SFD & BMD of beam with point force through distributed load

  1. Hi Guys,
    I'm having real difficulty trying to understand shear force and bending moment diagrams - both cantilever beams and supported ones like below. I've given it my best shot to solve the reactions at the points and would greatly appreciate any help on how to form the diagram and the equations after using method of sections.
    Thanks

    1. The problem statement, all variables and given/known data

    Create SFD and BFD of following beam.

    2. Relevant equations
    Fy=0
    Fx=0
    M=0

    3. The attempt at a solution
    Ma=0
    -Rb(6) +30(4.5)+[(10x4.5)/3.75]-20=0
    Rb=21.2kN

    Mb=0
    (30)(1.5)+[(10X4.5)/2.25]-20-6Ra=0
    Ra=7.5kN

    http://imageshack.us/photo/my-images/710/unledosv.jpg/
     
    Last edited: Aug 22, 2011
  2. jcsd
  3. Heres my attempt at using method of sections to write the equations:
    I
    0<x<a
    v=-7.5kN
    m=-20kNM

    II
    0<x<0
    v=-7.5kN + 10x
    m=-20kNm + (10x^2)/2

    III
    v=-7.5 kN + 10x + 30kN - 21.2kN
    m=-20kN + (10x^2)/2 + 30kN.x -21.2kN(6)

    As you can probably tell I'm struggling pretty bad on this lol. Any help is appreciated!
     
  4. SteamKing

    SteamKing 9,902
    Staff Emeritus
    Science Advisor
    Homework Helper

    You have not written the correct equilibrium equations for this beam. The sum of the forces must equal zero, and the sum of the moments, taken about a single reference point, also must equal zero. You have written moment equations about two different points. The expression for the moment of the distributed load is also incorrect. Until you calculate the reactions, you will not be able to construct the SF and BM diagrams for this beam.
     
  5. oh ok thanks. so you're not meant to take the moment of the two points? An example i saw did it that way i think so i thought i'd give it a go. oh well, back to the drawing board!

    ps. you calculate the moment of the distributed load by multiplying the magnitude by its length and then placing a point force at the middle of the distributed load, don't you? Sorry i'm struggling big time
     
    Last edited: Aug 22, 2011
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