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Moment at distributed load

  1. Jul 13, 2016 #1
    1. The problem statement, all variables and given/known data
    For region 8<x<12 , why there's an extra (60-30y +3.75y^2 ) - (30y-7.5y^2) ???
    How to get that? I have no idea at all...
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    2. Relevant equations


    3. The attempt at a solution
    here's my working, i have divided the triangle into three parts, i gt 129-80 -75- (60-30y=3.75y^2) - (30y-7.5y^2)-(3.75y^2) instead of 129-80 -75- (60-30y=3.75y^2) - (30y-7.5y^2)
    Is the author wrong?
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  2. jcsd
  3. Jul 17, 2016 #2

    haruspex

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    The aim is to find the net vertical force left of point a, which is y to the left of support B.
    The term in question is the contribution from q. The load per unit length from q is 7.5y at a. To avoid confusion, I'll introduce another variable w for a variable distance left of B, ranging from y to 4. The total force over that range from q is therefore ##\int _y^47.5w.dw##. If you evaluate that you should arrive at the above expression, though by what logic the author arrived at it I am not sure.
     
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