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<p>\[\begin{align}<br />v_{F}&amp;=-2,17 \mathrm{~mm} \\<br />w_{F}&amp;=1,61 \mathrm{~mm} <br />\end{align}\]</p>

<p>Tabelle zu den Werten der Teilprofile</p>


<p>\begin{array}{|c|ccccc|r|l|} \hline &amp; \text { Profil 1 } &amp; \text { Profil 2 } &amp; \text { Profil 3 } &amp; \text { Profil 4 } &amp; \text { Profil 5 } &amp; \text { Summe } &amp; \\ \hline A_{i} &amp; 40 &amp; 80 &amp; 200 &amp; 80 &amp; 40 &amp; 440 &amp; \mathrm{~mm}^{2} \\ y_{S i} &amp; 40 &amp; 20 &amp; 0 &amp; -20 &amp; -40 &amp; &amp; \mathrm{~mm} \\ z_{S i} &amp; 40 &amp; 50 &amp; 0 &amp; -50 &amp; -40 &amp; &amp; \mathrm{~mm} \\ \hline I_{Y i} &amp; 1333 &amp; 0 &amp; 166700 &amp; 0 &amp; 1333 &amp; 169400 &amp; \mathrm{~mm}^{4} \\ I_{Z i} &amp; 0 &amp; 10670 &amp; 0 &amp; 10670 &amp; 0 &amp; 21340 &amp; \mathrm{~mm}^{4} \\ \hline A_{i} &amp; 64000 &amp; 200000 &amp; 0 &amp; 200000 &amp; 64000 &amp; 528000 &amp; \mathrm{~mm}^{4} \\ y_{S i}^{2} A_{i} &amp; 64000 &amp; 32000 &amp; 0 &amp; 32000 &amp; 64000 &amp; 192000 &amp; \mathrm{~mm}^{4} \\ -y_{S i} z_{S i} A_{i} &amp; -64000 &amp; -80000 &amp; 0 &amp; -80000 &amp; -64000 &amp; -288000 &amp; \mathrm{~mm}^{4} \\ \hline \end{array}</p>


<p>\[<br />\begin{aligned}<br />&amp; I_{y}=169400+528000 \mathrm{~mm}^{4}=69,74 \mathrm{~cm}^{4} \\<br />&amp; I_{z}=21340+192000 \mathrm{~mm}^{4}=21,33 \mathrm{~cm}^{4} \\<br />&amp; I_{y z}=-28,80 \mathrm{~cm}^{4}<br />\end{aligned}</p>


<p>\[<br />\begin{aligned}<br />\sum M^{B} &amp;=0:-L A_{z}+\frac{L}{2} F=0 \\<br />&amp; \Rightarrow A_{z}=\frac{F}{2} \\\\<br />\sum M^{A} &amp;=0:-\frac{L}{2} F+L B_{z}=0 \\<br />&amp; \Rightarrow B_{z}=\frac{F}{2}<br />\end{aligned}</p>


<p>\begin{align}<br />Q_{z}(x)=-\left(-A_{z}+\left\langle x-\frac{L}{2}\right\rangle^{0} F\right)=F\left(\frac{1}{2}-\left\langle\frac{x}{L}-\frac{1}{2}\right\rangle^{0}\right) <br />\end{align}</p>


<p>\begin{align}<br />M_{y}(x)=F\left(\frac{x}{2}-L\left\langle\frac{x}{L}-\frac{1}{2}\right\rangle\right)=\frac{F L}{2}\left(\frac{x}{L}-\left\langle2 \frac{x}{L}-1\right\rangle\right) <br />\end{align}</p>


<p>\begin{align}<br />\bar{M}_{y}&amp;=\frac{1}{1-I_{y z}^{2} /\left(I_{y} I_{z}\right)} M_{y} \\\\ \bar{M}_{z}&amp;=-\frac{I_{y z} / I_{y}}{1-I_{y z}^{2} /\left(I_{y} I_{z}\right)} M_{y}=-\frac{I_{y z}}{I_{y}} \bar{M}_{y} <br />\end{align}</p>


