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Derivations for a Bending Moment and Angle from Koenig's Apparatus

  1. Mar 23, 2013 #1
    1. The problem statement, all variables and given/known data

    I'm having ALOT of trouble figuring out how to derive these equations. I'll post up photos and the equations as follows.

    C is the Bending Moment
    Y is the Young's Modulus of the material
    r is the Radius of Curvature of the neutral surface
    I is the geometrical moment of Inertia of the cross section of the beam

    Theta is the angle of deflection of the beam
    h is the change in height on the scales as the beam deviates
    d is the distance between 2 knife edges (points holding up the beam) of the beam
    D is the farthest knife edge to the scales

    PICTURES:

    For the Bending Moment:

    http://puu.sh/2mmq5 [Broken]

    (That thing on the right (next to P) is a C - for bending moment, I accidently cut it out)

    For Koenig's Apparatus:

    http://puu.sh/2mmp2 [Broken]

    2. Relevant equations

    For the Bending Moment the equation we need to derive is

    C = (Y.I)/r

    and for the angle of deviation, we need to derive

    Theta = h/(2(d + 2D))


    3. The attempt at a solution

    For the bending moment, I did some research online and found this link ( http://www.codecogs.com/reference/engineering/materials/bending_stress/bending_stress.php) , but I couldn't make much sense of it. The tutors in the lab were pretty unhelpful or atleast, didn't want to help much in case they straight up gave me the answer? Not entirely sure.

    Similarly for the koenig's apparatus one, except I couldn't find anything on it online.
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
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