http://www.mapleprimes.com/questions/144872-Finding-Forces-On-Arm-Crane en-us 2026 Maplesoft, A Division of Waterloo Maple Inc. Maplesoft Document System Thu, 11 Jun 2026 09:43:42 GMT Thu, 11 Jun 2026 09:43:42 GMT The latest answers and comments added to the Question, Finding Forces on Arm Crane http://www.mapleprimes.com/images/mapleprimeswhite.jpg http://www.mapleprimes.com/questions/144872-Finding-Forces-On-Arm-Crane http://www.mapleprimes.com/questions/144872-Finding-Forces-On-Arm-Crane?ref=Feed:MaplePrimes:Finding Forces on Arm Crane:Comments#answer145063 <p>Hm, I don't think the equations are quite right.&nbsp; </p> <p>Hm, I don't think the equations are quite right.&nbsp; </p> 145063 Tue, 26 Mar 2013 00:22:31 Z Christopher2222 Christopher2222 http://www.mapleprimes.com/questions/144872-Finding-Forces-On-Arm-Crane?ref=Feed:MaplePrimes:Finding Forces on Arm Crane:Comments#comment145176 <p>This should be the right solution.&nbsp; It is worked out for the case of alpha=0 and answers shown in terms of an unknown load L.&nbsp; Negative values indicate that member is in compression, while positive under tension.&nbsp; Near the end of the worksheet I was only trying to verify that the equations matched my worked out paper version equations for alpha=0. </p> <form name="worksheet_form"> <table style="width: 576px;" align="center"> <tbody> <tr> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;">Setting up the force sums on each node</span></p> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=145176/457176/e6d985877d8ed2611a628a432ba67a83.gif" alt="restart; gc()" width="96" height="23"></p> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -33;" src="/view.aspx?sf=145176/457176/19814e513e0bfe1db0c4e70b5c28a374.gif" alt="Ax := HA+T1*cos(alpha)+T2*cos((1/4)*Pi+alpha) = 0; 1; Ay := VA+T1*sin(alpha)+T2*sin((1/4)*Pi+alpha) = 0" width="576" height="62" align="middle"></p> <table> <tbody> <tr valign="baseline"> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -16;" src="/view.aspx?sf=145176/457176/07c57e5db30eb98bd047478f2b74ef7f.gif" alt="VA+T1*sin(alpha)+T2*sin((1/4)*Pi+alpha) = 0" width="289" height="45"></p> </td> <td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(1)</td> </tr> </tbody> </table> <table> <tbody> <tr valign="baseline"> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -6;" src="/view.aspx?sf=145176/457176/96c3ef146a7268fdbb894ddae1af8014.gif" alt="" width="151" height="23"></p> </td> <td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(2)</td> </tr> </tbody> </table> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -55;" src="/view.aspx?sf=145176/457176/6fa49d592c0b3f0c8a18291186ee4c05.gif" alt="Bx := -HB-T2*cos((1/4)*Pi+alpha)+T3*cos((1/4)*Pi-alpha)+T4*cos(alpha) = 0;" width="576" height="84" align="middle"></p> <table> <tbody> <tr valign="baseline"> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -16;" src="/view.aspx?sf=145176/457176/5fc7046d9a10f31339fd82957e7cc0e1.gif" alt="-T2*sin((1/4)*Pi+alpha)-T3*sin((1/4)*Pi+alpha)+T4*sin(alpha) = 0" width="382" height="45"></p> </td> <td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(3)</td> </tr> </tbody> </table> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -55;" src="/view.aspx?sf=145176/457176/10fc979556bda315efdc898f4f5c386a.gif" alt="Cx := -T1*cos(alpha)-T3*cos((1/4)*Pi-alpha)+T5*cos((1/4)*Pi+alpha)+T6*cos(alpha) = 0;" width="576" height="84" align="middle"></p> <table> <tbody> <tr valign="baseline"> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -16;" src="/view.aspx?sf=145176/457176/bc6a76f8c010b93967aa3f5337863f3a.gif" alt="-T1*sin(alpha)+T3*cos((1/4)*Pi+alpha)+T5*sin((1/4)*Pi+alpha)+T6*sin(alpha) = 0" width="465" height="45"></p> </td> <td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(4)</td> </tr> </tbody> </table> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -55;" src="/view.aspx?sf=145176/457176/5f035ffa534b5559097e54aada1e1250.gif" alt="Dx := -T4*cos(alpha)-T5*cos((1/4)*Pi+alpha)+T7*cos((1/4)*Pi-alpha) = 0;" width="576" height="84" align="middle"></p> <table> <tbody> <tr valign="baseline"> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -16;" src="/view.aspx?sf=145176/457176/367523167e52259a385b1196c2575662.gif" alt="-T4*sin(alpha)-T5*sin((1/4)*Pi+alpha)-T7*cos((1/4)*Pi+alpha) = 0" width="386" height="45"></p> </td> <td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(5)</td> </tr> </tbody> </table> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -16;" src="/view.aspx?sf=145176/457176/af95e9d8a8a81b60eec19c4016dc43f3.gif" alt="Ex := -T6*cos(alpha)-T7*cos((1/4)*Pi-alpha) = 0;" width="568" height="45"></p> <table> <tbody> <tr valign="baseline"> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -16;" src="/view.aspx?sf=145176/457176/c47cf8b0c747d334b2ff9ce3755b4f89.gif" alt="-L-T6*sin(alpha)+T7*cos((1/4)*Pi+alpha) = 