<p>\begin{align}<br />E I_{y} \frac{d^{2} w}{d x^{2}}&amp;=-\bar{M}_{y}=\frac{-F L}{2\left(1-I_{y z}^{2} /\left(I_{y} I_{z}\right)\right)}\left[\frac{x}{L}-\left\langle 2 \frac{x}{L}-1\right\rangle\right]\\\\<br />E I_{y} \frac{d w}{d x}&amp;=\frac{-F L^{2}}{2\left(1-I_{y z}^{2} /\left(I_{y} I_{z}\right)\right)}\left[\frac{1}{2} \frac{x^{2}}{L^{2}}-\frac{1}{4}\left\langle 2 \frac{x}{L}-1\right\rangle^{2}+c_{1}\right] \\\\<br />E I_{y} w&amp;=\frac{-F L^{3}}{2\left(1-I_{y z}^{2} /\left(I_{y} I_{z}\right)\right)}\left[\frac{1}{6} \frac{x^{3}}{L^{3}}-\frac{1}{24}\left\langle 2 \frac{x}{L}-1\right \rangle^{3}+c_{1} x+c_{2}\right]<br />\end{align}</p>


<p>\begin{align}<br />w(0)&amp;=0 \quad \Rightarrow c_{2}=0 \\\\<br />w(L)&amp;=0: \quad  \frac{1}{6}-\frac{1}{24}+c_{1} L=0 \quad \Rightarrow c_{1}=-\frac{3}{24} \frac{1}{L}=-\frac{1}{8 L} <br />\end{align}</p>


<p>\begin{align}<br />w(x)=-\frac{1}{1-I_{y z}^{2} /\left(I_{y} I_{z}\right)} \frac{F L^{3}}{48 E I_{y}}\left[4\left(\frac{x}{L}\right)^{3}-\left\langle2 \frac{x}{L}-1\right\rangle^{3}-3 \frac{x}{L}\right] <br />\end{align}</p>


<p>\begin{align}<br />w_{F}=w\left(\frac{L}{2}\right)&amp;=-\frac{1}{1-I_{y z}^{2} /\left(I_{y} I_{z}\right)} \frac{F L^{3}}{48 E I_{y}}\left(\frac{4}{2^{3}}-\frac{3}{2}\right) \\\\<br />&amp;=\frac{1}{1-I_{y z}^{2} /\left(I_{y} I_{z}\right)} \frac{F L^{3}}{48 E I_{y}} <br />\end{align}</p>


<p>Da die Randbedingungen für die Verschiebung \( v(x) \) mit denen für die Verschiebung \( w(x) \) übereinstimmen, gilt:</p>


