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Simple integration problems

  1. Apr 13, 2009 #1
    1. The problem statement, all variables and given/known data

    Two questions are of the same problem (these are taken from a textbook):

    EIdy/dx = - (Fx^2)/4 + A

    The constant A can be obtained from the boundary conditions: slope dy/dx = 0, x = 1/2L. Thus A = (FL^2)/16 hence

    EIdy/dx = - (Fx^2)/4 + (FL^2)/16

    My problem 1: I have absolutely no idea why A = (FL^2)/16. If someone could please show me in a few small steps how A was determined, I should be very grateful!

    Integrating again (with respect to x), the second constant, B, equals zero thus

    EIy = - (Fx^2)/4 + (FL^2)/16 + B

    B = 0

    y = (Fx/48EI) (3L^2 - 4x^2)

    x = 1/2 L thus

    ymax = (FL^3)/48EI

    My problem 2: I have no idea how the solution for ymax was determined. I Also have no idea why y = (Fx/48EI) (3L^2 - 4x^2) when EIy = - (Fx^2)/4 + (FL^2)/16 + B. Is the equation for y simply the equation for EIy transposed for y? Because when I tried them I ended up with values which did not fit. (Did I make a simple error in my calculating, or is something else going on?)

    Please could you explain to me what is going on in the above equations?
     
    Last edited: Apr 13, 2009
  2. jcsd
  3. Apr 13, 2009 #2
    This is a scan of the book from whence the equations originated:

    http://img16.imageshack.us/img16/9725/beamproblembookscan.png [Broken]
     
    Last edited by a moderator: May 4, 2017
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