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Uniformly Varying Load/Uniform Load to Concentrated Point Load

  1. Sep 19, 2009 #1
    Hi all,
    I'm taking a Structures course in University and are learning about Freebody diagrams and figuring out Reaction forces (magnitude, direction, sense etc) and have a very basic question. Can someone please tell me how to convert a uniformly varying load into a concentrated point load, and how does one figure out at which point on the member to place this concentrated point load? i've attached a scan from my book but it doesn't show how to derive the point load. appreciate thanks.

    I do know how to convert a uniform load into a concentrated point load.

    Also if anyone would like to tutor me in Structures, (i will reimburse in an hourly basis or we could work out a deal), please let me know? I'm having difficulty in my Structures class, and desperately need to pass it and would like to have a tutor who I can depend on to have questions that I may have answered. thanks

    3935107595_df4b1538de_o.jpg
     
  2. jcsd
  3. Sep 19, 2009 #2

    FredGarvin

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    Science Advisor

    The point load is placed in line with the centroid of the right triangle. It is found by

    [tex]X = \frac{2B}{3}[/tex]

    where

    B = The length of the total varying load.
    X = distance from the large end of the load triangle (in this case, where the large dot is right below the 15 k/ft)

    Look here for a reference:
    http://www.ele.uri.edu/~daly/106/06/project/centroid/centroid.html
     
  4. Sep 20, 2009 #3
    Thanks Fred... can you tell me how does one arrive at the value concentrated load of 67.5? I know with a uniform load we have to multiply the uniform load and the length it affects. eg: 2k/ft x 6ft
     
  5. Sep 20, 2009 #4

    FredGarvin

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    If you think of a triangle as one half of a rectangle...
     
  6. Oct 26, 2009 #5
    It is very simple. Just find the area of triangular load. (1/2)*(3+6)*15 = 67.5. And place the load at the centroid of the triangle (1/3)*9= 3..
     
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