<p>Da die Randbedingungen für die Verschiebung <mjx-container class="MathJax" jax="SVG"><svg alt=" v(x) " style="vertical-align: -0.566ex" xmlns="http://www.w3.org/2000/svg" width="4.152ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 1835 1000" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-698-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path id="MJX-698-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-698-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-698-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D463" xlink:href="#MJX-698-TEX-I-1D463"></use></g><g data-mml-node="mo" transform="translate(485,0)"><use data-c="28" xlink:href="#MJX-698-TEX-N-28"></use></g><g data-mml-node="mi" transform="translate(874,0)"><use data-c="1D465" xlink:href="#MJX-698-TEX-I-1D465"></use></g><g data-mml-node="mo" transform="translate(1446,0)"><use data-c="29" xlink:href="#MJX-698-TEX-N-29"></use></g></g></g></svg></mjx-container> mit denen für die Verschiebung <mjx-container class="MathJax" jax="SVG"><svg alt=" w(x) " style="vertical-align: -0.566ex" xmlns="http://www.w3.org/2000/svg" width="4.674ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 2066 1000" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-699-TEX-I-1D464" d="M580 385Q580 406 599 424T641 443Q659 443 674 425T690 368Q690 339 671 253Q656 197 644 161T609 80T554 12T482 -11Q438 -11 404 5T355 48Q354 47 352 44Q311 -11 252 -11Q226 -11 202 -5T155 14T118 53T104 116Q104 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Q21 293 29 315T52 366T96 418T161 441Q204 441 227 416T250 358Q250 340 217 250T184 111Q184 65 205 46T258 26Q301 26 334 87L339 96V119Q339 122 339 128T340 136T341 143T342 152T345 165T348 182T354 206T362 238T373 281Q402 395 406 404Q419 431 449 431Q468 431 475 421T483 402Q483 389 454 274T422 142Q420 131 420 107V100Q420 85 423 71T442 42T487 26Q558 26 600 148Q609 171 620 213T632 273Q632 306 619 325T593 357T580 385Z"></path><path id="MJX-699-TEX-N-28" d="M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z"></path><path id="MJX-699-TEX-I-1D465" d="M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z"></path><path id="MJX-699-TEX-N-29" d="M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D464" xlink:href="#MJX-699-TEX-I-1D464"></use></g><g data-mml-node="mo" transform="translate(716,0)"><use data-c="28" xlink:href="#MJX-699-TEX-N-28"></use></g><g data-mml-node="mi" transform="translate(1105,0)"><use data-c="1D465" xlink:href="#MJX-699-TEX-I-1D465"></use></g><g data-mml-node="mo" transform="translate(1677,0)"><use data-c="29" xlink:href="#MJX-699-TEX-N-29"></use></g></g></g></svg></mjx-container> übereinstimmen, gilt:</p>


<p>\begin{align}<br />E I_{z} \frac{d^{2} v}{d x^{2}}=\bar{M}_{z}=-\frac{I_{y z}}{I_{y}} \bar{M}_{y} <br />\end{align}</p>


<p>\begin{align}<br />E I_{z} v(x)=-\frac{I_{y z}}{I_{y}} \frac{F L^{3}}{2\left(1-I_{y z}^{2} /\left(I_{y} I_{z}\right)\right)}\left[\frac{1}{6} \frac{x^{3}}{L^{3}}-\frac{1}{24}\left\langle 2 \frac{x}{L}-1\right\rangle^{3}-\frac{1}{8} \frac{x}{L}\right]<br />\end{align}</p>


<p>\begin{align}<br />v(x)=-\frac{I_{y z}}{I_{y}} \frac{F L^{3}}{48 E I_{z}}\left[4\left(\frac{x}{L}\right)^{3}-\left\langle x \frac{x}{L}-1\right\rangle^{3}-3 \frac{x}{L}\right]=\frac{I_{y z}}{I_{z}} w(x)<br />\end{align}</p>


<p>\begin{align}<br />v_{F}=v\left(\frac{L}{2}\right)=\frac{I_{y z}}{I_{z}} w_{F} <br />\end{align}</p>


<p>\begin{align}<br />1-\frac{I_{y z}^{2}}{I_{y} I_{z}}=1-\frac{28,80^{2}}{69,74 \cdot 21,33}=0,4424 <br />\end{align}</p>


<p>\begin{align}<br />\frac{F L^{3}}{48 E I_{y}}=\frac{5 \cdot 10^{3} \mathrm{~N} \cdot 1000^{3} \mathrm{~mm}^{3}}{48 \cdot 2,1 \cdot 10^{5} \mathrm{~N} / \mathrm{mm}^{2} \cdot 69,74 \cdot 10^{4} \mathrm{~mm}^{4}}=0,7113 \mathrm{~mm} <br />\end{align}</p>


<p>\begin{align}<br />w_{F}=\frac{0,7113 \mathrm{~mm}}{0,4424}=1,608 \mathrm{~mm}<br />\end{align}</p>


