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Homework Help: Finding the bending moment

  1. Apr 15, 2010 #1
    1. The problem statement, all variables and given/known data
    A steel (Young's modulus = 210x109N/mm2) propped cantilever beam (Figure 1) supports a uniformly
    distributed load (UDL) of 20kN/m. The beam cross section is a 150mm x 75mm x 8mm rectangular
    hollow section (RHS), i.e. 150mm deep, 75mm wide and has an 8mm wall thickness. The cross
    section is oriented so that bending occurs about its major axis of bending.
    Figure 1
    a) Calculate the support reactions at A and B,
    b) Plot the shear force diagram,
    c) Plot the bending moment diagram (on the tension side) and indicate maximum bending moment
    value,
    d) Calculate the maximum bending stress and state where it occurs,
    e) Calculate the deflection at the mid-point between A and B.

    i'm working on part c and am a bit confused as to how the bending moment diagram works.

    2. Relevant equations
    just moment equations


    3. The attempt at a solution
    I have the shear stress diagram and part of the bending moment.

    the reaction forces at A and B are 26 2/3 and 53 1/3.

    the equations
    for Vx and Mx are as follows

    0<=x<=3
    Vx = 26 2/3 -20x
    mx = 26 2/3 x - 10x2

    3<=x<=4
    Vx = 53 1/3 - 20x
    Mx - 53 1/3 - 10x2

    but the peace i struggle with i'm getting the end peace of the beam to deflect by alot more then the middle part, so if you have any input it would be very much appreciated.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Apr 15, 2010 #2

    PhanthomJay

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You are incorrectly treating this beam as one on pinned supports at x=0 and x=3, , but it is given that the end at x=0 is a fixed end, which is capable of providing both force and moment. The problem is staticallly indeterminate to the first degree, so you have to use another equation besides the static equilibrium equations in order to solve for the reaction forces and moments. Then once you get them, I'm not sure of your graph in the middle, it seems to be an attempt at a deflection curve and not a bending moment diagram.
     
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