1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Statically Indeterminate Beam

  1. Jul 21, 2011 #1
    I have a fixed-end fixed-end beam with two roller supports as well and a load applied in the center of the beam, as shown below.

    wV8oH.png

    I've chosen my redundant forces to be the force at B (point up), the force at C (pointing up), the force at D (pointing up) and the moment at D (counter-clockwise).

    I'm solving for these reactions using deflection and slope equations for a cantilever beam; specifically:

    The sum of all the redundant force and the applied load will produce a net deflection at B=0
    The sum of all the redundant force and the applied load will produce a net deflection at C=0
    The sum of all the redundant force and the applied load will produce a net deflection at D=0
    The sum of all the redundant force and the applied load will produce a net slope at D=0

    using these equations: http://www.advancepipeliner.com/Resources/Others/Beams/Beam_Deflection_Formulae.pdf

    I wrote up a worksheet in MathCAD and used matrix inversion to solve for the redundant forces. However, I am highly suspicious of the answers because the reactionary forces at B and C are not the same (as I'd assume they would be due to symmetry). Here is my worksheet:

    6UqDQ.png

    Anyone see any errors that I have made?
     
  2. jcsd
  3. Jul 21, 2011 #2
    What happened to the force and momentum at A? I understand that they should be the same as at D? You basically have a symmetric problem here.
     
  4. Jul 22, 2011 #3
    The force and moment at A doesn't factor into this (just yet at least). The compatibility equations are used to solve for the redundant forces.

    See here for a detailed explanation: http://www.sut.ac.th/engineering/civil/courseonline/430331/pdf/09_Indeterminate.pdf
     
  5. Jul 23, 2011 #4

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    An inspection of your A matrix shows that it is symmetric about the main diagonal except for A(1,2) and A(2,1).

    On a numerical analysis note, since the beam is composed of the same material throughout and the I of each segment is the same, the quantity EI can be set to 1 without affecting the C vector.
     
  6. Jul 25, 2011 #5
    Ack! Good catch! I wrote the wrong equation for A(1,2) :blushing:; checking the general formula gives an equation that is the same as A(2,1) (as you pointed out). Making this adjustment gives me symmetric results that make sense.

    Very good point; the E*I can be factored out of both matrices.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Statically Indeterminate Beam
  1. Beam Deflection (Replies: 4)

  2. Beam Calculator (Replies: 2)

Loading...