1. ## Bending moment

Hello .the question is ,The bending moment,M.at a position x m from the end of a simply supported beam of lenght l m carrying a uniformly distrbuted load
of wkNm-1 is given by
M= w/2 l (l -x)-w/2 (l-x)^2
Show using the above expression, that the maximum bending moment occurs atthe mid point of beam and determines its value interms of w and l
I have not got a clue !

2. Originally Posted by Jaffa
Hello .the question is ,The bending moment,M.at a position x m from the end of a simply supported beam of lenght l m carrying a uniformly distrbuted load
of wkNm-1 is given by
M= w/2 l (l -x)-w/2 (l-x)^2
Show using the above expression, that the maximum bending moment occurs atthe mid point of beam and determines its value interms of w and l
I have not got a clue !
your notation leaves much to be desired. Is the equation ...

$M = \frac{w}{2} L(L-x) - \frac{w}{2} (L-x)^2$

or

$M = \frac{w}{2L(L-x)} - \frac{w}{(L-x)^2}$

or something else?

3. Sorry , the first one is how it is meant to be, hope you can help

4. $M = \frac{w}{2} L(L-x) - \frac{w}{2} (L-x)^2$

$\frac{dM}{dx} = -\frac{w}{2}L + w(L-x)$

set $\frac{dM}{dx} = 0$

$w(L-x) = \frac{w}{2}L$

$L-x = \frac{L}{2}$

$x = \frac{L}{2}$

$\frac{d^2M}{dx^2} = -w < 0$ ... $x = \frac{L}{2}$ is where $M$ will be a maximum

substitute $\frac{L}{2}$ for $x$ in the original equation and determine the maximum value of $M$.

5. Thanks for your help,makes things clearer.