0" width="291" height="45"></p> </td> <td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(6)</td> </tr> </tbody> </table> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=145176/457176/1e32bf5055e2f9041117929205aba47a.gif" alt="eq := [Ax, Ay, Bx, By, Cx, Cy, Dx, Dy, Ex, Ey]" width="278" height="23"></p> <table> <tbody> <tr valign="baseline"> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -250;" src="/view.aspx?sf=145176/457176/c6ede4958c3212fff6ad3a868d84da55.gif" alt="[HA+T1*cos(alpha)+T2*cos((1/4)*Pi+alpha) = 0, VA+T1*sin(alpha)+T2*sin((1/4)*Pi+alpha) = 0, -HB-T2*cos((1/4)*Pi+alpha)+T3*cos(-(1/4)*Pi+alpha)+T4*cos(alpha) = 0, -T2*sin((1/4)*Pi+alpha)-T3*sin((1/4)*Pi+alpha)+T4*sin(alpha) = 0, -T1*cos(alpha)-T3*cos(-(1/4)*Pi+alpha)+T5*cos((1/4)*Pi+alpha)+T6*cos(alpha) = 0, -T1*sin(alpha)+T3*cos((1/4)*Pi+alpha)+T5*sin((1/4)*Pi+alpha)+T6*sin(alpha) = 0, -T4*cos(alpha)-T5*cos((1/4)*Pi+alpha)+T7*cos(-(1/4)*Pi+alpha) = 0, -T4*sin(alpha)-T5*sin((1/4)*Pi+alpha)-T7*cos((1/4)*Pi+alpha) = 0, -T6*cos(alpha)-T7*cos(-(1/4)*Pi+alpha) = 0, -L-T6*sin(alpha)+T7*cos((1/4)*Pi+alpha) = 0]" width="546" height="279" align="middle"></p> </td> <td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(7)</td> </tr> </tbody> </table> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=145176/457176/12b044ed1118de43f38daabb18773dee.gif" alt="var := [HA, VA, HB, T1, T2, T3, T4, T5, T6, T7]" width="288" height="23"></p> <table> <tbody> <tr valign="baseline"> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -6;" src="/view.aspx?sf=145176/457176/780b582fbf4634b874a745dd5a698b21.gif" alt="[HA, VA, HB, T1, T2, T3, T4, T5, T6, T7]" width="288" height="23"></p> </td> <td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(8)</td> </tr> </tbody> </table> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=145176/457176/b073f96b54f823348449e095de4d0969.gif" alt="with(Student[LinearAlgebra]):" width="202" height="23"></p> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=145176/457176/2fce378ea2d81c5c3df9c55ea86c3c8b.gif" alt="interface(rtablesize = 20):" width="174" height="23"></p> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=145176/457176/b845087e0a442f911aef0bcf6b84930d.gif" alt="sol1 := GenerateMatrix(eq, var, augmented = true)" width="319" height="23"></p> <table> <tbody> <tr valign="baseline"> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -367;" src="/view.aspx?sf=145176/457176/7ba3d3306b07806888446f3d27b1ce11.gif" alt="sol1 := Matrix(10, 11, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 0, (1, 4) = cos(alpha), (1, 5) = cos((1/4)*Pi+alpha), (1, 6) = 0, (1, 7) = 0, (1, 8) = 0, (1, 9) = 0, (1, 10) = 0, (1, 11) = 0, (2, 1) = 0, (2, 2) = 1, (2, 3) = 0, (2, 4) = sin(alpha), (2, 5) = sin((1/4)*Pi+alpha), (2, 6) = 0, (2, 7) = 0, (2, 8) = 0, (2, 9) = 0, (2, 10) = 0, (2, 11) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = -1, (3, 4) = 0, (3, 5) = -cos((1/4)*Pi+alpha), (3, 6) = cos(-(1/4)*Pi+alpha), (3, 7) = cos(alpha), (3, 8) = 0, (3, 9) = 0, (3, 10) = 0, (3, 11) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = 0, (4, 5) = -sin((1/4)*Pi+alpha), (4, 6) = -sin((1/4)*Pi+alpha), (4, 7) = sin(alpha), (4, 8) = 0, (4, 9) = 0, (4, 10) = 0, (4, 11) = 0, (5, 1) = 0, (5, 2) = 0, (5, 3) = 0, (5, 4) = -cos(alpha), (5, 5) = 0, (5, 6) = -cos(-(1/4)*Pi+alpha), (5, 7) = 0, (5, 8) = cos((1/4)*Pi+alpha), (5, 9) = cos(alpha), (5, 10) = 0, (5, 11) = 0, (6, 1) = 0, (6, 2) = 0, (6, 3) = 0, (6, 4) = -sin(alpha), (6, 5) = 0, (6, 6) = cos((1/4)*Pi+alpha), (6, 7) = 0, (6, 8) = sin((1/4)*Pi+alpha), (6, 9) = sin(alpha), (6, 10) = 0, (6, 11) = 0, (7, 1) = 0, (7, 2) = 0, (7, 3) = 0, (7, 4) = 0, (7, 5) = 0, (7, 6) = 0, (7, 7) = -cos(alpha), (7, 8) = -cos((1/4)*Pi+alpha), (7, 9) = 0, (7, 10) = cos(-(1/4)*Pi+alpha), (7, 11) = 0, (8, 1) = 0, (8, 2) = 0, (8, 3) = 0, (8, 4) = 0, (8, 5) = 0, (8, 6) = 0, (8, 7) = -sin(alpha), (8, 8) = -sin((1/4)*Pi+alpha), (8, 9) = 0, (8, 10) = -cos((1/4)*Pi+alpha), (8, 11) = 0, (9, 1) = 0, (9, 2) = 0, (9, 3) = 0, (9, 4) = 0, (9, 5) = 0, (9, 6) = 0, (9, 7) = 0, (9, 8) = 0, (9, 9) = -cos(alpha), (9, 10) = -cos(-(1/4)*Pi+alpha), (9, 11) = 0, (10, 1) = 0, (10, 2) = 0, (10, 3) = 0, (10, 4) = 0, (10, 5) = 0, (10, 6) = 0, (10, 7) = 0, (10, 8) = 0, (10, 9) = -sin(alpha), (10, 10) = cos((1/4)*Pi+alpha), (10, 11) = L})" width="546" height="396" align="middle"></p> </td> <td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(9)</td> </tr> </tbody> </table> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -7;" src="/view.aspx?sf=145176/457176/c166ef1bc06a45a1105f13435d954c36.gif" alt="sol2 := GenerateMatrix(subs(alpha = 0, eq), var)" width="372" height="26"></p> <table> <tbody> <tr valign="baseline"> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -367;" src="/view.aspx?sf=145176/457176/d0d63713c4923f102e1446185fb803a4.gif" alt="sol2 := Matrix(10, 11, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 0, (1, 4) = cos(0), (1, 5) = cos((1/4)*Pi), (1, 6) = 0, (1, 7) = 0, (1, 8) = 0, (1, 9) = 0, (1, 10) = 0, (1, 11) = 0, (2, 1) = 0, (2, 2) = 1, (2, 3) = 0, (2, 4) = sin(0), (2, 5) = sin((1/4)*Pi), (2, 6) = 0, (2, 7) = 0, (2, 8) = 0, (2, 9) = 0, (2, 10) = 0, (2, 11) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = -1, (3, 4) = 0, (3, 5) = -cos((1/4)*Pi), (3, 6) = cos(-(1/4)*Pi), (3, 7) = cos(0), (3, 8) = 0, (3, 9) = 0, (3, 10) = 0, (3, 11) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = 0, (4, 5) = -sin((1/4)*Pi), (4, 6) = -sin((1/4)*Pi), (4, 7) = sin(0), (4, 8) = 0, (4, 9) = 0, (4, 10) = 0, (4, 11) = 0, (5, 1) = 0, (5, 2) = 0, (5, 3) = 0, (5, 4) = -cos(0), (5, 5) = 0, (5, 6) = -cos(-(1/4)*Pi), (5, 7) = 0, (5, 8) = cos((1/4)*Pi), (5, 9) = cos(0), (5, 10) = 0, (5, 11) = 0, (6, 1) = 0, (6, 2) = 0, (6, 3) = 0, (6, 4) = -sin(0), (6, 5) = 0, (6, 6) = cos((1/4)*Pi), (6, 7) = 0, (6, 8) = sin((1/4)*Pi), (6, 9) = sin(0), (6, 10) = 0, (6, 11) = 0, (7, 1) = 0, (7, 2) = 0, (7, 3) = 0, (7, 4) = 0, (7, 5) = 0, (7, 6) = 0, (7, 7) = -cos(0), (7, 8) = -cos((1/4)*Pi), (7, 9) = 0, (7, 10) = cos(-(1/4)*Pi), (7, 11) = 0, (8, 1) = 0, (8, 2) = 0, (8, 3) = 0, (8, 4) = 0, (8, 5) = 0, (8, 6) = 0, (8, 7) = -sin(0), (8, 8) = -sin((1/4)*Pi), (8, 9) = 0, (8, 10) = -cos((1/4)*Pi), (8, 11) = 0, (9, 1) = 0, (9, 2) = 0, (9, 3) = 0, (9, 4) = 0, (9, 5) = 0, (9, 6) = 0, (9, 7) = 0, (9, 8) = 0, (9, 9) = -cos(0), (9, 10) = -cos(-(1/4)*Pi), (9, 11) = 0, (10, 1) = 0, (10, 2) = 0, (10, 3) = 0, (10, 4) = 0, (10, 5) = 0, (10, 6) = 0, (10, 7) = 0, (10, 8) = 0, (10, 9) = -sin(0), (10, 10) = cos((1/4)*Pi), (10, 11) = L})" width="536" height="396" align="middle"></p> </td> <td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(10)</td> </tr> </tbody> </table> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=145176/457176/018211d3dc9898247dd4a0f234521fff.gif" alt="sol3 := convert(sol2, radical)" width="190" height="23"></p> <table> <tbody> <tr valign="baseline"> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -233;" src="/view.aspx?sf=145176/457176/a51853d6bf153fcb467134694f98dd97.gif" alt="sol3 := Matrix(10, 11, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 0, (1, 4) = 1, (1, 5) = (1/2)*sqrt(2), (1, 6) = 0, (1, 7) = 0, (1, 8) = 0, (1, 9) = 0, (1, 10) = 0, (1, 11) = 0, (2, 1) = 0, (2, 2) = 1, (2, 3) = 0, (2, 4) = 0, (2, 5) = (1/2)*sqrt(2), (2, 6) = 0, (2, 7) = 0, (2, 8) = 0, (2, 9) = 0, (2, 10) = 0, (2, 11) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = -1, (3, 4) = 0, (3, 5) = -(1/2)*sqrt(2), (3, 6) = (1/2)*sqrt(2), (3, 7) = 1, (3, 8) = 0, (3, 9) = 0, (3, 10) = 0, (3, 11) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = 0, (4, 5) = -(1/2)*sqrt(2), (4, 6) = -(1/2)*sqrt(2), (4, 7) = 0, (4, 8) = 0, (4, 9) = 0, (4, 10) = 0, (4, 11) = 0, (5, 1) = 0, (5, 2) = 0, (5, 3) = 0, (5, 4) = -1, (5, 5) = 0, (5, 6) = -(1/2)*sqrt(2), (5, 7) = 0, (5, 8) = (1/2)*sqrt(2), (5, 9) = 1, (5, 10) = 0, (5, 11) = 0, (6, 1) = 0, (6, 2) = 0, (6, 3) = 0, (6, 4) = 0, (6, 5) = 0, (6, 6) = (1/2)*sqrt(2), (6, 7) = 0, (6, 8) = (1/2)*sqrt(2), (6, 9) = 0, (6, 10) = 0, (6, 11) = 0, (7, 1) = 0, (7, 2) = 0, (7, 3) = 0, (7, 4) = 0, (7, 5) = 0, (7, 6) = 0, (7, 7) = -1, (7, 8) = -(1/2)*sqrt(2), (7, 9) = 0, (7, 10) = (1/2)*sqrt(2), (7, 11) = 0, (8, 1) = 0, (8, 2) = 0, (8, 3) = 0, (8, 4) = 0, (8, 5) = 0, (8, 6) = 0, (8, 7) = 0, (8, 8) = -(1/2)*sqrt(2), (8, 9) = 0, (8, 10) = -(1/2)*sqrt(2), (8, 11) = 0, (9, 1) = 0, (9, 2) = 0, (9, 3) = 0, (9, 4) = 0, (9, 5) = 0, (9, 6) = 0, (9, 7) = 0, (9, 8) = 0, (9, 9) = -1, (9, 10) = -(1/2)*sqrt(2), (9, 11) = 0, (10, 1) = 0, (10, 2) = 0, (10, 3) = 0, (10, 4) = 0, (10, 5) = 0, (10, 6) = 0, (10, 7) = 0, (10, 8) = 0, (10, 9) = 0, (10, 10) = (1/2)*sqrt(2), (10, 11) = L})" width="440" height="477"></p> </td> <td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(11)</td> </tr> </tbody> </table> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=145176/457176/c0ebec5b3e8ec63f70004514c543eff3.gif" alt="sol4 := ReducedRowEchelonForm(sol3)" width="256" height="23"></p> <table> <tbody> <tr valign="baseline"> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -126;" src="/view.aspx?sf=145176/457176/890f9c5c437466a7ecd2d276110a9045.gif" alt="sol4 := Matrix(10, 11, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (1, 5) = 0, (1, 6) = 0, (1, 7) = 0, (1, 8) = 0, (1, 9) = 0, (1, 10) = 0, (1, 11) = 4*L, (2, 1) = 0, (2, 2) = 1, (2, 3) = 0, (2, 4) = 0, (2, 5) = 0, (2, 6) = 0, (2, 7) = 0, (2, 8) = 0, (2, 9) = 0, (2, 10) = 0, (2, 11) = L, (3, 1) = 0, (3, 2) = 0, (3, 3) = 1, (3, 4) = 0, (3, 5) = 0, (3, 6) = 0, (3, 7) = 0, (3, 8) = 0, (3, 9) = 0, (3, 10) = 0, (3, 11) = 4*L, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = 1, (4, 5) = 0, (4, 6) = 0, (4, 7) = 