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Calculator for Applying Plane Strain Coordinate Transforms

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"> <!--- ROS In-Article ---> <div style=""> <!--- Google Adsense ---> <script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script> <ins class="adsbygoogle" style="display:block; text-align:center;" data-ad-layout="in-article" data-ad-format="fluid" data-ad-client="ca-pub-4893968732705577" data-ad-slot="7922155920"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script> <!--- End of Google Adsense ---> </div> </div> <div class="main-meat"> <table width="100%" border="0" cellspacing="0" cellpadding="0"> <tr><td height="20"></td></tr> <tr><td class="SectionTitle"><b><a name="Calculator">Calculator Introduction</a></b></td></tr> <tr><td height="4"><img src="../../../images/section_bar_1.png"></td></tr> <tr><td height="10"></td></tr> <tr><td class="smalltext"> <p>Given the strains at a space point in the body, this calculator computes the strains of the same space point in a rotated coordinate system. <p><div align="center"><img src="images/StrainTransform.gif" width=567 height=302 border=0 alt=""></div> <div class="text" style="color:Navy; padding:30px 0px 10px 0px;"><b>Inputs</b></div> <form action="calc_strain_transform.cfm#calc" method="post" style="margin:0px;"> <div class="section_border_gray" style="width:100%; background-color:#F9F9F9"><div class="section_corner_gray"><div class="top_left"><img src="/images/pixel.png"></div><div class="top_right"><img src="/images/pixel.png"></div></div><div align="center" style="width:100%; padding:10px;"> <table width="100%" cellspacing="1" cellpadding="3" border="0"> <tr bgcolor="DEECC3"> <td align="right" class="smalltext" style="white-space:nowrap;">&nbsp; Normal Strain <span class="blue"><font face="Symbol">e</font><sub><i>x</i></sub></span>:</td> <td align="left" class="smalltext">&nbsp; <input type="text" name="sx1" value="1" size="5" maxlength="10" class="smalltext"></td> <td align="left" class="smalltext">&nbsp; </td> </tr> <tr bgcolor="EEF2E7"> <td align="right" class="smalltext" style="white-space:nowrap;">&nbsp; Normal Strain <span class="blue"><font face="Symbol">e</font><sub><i>y</i></sub></span>:</td> <td align="left" class="smalltext">&nbsp; <input type="text" name="sy1" value="-1" size="5" maxlength="10" class="smalltext"></td> <td align="left" class="smalltext">&nbsp; </td> </tr> <tr bgcolor="DEECC3"> <td align="right" class="smalltext" style="white-space:nowrap;">&nbsp; Shear Strain<span class="blue"><font face="Symbol">e</font><sub><i>xy</i></sub></span>:</td> <td align="left" class="smalltext">&nbsp; <input type="text" name="txy1" value="0" size="5" maxlength="10" class="smalltext"></td> <td align="left" class="smalltext">&nbsp; </td> </tr> <tr bgcolor="EEF2E7"> <td align="right" class="smalltext" style="white-space:nowrap;">&nbsp; Coordinate Rotation <font face="Symbol">q</font>:</td> <td align="left" class="smalltext">&nbsp; <input type="text" name="th" value="45" size="5" maxlength="10" class="smalltext"></td> <td align="left" class="smalltext">&nbsp; <select name="th_units" class="smalltext"> <option value="rad" > rad</option> <option value="deg" selected> deg</option> </select> </td> </tr> </table> </div><div class="section_corner_gray"><div class="bottom_left"><img src="/images/pixel.png"></div><div class="bottom_right"><img src="/images/pixel.png"></div></div></div> <div class="text" style="color:Navy; padding:30px 0px 10px 0px;"><b>Answers</b></div> <div class="section_border_gray" style="width:100%; background-color:FFFDFB"><div class="section_corner_gray"><div class="top_left"><img src="/images/pixel.png"></div><div class="top_right"><img src="/images/pixel.png"></div></div><div align="center" style="width:100%; padding:10px;"> <table width="100%" cellspacing="0" cellpadding="0" border="0"> <tr> <td valign="top"> <table width="100%" cellspacing="1" cellpadding="3" border="0"> <tr bgcolor="FFEDC3"> <td height="25" align="right" class="smalltext" nowrap >&nbsp; New Normal Strain <span class="green"><font face="Symbol">e</font><sub><i>x'</i></sub></span>:</td> <td align="center" class="smalltext" style="padding-right:10px; white-space:nowrap;"> &nbsp;0 &nbsp; </td> <td align="left" class="smalltext" style="padding-left:10px;"> </td> </tr> <tr bgcolor="FFF8E9"> <td height="25" align="right" class="smalltext" nowrap >&nbsp; New Normal Strain <span class="green"><font face="Symbol">e</font><sub><i>y'</i></sub></span>:</td> <td align="center" class="smalltext" style="padding-right:10px; white-space:nowrap;"> &nbsp;0 &nbsp; </td> <td align="left" class="smalltext" style="padding-left:10px;"> </td> </tr> <tr bgcolor="FFEDC3"> <td height="25" align="right" class="smalltext" nowrap >&nbsp; New Shear Strain <span class="green"><font face="Symbol">e</font><sub><i>x'y'</i></sub></span>:</td> <td align="center" class="smalltext" style="padding-right:10px; white-space:nowrap;"> &nbsp;-1.00 &nbsp; </td> <td align="left" class="smalltext" style="padding-left:10px;"> </td> </tr> </table> </td> </tr> </table> <table