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">σ.mi</e>
        </input>
        <contract>
          <e type="operand" style="unit">lbf</e>
          <e type="operand" style="unit">in</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">/</e>
        </contract>
        <result action="numeric">
          <e type="operand">42281.36</e>
        </result>
      </math>
    </region>
    <region left="162" top="5508" width="190" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Courier New" fontSize="10">
        <content>
          <p>Similarly in the cone:</p>
        </content>
      </text>
    </region>
    <region left="207" top="5544" width="162" height="54" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">σ.1</e>
          <e type="operand">σ.10</e>
          <e type="operand">α</e>
          <e type="function" args="1">sin</e>
          <e type="operand">Q.o</e>
          <e type="operator" args="2">*</e>
          <e type="operand">t.0</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">+</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="549" top="5553" width="132" height="50" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">σ.1</e>
        </input>
        <contract>
          <e type="operand" style="unit">lbf</e>
          <e type="operand" style="unit">in</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">/</e>
        </contract>
        <result action="numeric">
          <e type="operand">4767.11</e>
        </result>
      </math>
    </region>
    <region left="207" top="5598" width="341" height="144" color="#000000" fontSize="10">
      <math breaking="40">
        <input>
          <e type="operand">σ.2</e>
          <e type="operand">σ.20</e>
          <e type="operand">Q.o</e>
          <e type="operand">α</e>
          <e type="function" args="1">sin</e>
          <e type="operator" args="2">*</e>
          <e type="operand">k.A</e>
          <e type="operator" args="2">*</e>
          <e type="operand">2</e>
          <e type="function" args="1">sqrt</e>
          <e type="operand">C.1</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">/</e>
          <e type="operand">F.4A</e>
          <e type="operand">2</e>
          <e type="function" args="1">sqrt</e>
          <e type="operand">ν</e>
          <e type="operator" args="2">*</e>
          <e type="operand">k.A</e>
          <e type="operator" args="2">/</e>
          <e type="operand">F.8A</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">t.0</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">+</e>
          <e type="operand">M.o</e>
          <e type="operand">β</e>
          <e type="operand">t.0</e>
          <e type="operand">C.1</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">/</e>
          <e type="operand">F.7A</e>
          <e type="operator" args="2">*</e>
          <e type="bracket">(</e>
          <e type="operator" args="2">*</e>
          <e type="operand">t.0</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">+</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="549" top="5625" width="145" height="50" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">σ.2</e>
        </input>
        <contract>
          <e type="operand" style="unit">lbf</e>
          <e type="operand" style="unit">in</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">/</e>
        </contract>
        <result action="numeric">
          <e type="operand">5936.73</e>
          <e type="operator" args="1">-</e>
        </result>
      </math>
    </region>
    <region left="189" top="5742" width="192" height="62" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">σ'.1</e>
          <e type="operand">σ'.10</e>
          <e type="operand">σ'.11</e>
          <e type="operator" args="2">+</e>
          <e type="operand">6</e>
          <e type="operand">M.o</e>
          <e type="operand">t.0</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="operator" args="2">-</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="549" top="5751" width="161" height="50" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">σ'.1</e>
        </input>
        <contract>
          <e type="operand" style="unit">lbf</e>
          <e type="operand" style="unit">in</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">/</e>
        </contract>
        <result action="numeric">
          <e type="operand">25723.21</e>
          <e type="operator" args="1">-</e>
        </result>
      </math>
    </region>
    <region left="189" top="5823" width="356" height="133" color="#000000" fontSize="10">
      <math breaking="58">
        <input>
          <e type="operand">σ'.2</e>
          <e type="operand">σ'.20</e>
          <e type="operand">Q.o</e>
          <e type="operand">α</e>
          <e type="function" args="1">sin</e>
          <e type="operator" args="2">*</e>
          <e type="operand">1</e>
          <e type="operand">ν</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="operand">t.0</e>
          <e type="operator" args="2">*</e>
          <e type="operand">β</e>
          <e type="operand">C.1</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">/</e>
          <e type="operand">F.10A</e>
          <e type="operator" args="2">*</e>
          <e type="operand">6</e>
          <e type="operand">t.0</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="operator" args="2">-</e>
          <e type="operand">M.o</e>
          <e type="operator" args="1">-</e>
          <e type="bracket">(</e>
          <e type="operand">ν</e>
          <e type="operand">2</e>
          <e type="operand">2</e>
          <e type="function" args="1">sqrt</e>
          <e type="operator" args="2">*</e>
          <e type="operand">1</e>
          <e type="operand">ν</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="operand">k.A</e>
          <e type="operand">C.1</e>
