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      <div class="title_refTopic" id="xps10_pagetitle">PBCOMP </div>
      <hr noshade="true">
      <h4 class="refClassification">Beam Property (Alternate Form of PBEAM) </h4>
      <p class="para_refTopic">Alternate form of the PBEAM entry to define properties of a uniform cross-sectional beam referenced by a CBEAM entry.  This entry is also used to specify lumped areas of the beam cross section for nonlinear analysis and/or composite analysis. </p>
      <div class="title_refCategory">Format: </div>
      <div class="refCategoryContent">
         <table border="1" width="100%" align="center">
            <colgroup span="1">
               <col span="1" width="11.51*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="10*">
               <col span="1" width="8.49*">
            </colgroup>
            <thead>
               <tr>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">1 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">2 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">3 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">4 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">5 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">6 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">7 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">8 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">9 </p>
                  </th>
                  <th align="center" colspan="1" rowspan="1">
                     <p class="para_th">10 </p>
                  </th>
               </tr>
            </thead>
            <tbody>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">PBCOMP </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">PID </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">MID </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">A </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">I1 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">I2 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">I12 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">J </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">NSM </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">K1 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">K2 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">M1 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">M2 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">N1 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">N2 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">SYMOPT </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">Y1 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">Z1 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">C1 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">MID1 </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">Y2 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">Z2 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">C2 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">MID2 </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">-etc.- </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" bgcolor="gray" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
               </tr>
            </tbody>
         </table><br></div>
      <div class="title_refCategory">Example: </div>
      <div class="refCategoryContent">
         <table border="1" width="100%" align="center">
            <colgroup span="1">
               <col span="1" width="11.72*">
               <col span="1" width="10.02*">
               <col span="1" width="10.02*">
               <col span="1" width="10.02*">
               <col span="1" width="10.02*">
               <col span="1" width="10.02*">
               <col span="1" width="10.02*">
               <col span="1" width="10.02*">
               <col span="1" width="10.02*">
               <col span="1" width="8.13*">
            </colgroup>
            <tbody>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">PBCOMP </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">39 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">6 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">2.9 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">1 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">-0.5 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">1.2 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">0.1 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">18 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">0.2 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">0.9 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">0.15 </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
                  <td align="center" colspan="1" rowspan="1">
                     <p class="para_td">&nbsp; </p>
                  </td>
               </tr>
            </tbody>
         </table><br></div>
      <div class="title_refCategory">Fields:</div>
      <div class="refCategoryContent">
         <table cellpadding="9" width="100%" align="center">
            <colgroup span="1">
               <col span="1" width="16*">
               <col span="1" width="84*">
            </colgroup>
            <thead>
               <tr>
                  <th align="left" colspan="1" rowspan="1">
                     <p class="para_th"><b class="uiTerm">Field </b></p>
                  </th>
                  <th align="left" colspan="1" rowspan="1">
                     <p class="para_th"><b class="uiTerm">Contents </b></p>
                  </th>
               </tr>
            </thead>
            <tbody>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">PID </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Property identification number.  See Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/18topic_19.html#ref15992');return(false);">24-1. </a> (Integer &gt; 0) 
                     </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">MID </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Material identification number.  See Remarks <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/18topic_19.html#ref90135');return(false);">24-2</a> and <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/18topic_19.html#ref69230');return(false);">24-5. </a> (Integer &gt; 0) 
                     </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">A </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Area of beam cross section.  (Real &gt; 0.0) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">I1 </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Area moment of inertia in plane 1 about the neutral axis.  See Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/18topic_19.html#ref88360');return(false);">24-6. </a> (Real &gt; 0.0) 