cellspacing="1" cellpadding="1" border="0" align="center"> <tr><td height="10" colspan="3"></td></tr> <tr> <td align="center"><input type="submit" value="Calculate Again" class="smalltext" style="width:200px; height:25px;"></td> <td width="50"></td> </form> <form action="calc_strain_transform.cfm#calc" method="post" style="margin:0px;"> <td align="center"><input type="submit" value="Default Values" class="smalltext" style="width:200px; height:25px;"></td> </form> </tr> </table> </div><div class="section_corner_gray"><div class="bottom_left"><img src="/images/pixel.png"></div><div class="bottom_right"><img src="/images/pixel.png"></div></div></div> <div class="smalltext" style="height:30px;">&nbsp;</div> </td></tr> <tr><td class="smalltext"> &nbsp;<br> </td></tr> <tr><td class="smalltext"> <p><span class="red"><b>Note</b></span>: The strain measure <font face="Symbol">e</font><sub><i>xy</i></sub> is used in this calculation. Please adjust accordingly when using the <a href="strain.cfm#engstrain">engineering shear strain</a> <img src="images/EngShearStress.gif" width=153 height=26 border=0 align="absmiddle" alt="">. </td></tr> <tr><td height="20"></td></tr> <tr><td class="SectionTitle"><b><a name="Equations">Equations behind the Calculator</a></b></td></tr> <tr><td height="4"><img src="../../../images/section_bar_1.png"></td></tr> <tr><td height="10"></td></tr> <tr><td class="smalltext"> The following <a href="plane_strain.cfm#transform">coordinate transformation</a> equations were used, <p> <div align="center"><img src="images/TransStrainAll.gif" width=298 height=165 border=0 alt=""></div> </td></tr></table> </div> <div class="SectionTitle" style="margin-top:40px;"><a class="title1" href="https://efunda.tradepub.com"><b>FREE Publications</b></a></div> <div><img src="/images/section_bar_1.png"></div> <div style="padding:10px 0; display:flex; flex-direction:row; flex-wrap:wrap; justify-content:space-between; margin-bottom:30px;"> <div style="position:relative; width:48%; padding:5px 0;"> <div style="width:20%; float:left;"><a href="https://efunda.tradepub.com/free/w_xome12/prgm.cgi"><img style="width:100%; height:auto;" src="https://img.tradepub.com/free/w_xome12/images/w_xome12c2.gif" align="left"></a></div> <div style="width:80%; float:right; font-weight:300"><a href="https://efunda.tradepub.com/free/w_xome12/prgm.cgi" style="font-size:1rem;" onmouseover="showDynamicBalloon('divDynamicBalloon', findPosX(this), findPosY(this), this.offsetWidth, 0, 0);" onmouseout="mouseIntoDiv(this,event);"><b>CNC Machining Design Guide</b></a><p style="margin:0px; margin-top:3px; font-size:0.9rem; line-height:1.2rem">Optimize your designs, reduce machining time, and lower your costs.</p></div> </div> <div style="position:relative; width:48%; padding:5px 0;"> <div style="width:20%; float:left;"><a href="https://efunda.tradepub.com/free/w_bund37/prgm.cgi"><img style="width:100%; height:auto;" src="https://img.tradepub.com/free/w_bund37/images/w_bund37c2.gif" align="left"></a></div> <div style="width:80%; float:right; font-weight:300"><a href="https://efunda.tradepub.com/free/w_bund37/prgm.cgi" style="font-size:1rem;" onmouseover="showDynamicBalloon('divDynamicBalloon', findPosX(this), findPosY(this), this.offsetWidth, 0, 1);" onmouseout="mouseIntoDiv(this,event);"><b>Essentials of Manufacturing</b></a><p style="margin:0px; margin-top:3px; font-size:0.9rem; line-height:1.2rem">Information, coverage of important developments and expert commentary in manufacturing.</p></div> </div> <div style="position:relative; width:48%; padding:5px 0;"> <div style="width:20%; float:left;"><a href="https://efunda.tradepub.com/free/w_aaaa3627/prgm.cgi"><img style="width:100%; height:auto;" src="https://img.tradepub.com/free/w_aaaa3627/images/w_aaaa3627c2.gif" align="left"></a></div> <div style="width:80%; float:right; font-weight:300"><a href="https://efunda.tradepub.com/free/w_aaaa3627/prgm.cgi" style="font-size:1rem;" onmouseover="showDynamicBalloon('divDynamicBalloon', findPosX(this), findPosY(this), this.offsetWidth, 0, 2);" onmouseout="mouseIntoDiv(this,event);"><b>Selecting the Right 3D Printer</b></a><p style="margin:0px; margin-top:3px; font-size:0.9rem; line-height:1.2rem">Discover how to choose the right 3D printer for your needs and the key performance attributes to consider.</p></div> </div> <div style="position:relative; width:48%; padding:5px 0;"> <div style="width:20%; float:left;"><a href="https://efunda.tradepub.com/free/w_hubc40/prgm.cgi"><img style="width:100%; height:auto;" src="https://img.tradepub.com/free/w_hubc40/images/w_hubc40c2.gif" align="left"></a></div> <div style="width:80%; float:right; font-weight:300"><a href="https://efunda.tradepub.com/free/w_hubc40/prgm.cgi" style="font-size:1rem;" onmouseover="showDynamicBalloon('divDynamicBalloon', findPosX(this), findPosY(this), this.offsetWidth, 0, 3);" onmouseout="mouseIntoDiv(this,event);"><b>Mechanical Engineers Outlook</b></a><p style="margin:0px; margin-top:3px; font-size:0.9rem; line-height:1.2rem">Guide for those interested in becoming a mechanical engineer. 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