Solving for VA and VB: Support Reaction Homework Solution

[chetzread]

Homework Statement

I'm asked to find the VA and VB in this question .

Homework Equations

The Attempt at a Solution

Here's my working :
VA +VB =1000(6) =5000+0.5(400x3)
VA +VB = 11600

total moment about A = 0 , sum of moment about A = 5000(6) -9000 + (4000/2)(9 +3(2/3) ) -VB(9) =0
hence VB = 9667N pointed upwards

total moment about B = 0 , sum of moment about B = 1000(6)(9) -VA(9) +9000+5000(3)-4000(3/2)(2) = 0
VA = 7333N (upwards)

But , the ans provided is VA = 8000N , VB = 9000N , which part i did wrongly ?
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[CWatters]

VA +VB =1000(6) =5000+0.5(400x3)

Is that meant to read VA + VB = 1000(6) + 5000 + 0.5(400*3) ?

If so then..
Where does the 6 come from?
Where does the 400 come from?

 

[chetzread]

Is that meant to read VA + VB = 1000(6) + 5000 + 0.5(400*3) ?

If so then..
Where does the 6 come from?
Where does the 400 come from?

sorry , i made a mistake , it should be VA + VB = 1000(6) + 5000 + 0.5(4000x 3) =17000N ...

 

[CWatters]

and the 6?

 

[chetzread]

and the 6?

The 1000 N /m has 6 m

 

[CWatters]

Ok yes I agree. 1000N/M for 6m.

 

[CWatters]

Ill try and have a look at the rest tomorrow.

 

[CWatters]

total moment about A = 0 , sum of moment about A = 5000(6) -9000 + (4000/2)(9 +3(2/3) ) -VB(9) =0

The centre of mass of the "triangular load" is 1/3rd of the base from it's left hand edge not 2/3rds so it should be..

5000(6) -9000 + (4000/2)(9 +3(1/3) ) -VB(9) = 0