                     </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">I2 </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Area moment of inertia in plane 2 about the neutral axis.  See Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/18topic_19.html#ref88360');return(false);">24-6. </a> (Real &gt; 0.0) 
                     </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">I12 </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Area product of inertia.  See Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/18topic_19.html#ref88360');return(false);">24-6. </a> (Real; Default = 0.0, but  I1 · I2 − (I12)<sup class="superscript">2</sup>&gt; 0.0) 
                     </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">J </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Torsional stiffness parameter.  See Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/18topic_19.html#ref88360');return(false);">24-6. </a> (Real &gt; 0.0; Default = 0.0) 
                     </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">NSM </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Nonstructural mass per unit length.  (Real &gt; 0.0; Default = 0.0) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">K1, K2 </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Shear stiffness factor K in K*A*G for plane 1 and plane 2.  See Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/18topic_19.html#ref92755');return(false);">24-4. </a> (Real &gt; 0.0; Default = 1.0) 
                     </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">M1, M2 </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">The (y,z) coordinates of center of gravity of nonstructural mass.  See the figure in the CBEAM entry description.  (Real; Default = 0.0) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">N1, N2 </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">The (y,z) coordinates of neutral axis.  See the figure in the CBEAM entry description.  (Real; Default = 0.0) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">SYMOPT </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Symmetry option to input lumped areas for the beam cross section.  See <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/18topic_19.html#ref71865');return(false);">Figure 17-</a> and Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/18topic_19.html#ref19998');return(false);">24-7. </a> (0 &le; Integer &le; 5; Default = 0) 
                     </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Yi, Zi </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">The (y,z) coordinates of the lumped areas in the element coordinate system.  See Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/18topic_19.html#ref15992');return(false);">24-1. </a> (Real) 
                     </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Ci </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Fraction of the total area for the i-th lumped area.  (Real &gt; 0.0; Default = 0.0) </p>
                  </td>
               </tr>
               <tr>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">MIDi </p>
                  </td>
                  <td align="left" colspan="1" rowspan="1" valign="top">
                     <p class="para_td">Material identification number for the i-th integration point.  See Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/18topic_19.html#ref69230');return(false);">24-5. </a> (Integer &gt; 0) 
                     </p>
                  </td>
               </tr>
            </tbody>
         </table><br></div>
      <div class="title_refCategory">Remarks: </div>
      <div class="refCategoryContent">
         <ol type="1" start="1">
            <li><a name="ref15992"></a><p class="para_item">The PID number must be unique with respect to other PBCOMP entries as well as PBEAM entries.  The second continuation entry may be repeated 18 more times.  If SECTION = 5 a maximum of 21 continuation entries is allowed; i.e., a maximum of 20 lumped areas may be input.  If SECTION = 1 through 4, the total number of areas input plus the total number generated by symmetry must not exceed 20.  If these are not specified, the program defaults, as usual, to the elliptically distributed eight nonlinear rods.  See <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/18topic_19.html#ref41422');return(false);">Figure 17-</a>. 
               </p><a name="ref41422"></a><div class="figure">
                  <p align="left"><img align="bottom" src="graphics/bulkp-fig04.gif"></p>
               </div>
               <div class="title_figure">Figure. PBCOMP Entry SYMOPT Type Examples with 8 Lumped Areas </div>
               <p class="para_item">Figure Example Notes: </p>
               <p class="para_item">Integration points (lumped area) are numbered 1 through 8. </p>
               <p class="para_item">User-specified points are denoted by ● and the program default point is denoted by ○. </p>
            </li>
            <li><a name="ref90135"></a><p class="para_item">For structural problems, MID and MIDi must reference a MAT1 material entry.  For material nonlinear analysis, the material should be perfectly plastic since the plastic hinge formulation is not valid for strain hardening.  For heat transfer problems, MID and MIDi must reference a MAT4 or MAT5 material entry. </p>
            </li>
            <li>
               <p class="para_item">For the case where the user specifies I1, I2 and I12 on the parent entry, the stress-output location may also be specified on continuation entries.  The (y,z) coordinates specified on these entries will serve as stress output locations with the corresponding Ci&rsquo;s set to 0.  Stress output is provided at the first four lumped area locations only.  If one of the symmetry options is used and fewer than four lumped areas are input explicitly, the sequence of output locations in the imaged quadrants is shown in <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/18topic_19.html#ref41422');return(false);">Figure 17-</a>.  For one specific example in the model shown in Remark <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/18topic_19.html#ref19998');return(false);">24-7</a> (<a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/18topic_19.html#ref71865');return(false);">Figure 17-</a>), output can be obtained at points 1 and 2 and in the image points 3 and 4. 
