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fffffffffffffff00ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff0ffffffff fffffffffffffffffffffffffffffffffffffffffffffff00fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff fffffffffffffffffffffff0fffffffffffffffffffffffffffffffffffffffffffffffffffffff00fffffffffffffffffffffffffffffffffffffffffffffff fffffffffffffffffffffffffffffffffffffffffffffffffffffff0ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff0ffffffffffffffffffffffffffffffffffffffff fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff0ffffffff ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff fffffffffffffffffffffff0fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff0030000000000}}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid5704248 \par }\pard \ltrpar\ql \li0\ri0\nowidctlpar\phmrg\posx2439\posy5055\absh792\absw6063\wrapdefault\faauto\rin0\lin0\itap0 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid5704248 \hich\af0\dbch\af31505\loch\f0 Note: For thick-walled hollow rectangles, see Refs. 16 and 25. Reference 25 illustrates how to extend the work presented to cases with more than one enc\hich\af0\dbch\af31505\loch\f0 losed region. \par }\pard \ltrpar\ql \li0\ri0\nowidctlpar\wrapdefault\faauto\rin0\lin0\itap0 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid5704248 \page \par }\pard \ltrpar\ql \li0\ri0\nowidctlpar\phmrg\posx128\posy269\absh552\absw2231\wrapdefault\faauto\rin0\lin0\itap0 {\rtlch\fcs1 \ab\af0 \ltrch\fcs0 \b\ul\cf13\insrsid5704248 \hich\af0\dbch\af31505\loch\f0 Notation file}{\rtlch\fcs1 \ab\af0 \ltrch\fcs0 \b\cf13\insrsid5704248 \par }\pard \ltrpar\ql \li0\ri0\nowidctlpar\phmrg\posx2439\posy281\absh528\absw6186\wrapdefault\faauto\rin0\lin0\itap0 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid5704248 \hich\af0\dbch\af31505\loch\f0 Provides a description of Table 20 and the notation used. \par }\pard \ltrpar\ql \li0\ri0\nowidctlpar\phmrg\posx128\posy1003\absh828\absw2491\wrapdefault\faauto\rin0\lin0\itap0 {\rtlch\fcs1 \ab\af0 \ltrch\fcs0 \b\cf13\insrsid5704248 \hich\af0\dbch\af31505\loch\f0 Enter dimensions, properties and loading \par }\pard \ltrpar\ql \li0\ri0\nowidctlpar\phmrg\posx2439\posy1003\absh1104\absw5980\wrapdefault\faauto\rin0\lin0\itap0 {\rtlch\fcs1 \ab\af0 \ltrch\fcs0 \b\insrsid5704248 \hich\af0\dbch\af31505\loch\f0 Before progressing further, calculate the modulus of rigidity (G). You may need to flip to the preliminary calculations section\hich\af0\dbch\af31505\loch\f0 of the notation file to determine the value. Enter the quantity below:}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid5704248 \par }\pard \ltrpar\ql \li0\ri0\nowidctlpar\phmrg\posx128\posy2717\absh552\absw2231\wrapdefault\faauto\rin0\lin0\itap0 {\rtlch\fcs1 \ab\af0 \ltrch\fcs0 \b\ul\cf13\insrsid5704248 \hich\af0\dbch\af31505\loch\f0 Notation file}{\rtlch\fcs1 \ab\af0 \ltrch\fcs0 \b\cf13\insrsid5704248 \par }\pard \ltrpar\ql \li0\ri0\nowidctlpar\phmrg\posx2439\posy2729\absh528\absw2766\wrapdefault\faauto\rin0\lin0\itap0 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid5704248 \hich\af0\dbch\af31505\loch\f0 Modulus of rigidity: \par }\pard \ltrpar\ql \li0\ri0\nowidctlpar\phmrg\posx6805\posy2619\absh636\absw2330\wrapdefault\faauto\rin0\lin0\itap0 {\rtlch\fcs1 \af0 \ltrch\fcs0 \dn32\insrsid5704248 {\pict{\*\picprop\shplid1027{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}} {\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0 \picw2604\pich1122\picwgoal1476\pichgoal636\wmetafile8\bliptag-1268846575\blipupi119{\*\blipuid b45ef011356fe0931ed54de40ae8e99a} 0100090000038902000009001c00000000000400000003010800050000000c0235007b00050000000b020000000008000000fa02000001000000000000020400 00002d01000007000000fc020000ffffff020000040000002d01010005000000090200000000050000000102ffffff0205000000020101000000050000000902 000000001c000000fb02f0ff0000000000009001000000000400000054696d6573204e657720526f6d616e00e8b1f377f1b1f3772040f577ed1366bb04000000 2d010200050000002e011800000005000000090200000000070000002105010047001b00020005000000090200000000050000000902000000001c000000fb02 f0ff0000000000009001000000000400000054696d6573204e657720526f6d616e00e8b1f377f1b1f3772040f577ed1366bb040000002d010300090000002105 050031312e3534001b00220005000000090200000000040000002d01020005000000090200000000040000002d010300070000002105020031301b004b000500 