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Resolucion de la ecuaci\303\263n de la el\303\241stica para una viga simplemente apoyada con carga distribuida q(x), por el m\303\251todo aproximado de las series de Fourier

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

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

Ki5JI0xhRzYiIiIiSSllY3VhY2lvbkdGJEYlSSNkZUdGJEYlSSNsYUdGJEYlSSllbGFzdGljYUdGJEYlSSNlc0dGJEYl

Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtRiQ2JC1GJDYkLUYkNiQtSSJ5RzYiNiNJInhHRi9GMUYxRjFGMSooLUkicUdGL0YwIiIiSSJFR0YvISIiSSJKR0YvRjc=

Ki5JKFRvbWFtb3NHNiIiIiJJJGxvc0dGJEYlSStwYXJ8XHltZXRyb3NHRiRGJUkjZW5HRiRGJUkmZm9ybWFHRiRGJUkpZ2VufGR5cmljYUdGJEYl

SSJORzYi

SSJFRzYi

SSJKRzYi

SSJsRzYi

Donde :

N = N\303\272mero de t\303\251rminos de la serie a desarrollar

E = M\303\263dulo de elasticidad longitudinal

J = Momento de inercia respecto del eje sobre el que act\303\272a el momento flector

l = Longitud de la viga

Las condiciones de borde para el caso de la viga simplemente apoyada son:

y(0) = y(l) = 0 el descenso en los apoyos es nulo

M(0) = -EJ y''(0) = M(l) = -EJ y''(l) = 0 el momento en los apoyos es nulo

Desarrollando en series de Fourier la funci\303\263n y(x), la cual satisface automaticamente las condiciones de borde, tenemos:

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

LUkkc3VtRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQqJiZJIndHRic2I0kjbnxpckdGJyIiIi1JJHNpbkdGJDYjKipGLUYuSSNQaUdGJUYuSSJ4R0YnRi5JImxHRichIiJGLi9GLTtGLkkiTkdGJw==

Desarrollando tambi\303\251n en series de Fourier la funci\303\263n q(x), tenemos:

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

LUkkc3VtRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQqJiZJInFHRic2I0kjbnxpckdGJyIiIi1JJHNpbkdGJDYjKipGLUYuSSNQaUdGJUYuSSJ4R0YnRi5JImxHRichIiJGLi9GLTtGLkkiTkdGJw==

Donde hemos llamado qf(x,N) a la funcion q(x) expresada en series de Fourier

Teniendo en cuenta la ecuacion de la el\303\241stica nos queda:

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

Ly1JJHN1bUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkKiwmSSJ3R0YoNiNJI258aXJHRigiIiItSSRzaW5HRiU2IyoqRi5GL0kjUGlHRiZGL0kieEdGKEYvSSJsR0YoISIiRi8pRi4iIiVGLylGNEY5Ri8pRjZGOUY3L0YuO0YvSSJOR0YoKigtRiQ2JComJkkicUdGKEYtRi9GMEYvRjxGL0kiRUdGKEY3SSJKR0YoRjc=

De la expesi\303\263n anterior se observa que existe la siguiente igualdad:

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYtLUkjbWlHRiQ2JVEpaWd1YWxkYWRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSomY29sb25lcTtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JJm1mcmFjR0YkNigtRiM2Ky1JJW1zdWJHRiQ2JS1GLDYlUSJ3RidGL0YyLUYjNiUtRiw2JVEjbnxpckYnRi9GMi8lK2V4ZWN1dGFibGVHRj1GOS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUY2Ni1RMSZJbnZpc2libGVUaW1lcztGJ0Y5RjtGPkZARkJGREZGRkgvRktRJjAuMGVtRicvRk5GYm8tRiM2Jy1GLDYlUSRzaW5GJy9GMEY9RjktRjY2LVEwJkFwcGx5RnVuY3Rpb247RidGOUY7Rj5GQEZCRkRGRkZIRmFvRmNvLUkobWZlbmNlZEdGJDYkLUYjNiUtRlA2KC1GIzYpRmZuRl5vLUYsNiVRJSZwaTtGJ0Zpb0Y5Rl5vLUYsNiVRInhGJ0YvRjJGaW5GOS1GIzYlLUYsNiVRImxGJ0YvRjJGaW5GOS8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGZnEvJSliZXZlbGxlZEdGPUZpbkY5RjlGaW5GOUZeby1JJW1zdXBHRiQ2JUZmbi1JI21uR0YkNiRRIjRGJ0Y5LyUxc3VwZXJzY3JpcHRzaGlmdEdGXW9GXm8tRlxyNiVGZnBGXnJGYnJGaW5GOS1GIzYlLUZccjYlRl5xRl5yRmJyRmluRjlGYXFGZHFGZ3FGaXEtRjY2LVEiPUYnRjlGO0Y+RkBGQkZERkZGSEZKRk0tRlA2KC1GIzYoLUZVNiUtRiw2JVEicUYnRi9GMkZaRltvRl5vRmZvRl1wRmluRjktRiM2Jy1GLDYlUSJFRidGL0YyLUY2Ni1RJyZzZG90O0YnRjlGO0Y+RkBGQkZERkZGSEZhb0Zjby1GLDYlUSJKRidGL0YyRmluRjlGYXFGZHFGZ3FGaXEtRjY2LVEiOkYnRjlGO0Y+RkBGQkZERkZGSEZKRk0tRjY2LVEifkYnRjlGO0Y+RkBGQkZERkZGSEZhb0Zjb0YrLUY2Ni1RIjtGJ0Y5RjsvRj9GMUZARkJGREZGRkhGYW9GTUZpbkY5