0, (4, 8) = 0, (4, 9) = 0, (4, 10) = 0, (4, 11) = -3*L, (5, 1) = 0, (5, 2) = 0, (5, 3) = 0, (5, 4) = 0, (5, 5) = 1, (5, 6) = 0, (5, 7) = 0, (5, 8) = 0, (5, 9) = 0, (5, 10) = 0, (5, 11) = -L*sqrt(2), (6, 1) = 0, (6, 2) = 0, (6, 3) = 0, (6, 4) = 0, (6, 5) = 0, (6, 6) = 1, (6, 7) = 0, (6, 8) = 0, (6, 9) = 0, (6, 10) = 0, (6, 11) = L*sqrt(2), (7, 1) = 0, (7, 2) = 0, (7, 3) = 0, (7, 4) = 0, (7, 5) = 0, (7, 6) = 0, (7, 7) = 1, (7, 8) = 0, (7, 9) = 0, (7, 10) = 0, (7, 11) = 2*L, (8, 1) = 0, (8, 2) = 0, (8, 3) = 0, (8, 4) = 0, (8, 5) = 0, (8, 6) = 0, (8, 7) = 0, (8, 8) = 1, (8, 9) = 0, (8, 10) = 0, (8, 11) = -L*sqrt(2), (9, 1) = 0, (9, 2) = 0, (9, 3) = 0, (9, 4) = 0, (9, 5) = 0, (9, 6) = 0, (9, 7) = 0, (9, 8) = 0, (9, 9) = 1, (9, 10) = 0, (9, 11) = -L, (10, 1) = 0, (10, 2) = 0, (10, 3) = 0, (10, 4) = 0, (10, 5) = 0, (10, 6) = 0, (10, 7) = 0, (10, 8) = 0, (10, 9) = 0, (10, 10) = 1, (10, 11) = L*sqrt(2)})" width="273" height="263"></p> </td> <td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(12)</td> </tr> </tbody> </table> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=145176/457176/c5449526082f743b194c48fcd8f76792.gif" alt="sol5 := GenerateEquations(sol4, var)" width="238" height="23"></p> <table> <tbody> <tr valign="baseline"> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -27;" src="/view.aspx?sf=145176/457176/e0615e6605aed76c3f5524e79311a92c.gif" alt="[HA = 4*L, VA = L, HB = 4*L, T1 = -3*L, T2 = -L*2^(1/2), T3 = L*2^(1/2), T4 = 2*L, T5 = -L*2^(1/2), T6 = -L, T7 = L*2^(1/2)]" width="536" height="48" align="middle"></p> </td> <td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(13)</td> </tr> </tbody> </table> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -40;" src="/view.aspx?sf=145176/457176/0435df92c5cbcc0b7c295d8854c3713d.gif" alt="for i to nops(sol5) do sol5[i] end do" width="576" height="57" align="middle"></p> <table> <tbody> <tr valign="baseline"> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -6;" src="/view.aspx?sf=145176/457176/b14587fe7b019536e2073b026865be22.gif" alt="T7 = L*2^(1/2)" width="72" height="27"></p> </td> <td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(14)</td> </tr> </tbody> </table> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=145176/457176/56899419b429bc77e298c0014d90c76a.gif" alt="``" width="11" height="23"></p> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><span style="color: #ff0000; font-size: 100%; font-family: monospace,monospace; font-weight: bold; font-style: normal;">&nbsp; </span></p> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=145176/457176/07a8f4c2f999468bb479c740b1be2e48.gif" alt="``" width="11" height="23"><img style="vertical-align: -7;" src="/view.aspx?sf=145176/457176/71adf897c6c7c8119544faca070a650e.gif" alt="subs(alpha = 0, eq)" width="101" height="26"></p> <table> <tbody> <tr valign="baseline"> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -211;" src="/view.aspx?sf=145176/457176/9fad29cd4208a463c4900d81faf004d5.gif" alt="[HA+T1*cos(0)+T2*cos((1/4)*Pi) = 0, VA+T1*sin(0)+T2*sin((1/4)*Pi) = 0, -HB-T2*cos((1/4)*Pi)+T3*cos(-(1/4)*Pi)+T4*cos(0) = 0, -T2*sin((1/4)*Pi)-T3*sin((1/4)*Pi)+T4*sin(0) = 0, -T1*cos(0)-T3*cos(-(1/4)*Pi)+T5*cos((1/4)*Pi)+T6*cos(0) = 0, -T1*sin(0)+T3*cos((1/4)*Pi)+T5*sin((1/4)*Pi)+T6*sin(0) = 0, -T4*cos(0)-T5*cos((1/4)*Pi)+T7*cos(-(1/4)*Pi) = 0, -T4*sin(0)-T5*sin((1/4)*Pi)-T7*cos((1/4)*Pi) = 0, -T6*cos(0)-T7*cos(-(1/4)*Pi) = 0, -L-T6*sin(0)+T7*cos((1/4)*Pi) = 0]" width="536" height="240" align="middle"></p> </td> <td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(15)</td> </tr> </tbody> </table> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=145176/457176/bee7f677f48698e8a1a2101018d34867.gif" alt="simplify(%)" width="79" height="23"></p> <table> <tbody> <tr valign="baseline"> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -136;" src="/view.aspx?sf=145176/457176/c6d7d302f7a275278168557b1d1b7c46.gif" alt="[HA+T1+(1/2)*T2*2^(1/2) = 0, VA+(1/2)*T2*2^(1/2) = 0, -HB-(1/2)*T2*2^(1/2)+(1/2)*T3*2^(1/2)+T4 = 0, -(1/2)*T2*2^(1/2)-(1/2)*T3*2^(1/2) = 0, -T1-(1/2)*T3*2^(1/2)+(1/2)*T5*2^(1/2)+T6 = 0, (1/2)*T3*2^(1/2)+(1/2)*T5*2^(1/2) = 0, -T4-(1/2)*T5*2^(1/2)+(1/2)*T7*2^(1/2) = 0, -(1/2)*T5*2^(1/2)-(1/2)*T7*2^(1/2) = 0, -T6-(1/2)*T7*2^(1/2) = 0, -L+(1/2)*T7*2^(1/2) = 0]" width="536" height="166" align="middle"></p> </td> <td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(16)</td> </tr> </tbody> </table> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=145176/457176/7cbf6bd2dc9716ebd39dff7107baa639.gif" alt="NULL" width="11" height="23"></p> </td> </tr> </tbody> </table> <input type="hidden" name="sequence" value="1"> <input type="hidden" name="cmd" value="none"></form> <p>&nbsp;</p> <p><a href="/view.aspx?sf=145176/457176/truss2.mw">Download truss2.mw</a></p> <p>&nbsp;</p> <p>The general case is quite messy but can easily be found, but subsituting a value for alpha gave it a cleaner look.&nbsp; Also you can see what happens if alpha is set to 180 degrees that the CE member value becomes positive (under tension).&nbsp;&nbsp;</p> <p>This solution is one way to do it.&nbsp; I haven't actually tried to figure out where your mistake is in your code.</p> <p>This should be the right solution.&nbsp; It is worked out for the case of alpha=0 and answers shown in terms of an unknown load L.&nbsp; Negative values indicate that member is in compression, while positive under tension.&nbsp; Near the end of the worksheet I was only trying to verify that the equations matched my worked out paper version equations for alpha=0. </p> <form name="worksheet_form"> <table style="width: 576px;" align="center"> <tbody> <tr> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><span style="color: #000000; font-size: 100%; font-family: Times New Roman,serif; font-weight: normal; font-style: normal;">Setting up the force sums on each node</span></p> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=145176/457176/e6d985877d8ed2611a628a432ba67a83.gif" alt="restart; gc()" width="96" height="23"></p> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -33;" src="/view.aspx?sf=145176/457176/19814e513e0bfe1db0c4e70b5c28a374.gif" alt="Ax := HA+T1*cos(alpha)+T2*cos((1/4)*Pi+alpha) = 0; 1; Ay := VA+T1*sin(alpha)+T2*sin((1/4)*Pi+alpha) = 0" width="576" height="62" align="middle"></p> <table> <tbody> <tr valign="baseline"> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -16;" src="/view.aspx?sf=145176/457176/07c57e5db30eb98bd047478f2b74ef7f.gif" alt="VA+T1*sin(alpha)+T2*sin((1/4)*Pi+alpha) = 0" width="289" height="45"></p> </td> <td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(1)</td> </tr> </tbody> </table> <table> <tbody> <tr valign="baseline"> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -6;" src="/view.aspx?sf=145176/457176/96c3ef146a7268fdbb894ddae1af8014.gif" alt="" width="151" height="23"></p> </td> <td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(2)</td> </tr> </tbody> </table> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -55;" src="/view.aspx?sf=145176/457176/6fa49d592c0b3f0c8a18291186ee4c05.gif" alt="Bx := -HB-T2*cos((1/4)*Pi+alpha)+T3*cos((1/4)*Pi-alpha)+T4*cos(alpha) = 0;" width="576" height="84" align="middle"></p> <table> <tbody> <tr valign="baseline"> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -16;" src="/view.aspx?sf=145176/457176/5fc7046d9a10f31339fd82957e7cc0e1.gif" alt="-T2*sin((1/4)*Pi+alpha)-T3*sin((1/4)*Pi+alpha)+T4*sin(alpha) = 0" width="382" height="45"></p> </td> <td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(3)</td> </tr> </tbody> </table> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -55;" src="/view.aspx?sf=145176/457176/10fc979556bda315efdc898f4f5c386a.gif" alt="Cx := -T1*cos(alpha)-T3*cos((1/4)*Pi-alpha)+T5*cos((1/4)*Pi+alpha)+T6*cos(alpha) = 0;" width="576" height="84" align="middle"></p> <table> <tbody> <tr valign="baseline"> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -16;" src="/view.aspx?sf=145176/457176/bc6a76f8c010b93967aa3f5337863f3a.gif" alt="-T1*sin(alpha)+T3*cos((1/4)*Pi+alpha)+T5*sin((1/4)*Pi+alpha)+T6*sin(alpha) = 0" width="465" height="45"></p> </td> <td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(4)</td> </tr> </tbody> </table> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -55;" src="/view.aspx?sf=145176/457176/5f035ffa534b5559097e54aada1e1250.gif" alt="Dx := -T4*cos(alpha)-T5*cos((1/4)*Pi+alpha)+T7*cos((1/4)*Pi-alpha) = 0;" width="576" height="84" align="middle"></p> <table> <tbody> <tr valign="baseline"> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -16;" src="/view.aspx?sf=145176/457176/367523167e52259a385b1196c2575662.gif" alt="-T4*sin(alpha)-T5*sin((1/4)*Pi+alpha)-T7*cos((1/4)*Pi+alpha) = 0" width="386" height="45"></p> </td> <td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(5)</td> </tr> </tbody> </table> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -16;" src="/view.aspx?sf=145176/457176/af95e9d8a8a81b60eec19c4016dc43f3.gif" alt="Ex := -T6*cos(alpha)-T7*cos((1/4)*Pi-alpha) = 0;" width="568" height="45"></p> <table> <tbody> <tr valign="baseline"> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -16;" src="/view.aspx?sf=145176/457176/c47cf8b0c747d334b2ff9ce3755b4f89.gif" alt="-L-T6*sin(alpha)+T7*cos((1/4)*Pi+alpha) = 0" width="291" height="45"></p> </td> <td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(6)</td> </tr> </tbody> </table> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=145176/457176/1e32bf5055e2f9041117929205aba47a.gif" alt="eq := [Ax, Ay, Bx, By, Cx, Cy, Dx, Dy, Ex, Ey]" width="278" height="23"></p> <table> <tbody> <tr valign="baseline"> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -250;" src="/view.aspx?sf=145176/457176/c6ede4958c3212fff6ad3a868d84da55.gif" alt="[HA+T1*cos(alpha)+T2*cos((1/4)*Pi+alpha) = 0, VA+T1*sin(alpha)+T2*sin((1/4)*Pi+alpha) = 0, -HB-T2*cos((1/4)*Pi+alpha)+T3*cos(-(1/4)*Pi+alpha)+T4*cos(alpha) = 0, -T2*sin((1/4)*Pi+alpha)-T3*sin((1/4)*Pi+alpha)+T4*sin(alpha) = 0, -T1*cos(alpha)-T3*cos(-(1/4)*Pi+alpha)+T5*cos((1/4)*Pi+alpha)+T6*cos(alpha) = 0, -T1*sin(alpha)+T3*cos((1/4)*Pi+alpha)+T5*sin((1/4)*Pi+alpha)+T6*sin(alpha) = 0, -T4*cos(alpha)-T5*cos((1/4)*Pi+alpha)+T7*cos(-(1/4)*Pi+alpha) = 0, -T4*sin(alpha)-T5*sin((1/4)*Pi+alpha)-T7*cos((1/4)*Pi+alpha) = 0, -T6*cos(alpha)-T7*cos(-(1/4)*Pi+alpha) = 0, -L-T6*sin(alpha)+T7*cos((1/4)*Pi+alpha) = 0]" width="546" height="279" align="middle"></p> </td> <td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(7)</td> </tr> </tbody> </table> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=145176/457176/12b044ed1118de43f38daabb18773dee.gif" alt="var := [HA, VA, HB, T1, T2, T3, T4, T5, T6, T7]" width="288" height="23"></p> <table> <tbody> <tr valign="baseline"> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -6;" src="/view.aspx?sf=145176/457176/780b582fbf4634b874a745dd5a698b21.gif" alt="[HA, VA, HB, T1, T2, T3, T4, T5, T6, T7]" width="288" height="23"></p> </td> <td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(8)</td> </tr> </tbody> </table> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=145176/457176/b073f96b54f823348449e095de4d0969.gif" alt="with(Student[LinearAlgebra]):" width="202" height="23"></p> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=145176/457176/2fce378ea2d81c5c3df9c55ea86c3c8b.gif" alt="interface(rtablesize = 20):" width="174" height="23"></p> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=145176/457176/b845087e0a442f911aef0bcf6b84930d.gif" alt="sol1 := GenerateMatrix(eq, var, augmented = true)" width="319" height="23"></p> <table> <tbody> <tr valign="baseline"> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -367;" src="/view.aspx?sf=145176/457176/7ba3d3306b07806888446f3d27b1ce11.gif" alt="sol1 := Matrix(10, 11, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 0, (1, 4) = cos(alpha), (1, 5) = cos((1/4)*Pi+alpha), (1, 6) = 0, (1, 7) = 0, (1, 8) = 0, (1, 9) = 0, (1, 10) = 0, (1, 11) = 0, (2, 1) = 0, (2, 2) = 1, (2, 3) = 0, (2, 4) = sin(alpha), (2, 5) = sin((1/4)*Pi+alpha), (2, 6) = 0, (2, 7) = 0, (2, 8) = 0, (2, 9) = 0, (2, 10) = 0, (2, 11) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = -1, (3, 4) = 0, (3, 5) = -cos((1/4)*Pi+alpha), (3, 6) = cos(-(1/4)*Pi+alpha), (3, 7) = cos(alpha), (3, 8) = 0, (3, 9) = 0, (3, 10) = 0, (3, 11) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = 0, (4, 5) = -sin((1/4)*Pi+alpha), (4, 6) = -sin((1/4)*Pi+alpha), (4, 7) = sin(alpha), (4, 8) = 0, (4, 9) = 0, (4, 10) = 0, (4, 11) = 0, (5, 1) = 0, (5, 2) = 0, (5, 3) = 0, (5, 4) = -cos(alpha), (5, 5) = 0, (5, 6) = -cos(-(1/4)*Pi+alpha), (5, 7) = 0, (5, 8) = cos((1/4)*Pi+alpha), (5, 9) = cos(alpha), (5, 10) = 0, (5, 11) = 0, (6, 1) = 0, (6, 2) = 0, (6, 3) = 0, (6, 4) = -sin(alpha), (6, 5) = 0, (6, 6) = cos((1/4)*Pi+alpha), (6, 7) = 0, (6, 8) = sin((1/4)*Pi+alpha), (6, 9) = sin(alpha), (6, 10) = 0, (6, 11) = 0, (7, 1) = 0, (7, 2) = 0, (7, 3) = 0, (7, 4) = 0, (7, 5) = 0, (7, 6) = 0, (7, 7) = -cos(alpha), (7, 8) = -cos((1/4)*Pi+alpha), (7, 9) = 0, (7, 10) = cos(-(1/4)*Pi+alpha), (7, 11) = 0, (8, 1) = 0, (8, 2) = 0, (8, 3) = 0, (8, 4) = 0, (8, 5) = 0, (8, 6) = 0, (8, 7) = -sin(alpha), (8, 8) = -sin((1/4)*Pi+alpha), (8, 9) = 0, (8, 10) = -cos((1/4)*Pi+alpha), (8, 11) = 0, (9, 1) = 0, (9, 2) = 0, (9, 3) = 0, (9, 4) = 0, (9, 5) = 0, (9, 6) = 0, (9, 7) = 0, (9, 8) = 0, (9, 9) = -cos(alpha), (9, 10) = -cos(-(1/4)*Pi+alpha), (9, 11) = 0, (10, 1) = 0, (10, 2) = 0, (10, 3) = 0, (10, 4) = 0, (10, 5) = 0, (10, 6) = 0, (10, 7) = 0, (10, 8) = 0, (10, 9) = -sin(alpha), (10, 10) = cos((1/4)*Pi+alpha), (10, 11) = L})" width="546" height="396" align="middle"></p> </td> <td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(9)</td> </tr> </tbody> </table> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -7;" src="/view.aspx?sf=145176/457176/c166ef1bc06a45a1105f13435d954c36.gif" alt="sol2 := GenerateMatrix(subs(alpha = 0, eq), var)" width="372" height="26"></p> <table> <tbody> <tr valign="baseline"> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -367;" src="/view.aspx?sf=145176/457176/d0d63713c4923f102e1446185fb803a4.gif" alt="sol2 := Matrix(10, 11, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 0, (1, 4) = cos(0), (1, 5) = cos((1/4)*Pi), (1, 6) = 0, (1, 7) = 0, (1, 8) = 0, (1, 9) = 0, (1, 10) = 0, (1, 11) = 0, (2, 1) = 0, (2, 2) = 1, (2, 3) = 0, (2, 4) = sin(0), (2, 5) = sin((1/4)*Pi), (2, 6) = 0, (2, 7) = 0, (2, 8) = 0, (2, 9) = 0, (2, 10) = 0, (2, 11) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = -1, (3, 