Fixed end moment

In the following examples, clockwise moments are positive.

The two cases with distributed loads can be derived from the case with concentrated load by integration. For example, when a uniformly distributed load of intensity $q$ is acting on a beam, then an infinitely small part $dx$ distance $x$ apart from the left end of this beam can be seen as being under a concentrated load of magnitude $qdx$. Then,

:$M\_\{\backslash mathrm\{right\}\}^\{\backslash mathrm\{fixed\}\}\; =\; \backslash int\_\{0\}^\{L\}\; \backslash frac\{q\; dx\; \backslash ,\; x^2\; (L-x)\}\{L^2\}\; =\; \backslash frac\{q\; L^2\}\{12\}$

:$M\_\{\backslash mathrm\{left\}\}^\{\backslash mathrm\{fixed\}\}\; =\; \backslash int\_\{0\}^\{L\}\; \backslash left\; \backslash \{\; -\; \backslash frac\{q\; dx\; \backslash ,\; x^2\; (L-x)\; \}\{L^2\}\; \backslash right\; \backslash \}=\; -\; \backslash frac\{q\; L^2\}\{12\}$

Where the expressions within the integrals on the right hand sides are the fixed end moments caused by the concentrated load $qdx$.

For the case with linearly distributed load of maximum intensity $q\_0$,

:$M\_\{\backslash mathrm\{right\}\}^\{\backslash mathrm\{fixed\}\}\; =\; \backslash int\_\{0\}^\{L\}\; q\_0\; \backslash frac\{x\}\{L\}\; dx\; \backslash frac\{\; x^2\; (L-x)\}\{L^2\}\; =\; \backslash frac\{q\_0\; L^2\}\{20\}$

:$M\_\{\backslash mathrm\{left\}\}^\{\backslash mathrm\{fixed\}\}\; =\; \backslash int\_\{0\}^\{L\}\; \backslash left\; \backslash \{\; -\; q\_0\; \backslash frac\{x\}\{L\}\; dx\; \backslash frac\{x\; (L-x)^2\}\{L^2\}\; \backslash right\; \backslash \}\; =\; -\; \backslash frac\{q\_0\; L^2\}\{30\}$

• Moment distribution method
• Statically Indeterminate
• Slope deflection method
• Matrix method

• {{cite book|last=Yang|first=Chang-hyeon|title=Structural Analysis|url=http://www.cmgbook.co.kr/category/sub_detail.html?no=1017|edition=4th|date=2001-01-10|publisher=Cheong Moon Gak Publishers|language=Korean|location=Seoul|isbn=89-7088-709-1|access-date=2007-09-03|archive-url=https://web.archive.org/web/20071008135424/http://www.cmgbook.co.kr/category/sub_detail.html?no=1017|archive-date=2007-10-08|url-status=dead}}

Category:Structural analysis

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