For the previous problem, calculate the deflection at point C on the beam.

Question

Accepted Answer

From the previous problem, we note that the flexure curve is given by

[latex] (E I) y=-\frac{R_{ A } x^3}{6}-\frac{M_{ A } x^2}{2}+\frac{w_{ o }}{24}\left\langle x-\frac{L}{2} ight angle^4 [/latex]

or [latex] (E I) y=-\frac{23 w_{ o } L}{768} x^3+\frac{7 w_{ o } L^2 x^2}{256}+\frac{w_{ o }}{24}\left\langle x-\frac{L}{2} ight angle^4 [/latex] (1)

(by putting the values of [latex] R_{ A } ext { and } M_{ A } [/latex] from the previous problem).
Now substituting x = L/2 in Eq. (1), we obtain

[latex] \begin{aligned} \left.(E I) y ight|_{x=L / 2} & =-\frac{23 w_{ o } L}{768}\left\lgroup\frac{L}{2} ight group^3+\frac{7 w_{ o } L^2}{256}\left\lgroup\frac{L}{2} ight group^2 \ & =\frac{7 w_{ o } L^4}{1024}-\frac{23 w_{ o } L^4}{6144}=\frac{19 w_{ o } L^4}{6144} \end{aligned} [/latex]

Therefore,

[latex] \left.y ight|_{x=L / 2}=\delta_{ C }=\frac{19 w_{ o } L^4}{6144 E I} [/latex]

Thus,

[latex] \delta_{ C }=\frac{19 w_{ o } L^4}{6144 E I}(\downarrow) [/latex]

Question 7.18: For the previous problem, calculate the deflection at point ...

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