          <e type="operator" args="2">*</e>
          <e type="operator" args="2">/</e>
          <e type="operand">F.2A</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">6</e>
          <e type="operand">t.0</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="operator" args="2">+</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="549" top="5841" width="153" height="50" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">σ'.2</e>
        </input>
        <contract>
          <e type="operand" style="unit">lbf</e>
          <e type="operand" style="unit">in</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">/</e>
        </contract>
        <result action="numeric">
          <e type="operand">5906.55</e>
          <e type="operator" args="1">-</e>
        </result>
      </math>
    </region>
    <region left="162" top="5958" width="502" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Courier New" fontSize="10">
        <content>
          <p>The combined hoop stresses on the outside/inside are sho/shi:</p>
        </content>
      </text>
    </region>
    <region left="549" top="5985" width="159" height="50" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">σ.ho</e>
        </input>
        <contract>
          <e type="operand" style="unit">lbf</e>
          <e type="operand" style="unit">in</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">/</e>
        </contract>
        <result action="numeric">
          <e type="operand">14856.71</e>
          <e type="operator" args="1">-</e>
        </result>
      </math>
    </region>
    <region left="189" top="5994" width="108" height="30" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">σ.ho</e>
          <e type="operand">σ.2</e>
          <e type="operand">σ'.2</e>
          <e type="operator" args="2">+</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="549" top="6021" width="139" height="50" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">σ.hi</e>
        </input>
        <contract>
          <e type="operand" style="unit">lbf</e>
          <e type="operand" style="unit">in</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">/</e>
        </contract>
        <result action="numeric">
          <e type="operand">3440.36</e>
        </result>
      </math>
    </region>
    <region left="189" top="6030" width="106" height="30" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">σ.hi</e>
          <e type="operand">σ.2</e>
          <e type="operand">σ'.2</e>
          <e type="operator" args="2">-</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="162" top="6075" width="550" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Courier New" fontSize="10">
        <content>
          <p>The combined meridional stresses on the outside/inside are smo/smi:</p>
        </content>
      </text>
    </region>
    <region left="540" top="6093" width="159" height="50" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">σ.mo</e>
        </input>
        <contract>
          <e type="operand" style="unit">lbf</e>
          <e type="operand" style="unit">in</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">/</e>
        </contract>
        <result action="numeric">
          <e type="operand">30906.95</e>
          <e type="operator" args="1">-</e>
        </result>
      </math>
    </region>
    <region left="189" top="6102" width="108" height="30" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">σ.mo</e>
          <e type="operand">σ.1</e>
          <e type="operand">σ'.1</e>
          <e type="operator" args="2">+</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="540" top="6129" width="147" height="50" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">σ.mi</e>
        </input>
        <contract>
          <e type="operand" style="unit">lbf</e>
          <e type="operand" style="unit">in</e>
          <e type="operand">2</e>
          <e type="operator" args="2">^</e>
          <e type="operator" args="2">/</e>
        </contract>
        <result action="numeric">
          <e type="operand">42281.36</e>
        </result>
      </math>
    </region>
    <region left="189" top="6138" width="106" height="30" color="#000000" fontSize="10">
      <math>
        <input>
          <e type="operand">σ.mi</e>
          <e type="operand">σ.1</e>
          <e type="operand">σ'.1</e>
          <e type="operator" args="2">-</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region left="162" top="6201" width="582" height="53" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Courier New" fontSize="10">
        <content>
          <p>These stress values are in substantial agreement with the computed and experimental values cited in Refs. 17 and 26. Note that the radial deflections are much less than the wall thicknesses.</p>
        </content>
      </text>
    </region>
    <region left="9" top="6318" width="94" height="23" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Courier New" fontSize="10">
        <content>
          <p>References</p>
        </content>
      </text>
    </region>
    <region left="162" top="6318" width="598" height="53" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Courier New" fontSize="10">
        <content>
          <p>Ref. 17. O'Brien, G. J., E. Wetterstrom, M.G. Dykhuizen, and R. G. Sturm: Design Correlations for Cylindrical Pressure Vessels with Conical or Toriconical Heads, Weld. Res. Suppl., vol. 15, no. 7, p. 336, 1950.</p>
        </content>
      </text>
    </region>
    <region left="162" top="6408" width="550" height="38" color="#000000" fontSize="10">
      <text lang="eng" fontFamily="Courier New" fontSize="10">
        <content>
          <p>Ref. 26. Final Report, Purdue University Project, Design Division, Pressure Vessel Research Committee, Welding Research Council, 1952.</p>
        </content>
      </text>
    </region>
  </regions>
</worksheet>