0000090200000000040000002d010200050000000902000000001c000000fb02f1ff0000000000009001000000000400000054696d6573204e657720526f6d61 6e00e8b1f377f1b1f3772040f577ed1366bb040000002d010400050000000902000000001c000000fb02f1ff0000000000009001000000000400000054696d65 73204e657720526f6d616e00e8b1f377f1b1f3772040f577ed1366bb040000002d0105000700000021050100360011005b000500000009020000000004000000 2d01040005000000090200000000040000002d010200050000000902000000001c000000fb02f0ff0000000000009001000000020700000053796d626f6c0000 bb270abed0e4ea00e8b1f377f1b1f3772040f577ed1366bb040000002d010600050000002e01180000000700000021050100d7001b004700050000002e011800 000005000000090200000000040000002d0102000500000009020000000008000000210503006c62660010006900050000000902000000000500000009020000 00000700000021050200696e300069000500000009020000000005000000090200000000040000002d01040005000000090200000000040000002d0105000700 00002105010032002600730005000000090200000000040000002d01040005000000090200000000040000002d01020005000000090200000000040000002d01 060008000000fa0200000100000000000002040000002d0107000500000014021600680005000000130216007a00040000002d01000004000000f00107000500 0000090200000000040000002d01020005000000090200000000040000002d010600050000002e01180000000700000021050100d7001b006300050000002e01 1800000005000000090200000000040000002d01020005000000090200000000040000002d010600050000002e01180000000700000021050100ba001b001300 050000002e011800000005000000090200000000040000002d010200050000002e0100000000050000000902000000001c000000fb020c000900000000009001 00000000000202024d532053616e73205365726966000a0027008a01000000000700000040e9ea00040000002d01070008000000fa0200000000000000000000 040000002d01080004000000f001000007000000fc020000000000000000040000002d01000004000000f001010005000000090200000000050000000102ffffff0205000000020102000000030000000000}}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid5704248 \par }\pard \ltrpar\ql \li0\ri0\nowidctlpar\phmrg\posx2439\posy3341\absh528\absw3150\wrapdefault\faauto\rin0\lin0\itap0 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid5704248 \hich\af0\dbch\af31505\loch\f0 Base of outer rectangle: \par }\pard \ltrpar\ql \li0\ri0\nowidctlpar\phmrg\posx6805\posy3366\absh252\absw2467\wrapdefault\faauto\rin0\lin0\itap0 {\rtlch\fcs1 \af0 \ltrch\fcs0 \dn7\insrsid5704248 {\pict{\*\picprop\shplid1028{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}} {\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0 \picw1270\pich445\picwgoal720\pichgoal252\wmetafile8\bliptag-1132362887\blipupi119{\*\blipuid bc818379a3f2f266798b308673995d26}0100090000037b01000007001c00000000000400000003010800050000000c0215003c00050000000b020000000008000000fa02000001000000000000020400 00002d01000007000000fc020000ffffff020000040000002d01010005000000090200000000050000000102ffffff0205000000020101000000050000000902 000000001c000000fb02f0ff0000000000009001000000000400000054696d6573204e657720526f6d616e00e8b1f377f1b1f3772040f5777f1b665604000000 2d010200050000002e011800000005000000090200000000070000002105010061001000020005000000090200000000050000000902000000001c000000fb02 f0ff0000000000009001000000000400000054696d6573204e657720526f6d616e00e8b1f377f1b1f3772040f5777f1b6656040000002d010300070000002105 0200313510001e0005000000090200000000040000002d010200050000000902000000000700000021050200696e100033000500000009020000000005000000 0902000000001c000000fb02f0ff0000000000009001000000020700000053796d626f6c0000bb270abe1ce5ea00e8b1f377f1b1f3772040f5777f1b66560400 00002d010400050000002e01180000000700000021050100d70010002f00050000002e011800000005000000090200000000040000002d010200050000000902 00000000040000002d010400050000002e01180000000700000021050100ba0010000f00050000002e011800000005000000090200000000040000002d010200 050000002e0100000000050000000902000000001c000000fb020c00090000000000900100000000000202024d532053616e73205365726966000a0027008a01 00000000ffffffff40e9ea00040000002d01050008000000fa0200000000000000000000040000002d01060004000000f001000007000000fc020000000000000000040000002d01000004000000f001010005000000090200000000050000000102ffffff0205000000020102000000030000000000}}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid5704248 \par }\pard \ltrpar\ql \li0\ri0\nowidctlpar\phmrg\posx2439\posy3953\absh528\absw3294\wrapdefault\faauto\rin0\lin0\itap0 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid5704248 \hich\af0\dbch\af31505\loch\f0 Height of outer rectangle: \par }\pard \ltrpar\ql \li0\ri0\nowidctlpar\phmrg\posx6805\posy3978\absh252\absw2479\wrapdefault\faauto\rin0\lin0\itap0 {\rtlch\fcs1 \af0 \ltrch\fcs0 \dn7\insrsid5704248 {\pict{\*\picprop\shplid1029{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}} {\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0 \picw1291\pich445\picwgoal732\pichgoal252\wmetafile8\bliptag-370806382\blipupi119{\*\blipuid e9e5f192cfa1e6770d91df5608c2c67d}0100090000037b01000007001c00000000000400000003010800050000000c0215003d00050000000b020000000008000000fa02000001000000000000020400 00002d01000007000000fc020000ffffff020000040000002d01010005000000090200000000050000000102ffffff0205000000020101000000050000000902 000000001c000000fb02f0ff0000000000009001000000000400000054696d6573204e657720526f6d616e00e8b1f377f1b1f3772040f577f72b669f04000000 2d010200050000002e011800000005000000090200000000070000002105010062001000020005000000090200000000050000000902000000001c000000fb02 f0ff0000000000009001000000000400000054696d6573204e657720526f6d616e00e8b1f377f1b1f3772040f577f72b669f040000002d010300070000002105 0200313010001f0005000000090200000000040000002d010200050000000902000000000700000021050200696e100034000500000009020000000005000000 0902000000001c000000fb02f0ff0000000000009001000000020700000053796d626f6c0000bb270abe1ce5ea00e8b1f377f1b1f3772040f577f72b669f0400 00002d010400050000002e01180000000700000021050100d70010003000050000002e011800000005000000090200000000040000002d010200050000000902 00000000040000002d010400050000002e01180000000700000021050100ba0010001000050000002e011800000005000000090200000000040000002d010200 050000002e0100000000050000000902000000001c000000fb020c00090000000000900100000000000202024d532053616e73205365726966000a0027008a01 00000000ffffffff40e9ea00040000002d01050008000000fa0200000000000000000000040000002d01060004000000f001000007000000fc020000000000000000040000002d01000004000000f001010005000000090200000000050000000102ffffff0205000000020102000000030000000000}}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid5704248 \par }\pard \ltrpar\ql \li0\ri0\nowidctlpar\phmrg\posx2439\posy4565\absh528\absw3438\wrapdefault\faauto\rin0\lin0\itap0 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid5704248 \hich\af0\dbch\af31505\loch\f0 Thickness of base and top: \par }\pard \ltrpar\ql \li0\ri0\nowidctlpar\phmrg\posx6805\posy4590\absh288\absw2331\wrapdefault\faauto\rin0\lin0\itap0 {\rtlch\fcs1 \af0 \ltrch\fcs0 \dn10\insrsid5704248 {\pict{\*\picprop\shplid1030{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}} {\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0 \picw1249\pich508\picwgoal708\pichgoal288\wmetafile8\bliptag1797411531\blipupi119{\*\blipuid 6b2252cb619a0411cdc8b54c4b7d001d}010009000003f201000009001c00000000000400000003010800050000000c0218003b00050000000b020000000008000000fa02000001000000000000020400 00002d01000007000000fc020000ffffff020000040000002d01010005000000090200000000050000000102ffffff0205000000020101000000050000000902 000000001c000000fb02f0ff0000000000009001000000000400000054696d6573204e657720526f6d616e00e8b1f377f1b1f3772040f5773e2f66a104000000 2d010200050000002e01180000000500000009020000000005000000090200000000050000000902000000000700000021050100740010000200050000000902 000000001c000000fb02f1ff0000000000009001000000000400000054696d6573204e657720526f6d616e00e8b1f377f1b1f3772040f5773e2f66a104000000 2d010300050000000902000000001c000000fb02f3ff0000000000009001000000000400000054696d6573204e657720526f6d616e00e8b1f377f1b1f3772040 f5773e2f66a1040000002d01040005000000090200000000070000002105010031001300060005000000090200000000040000002d0103000500000009020000 0000040000002d0102000500000009020000000005000000090200000000050000000902000000001c000000fb02f0ff00000000000090010000000004000000 54696d6573204e657720526f6d616e00e8b1f377f1b1f3772040f5773e2f66a1040000002d01050007000000210502002e351000210005000000090200000000 040000002d010200050000000902000000000700000021050200696e1000320005000000090200000000050000000902000000001c000000fb02f0ff00000000 00009001000000020700000053796d626f6c0000bb270abe1ce5ea00e8b1f377f1b1f3772040f5773e2f66a1040000002d010600050000002e01180000000700 000021050100d70010002e00050000002e011800000005000000090200000000040000002d01020005000000090200000000040000002d010600050000002e01 