Find the maximum bending moment

[SteveMckenna]

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 wkN m^-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.

I know that the max bending moment will occur at the root of the equation: d/dx M(x) = 0

 

[Mark44]

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 wkN m^-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.

I know that the max bending moment will occur at the root of the equation: d/dx M(x) = 0

Sounds good to me. Go for it!

Homework Statement

Homework Equations

The Attempt at a Solution

You need to make some sort of attempt before anyone here will help you out. The function you're working can be differentiated fairly easily.

 

[SteveMckenna]

I believe that dM/dx = wl/2 - w(l-x) thus far!

Is this correct before I continue?

 

[Mark44]

Your signs are wrong. For example, d/dx(w/2 * l(l - x)) = -w/2 * l