# Thread: Maxima / Minima problem?

1. ## Maxima / Minima problem?

The bending moment, M , at position x meters from the end of a simply supported beam of length l meters carrying a uniformly distributed load of w kN meters^-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 at the mid-point of the beam and determine its value in terms of w and l.

2. Originally Posted by Steve Mckenna
The bending moment, M , at position x meters from the end of a simply supported beam of length l meters carrying a uniformly distributed load of w kN meters^-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 at the mid-point of the beam and determine its value in terms of w and l.
The maximum bending moment occurs at a root of the equation:

$\displaystyle \frac{d}{dx}M(x)=0$

you need to find the roots of this equation and classify it as a maxima or mininma or a point of inflection. In this case there is only one root and it should be obvious that it must correspond to a maximum. You should be able to do all this, if you have further problems please tell us exactly where they occur so we provide the specific help that you need to understand and solve this problem.

CB

3. I believew that dM/dx = wl/2 - w(l-x)

Is this correct thus far?

4. Originally Posted by Steve Mckenna
The bending moment, M , at position x meters from the end of a simply supported beam of length l meters carrying a uniformly distributed load of w kN meters^-1 is given by:

M = w/2 l (l-x) - w/2 (l-x)^2
Does the above mean either of the following?

. . . . .$\displaystyle M\, =\, \frac{w}{2l}(l\, -\, x)\, -\, \frac{w}{2}(l\, -\, x)^2$

. . . . .$\displaystyle M\, =\, \frac{w}{2l(l\, -\, x)}\, -\, \frac{w}{2(l\, -\, x)^2}$

Or something else?

Thank you!

5. The first equation.