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Moment about distributed load (trapezium)

  1. Oct 25, 2015 #1
    1. The problem statement, all variables and given/known data
    i am asked to find the reaction at A and B ...
    Here's my working :
    15(3/2) +15(5) +15(6)+5(6/2)=RA +RB

    moment about A = 15(3/2)(3x2/3) + (15)(5)(8) + (5x6/2)(8+4) + (15)(6)(14) -RB(14) = 0
    so , i have my RB=148.9N , RA= 53.5N , which is wrong ? which part of my working is nt correct?
    i have 15(3/2)(3x2/3) because the centroid is located 2/3 of 3m from the triangle .
    I have (5x6/2)(8+4) because the centroid is located 8+(6x2/3) from A


    2. Relevant equations


    3. The attempt at a solution
     

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  3. Oct 25, 2015 #2

    PhanthomJay

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    Your errors are not with the triangular load but with the uniform loads. Your moment arms from the cg of the uniform loads are incorrect.
     
  4. Oct 25, 2015 #3
    moment about A = 15(3/2)(3x2/3) + (15)(5)(3+2.5) + (5x6/2)(8+4) + (15)(6)(12) -RB(14) = 0
    now , my RB = 122.67 , which part is wrong again ?
     
  5. Oct 25, 2015 #4

    PhanthomJay

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    Looks like the moment arm of the last uniformly distributed load is still wrong
     
  6. Oct 25, 2015 #5

    Mister T

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    Can you tell me the correct answers? It's been a while since I've looked at this kind of stuff.
     
  7. Oct 25, 2015 #6

    SteamKing

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    The centroid of the first triangular load is located @ (2/3) * 3 m from the toe of the triangle, or point A.
    This load calculation and location of the centroid from point A is correct.
    This part of the UDL is OK:
    (15)(5)(3+2.5)

    Did you check the location of the centroid for this part of the UDL?:
    (15)(6)(12)

    The left end of this UDL starts at 8 m from point A and ends at 14 m from point A. Is 12 m midway between these two locations?
     
  8. Oct 25, 2015 #7

    Mister T

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    Never mind. I figured it out.
     
  9. Oct 27, 2015 #8
    After changing the third part of location of centroid to11, I have (15)(3/2)(3*2/3)+ (15)(5)(5.5) + (15)(6)(11) + (5)(6/2)(11) -FB(14)=0...
    FB=115.17N , RA=87.3N , which is still different from the ans given
     
  10. Oct 27, 2015 #9

    Mister T

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    My answers are slightly different.

    You had this:
    And SteamKing told you you had only one error. Now you have this:
    You have changed more than one thing! I'm not sure if I'm using the right terminology here, but between the positions of 8 m and 14 m you have a UDL of 15 kN, and above it a triangular load. Note that the centroid of the rectangle and the centroid of the triangle have different positions.
     
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