What is the distance of the resultant from point A on the beam?

[tigertan]

hi there,


I'm getting very very confused about distributed loads.

I am trying to figure out the resultant force of a distributed load on a beam. The function I've been given for q(x) is a polynomial (below x=0).

I have figured out the resultant for my function q(x)=x²-2x-4. I believe it is 9.1877 (positive being in the vertical direction). Length = 43/10

To find the distance of the resultant from point A on the beam, I have worked it out to be (1/2*(43/10).

I don't feel that the distance I have worked out it right and I'm not 100 percent sure about the resultant force either. Could someone please set me off in the right direction?

Thanks in advance.

 

[Jorris]

Hi,

The force of 9.1877 is correctly calculated. It is the integral of the load.

Now to find the position of the resultant, we first calculate the moment around the point x = 0.
M = int (x * q(x)) dx between x = 0 and x = 4.3
= int (x^3 - 2x^2 - 4x) dx between x = 0 and x = 4.3
= - 4.1546
(negative because load works vertically)
This has to be equal to the moment caused by the resultant:
M = Fd
with d the distance from the point x = 0.
Hence
d = M/F = 2.0350

This is close to your (1/2*(43/10), but not exactly the same. How did you get there?