               </p>
            </li>
            <li><a name="ref92755"></a><p class="para_item">Blank fields for K1 and K2 are defaulted to 1.0.  If a value of 0.0 is used for K1 and K2, the transverse shear stiffness becomes rigid and the transverse shear flexibilities are set to 0.0. </p>
            </li>
            <li><a name="ref69230"></a><p class="para_item">The values E<sub class="subscript">0</sub> and G<sub class="subscript">0</sub> are computed based on the value of MID on the parent entry.  MID is will follow the same symmetry rules as Ci depending on the value of SECTION.  If the MIDi field on a continuation entry is blank, the value will be that of MID on the parent entry.  MIDi values may be input on continuations without the corresponding Yi, Zi, and Ci values to allow different stress-strain laws. 
               </p>
            </li>
            <li><a name="ref88360"></a><p class="para_item">If the lumped cross-sectional areas are specified, fields I1, I2, and I12 will be ignored.  These and other modified values will be calculated based on the input data (Yi, Zi, Ci, MIDi) as follows: </p>
               <p align="center"><img align="bottom" src="graphics/bulkp-equ07.gif"></p>
               <p align="center"><img align="bottom" src="graphics/bulkp-equ08.gif"></p>
               <p align="center"><img align="bottom" src="graphics/bulkp-equ09.gif"></p>
               <p align="center"><img align="bottom" src="graphics/bulkp-equ10.gif"></p>
               <p align="center"><img align="bottom" src="graphics/bulkp-equ11.gif"></p>
               <p align="center"><img align="bottom" src="graphics/bulkp-equ12.gif"></p>
               <p align="center"><img align="bottom" src="graphics/bulkp-equ13.gif"></p>
               <p class="para_item">where n is the number of lumped cross-sectional areas specified. </p>
            </li>
            <li><a name="ref19998"></a><p class="para_item">As can be seen from <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/18topic_19.html#ref41422');return(false);">Figure 17-</a>, if the user chooses to leave the SECTION field blank, the program defaults to the elliptically distributed eight nonlinear rods, similar to the PBEAM entry.  For this particular case it is illegal to supply Ci and MIDi values.  For a doubly symmetric section (SECTION = 1), if the lumped areas are specified on either axis, the symmetry option will double the areas.  For example, for the section shown in <a class="links" href="javascript:void(0)" onclick="top.openFile('QRG/18topic_19.html#ref71865');return(false);">Figure 17-</a>, points 2 and 4 are coincident and so are points 6 and 8.  In such cases, it is recommended that users input the value of area as half of the actual value at point 2 to obtain the desired effect. 
               </p><a name="ref71865"></a><div class="figure">
                  <p align="center"><img align="bottom" src="graphics/bulkp-fig05.gif"></p>
               </div>
               <div class="title_figure">Figure. Doubly Symmetric PBCOMP Section </div>
            </li>
            <li>
               <p class="para_item">For SECTION = 5, at least one Yi and one Zi must be nonzero. </p>
            </li>
         </ol>
      </div>
      <div class="title_refCategory">Remarks related to SOLs 601 and 701: </div>
      <div class="refCategoryContent">
         <ol type="1" start="1">
            <li>
               <p class="para_item">Only MID, A, I1, I2, J, K1, and K2 are used to define the properties of a simple beam. All other fields are ignored. </p>
            </li>
            <li>
               <p class="para_item">The neutral axis and shear center are assumed to be coincident with the element x-axis. </p>
            </li>
            <li>
               <p class="para_item">The behavior of a CBEAM element is the same as a CBAR element in SOLs 601 and 701. </p>
            </li>
         </ol>
      </div>
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