<p>\begin{align}<br />v_{F}=\frac{-28,80}{21,33} \cdot 1,608 \mathrm{~mm}=-2,171 \mathrm{~mm} <br />\end{align}</p>

<p><img style="width: 100%;" src="https://storage.googleapis.com/max-academy-image-bucket/60309ea199dd3d08822199df.png" alt="Abbildung" /></p>
<p>Der abgebildete Balken ist an beiden Enden gelenkig gelagert. In der Mitte greift die Kraft \( F \) an. Gesucht sind die Verschiebungen \( v_{F} \) und \( w_{F} \) des Lastangriffspunkts.<br /><strong>Gegeben:</strong> \( E=210000 \mathrm{MPa}, \ F=5 \mathrm{kN} \)</p>

<p><img style="width: 100%;" src="https://storage.googleapis.com/max-academy-image-bucket/60309ea199dd3d08822199df.png" alt="Abbildung" /></p>
<p>Der abgebildete Balken ist an beiden Enden gelenkig gelagert. In der Mitte greift die Kraft <mjx-container class="MathJax" jax="SVG"><svg alt=" F " style="vertical-align: 0" xmlns="http://www.w3.org/2000/svg" width="1.695ex" height="1.538ex" role="img" focusable="false" viewBox="0 -680 749 680" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-684-TEX-I-1D439" d="M48 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H742Q749 676 749 669Q749 664 736 557T722 447Q720 440 702 440H690Q683 445 683 453Q683 454 686 477T689 530Q689 560 682 579T663 610T626 626T575 633T503 634H480Q398 633 393 631Q388 629 386 623Q385 622 352 492L320 363H375Q378 363 398 363T426 364T448 367T472 374T489 386Q502 398 511 419T524 457T529 475Q532 480 548 480H560Q567 475 567 470Q567 467 536 339T502 207Q500 200 482 200H470Q463 206 463 212Q463 215 468 234T473 274Q473 303 453 310T364 317H309L277 190Q245 66 245 60Q245 46 334 46H359Q365 40 365 39T363 19Q359 6 353 0H336Q295 2 185 2Q120 2 86 2T48 1Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D439" xlink:href="#MJX-684-TEX-I-1D439"></use></g></g></g></svg></mjx-container> an. Gesucht sind die Verschiebungen <mjx-container class="MathJax" jax="SVG"><svg alt=" v_{F} " style="vertical-align: -0.339ex" xmlns="http://www.w3.org/2000/svg" width="2.483ex" height="1.342ex" role="img" focusable="false" viewBox="0 -443 1097.6 593" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-685-TEX-I-1D463" d="M173 380Q173 405 154 405Q130 405 104 376T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Q21 294 29 316T53 368T97 419T160 441Q202 441 225 417T249 361Q249 344 246 335Q246 329 231 291T200 202T182 113Q182 86 187 69Q200 26 250 26Q287 26 319 60T369 139T398 222T409 277Q409 300 401 317T383 343T365 361T357 383Q357 405 376 424T417 443Q436 443 451 425T467 367Q467 340 455 284T418 159T347 40T241 -11Q177 -11 139 22Q102 54 102 117Q102 148 110 181T151 298Q173 362 173 380Z"></path><path id="MJX-685-TEX-I-1D439" d="M48 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H742Q749 676 749 669Q749 664 736 557T722 447Q720 440 702 440H690Q683 445 683 453Q683 454 686 477T689 530Q689 560 682 579T663 610T626 626T575 633T503 634H480Q398 633 393 631Q388 629 386 623Q385 622 352 492L320 363H375Q378 363 398 363T426 364T448 367T472 374T489 386Q502 398 511 419T524 457T529 475Q532 480 548 480H560Q567 475 567 470Q567 467 536 339T502 207Q500 200 482 200H470Q463 206 463 212Q463 215 468 234T473 274Q473 303 453 310T364 317H309L277 