180000000700000021050100ba0010001200050000002e011800000005000000090200000000040000002d010200050000002e01000000000500000009020000 00001c000000fb020c00090000000000900100000000000202024d532053616e73205365726966000a0027008a0100000000ffffffff40e9ea00040000002d01 070008000000fa0200000000000000000000040000002d01080004000000f001000007000000fc020000000000000000040000002d01000004000000f001010005000000090200000000050000000102ffffff0205000000020102000000030000000000}}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid5704248 \par }\pard \ltrpar\ql \li0\ri0\nowidctlpar\phmrg\posx2439\posy5177\absh528\absw2718\wrapdefault\faauto\rin0\lin0\itap0 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid5704248 \hich\af0\dbch\af31505\loch\f0 Thickness of sides: \par }\pard \ltrpar\ql \li0\ri0\nowidctlpar\phmrg\posx6805\posy5202\absh252\absw2383\wrapdefault\faauto\rin0\lin0\itap0 {\rtlch\fcs1 \af0 \ltrch\fcs0 \dn7\insrsid5704248 {\pict{\*\picprop\shplid1031{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}} {\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0 \picw1122\pich445\picwgoal636\pichgoal252\wmetafile8\bliptag434220295\blipupi119{\*\blipuid 19e1ad07549089efd79a7eabbf021383}0100090000037b01000007001c00000000000400000003010800050000000c0215003500050000000b020000000008000000fa02000001000000000000020400 00002d01000007000000fc020000ffffff020000040000002d01010005000000090200000000050000000102ffffff0205000000020101000000050000000902 000000001c000000fb02f0ff0000000000009001000000000400000054696d6573204e657720526f6d616e00e8b1f377f1b1f3772040f577ed1366c204000000 2d010200050000002e0118000000050000000902000000000700000021050100740b1000020005000000090200000000050000000902000000001c000000fb02 f0ff0000000000009001000000000400000054696d6573204e657720526f6d616e00e8b1f377f1b1f3772040f577ed1366c2040000002d010300070000002105 02002e3310001b0005000000090200000000040000002d010200050000000902000000000700000021050200696e10002c000500000009020000000005000000 0902000000001c000000fb02f0ff0000000000009001000000020700000053796d626f6c0000bb270abe1ce5ea00e8b1f377f1b1f3772040f577ed1366c20400 00002d010400050000002e01180000000700000021050100d70b10002800050000002e011800000005000000090200000000040000002d010200050000000902 00000000040000002d010400050000002e01180000000700000021050100ba0b10000c00050000002e011800000005000000090200000000040000002d010200 050000002e0100000000050000000902000000001c000000fb020c00090000000000900100000000000202024d532053616e73205365726966000a0027008a01 00000000ffffffff40e9ea00040000002d01050008000000fa0200000000000000000000040000002d01060004000000f001000007000000fc020000000000000000040000002d01000004000000f001010005000000090200000000050000000102ffffff0205000000020102000000030000000000}}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid5704248 \par }\pard \ltrpar\ql \li0\ri0\nowidctlpar\phmrg\posx2439\posy5789\absh528\absw2598\wrapdefault\faauto\rin0\lin0\itap0 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid5704248 \hich\af0\dbch\af31505\loch\f0 Twisting moment: \par }\pard \ltrpar\ql \li0\ri0\nowidctlpar\phmrg\posx6805\posy5814\absh252\absw2923\wrapdefault\faauto\rin0\lin0\itap0 {\rtlch\fcs1 \af0 \ltrch\fcs0 \dn7\insrsid5704248 {\pict{\*\picprop\shplid1032{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}} {\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0 \picw2074\pich445\picwgoal1176\pichgoal252\wmetafile8\bliptag447075442\blipupi119{\*\blipuid 1aa5d472922edf926cf0b214b7d12265}010009000003b101000007001c00000000000400000003010800050000000c0215006200050000000b020000000008000000fa02000001000000000000020400 00002d01000007000000fc020000ffffff020000040000002d01010005000000090200000000050000000102ffffff0205000000020101000000050000000902 000000001c000000fb02f0ff0000000000009001000000000400000054696d6573204e657720526f6d616e00e8b1f377f1b1f3772040f5777f1b665e04000000 2d010200050000002e0118000000050000000902000000000700000021050100540b1000020005000000090200000000050000000902000000001c000000fb02 f0ff0000000000009001000000000400000054696d6573204e657720526f6d616e00e8b1f377f1b1f3772040f5777f1b665e040000002d010300080000002105 0400353030301000200005000000090200000000040000002d0102000500000009020000000008000000210503006c6266001000450005000000090200000000 050000000902000000001c000000fb02f0ff0000000000009001000000020700000053796d626f6c0000bb270abed0e4ea00e8b1f377f1b1f3772040f5777f1b 665e040000002d010400050000002e01180000000700000021050100d70b10004100050000002e011800000005000000090200000000040000002d0102000500 