Shear Force/Bending Moments Equation

Hi, question and solution attached.

I'm having trouble converting the second equation in 2 (b) to the corresponding bending moment equation. I have worked out everything else, I'm just unsure how the '-1562.5N' part is calculated.

http://snag.gy/Uqrel.jpg



Help is much appreciated, thanks!

 

So because Q is 1562.5 it is taken away from the second BM equation?

 

I'm not understanding how that constant is reached in this instance.

 

Yeah I get that.

Ok, so you just sub 5 into x. Why is the constant not present in the first bending moment equation though?

 

Also, in terms of this example here, just looking at the second equation in 2. (b), why is the constant not applied in the same way when integrating the second SF equation? It is in the 3rd, but not the second.




Sorry for the amount of questions, but I'm quite confused by this...

 

Ok, I'll give you two examples to illustrate where I'm seeing a lack of consistency.

In the second BM equation in the first example I provided after integrating the SF equation you get this...

-50x^2 + 562.5x + C
C = 50 x 5^2 - 562.5 x 5
= - 1562.5
BM = -50x^2 + 562.5x - 1562.5

That's the correct solution as shown in the answers provided and as you've explained.

Now again looking at the second BM but this time in the second example provided after SF is integrated you get...

-8x + C
C = 8x
= 8 x 5
= 40

That's incorrect, as shown in the solution C = 90.

So what am I missing out here?

I notice that if I carry out the same method on the third equation it does again provide the correct answer, it's just that last example I'm not understanding. I could do something with the 50 at 4m that would get an answer of 90 but that wasn't necessary in the other two equations.