4) = 0, (3, 5) = -cos((1/4)*Pi), (3, 6) = cos(-(1/4)*Pi), (3, 7) = cos(0), (3, 8) = 0, (3, 9) = 0, (3, 10) = 0, (3, 11) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = 0, (4, 5) = -sin((1/4)*Pi), (4, 6) = -sin((1/4)*Pi), (4, 7) = sin(0), (4, 8) = 0, (4, 9) = 0, (4, 10) = 0, (4, 11) = 0, (5, 1) = 0, (5, 2) = 0, (5, 3) = 0, (5, 4) = -cos(0), (5, 5) = 0, (5, 6) = -cos(-(1/4)*Pi), (5, 7) = 0, (5, 8) = cos((1/4)*Pi), (5, 9) = cos(0), (5, 10) = 0, (5, 11) = 0, (6, 1) = 0, (6, 2) = 0, (6, 3) = 0, (6, 4) = -sin(0), (6, 5) = 0, (6, 6) = cos((1/4)*Pi), (6, 7) = 0, (6, 8) = sin((1/4)*Pi), (6, 9) = sin(0), (6, 10) = 0, (6, 11) = 0, (7, 1) = 0, (7, 2) = 0, (7, 3) = 0, (7, 4) = 0, (7, 5) = 0, (7, 6) = 0, (7, 7) = -cos(0), (7, 8) = -cos((1/4)*Pi), (7, 9) = 0, (7, 10) = cos(-(1/4)*Pi), (7, 11) = 0, (8, 1) = 0, (8, 2) = 0, (8, 3) = 0, (8, 4) = 0, (8, 5) = 0, (8, 6) = 0, (8, 7) = -sin(0), (8, 8) = -sin((1/4)*Pi), (8, 9) = 0, (8, 10) = -cos((1/4)*Pi), (8, 11) = 0, (9, 1) = 0, (9, 2) = 0, (9, 3) = 0, (9, 4) = 0, (9, 5) = 0, (9, 6) = 0, (9, 7) = 0, (9, 8) = 0, (9, 9) = -cos(0), (9, 10) = -cos(-(1/4)*Pi), (9, 11) = 0, (10, 1) = 0, (10, 2) = 0, (10, 3) = 0, (10, 4) = 0, (10, 5) = 0, (10, 6) = 0, (10, 7) = 0, (10, 8) = 0, (10, 9) = -sin(0), (10, 10) = cos((1/4)*Pi), (10, 11) = L})" width="536" height="396" align="middle"></p> </td> <td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(10)</td> </tr> </tbody> </table> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=145176/457176/018211d3dc9898247dd4a0f234521fff.gif" alt="sol3 := convert(sol2, radical)" width="190" height="23"></p> <table> <tbody> <tr valign="baseline"> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -233;" src="/view.aspx?sf=145176/457176/a51853d6bf153fcb467134694f98dd97.gif" alt="sol3 := Matrix(10, 11, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 0, (1, 4) = 1, (1, 5) = (1/2)*sqrt(2), (1, 6) = 0, (1, 7) = 0, (1, 8) = 0, (1, 9) = 0, (1, 10) = 0, (1, 11) = 0, (2, 1) = 0, (2, 2) = 1, (2, 3) = 0, (2, 4) = 0, (2, 5) = (1/2)*sqrt(2), (2, 6) = 0, (2, 7) = 0, (2, 8) = 0, (2, 9) = 0, (2, 10) = 0, (2, 11) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = -1, (3, 4) = 0, (3, 5) = -(1/2)*sqrt(2), (3, 6) = (1/2)*sqrt(2), (3, 7) = 1, (3, 8) = 0, (3, 9) = 0, (3, 10) = 0, (3, 11) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = 0, (4, 5) = -(1/2)*sqrt(2), (4, 6) = -(1/2)*sqrt(2), (4, 7) = 0, (4, 8) = 0, (4, 9) = 0, (4, 10) = 0, (4, 11) = 0, (5, 1) = 0, (5, 2) = 0, (5, 3) = 0, (5, 4) = -1, (5, 5) = 0, (5, 6) = -(1/2)*sqrt(2), (5, 7) = 0, (5, 8) = (1/2)*sqrt(2), (5, 9) = 1, (5, 10) = 0, (5, 11) = 0, (6, 1) = 0, (6, 2) = 0, (6, 3) = 0, (6, 4) = 0, (6, 5) = 0, (6, 6) = (1/2)*sqrt(2), (6, 7) = 0, (6, 8) = (1/2)*sqrt(2), (6, 9) = 0, (6, 10) = 0, (6, 11) = 0, (7, 1) = 0, (7, 2) = 0, (7, 3) = 0, (7, 4) = 0, (7, 5) = 0, (7, 6) = 0, (7, 7) = -1, (7, 8) = -(1/2)*sqrt(2), (7, 9) = 0, (7, 10) = (1/2)*sqrt(2), (7, 11) = 0, (8, 1) = 0, (8, 2) = 0, (8, 3) = 0, (8, 4) = 0, (8, 5) = 0, (8, 6) = 0, (8, 7) = 0, (8, 8) = -(1/2)*sqrt(2), (8, 9) = 0, (8, 10) = -(1/2)*sqrt(2), (8, 11) = 0, (9, 1) = 0, (9, 2) = 0, (9, 3) = 0, (9, 4) = 0, (9, 5) = 0, (9, 6) = 0, (9, 7) = 0, (9, 8) = 0, (9, 9) = -1, (9, 10) = -(1/2)*sqrt(2), (9, 11) = 0, (10, 1) = 0, (10, 2) = 0, (10, 3) = 0, (10, 4) = 0, (10, 5) = 0, (10, 6) = 0, (10, 7) = 0, (10, 8) = 0, (10, 9) = 0, (10, 10) = (1/2)*sqrt(2), (10, 11) = L})" width="440" height="477"></p> </td> <td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(11)</td> </tr> </tbody> </table> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=145176/457176/c0ebec5b3e8ec63f70004514c543eff3.gif" alt="sol4 := ReducedRowEchelonForm(sol3)" width="256" height="23"></p> <table> <tbody> <tr valign="baseline"> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -126;" src="/view.aspx?sf=145176/457176/890f9c5c437466a7ecd2d276110a9045.gif" alt="sol4 := Matrix(10, 11, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (1, 5) = 0, (1, 6) = 0, (1, 7) = 0, (1, 8) = 0, (1, 9) = 0, (1, 10) = 0, (1, 11) = 4*L, (2, 1) = 0, (2, 2) = 1, (2, 3) = 0, (2, 4) = 0, (2, 5) = 0, (2, 6) = 0, (2, 7) = 0, (2, 8) = 0, (2, 9) = 0, (2, 10) = 0, (2, 11) = L, (3, 1) = 0, (3, 2) = 0, (3, 3) = 1, (3, 4) = 0, (3, 5) = 0, (3, 6) = 0, (3, 7) = 0, (3, 8) = 0, (3, 9) = 0, (3, 10) = 0, (3, 11) = 4*L, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = 1, (4, 5) = 0, (4, 6) = 0, (4, 7) = 0, (4, 8) = 0, (4, 9) = 0, (4, 10) = 0, (4, 11) = -3*L, (5, 1) = 0, (5, 2) = 0, (5, 3) = 0, (5, 4) = 0, (5, 5) = 1, (5, 6) = 0, (5, 7) = 0, (5, 8) = 0, (5, 9) = 0, (5, 10) = 0, (5, 11) = -L*sqrt(2), (6, 1) = 0, (6, 2) = 0, (6, 3) = 0, (6, 4) = 0, (6, 5) = 0, (6, 6) = 1, (6, 7) = 0, (6, 8) = 0, (6, 9) = 0, (6, 10) = 0, (6, 11) = L*sqrt(2), (7, 1) = 0, (7, 2) = 0, (7, 3) = 0, (7, 4) = 0, (7, 5) = 0, (7, 6) = 0, (7, 7) = 1, (7, 8) = 0, (7, 9) = 0, (7, 10) = 0, (7, 11) = 2*L, (8, 1) = 0, (8, 2) = 0, (8, 3) = 0, (8, 4) = 0, (8, 5) = 0, (8, 6) = 0, (8, 7) = 0, (8, 8) = 1, (8, 9) = 0, (8, 10) = 0, (8, 11) = -L*sqrt(2), (9, 1) = 0, (9, 2) = 0, (9, 3) = 0, (9, 4) = 0, (9, 5) = 0, (9, 6) = 0, (9, 7) = 0, (9, 8) = 0, (9, 9) = 1, (9, 10) = 0, (9, 11) = -L, (10, 1) = 0, (10, 2) = 0, (10, 3) = 0, (10, 4) = 0, (10, 5) = 0, (10, 6) = 0, (10, 7) = 0, (10, 8) = 0, (10, 9) = 0, (10, 10) = 1, (10, 11) = L*sqrt(2)})" width="273" height="263"></p> </td> <td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(12)</td> </tr> </tbody> </table> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=145176/457176/c5449526082f743b194c48fcd8f76792.gif" alt="sol5 := GenerateEquations(sol4, var)" width="238" height="23"></p> <table> <tbody> <tr valign="baseline"> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -27;" src="/view.aspx?sf=145176/457176/e0615e6605aed76c3f5524e79311a92c.gif" alt="[HA = 4*L, VA = L, HB = 4*L, T1 = -3*L, T2 = -L*2^(1/2), T3 = L*2^(1/2), T4 = 2*L, T5 = -L*2^(1/2), T6 = -L, T7 = L*2^(1/2)]" width="536" height="48" align="middle"></p> </td> <td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(13)</td> </tr> </tbody> </table> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -40;" src="/view.aspx?sf=145176/457176/0435df92c5cbcc0b7c295d8854c3713d.gif" alt="for i to nops(sol5) do sol5[i] end do" width="576" height="57" align="middle"></p> <table> <tbody> <tr valign="baseline"> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -6;" src="/view.aspx?sf=145176/457176/b14587fe7b019536e2073b026865be22.gif" alt="T7 = L*2^(1/2)" width="72" height="27"></p> </td> <td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(14)</td> </tr> </tbody> </table> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=145176/457176/56899419b429bc77e298c0014d90c76a.gif" alt="``" width="11" height="23"></p> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><span style="color: #ff0000; font-size: 100%; font-family: monospace,monospace; font-weight: bold; font-style: normal;">&nbsp; </span></p> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=145176/457176/07a8f4c2f999468bb479c740b1be2e48.gif" alt="``" width="11" height="23"><img style="vertical-align: -7;" src="/view.aspx?sf=145176/457176/71adf897c6c7c8119544faca070a650e.gif" alt="subs(alpha = 0, eq)" width="101" height="26"></p> <table> <tbody> <tr valign="baseline"> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -211;" src="/view.aspx?sf=145176/457176/9fad29cd4208a463c4900d81faf004d5.gif" alt="[HA+T1*cos(0)+T2*cos((1/4)*Pi) = 0, VA+T1*sin(0)+T2*sin((1/4)*Pi) = 0, -HB-T2*cos((1/4)*Pi)+T3*cos(-(1/4)*Pi)+T4*cos(0) = 0, -T2*sin((1/4)*Pi)-T3*sin((1/4)*Pi)+T4*sin(0) = 0, -T1*cos(0)-T3*cos(-(1/4)*Pi)+T5*cos((1/4)*Pi)+T6*cos(0) = 0, -T1*sin(0)+T3*cos((1/4)*Pi)+T5*sin((1/4)*Pi)+T6*sin(0) = 0, -T4*cos(0)-T5*cos((1/4)*Pi)+T7*cos(-(1/4)*Pi) = 0, -T4*sin(0)-T5*sin((1/4)*Pi)-T7*cos((1/4)*Pi) = 0, -T6*cos(0)-T7*cos(-(1/4)*Pi) = 0, -L-T6*sin(0)+T7*cos((1/4)*Pi) = 0]" width="536" height="240" align="middle"></p> </td> <td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(15)</td> </tr> </tbody> </table> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=145176/457176/bee7f677f48698e8a1a2101018d34867.gif" alt="simplify(%)" width="79" height="23"></p> <table> <tbody> <tr valign="baseline"> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -136;" src="/view.aspx?sf=145176/457176/c6d7d302f7a275278168557b1d1b7c46.gif" alt="[HA+T1+(1/2)*T2*2^(1/2) = 0, VA+(1/2)*T2*2^(1/2) = 0, -HB-(1/2)*T2*2^(1/2)+(1/2)*T3*2^(1/2)+T4 = 0, -(1/2)*T2*2^(1/2)-(1/2)*T3*2^(1/2) = 0, -T1-(1/2)*T3*2^(1/2)+(1/2)*T5*2^(1/2)+T6 = 0, (1/2)*T3*2^(1/2)+(1/2)*T5*2^(1/2) = 0, -T4-(1/2)*T5*2^(1/2)+(1/2)*T7*2^(1/2) = 0, -(1/2)*T5*2^(1/2)-(1/2)*T7*2^(1/2) = 0, -T6-(1/2)*T7*2^(1/2) = 0, -L+(1/2)*T7*2^(1/2) = 0]" width="536" height="166" align="middle"></p> </td> <td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(16)</td> </tr> </tbody> </table> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=145176/457176/7cbf6bd2dc9716ebd39dff7107baa639.gif" alt="NULL" width="11" height="23"></p> </td> </tr> </tbody> </table> <input type="hidden" name="sequence" value="1"> <input type="hidden" name="cmd" value="none"></form> <p>&nbsp;</p> <p><a href="/view.aspx?sf=145176/457176/truss2.mw">Download truss2.mw</a></p> <p>&nbsp;</p> <p>The general case is quite messy but can easily be found, but subsituting a value for alpha gave it a cleaner look.&nbsp; Also you can see what happens if alpha is set to 180 degrees that the CE member value becomes positive (under tension).&nbsp;&nbsp;</p> <p>This solution is one way to do it.&nbsp; I haven't actually tried to figure out where your mistake is in your code.</p> 145176 Wed, 27 Mar 2013 21:14:19 Z Christopher2222 Christopher2222