00000902000000000700000021050200667410005b000500000009020000000005000000090200000000040000002d010400050000002e011800000007000000 21050100d70b10005700050000002e011800000005000000090200000000040000002d01020005000000090200000000040000002d010400050000002e011800 00000700000021050100ba0b10001100050000002e011800000005000000090200000000040000002d010200050000002e010000000005000000090200000000 1c000000fb020c00090000000000900100000000000202024d532053616e73205365726966000a0027008a0100000000ffffffff40e9ea00040000002d010500 08000000fa0200000000000000000000040000002d01060004000000f001000007000000fc020000000000000000040000002d01000004000000f001010005000000090200000000050000000102ffffff0205000000020102000000030000000000}}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid5704248 \par }\pard \ltrpar\ql \li0\ri0\nowidctlpar\phmrg\posx2439\posy6401\absh528\absw2478\wrapdefault\faauto\rin0\lin0\itap0 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid5704248 \hich\af0\dbch\af31505\loch\f0 Length of beam: \par }\pard \ltrpar\ql \li0\ri0\nowidctlpar\phmrg\posx6805\posy6426\absh252\absw2371\wrapdefault\faauto\rin0\lin0\itap0 {\rtlch\fcs1 \af0 \ltrch\fcs0 \dn7\insrsid5704248 {\pict{\*\picprop\shplid1033{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}} {\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0 \picw1101\pich445\picwgoal624\pichgoal252\wmetafile8\bliptag-2115398423\blipupi119{\*\blipuid 81e994e90fd4e4a1a1a7eca689ee3d6c}0100090000037b01000007001c00000000000400000003010800050000000c0215003400050000000b020000000008000000fa02000001000000000000020400 00002d01000007000000fc020000ffffff020000040000002d01010005000000090200000000050000000102ffffff0205000000020101000000050000000902 000000001c000000fb02f0ff0000000000009001000000000400000054696d6573204e657720526f6d616e00e8b1f377f1b1f3772040f577f72b66a604000000 2d010200050000002e01180000000500000009020000000007000000210501004c0b1000020005000000090200000000050000000902000000001c000000fb02 f0ff0000000000009001000000000400000054696d6573204e657720526f6d616e00e8b1f377f1b1f3772040f577f72b66a6040000002d010300070000002105 0100380b1000200005000000090200000000040000002d010200050000000902000000000700000021050200667410002d000500000009020000000005000000 0902000000001c000000fb02f0ff0000000000009001000000020700000053796d626f6c0000bb270abe1ce5ea00e8b1f377f1b1f3772040f577f72b66a60400 00002d010400050000002e01180000000700000021050100d70b10002900050000002e011800000005000000090200000000040000002d010200050000000902 00000000040000002d010400050000002e01180000000700000021050100ba0b10001100050000002e011800000005000000090200000000040000002d010200 050000002e0100000000050000000902000000001c000000fb020c00090000000000900100000000000202024d532053616e73205365726966000a0027008a01 00000000ffffffff40e9ea00040000002d01050008000000fa0200000000000000000000040000002d01060004000000f001000007000000fc020000000000000000040000002d01000004000000f001010005000000090200000000050000000102ffffff0205000000020102000000030000000000}}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid5704248 \par }\pard \ltrpar\ql \li0\ri0\nowidctlpar\wrapdefault\faauto\rin0\lin0\itap0 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid5704248 \page \par }\pard\plain \ltrpar\s15\ql \li0\ri0\nowidctlpar\phmrg\posx128\posy269\absh1200\absw3651\wrapdefault\faauto\rin0\lin0\itap0 \rtlch\fcs1 \ab\af0\afs24\alang1025 \ltrch\fcs0 \b\fs24\cf13\lang1033\langfe1033\loch\af0\hich\af0\dbch\af31505\cgrid\langnp1033\langfenp1033 {\rtlch\fcs1 \ab0\af0 \ltrch\fcs0 \b0\insrsid5704248 \hich\af0\dbch\af31505\loch\f0 Ge}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid5704248 \hich\af0\dbch\af31505\loch\f0 neral formulas for \par }{\rtlch\fcs1 \ab0\af0 \ltrch\fcs0 \b0\insrsid5704248 \hich\af0\dbch\af31505\loch\f0 torsional stiffness, K;}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid5704248 \par }{\rtlch\fcs1 \ab0\af0 \ltrch\fcs0 \b0\insrsid5704248 \hich\af0\dbch\af31505\loch\f0 average shear stresses, }{\rtlch\fcs1 \af3 \ltrch\fcs0 \f3\insrsid5704248 \loch\af3\dbch\af31505\hich\f3 \'74}{\rtlch\fcs1 \af0 \ltrch\fcs0 \dn6\insrsid5704248 \hich\af0\dbch\af31505\loch\f0 average;}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid5704248 \par }{\rtlch\fcs1 \ab0\af0 \ltrch\fcs0 \b0\insrsid5704248 \hich\af0\dbch\af31505\loch\f0 and angle of twist, }{\rtlch\fcs1 \af3 \ltrch\fcs0 \f3\insrsid5704248 \loch\af3\dbch\af31505\hich\f3 \'71}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid5704248 \par }\pard\plain \ltrpar\ql \li0\ri0\nowidctlpar\phmrg\posx2439\posy1995\absh528\absw4650\wrapdefault\faauto\rin0\lin0\itap0 \rtlch\fcs1 \af0\afs24\alang1025 \ltrch\fcs0 \fs24\lang1033\langfe1033\loch\af0\hich\af0\dbch\af31505\cgrid\langnp1033\langfenp1033 { \rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid5704248 \hich\af0\dbch\af31505\loch\f0 Approximate torsional stiffness constant: \par }\pard \ltrpar\ql \li0\ri0\nowidctlpar\phmrg\posx2439\posy2607\absh804\absw2896\wrapdefault\faauto\rin0\lin0\itap0 {\rtlch\fcs1 \af0 \ltrch\fcs0 \dn36\insrsid5704248 {\pict{\*\picprop\shplid1034{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}} {\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0 \picw3937\pich1418\picwgoal2232\pichgoal804\wmetafile8\bliptag1938231594\blipupi120{\*\blipuid 7387112a81a1ca3c9086bb5cba2784af} 010009000003260600000a001c00000000000400000003010800050000000c024300ba00050000000b020000000008000000fa02000001000000000000020400 00002d01000007000000fc020000ffffff020000040000002d01010005000000090200000000050000000102ffffff0205000000020101000000050000000902 000000001c000000fb02f0ff0000000000009001000000000400000054696d6573204e657720526f6d616e00e8b1f377f1b1f3772040f5773e2f66a904000000 2d010200050000002e01180000000500000009020000000007000000210501004b0b2600020005000000090200000000050000000902000000001c000000fb02 f0ff0000000000009001000000000400000054696d6573204e657720526f6d616e00e8b1f377f1b1f3772040f5773e2f66a9040000002d010300070000002105 0100320b1800280005000000090200000000040000002d010200050000000902000000000700000021050100740b180035000500000009020000000005000000 0902000000001c000000fb02f0ff0000000000009001000000020700000053796d626f6c0000bb270abeece3ea00e8b1f377f1b1f3772040f5773e2f66a90400 00002d010400050000002e01180000000700000021050100d70b18003100050000002e011800000005000000090200000000040000002d010200050000000902 0000000005000000090200000000050000000902000000000700000021050100740b18003e00050000000902000000001c000000fb02f1ff0000000000009001 000000000400000054696d6573204e657720526f6d616e00e8b1f377f1b1f3772040f5773e2f66a9040000002d010500050000000902000000001c000000fb02 f3ff0000000000009001000000000400000054696d6573204e657720526f6d616e00e8b1f377f1b1f3772040f5773e2f66a9040000002d010600050000000902 000000000700000021050100310b1b00420005000000090200000000040000002d01050005000000090200000000040000002d01020005000000090200000000 0500000009020000000005000000090200000000040000002d010400050000002e01180000000700000021050100d70b18003a00050000002e01180000000500 0000090200000000040000002d010200050000000902000000000700000021050100610b18005300050000000902000000000500000009020000000007000000 21050100740b18006b000500000009020000000005000000090200000000040000002d010400050000002e011800000007000000210501002d0b18005e000500 00002e011800000005000000090200000000040000002d0102001c000000fb020c00090000000000900100000000000202024d532053616e7320536572696600 0a0027008a0100000000ffffffff88e5ea00040000002d010700040000002d0102000700000021050100280b18004d000700000021050100290b18006f000500 0000090200000000040000002d010500050000000902000000001c000000fb02f1ff0000000000009001000000000400000054696d6573204e657720526f6d61 6e00e8b1f377f1b1f3772040f5773e2f66a9040000002d0108000700000021050100320b0e00750005000000090200000000040000002d010500050000000902 00000000040000002d01020005000000090200000000040000002d010400050000002e01180000000700000021050100d70b18004900050000002e0118000000 05000000090200000000040000002d010200050000000902000000000700000021050100620b1800880005000000090200000000050000000902000000000500 0000090200000000050000000902000000000700000021050100740b1800a10005000000090200000000040000002d0105000500000009020000000004000000 2d010600050000000902000000000700000021050100310b1b00a50005000000090200000000040000002d01050005000000090200000000040000002d010200 050000000902000000000500000009020000000005000000090200000000040000002d010400050000002e011800000007000000210501002d0b180094000500 00002e011800000005000000090200000000040000002d01020005000000090200000000040000002d010400040000002d010700040000002d0104001c000000 fb02e7ff0a00000000009001000000020700000053796d626f6c0000f7250a7368e5ea00e8b1f377f1b1f3772040f5773e2f66a9040000002d01090007000000 