190Q245 66 245 60Q245 46 334 46H359Q365 40 365 39T363 19Q359 6 353 0H336Q295 2 185 2Q120 2 86 2T48 1Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="msub"><g data-mml-node="mi"><use data-c="1D463" xlink:href="#MJX-685-TEX-I-1D463"></use></g><g data-mml-node="TeXAtom" transform="translate(518,-150) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mi"><use data-c="1D439" xlink:href="#MJX-685-TEX-I-1D439"></use></g></g></g></g></g></svg></mjx-container> und <mjx-container class="MathJax" jax="SVG"><svg alt=" w_{F} " style="vertical-align: -0.339ex" xmlns="http://www.w3.org/2000/svg" width="3.006ex" height="1.342ex" role="img" focusable="false" viewBox="0 -443 1328.6 593" xmlns:xlink="http://www.w3.org/1999/xlink"><defs><path id="MJX-686-TEX-I-1D464" d="M580 385Q580 406 599 424T641 443Q659 443 674 425T690 368Q690 339 671 253Q656 197 644 161T609 80T554 12T482 -11Q438 -11 404 5T355 48Q354 47 352 44Q311 -11 252 -11Q226 -11 202 -5T155 14T118 53T104 116Q104 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Q21 293 29 315T52 366T96 418T161 441Q204 441 227 416T250 358Q250 340 217 250T184 111Q184 65 205 46T258 26Q301 26 334 87L339 96V119Q339 122 339 128T340 136T341 143T342 152T345 165T348 182T354 206T362 238T373 281Q402 395 406 404Q419 431 449 431Q468 431 475 421T483 402Q483 389 454 274T422 142Q420 131 420 107V100Q420 85 423 71T442 42T487 26Q558 26 600 148Q609 171 620 213T632 273Q632 306 619 325T593 357T580 385Z"></path><path id="MJX-686-TEX-I-1D439" d="M48 1Q31 1 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H742Q749 676 749 669Q749 664 736 557T722 447Q720 440 702 440H690Q683 445 683 453Q683 454 686 477T689 530Q689 560 682 579T663 610T626 626T575 633T503 634H480Q398 633 393 631Q388 629 386 623Q385 622 352 492L320 363H375Q378 363 398 363T426 364T448 367T472 374T489 386Q502 398 511 419T524 457T529 475Q532 480 548 480H560Q567 475 567 470Q567 467 536 339T502 207Q500 200 482 200H470Q463 206 463 212Q463 215 468 234T473 274Q473 303 453 310T364 317H309L277 190Q245 66 245 60Q245 46 334 46H359Q365 40 365 39T363 19Q359 6 353 0H336Q295 2 185 2Q120 2 86 2T48 1Z"></path></defs><g stroke="currentColor" fill="currentColor" stroke-width="0" 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640 191 642T193 659Q197 676 203 680H742Q749 676 749 669Q749 664 736 557T722 447Q720 440 702 440H690Q683 445 683 453Q683 454 686 477T689 530Q689 560 682 579T663 610T626 626T575 633T503 634H480Q398 633 393 631Q388 629 386 623Q385 622 352 492L320 363H375Q378 363 398 363T426 364T448 367T472 374T489 386Q502 398 511 419T524 457T529 475Q532 480 548 480H560Q567 475 567 470Q567 467 536 339T502 207Q500 200 482 200H470Q463 206 463 212Q463 215 468 234T473 274Q473 303 453 310T364 317H309L277 190Q245 66 245 60Q245 46 334 46H359Q365 40 365 39T363 19Q359 6 353 0H336Q295 2 185 2Q120 2 86 2T48 1Z"></path><path id="MJX-687-TEX-N-35" d="M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 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Dies ist eine interaktive Aufgabe zu: Biegelinie mit praktischen Tipps zum Lösen und einer Zusammenfassung der nötigen Theorie

Aufgabenstellung:

Lösungsweg:

Lösung: