Problem on stiffness matrix of beam and deflection of tapered beam

  1. 1.How do i derive the stiffness matrix for a beam with nodal linkage? ie the shear force at the first node is 0 but the usual shear and moment resistance is present for the second node.

    I thouth about solving the problem by just putting the first row of the stiffness matrix as 0 . Am i correct? Plee help in this

    2. How do i get the deflection of a tapered beam? i have the intertia as a function of x. How do i go about the problem?
    I thought of using the the the relation between EI and Moment equation and integrating it. But i a m not sure how to go further. Can someone please help me in this
     
  2. jcsd
  3. rock.freak667

    rock.freak667 6,228
    Homework Helper

    Your moment equation would be

    EI (d2y/dx2) = -M

    where I is a function of x.

    So you'd need to just do

    d2y/dx2 = -M/EI

    then integrate twice inputting your boundary conditions. This would depend on how your tapered beam is set up.
     
  4. SteamKing

    SteamKing 8,789
    Staff Emeritus
    Science Advisor
    Homework Helper

    1. I am having trouble visualizing your beam and the nature of this 'nodal linkage'. Can you provide a picture?
     
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