LyosJkkid0c2IjYjSSNufGlyR0YmIiIiLUkkc2luRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNiMqKkYoRilJI1BpR0YtRilJInhHRiZGKUkibEdGJiEiIkYpKUYoIiIlRikpRjFGNkYpKUYzRjZGNCoqJkkicUdGJkYnRilGKkYpSSJFR0YmRjRJIkpHRiZGNA==

De donde podemos obtener el valor de wn en funcion de qn:

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

PCMvJkkid0c2IjYjSSNufGlyRzYiKi4mSSJxRzYiNiNJI258aXJHNiIiIiIpSSJsRzYiIiIlIiIiKUkjbnxpckc2IiIiJSEiIilJI1BpRyUqcHJvdGVjdGVkRyIiJSEiIkkiRUc2IiEiIkkiSkc2IiEiIg==

La funci\303\263n q(x) tiene la forma:

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

Zio2I0kieEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCQqLCIiJSIiIkkjcW9HRiVGLEYkRiwsJkkibEdGJUYsRiQhIiJGLClGLyIiI0YwRixGJUYlRiU=

Determinamos el valor del coeficiente qn para el desarrollo en series de Fourier de la funci\303\263n q(x):

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

Zio2I0kieEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCQqKCIiIyIiIkkibEdGJSEiIi1JJGludEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYkKiZJInBHRiVGLC1JJHNpbkdGMTYjKipJIm5HRiVGLEkjUGlHRjJGLEYkRixGLUYuRiwvRiQ7IiIhRi1GLEYsRiVGJUYl

LCQqKiIjOyIiIiwmRiUhIiIpRidJI258aXJHNiJGJUYlKUYpIiIkRicpSSNQaUclKnByb3RlY3RlZEdGLEYnRic=

Por lo que wn valdr\303\241:

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

LCQqKiIjOyIiIiwmRiUhIiIpRidJI258aXJHNiJGJUYlKUYpIiIoRicpSSNQaUclKnByb3RlY3RlZEdGLEYnRic=

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

Donde debimos sustituir a qf(x,N) por ps(x,N) para poder intoducir en \303\251l, el valor determinado del coeficiente qn al que llamamos k

Entonces nuestro descenso y(x) ser\303\241:

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

LUkkc3VtRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQsJCosIiM7IiIiLCZGLCEiIilGLkkjbnxpckdGJ0YsRiwpRjAiIihGLilJI1BpR0YlRjJGLi1JJHNpbkdGJDYjKihGMEYsRjRGLEkieEdGJ0YsRixGLi9GMDtGLEkiTkdGJw==

El momento flector ser\303\241:

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

Zio2JEkieEc2IkkiTkdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCQqKEkiRUdGJSIiIkkiSkdGJUYtLUklZGlmZkclKnByb3RlY3RlZEc2JC1GMDYkLUkieUdGJUYjRiRGJEYtISIiRiVGJUYl

LCQtSSRzdW1HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JCwkKiwiIzsiIiIsJkYtISIiKUYvSSNufGlyR0YoRi1GLSlGMSIiJkYvKUkjUGlHRiZGM0YvLUkkc2luR0YlNiMqKEYxRi1GNUYtSSJ4R0YoRi1GLUYtL0YxO0YtSSJOR0YoRi8=

La carga distrbuda, denomina ahora ps(x) ser\303\241:

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

LUkkc3VtRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQsJCosIiM7IiIiLCZGLCEiIilGLkkjbnxpckdGJ0YsRiwpRjAiIiRGLilJI1BpR0YlRjJGLi1JJHNpbkdGJDYjKihGMEYsRjRGLEkieEdGJ0YsRixGLi9GMDtGLEkiTkdGJw==

Asignando valores particulares a los par\303\241metros tendremos:

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IiIi

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La g\303\241fica apoximada del momento flector ser\303\241:

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Dando valores particulares a "x" y a "N" se tiene:

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

JCIiJiEiIg==

IiQsIg==

El descenso en el punto "x" valdr\303\241:

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

JCErVSVwdmsjISM3

El valor del Momento Flector ser\303\241:

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

JCIrenUudkIhIio=

El valor de la carga ser\303\241:

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

JCErTU8/MEQhIzU=