21050100280b190081000700000021050100290b1900ab00040000002d01040004000000f001090005000000090200000000040000002d010200050000000902 00000000040000002d01050005000000090200000000040000002d0108000700000021050100320b0e00b20005000000090200000000040000002d0105000500 0000090200000000040000002d01020005000000090200000000040000002d010400050000002e01180000000700000021050100d70b18007d00050000002e01 1800000005000000090200000000040000002d010200050000000902000000000700000021050100610b3b003500050000000902000000000500000009020000 00000700000021050100740b3b0041000500000009020000000005000000090200000000040000002d010400050000002e01180000000700000021050100d70b 3b003d00050000002e011800000005000000090200000000040000002d010200050000000902000000000700000021050100620b3b0057000500000009020000 00000500000009020000000005000000090200000000050000000902000000000700000021050100740b3b00640005000000090200000000040000002d010500 05000000090200000000040000002d010600050000000902000000000700000021050100310b3e00680005000000090200000000040000002d01050005000000 090200000000040000002d010200050000000902000000000500000009020000000005000000090200000000040000002d010400050000002e01180000000700 000021050100d70b3b006000050000002e011800000005000000090200000000040000002d01020005000000090200000000040000002d010400050000002e01 1800000007000000210501002b0b3b004900050000002e011800000005000000090200000000040000002d010200050000000902000000000700000021050100 740b3b007f000500000009020000000005000000090200000000040000002d01050005000000090200000000040000002d0108000700000021050100320b3100 830005000000090200000000040000002d01050005000000090200000000040000002d01020005000000090200000000040000002d010400050000002e011800 000007000000210501002d0b3b007200050000002e011800000005000000090200000000040000002d0102000500000009020000000005000000090200000000 050000000902000000000700000021050100740b3b009b0005000000090200000000040000002d01050005000000090200000000040000002d01060005000000 0902000000000700000021050100310b3e009f0005000000090200000000040000002d01050005000000090200000000040000002d0102000500000009020000 00000500000009020000000005000000090200000000040000002d01050005000000090200000000040000002d0108000700000021050100320b3100a5000500 0000090200000000040000002d01050005000000090200000000040000002d01020005000000090200000000040000002d010400050000002e01180000000700 0000210501002d0b3b008e00050000002e011800000005000000090200000000040000002d01020005000000090200000000040000002d01040008000000fa02 00000100000000000002040000002d010900050000001402210027000500000013022100b900040000002d01000004000000f001090005000000090200000000 040000002d01020005000000090200000000040000002d010400050000002e011800000007000000210502003a3d26001300050000002e011800000005000000 090200000000040000002d010200050000002e010000000005000000090200000000040000002d01070008000000fa0200000000000000000000040000002d01 090004000000f001000007000000fc020000000000000000040000002d01000004000000f001010005000000090200000000050000000102ffffff0205000000020102000000030000000000}}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid5704248 \par }\pard \ltrpar\ql \li0\ri0\nowidctlpar\phmrg\posx6420\posy2778\absh348\absw2698\wrapdefault\faauto\rin0\lin0\itap0 {\rtlch\fcs1 \af0 \ltrch\fcs0 \dn7\insrsid5704248 {\pict{\*\picprop\shplid1035{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}} {\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0 \picw2223\pich614\picwgoal1260\pichgoal348\wmetafile8\bliptag806676595\blipupi119{\*\blipuid 3014e873293afa7bb893c8e1b944869f}010009000003be01000009001c00000000000400000003010800050000000c021d006900050000000b020000000008000000fa02000001000000000000020400 00002d01000007000000fc020000ffffff020000040000002d01010005000000090200000000050000000102ffffff0205000000020101000000050000000902 000000001c000000fb02f0ff0000000000009001000000000400000054696d6573204e657720526f6d616e00e8b1f377f1b1f3772040f577ed1366c904000000 2d010200050000002e01180000000500000009020000000007000000210501004b0b1800020005000000090200000000050000000902000000001c000000fb02 f0ff0000000000009001000000000400000054696d6573204e657720526f6d616e00e8b1f377f1b1f3772040f577ed1366c9040000002d0103000a0000002105 07003633382e373136001800230005000000090200000000040000002d010200050000000902000000000700000021050200696e180059000500000009020000 0000050000000902000000001c000000fb02f1ff0000000000009001000000000400000054696d6573204e657720526f6d616e00e8b1f377f1b1f3772040f577 ed1366c9040000002d010400050000000902000000001c000000fb02f1ff0000000000009001000000000400000054696d6573204e657720526f6d616e00e8b1 f377f1b1f3772040f577ed1366c9040000002d0105000700000021050100340b0e00630005000000090200000000040000002d01040005000000090200000000 040000002d010200050000000902000000001c000000fb02f0ff0000000000009001000000020700000053796d626f6c0000bb270abe4ce6ea00e8b1f377f1b1 f3772040f577ed1366c9040000002d010600050000002e011800000007000000210501003d0b18001400050000002e0118000000050000000902000000000400 00002d010200050000002e0100000000050000000902000000001c000000fb020c00090000000000900100000000000202024d532053616e7320536572696600 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\ltrch\fcs0 \dn32\insrsid5704248 {\pict{\*\picprop\shplid1037{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}} {\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0 \picw3112\pich1122\picwgoal1764\pichgoal636\wmetafile8\bliptag-1199682985\blipupi119{\*\blipuid b87e4a5798d11fe44575ffeeb3542b45} 010009000003bd0200000b001c00000000000400000003010800050000000c0235009300050000000b020000000008000000fa02000001000000000000020400 00002d01000007000000fc020000ffffff020000040000002d01010005000000090200000000050000000102ffffff0205000000020101000000050000000902 000000001c000000fb02f0ff0000000000009001000000000400000054696d6573204e657720526f6d616e00e8b1f377f1b1f3772040f577f72b66ad04000000 2d010200050000002e011800000005000000090200000000050000000902000000001c000000fb02f0ff0000000000009001000000020700000053796d626f6c 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75}}{\sp{\sn fFlipH}{\sv 0}} {\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0 \picw4255\pich1016\picwgoal2412\pichgoal576\wmetafile8\bliptag-138079086\blipupi119{\*\blipuid f7c5149270a034394a3334bdf2358799} 010009000003490400000a001c00000000000400000003010800050000000c023000c900050000000b020000000008000000fa02000001000000000000020400 00002d01000007000000fc020000ffffff020000040000002d01010005000000090200000000050000000102ffffff0205000000020101000000050000000902 000000001c000000fb02f0ff0000000000009001000000000400000054696d6573204e657720526f6d616e00e8b1f377f1b1f3772040f5773e2f66b104000000 2d010200050000002e011800000005000000090200000000050000000902000000001c000000fb02f0ff0000000000009001000000020700000053796d626f6c 0000bc270a6d6ce5ea00e8b1f377f1b1f3772040f5773e2f66b1040000002d01030005000000090200000000040000002d010200050000000902000000000500 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\hich\af0\dbch\af31505\loch\f0 There will be higher stresses at inner corners unless fillets of fairly large radius are provided. \par }\pard \ltrpar\ql \li0\ri0\nowidctlpar\phmrg\posx2439\posy8604\absh792\absw5823\wrapdefault\faauto\rin0\lin0\itap0 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid5704248 \hich\af0\dbch\af31505\loch\f0 Approximate angle of twist: \par \hich\af0\dbch\af31505\loch\f0 This is the angular deformation of the beam over its entire length. \par }\pard \ltrpar\ql \li0\ri0\nowidctlpar\phmrg\posx2439\posy9596\absh540\absw1796\wrapdefault\faauto\rin0\lin0\itap0 {\rtlch\fcs1 \af0 \ltrch\fcs0 \dn22\insrsid5704248 {\pict{\*\picprop\shplid1040{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}} {\sp{\sn fFlipV}{\sv 0}}{\sp{\sn fLine}{\sv 0}}{\sp{\sn fLayoutInCell}{\sv 1}}}\picscalex100\picscaley100\piccropl0\piccropr0\piccropt0\piccropb0 \picw1397\pich953\picwgoal792\pichgoal540\wmetafile8\bliptag783627438\blipupi119{\*\blipuid 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\hich\af0\dbch\af31505\loch\f0 References \par }\pard \ltrpar\ql \li0\ri0\nowidctlpar\phmrg\posx2439\posy10685\absh1848\absw6014\wrapdefault\faauto\rin0\lin0\itap0 {\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid5704248 \hich\af0\dbch\af31505\loch\f0 Ref. 16. Abramyan, B. L.: Torsion and Bending of Prismatic Roads of Hollow Rectangular Section, }{\rtlch\fcs1 \ai\af0 \ltrch\fcs0 \i\insrsid5704248 \hich\af0\dbch\af31505\loch\f0 NACA Tech. Memo.}{\rtlch\fcs1 \af0 \ltrch\fcs0 \insrsid5704248 \hich\af0\dbch\af31505\loch\f0 1319, November 1951. \par \par \hich\af0\dbch\af31505\loch\f0 Ref. 25. Marshall, J.: Derivation of Torsion Formulas for M\hich\af0\dbch\af31505\loch\f0 ultiply Connected Thick-Walled Rectangular Section, }{\rtlch\fcs1 \ai\af0 \ltrch\fcs0 \i\insrsid5704248 \hich\af0\dbch\af31505\loch\f0 ASME J. Appl. 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